Finite Group Databasebeta

← #29656813

Subgroups — #29656813

Order 15616.

994 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
1#21457181C211yesmaximal, characteristic, complemented
2#21456553C211yesmaximal, characteristic, complemented
3#21455274C211yesmaximal, characteristic, complemented
4#21445089C211yesmaximal, characteristic, complemented
5#21445082C211yesmaximal, characteristic, complemented
6#21445005C211yesmaximal, characteristic, complemented
7#21444998C211yesmaximal, characteristic, complemented
8#21444929C211yesmaximal, characteristic, complemented
9#21444922C211yesmaximal, characteristic, complemented
10#21444878C211yesmaximal, characteristic, complemented
11#21444873C211yesmaximal, characteristic, complemented
12#21444496C211yesmaximal, characteristic, complemented
13#21444258C211yesmaximal, characteristic, complemented
14#21444232C211yesmaximal, characteristic, complemented
15C61×#3514C211yesmaximal, characteristic, complemented
16C2×#14519797—21no—
17#16840312C2211yescharacteristic, complemented
18#16840158C2211yescharacteristic, complemented
19#16840138C2211yescharacteristic
20#16840110C2211yescharacteristic, complemented
21#16840108C2211yescharacteristic
22#16840059—21no—
23#16840047C2211yescharacteristic, complemented
24#16840042C2211yescharacteristic
25#16840013—21no—
26#16840013—22no—
27#16840010—21no—
28#16839984—21no—
29#16839977—21no—
30#16839974—21no—
31#16839972C2211yescharacteristic, complemented
32#16839967C2211yescharacteristic
33#16839962C2211yescharacteristic, complemented
34#16839962C2211yescharacteristic, complemented
35#16839957C2211yescharacteristic
36#16839957C2211yescharacteristic
37#16839872—22no—
38#16839786C2211yescharacteristic, complemented
39C2×C4⋊#92418C2211yescharacteristic, complemented
40#16839756—21no—
41C4×#11758194C2211yescharacteristic, complemented
42#16839508C2211yescharacteristic, complemented
43#16839508C2211yescharacteristic, complemented
44#16839506C2211yescharacteristic
45#16839506C2211yescharacteristic
46Q8⋊#92418C2211yescharacteristic, complemented
47Q8⋊#92418C2211yescharacteristic, complemented
48Q8⋊#92418C2211yescharacteristic, complemented
49Q8⋊#92418C2211yescharacteristic, complemented
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54C61×#559C2211yescharacteristic
55C61×#556C2211yescharacteristic
56C61×#555—21no—
57C61×#551—22no—
58D4×Q8×C61C2211yescharacteristic
59C61×#548—21no—
60C61×#546—21no—
61C61×#546—21no—
62D42×C61C2211yescharacteristic
63C61×#542—21no—
64C61×#538—22no—
65C61×#532C2211yescharacteristic
66C61×#529—21no—
67C61×#529C2211yescharacteristic
68C2×#124×C61—21no—
69C61×#518—21no—
70C4×#41×C61C2211yescharacteristic
71C2×#11758222—21no—
72#14519797—44no—
73C2×#11758202—21no—
74C2×#11758200—21no—
75C2×#11758201—21no—
76C2×#11758201—21no—
77C2×#11758199—21no—
78C2×#11758199—22no—
79C2×#11758199—21no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82C22×#92418—21no—
83#14519777C2311yescharacteristic
84#14519774C2311yescharacteristic
85#14519765—21no—
86#14519751—21no—
87#14519751—21no—
88C4×D244—21no—
89C4×D244—21no—
90#14519710—21no—
91#14519708—21no—
92#14519708—22no—
93C4⋊#92418—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519701—21no—
100#14519700—21no—
101#14519700—21no—
102#14519698—21no—
103#14519698—22no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—22no—
109#14519688—21no—
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C2×#41×C61—21no—
113C2×#41×C61D411yescharacteristic
114C22×Q8×C61—21no—
115C22×D4×C61—21no—
116C22×D4×C61—21no—
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61C2311yescharacteristic
119#127×C61C2311yescharacteristic
120#126×C61—22no—
121#126×C61—22no—
122#126×C61—21no—
123#125×C61D411yescharacteristic
124#124×C61—22no—
125#124×C61—22no—
126#124×C61—22no—
127#124×C61—21no—
128#124×C61—21no—
129#124×C61—21no—
130#124×C61—21no—
131#124×C61D411yescharacteristic
132#123×C61—22no—
133#123×C61—22no—
134#123×C61—22no—
135#123×C61—21no—
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—22no—
139C22⋊Q8×C61—21no—
140C22⋊Q8×C61D411yescharacteristic
141#121×C61—22no—
142#121×C61—22no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61D412yes—
147#121×C61D411yescharacteristic
148#120×C61—22no—
149#120×C61—22no—
150C4×Q8×C61—21no—
151C4×Q8×C61D411yescharacteristic
152C4×Q8×C61C2311yescharacteristic
153C4×Q8×C61C2311yescharacteristic
154C4×D4×C61—22no—
155C4×D4×C61—22no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61D412yes—
164C4×D4×C61D411yescharacteristic
165C4×D4×C61C2311yescharacteristic
166C4×D4×C61C2311yescharacteristic
167#117×C61—22no—
168#117×C61—21no—
169#117×C61—21no—
170#117×C61—21no—
171#117×C61D411yescharacteristic
172C2×C22⋊C4×C61—22no—
173C2×C22⋊C4×C61—22no—
174C2×C22⋊C4×C61—22no—
175C2×C42×C61—21no—
176C2×C42×C61C2311yescharacteristic
177C24×C61—22no—
178#41×C61—22no—
179#41×C61—41no—
180#41×C61—81no—
181#41×C61—81no—
182C2×Q8×C61—22no—
183C2×Q8×C61—21no—
184C2×Q8×C61—81no—
185C2×Q8×C61—81no—
186C2×Q8×C61C2×D411yescharacteristic
187C2×Q8×C61C2×D411yescharacteristic
188C2×D4×C61—22no—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—42no—
196C2×D4×C61—42no—
197C2×D4×C61—81no—
198C2×D4×C61—81no—
199C2×D4×C61C2×D411yescharacteristic
200C2×D4×C61C2×D411yescharacteristic
201C2×D4×C61C2×D412yes—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—22no—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C2×C22⋊D61—41no—
213#11758222—42no—
214#11758222—42no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×C4×D61—41no—
219C2×Dic122—21no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61C2×D411yescharacteristic
230C4⋊C4×C61C2×D411yescharacteristic
231C4⋊C4×C61C2×D411yescharacteristic
232C4⋊C4×C61C2×D412yes—
233C4⋊C4×C61C2×D411yescharacteristic
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—21no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C42×C61—22no—
252C42×C61—21no—
253C42×C61—21no—
254C42×C61—21no—
255C42×C61—21no—
256C42×C61C2×D411yescharacteristic
257C42×C61C2×D411yescharacteristic
258C42×C61C2×D411yescharacteristic
259C42×C61C2411yescharacteristic
260#11758202—42no—
261#11758201—42no—
262#11758201—81no—
263#11758200—42no—
264#11758199—44no—
265#11758199—42no—
266#11758199—81no—
267#11758198—41no—
268#11758198—41no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271#11758194—42no—
272#11758194—81no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—42no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—22no—
283C23×C61—44no—
284C23×C61—82no—
285C23×C61—82no—
286C23×C61#12011yescharacteristic
287C22×D61—41no—
288Q8×C61—21no—
289Q8×C61—21no—
290Q8×C61—21no—
291Q8×C61—21no—
292Q8×C61—41no—
293Q8×C61—41no—
294Q8×C61—82no—
295D4×C61—21no—
296D4×C61—21no—
297D4×C61—21no—
298D4×C61—42no—
299D4×C61—42no—
300D4×C61—44no—
301D4×C61—41no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61—41no—
305D4×C61—81no—
306D4×C61—82no—
307D4×C61—82no—
308D4×C61AGL(1,ℤ/8)12yes—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—22no—
320C2×C4×C61—41no—
321C2×C4×C61—42no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—81no—
327C2×C4×C61—82no—
328C2×C4×C61—82no—
329C2×C4×C61—82no—
330C2×C4×C61#12011yescharacteristic
331C2×C4×C61#12011yescharacteristic
332C2×C4×C61#12011yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C22⋊D61—82no—
337C2×Dic61—41no—
338D244—42no—
339D244—41no—
340D244—41no—
341D244—41no—
342D244—41no—
343C4×D61—82no—
344Dic122—41no—
345Dic122—41no—
346#92418—22no—
347#92418—41no—
348#92418—41no—
349#92418—41no—
350#92418—41no—
351#92418—41no—
352#18594—611nomaximal, Sylow
353C22×C61—21no—
354C22×C61—22no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—41no—
363C22×C61—42no—
364C22×C61—41no—
365C22×C61—164no—
366C22×C61C2×#12011yescharacteristic
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—81no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61—41no—
377C4×C61—42no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
382C4×C61#57511yescharacteristic
383C4×C61#57611yescharacteristic
384C4×C61#57711yescharacteristic
385Dic61—81no—
386#3514D6111yescharacteristic, complemented
387#3251—611no—
388#3184—611no—
389#3035—611no—
390#1652—611no—
391#1651—611no—
392#1640—611no—
393#1639—611no—
394#1628—611no—
395#1627—611no—
396#1620—611no—
397#1619—611no—
398#1547—611no—
399#1489—611no—
400#1483—611no—
401C2×C61—41no—
402C2×C61—42no—
403C2×C61—82no—
404C2×C61—81no—
405C2×C61#300611yescharacteristic
406C2×C61#301211yescharacteristic
407C2×C61#301811yescharacteristic
408D61—161no—
409C2×#135—1221no—
410#559C2×D6111yescharacteristic
411#556C2×D6111yescharacteristic
412#555—21no—
413#551—22no—
414D4×Q8C2×D6111yescharacteristic
415#548—21no—
416#546—21no—
417#546—21no—
418D42C2×D6111yescharacteristic
419#542—21no—
420#538—22no—
421#532—611no—
422#532C2×D6111yescharacteristic
423#529—21no—
424#529C2×D6111yescharacteristic
425C2×#124—21no—
426#518—21no—
427C4×#41C2×D6111yescharacteristic
428#498—611no—
429#493—611no—
430#486—611no—
431#486—611no—
432#478—1221no—
433#475—611no—
434#474—611no—
435#469—1222no—
436#469—1221no—
437#468—1221no—
438#464—1221no—
439#463—1221no—
440#463—1221no—
441#462—611no—
442#461—611no—
443#460—611no—
444#460—611no—
445#459—611no—
446#459—611no—
447#442—1222no—
448#423—611no—
449C2×C4⋊C8—611no—
450#416—1221no—
451C4×M16—611no—
452#332—611no—
453#332—611no—
454#331—611no—
455#331—611no—
456Q8⋊C8—611no—
457Q8⋊C8—611no—
458Q8⋊C8—611no—
459Q8⋊C8—611no—
460D4⋊C8—611no—
461D4⋊C8—611no—
462D4⋊C8—611no—
463D4⋊C8—611no—
464C61#1859411yescharacteristic, complemented, Sylow
465C2×#41—21no—
466C2×#41—1221no—
467C2×#41C22⋊D6111yescharacteristic
468C22×Q8—21no—
469C22×D4—21no—
470C22×D4—21no—
471#135—2444no—
472C2×Q16—1221no—
473C2×SD16—1221no—
474C2×SD16—1221no—
475C2×SD16—1221no—
476C2×D8—1221no—
477C2×D8—1221no—
478C2×D8—1222no—
479C2×M16—1221no—
480C2×M16—1221no—
481C22×C8—1221no—
482C4⋊Q8—21no—
483C4⋊Q8—611no—
484C4⋊Q8C22×D6111yescharacteristic
485#127—611no—
486#127C22×D6111yescharacteristic
487#126—22no—
488#126—22no—
489#126—21no—
490#125C22⋊D6111yescharacteristic
491#124—22no—
492#124—22no—
493#124—22no—
494#124—21no—
495#124—21no—
496#124—21no—
497#124—21no—
498#124—1221no—
499#124C22⋊D6111yescharacteristic
500#123—22no—
501#123—22no—
502#123—22no—
503#123—21no—
504C22⋊Q8—22no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8C22⋊D6111yescharacteristic
509#121—22no—
510#121—22no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—1221no—
515#121—1221no—
516#121C22⋊D6111yescharacteristic
517#121C22⋊D6112yes—
518#120—22no—
519#120—22no—
520C4×Q8—21no—
521C4×Q8C22⋊D6111yescharacteristic
522C4×Q8C22×D6111yescharacteristic
523C4×Q8C22×D6111yescharacteristic
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4C22⋊D6111yescharacteristic
536C4×D4C22⋊D6112yes—
537C4×D4C22×D6111yescharacteristic
538C4×D4C22×D6111yescharacteristic
539#117—22no—
540#117—21no—
541#117—21no—
542#117—21no—
543#117C22⋊D6111yescharacteristic
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C42—21no—
548C2×C42C22×D6111yescharacteristic
549#107—1221no—
550#106—1222no—
551#106—1221no—
552C4⋊C8—611no—
553C4⋊C8—611no—
554C4⋊C8—611no—
555C4⋊C8—611no—
556C4⋊C8—1221no—
557C4⋊C8—1221no—
558#103—1221no—
559#103—1221no—
560#103—1221no—
561#102—1222no—
562#102—1221no—
563#102—1221no—
564#102—1221no—
565#102—1222no—
566#102—1221no—
567#102—1221no—
568#97—1221no—
569C4×C8—611no—
570C4×C8—611no—
571C24—22no—
572#41—22no—
573#41—41no—
574#41—81no—
575#41—81no—
576#41—2442no—
577#41—2442no—
578C2×Q8—22no—
579C2×Q8—21no—
580C2×Q8—81no—
581C2×Q8—81no—
582C2×Q8—1221no—
583C2×Q8C2×C22⋊D6111yescharacteristic
584C2×Q8C2×C22⋊D6111yescharacteristic
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—1221no—
599C2×D4—2441no—
600C2×D4C2×C22⋊D6111yescharacteristic
601C2×D4C2×C22⋊D6111yescharacteristic
602C2×D4C2×C22⋊D6112yes—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—2441no—
611C22×C4C2×C22⋊D6111yescharacteristic
612C22×C4C2×C22⋊D6111yescharacteristic
613C22×C4C2×C22⋊D6111yescharacteristic
614Q16—2442no—
615SD16—4881no—
616SD16—2442no—
617SD16—2442no—
618D8—4881no—
619D8—2444no—
620D8—2442no—
621M16—4881no—
622M16—2442no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—2442no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4C2×C22⋊D6111yescharacteristic
642C4⋊C4C2×C22⋊D6111yescharacteristic
643C4⋊C4C2×C22⋊D6111yescharacteristic
644C4⋊C4C2×C22⋊D6112yes—
645C4⋊C4C2×C22⋊D6111yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—2441no—
664C22⋊C4—2441no—
665C42—22no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42C2×C22⋊D6111yescharacteristic
671C42C2×C22⋊D6111yescharacteristic
672C42C2×C22⋊D6111yescharacteristic
673C42C23×D6111yescharacteristic
674C23—21no—
675C23—21no—
676C23—22no—
677C23—44no—
678C23—82no—
679C23—82no—
680C23—2441no—
681C23#1451974611yescharacteristic
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—41no—
687Q8—41no—
688Q8—82no—
689Q8—2441no—
690Q8—2441no—
691D4—21no—
692D4—21no—
693D4—21no—
694D4—42no—
695D4—42no—
696D4—44no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—81no—
702D4—82no—
703D4—82no—
704D4—4882no—
705D4—2442no—
706D4—2441no—
707D4—2441no—
708D4—2441no—
709D4—2441no—
710D4#1451980212yes—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—81no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—4882no—
733C2×C4—2441no—
734C2×C4#1451974611yescharacteristic
735C2×C4#1451974611yescharacteristic
736C2×C4#1451974611yescharacteristic
737C2×C4C22×C22⋊D6111yescharacteristic
738C2×C4C22×C22⋊D6111yescharacteristic
739C2×C4C22×C22⋊D6111yescharacteristic
740C8—1222no—
741C8—2441no—
742C8—2441no—
743C8—2441no—
744C8—2441no—
745C8—2441no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—164no—
759C22—4881no—
760C22—4881no—
761C22—4881no—
762C22C2×#1451974611yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—4881no—
775C4C2×#1451980211yescharacteristic
776C4#1684056011yescharacteristic
777C4#1684056511yescharacteristic
778C4#1684057311yescharacteristic
779C2—41no—
780C2—42no—
781C2—81no—
782C2—82no—
783C2—9761no—
784C2#2145507111yescharacteristic
785C2#2145512311yescharacteristic
786C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3514C2
socleC22×C61C2×#120
hypercenter#3514D61
hypocenterC61#18594
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3514

Complements

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

NH ≅ G/Ntype
1. #21457181C2semidirect
2. #21456553C2semidirect
3. #21455274C2semidirect
4. #21445089C2semidirect
5. #21445082C2semidirect
6. #21445005C2semidirect
7. #21444998C2semidirect
8. #21444929C2semidirect
9. #21444922C2semidirect
10. #21444878C2semidirect
11. #21444873C2semidirect
12. #21444496C2semidirect
13. #21444258C2semidirect
14. #21444232C2semidirect
15. C61×#3514C2semidirect
17. #16840312C22semidirect
18. #16840158C22semidirect
20. #16840110C22semidirect
23. #16840047C22semidirect
31. #16839972C22semidirect
33. #16839962C22semidirect
34. #16839962C22semidirect
38. #16839786C22semidirect
39. C2×C4⋊#92418C22semidirect
41. C4×#11758194C22semidirect
42. #16839508C22semidirect
43. #16839508C22semidirect
46. Q8⋊#92418C22semidirect
47. Q8⋊#92418C22semidirect
48. Q8⋊#92418C22semidirect
49. Q8⋊#92418C22semidirect
386. #3514D61semidirect
464. C61#18594semidirect

Maximal subgroups

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

subgroupindex
#214571812
#214565532
#214552742
#214450892
#214450822
#214450052
#214449982
#214449292
#214449222
#214448782
#214448732
#214444962
#214442582
#214442322
C61×#35142
#1859461