Finite Group Databasebeta

← C61×#23863 #29527296

Subgroups — C61×#23863 #29527296

Order 15616.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
2C2×C61×#546C211yesmaximal, characteristic, complemented
3C2×C61×#452C211yesmaximal, characteristic, complemented
4C2×C61×#452C211yesmaximal, characteristic, complemented
5C2×C61×#449C211yesmaximal, characteristic, complemented
6C61×#2407C211yesmaximal, characteristic, complemented
7C61×#2015C211yesmaximal, characteristic, complemented
8C61×#2012C211yesmaximal, characteristic, complemented
9C61×#2000C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1894C211yesmaximal, characteristic, complemented
12C61×#1879C211yesmaximal, characteristic, complemented
13C61×#1877C211yesmaximal, characteristic, complemented
14C61×#1870C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C61—24no—
20C2×AGL(1,ℤ/8)×C61—24no—
21C2×AGL(1,ℤ/8)×C61—24no—
22C22×Q16×C61C2211yescharacteristic, complemented
23C22×SD16×C61C2211yescharacteristic
24C22×SD16×C61C2211yescharacteristic
25C22×SD16×C61C2211yescharacteristic, complemented
26C22×D8×C61C2211yescharacteristic
27C22×D8×C61C2211yescharacteristic
28C22×M16×C61C2211yescharacteristic
29C61×#546—24no—
30C61×#546—24no—
31C2×#124×C61C2211yescharacteristic
32C2×#123×C61—21no—
33C2×C22⋊Q8×C61C2211yescharacteristic
34C2×C22⋊Q8×C61C2211yescharacteristic, complemented
35C2×#121×C61—21no—
36C2×#121×C61C2211yescharacteristic
37C2×#121×C61C2211yescharacteristic, complemented
38C2×#120×C61—21no—
39C2×C4×D4×C61C2211yescharacteristic
40C2×C4×D4×C61C2211yescharacteristic
41C22×C22⋊C4×C61—21no—
42C61×#452—24no—
43C61×#452—24no—
44C61×#449—24no—
45C2×#103×C61C2211yescharacteristic, complemented
46C2×#103×C61C2211yescharacteristic, complemented
47C2×#103×C61C2211yescharacteristic, complemented
48C2×#102×C61C2211yescharacteristic
49C2×#102×C61C2211yescharacteristic
50C2×#102×C61C2211yescharacteristic
51C2×#102×C61C2211yescharacteristic
52C2×#102×C61C2211yescharacteristic, complemented
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic, complemented
55C2×C22⋊C8×C61C2211yescharacteristic, complemented
56C61×#394—21no—
57C61×#392—21no—
58C61×#391C2211yescharacteristic, complemented
59C61×#390C2211yescharacteristic, complemented
60C61×#386—21no—
61C61×#385—21no—
62C61×#380C2211yescharacteristic
63C61×#340C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C61×#336C2211yescharacteristic, complemented
66C61×#336C2211yescharacteristic, complemented
67C25×C61—21no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—22no—
71C2×#41×C61—22no—
72C2×#41×C61—22no—
73C2×#41×C61—22no—
74C2×#41×C61—22no—
75C2×#41×C61—22no—
76C2×#41×C61—41no—
77C2×#41×C61—41no—
78C2×#41×C61—41no—
79C2×#41×C61—41no—
80C22×Q8×C61C2311yescharacteristic
81C22×Q8×C61C2311yescharacteristic
82C22×D4×C61—22no—
83C22×D4×C61—22no—
84C22×D4×C61—21no—
85C22×D4×C61—21no—
86C22×D4×C61—21no—
87C22×D4×C61—21no—
88C22×D4×C61—22no—
89C22×D4×C61—21no—
90C22×D4×C61—41no—
91C22×D4×C61—41no—
92C22×D4×C61D411yescharacteristic
93C22×D4×C61D414yescomplemented
94C22×D4×C61C2311yescharacteristic
95C22×D4×C61C2311yescharacteristic
96C22×D4×C61C2311yescharacteristic
97C23×C4×C61—21no—
98C23×C4×C61—21no—
99C23×C4×C61—21no—
100C23×C4×C61C2311yescharacteristic
101C23×C4×C61C2311yescharacteristic
102AGL(1,ℤ/8)×C61—232no—
103C2×Q16×C61—22no—
104C2×Q16×C61—22no—
105C2×Q16×C61—41no—
106C2×SD16×C61—22no—
107C2×SD16×C61—22no—
108C2×SD16×C61—22no—
109C2×SD16×C61—22no—
110C2×SD16×C61—22no—
111C2×SD16×C61—22no—
112C2×SD16×C61—22no—
113C2×SD16×C61—41no—
114C2×SD16×C61D414yescomplemented
115C2×D8×C61—22no—
116C2×D8×C61—22no—
117C2×D8×C61—22no—
118C2×D8×C61—22no—
119C2×D8×C61—22no—
120C2×D8×C61D414yescomplemented
121C2×M16×C61—22no—
122C2×M16×C61—22no—
123C2×M16×C61—22no—
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128#124×C61—22no—
129#124×C61—22no—
130#123×C61—28no—
131C22⋊Q8×C61—22no—
132C22⋊Q8×C61—22no—
133C22⋊Q8×C61—41no—
134C22⋊Q8×C61D414yescomplemented
135#121×C61—28no—
136#121×C61—22no—
137#121×C61—22no—
138#121×C61—22no—
139#121×C61—41no—
140#120×C61—28no—
141C4×D4×C61—22no—
142C4×D4×C61—22no—
143C4×D4×C61—22no—
144C4×D4×C61—22no—
145C2×C4⋊C4×C61—21no—
146C2×C4⋊C4×C61—21no—
147C2×C4⋊C4×C61D411yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C22⋊C4×C61—28no—
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61D411yescharacteristic
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C42×C61C2311yescharacteristic
165#103×C61—22no—
166#103×C61—22no—
167#103×C61—22no—
168#102×C61—22no—
169#102×C61—22no—
170#102×C61—22no—
171#102×C61—41no—
172#102×C61—41no—
173C22⋊C8×C61—22no—
174C22⋊C8×C61—22no—
175C22⋊C8×C61—22no—
176#95×C61—21no—
177#95×C61—21no—
178#95×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—24no—
183C24×C61—42no—
184C24×C61—42no—
185C24×C61—42no—
186C24×C61—42no—
187C24×C61—81no—
188C24×C61—81no—
189C24×C61C2×D411yescharacteristic
190C24×C61C2×D411yescharacteristic
191#41×C61—28no—
192#41×C61—44no—
193#41×C61—44no—
194#41×C61—44no—
195#41×C61—44no—
196#41×C61—44no—
197#41×C61—44no—
198#41×C61—44no—
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61—21no—
202C2×Q8×C61—21no—
203C2×Q8×C61—21no—
204C2×Q8×C61—21no—
205C2×Q8×C61—21no—
206C2×Q8×C61—21no—
207C2×Q8×C61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61C2×D412yes—
210C2×Q8×C61C2×D412yes—
211C2×D4×C61—28no—
212C2×D4×C61—24no—
213C2×D4×C61—22no—
214C2×D4×C61—24no—
215C2×D4×C61—24no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—44no—
230C2×D4×C61—44no—
231C2×D4×C61—44no—
232C2×D4×C61—41no—
233C2×D4×C61—41no—
234C2×D4×C61—42no—
235C2×D4×C61—42no—
236C2×D4×C61—42no—
237C2×D4×C61—42no—
238C2×D4×C61—42no—
239C2×D4×C61—42no—
240C2×D4×C61—42no—
241C2×D4×C61—42no—
242C2×D4×C61—42no—
243C2×D4×C61—81no—
244C2×D4×C61—81no—
245C2×D4×C61—81no—
246C2×D4×C61C2×D412yes—
247C2×D4×C61C2×D412yes—
248C2×D4×C61C2×D412yes—
249C2×D4×C61C2×D412yes—
250C2×D4×C61C2×D412yes—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—24no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—24no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—42no—
269C22×C4×C61—42no—
270C22×C4×C61—42no—
271C22×C4×C61—42no—
272C22×C4×C61—42no—
273C22×C4×C61—81no—
274C22×C4×C61—81no—
275C22×C4×C61C2×D411yescharacteristic
276C22×C4×C61C2×D411yescharacteristic
277C22×C4×C61C2×D411yescharacteristic
278C22×C4×C61C2×D411yescharacteristic
279C22×C4×C61C2×D412yes—
280C22×C4×C61C2×D412yes—
281C22×C4×C61C2411yescharacteristic
282Q16×C61—44no—
283SD16×C61—28no—
284SD16×C61—28no—
285SD16×C61—44no—
286D8×C61—28no—
287D8×C61—28no—
288M16×C61—28no—
289C2×C8×C61—21no—
290C2×C8×C61—21no—
291C2×C8×C61—21no—
292C2×C8×C61—21no—
293C2×C8×C61—21no—
294C2×C8×C61—21no—
295C2×C8×C61—21no—
296C2×C8×C61—21no—
297C2×C8×C61—21no—
298C2×C8×C61—21no—
299C2×C8×C61C2×D412yes—
300C2×C8×C61C2×D412yes—
301C4⋊C4×C61—24no—
302C4⋊C4×C61—22no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61—21no—
306C4⋊C4×C61—21no—
307C4⋊C4×C61—21no—
308C4⋊C4×C61—42no—
309C4⋊C4×C61C2×D412yes—
310C22⋊C4×C61—24no—
311C22⋊C4×C61—24no—
312C22⋊C4×C61—24no—
313C22⋊C4×C61—24no—
314C22⋊C4×C61—22no—
315C22⋊C4×C61—24no—
316C22⋊C4×C61—22no—
317C22⋊C4×C61—42no—
318C22⋊C4×C61—42no—
319C22⋊C4×C61—42no—
320C22⋊C4×C61—81no—
321C22⋊C4×C61—81no—
322C42×C61—21no—
323C42×C61—21no—
324C23×C61—22no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—21no—
330C23×C61—21no—
331C23×C61—21no—
332C23×C61—21no—
333C23×C61—22no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—22no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—48no—
343C23×C61—48no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—84no—
361C23×C61—84no—
362C23×C61—84no—
363C23×C61—84no—
364C23×C61—84no—
365C23×C61#12012yes—
366C23×C61C22×D411yescharacteristic
367Q8×C61—22no—
368Q8×C61—22no—
369Q8×C61—22no—
370Q8×C61—22no—
371Q8×C61—41no—
372Q8×C61—41no—
373Q8×C61—41no—
374Q8×C61—41no—
375D4×C61—22no—
376D4×C61—22no—
377D4×C61—22no—
378D4×C61—22no—
379D4×C61—22no—
380D4×C61—22no—
381D4×C61—22no—
382D4×C61—48no—
383D4×C61—44no—
384D4×C61—48no—
385D4×C61—48no—
386D4×C61—41no—
387D4×C61—41no—
388D4×C61—41no—
389D4×C61—41no—
390D4×C61—84no—
391D4×C61—84no—
392D4×C61#12014yes—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—22no—
402C2×C4×C61—21no—
403C2×C4×C61—22no—
404C2×C4×C61—21no—
405C2×C4×C61—22no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—48no—
412C2×C4×C61—48no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—84no—
430C2×C4×C61#12012yes—
431C2×C4×C61C22×D411yescharacteristic
432C2×C4×C61C22×D411yescharacteristic
433C2×C4×C61C22×D411yescharacteristic
434C2×C4×C61C22×D411yescharacteristic
435C2×C4×C61H(5,𝔽2)11yescharacteristic
436C2×C4×C61H(5,𝔽2)11yescharacteristic
437C8×C61—22no—
438C8×C61—22no—
439C8×C61—41no—
440C8×C61—41no—
441#23863C6111yesmaximal, characteristic, direct product factor, Sylow
442C22×C61—22no—
443C22×C61—24no—
444C22×C61—22no—
445C22×C61—22no—
446C22×C61—42no—
447C22×C61—41no—
448C22×C61—42no—
449C22×C61—42no—
450C22×C61—41no—
451C22×C61—42no—
452C22×C61—41no—
453C22×C61—42no—
454C22×C61—41no—
455C22×C61—42no—
456C22×C61—42no—
457C22×C61—41no—
458C22×C61—42no—
459C22×C61—41no—
460C22×C61—42no—
461C22×C61—41no—
462C22×C61—42no—
463C22×C61—41no—
464C22×C61—42no—
465C22×C61—41no—
466C22×C61—41no—
467C22×C61—42no—
468C22×C61—41no—
469C22×C61—816no—
470C22×C61—81no—
471C22×C61—81no—
472C22×C61—81no—
473C22×C61—81no—
474C22×C61—81no—
475C22×C61—81no—
476C22×C61—81no—
477C22×C61—81no—
478C22×C61C2×#12011yescharacteristic
479C22×C61D4211yescharacteristic
480C22×C61D4211yescharacteristic
481C22×C61#57511yescharacteristic
482C22×C61#57511yescharacteristic
483C22×C61#57611yescharacteristic
484C22×C61#57711yescharacteristic
485C4×C61—22no—
486C4×C61—41no—
487C4×C61—42no—
488C4×C61—42no—
489C4×C61—41no—
490C4×C61—41no—
491C4×C61—42no—
492C4×C61—81no—
493C4×C61—81no—
494C4×C61C2×#12011yescharacteristic
495C4×C61#53411yescharacteristic
496C4×C61D4211yescharacteristic
497C4×C61D4211yescharacteristic
498C22×AGL(1,ℤ/8)C2×C6111yescharacteristic, complemented
499C2×#546C2×C6111yescharacteristic, complemented
500C2×#452C2×C6111yescharacteristic, complemented
501C2×#452C2×C6111yescharacteristic, complemented
502C2×#449C2×C6111yescharacteristic, complemented
503#2407C2×C6111yescharacteristic, complemented
504#2015C2×C6111yescharacteristic, complemented
505#2012C2×C6111yescharacteristic, complemented
506#2000C2×C6111yescharacteristic, complemented
507#1999C2×C6111yescharacteristic, complemented
508#1894C2×C6111yescharacteristic, complemented
509#1879C2×C6111yescharacteristic, complemented
510#1877C2×C6111yescharacteristic, complemented
511#1870C2×C6111yescharacteristic, complemented
512#1786C2×C6111yescharacteristic, complemented
513C2×C61—42no—
514C2×C61—44no—
515C2×C61—81no—
516C2×C61—82no—
517C2×C61—82no—
518C2×C61#240311yescharacteristic
519C2×C61#300511yescharacteristic
520C2×C61#301211yescharacteristic
521C2×C61#326711yescharacteristic
522C2×C61#326811yescharacteristic
523C2×C61#327311yescharacteristic
524C2×C61#327511yescharacteristic
525C22×#41C22×C6111yescharacteristic
526C22×#41C22×C6111yescharacteristic
527C23×D4C22×C6111yescharacteristic
528C2×AGL(1,ℤ/8)—24no—
529C2×AGL(1,ℤ/8)—24no—
530C2×AGL(1,ℤ/8)—24no—
531C22×Q16C22×C6111yescharacteristic, complemented
532C22×SD16C22×C6111yescharacteristic
533C22×SD16C22×C6111yescharacteristic
534C22×SD16C22×C6111yescharacteristic, complemented
535C22×D8C22×C6111yescharacteristic
536C22×D8C22×C6111yescharacteristic
537C22×M16C22×C6111yescharacteristic
538#546—24no—
539#546—24no—
540C2×#124C22×C6111yescharacteristic
541C2×#123—21no—
542C2×C22⋊Q8C22×C6111yescharacteristic
543C2×C22⋊Q8C22×C6111yescharacteristic, complemented
544C2×#121—21no—
545C2×#121C22×C6111yescharacteristic
546C2×#121C22×C6111yescharacteristic, complemented
547C2×#120—21no—
548C2×C4×D4C22×C6111yescharacteristic
549C2×C4×D4C22×C6111yescharacteristic
550C22×C22⋊C4—21no—
551#452—24no—
552#452—24no—
553#449—24no—
554C2×#103C22×C6111yescharacteristic, complemented
555C2×#103C22×C6111yescharacteristic, complemented
556C2×#103C22×C6111yescharacteristic, complemented
557C2×#102C22×C6111yescharacteristic
558C2×#102C22×C6111yescharacteristic
559C2×#102C22×C6111yescharacteristic
560C2×#102C22×C6111yescharacteristic
561C2×#102C22×C6111yescharacteristic, complemented
562C2×C22⋊C8C22×C6111yescharacteristic
563C2×C22⋊C8C22×C6111yescharacteristic, complemented
564C2×C22⋊C8C22×C6111yescharacteristic, complemented
565#394—21no—
566#392—21no—
567#391C22×C6111yescharacteristic, complemented
568#390C22×C6111yescharacteristic, complemented
569#386—21no—
570#385—21no—
571#380C22×C6111yescharacteristic
572#340C22×C6111yescharacteristic, complemented
573#340C22×C6111yescharacteristic, complemented
574#336C22×C6111yescharacteristic, complemented
575#336C22×C6111yescharacteristic, complemented
576C61#2386311yescharacteristic, direct product factor, Sylow
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—22no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41—41no—
590C22×Q8C23×C6111yescharacteristic
591C22×Q8C23×C6111yescharacteristic
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—41no—
601C22×D4—41no—
602C22×D4D4×C6111yescharacteristic
603C22×D4D4×C6114yescomplemented
604C22×D4C23×C6111yescharacteristic
605C22×D4C23×C6111yescharacteristic
606C22×D4C23×C6111yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C6111yescharacteristic
611C23×C4C23×C6111yescharacteristic
612AGL(1,ℤ/8)—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—41no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C6114yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—22no—
630C2×D8D4×C6114yescomplemented
631C2×M16—22no—
632C2×M16—22no—
633C2×M16—22no—
634C22×C8C23×C6111yescharacteristic
635C22×C8C23×C6111yescharacteristic
636C22×C8C23×C6111yescharacteristic
637C22×C8C23×C6111yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—41no—
644C22⋊Q8D4×C6114yescomplemented
645#121—28no—
646#121—22no—
647#121—22no—
648#121—22no—
649#121—41no—
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C6111yescharacteristic
658C2×C4⋊C4C23×C6111yescharacteristic
659C2×C4⋊C4C23×C6111yescharacteristic
660C2×C4⋊C4C23×C6111yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C6111yescharacteristic
673C2×C22⋊C4D4×C6111yescharacteristic
674C2×C42C23×C6111yescharacteristic
675#103—22no—
676#103—22no—
677#103—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—41no—
682#102—41no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—24no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C6111yescharacteristic
700C24C2×D4×C6111yescharacteristic
701#41—28no—
702#41—44no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C6112yes—
720C2×Q8C2×D4×C6112yes—
721C2×D4—28no—
722C2×D4—24no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C6112yes—
757C2×D4C2×D4×C6112yes—
758C2×D4C2×D4×C6112yes—
759C2×D4C2×D4×C6112yes—
760C2×D4C2×D4×C6112yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—24no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C6111yescharacteristic
786C22×C4C2×D4×C6111yescharacteristic
787C22×C4C2×D4×C6111yescharacteristic
788C22×C4C2×D4×C6111yescharacteristic
789C22×C4C2×D4×C6112yes—
790C22×C4C2×D4×C6112yes—
791C22×C4C24×C6111yescharacteristic
792Q16—44no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—28no—
798M16—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C6112yes—
810C2×C8C2×D4×C6112yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C6112yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—24no—
826C22⋊C4—22no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—22no—
843C23—21no—
844C23—22no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—22no—
851C23—21no—
852C23—48no—
853C23—48no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23#120×C6112yes—
876C23C22×D4×C6111yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—48no—
893D4—44no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C6114yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C6112yes—
941C2×C4C22×D4×C6111yescharacteristic
942C2×C4C22×D4×C6111yescharacteristic
943C2×C4C22×D4×C6111yescharacteristic
944C2×C4C22×D4×C6111yescharacteristic
945C2×C4H(5,𝔽2)×C6111yescharacteristic
946C2×C4H(5,𝔽2)×C6111yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—42no—
965C22—42no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—41no—
973C22—42no—
974C22—41no—
975C22—41no—
976C22—42no—
977C22—41no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C6111yescharacteristic
988C22D42×C6111yescharacteristic
989C22D42×C6111yescharacteristic
990C22C61×#57511yescharacteristic
991C22C61×#57511yescharacteristic
992C22C61×#57611yescharacteristic
993C22C61×#57711yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C6111yescharacteristic
1004C4C61×#53411yescharacteristic
1005C4D42×C6111yescharacteristic
1006C4D42×C6111yescharacteristic
1007C2—42no—
1008C2—44no—
1009C2—81no—
1010C2—82no—
1011C2—82no—
1012C2C61×#240311yescharacteristic
1013C2C61×#300511yescharacteristic
1014C2C61×#301211yescharacteristic
1015C2C61×#326711yescharacteristic
1016C2C61×#326811yescharacteristic
1017C2C61×#327311yescharacteristic
1018C2C61×#327511yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C61C2semidirect
2. C2×C61×#546C2semidirect
3. C2×C61×#452C2semidirect
4. C2×C61×#452C2semidirect
5. C2×C61×#449C2semidirect
6. C61×#2407C2semidirect
7. C61×#2015C2semidirect
8. C61×#2012C2semidirect
9. C61×#2000C2semidirect
10. C61×#1999C2semidirect
11. C61×#1894C2semidirect
12. C61×#1879C2semidirect
13. C61×#1877C2semidirect
14. C61×#1870C2semidirect
15. C61×#1786C2semidirect
22. C22×Q16×C61C22semidirect
25. C22×SD16×C61C22semidirect
34. C2×C22⋊Q8×C61C22semidirect
37. C2×#121×C61C22semidirect
45. C2×#103×C61C22semidirect
46. C2×#103×C61C22semidirect
47. C2×#103×C61C22semidirect
52. C2×#102×C61C22semidirect
54. C2×C22⋊C8×C61C22semidirect
55. C2×C22⋊C8×C61C22semidirect
58. C61×#391C22semidirect
59. C61×#390C22semidirect
63. C61×#340C22semidirect
64. C61×#340C22semidirect
65. C61×#336C22semidirect
66. C61×#336C22semidirect
93. C22×D4×C61D4semidirect
114. C2×SD16×C61D4semidirect
120. C2×D8×C61D4semidirect
134. C22⋊Q8×C61D4semidirect
441. #23863C61direct (N × H)
498. C22×AGL(1,ℤ/8)C2×C61semidirect
499. C2×#546C2×C61semidirect
500. C2×#452C2×C61semidirect
501. C2×#452C2×C61semidirect
502. C2×#449C2×C61semidirect
503. #2407C2×C61semidirect
504. #2015C2×C61semidirect
505. #2012C2×C61semidirect
506. #2000C2×C61semidirect
507. #1999C2×C61semidirect
508. #1894C2×C61semidirect
509. #1879C2×C61semidirect
510. #1877C2×C61semidirect
511. #1870C2×C61semidirect
512. #1786C2×C61semidirect
531. C22×Q16C22×C61semidirect
534. C22×SD16C22×C61semidirect
543. C2×C22⋊Q8C22×C61semidirect
546. C2×#121C22×C61semidirect
554. C2×#103C22×C61semidirect
555. C2×#103C22×C61semidirect
556. C2×#103C22×C61semidirect
561. C2×#102C22×C61semidirect
563. C2×C22⋊C8C22×C61semidirect
564. C2×C22⋊C8C22×C61semidirect
567. #391C22×C61semidirect
568. #390C22×C61semidirect
572. #340C22×C61semidirect
573. #340C22×C61semidirect
574. #336C22×C61semidirect
575. #336C22×C61semidirect
576. C61#23863direct (N × H)
603. C22×D4D4×C61semidirect
624. C2×SD16D4×C61semidirect
630. C2×D8D4×C61semidirect
644. C22⋊Q8D4×C61semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C612
C2×C61×#5462
C2×C61×#4522
C2×C61×#4492
C61×#24072
C61×#20152
C61×#20122
C61×#20002
C61×#19992
C61×#18942
C61×#18792
C61×#18772
C61×#18702
C61×#17862
#2386361