Finite Group Databasebeta

← #30622480

Subgroups — #30622480

Order 15616.

854 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462348C211yesmaximal, characteristic, complemented
2#21462340C211yesmaximal, characteristic
3#21461969C211yesmaximal, characteristic
4#21461964C211yesmaximal, characteristic
5#21461950C211yesmaximal, characteristic, complemented
6#21461932C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461898C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic
10#21461815C211yesmaximal, characteristic
11#21461620C211yesmaximal, characteristic, complemented
12#21461592C211yesmaximal, characteristic, complemented
13#21461589C211yesmaximal, characteristic
14#103×#6923C211yesmaximal, characteristic, complemented
15#461×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519840C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26#16840721C2211yescharacteristic
27C2×#14519831C2211yescharacteristic
28C2×C8×#6923C2211yescharacteristic
29(C2×#6923)⋊Q8C2211yescharacteristic
30(C2×#6923)⋊Q8C2211yescharacteristic
31#16840714C2211yescharacteristic
32#16840714C2211yescharacteristic
33#16840713—21no—
34#16840712—21no—
35#16840712—21no—
36#16840711—21no—
37#16840711—21no—
38#16840706C2211yescharacteristic
39#16840705—21no—
40C4⋊C4×#6923—21no—
41C4⋊C4×#6923C2211yescharacteristic
42C4⋊C4×#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44C4×C4⋊#6923C2211yescharacteristic
45C4×C22⋊#6923—21no—
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C2×SD16×D61C2211yescharacteristic
54C4⋊Q8×D61C2211yescharacteristic
55C4×D4×D61C2211yescharacteristic
56#16839968C411yescharacteristic, complemented
57#16839967C411yescharacteristic, complemented
58#16839966C411yescharacteristic, complemented
59#16839966C411yescharacteristic, complemented
60#16839965C411yescharacteristic, complemented
61#16839965C411yescharacteristic, complemented
62#16839964C411yescharacteristic, complemented
63C4⋊C8×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#103×D61C2211yescharacteristic
66C61×#461C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69Q8×#6923—22no—
70Q8×#6923—22no—
71Q8×#6923—41no—
72Q8×#6923—41no—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923D411yescharacteristic
76C2×C4⋊#6923D411yescharacteristic
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923C2311yescharacteristic
91C2×C4×#6923C2311yescharacteristic
92#14519846—41no—
93#14519845—41no—
94#14519840—22no—
95#14519840—22no—
96#14519840—41no—
97#14519840—41no—
98#14519839—22no—
99#14519839—22no—
100#14519832—21no—
101#14519832—21no—
102#14519831—41no—
103C8×#6923—41no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4D411yescharacteristic
114(C2×#6923)⋊C4D411yescharacteristic
115C2×Q8×D61C2311yescharacteristic
116C2×Q8×D61C2311yescharacteristic
117C2×D4×D61C2311yescharacteristic
118C22×C4×D61—21no—
119C2×#11758190C2×C411yescharacteristic
120C2×#11758190C2×C411yescharacteristic
121C2×#11758200C2×C411yescharacteristic
122C2×#11758200C2×C411yescharacteristic
123C2×#11758201C2×C411yescharacteristic
124C2×#11758201C2×C411yescharacteristic
125SD16×D61—41no—
126SD16×D61—41no—
127SD16×D61—41no—
128SD16×D61—41no—
129C2×C8×D61C2311yescharacteristic
130C2×C8×D61C2311yescharacteristic
131#14519777C2×C411yescharacteristic
132#14519776—21no—
133#14519776—21no—
134#14519775C2×C411yescharacteristic
135#14519775C2×C411yescharacteristic
136C4×D244C2×C411yescharacteristic
137D4×Dic61C2×C411yescharacteristic
138#14519739C2×C411yescharacteristic
139C4×C22⋊D61—21no—
140#14519737—21no—
141C4⋊C4×D61—21no—
142C4⋊C4×D61—21no—
143C4⋊C4×D61C2311yescharacteristic
144C22⋊C4×D61—21no—
145C42×D61C2311yescharacteristic
146C4⋊#92418C2×C411yescharacteristic
147#14519706C2×C411yescharacteristic
148#14519706C2×C411yescharacteristic
149#14519702C2×C411yescharacteristic
150#14519702C2×C411yescharacteristic
151#14519701C2×C411yescharacteristic
152#14519701C2×C411yescharacteristic
153#14519700C2×C411yescharacteristic
154#14519700C2×C411yescharacteristic
155C2×SD16×C61C2×C411yescharacteristic
156C2×SD16×C61C2×C411yescharacteristic
157C4⋊Q8×C61C2×C411yescharacteristic
158C4×D4×C61C2×C411yescharacteristic
159C4⋊C8×C61C2×C411yescharacteristic
160#103×C61C2×C411yescharacteristic
161#103×C61C2×C411yescharacteristic
162C23×D61—21no—
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C22×#6923C2×D411yescharacteristic
171C2×Q8×C61C22×C411yescharacteristic
172C2×Q8×C61C22×C411yescharacteristic
173C2×D4×C61C22×C411yescharacteristic
174C22×C4×C61—21no—
175C2×C22⋊D61—21no—
176C22×Dic61—21no—
177Q8×D61—21no—
178Q8×D61—21no—
179Q8×D61—21no—
180Q8×D61—21no—
181Q8×D61—21no—
182Q8×D61—21no—
183Q8×D61—21no—
184Q8×D61—21no—
185D4×D61—21no—
186D4×D61—21no—
187D4×D61—21no—
188D4×D61—21no—
189C2×D244C22×C411yescharacteristic
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C2×C4×D61C2×D411yescharacteristic
198C2×C4×D61C2×D411yescharacteristic
199C2×C4×D61C2411yescharacteristic
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122C22×C411yescharacteristic
203C2×Dic122C22×C411yescharacteristic
204C22⋊#6923—42no—
205C22⋊#6923—42no—
206C22⋊#6923—81no—
207C22⋊#6923—81no—
208C2×#92420—21no—
209C2×#92420—21no—
210C4⋊#6923—22no—
211C4⋊#6923—21no—
212C4⋊#6923—21no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923—21no—
216C4⋊#6923—21no—
217C4⋊#6923—21no—
218C4⋊#6923—41no—
219C4⋊#6923—42no—
220C4⋊#6923—42no—
221C4⋊#6923#4112yes—
222C4×#6923—21no—
223C4×#6923—21no—
224C4×#6923—21no—
225C4×#6923—21no—
226C4×#6923—42no—
227C4×#6923—42no—
228C4×#6923—42no—
229C4×#6923—81no—
230C4×#6923—81no—
231D61⋊C8—21no—
232D61⋊C8—21no—
233D61⋊C8—21no—
234D61⋊C8#4112yes—
235SD16×C61—41no—
236SD16×C61—41no—
237C2×C8×C61C22×C411yescharacteristic
238C2×C8×C61C22×C411yescharacteristic
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61C22×C411yescharacteristic
242C22⋊C4×C61—21no—
243C42×C61C22×C411yescharacteristic
244C22⋊Dic61—21no—
245#11758201—41no—
246#11758201—41no—
247#11758200—41no—
248#11758200—41no—
249#11758198—21no—
250#11758198—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61C22×C411yescharacteristic
254#11758196—21no—
255#11758196—21no—
256#11758196—21no—
257#11758196—21no—
258#11758196—21no—
259C4×Dic61C22×C411yescharacteristic
260C4×Dic61#4111yescharacteristic
261C4×Dic61#4111yescharacteristic
262C2×#92418C22×C411yescharacteristic
263C2×#92418C22×C411yescharacteristic
264#11758190—41no—
265#11758190—41no—
266C8×D61—21no—
267C8×D61—21no—
268C8×D61—21no—
269C8×D61—21no—
270C23×C61—21no—
271C22×D61—21no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61C22×D411yescharacteristic
279C2×#6923—21no—
280C2×#6923—21no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—21no—
284C2×#6923—22no—
285C2×#6923—21no—
286C2×#6923—21no—
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—41no—
292C2×#6923—41no—
293C2×#6923—41no—
294C2×#6923—41no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923—41no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923#13712yes—
303Q8×C61—21no—
304Q8×C61—21no—
305Q8×C61—21no—
306Q8×C61—21no—
307D4×C61—21no—
308D4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—81no—
313C2×C4×C61C4×D411yescharacteristic
314C2×C4×C61C4×D411yescharacteristic
315C2×C4×C61C23×C411yescharacteristic
316C22⋊D61—41no—
317C22⋊D61—41no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—81no—
322C2×Dic61C4×D411yescharacteristic
323C2×Dic61C4×D411yescharacteristic
324C2×Dic61C2×#4111yescharacteristic
325D244—21no—
326D244—21no—
327C4×D61—21no—
328C4×D61—21no—
329C4×D61—21no—
330C4×D61—21no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—81no—
338C4×D61—81no—
339C4×D61C2×#4111yescharacteristic
340C4×D61C2×#4111yescharacteristic
341C4×D61H(5,𝔽2)11yescharacteristic
342C4×D61H(5,𝔽2)11yescharacteristic
343Dic122—21no—
344Dic122—21no—
345Dic122—21no—
346Dic122—21no—
347Dic122—41no—
348Dic122—41no—
349Dic122—41no—
350Dic122—41no—
351#92420—22no—
352#92420—41no—
353C8×C61—21no—
354C8×C61—21no—
355#92418—21no—
356#92418—21no—
357#23112—611nomaximal, Sylow
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61C2×C4×D411yescharacteristic
362C2×D61—41no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61#54611yescharacteristic
370C2×D61#55011yescharacteristic
371C2×D61C2×#13711yescharacteristic
372C2×D61#57511yescharacteristic
373C2×D61#57711yescharacteristic
374C2×D61#57711yescharacteristic
375#6923—22no—
376#6923—41no—
377#6923—41no—
378#6923—42no—
379#6923—41no—
380#6923—81no—
381#6923—81no—
382#6923—81no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61C4×#4111yescharacteristic
389C4×C61#51811yescharacteristic
390Dic61—21no—
391Dic61—21no—
392Dic61—41no—
393Dic61—41no—
394Dic61—41no—
395Dic61#55311yescharacteristic
396Dic61#55511yescharacteristic
397C2×#461—611no—
398#2365—611no—
399#2357—611no—
400#1973—611no—
401#1968—611no—
402#1960—611no—
403#1949—611no—
404#1928—611no—
405#1927—611no—
406#1880—611no—
407#1880—611no—
408#1771—611no—
409#1763—611no—
410#1762—611no—
411C4×#103—611no—
412C2×C61—81no—
413C2×C61#236311yescharacteristic
414C2×C61C4×#13711yescharacteristic
415C2×C61#294911yescharacteristic
416D61—81no—
417D61#330711yescharacteristic
418D61#332011yescharacteristic
419D61#340011yescharacteristic
420D61#340111yescharacteristic
421C22×SD16—611no—
422C22×SD16—611no—
423C2×C4⋊Q8—611no—
424C2×C4×Q8—611no—
425C2×C4×Q8—611no—
426C2×C4×D4—611no—
427#461—611no—
428#461—611no—
429#461—611no—
430#461—611no—
431#461—611no—
432#461—611no—
433#461—611no—
434#461#692311yescharacteristic, complemented
435C2×#107—611no—
436C2×#106—611no—
437C2×C4⋊C8—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#97—611no—
447C2×#97—611no—
448C2×C4×C8—611no—
449#391—611no—
450#391—611no—
451#390—611no—
452#390—611no—
453#389—1221no—
454#388—1221no—
455#388—1221no—
456#387—1221no—
457#387—1221no—
458#382—611no—
459#381—1221no—
460C4×C4⋊C4—611no—
461C4×C4⋊C4—611no—
462C4×C4⋊C4—611no—
463C4×C4⋊C4—611no—
464C4×C4⋊C4—1221no—
465C4×C22⋊C4—1221no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470#336—611no—
471#336—611no—
472C61#2311211yescharacteristic, complemented, Sylow
473C22×Q8—611no—
474C22×Q8—611no—
475C22×D4—611no—
476C23×C4—1221no—
477C2×SD16—611no—
478C2×SD16—611no—
479C2×SD16—611no—
480C2×SD16—611no—
481C2×SD16—611no—
482C2×SD16—611no—
483C2×SD16—2441no—
484C2×SD16—2441no—
485C2×SD16—2441no—
486C2×SD16—2441no—
487C2×SD16C2×#692311yescharacteristic
488C2×SD16C2×#692311yescharacteristic
489C22×C8—611no—
490C22×C8—611no—
491C22×C8—611no—
492C22×C8—611no—
493C4⋊Q8—611no—
494C4⋊Q8—611no—
495C4⋊Q8—611no—
496C4⋊Q8—1221no—
497C4⋊Q8—1221no—
498C4⋊Q8C2×#692311yescharacteristic
499C4×Q8—1222no—
500C4×Q8—1222no—
501C4×Q8—2441no—
502C4×Q8—2441no—
503C4×D4—611no—
504C4×D4—611no—
505C4×D4—611no—
506C4×D4—1221no—
507C4×D4—1221no—
508C4×D4C2×#692311yescharacteristic
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C42—611no—
526C2×C42—611no—
527C2×C42—611no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42—1221no—
533#107—2441no—
534#106—2441no—
535C4⋊C8—611no—
536C4⋊C8—611no—
537C4⋊C8—611no—
538C4⋊C8C2×#692311yescharacteristic
539#103—611no—
540#103—611no—
541#103—611no—
542#103—611no—
543#103—611no—
544#103—611no—
545#103—1222no—
546#103—1222no—
547#103—2441no—
548#103—2441no—
549#103C2×#692311yescharacteristic
550#103C2×#692311yescharacteristic
551#102—1222no—
552#102—1222no—
553#97—1221no—
554#97—1221no—
555#97—2441no—
556C4×C8—2441no—
557#95—611no—
558#95—611no—
559#95—1221no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566#95—1221no—
567#95—1221no—
568C24—1221no—
569C2×Q8—611no—
570C2×Q8—611no—
571C2×Q8—1221no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8C22×#692311yescharacteristic
582C2×Q8C22×#692311yescharacteristic
583C2×D4—611no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4C22×#692311yescharacteristic
590C22×C4—21no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—4881no—
609C22×C4—4881no—
610SD16—41no—
611SD16—41no—
612SD16—2441no—
613SD16—2441no—
614SD16—2441no—
615SD16—2441no—
616SD16—2441no—
617SD16—2441no—
618C2×C8—612no—
619C2×C8—611no—
620C2×C8—611no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8C22×#692311yescharacteristic
631C2×C8C22×#692311yescharacteristic
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—612no—
635C4⋊C4—611no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1222no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—2441no—
652C4⋊C4—2442no—
653C4⋊C4—2442no—
654C4⋊C4C22×#692311yescharacteristic
655C22⋊C4—21no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—1221no—
659C22⋊C4—4881no—
660C22⋊C4—4881no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C42—611no—
664C42—611no—
665C42—611no—
666C42—1221no—
667C42—1221no—
668C42—1221no—
669C42—1221no—
670C42—4881no—
671C42—4881no—
672C42—2442no—
673C42—2442no—
674C42—2442no—
675C42C22×#692311yescharacteristic
676C23—21no—
677C23—611no—
678C23—1221no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—1221no—
690Q8—1221no—
691Q8—1221no—
692Q8—1221no—
693Q8—2441no—
694Q8—2441no—
695Q8—2441no—
696Q8—2441no—
697D4—21no—
698D4—21no—
699D4—1221no—
700D4—1221no—
701D4—2441no—
702D4—2441no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—81no—
707C2×C4—611no—
708C2×C4—611no—
709C2×C4—611no—
710C2×C4—611no—
711C2×C4—611no—
712C2×C4—612no—
713C2×C4—611no—
714C2×C4—611no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1222no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—4881no—
735C2×C4—4881no—
736C2×C4—4881no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4D4×#692311yescharacteristic
755C2×C4D4×#692311yescharacteristic
756C2×C4C23×#692311yescharacteristic
757C8—21no—
758C8—21no—
759C8—1222no—
760C8—1221no—
761C8—1221no—
762C8—2441no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—611no—
767C22—611no—
768C22—611no—
769C22—611no—
770C22—611no—
771C22—611no—
772C22—4881no—
773C22—4881no—
774C22—4881no—
775C22—4881no—
776C22—2441no—
777C22—2441no—
778C22—2441no—
779C22C2×D4×#692311yescharacteristic
780C4—21no—
781C4—21no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—611no—
786C4—611no—
787C4—1222no—
788C4—1221no—
789C4—1221no—
790C4—4881no—
791C4—4881no—
792C4—4881no—
793C4—2441no—
794C4—2441no—
795C4—2441no—
796C4—2442no—
797C4—2441no—
798C4—2441no—
799C4—2441no—
800C4#41×#692311yescharacteristic
801C4#1684082911yescharacteristic
802C2—81no—
803C2—611no—
804C2—611no—
805C2—611no—
806C2—611no—
807C2—4881no—
808C2#2146234611yescharacteristic
809C2#137×#692311yescharacteristic
810C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#461C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#461#6923
hypocenterC61#23112
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #21462348C2semidirect
5. #21461950C2semidirect
6. #21461932C2semidirect
7. #21461899C2semidirect
8. #21461898C2semidirect
11. #21461620C2semidirect
12. #21461592C2semidirect
14. #103×#6923C2semidirect
56. #16839968C4semidirect
57. #16839967C4semidirect
58. #16839966C4semidirect
59. #16839966C4semidirect
60. #16839965C4semidirect
61. #16839965C4semidirect
62. #16839964C4semidirect
66. C61×#461C4semidirect
434. #461#6923semidirect
472. C61#23112semidirect

Maximal subgroups

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

subgroupindex
#214623482
#214623402
#214619692
#214619642
#214619502
#214619322
#214618992
#214618982
#214618152
#214616202
#214615922
#214615892
#103×#69232
#461×D612
#2311261