Finite Group Databasebeta

← #29657109

Subgroups — #29657109

Order 15616.

1084 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457145C211yesmaximal, characteristic, complemented
2#21456245C211yesmaximal, characteristic, complemented
3#21455910C211yesmaximal, characteristic, complemented
4#21444964C211yesmaximal, characteristic, complemented
5#21444953C211yesmaximal, characteristic, complemented
6#21444946C211yesmaximal, characteristic, complemented
7#21444935C211yesmaximal, characteristic, complemented
8#21444902C211yesmaximal, characteristic, complemented
9#21444891C211yesmaximal, characteristic, complemented
10#21444884C211yesmaximal, characteristic, complemented
11#21444873C211yesmaximal, characteristic, complemented
12#21444514C211yesmaximal, characteristic, complemented
13#21444279C211yesmaximal, characteristic, complemented
14C2×D4⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3519C211yesmaximal, characteristic, complemented
16C2×#14519797—22no—
17#16840312C2211yescharacteristic, complemented
18#16840144—22no—
19#16840141C2211yescharacteristic, complemented
20#16840138C2211yescharacteristic, complemented
21#16840136C2211yescharacteristic, complemented
22#16840134C2211yescharacteristic, complemented
23#16840080—21no—
24#16840059—21no—
25#16840057C2211yescharacteristic, complemented
26#16840052C2211yescharacteristic
27#16840052C2211yescharacteristic, complemented
28#16840052C2211yescharacteristic, complemented
29#16839996—21no—
30#16839993—21no—
31#16839974—21no—
32#16839962C2211yescharacteristic, complemented
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic, complemented
35#16839957C2211yescharacteristic, complemented
36#16839896—21no—
37#16839872—21no—
38#16839872—21no—
39#16839819C2211yescharacteristic, complemented
40C2×C4⋊#92418C2211yescharacteristic, complemented
41C2×C4×#92418C2211yescharacteristic, complemented
42#16839511C2211yescharacteristic, complemented
43#16839511C2211yescharacteristic, complemented
44#16839506C2211yescharacteristic, complemented
45#16839506C2211yescharacteristic, complemented
46Q8⋊#92418C2211yescharacteristic, complemented
47Q8⋊#92418C2211yescharacteristic, complemented
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic, complemented
51D4⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54C61×#555C2211yescharacteristic
55C61×#554C2211yescharacteristic
56C61×#553—21no—
57C61×#553—21no—
58C61×#550C2211yescharacteristic
59C61×#546—22no—
60C61×#546—21no—
61D42×C61—21no—
62D42×C61C2211yescharacteristic
63C61×#540—21no—
64C61×#538—22no—
65C61×#532C2211yescharacteristic
66C61×#529C2211yescharacteristic
67C61×#525—21no—
68C2×#121×C61—21no—
69C61×#518—21no—
70C2×C4×D4×C61C2211yescharacteristic
71C2×#11758222—21no—
72#14519797—48no—
73C2×#11758202—22no—
74C2×#11758200—22no—
75C2×#11758201—22no—
76C2×#11758201—21no—
77C2×#11758199—21no—
78C2×#11758199—21no—
79C2×#11758199—22no—
80C2×#11758199—21no—
81C22×#92418—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—21no—
93#14519708—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519701—21no—
100#14519698—21no—
101#14519698—21no—
102#14519698—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107C22⋊#92418—21no—
108#14519688—21no—
109C4×#92418—21no—
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C2×#41×C61—21no—
113C2×#41×C61D412yes—
114C22×D4×C61—22no—
115C22×D4×C61—21no—
116C22×D4×C61—21no—
117C22×D4×C61D411yescharacteristic
118C23×C4×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120#127×C61—21no—
121#127×C61C2311yescharacteristic
122#126×C61—22no—
123#126×C61—21no—
124#125×C61—21no—
125#125×C61D411yescharacteristic
126#124×C61—22no—
127#124×C61D412yes—
128#124×C61D411yescharacteristic
129#123×C61—22no—
130#123×C61—22no—
131#123×C61—22no—
132#123×C61—21no—
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61D411yescharacteristic
136#121×C61—22no—
137#121×C61—22no—
138#121×C61—22no—
139#121×C61—22no—
140#121×C61—22no—
141#121×C61—21no—
142#121×C61—21no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61—21no—
148#121×C61D411yescharacteristic
149#120×C61—22no—
150#120×C61—22no—
151#120×C61—22no—
152C4×Q8×C61C2311yescharacteristic
153C4×D4×C61—22no—
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×C61D411yescharacteristic
164C4×D4×C61D411yescharacteristic
165C4×D4×C61C2311yescharacteristic
166C4×D4×C61C2311yescharacteristic
167C4×D4×C61C2311yescharacteristic
168#117×C61—21no—
169#117×C61—21no—
170#117×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61—22no—
174C2×C22⋊C4×C61—22no—
175C2×C22⋊C4×C61—21no—
176C2×C42×C61C2311yescharacteristic
177C24×C61—22no—
178C24×C61—21no—
179#41×C61—44no—
180#41×C61—81no—
181#41×C61—81no—
182C2×Q8×C61C2×D411yescharacteristic
183C2×Q8×C61C2×D412yes—
184C2×D4×C61—22no—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—41no—
196C2×D4×C61—42no—
197C2×D4×C61—42no—
198C2×D4×C61—81no—
199C2×D4×C61—81no—
200C2×D4×C61—84no—
201C2×D4×C61C2×D411yescharacteristic
202C2×D4×C61C2×D411yescharacteristic
203C2×D4×C61C2×D411yescharacteristic
204C2×D4×C61C2×D412yes—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—22no—
213C22×C4×C61—21no—
214C22×C4×C61—81no—
215C22×C4×C61—81no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C2×C22⋊D61—41no—
220#11758222—44no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×C4×D61—41no—
225C2×Dic122—21no—
226C4⋊C4×C61—22no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2×D411yescharacteristic
236C4⋊C4×C61C2×D411yescharacteristic
237C4⋊C4×C61C2×D411yescharacteristic
238C4⋊C4×C61C2×D411yescharacteristic
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—21no—
247C22⋊C4×C61—21no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C42×C61—22no—
256C42×C61—21no—
257C42×C61C2×D411yescharacteristic
258C42×C61C2×D411yescharacteristic
259C42×C61C2×D411yescharacteristic
260C42×C61C2411yescharacteristic
261#11758202—44no—
262#11758201—44no—
263#11758201—81no—
264#11758200—44no—
265#11758199—44no—
266#11758199—42no—
267#11758199—42no—
268#11758199—81no—
269#11758198—41no—
270#11758198—41no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C2×#92418—24no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—81no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—22no—
285C23×C61—42no—
286C23×C61—44no—
287C23×C61—42no—
288C23×C61—81no—
289C23×C61—82no—
290C23×C61—82no—
291C23×C61#12011yescharacteristic
292C22×D61—41no—
293Q8×C61—21no—
294Q8×C61—21no—
295Q8×C61—42no—
296D4×C61—21no—
297D4×C61—21no—
298D4×C61—21no—
299D4×C61—21no—
300D4×C61—21no—
301D4×C61—42no—
302D4×C61—42no—
303D4×C61—44no—
304D4×C61—42no—
305D4×C61—44no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—82no—
311D4×C61—82no—
312D4×C61—82no—
313D4×C61—82no—
314D4×C61#13512yescomplemented
315C2×C4×C61—22no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—81no—
333C2×C4×C61—81no—
334C2×C4×C61—82no—
335C2×C4×C61—81no—
336C2×C4×C61—82no—
337C2×C4×C61—82no—
338C2×C4×C61#12011yescharacteristic
339C2×C4×C61#12011yescharacteristic
340C2×C4×C61#12011yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C22⋊D61—82no—
345C2×Dic61—41no—
346D244—42no—
347D244—41no—
348D244—41no—
349D244—41no—
350D244—41no—
351C4×D61—82no—
352Dic122—42no—
353#92418—22no—
354#92418—22no—
355#92418—41no—
356#92418—41no—
357#92418—41no—
358#92418—41no—
359#18618—611nomaximal, Sylow
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—22no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—42no—
368C22×C61—41no—
369C22×C61—42no—
370C22×C61—41no—
371C22×C61—42no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—84no—
375C22×C61—164no—
376C22×C61#45312yes—
377C22×C61C2×#12011yescharacteristic
378C2×D61—81no—
379C2×D61—81no—
380C2×D61—81no—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—42no—
391C4×C61C2×#13511yescharacteristic
392C4×C61#57511yescharacteristic
393C4×C61#57611yescharacteristic
394C4×C61#57711yescharacteristic
395Dic61—81no—
396#3519D6111yescharacteristic, complemented
397#3247—611no—
398#3147—611no—
399#3109—611no—
400#1634—611no—
401#1632—611no—
402#1631—611no—
403#1629—611no—
404#1624—611no—
405#1622—611no—
406#1621—611no—
407#1619—611no—
408#1551—611no—
409#1494—611no—
410C2×D4⋊C8—611no—
411C2×C61—22no—
412C2×C61—42no—
413C2×C61—81no—
414C2×C61—82no—
415C2×C61—81no—
416C2×C61#300211yescharacteristic
417C2×C61#301211yescharacteristic
418C2×C61C2×#45311yescharacteristic
419D61—161no—
420C2×#135—1222no—
421#555C2×D6111yescharacteristic
422#554C2×D6111yescharacteristic
423#553—21no—
424#553—21no—
425#550C2×D6111yescharacteristic
426#546—22no—
427#546—21no—
428D42—21no—
429D42C2×D6111yescharacteristic
430#540—21no—
431#538—22no—
432#532—611no—
433#532C2×D6111yescharacteristic
434#529C2×D6111yescharacteristic
435#525—21no—
436C2×#121—21no—
437#518—21no—
438C2×C4×D4C2×D6111yescharacteristic
439#495—1222no—
440#494—611no—
441#493—611no—
442#492—611no—
443#492—611no—
444#481—1221no—
445#478—1221no—
446#477—611no—
447#476—611no—
448#476—611no—
449#476—611no—
450#466—1221no—
451#465—1221no—
452#463—1221no—
453#460—611no—
454#459—611no—
455#459—611no—
456#459—611no—
457#447—1221no—
458#442—1221no—
459#442—1221no—
460#432—611no—
461C2×C4⋊C8—611no—
462C2×C4×C8—611no—
463#333—611no—
464#333—611no—
465#331—611no—
466#331—611no—
467Q8⋊C8—611no—
468Q8⋊C8—611no—
469D4⋊C8—611no—
470D4⋊C8—611no—
471D4⋊C8—611no—
472D4⋊C8—611no—
473D4⋊C8—611no—
474D4⋊C8—611no—
475C61#1861811yescharacteristic, complemented, Sylow
476C2×#41—21no—
477C2×#41—1221no—
478C2×#41C22⋊D6112yes—
479C22×D4—22no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4C22⋊D6111yescharacteristic
483C23×C4—21no—
484#135—2448no—
485C2×Q16—1222no—
486C2×SD16—1221no—
487C2×SD16—1222no—
488C2×SD16—1222no—
489C2×D8—1221no—
490C2×D8—1222no—
491C2×D8—1221no—
492C2×D8—1221no—
493C22×C8—1221no—
494C22×C8—1221no—
495C4⋊Q8—611no—
496C4⋊Q8C22×D6111yescharacteristic
497#127—21no—
498#127—611no—
499#127C22×D6111yescharacteristic
500#126—22no—
501#126—21no—
502#125—21no—
503#125C22⋊D6111yescharacteristic
504#124—22no—
505#124—1221no—
506#124C22⋊D6111yescharacteristic
507#124C22⋊D6112yes—
508#123—22no—
509#123—22no—
510#123—22no—
511#123—21no—
512C22⋊Q8—21no—
513C22⋊Q8—22no—
514C22⋊Q8C22⋊D6111yescharacteristic
515#121—22no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—21no—
520#121—22no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—1221no—
528#121—1221no—
529#121C22⋊D6111yescharacteristic
530#120—22no—
531#120—22no—
532#120—22no—
533C4×Q8C22×D6111yescharacteristic
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4C22⋊D6111yescharacteristic
547C4×D4C22⋊D6111yescharacteristic
548C4×D4C22×D6111yescharacteristic
549C4×D4C22×D6111yescharacteristic
550C4×D4C22×D6111yescharacteristic
551#117—21no—
552#117—21no—
553#117—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4C22⋊D6111yescharacteristic
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—21no—
559C2×C42C22×D6111yescharacteristic
560#107—1221no—
561#106—1221no—
562#106—1221no—
563#106—1221no—
564C4⋊C8—611no—
565C4⋊C8—611no—
566C4⋊C8—611no—
567C4⋊C8—611no—
568C4⋊C8—1221no—
569#103—1221no—
570#102—1221no—
571#102—1221no—
572#102—1221no—
573#102—1221no—
574#102—1221no—
575#102—1221no—
576#102—1221no—
577C22⋊C8—1221no—
578#97—1221no—
579C4×C8—611no—
580C4×C8—611no—
581C4×C8—1221no—
582C24—22no—
583C24—21no—
584#41—44no—
585#41—81no—
586#41—81no—
587#41—2444no—
588C2×Q8—1221no—
589C2×Q8C2×C22⋊D6111yescharacteristic
590C2×Q8C2×C22⋊D6112yes—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—41no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—84no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—2441no—
612C2×D4C2×C22⋊D6111yescharacteristic
613C2×D4C2×C22⋊D6111yescharacteristic
614C2×D4C2×C22⋊D6111yescharacteristic
615C2×D4C2×C22⋊D6112yes—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—81no—
626C22×C4—81no—
627C22×C4—2441no—
628C22×C4C2×C22⋊D6111yescharacteristic
629C22×C4C2×C22⋊D6111yescharacteristic
630C22×C4C2×C22⋊D6111yescharacteristic
631Q16—2444no—
632SD16—4881no—
633SD16—2444no—
634SD16—2444no—
635D8—4881no—
636D8—2444no—
637D8—2442no—
638D8—2442no—
639C2×C8—1224no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—4881no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4C2×C22⋊D6111yescharacteristic
659C4⋊C4C2×C22⋊D6111yescharacteristic
660C4⋊C4C2×C22⋊D6111yescharacteristic
661C4⋊C4C2×C22⋊D6111yescharacteristic
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—22no—
678C22⋊C4—2441no—
679C22⋊C4—2441no—
680C42—22no—
681C42—21no—
682C42C2×C22⋊D6111yescharacteristic
683C42C2×C22⋊D6111yescharacteristic
684C42C2×C22⋊D6111yescharacteristic
685C42C23×D6111yescharacteristic
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—42no—
691C23—44no—
692C23—42no—
693C23—81no—
694C23—82no—
695C23—82no—
696C23—2441no—
697C23#1451974611yescharacteristic
698Q8—21no—
699Q8—21no—
700Q8—42no—
701Q8—2442no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—42no—
708D4—42no—
709D4—44no—
710D4—42no—
711D4—44no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—4882no—
721D4—2442no—
722D4—2441no—
723D4—2441no—
724D4—2441no—
725D4—2441no—
726D4#1451979712yescomplemented
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—82no—
747C2×C4—81no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4—4882no—
751C2×C4—2441no—
752C2×C4#1451974611yescharacteristic
753C2×C4#1451974611yescharacteristic
754C2×C4#1451974611yescharacteristic
755C2×C4C22×C22⋊D6111yescharacteristic
756C2×C4C22×C22⋊D6111yescharacteristic
757C2×C4C22×C22⋊D6111yescharacteristic
758C8—1222no—
759C8—1222no—
760C8—2441no—
761C8—2441no—
762C8—2441no—
763C8—2441no—
764C22—21no—
765C22—21no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—84no—
779C22—164no—
780C22—4881no—
781C22—4881no—
782C22—4881no—
783C22#1683993012yes—
784C22C2×#1451974611yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—42no—
794C4—41no—
795C4—4881no—
796C4C2×#1451979711yescharacteristic
797C4#1684056011yescharacteristic
798C4#1684056511yescharacteristic
799C4#1684057311yescharacteristic
800C2—22no—
801C2—42no—
802C2—81no—
803C2—81no—
804C2—82no—
805C2—9761no—
806C2#2145503711yescharacteristic
807C2#2145512311yescharacteristic
808C2C2×#1683993011yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3519C2
socleC22×C61C2×#120
hypercenter#3519D61
hypocenterC61#18618
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3519

Complements

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

NH ≅ G/Ntype
1. #21457145C2semidirect
2. #21456245C2semidirect
3. #21455910C2semidirect
4. #21444964C2semidirect
5. #21444953C2semidirect
6. #21444946C2semidirect
7. #21444935C2semidirect
8. #21444902C2semidirect
9. #21444891C2semidirect
10. #21444884C2semidirect
11. #21444873C2semidirect
12. #21444514C2semidirect
13. #21444279C2semidirect
14. C2×D4⋊#92418C2semidirect
15. C61×#3519C2semidirect
17. #16840312C22semidirect
19. #16840141C22semidirect
20. #16840138C22semidirect
21. #16840136C22semidirect
22. #16840134C22semidirect
25. #16840057C22semidirect
27. #16840052C22semidirect
28. #16840052C22semidirect
32. #16839962C22semidirect
34. #16839957C22semidirect
35. #16839957C22semidirect
39. #16839819C22semidirect
40. C2×C4⋊#92418C22semidirect
41. C2×C4×#92418C22semidirect
42. #16839511C22semidirect
43. #16839511C22semidirect
44. #16839506C22semidirect
45. #16839506C22semidirect
46. Q8⋊#92418C22semidirect
47. Q8⋊#92418C22semidirect
50. D4⋊#92418C22semidirect
51. D4⋊#92418C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
314. D4×C61#135semidirect
396. #3519D61semidirect
475. C61#18618semidirect
726. D4#14519797semidirect

Maximal subgroups

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

subgroupindex
#214571452
#214562452
#214559102
#214449642
#214449532
#214449462
#214449352
#214449022
#214448912
#214448842
#214448732
#214445142
#214442792
C2×D4⋊#924182
C61×#35192
#1861861