Finite Group Databasebeta

← C61×#22419 #29525852

Subgroups — C61×#22419 #29525852

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#546C211yesmaximal, characteristic
2C2×C61×#435C211yesmaximal, characteristic, complemented
3C2×C61×#417C211yesmaximal, characteristic, complemented
4C22×#102×C61C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
6C61×#1983C211yesmaximal, characteristic, complemented
7C61×#1959C211yesmaximal, characteristic, complemented
8C61×#1895C211yesmaximal, characteristic, complemented
9C61×#1892C211yesmaximal, characteristic, complemented
10C61×#1874C211yesmaximal, characteristic, complemented
11C61×#1872C211yesmaximal, characteristic, complemented
12C61×#1802C211yesmaximal, characteristic, complemented
13C61×#1788C211yesmaximal, characteristic, complemented
14C61×#1786C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic, complemented
19C23×C8×C61C2211yescharacteristic
20C61×#546—24no—
21C61×#546C418yescomplemented
22C2×#124×C61C2211yescharacteristic
23C2×#123×C61—21no—
24C2×C22⋊Q8×C61C2211yescharacteristic
25C2×#121×C61—21no—
26C2×#121×C61C2211yescharacteristic
27C2×#120×C61—21no—
28C2×C4×D4×C61—21no—
29C2×C4×D4×C61C2211yescharacteristic
30C2×C4×D4×C61C2211yescharacteristic
31C22×C4⋊C4×C61C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic, complemented
33C22×C22⋊C4×C61—21no—
34C61×#435—24no—
35C2×C4⋊C8×C61C2211yescharacteristic, complemented
36C61×#417—24no—
37C2×#103×C61C2211yescharacteristic, complemented
38C2×#103×C61C2211yescharacteristic, complemented
39C2×#103×C61C2211yescharacteristic, complemented
40C2×#103×C61C2211yescharacteristic, complemented
41C2×#102×C61—24no—
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#102×C61C2211yescharacteristic
49C2×#102×C61C2211yescharacteristic
50C2×C22⋊C8×C61C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic, complemented
52C2×#97×C61C2211yescharacteristic, complemented
53C61×#389—21no—
54C61×#385—21no—
55C61×#385—21no—
56C61×#384C2211yescharacteristic, complemented
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic, complemented
59C4×C4⋊C4×C61C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C25×C61—21no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—41no—
69C2×#41×C61—41no—
70C2×#41×C61C2×C414yescomplemented
71C22×Q8×C61C2311yescharacteristic
72C22×D4×C61—22no—
73C22×D4×C61—22no—
74C22×D4×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—22no—
77C22×D4×C61—21no—
78C22×D4×C61—41no—
79C22×D4×C61—41no—
80C22×D4×C61C2×C414yescomplemented
81C22×D4×C61D411yescharacteristic
82C22×D4×C61C2311yescharacteristic
83C22×D4×C61C2311yescharacteristic
84C23×C4×C61—21no—
85C23×C4×C61—21no—
86C23×C4×C61—21no—
87C23×C4×C61—21no—
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C2×M16×C61—22no—
91C2×M16×C61—22no—
92C2×M16×C61—41no—
93C22×C8×C61—22no—
94C22×C8×C61—22no—
95C22×C8×C61—41no—
96C22×C8×C61C2311yescharacteristic
97C22×C8×C61C2311yescharacteristic
98C22×C8×C61C2311yescharacteristic
99C22×C8×C61C2311yescharacteristic
100#124×C61—22no—
101#124×C61C2×C414yescomplemented
102#123×C61—28no—
103C22⋊Q8×C61—22no—
104C22⋊Q8×C61C2×C414yescomplemented
105#121×C61—22no—
106#121×C61—28no—
107#121×C61C2×C414yescomplemented
108#120×C61—28no—
109C4×D4×C61—22no—
110C4×D4×C61—44no—
111C4×D4×C61C2×C414yes—
112C4×D4×C61C2×C414yescomplemented
113C4×D4×C61D414yes—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—22no—
116C2×C4⋊C4×C61—22no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—41no—
122C2×C4⋊C4×C61—41no—
123C2×C4⋊C4×C61D411yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—28no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C42×C61—21no—
140C2×C42×C61C2311yescharacteristic
141C4⋊C8×C61—22no—
142#103×C61—22no—
143#103×C61—22no—
144#103×C61—41no—
145#103×C61—41no—
146#102×C61—22no—
147#102×C61—22no—
148#102×C61—22no—
149#102×C61—22no—
150#102×C61—22no—
151#102×C61—41no—
152#102×C61—41no—
153#102×C61D414yescomplemented
154C22⋊C8×C61—22no—
155C22⋊C8×C61—22no—
156#97×C61—22no—
157#95×C61—21no—
158#95×C61—21no—
159#95×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—24no—
163C24×C61—42no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—42no—
167C24×C61—81no—
168C24×C61—81no—
169C24×C61C2×D411yescharacteristic
170C24×C61C2×D411yescharacteristic
171#41×C61—28no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61C22×C412yes—
181C2×D4×C61—22no—
182C2×D4×C61—22no—
183C2×D4×C61—28no—
184C2×D4×C61—24no—
185C2×D4×C61—24no—
186C2×D4×C61—24no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—44no—
196C2×D4×C61—44no—
197C2×D4×C61—44no—
198C2×D4×C61—42no—
199C2×D4×C61—42no—
200C2×D4×C61—42no—
201C2×D4×C61—42no—
202C2×D4×C61—81no—
203C2×D4×C61—81no—
204C2×D4×C61C22⋊C414yes—
205C2×D4×C61C22×C412yes—
206C2×D4×C61C22×C412yes—
207C2×D4×C61C2×D412yes—
208C2×D4×C61#4112yes—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—24no—
221C22×C4×C61—24no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—42no—
226C22×C4×C61—42no—
227C22×C4×C61—42no—
228C22×C4×C61—42no—
229C22×C4×C61—42no—
230C22×C4×C61—42no—
231C22×C4×C61—81no—
232C22×C4×C61—81no—
233C22×C4×C61—81no—
234C22×C4×C61—81no—
235C22×C4×C61C22×C412yes—
236C22×C4×C61C22×C412yes—
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2×D412yes—
242C22×C4×C61C2×D412yes—
243C22×C4×C61C2411yescharacteristic
244M16×C61—44no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—44no—
257C2×C8×C61C2×D412yes—
258C4⋊C4×C61—24no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—42no—
268C4⋊C4×C61—42no—
269C4⋊C4×C61—42no—
270C4⋊C4×C61—81no—
271C4⋊C4×C61C22⋊C414yes—
272C4⋊C4×C61C22×C412yes—
273C4⋊C4×C61C2×D412yes—
274C22⋊C4×C61—24no—
275C22⋊C4×C61—24no—
276C22⋊C4×C61—24no—
277C22⋊C4×C61—24no—
278C22⋊C4×C61—24no—
279C22⋊C4×C61—42no—
280C22⋊C4×C61—42no—
281C22⋊C4×C61C22⋊C414yes—
282C22⋊C4×C61C22⋊C414yes—
283C42×C61—42no—
284C42×C61C22×C412yes—
285C42×C61C2×D412yes—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—22no—
291C23×C61—21no—
292C23×C61—22no—
293C23×C61—21no—
294C23×C61—22no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—22no—
300C23×C61—48no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—48no—
312C23×C61—84no—
313C23×C61—84no—
314C23×C61—84no—
315C23×C61—84no—
316C23×C61—84no—
317C23×C61C2×C22⋊C412yes—
318C23×C61C2×C22⋊C412yes—
319C23×C61AGL(1,ℤ/8)12yes—
320C23×C61#13712yes—
321C23×C61C22×D411yescharacteristic
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—41no—
325Q8×C61—41no—
326D4×C61—28no—
327D4×C61—22no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—22no—
331D4×C61—22no—
332D4×C61—48no—
333D4×C61—48no—
334D4×C61—41no—
335D4×C61—41no—
336D4×C61—84no—
337D4×C61C4×D414yescomplemented
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—48no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—84no—
374C2×C4×C61—84no—
375C2×C4×C61—84no—
376C2×C4×C61C2×C22⋊C412yes—
377C2×C4×C61C2×C22⋊C412yes—
378C2×C4×C61C2×C22⋊C412yes—
379C2×C4×C61C2×C22⋊C412yes—
380C2×C4×C61C23×C411yescharacteristic
381C2×C4×C61C22×D411yescharacteristic
382C2×C4×C61C22×D411yescharacteristic
383C2×C4×C61C2×#4111yescharacteristic
384C2×C4×C61H(5,𝔽2)11yescharacteristic
385C2×C4×C61H(5,𝔽2)11yescharacteristic
386C8×C61—22no—
387C8×C61—41no—
388C8×C61—41no—
389C8×C61—41no—
390#22419C6111yesmaximal, characteristic, direct product factor, Sylow
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—24no—
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—41no—
404C22×C61—42no—
405C22×C61—41no—
406C22×C61—42no—
407C22×C61—41no—
408C22×C61—42no—
409C22×C61—41no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—816no—
415C22×C61—81no—
416C22×C61—81no—
417C22×C61—81no—
418C22×C61—81no—
419C22×C61#41714yescomplemented
420C22×C61C22×C22⋊C411yescharacteristic
421C22×C61D4211yescharacteristic
422C22×C61#54611yescharacteristic
423C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C61C2×#13711yescharacteristic
425C22×C61#57611yescharacteristic
426C22×C61#57711yescharacteristic
427C4×C61—22no—
428C4×C61—22no—
429C4×C61—22no—
430C4×C61—22no—
431C4×C61—42no—
432C4×C61—42no—
433C4×C61—42no—
434C4×C61—81no—
435C4×C61—81no—
436C4×C61—81no—
437C4×C61C2×C4×D411yescharacteristic
438C4×C61#51811yescharacteristic
439C4×C61D4211yescharacteristic
440C4×C61#54611yescharacteristic
441C2×#546C2×C6111yescharacteristic
442C2×#435C2×C6111yescharacteristic, complemented
443C2×#417C2×C6111yescharacteristic, complemented
444C22×#102C2×C6111yescharacteristic, complemented
445D4×C4⋊C4C2×C6111yescharacteristic, complemented
446#1983C2×C6111yescharacteristic, complemented
447#1959C2×C6111yescharacteristic, complemented
448#1895C2×C6111yescharacteristic, complemented
449#1892C2×C6111yescharacteristic, complemented
450#1874C2×C6111yescharacteristic, complemented
451#1872C2×C6111yescharacteristic, complemented
452#1802C2×C6111yescharacteristic, complemented
453#1788C2×C6111yescharacteristic, complemented
454#1786C2×C6111yescharacteristic, complemented
455#1762C2×C6111yescharacteristic, complemented
456C2×C61—24no—
457C2×C61—42no—
458C2×C61—44no—
459C2×C61—82no—
460C2×C61D4×C22⋊C411yescharacteristic
461C2×C61C2×#41711yescharacteristic
462C2×C61#289711yescharacteristic
463C2×C61#326411yescharacteristic
464C2×C61#326611yescharacteristic
465C2×C61#330611yescharacteristic
466C2×C61#331411yescharacteristic
467C22×#41C22×C6111yescharacteristic
468C23×D4C22×C6111yescharacteristic
469C22×M16C22×C6111yescharacteristic, complemented
470C23×C8C22×C6111yescharacteristic
471#546—24no—
472#546C4×C6118yescomplemented
473C2×#124C22×C6111yescharacteristic
474C2×#123—21no—
475C2×C22⋊Q8C22×C6111yescharacteristic
476C2×#121—21no—
477C2×#121C22×C6111yescharacteristic
478C2×#120—21no—
479C2×C4×D4—21no—
480C2×C4×D4C22×C6111yescharacteristic
481C2×C4×D4C22×C6111yescharacteristic
482C22×C4⋊C4C22×C6111yescharacteristic
483C22×C4⋊C4C22×C6111yescharacteristic, complemented
484C22×C22⋊C4—21no—
485#435—24no—
486C2×C4⋊C8C22×C6111yescharacteristic, complemented
487#417—24no—
488C2×#103C22×C6111yescharacteristic, complemented
489C2×#103C22×C6111yescharacteristic, complemented
490C2×#103C22×C6111yescharacteristic, complemented
491C2×#103C22×C6111yescharacteristic, complemented
492C2×#102—24no—
493C2×#102C22×C6111yescharacteristic
494C2×#102C22×C6111yescharacteristic
495C2×#102C22×C6111yescharacteristic
496C2×#102C22×C6111yescharacteristic
497C2×#102C22×C6111yescharacteristic
498C2×#102C22×C6111yescharacteristic
499C2×#102C22×C6111yescharacteristic
500C2×#102C22×C6111yescharacteristic
501C2×C22⋊C8C22×C6111yescharacteristic
502C2×C22⋊C8C22×C6111yescharacteristic, complemented
503C2×#97C22×C6111yescharacteristic, complemented
504#389—21no—
505#385—21no—
506#385—21no—
507#384C22×C6111yescharacteristic, complemented
508#380C22×C6111yescharacteristic
509#380C22×C6111yescharacteristic, complemented
510C4×C4⋊C4C22×C6111yescharacteristic, complemented
511#340C22×C6111yescharacteristic, complemented
512#340C22×C6111yescharacteristic, complemented
513#340C22×C6111yescharacteristic, complemented
514#340C22×C6111yescharacteristic, complemented
515C61#2241911yescharacteristic, direct product factor, Sylow
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×C4×C6114yescomplemented
523C22×Q8C23×C6111yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×C4×C6114yescomplemented
533C22×D4D4×C6111yescharacteristic
534C22×D4C23×C6111yescharacteristic
535C22×D4C23×C6111yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C23×C6111yescharacteristic
541C23×C4C23×C6111yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C23×C6111yescharacteristic
549C22×C8C23×C6111yescharacteristic
550C22×C8C23×C6111yescharacteristic
551C22×C8C23×C6111yescharacteristic
552#124—22no—
553#124C2×C4×C6114yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×C4×C6114yescomplemented
557#121—22no—
558#121—28no—
559#121C2×C4×C6114yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—44no—
563C4×D4C2×C4×C6114yes—
564C4×D4C2×C4×C6114yescomplemented
565C4×D4D4×C6114yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4D4×C6111yescharacteristic
576C2×C4⋊C4C23×C6111yescharacteristic
577C2×C4⋊C4C23×C6111yescharacteristic
578C2×C4⋊C4C23×C6111yescharacteristic
579C2×C4⋊C4C23×C6111yescharacteristic
580C2×C4⋊C4C23×C6111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C6111yescharacteristic
590C2×C22⋊C4D4×C6111yescharacteristic
591C2×C42—21no—
592C2×C42C23×C6111yescharacteristic
593C4⋊C8—22no—
594#103—22no—
595#103—22no—
596#103—41no—
597#103—41no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604#102—41no—
605#102D4×C6114yescomplemented
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×D4×C6111yescharacteristic
622C24C2×D4×C6111yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×C4×C6112yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊C4×C6114yes—
657C2×D4C22×C4×C6112yes—
658C2×D4C22×C4×C6112yes—
659C2×D4C2×D4×C6112yes—
660C2×D4#41×C6112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—81no—
684C22×C4—81no—
685C22×C4—81no—
686C22×C4—81no—
687C22×C4C22×C4×C6112yes—
688C22×C4C22×C4×C6112yes—
689C22×C4C2×D4×C6111yescharacteristic
690C22×C4C2×D4×C6111yescharacteristic
691C22×C4C2×D4×C6111yescharacteristic
692C22×C4C2×D4×C6111yescharacteristic
693C22×C4C2×D4×C6112yes—
694C22×C4C2×D4×C6112yes—
695C22×C4C24×C6111yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8C2×D4×C6112yes—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—81no—
723C4⋊C4C22⋊C4×C6114yes—
724C4⋊C4C22×C4×C6112yes—
725C4⋊C4C2×D4×C6112yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4C22⋊C4×C6114yes—
734C22⋊C4C22⋊C4×C6114yes—
735C42—42no—
736C42C22×C4×C6112yes—
737C42C2×D4×C6112yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—21no—
745C23—22no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—48no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊C4×C6112yes—
770C23C2×C22⋊C4×C6112yes—
771C23AGL(1,ℤ/8)×C6112yes—
772C23#137×C6112yes—
773C23C22×D4×C6111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4C4×D4×C6114yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—84no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C6112yes—
829C2×C4C2×C22⋊C4×C6112yes—
830C2×C4C2×C22⋊C4×C6112yes—
831C2×C4C2×C22⋊C4×C6112yes—
832C2×C4C23×C4×C6111yescharacteristic
833C2×C4C22×D4×C6111yescharacteristic
834C2×C4C22×D4×C6111yescharacteristic
835C2×C4C2×#41×C6111yescharacteristic
836C2×C4H(5,𝔽2)×C6111yescharacteristic
837C2×C4H(5,𝔽2)×C6111yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22C61×#41714yescomplemented
871C22C22×C22⋊C4×C6111yescharacteristic
872C22D42×C6111yescharacteristic
873C22C61×#54611yescharacteristic
874C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
875C22C2×#137×C6111yescharacteristic
876C22C61×#57611yescharacteristic
877C22C61×#57711yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4C2×C4×D4×C6111yescharacteristic
889C4C61×#51811yescharacteristic
890C4D42×C6111yescharacteristic
891C4C61×#54611yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊C4×C6111yescharacteristic
897C2C2×C61×#41711yescharacteristic
898C2C61×#289711yescharacteristic
899C2C61×#326411yescharacteristic
900C2C61×#326611yescharacteristic
901C2C61×#330611yescharacteristic
902C2C61×#331411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#546C2
LCSG ▷ C2×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
2. C2×C61×#435C2semidirect
3. C2×C61×#417C2semidirect
4. C22×#102×C61C2semidirect
5. D4×C4⋊C4×C61C2semidirect
6. C61×#1983C2semidirect
7. C61×#1959C2semidirect
8. C61×#1895C2semidirect
9. C61×#1892C2semidirect
10. C61×#1874C2semidirect
11. C61×#1872C2semidirect
12. C61×#1802C2semidirect
13. C61×#1788C2semidirect
14. C61×#1786C2semidirect
15. C61×#1762C2semidirect
18. C22×M16×C61C22semidirect
21. C61×#546C4semidirect
32. C22×C4⋊C4×C61C22semidirect
35. C2×C4⋊C8×C61C22semidirect
37. C2×#103×C61C22semidirect
38. C2×#103×C61C22semidirect
39. C2×#103×C61C22semidirect
40. C2×#103×C61C22semidirect
51. C2×C22⋊C8×C61C22semidirect
52. C2×#97×C61C22semidirect
56. C61×#384C22semidirect
58. C61×#380C22semidirect
59. C4×C4⋊C4×C61C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
70. C2×#41×C61C2×C4semidirect
80. C22×D4×C61C2×C4semidirect
101. #124×C61C2×C4semidirect
104. C22⋊Q8×C61C2×C4semidirect
107. #121×C61C2×C4semidirect
112. C4×D4×C61C2×C4semidirect
153. #102×C61D4semidirect
337. D4×C61C4×D4semidirect
390. #22419C61direct (N × H)
419. C22×C61#417semidirect
442. C2×#435C2×C61semidirect
443. C2×#417C2×C61semidirect
444. C22×#102C2×C61semidirect
445. D4×C4⋊C4C2×C61semidirect
446. #1983C2×C61semidirect
447. #1959C2×C61semidirect
448. #1895C2×C61semidirect
449. #1892C2×C61semidirect
450. #1874C2×C61semidirect
451. #1872C2×C61semidirect
452. #1802C2×C61semidirect
453. #1788C2×C61semidirect
454. #1786C2×C61semidirect
455. #1762C2×C61semidirect
469. C22×M16C22×C61semidirect
472. #546C4×C61semidirect
483. C22×C4⋊C4C22×C61semidirect
486. C2×C4⋊C8C22×C61semidirect
488. C2×#103C22×C61semidirect
489. C2×#103C22×C61semidirect
490. C2×#103C22×C61semidirect
491. C2×#103C22×C61semidirect
502. C2×C22⋊C8C22×C61semidirect
503. C2×#97C22×C61semidirect
507. #384C22×C61semidirect
509. #380C22×C61semidirect
510. C4×C4⋊C4C22×C61semidirect
511. #340C22×C61semidirect
512. #340C22×C61semidirect
513. #340C22×C61semidirect
514. #340C22×C61semidirect
515. C61#22419direct (N × H)
522. C2×#41C2×C4×C61semidirect
532. C22×D4C2×C4×C61semidirect
553. #124C2×C4×C61semidirect
556. C22⋊Q8C2×C4×C61semidirect
559. #121C2×C4×C61semidirect
564. C4×D4C2×C4×C61semidirect
605. #102D4×C61semidirect
789. D4C4×D4×C61semidirect
870. C22C61×#417semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5462
C2×C61×#4352
C2×C61×#4172
C22×#102×C612
D4×C4⋊C4×C612
C61×#19832
C61×#19592
C61×#18952
C61×#18922
C61×#18742
C61×#18722
C61×#18022
C61×#17882
C61×#17862
C61×#17622
#2241961