Finite Group Databasebeta

← C2×#21457885 #30556747

Subgroups — C2×#21457885 #30556747

Order 15616.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840482C211yesmaximal, characteristic, complemented
2#21457885C2116yesmaximal, direct product factor
3C2×#16840121C211yesmaximal, characteristic, complemented
4C2×#16840100C211yesmaximal, characteristic, complemented
5C2×#16840083C211yesmaximal, characteristic, complemented
6C2×#16840057C211yesmaximal, characteristic, complemented
7C2×#16840006C211yesmaximal, characteristic, complemented
8C2×#16840001C211yesmaximal, characteristic, complemented
9C2×#16839981C211yesmaximal, characteristic, complemented
10C2×#16839924C211yesmaximal, characteristic, complemented
11C2×#16839918C211yesmaximal, characteristic, complemented
12C2×#16839867C211yesmaximal, characteristic, complemented
13C2×#16839834C211yesmaximal, characteristic, complemented
14C2×#16839771C211yesmaximal, characteristic, complemented
15C2×#16839758C211yesmaximal, characteristic, complemented
16C2×C61×#548C211yesmaximal, characteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22#16840482—24no—
23#16840482C2218yescomplemented
24C2×#14519777C2211yescharacteristic
25C2×#14519770—21no—
26C2×#14519770—21no—
27C2×#14519764—21no—
28C2×#14519756C2211yescharacteristic
29C2×#14519756C2211yescharacteristic
30C2×C4×Dic122C2211yescharacteristic
31C2×#14519742—21no—
32C2×#14519736C2211yescharacteristic
33C2×#14519736C2211yescharacteristic
34#16840121C2218yescomplemented
35#16840100C2218yescomplemented
36#16840083C2218yescomplemented
37#16840057C2218yescomplemented
38#16840006C2218yescomplemented
39#16840001C2218yescomplemented
40#16839981C2218yescomplemented
41#16839924C2218yescomplemented
42#16839918C2218yescomplemented
43#16839867C2218yescomplemented
44#16839834C2218yescomplemented
45C2×#14519710C2211yescharacteristic
46C2×#14519710C2211yescharacteristic
47C2×#14519708C2211yescharacteristic
48C2×C4⋊#92418C2211yescharacteristic
49#16839771C2218yescomplemented
50#16839758C2218yescomplemented
51C2×#14519701C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519701C2211yescharacteristic
54C2×#14519701C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519701C2211yescharacteristic
57C2×#14519700C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×#14519698C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic
63C2×#14519688C2211yescharacteristic
64C22×#41×C61C2211yescharacteristic
65C23×Q8×C61C2211yescharacteristic
66C61×#548—24no—
67C61×#548C2218yes—
68C2×#124×C61—21no—
69C2×#124×C61C2211yescharacteristic
70C2×C22⋊Q8×C61—21no—
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×#121×C61—21no—
73C2×#121×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C2×C4×D4×C61—21no—
76C2×C4×D4×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C2×#11758202—24no—
80C2×#11758202—42no—
81C2×#11758202C2314yes—
82C2×#11758202C2314yes—
83C2×#11758200—42no—
84C2×#11758200C2314yes—
85C2×#11758194—42no—
86C2×#11758194C2314yes—
87C22×#92418—42no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C22×#92418C2314yes—
93#14519777—22no—
94#14519777C2314yes—
95#14519770—28no—
96#14519770—28no—
97#14519764—28no—
98#14519756—22no—
99#14519756—22no—
100#14519756C2314yes—
101#14519756C2314yes—
102C4×Dic122—22no—
103C4×Dic122C2314yes—
104#14519742—28no—
105#14519736—22no—
106#14519736—22no—
107#14519736C2314yes—
108#14519736C2314yes—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×#11758196—21no—
116C2×C22⋊Dic61—21no—
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61—21no—
119C2×C22⋊Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123#14519710C2314yes—
124#14519710C2314yes—
125#14519708C2314yes—
126C4⋊#92418C2314yes—
127#14519701C2314yes—
128#14519701C2314yes—
129#14519701C2314yes—
130#14519701C2314yes—
131#14519701C2314yes—
132#14519701C2314yes—
133#14519700C2314yes—
134#14519698C2314yes—
135#14519698C2314yes—
136#14519698C2314yes—
137C22⋊#92418C2314yes—
138C22⋊#92418C2314yes—
139#14519688C2314yes—
140C2×#41×C61—22no—
141C2×#41×C61—24no—
142C2×#41×C61—42no—
143C2×#41×C61C2314yes—
144C22×Q8×C61—22no—
145C22×Q8×C61—21no—
146C22×Q8×C61—24no—
147C22×Q8×C61—42no—
148C22×Q8×C61C2311yescharacteristic
149C22×Q8×C61C2314yes—
150C22×Q8×C61C2311yescharacteristic
151C22×D4×C61—21no—
152C22×D4×C61—21no—
153C22×D4×C61D411yescharacteristic
154C22×D4×C61C2311yescharacteristic
155C23×C4×C61—21no—
156C23×C4×C61—21no—
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159#124×C61—28no—
160#124×C61—22no—
161#124×C61C2314yes—
162C22⋊Q8×C61—22no—
163C22⋊Q8×C61—28no—
164C22⋊Q8×C61C2314yes—
165#121×C61—28no—
166#121×C61—22no—
167#121×C61C2314yes—
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yes—
170C4×D4×C61—28no—
171C4×D4×C61D414yes—
172C4×D4×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61D411yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61D411yescharacteristic
182C2×C22⋊C4×C61D411yescharacteristic
183C2×C42×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C24×C61C2×D411yescharacteristic
188#41×C61—28no—
189#41×C61—44no—
190#41×C61—48no—
191C2×Q8×C61—21no—
192C2×Q8×C61—24no—
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61—28no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61—44no—
199C2×Q8×C61—44no—
200C2×Q8×C61—48no—
201C2×Q8×C61#4114yes—
202C2×Q8×C61C2412yes—
203C2×Q8×C61C2412yes—
204C2×D4×C61—24no—
205C2×D4×C61—24no—
206C2×D4×C61—21no—
207C2×D4×C61—22no—
208C2×D4×C61—22no—
209C2×D4×C61—42no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61C2×D414yes—
213C2×D4×C61C2412yes—
214C22×C4×C61—21no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—24no—
222C22×C4×C61—24no—
223C22×C4×C61—44no—
224C22×C4×C61—44no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2412yes—
232C22×C4×C61C2412yes—
233C22×C4×C61C2411yescharacteristic
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—24no—
241C2×Dic122—21no—
242C2×Dic122—44no—
243C2×Dic122C2412yes—
244C4⋊C4×C61—24no—
245C4⋊C4×C61—24no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C2×D414yes—
248C4⋊C4×C61C2412yes—
249C22⋊C4×C61—24no—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61C2×D414yes—
254C22⋊C4×C61C2×D414yes—
255C42×C61—24no—
256C42×C61C2×D412yes—
257C42×C61C2412yes—
258C22⋊Dic61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261C22⋊Dic61—24no—
262#11758202—28no—
263#11758202—44no—
264#11758200—44no—
265C4⋊Dic61—24no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61C2412yes—
270C4⋊Dic61C2412yes—
271C4⋊Dic61C2412yes—
272#11758196—24no—
273#11758196—24no—
274#11758196—24no—
275C4×Dic61—24no—
276C4×Dic61—24no—
277C4×Dic61—24no—
278#11758194—44no—
279C2×#92418—22no—
280C2×#92418—22no—
281C2×#92418—22no—
282C2×#92418—22no—
283C2×#92418—44no—
284C2×#92418C2412yes—
285C2×#92418C2412yes—
286C2×#92418C2412yes—
287C2×#92418C2412yes—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61C22×D412yes—
299C23×C61C22×D412yes—
300C23×C61C22×D411yescharacteristic
301Q8×C61—24no—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61—48no—
306Q8×C61—42no—
307Q8×C61C2×#4114yes—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—44no—
311D4×C61—48no—
312D4×C61—48no—
313D4×C61—42no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—24no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—24no—
321C2×C4×C61—24no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—48no—
329C2×C4×C61—48no—
330C2×C4×C61—42no—
331C2×C4×C61—42no—
332C2×C4×C61C22×D412yes—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C2×#4112yes—
338C2×C4×C61H(5,𝔽2)12yes—
339C2×C4×C61C2511yescharacteristic
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348Dic122—22no—
349Dic122—22no—
350Dic122—48no—
351Dic122—42no—
352#92418—22no—
353#92418—22no—
354#92418—22no—
355#92418—22no—
356C2×#3313—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—44no—
364C22×C61—44no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—84no—
369C22×C61#54612yes—
370C22×C61#57512yes—
371C22×C61#57812yes—
372C22×C61C23×D411yescharacteristic
373C4×C61—22no—
374C4×C61—22no—
375C4×C61—24no—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61#54612yes—
381C4×C61C22×#4111yescharacteristic
382C4×C61C2×H(5,𝔽2)11yescharacteristic
383Dic61—42no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387C2×#556—611no—
388C2×#548D6111yescharacteristic
389#3313—6116no—
390C2×#489—611no—
391C2×#485—611no—
392C2×#482—611no—
393C2×#477—611no—
394C2×#468—611no—
395C2×#467—611no—
396C2×#464—611no—
397C2×#452—611no—
398C2×#451—611no—
399C2×#441—611no—
400C2×#435—611no—
401C2×#419—611no—
402C2×#416—611no—
403C2×C61—42no—
404C2×C61—42no—
405C2×C61—82no—
406C2×C61#331314yescomplemented
407C2×C61C2×#54611yescharacteristic
408C2×C61C2×#57511yescharacteristic
409C2×C61C2×#57811yescharacteristic
410C22×#41C2×D6111yescharacteristic
411C23×Q8C2×D6111yescharacteristic
412C22×Q16—611no—
413C22×Q16—611no—
414C22×SD16—611no—
415C22×M16—611no—
416C23×C8—611no—
417#556—618no—
418#556—1224no—
419#548—24no—
420#548C2×D6118yes—
421C2×C4⋊Q8—611no—
422C2×#126—1221no—
423C2×#126—1221no—
424C2×#124—21no—
425C2×#124—1221no—
426C2×#124C2×D6111yescharacteristic
427C2×C22⋊Q8—21no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8—611no—
430C2×C22⋊Q8C2×D6111yescharacteristic
431C2×#121—21no—
432C2×#121C2×D6111yescharacteristic
433C2×C4×Q8—611no—
434C2×C4×Q8—1221no—
435C2×C4×Q8C2×D6111yescharacteristic
436C2×C4×D4—21no—
437C2×C4×D4C2×D6111yescharacteristic
438C2×#117—611no—
439C2×#117—611no—
440#489—618no—
441#485—618no—
442#482—618no—
443#477—618no—
444#468—618no—
445#467—618no—
446#464—618no—
447#452—618no—
448#451—618no—
449#441—618no—
450#435—618no—
451C2×#107—611no—
452C2×#107—611no—
453C2×#106—611no—
454C2×C4⋊C8—611no—
455#419—618no—
456#416—618no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×#97—611no—
470C61C2×#331311yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41C22×D6114yes—
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8—611no—
480C22×Q8—1221no—
481C22×Q8C22×D6111yescharacteristic
482C22×Q8C22×D6114yes—
483C22×Q8C22×D6111yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4C22⋊D6111yescharacteristic
487C22×D4C22×D6111yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C22×D6111yescharacteristic
491C23×C4C22×D6111yescharacteristic
492C2×Q16—614no—
493C2×Q16—614no—
494C2×Q16—1224no—
495C2×Q16—2442no—
496C2×SD16—614no—
497C2×SD16—2442no—
498C2×M16—614no—
499C2×M16—2442no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—614no—
505C22×C8—2442no—
506C4⋊Q8—614no—
507C4⋊Q8—1222no—
508#126—1228no—
509#126—1228no—
510#124—28no—
511#124—22no—
512#124—1228no—
513#124C22×D6114yes—
514C22⋊Q8—22no—
515C22⋊Q8—28no—
516C22⋊Q8—614no—
517C22⋊Q8—614no—
518C22⋊Q8—1222no—
519C22⋊Q8—1222no—
520C22⋊Q8C22×D6114yes—
521#121—28no—
522#121—22no—
523#121C22×D6114yes—
524C4×Q8—22no—
525C4×Q8—614no—
526C4×Q8—1228no—
527C4×Q8—1222no—
528C4×Q8C22×D6114yes—
529C4×D4—28no—
530C4×D4C22⋊D6114yes—
531C4×D4C22×D6114yes—
532#117—614no—
533#117—614no—
534#117—1222no—
535#117—1222no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4C22⋊D6111yescharacteristic
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4C22⋊D6111yescharacteristic
556C2×C22⋊C4C22⋊D6111yescharacteristic
557C2×C42—21no—
558C2×C42—1221no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562#107—614no—
563#107—614no—
564#106—614no—
565C4⋊C8—614no—
566#103—614no—
567#103—614no—
568#103—614no—
569#103—614no—
570#103—614no—
571#103—614no—
572#103—614no—
573#102—614no—
574#102—614no—
575#102—614no—
576C22⋊C8—614no—
577C22⋊C8—614no—
578#97—614no—
579C24—21no—
580C24C2×C22⋊D6111yescharacteristic
581C24C2×C22⋊D6111yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585C2×Q8—21no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—28no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—48no—
595C2×Q8—612no—
596C2×Q8—1221no—
597C2×Q8—1224no—
598C2×Q8—1222no—
599C2×Q8—1222no—
600C2×Q8—2444no—
601C2×Q8#1175822414yes—
602C2×Q8C23×D6112yes—
603C2×Q8C23×D6112yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—21no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—42no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4C2×C22⋊D6114yes—
613C2×D4C23×D6112yes—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4C2×C22⋊D6112yes—
630C22×C4C2×C22⋊D6112yes—
631C22×C4C2×C22⋊D6111yescharacteristic
632C22×C4C2×C22⋊D6111yescharacteristic
633C22×C4C2×C22⋊D6111yescharacteristic
634C22×C4C2×C22⋊D6111yescharacteristic
635C22×C4C23×D6112yes—
636C22×C4C23×D6112yes—
637C22×C4C23×D6111yescharacteristic
638Q16—1228no—
639Q16—2444no—
640SD16—2444no—
641M16—2444no—
642C2×C8—612no—
643C2×C8—612no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—1222no—
649C2×C8—1222no—
650C2×C8—2444no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1224no—
663C4⋊C4—1224no—
664C4⋊C4C2×C22⋊D6114yes—
665C4⋊C4C23×D6112yes—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C22⋊C4C2×C22⋊D6114yes—
675C22⋊C4C2×C22⋊D6114yes—
676C42—24no—
677C42—1224no—
678C42—1224no—
679C42—1224no—
680C42C2×C22⋊D6112yes—
681C42C23×D6112yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23C22×C22⋊D6112yes—
693C23C22×C22⋊D6112yes—
694C23C22×C22⋊D6111yescharacteristic
695Q8—22no—
696Q8—24no—
697Q8—22no—
698Q8—22no—
699Q8—48no—
700Q8—42no—
701Q8—1222no—
702Q8—1222no—
703Q8—2448no—
704Q8—2442no—
705Q8C2×#1175822414yes—
706D4—22no—
707D4—22no—
708D4—44no—
709D4—48no—
710D4—48no—
711D4—42no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—48no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4C22×C22⋊D6112yes—
739C2×C4C22×C22⋊D6112yes—
740C2×C4C22×C22⋊D6112yes—
741C2×C4C22×C22⋊D6112yes—
742C2×C4C22×C22⋊D6111yescharacteristic
743C2×C4C2×#1175822412yes—
744C2×C4#1451982212yes—
745C2×C4C24×D6111yescharacteristic
746C8—1222no—
747C8—1222no—
748C8—1222no—
749C8—1222no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22#1684040612yes—
763C22#1684056012yes—
764C22#1684057712yes—
765C22C23×C22⋊D6111yescharacteristic
766C4—22no—
767C4—22no—
768C4—24no—
769C4—22no—
770C4—22no—
771C4—42no—
772C4—42no—
773C4—2442no—
774C4—2442no—
775C4—2442no—
776C4—2442no—
777C4#1684040612yes—
778C4C22×#1175822411yescharacteristic
779C4C2×#1451982211yescharacteristic
780C2—42no—
781C2—42no—
782C2—82no—
783C2#2145788514yesdirect product factor
784C2C2×#1684040611yescharacteristic
785C2C2×#1684056011yescharacteristic
786C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
Fitting, prime radicalC2×C61×#548C2
socleC23×C61C22×D4
hypercenterC2×#548D61
hypocenterC61C2×#3313
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16840482C2semidirect
2. #21457885C2direct (N × H)
3. C2×#16840121C2semidirect
4. C2×#16840100C2semidirect
5. C2×#16840083C2semidirect
6. C2×#16840057C2semidirect
7. C2×#16840006C2semidirect
8. C2×#16840001C2semidirect
9. C2×#16839981C2semidirect
10. C2×#16839924C2semidirect
11. C2×#16839918C2semidirect
12. C2×#16839867C2semidirect
13. C2×#16839834C2semidirect
14. C2×#16839771C2semidirect
15. C2×#16839758C2semidirect
23. #16840482C22semidirect
34. #16840121C22semidirect
35. #16840100C22semidirect
36. #16840083C22semidirect
37. #16840057C22semidirect
38. #16840006C22semidirect
39. #16840001C22semidirect
40. #16839981C22semidirect
41. #16839924C22semidirect
42. #16839918C22semidirect
43. #16839867C22semidirect
44. #16839834C22semidirect
49. #16839771C22semidirect
50. #16839758C22semidirect
406. C2×C61#3313semidirect
470. C61C2×#3313semidirect
783. C2#21457885direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404822
#214578852
C2×#168401212
C2×#168401002
C2×#168400832
C2×#168400572
C2×#168400062
C2×#168400012
C2×#168399812
C2×#168399242
C2×#168399182
C2×#168398672
C2×#168398342
C2×#168397712
C2×#168397582
C2×C61×#5482
C2×#331361