Finite Group Databasebeta

← C61×#61066 #29564499

Subgroups — C61×#61066 #29564499

Order 15616.

2912 conjugacy classes of subgroups.

The subgroup lattice has 1616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#575C211yesmaximal, characteristic, complemented
2C22×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
3D4×#41×C61C211yesmaximal, characteristic, complemented
4C2×C61×#546C211yesmaximal, characteristic, complemented
5C61×#3282C212yesmaximal, complemented
6C61×#3280C212yesmaximal, complemented
7C61×#3275C212yesmaximal, complemented
8C61×#3273C212yesmaximal, complemented
9C61×#3268C212yesmaximal, complemented
10C61×#3267C212yesmaximal, complemented
11C61×#3266C212yesmaximal, complemented
12C61×#3264C212yesmaximal, complemented
13C61×#3153C211yesmaximal, characteristic, complemented
14C61×#3056C211yesmaximal, characteristic, complemented
15C61×#3055C211yesmaximal, characteristic, complemented
16C61×#3040C211yesmaximal, characteristic, complemented
17C61×#3036C211yesmaximal, characteristic, complemented
18C61×#3007C211yesmaximal, characteristic, complemented
19C61×#3006C211yesmaximal, characteristic, complemented
20C61×#3005C211yesmaximal, characteristic, complemented
21C61×#3003C211yesmaximal, characteristic, complemented
22C4×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
23D4×M16×C61C211yesmaximal, characteristic, complemented
24C22×#41×C61C2211yescharacteristic
25C22×#41×C61C2211yescharacteristic, complemented
26C22×#41×C61C2211yescharacteristic, complemented
27C23×D4×C61C2211yescharacteristic, complemented
28C61×#575—28no—
29C2×#137×C61C2211yescharacteristic, complemented
30C2×#137×C61C2211yescharacteristic, complemented
31C2×#137×C61C2211yescharacteristic, complemented
32C2×#137×C61C2212yescomplemented
33C2×AGL(1,ℤ/8)×C61—28no—
34C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
35C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
36C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
38C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
39C2×AGL(1,ℤ/8)×C61C2212yescomplemented
40C2×AGL(1,ℤ/8)×C61C2212yescomplemented
41C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
42C2×AGL(1,ℤ/8)×C61C2212yescomplemented
43C2×#135×C61C2212yescomplemented
44C2×#135×C61C2212yescomplemented
45C22×SD16×C61C2212yescomplemented
46C22×D8×C61C2212yescomplemented
47C22×M16×C61C2211yescharacteristic, complemented
48C22×M16×C61C2211yescharacteristic, complemented
49C61×#550C2211yescharacteristic, complemented
50D4×Q8×C61C2211yescharacteristic, complemented
51C61×#548C2211yescharacteristic, complemented
52C61×#548C2211yescharacteristic, complemented
53C61×#547—21no—
54C61×#547C2211yescharacteristic, complemented
55C61×#546—21no—
56C61×#546—21no—
57C61×#546—21no—
58C61×#546—21no—
59C61×#546—21no—
60C61×#546—21no—
61C61×#546C2212yes—
62C61×#546C2212yescomplemented
63C61×#546C2212yescomplemented
64C61×#546C2212yescomplemented
65C61×#546C2211yescharacteristic, complemented
66C61×#546C2211yescharacteristic, complemented
67D42×C61—21no—
68D42×C61C2211yescharacteristic, complemented
69C61×#532—21no—
70C61×#532C2211yescharacteristic, complemented
71C2×#124×C61C2211yescharacteristic, complemented
72C61×#525—21no—
73C61×#525—21no—
74C61×#525C2211yescharacteristic
75C61×#525C2211yescharacteristic, complemented
76C2×#123×C61—21no—
77C2×C22⋊Q8×C61C2211yescharacteristic, complemented
78C2×#121×C61—21no—
79C2×#121×C61C2211yescharacteristic, complemented
80C2×#120×C61—21no—
81C4×#41×C61C2211yescharacteristic, complemented
82C2×C4×D4×C61—21no—
83C2×C4×D4×C61C2211yescharacteristic
84C2×C4×D4×C61C2211yescharacteristic, complemented
85C22×C22⋊C4×C61—21no—
86C61×#497C2212yescomplemented
87C61×#496C2212yescomplemented
88C61×#495C2212yescomplemented
89C61×#495C2212yescomplemented
90C61×#470C2212yescomplemented
91C61×#469C2212yescomplemented
92C61×#468C2212yescomplemented
93C61×#468C2212yescomplemented
94C61×#467C2212yescomplemented
95C61×#466C2212yescomplemented
96C61×#465C2212yescomplemented
97C61×#465C2212yescomplemented
98C61×#464C2212yescomplemented
99C61×#464C2212yescomplemented
100C61×#463C2212yescomplemented
101C61×#463C2212yescomplemented
102C61×#463C2212yescomplemented
103C61×#463C2212yescomplemented
104C61×#461C2212yescomplemented
105C61×#459C2212yescomplemented
106C61×#452C2212yescomplemented
107C61×#452C2212yescomplemented
108C61×#452C2212yescomplemented
109C61×#452C2212yescomplemented
110C61×#451C2212yescomplemented
111C61×#450C2212yescomplemented
112C61×#450C2212yescomplemented
113C61×#450C2212yescomplemented
114C61×#449C2212yescomplemented
115C61×#449C2212yescomplemented
116C61×#449C2212yescomplemented
117C61×#449C2212yescomplemented
118C61×#448C2212yescomplemented
119C61×#447C2212yescomplemented
120C61×#447C2212yescomplemented
121C61×#447C2212yescomplemented
122C61×#442C2212yescomplemented
123C61×#440C2212yescomplemented
124C4×SD16×C61C2212yescomplemented
125C4×D8×C61C2212yescomplemented
126C61×#436C2212yescomplemented
127C61×#435C2212yescomplemented
128C61×#435C2212yescomplemented
129C8×D4×C61C2212yescomplemented
130C61×#428C2211yescharacteristic, complemented
131C61×#423C2211yescharacteristic, complemented
132C61×#419C2211yescharacteristic, complemented
133C61×#418C2211yescharacteristic, complemented
134C61×#418C2211yescharacteristic, complemented
135C61×#417C2211yescharacteristic, complemented
136C61×#417C2211yescharacteristic, complemented
137C61×#417C2211yescharacteristic, complemented
138C61×#407C2211yescharacteristic, complemented
139C61×#407C2211yescharacteristic, complemented
140C4×M16×C61C2211yescharacteristic, complemented
141C25×C61—21no—
142C2×#41×C61—21no—
143C2×#41×C61—21no—
144C2×#41×C61—21no—
145C2×#41×C61—21no—
146C2×#41×C61—21no—
147C2×#41×C61—21no—
148C2×#41×C61—24no—
149C2×#41×C61—24no—
150C2×#41×C61—24no—
151C2×#41×C61—42no—
152C2×#41×C61—42no—
153C2×#41×C61—42no—
154C2×#41×C61C2311yescharacteristic
155C2×#41×C61C2311yescharacteristic
156C2×#41×C61C2312yes—
157C2×#41×C61C2312yes—
158C2×#41×C61C2311yescharacteristic
159C2×#41×C61C2311yescharacteristic
160C2×#41×C61C2311yescharacteristic
161C2×#41×C61C2311yescharacteristic, complemented
162C2×#41×C61C2311yescharacteristic, complemented
163C22×Q8×C61C2311yescharacteristic
164C22×Q8×C61C2311yescharacteristic
165C22×Q8×C61C2311yescharacteristic, complemented
166C22×D4×C61—24no—
167C22×D4×C61—21no—
168C22×D4×C61—21no—
169C22×D4×C61—21no—
170C22×D4×C61—21no—
171C22×D4×C61—21no—
172C22×D4×C61—21no—
173C22×D4×C61—21no—
174C22×D4×C61—21no—
175C22×D4×C61—42no—
176C22×D4×C61D411yescharacteristic
177C22×D4×C61C2311yescharacteristic
178C22×D4×C61C2311yescharacteristic
179C22×D4×C61C2312yes—
180C22×D4×C61C2312yes—
181C22×D4×C61C2311yescharacteristic
182C22×D4×C61C2311yescharacteristic, complemented
183C23×C4×C61—21no—
184C23×C4×C61—21no—
185C23×C4×C61—21no—
186C23×C4×C61—21no—
187C23×C4×C61C2311yescharacteristic
188C23×C4×C61C2311yescharacteristic
189#137×C61—24no—
190#137×C61—28no—
191#137×C61—24no—
192#137×C61—42no—
193AGL(1,ℤ/8)×C61—24no—
194AGL(1,ℤ/8)×C61—24no—
195AGL(1,ℤ/8)×C61—24no—
196AGL(1,ℤ/8)×C61—28no—
197AGL(1,ℤ/8)×C61—28no—
198AGL(1,ℤ/8)×C61—28no—
199AGL(1,ℤ/8)×C61—24no—
200AGL(1,ℤ/8)×C61—42no—
201AGL(1,ℤ/8)×C61D418yescomplemented
202#135×C61—28no—
203#135×C61—28no—
204C2×Q16×C61C2312yescomplemented
205C2×Q16×C61C2312yescomplemented
206C2×Q16×C61C2312yescomplemented
207C2×SD16×C61—28no—
208C2×SD16×C61C2312yes—
209C2×SD16×C61C2312yes—
210C2×SD16×C61C2312yes—
211C2×SD16×C61C2312yes—
212C2×SD16×C61C2312yes—
213C2×SD16×C61C2312yes—
214C2×SD16×C61C2312yescomplemented
215C2×SD16×C61C2312yescomplemented
216C2×SD16×C61C2312yescomplemented
217C2×D8×C61—28no—
218C2×D8×C61C2312yes—
219C2×D8×C61C2312yes—
220C2×D8×C61C2312yes—
221C2×D8×C61C2312yes—
222C2×D8×C61C2312yes—
223C2×D8×C61C2312yes—
224C2×M16×C61—24no—
225C2×M16×C61—24no—
226C2×M16×C61C2311yescharacteristic
227C2×M16×C61C2312yes—
228C2×M16×C61C2311yescharacteristic
229C2×M16×C61C2311yescharacteristic
230C2×M16×C61C2311yescharacteristic
231C2×M16×C61C2312yescomplemented
232C22×C8×C61C2312yes—
233C22×C8×C61C2312yescomplemented
234C4⋊Q8×C61—21no—
235C4⋊Q8×C61C2311yescharacteristic, complemented
236#127×C61—21no—
237#127×C61C2311yescharacteristic, complemented
238#124×C61—21no—
239#124×C61—21no—
240#124×C61—21no—
241#124×C61—21no—
242#124×C61C2312yes—
243#124×C61C2312yes—
244#124×C61C2311yescharacteristic, complemented
245#124×C61C2311yescharacteristic, complemented
246#123×C61—21no—
247#123×C61—21no—
248#123×C61—22no—
249#123×C61—22no—
250#123×C61—22no—
251#123×C61—22no—
252#123×C61—21no—
253#123×C61—21no—
254#123×C61—21no—
255#123×C61—21no—
256C22⋊Q8×C61—21no—
257C22⋊Q8×C61—21no—
258C22⋊Q8×C61—21no—
259C22⋊Q8×C61—21no—
260C22⋊Q8×C61—21no—
261C22⋊Q8×C61—21no—
262C22⋊Q8×C61C2312yes—
263C22⋊Q8×C61C2312yes—
264C22⋊Q8×C61C2311yescharacteristic
265C22⋊Q8×C61C2311yescharacteristic
266C22⋊Q8×C61C2311yescharacteristic, complemented
267C22⋊Q8×C61C2311yescharacteristic, complemented
268#121×C61—21no—
269#121×C61—21no—
270#121×C61—21no—
271#121×C61—21no—
272#121×C61—21no—
273#121×C61—21no—
274#121×C61—21no—
275#121×C61—21no—
276#121×C61—21no—
277#121×C61—21no—
278#121×C61—22no—
279#121×C61—22no—
280#121×C61—22no—
281#121×C61—22no—
282#121×C61—21no—
283#121×C61—21no—
284#121×C61C2311yescharacteristic
285#121×C61C2312yes—
286#121×C61C2312yes—
287#121×C61C2311yescharacteristic
288#121×C61C2311yescharacteristic, complemented
289#121×C61C2311yescharacteristic, complemented
290#120×C61—21no—
291#120×C61—21no—
292#120×C61—21no—
293#120×C61—21no—
294#120×C61—22no—
295#120×C61—22no—
296#120×C61—22no—
297#120×C61—22no—
298#120×C61—21no—
299#120×C61—21no—
300C4×Q8×C61C2311yescharacteristic, complemented
301C4×Q8×C61C2311yescharacteristic, complemented
302C4×D4×C61—21no—
303C4×D4×C61—21no—
304C4×D4×C61—21no—
305C4×D4×C61—21no—
306C4×D4×C61—21no—
307C4×D4×C61—21no—
308C4×D4×C61—21no—
309C4×D4×C61—21no—
310C4×D4×C61—21no—
311C4×D4×C61—21no—
312C4×D4×C61—21no—
313C4×D4×C61—21no—
314C4×D4×C61—21no—
315C4×D4×C61—21no—
316C4×D4×C61D411yescharacteristic
317C4×D4×C61D411yescharacteristic
318C4×D4×C61D411yescharacteristic
319C4×D4×C61D411yescharacteristic
320C4×D4×C61C2312yes—
321C4×D4×C61C2312yes—
322C4×D4×C61C2311yescharacteristic
323C4×D4×C61C2311yescharacteristic
324C4×D4×C61C2311yescharacteristic
325C4×D4×C61C2311yescharacteristic
326C4×D4×C61C2311yescharacteristic, complemented
327C4×D4×C61C2311yescharacteristic, complemented
328#117×C61—21no—
329#117×C61C2311yescharacteristic
330C2×C4⋊C4×C61—21no—
331C2×C4⋊C4×C61—21no—
332C2×C4⋊C4×C61D411yescharacteristic
333C2×C4⋊C4×C61C2311yescharacteristic
334C2×C22⋊C4×C61—21no—
335C2×C22⋊C4×C61—21no—
336C2×C22⋊C4×C61—21no—
337C2×C22⋊C4×C61—21no—
338C2×C22⋊C4×C61—21no—
339C2×C22⋊C4×C61—22no—
340C2×C22⋊C4×C61—22no—
341C2×C22⋊C4×C61—22no—
342C2×C22⋊C4×C61—22no—
343C2×C22⋊C4×C61—21no—
344C2×C22⋊C4×C61—21no—
345C2×C22⋊C4×C61D411yescharacteristic
346C2×C22⋊C4×C61D411yescharacteristic
347C2×C42×C61—21no—
348C2×C42×C61C2311yescharacteristic
349#107×C61C2312yescomplemented
350#106×C61C2312yescomplemented
351C4⋊C8×C61C2312yescomplemented
352C4⋊C8×C61C2312yescomplemented
353#103×C61C2312yescomplemented
354#103×C61C2312yescomplemented
355#103×C61C2312yescomplemented
356#103×C61C2312yescomplemented
357#103×C61C2312yescomplemented
358#102×C61C2312yes—
359#102×C61C2312yes—
360#102×C61C2312yes—
361#102×C61C2312yes—
362#102×C61C2312yescomplemented
363#102×C61C2312yescomplemented
364#102×C61C2312yescomplemented
365C22⋊C8×C61C2312yes—
366C22⋊C8×C61C2312yes—
367C22⋊C8×C61C2312yescomplemented
368C22⋊C8×C61C2312yescomplemented
369#97×C61C2312yescomplemented
370C4×C8×C61C2312yescomplemented
371C24×C61—21no—
372C24×C61—21no—
373C24×C61—22no—
374C24×C61—22no—
375C24×C61—21no—
376C24×C61—21no—
377C24×C61—44no—
378C24×C61—44no—
379C24×C61—82no—
380C24×C61C2×D411yescharacteristic
381C24×C61C2×D411yescharacteristic
382#41×C61—22no—
383#41×C61—22no—
384#41×C61—22no—
385#41×C61—24no—
386#41×C61—22no—
387#41×C61—22no—
388#41×C61—24no—
389#41×C61—22no—
390#41×C61—22no—
391#41×C61—22no—
392#41×C61—22no—
393#41×C61—44no—
394#41×C61—44no—
395#41×C61—41no—
396#41×C61—41no—
397#41×C61—42no—
398#41×C61—42no—
399#41×C61—41no—
400#41×C61—41no—
401#41×C61—44no—
402#41×C61—44no—
403#41×C61—44no—
404#41×C61—44no—
405#41×C61C2×D414yes—
406C2×Q8×C61—21no—
407C2×Q8×C61—21no—
408C2×Q8×C61—21no—
409C2×Q8×C61—22no—
410C2×Q8×C61—22no—
411C2×Q8×C61—22no—
412C2×Q8×C61—22no—
413C2×Q8×C61—41no—
414C2×Q8×C61—41no—
415C2×Q8×C61C2412yes—
416C2×Q8×C61C2411yescharacteristic
417C2×Q8×C61C2411yescharacteristic
418C2×Q8×C61C2411yescharacteristic
419C2×D4×C61—21no—
420C2×D4×C61—22no—
421C2×D4×C61—24no—
422C2×D4×C61—24no—
423C2×D4×C61—22no—
424C2×D4×C61—21no—
425C2×D4×C61—21no—
426C2×D4×C61—22no—
427C2×D4×C61—22no—
428C2×D4×C61—21no—
429C2×D4×C61—21no—
430C2×D4×C61—21no—
431C2×D4×C61—21no—
432C2×D4×C61—21no—
433C2×D4×C61—21no—
434C2×D4×C61—21no—
435C2×D4×C61—21no—
436C2×D4×C61—22no—
437C2×D4×C61—22no—
438C2×D4×C61—21no—
439C2×D4×C61—22no—
440C2×D4×C61—21no—
441C2×D4×C61—21no—
442C2×D4×C61—21no—
443C2×D4×C61—22no—
444C2×D4×C61—22no—
445C2×D4×C61—21no—
446C2×D4×C61—21no—
447C2×D4×C61—22no—
448C2×D4×C61—22no—
449C2×D4×C61—42no—
450C2×D4×C61—42no—
451C2×D4×C61—41no—
452C2×D4×C61—41no—
453C2×D4×C61—44no—
454C2×D4×C61—44no—
455C2×D4×C61—44no—
456C2×D4×C61—42no—
457C2×D4×C61—44no—
458C2×D4×C61—44no—
459C2×D4×C61—44no—
460C2×D4×C61—44no—
461C2×D4×C61—82no—
462C2×D4×C61C2×D411yescharacteristic
463C2×D4×C61C2×D411yescharacteristic
464C2×D4×C61C2×D411yescharacteristic
465C2×D4×C61C2×D411yescharacteristic
466C2×D4×C61C2×D414yescomplemented
467C2×D4×C61C2412yes—
468C2×D4×C61C2411yescharacteristic
469C2×D4×C61C2411yescharacteristic
470C2×D4×C61C2412yes—
471C2×D4×C61C2411yescharacteristic
472C22×C4×C61—21no—
473C22×C4×C61—22no—
474C22×C4×C61—22no—
475C22×C4×C61—22no—
476C22×C4×C61—22no—
477C22×C4×C61—21no—
478C22×C4×C61—21no—
479C22×C4×C61—21no—
480C22×C4×C61—21no—
481C22×C4×C61—21no—
482C22×C4×C61—22no—
483C22×C4×C61—22no—
484C22×C4×C61—21no—
485C22×C4×C61—21no—
486C22×C4×C61—21no—
487C22×C4×C61—21no—
488C22×C4×C61—21no—
489C22×C4×C61—21no—
490C22×C4×C61—21no—
491C22×C4×C61—22no—
492C22×C4×C61—22no—
493C22×C4×C61—44no—
494C22×C4×C61—44no—
495C22×C4×C61—44no—
496C22×C4×C61—82no—
497C22×C4×C61C2×D411yescharacteristic
498C22×C4×C61C2×D411yescharacteristic
499C22×C4×C61C2×D411yescharacteristic
500C22×C4×C61C2×D411yescharacteristic
501C22×C4×C61C2×D411yescharacteristic
502C22×C4×C61C2×D411yescharacteristic
503C22×C4×C61C2×D411yescharacteristic
504C22×C4×C61C2×D411yescharacteristic
505C22×C4×C61C2411yescharacteristic
506C22×C4×C61C2411yescharacteristic
507C22×C4×C61C2411yescharacteristic
508C22×C4×C61C2411yescharacteristic
509C22×C4×C61C2411yescharacteristic
510Q16×C61—24no—
511Q16×C61—24no—
512Q16×C61—42no—
513SD16×C61—24no—
514SD16×C61—24no—
515SD16×C61—24no—
516SD16×C61—24no—
517SD16×C61—24no—
518SD16×C61—24no—
519SD16×C61—42no—
520SD16×C61—42no—
521SD16×C61C2×D418yescomplemented
522D8×C61—24no—
523D8×C61—24no—
524D8×C61—24no—
525D8×C61—24no—
526D8×C61—42no—
527D8×C61C2×D418yescomplemented
528M16×C61—22no—
529M16×C61—22no—
530M16×C61—22no—
531M16×C61—24no—
532M16×C61—24no—
533M16×C61C2×D414yescomplemented
534C2×C8×C61—24no—
535C2×C8×C61—24no—
536C2×C8×C61C2412yes—
537C2×C8×C61C2412yes—
538C2×C8×C61C2412yes—
539C2×C8×C61C2412yes—
540C4⋊C4×C61—21no—
541C4⋊C4×C61—21no—
542C4⋊C4×C61—21no—
543C4⋊C4×C61—22no—
544C4⋊C4×C61—22no—
545C4⋊C4×C61—21no—
546C4⋊C4×C61—21no—
547C4⋊C4×C61—21no—
548C4⋊C4×C61—21no—
549C4⋊C4×C61—21no—
550C4⋊C4×C61—21no—
551C4⋊C4×C61C2×D411yescharacteristic
552C4⋊C4×C61C2×D411yescharacteristic
553C4⋊C4×C61C2×D411yescharacteristic
554C4⋊C4×C61C2×D411yescharacteristic
555C4⋊C4×C61C2411yescharacteristic
556C4⋊C4×C61C2411yescharacteristic
557C4⋊C4×C61C2412yes—
558C22⋊C4×C61—22no—
559C22⋊C4×C61—22no—
560C22⋊C4×C61—21no—
561C22⋊C4×C61—21no—
562C22⋊C4×C61—21no—
563C22⋊C4×C61—21no—
564C22⋊C4×C61—21no—
565C22⋊C4×C61—22no—
566C22⋊C4×C61—22no—
567C22⋊C4×C61—22no—
568C22⋊C4×C61—22no—
569C22⋊C4×C61—21no—
570C22⋊C4×C61—21no—
571C22⋊C4×C61—21no—
572C22⋊C4×C61—21no—
573C22⋊C4×C61—22no—
574C22⋊C4×C61—22no—
575C22⋊C4×C61—22no—
576C22⋊C4×C61—22no—
577C22⋊C4×C61—21no—
578C22⋊C4×C61—21no—
579C22⋊C4×C61—21no—
580C22⋊C4×C61—21no—
581C22⋊C4×C61—21no—
582C22⋊C4×C61—21no—
583C22⋊C4×C61C2×D411yescharacteristic
584C22⋊C4×C61C2×D411yescharacteristic
585C22⋊C4×C61C2×D411yescharacteristic
586C22⋊C4×C61C2×D411yescharacteristic
587C22⋊C4×C61C2×D411yescharacteristic
588C22⋊C4×C61C2×D411yescharacteristic
589C22⋊C4×C61C2×D411yescharacteristic
590C22⋊C4×C61C2×D411yescharacteristic
591C42×C61—21no—
592C42×C61—21no—
593C42×C61—21no—
594C42×C61C2×D411yescharacteristic
595C42×C61C2×D411yescharacteristic
596C42×C61C2411yescharacteristic
597C42×C61C2411yescharacteristic
598C23×C61—22no—
599C23×C61—24no—
600C23×C61—22no—
601C23×C61—21no—
602C23×C61—22no—
603C23×C61—22no—
604C23×C61—22no—
605C23×C61—21no—
606C23×C61—21no—
607C23×C61—41no—
608C23×C61—41no—
609C23×C61—41no—
610C23×C61—42no—
611C23×C61—42no—
612C23×C61—44no—
613C23×C61—44no—
614C23×C61—42no—
615C23×C61—42no—
616C23×C61—42no—
617C23×C61—42no—
618C23×C61—42no—
619C23×C61—44no—
620C23×C61—42no—
621C23×C61—42no—
622C23×C61—44no—
623C23×C61—81no—
624C23×C61—81no—
625C23×C61—82no—
626C23×C61—82no—
627C23×C61—816no—
628C23×C61C22×D411yescharacteristic
629C23×C61C22×D411yescharacteristic
630C23×C61C22×D411yescharacteristic
631C23×C61C22×D411yescharacteristic
632C23×C61C22×D411yescharacteristic
633Q8×C61—21no—
634Q8×C61—21no—
635Q8×C61—21no—
636Q8×C61—22no—
637Q8×C61—21no—
638Q8×C61—22no—
639Q8×C61—21no—
640Q8×C61—42no—
641Q8×C61—42no—
642Q8×C61—42no—
643Q8×C61C22×D412yes—
644D4×C61—24no—
645D4×C61—22no—
646D4×C61—22no—
647D4×C61—24no—
648D4×C61—21no—
649D4×C61—22no—
650D4×C61—21no—
651D4×C61—22no—
652D4×C61—21no—
653D4×C61—21no—
654D4×C61—22no—
655D4×C61—21no—
656D4×C61—41no—
657D4×C61—41no—
658D4×C61—44no—
659D4×C61—44no—
660D4×C61—42no—
661D4×C61—42no—
662D4×C61—42no—
663D4×C61—42no—
664D4×C61—42no—
665D4×C61—44no—
666D4×C61—42no—
667D4×C61—44no—
668D4×C61—42no—
669D4×C61—42no—
670D4×C61—42no—
671D4×C61—42no—
672D4×C61—42no—
673D4×C61—42no—
674D4×C61—81no—
675D4×C61—81no—
676D4×C61—81no—
677D4×C61—82no—
678D4×C61—82no—
679D4×C61C22×D412yes—
680D4×C61C22×D414yes—
681C2×C4×C61—22no—
682C2×C4×C61—22no—
683C2×C4×C61—21no—
684C2×C4×C61—22no—
685C2×C4×C61—22no—
686C2×C4×C61—22no—
687C2×C4×C61—22no—
688C2×C4×C61—24no—
689C2×C4×C61—21no—
690C2×C4×C61—21no—
691C2×C4×C61—21no—
692C2×C4×C61—21no—
693C2×C4×C61—21no—
694C2×C4×C61—21no—
695C2×C4×C61—21no—
696C2×C4×C61—21no—
697C2×C4×C61—21no—
698C2×C4×C61—21no—
699C2×C4×C61—22no—
700C2×C4×C61—22no—
701C2×C4×C61—21no—
702C2×C4×C61—21no—
703C2×C4×C61—41no—
704C2×C4×C61—41no—
705C2×C4×C61—42no—
706C2×C4×C61—42no—
707C2×C4×C61—42no—
708C2×C4×C61—42no—
709C2×C4×C61—42no—
710C2×C4×C61—44no—
711C2×C4×C61—42no—
712C2×C4×C61—44no—
713C2×C4×C61—42no—
714C2×C4×C61—42no—
715C2×C4×C61—42no—
716C2×C4×C61—42no—
717C2×C4×C61—42no—
718C2×C4×C61—81no—
719C2×C4×C61—82no—
720C2×C4×C61—82no—
721C2×C4×C61C22×D411yescharacteristic
722C2×C4×C61C22×D411yescharacteristic
723C2×C4×C61C22×D411yescharacteristic
724C2×C4×C61C22×D411yescharacteristic
725C2×C4×C61C22×D411yescharacteristic
726C2×C4×C61C22×D411yescharacteristic
727C2×C4×C61C22×D411yescharacteristic
728C2×C4×C61C22×D411yescharacteristic
729C2×C4×C61C22×D411yescharacteristic
730C2×C4×C61C22×D412yes—
731C2×C4×C61H(5,𝔽2)12yes—
732C2×C4×C61C2511yescharacteristic
733C8×C61—22no—
734C8×C61—22no—
735C8×C61—22no—
736C8×C61C22×D414yes—
737#61066C6111yesmaximal, characteristic, direct product factor, Sylow
738C22×C61—21no—
739C22×C61—21no—
740C22×C61—21no—
741C22×C61—21no—
742C22×C61—21no—
743C22×C61—21no—
744C22×C61—21no—
745C22×C61—21no—
746C22×C61—21no—
747C22×C61—21no—
748C22×C61—22no—
749C22×C61—24no—
750C22×C61—21no—
751C22×C61—21no—
752C22×C61—21no—
753C22×C61—44no—
754C22×C61—48no—
755C22×C61—42no—
756C22×C61—41no—
757C22×C61—41no—
758C22×C61—42no—
759C22×C61—42no—
760C22×C61—41no—
761C22×C61—41no—
762C22×C61—41no—
763C22×C61—41no—
764C22×C61—42no—
765C22×C61—41no—
766C22×C61—41no—
767C22×C61—42no—
768C22×C61—82no—
769C22×C61—84no—
770C22×C61—88no—
771C22×C61—84no—
772C22×C61—84no—
773C22×C61—88no—
774C22×C61D4212yes—
775C22×C61#57512yescomplemented
776C22×C61C23×D411yescharacteristic
777C4×C61—21no—
778C4×C61—21no—
779C4×C61—21no—
780C4×C61—21no—
781C4×C61—21no—
782C4×C61—21no—
783C4×C61—22no—
784C4×C61—21no—
785C4×C61—21no—
786C4×C61—42no—
787C4×C61—41no—
788C4×C61—42no—
789C4×C61—41no—
790C4×C61—41no—
791C4×C61—41no—
792C4×C61D4212yes—
793C4×C61C23×D411yescharacteristic
794C4×C61C2×H(5,𝔽2)11yescharacteristic
795C2×#575C2×C6111yescharacteristic, complemented
796C22×AGL(1,ℤ/8)C2×C6111yescharacteristic, complemented
797D4×#41C2×C6111yescharacteristic, complemented
798C2×#546C2×C6111yescharacteristic, complemented
799#3282C2×C6112yescomplemented
800#3280C2×C6112yescomplemented
801#3275C2×C6112yescomplemented
802#3273C2×C6112yescomplemented
803#3268C2×C6112yescomplemented
804#3267C2×C6112yescomplemented
805#3266C2×C6112yescomplemented
806#3264C2×C6112yescomplemented
807#3153C2×C6111yescharacteristic, complemented
808#3056C2×C6111yescharacteristic, complemented
809#3055C2×C6111yescharacteristic, complemented
810#3040C2×C6111yescharacteristic, complemented
811#3036C2×C6111yescharacteristic, complemented
812#3007C2×C6111yescharacteristic, complemented
813#3006C2×C6111yescharacteristic, complemented
814#3005C2×C6111yescharacteristic, complemented
815#3003C2×C6111yescharacteristic, complemented
816C4×AGL(1,ℤ/8)C2×C6111yescharacteristic, complemented
817D4×M16C2×C6111yescharacteristic, complemented
818C2×C61—22no—
819C2×C61—22no—
820C2×C61—41no—
821C2×C61—41no—
822C2×C61—41no—
823C2×C61—44no—
824C2×C61—42no—
825C2×C61—81no—
826C2×C61—81no—
827C2×C61—82no—
828C2×C61C2×D4211yescharacteristic
829C2×C61C2×#57511yescharacteristic
830C2×C61#358511yescharacteristic
831C22×#41C22×C6111yescharacteristic
832C22×#41C22×C6111yescharacteristic, complemented
833C22×#41C22×C6111yescharacteristic, complemented
834C23×D4C22×C6111yescharacteristic, complemented
835#575—28no—
836C2×#137C22×C6111yescharacteristic, complemented
837C2×#137C22×C6111yescharacteristic, complemented
838C2×#137C22×C6111yescharacteristic, complemented
839C2×#137C22×C6112yescomplemented
840C2×AGL(1,ℤ/8)—28no—
841C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
842C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
843C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
844C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
845C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
846C2×AGL(1,ℤ/8)C22×C6112yescomplemented
847C2×AGL(1,ℤ/8)C22×C6112yescomplemented
848C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
849C2×AGL(1,ℤ/8)C22×C6112yescomplemented
850C2×#135C22×C6112yescomplemented
851C2×#135C22×C6112yescomplemented
852C22×SD16C22×C6112yescomplemented
853C22×D8C22×C6112yescomplemented
854C22×M16C22×C6111yescharacteristic, complemented
855C22×M16C22×C6111yescharacteristic, complemented
856#550C22×C6111yescharacteristic, complemented
857D4×Q8C22×C6111yescharacteristic, complemented
858#548C22×C6111yescharacteristic, complemented
859#548C22×C6111yescharacteristic, complemented
860#547—21no—
861#547C22×C6111yescharacteristic, complemented
862#546—21no—
863#546—21no—
864#546—21no—
865#546—21no—
866#546—21no—
867#546—21no—
868#546C22×C6112yes—
869#546C22×C6112yescomplemented
870#546C22×C6112yescomplemented
871#546C22×C6112yescomplemented
872#546C22×C6111yescharacteristic, complemented
873#546C22×C6111yescharacteristic, complemented
874D42—21no—
875D42C22×C6111yescharacteristic, complemented
876#532—21no—
877#532C22×C6111yescharacteristic, complemented
878C2×#124C22×C6111yescharacteristic, complemented
879#525—21no—
880#525—21no—
881#525C22×C6111yescharacteristic
882#525C22×C6111yescharacteristic, complemented
883C2×#123—21no—
884C2×C22⋊Q8C22×C6111yescharacteristic, complemented
885C2×#121—21no—
886C2×#121C22×C6111yescharacteristic, complemented
887C2×#120—21no—
888C4×#41C22×C6111yescharacteristic, complemented
889C2×C4×D4—21no—
890C2×C4×D4C22×C6111yescharacteristic
891C2×C4×D4C22×C6111yescharacteristic, complemented
892C22×C22⋊C4—21no—
893#497C22×C6112yescomplemented
894#496C22×C6112yescomplemented
895#495C22×C6112yescomplemented
896#495C22×C6112yescomplemented
897#470C22×C6112yescomplemented
898#469C22×C6112yescomplemented
899#468C22×C6112yescomplemented
900#468C22×C6112yescomplemented
901#467C22×C6112yescomplemented
902#466C22×C6112yescomplemented
903#465C22×C6112yescomplemented
904#465C22×C6112yescomplemented
905#464C22×C6112yescomplemented
906#464C22×C6112yescomplemented
907#463C22×C6112yescomplemented
908#463C22×C6112yescomplemented
909#463C22×C6112yescomplemented
910#463C22×C6112yescomplemented
911#461C22×C6112yescomplemented
912#459C22×C6112yescomplemented
913#452C22×C6112yescomplemented
914#452C22×C6112yescomplemented
915#452C22×C6112yescomplemented
916#452C22×C6112yescomplemented
917#451C22×C6112yescomplemented
918#450C22×C6112yescomplemented
919#450C22×C6112yescomplemented
920#450C22×C6112yescomplemented
921#449C22×C6112yescomplemented
922#449C22×C6112yescomplemented
923#449C22×C6112yescomplemented
924#449C22×C6112yescomplemented
925#448C22×C6112yescomplemented
926#447C22×C6112yescomplemented
927#447C22×C6112yescomplemented
928#447C22×C6112yescomplemented
929#442C22×C6112yescomplemented
930#440C22×C6112yescomplemented
931C4×SD16C22×C6112yescomplemented
932C4×D8C22×C6112yescomplemented
933#436C22×C6112yescomplemented
934#435C22×C6112yescomplemented
935#435C22×C6112yescomplemented
936C8×D4C22×C6112yescomplemented
937#428C22×C6111yescharacteristic, complemented
938#423C22×C6111yescharacteristic, complemented
939#419C22×C6111yescharacteristic, complemented
940#418C22×C6111yescharacteristic, complemented
941#418C22×C6111yescharacteristic, complemented
942#417C22×C6111yescharacteristic, complemented
943#417C22×C6111yescharacteristic, complemented
944#417C22×C6111yescharacteristic, complemented
945#407C22×C6111yescharacteristic, complemented
946#407C22×C6111yescharacteristic, complemented
947C4×M16C22×C6111yescharacteristic, complemented
948C61#6106611yescharacteristic, direct product factor, Sylow
949C25—21no—
950C2×#41—21no—
951C2×#41—21no—
952C2×#41—21no—
953C2×#41—21no—
954C2×#41—21no—
955C2×#41—21no—
956C2×#41—24no—
957C2×#41—24no—
958C2×#41—24no—
959C2×#41—42no—
960C2×#41—42no—
961C2×#41—42no—
962C2×#41C23×C6111yescharacteristic
963C2×#41C23×C6111yescharacteristic
964C2×#41C23×C6112yes—
965C2×#41C23×C6112yes—
966C2×#41C23×C6111yescharacteristic
967C2×#41C23×C6111yescharacteristic
968C2×#41C23×C6111yescharacteristic
969C2×#41C23×C6111yescharacteristic, complemented
970C2×#41C23×C6111yescharacteristic, complemented
971C22×Q8C23×C6111yescharacteristic
972C22×Q8C23×C6111yescharacteristic
973C22×Q8C23×C6111yescharacteristic, complemented
974C22×D4—24no—
975C22×D4—21no—
976C22×D4—21no—
977C22×D4—21no—
978C22×D4—21no—
979C22×D4—21no—
980C22×D4—21no—
981C22×D4—21no—
982C22×D4—21no—
983C22×D4—42no—
984C22×D4D4×C6111yescharacteristic
985C22×D4C23×C6111yescharacteristic
986C22×D4C23×C6111yescharacteristic
987C22×D4C23×C6112yes—
988C22×D4C23×C6112yes—
989C22×D4C23×C6111yescharacteristic
990C22×D4C23×C6111yescharacteristic, complemented
991C23×C4—21no—
992C23×C4—21no—
993C23×C4—21no—
994C23×C4—21no—
995C23×C4C23×C6111yescharacteristic
996C23×C4C23×C6111yescharacteristic
997#137—24no—
998#137—28no—
999#137—24no—
1000#137—42no—
1001AGL(1,ℤ/8)—24no—
1002AGL(1,ℤ/8)—24no—
1003AGL(1,ℤ/8)—24no—
1004AGL(1,ℤ/8)—28no—
1005AGL(1,ℤ/8)—28no—
1006AGL(1,ℤ/8)—28no—
1007AGL(1,ℤ/8)—24no—
1008AGL(1,ℤ/8)—42no—
1009AGL(1,ℤ/8)D4×C6118yescomplemented
1010#135—28no—
1011#135—28no—
1012C2×Q16C23×C6112yescomplemented
1013C2×Q16C23×C6112yescomplemented
1014C2×Q16C23×C6112yescomplemented
1015C2×SD16—28no—
1016C2×SD16C23×C6112yes—
1017C2×SD16C23×C6112yes—
1018C2×SD16C23×C6112yes—
1019C2×SD16C23×C6112yes—
1020C2×SD16C23×C6112yes—
1021C2×SD16C23×C6112yes—
1022C2×SD16C23×C6112yescomplemented
1023C2×SD16C23×C6112yescomplemented
1024C2×SD16C23×C6112yescomplemented
1025C2×D8—28no—
1026C2×D8C23×C6112yes—
1027C2×D8C23×C6112yes—
1028C2×D8C23×C6112yes—
1029C2×D8C23×C6112yes—
1030C2×D8C23×C6112yes—
1031C2×D8C23×C6112yes—
1032C2×M16—24no—
1033C2×M16—24no—
1034C2×M16C23×C6111yescharacteristic
1035C2×M16C23×C6112yes—
1036C2×M16C23×C6111yescharacteristic
1037C2×M16C23×C6111yescharacteristic
1038C2×M16C23×C6111yescharacteristic
1039C2×M16C23×C6112yescomplemented
1040C22×C8C23×C6112yes—
1041C22×C8C23×C6112yescomplemented
1042C4⋊Q8—21no—
1043C4⋊Q8C23×C6111yescharacteristic, complemented
1044#127—21no—
1045#127C23×C6111yescharacteristic, complemented
1046#124—21no—
1047#124—21no—
1048#124—21no—
1049#124—21no—
1050#124C23×C6112yes—
1051#124C23×C6112yes—
1052#124C23×C6111yescharacteristic, complemented
1053#124C23×C6111yescharacteristic, complemented
1054#123—21no—
1055#123—21no—
1056#123—22no—
1057#123—22no—
1058#123—22no—
1059#123—22no—
1060#123—21no—
1061#123—21no—
1062#123—21no—
1063#123—21no—
1064C22⋊Q8—21no—
1065C22⋊Q8—21no—
1066C22⋊Q8—21no—
1067C22⋊Q8—21no—
1068C22⋊Q8—21no—
1069C22⋊Q8—21no—
1070C22⋊Q8C23×C6112yes—
1071C22⋊Q8C23×C6112yes—
1072C22⋊Q8C23×C6111yescharacteristic
1073C22⋊Q8C23×C6111yescharacteristic
1074C22⋊Q8C23×C6111yescharacteristic, complemented
1075C22⋊Q8C23×C6111yescharacteristic, complemented
1076#121—21no—
1077#121—21no—
1078#121—21no—
1079#121—21no—
1080#121—21no—
1081#121—21no—
1082#121—21no—
1083#121—21no—
1084#121—22no—
1085#121—22no—
1086#121—22no—
1087#121—22no—
1088#121—21no—
1089#121—21no—
1090#121—21no—
1091#121—21no—
1092#121C23×C6112yes—
1093#121C23×C6112yes—
1094#121C23×C6111yescharacteristic
1095#121C23×C6111yescharacteristic
1096#121C23×C6111yescharacteristic, complemented
1097#121C23×C6111yescharacteristic, complemented
1098#120—21no—
1099#120—21no—
1100#120—22no—
1101#120—22no—
1102#120—22no—
1103#120—22no—
1104#120—21no—
1105#120—21no—
1106#120—21no—
1107#120—21no—
1108C4×Q8C23×C6111yescharacteristic, complemented
1109C4×Q8C23×C6111yescharacteristic, complemented
1110C4×D4—21no—
1111C4×D4—21no—
1112C4×D4—21no—
1113C4×D4—21no—
1114C4×D4—21no—
1115C4×D4—21no—
1116C4×D4—21no—
1117C4×D4—21no—
1118C4×D4—21no—
1119C4×D4—21no—
1120C4×D4—21no—
1121C4×D4—21no—
1122C4×D4—21no—
1123C4×D4—21no—
1124C4×D4D4×C6111yescharacteristic
1125C4×D4D4×C6111yescharacteristic
1126C4×D4D4×C6111yescharacteristic
1127C4×D4D4×C6111yescharacteristic
1128C4×D4C23×C6112yes—
1129C4×D4C23×C6112yes—
1130C4×D4C23×C6111yescharacteristic
1131C4×D4C23×C6111yescharacteristic
1132C4×D4C23×C6111yescharacteristic
1133C4×D4C23×C6111yescharacteristic
1134C4×D4C23×C6111yescharacteristic, complemented
1135C4×D4C23×C6111yescharacteristic, complemented
1136#117—21no—
1137#117C23×C6111yescharacteristic
1138C2×C4⋊C4—21no—
1139C2×C4⋊C4—21no—
1140C2×C4⋊C4D4×C6111yescharacteristic
1141C2×C4⋊C4C23×C6111yescharacteristic
1142C2×C22⋊C4—21no—
1143C2×C22⋊C4—21no—
1144C2×C22⋊C4—21no—
1145C2×C22⋊C4—21no—
1146C2×C22⋊C4—21no—
1147C2×C22⋊C4—22no—
1148C2×C22⋊C4—22no—
1149C2×C22⋊C4—22no—
1150C2×C22⋊C4—22no—
1151C2×C22⋊C4—21no—
1152C2×C22⋊C4—21no—
1153C2×C22⋊C4D4×C6111yescharacteristic
1154C2×C22⋊C4D4×C6111yescharacteristic
1155C2×C42—21no—
1156C2×C42C23×C6111yescharacteristic
1157#107C23×C6112yescomplemented
1158#106C23×C6112yescomplemented
1159C4⋊C8C23×C6112yescomplemented
1160C4⋊C8C23×C6112yescomplemented
1161#103C23×C6112yescomplemented
1162#103C23×C6112yescomplemented
1163#103C23×C6112yescomplemented
1164#103C23×C6112yescomplemented
1165#103C23×C6112yescomplemented
1166#102C23×C6112yes—
1167#102C23×C6112yes—
1168#102C23×C6112yes—
1169#102C23×C6112yes—
1170#102C23×C6112yescomplemented
1171#102C23×C6112yescomplemented
1172#102C23×C6112yescomplemented
1173C22⋊C8C23×C6112yes—
1174C22⋊C8C23×C6112yes—
1175C22⋊C8C23×C6112yescomplemented
1176C22⋊C8C23×C6112yescomplemented
1177#97C23×C6112yescomplemented
1178C4×C8C23×C6112yescomplemented
1179C24—21no—
1180C24—21no—
1181C24—22no—
1182C24—22no—
1183C24—21no—
1184C24—21no—
1185C24—44no—
1186C24—44no—
1187C24—82no—
1188C24C2×D4×C6111yescharacteristic
1189C24C2×D4×C6111yescharacteristic
1190#41—22no—
1191#41—22no—
1192#41—22no—
1193#41—24no—
1194#41—22no—
1195#41—22no—
1196#41—24no—
1197#41—22no—
1198#41—22no—
1199#41—22no—
1200#41—22no—
1201#41—44no—
1202#41—44no—
1203#41—41no—
1204#41—41no—
1205#41—42no—
1206#41—42no—
1207#41—41no—
1208#41—41no—
1209#41—44no—
1210#41—44no—
1211#41—44no—
1212#41—44no—
1213#41C2×D4×C6114yes—
1214C2×Q8—21no—
1215C2×Q8—21no—
1216C2×Q8—21no—
1217C2×Q8—22no—
1218C2×Q8—22no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—41no—
1222C2×Q8—41no—
1223C2×Q8C24×C6112yes—
1224C2×Q8C24×C6111yescharacteristic
1225C2×Q8C24×C6111yescharacteristic
1226C2×Q8C24×C6111yescharacteristic
1227C2×D4—21no—
1228C2×D4—22no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—22no—
1232C2×D4—21no—
1233C2×D4—21no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—21no—
1237C2×D4—21no—
1238C2×D4—21no—
1239C2×D4—21no—
1240C2×D4—21no—
1241C2×D4—21no—
1242C2×D4—21no—
1243C2×D4—21no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—21no—
1247C2×D4—22no—
1248C2×D4—21no—
1249C2×D4—21no—
1250C2×D4—21no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—21no—
1254C2×D4—21no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—42no—
1258C2×D4—42no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—44no—
1262C2×D4—44no—
1263C2×D4—44no—
1264C2×D4—42no—
1265C2×D4—44no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—44no—
1269C2×D4—82no—
1270C2×D4C2×D4×C6111yescharacteristic
1271C2×D4C2×D4×C6111yescharacteristic
1272C2×D4C2×D4×C6111yescharacteristic
1273C2×D4C2×D4×C6111yescharacteristic
1274C2×D4C2×D4×C6114yescomplemented
1275C2×D4C24×C6112yes—
1276C2×D4C24×C6111yescharacteristic
1277C2×D4C24×C6111yescharacteristic
1278C2×D4C24×C6112yes—
1279C2×D4C24×C6111yescharacteristic
1280C22×C4—21no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—21no—
1286C22×C4—21no—
1287C22×C4—21no—
1288C22×C4—21no—
1289C22×C4—21no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—21no—
1293C22×C4—21no—
1294C22×C4—21no—
1295C22×C4—21no—
1296C22×C4—21no—
1297C22×C4—21no—
1298C22×C4—21no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—44no—
1302C22×C4—44no—
1303C22×C4—44no—
1304C22×C4—82no—
1305C22×C4C2×D4×C6111yescharacteristic
1306C22×C4C2×D4×C6111yescharacteristic
1307C22×C4C2×D4×C6111yescharacteristic
1308C22×C4C2×D4×C6111yescharacteristic
1309C22×C4C2×D4×C6111yescharacteristic
1310C22×C4C2×D4×C6111yescharacteristic
1311C22×C4C2×D4×C6111yescharacteristic
1312C22×C4C2×D4×C6111yescharacteristic
1313C22×C4C24×C6111yescharacteristic
1314C22×C4C24×C6111yescharacteristic
1315C22×C4C24×C6111yescharacteristic
1316C22×C4C24×C6111yescharacteristic
1317C22×C4C24×C6111yescharacteristic
1318Q16—24no—
1319Q16—24no—
1320Q16—42no—
1321SD16—24no—
1322SD16—24no—
1323SD16—24no—
1324SD16—24no—
1325SD16—24no—
1326SD16—24no—
1327SD16—42no—
1328SD16—42no—
1329SD16C2×D4×C6118yescomplemented
1330D8—24no—
1331D8—24no—
1332D8—24no—
1333D8—24no—
1334D8—42no—
1335D8C2×D4×C6118yescomplemented
1336M16—22no—
1337M16—22no—
1338M16—22no—
1339M16—24no—
1340M16—24no—
1341M16C2×D4×C6114yescomplemented
1342C2×C8—24no—
1343C2×C8—24no—
1344C2×C8C24×C6112yes—
1345C2×C8C24×C6112yes—
1346C2×C8C24×C6112yes—
1347C2×C8C24×C6112yes—
1348C4⋊C4—21no—
1349C4⋊C4—21no—
1350C4⋊C4—21no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—21no—
1354C4⋊C4—21no—
1355C4⋊C4—21no—
1356C4⋊C4—21no—
1357C4⋊C4—21no—
1358C4⋊C4—21no—
1359C4⋊C4C2×D4×C6111yescharacteristic
1360C4⋊C4C2×D4×C6111yescharacteristic
1361C4⋊C4C2×D4×C6111yescharacteristic
1362C4⋊C4C2×D4×C6111yescharacteristic
1363C4⋊C4C24×C6111yescharacteristic
1364C4⋊C4C24×C6111yescharacteristic
1365C4⋊C4C24×C6112yes—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—21no—
1369C22⋊C4—21no—
1370C22⋊C4—21no—
1371C22⋊C4—21no—
1372C22⋊C4—21no—
1373C22⋊C4—22no—
1374C22⋊C4—22no—
1375C22⋊C4—22no—
1376C22⋊C4—22no—
1377C22⋊C4—21no—
1378C22⋊C4—21no—
1379C22⋊C4—21no—
1380C22⋊C4—21no—
1381C22⋊C4—22no—
1382C22⋊C4—22no—
1383C22⋊C4—22no—
1384C22⋊C4—22no—
1385C22⋊C4—21no—
1386C22⋊C4—21no—
1387C22⋊C4—21no—
1388C22⋊C4—21no—
1389C22⋊C4—21no—
1390C22⋊C4—21no—
1391C22⋊C4C2×D4×C6111yescharacteristic
1392C22⋊C4C2×D4×C6111yescharacteristic
1393C22⋊C4C2×D4×C6111yescharacteristic
1394C22⋊C4C2×D4×C6111yescharacteristic
1395C22⋊C4C2×D4×C6111yescharacteristic
1396C22⋊C4C2×D4×C6111yescharacteristic
1397C22⋊C4C2×D4×C6111yescharacteristic
1398C22⋊C4C2×D4×C6111yescharacteristic
1399C42—21no—
1400C42—21no—
1401C42—21no—
1402C42C2×D4×C6111yescharacteristic
1403C42C2×D4×C6111yescharacteristic
1404C42C24×C6111yescharacteristic
1405C42C24×C6111yescharacteristic
1406C23—22no—
1407C23—24no—
1408C23—22no—
1409C23—21no—
1410C23—22no—
1411C23—22no—
1412C23—22no—
1413C23—21no—
1414C23—21no—
1415C23—41no—
1416C23—41no—
1417C23—41no—
1418C23—42no—
1419C23—42no—
1420C23—44no—
1421C23—44no—
1422C23—42no—
1423C23—42no—
1424C23—42no—
1425C23—42no—
1426C23—42no—
1427C23—44no—
1428C23—42no—
1429C23—42no—
1430C23—44no—
1431C23—81no—
1432C23—81no—
1433C23—82no—
1434C23—82no—
1435C23—816no—
1436C23C22×D4×C6111yescharacteristic
1437C23C22×D4×C6111yescharacteristic
1438C23C22×D4×C6111yescharacteristic
1439C23C22×D4×C6111yescharacteristic
1440C23C22×D4×C6111yescharacteristic
1441Q8—21no—
1442Q8—21no—
1443Q8—21no—
1444Q8—22no—
1445Q8—21no—
1446Q8—22no—
1447Q8—21no—
1448Q8—42no—
1449Q8—42no—
1450Q8—42no—
1451Q8C22×D4×C6112yes—
1452D4—24no—
1453D4—22no—
1454D4—22no—
1455D4—24no—
1456D4—21no—
1457D4—22no—
1458D4—21no—
1459D4—22no—
1460D4—21no—
1461D4—21no—
1462D4—22no—
1463D4—21no—
1464D4—41no—
1465D4—41no—
1466D4—44no—
1467D4—44no—
1468D4—42no—
1469D4—42no—
1470D4—42no—
1471D4—42no—
1472D4—42no—
1473D4—44no—
1474D4—42no—
1475D4—44no—
1476D4—42no—
1477D4—42no—
1478D4—42no—
1479D4—42no—
1480D4—42no—
1481D4—42no—
1482D4—81no—
1483D4—81no—
1484D4—81no—
1485D4—82no—
1486D4—82no—
1487D4C22×D4×C6112yes—
1488D4C22×D4×C6114yes—
1489C2×C4—22no—
1490C2×C4—22no—
1491C2×C4—21no—
1492C2×C4—22no—
1493C2×C4—22no—
1494C2×C4—22no—
1495C2×C4—22no—
1496C2×C4—24no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—22no—
1508C2×C4—22no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—41no—
1512C2×C4—41no—
1513C2×C4—42no—
1514C2×C4—42no—
1515C2×C4—42no—
1516C2×C4—42no—
1517C2×C4—42no—
1518C2×C4—44no—
1519C2×C4—42no—
1520C2×C4—44no—
1521C2×C4—42no—
1522C2×C4—42no—
1523C2×C4—42no—
1524C2×C4—42no—
1525C2×C4—42no—
1526C2×C4—81no—
1527C2×C4—82no—
1528C2×C4—82no—
1529C2×C4C22×D4×C6111yescharacteristic
1530C2×C4C22×D4×C6111yescharacteristic
1531C2×C4C22×D4×C6111yescharacteristic
1532C2×C4C22×D4×C6111yescharacteristic
1533C2×C4C22×D4×C6111yescharacteristic
1534C2×C4C22×D4×C6111yescharacteristic
1535C2×C4C22×D4×C6111yescharacteristic
1536C2×C4C22×D4×C6111yescharacteristic
1537C2×C4C22×D4×C6111yescharacteristic
1538C2×C4C22×D4×C6112yes—
1539C2×C4H(5,𝔽2)×C6112yes—
1540C2×C4C25×C6111yescharacteristic
1541C8—22no—
1542C8—22no—
1543C8—22no—
1544C8C22×D4×C6114yes—
1545C22—21no—
1546C22—21no—
1547C22—21no—
1548C22—21no—
1549C22—21no—
1550C22—21no—
1551C22—21no—
1552C22—21no—
1553C22—21no—
1554C22—21no—
1555C22—21no—
1556C22—21no—
1557C22—21no—
1558C22—22no—
1559C22—24no—
1560C22—44no—
1561C22—48no—
1562C22—41no—
1563C22—42no—
1564C22—42no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—42no—
1569C22—42no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—42no—
1575C22—82no—
1576C22—84no—
1577C22—88no—
1578C22—84no—
1579C22—84no—
1580C22—88no—
1581C22D42×C6112yes—
1582C22C61×#57512yescomplemented
1583C22C23×D4×C6111yescharacteristic
1584C4—21no—
1585C4—21no—
1586C4—21no—
1587C4—21no—
1588C4—21no—
1589C4—21no—
1590C4—21no—
1591C4—21no—
1592C4—22no—
1593C4—41no—
1594C4—42no—
1595C4—41no—
1596C4—42no—
1597C4—41no—
1598C4—41no—
1599C4D42×C6112yes—
1600C4C23×D4×C6111yescharacteristic
1601C4C2×H(5,𝔽2)×C6111yescharacteristic
1602C2—22no—
1603C2—22no—
1604C2—41no—
1605C2—41no—
1606C2—41no—
1607C2—44no—
1608C2—42no—
1609C2—82no—
1610C2—81no—
1611C2—81no—
1612C2C2×D42×C6111yescharacteristic
1613C2C2×C61×#57511yescharacteristic
1614C2C61×#358511yescharacteristic
subgroupG/H
center, socleC22×C61C23×D4
commutator, Frattini, cosocleC2×C4C25×C61
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C61×#575C2semidirect
2. C22×AGL(1,ℤ/8)×C61C2semidirect
3. D4×#41×C61C2semidirect
4. C2×C61×#546C2semidirect
5. C61×#3282C2semidirect
6. C61×#3280C2semidirect
7. C61×#3275C2semidirect
8. C61×#3273C2semidirect
9. C61×#3268C2semidirect
10. C61×#3267C2semidirect
11. C61×#3266C2semidirect
12. C61×#3264C2semidirect
13. C61×#3153C2semidirect
14. C61×#3056C2semidirect
15. C61×#3055C2semidirect
16. C61×#3040C2semidirect
17. C61×#3036C2semidirect
18. C61×#3007C2semidirect
19. C61×#3006C2semidirect
20. C61×#3005C2semidirect
21. C61×#3003C2semidirect
22. C4×AGL(1,ℤ/8)×C61C2semidirect
23. D4×M16×C61C2semidirect
25. C22×#41×C61C22semidirect
26. C22×#41×C61C22semidirect
27. C23×D4×C61C22semidirect
29. C2×#137×C61C22semidirect
30. C2×#137×C61C22semidirect
31. C2×#137×C61C22semidirect
32. C2×#137×C61C22semidirect
36. C2×AGL(1,ℤ/8)×C61C22semidirect
37. C2×AGL(1,ℤ/8)×C61C22semidirect
38. C2×AGL(1,ℤ/8)×C61C22semidirect
39. C2×AGL(1,ℤ/8)×C61C22semidirect
40. C2×AGL(1,ℤ/8)×C61C22semidirect
41. C2×AGL(1,ℤ/8)×C61C22semidirect
42. C2×AGL(1,ℤ/8)×C61C22semidirect
43. C2×#135×C61C22semidirect
44. C2×#135×C61C22semidirect
45. C22×SD16×C61C22semidirect
46. C22×D8×C61C22semidirect
47. C22×M16×C61C22semidirect
48. C22×M16×C61C22semidirect
49. C61×#550C22semidirect
50. D4×Q8×C61C22semidirect
51. C61×#548C22semidirect
52. C61×#548C22semidirect
54. C61×#547C22semidirect
62. C61×#546C22semidirect
63. C61×#546C22semidirect
64. C61×#546C22semidirect
65. C61×#546C22semidirect
66. C61×#546C22semidirect
68. D42×C61C22semidirect
70. C61×#532C22semidirect
71. C2×#124×C61C22semidirect
75. C61×#525C22semidirect
77. C2×C22⋊Q8×C61C22semidirect
79. C2×#121×C61C22semidirect
81. C4×#41×C61C22semidirect
84. C2×C4×D4×C61C22semidirect
86. C61×#497C22semidirect
87. C61×#496C22semidirect
88. C61×#495C22semidirect
89. C61×#495C22semidirect
90. C61×#470C22semidirect
91. C61×#469C22semidirect
92. C61×#468C22semidirect
93. C61×#468C22semidirect
94. C61×#467C22semidirect
95. C61×#466C22semidirect
96. C61×#465C22semidirect
97. C61×#465C22semidirect
98. C61×#464C22semidirect
99. C61×#464C22semidirect
100. C61×#463C22semidirect
101. C61×#463C22semidirect
102. C61×#463C22semidirect
103. C61×#463C22semidirect
104. C61×#461C22semidirect
105. C61×#459C22semidirect
106. C61×#452C22semidirect
107. C61×#452C22semidirect
108. C61×#452C22semidirect
109. C61×#452C22semidirect
110. C61×#451C22semidirect
111. C61×#450C22semidirect
112. C61×#450C22semidirect
113. C61×#450C22semidirect
114. C61×#449C22semidirect
115. C61×#449C22semidirect
116. C61×#449C22semidirect
117. C61×#449C22semidirect
118. C61×#448C22semidirect
119. C61×#447C22semidirect
120. C61×#447C22semidirect
121. C61×#447C22semidirect
122. C61×#442C22semidirect
123. C61×#440C22semidirect
124. C4×SD16×C61C22semidirect
125. C4×D8×C61C22semidirect
126. C61×#436C22semidirect
127. C61×#435C22semidirect
128. C61×#435C22semidirect
129. C8×D4×C61C22semidirect
130. C61×#428C22semidirect
131. C61×#423C22semidirect
132. C61×#419C22semidirect
133. C61×#418C22semidirect
134. C61×#418C22semidirect
135. C61×#417C22semidirect
136. C61×#417C22semidirect
137. C61×#417C22semidirect
138. C61×#407C22semidirect
139. C61×#407C22semidirect
140. C4×M16×C61C22semidirect
161. C2×#41×C61C23semidirect
162. C2×#41×C61C23semidirect
165. C22×Q8×C61C23semidirect
182. C22×D4×C61C23semidirect
201. AGL(1,ℤ/8)×C61D4semidirect
204. C2×Q16×C61C23semidirect
205. C2×Q16×C61C23semidirect
206. C2×Q16×C61C23semidirect
214. C2×SD16×C61C23semidirect
215. C2×SD16×C61C23semidirect
216. C2×SD16×C61C23semidirect
231. C2×M16×C61C23semidirect
233. C22×C8×C61C23semidirect
235. C4⋊Q8×C61C23semidirect
237. #127×C61C23semidirect
244. #124×C61C23semidirect
245. #124×C61C23semidirect
266. C22⋊Q8×C61C23semidirect
267. C22⋊Q8×C61C23semidirect
288. #121×C61C23semidirect
289. #121×C61C23semidirect
300. C4×Q8×C61C23semidirect
301. C4×Q8×C61C23semidirect
326. C4×D4×C61C23semidirect
327. C4×D4×C61C23semidirect
349. #107×C61C23semidirect
350. #106×C61C23semidirect
351. C4⋊C8×C61C23semidirect
352. C4⋊C8×C61C23semidirect
353. #103×C61C23semidirect
354. #103×C61C23semidirect
355. #103×C61C23semidirect
356. #103×C61C23semidirect
357. #103×C61C23semidirect
362. #102×C61C23semidirect
363. #102×C61C23semidirect
364. #102×C61C23semidirect
367. C22⋊C8×C61C23semidirect
368. C22⋊C8×C61C23semidirect
369. #97×C61C23semidirect
370. C4×C8×C61C23semidirect
466. C2×D4×C61C2×D4semidirect
521. SD16×C61C2×D4semidirect
527. D8×C61C2×D4semidirect
533. M16×C61C2×D4semidirect
737. #61066C61direct (N × H)
775. C22×C61#575semidirect
795. C2×#575C2×C61semidirect
796. C22×AGL(1,ℤ/8)C2×C61semidirect
797. D4×#41C2×C61semidirect
798. C2×#546C2×C61semidirect
799. #3282C2×C61semidirect
800. #3280C2×C61semidirect
801. #3275C2×C61semidirect
802. #3273C2×C61semidirect
803. #3268C2×C61semidirect
804. #3267C2×C61semidirect
805. #3266C2×C61semidirect
806. #3264C2×C61semidirect
807. #3153C2×C61semidirect
808. #3056C2×C61semidirect
809. #3055C2×C61semidirect
810. #3040C2×C61semidirect
811. #3036C2×C61semidirect
812. #3007C2×C61semidirect
813. #3006C2×C61semidirect
814. #3005C2×C61semidirect
815. #3003C2×C61semidirect
816. C4×AGL(1,ℤ/8)C2×C61semidirect
817. D4×M16C2×C61semidirect
832. C22×#41C22×C61semidirect
833. C22×#41C22×C61semidirect
834. C23×D4C22×C61semidirect
836. C2×#137C22×C61semidirect
837. C2×#137C22×C61semidirect
838. C2×#137C22×C61semidirect
839. C2×#137C22×C61semidirect
843. C2×AGL(1,ℤ/8)C22×C61semidirect
844. C2×AGL(1,ℤ/8)C22×C61semidirect
845. C2×AGL(1,ℤ/8)C22×C61semidirect
846. C2×AGL(1,ℤ/8)C22×C61semidirect
847. C2×AGL(1,ℤ/8)C22×C61semidirect
848. C2×AGL(1,ℤ/8)C22×C61semidirect
849. C2×AGL(1,ℤ/8)C22×C61semidirect
850. C2×#135C22×C61semidirect
851. C2×#135C22×C61semidirect
852. C22×SD16C22×C61semidirect
853. C22×D8C22×C61semidirect
854. C22×M16C22×C61semidirect
855. C22×M16C22×C61semidirect
856. #550C22×C61semidirect
857. D4×Q8C22×C61semidirect
858. #548C22×C61semidirect
859. #548C22×C61semidirect
861. #547C22×C61semidirect
869. #546C22×C61semidirect
870. #546C22×C61semidirect
871. #546C22×C61semidirect
872. #546C22×C61semidirect
873. #546C22×C61semidirect
875. D42C22×C61semidirect
877. #532C22×C61semidirect
878. C2×#124C22×C61semidirect
882. #525C22×C61semidirect
884. C2×C22⋊Q8C22×C61semidirect
886. C2×#121C22×C61semidirect
888. C4×#41C22×C61semidirect
891. C2×C4×D4C22×C61semidirect
893. #497C22×C61semidirect
894. #496C22×C61semidirect
895. #495C22×C61semidirect
896. #495C22×C61semidirect
897. #470C22×C61semidirect
898. #469C22×C61semidirect
899. #468C22×C61semidirect
900. #468C22×C61semidirect
901. #467C22×C61semidirect
902. #466C22×C61semidirect
903. #465C22×C61semidirect
904. #465C22×C61semidirect
905. #464C22×C61semidirect
906. #464C22×C61semidirect
907. #463C22×C61semidirect
908. #463C22×C61semidirect
909. #463C22×C61semidirect
910. #463C22×C61semidirect
911. #461C22×C61semidirect
912. #459C22×C61semidirect
913. #452C22×C61semidirect
914. #452C22×C61semidirect
915. #452C22×C61semidirect
916. #452C22×C61semidirect
917. #451C22×C61semidirect
918. #450C22×C61semidirect
919. #450C22×C61semidirect
920. #450C22×C61semidirect
921. #449C22×C61semidirect
922. #449C22×C61semidirect
923. #449C22×C61semidirect
924. #449C22×C61semidirect
925. #448C22×C61semidirect
926. #447C22×C61semidirect
927. #447C22×C61semidirect
928. #447C22×C61semidirect
929. #442C22×C61semidirect
930. #440C22×C61semidirect
931. C4×SD16C22×C61semidirect
932. C4×D8C22×C61semidirect
933. #436C22×C61semidirect
934. #435C22×C61semidirect
935. #435C22×C61semidirect
936. C8×D4C22×C61semidirect
937. #428C22×C61semidirect
938. #423C22×C61semidirect
939. #419C22×C61semidirect
940. #418C22×C61semidirect
941. #418C22×C61semidirect
942. #417C22×C61semidirect
943. #417C22×C61semidirect
944. #417C22×C61semidirect
945. #407C22×C61semidirect
946. #407C22×C61semidirect
947. C4×M16C22×C61semidirect
948. C61#61066direct (N × H)
969. C2×#41C23×C61semidirect
970. C2×#41C23×C61semidirect
973. C22×Q8C23×C61semidirect
990. C22×D4C23×C61semidirect
1009. AGL(1,ℤ/8)D4×C61semidirect
1012. C2×Q16C23×C61semidirect
1013. C2×Q16C23×C61semidirect
1014. C2×Q16C23×C61semidirect
1022. C2×SD16C23×C61semidirect
1023. C2×SD16C23×C61semidirect
1024. C2×SD16C23×C61semidirect
1039. C2×M16C23×C61semidirect
1041. C22×C8C23×C61semidirect
1043. C4⋊Q8C23×C61semidirect
1045. #127C23×C61semidirect
1052. #124C23×C61semidirect
1053. #124C23×C61semidirect
1074. C22⋊Q8C23×C61semidirect
1075. C22⋊Q8C23×C61semidirect
1096. #121C23×C61semidirect
1097. #121C23×C61semidirect
1108. C4×Q8C23×C61semidirect
1109. C4×Q8C23×C61semidirect
1134. C4×D4C23×C61semidirect
1135. C4×D4C23×C61semidirect
1157. #107C23×C61semidirect
1158. #106C23×C61semidirect
1159. C4⋊C8C23×C61semidirect
1160. C4⋊C8C23×C61semidirect
1161. #103C23×C61semidirect
1162. #103C23×C61semidirect
1163. #103C23×C61semidirect
1164. #103C23×C61semidirect
1165. #103C23×C61semidirect
1170. #102C23×C61semidirect
1171. #102C23×C61semidirect
1172. #102C23×C61semidirect
1175. C22⋊C8C23×C61semidirect
1176. C22⋊C8C23×C61semidirect
1177. #97C23×C61semidirect
1178. C4×C8C23×C61semidirect
1274. C2×D4C2×D4×C61semidirect
1329. SD16C2×D4×C61semidirect
1335. D8C2×D4×C61semidirect
1341. M16C2×D4×C61semidirect
1582. C22C61×#575semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C61×#5752
C22×AGL(1,ℤ/8)×C612
D4×#41×C612
C2×C61×#5462
C61×#32822
C61×#32802
C61×#32752
C61×#32732
C61×#32682
C61×#32672
C61×#32662
C61×#32642
C61×#31532
C61×#30562
C61×#30552
C61×#30402
C61×#30362
C61×#30072
C61×#30062
C61×#30052
C61×#30032
C4×AGL(1,ℤ/8)×C612
D4×M16×C612
#6106661