Finite Group Databasebeta

← #29690337

Subgroups — #29690337

Order 15616.

894 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454263C211yesmaximal, characteristic
2#21454262C211yesmaximal, characteristic
3C2×#16839727C211yesmaximal, characteristic
4#21446026C211yesmaximal, characteristic, complemented
5#21446025C211yesmaximal, characteristic, complemented
6#21446025C211yesmaximal, characteristic, complemented
7#21446024C211yesmaximal, characteristic, complemented
8#21446023C211yesmaximal, characteristic, complemented
9#21446022C211yesmaximal, characteristic, complemented
10#21446022C211yesmaximal, characteristic, complemented
11#21445860C211yesmaximal, characteristic, complemented
12#21445858C211yesmaximal, characteristic, complemented
13#21445856C211yesmaximal, characteristic, complemented
14#21445854C211yesmaximal, characteristic, complemented
15C61×#1855C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22C2×#14519713C2211yescharacteristic
23C2×#14519713C2211yescharacteristic
24C2×#14519712C2211yescharacteristic
25C2×#14519712C2211yescharacteristic
26C2×#14519712C2211yescharacteristic
27C2×#14519712C2211yescharacteristic
28#16839730—21no—
29#16839730—21no—
30#16839728—21no—
31#16839728—21no—
32#16839727—21no—
33#16839727—21no—
34#16839727—21no—
35#16839727—21no—
36#16839727C412yes—
37#16839727C412yes—
38#16839727C412yes—
39#16839727C412yes—
40#16839726C2211yescharacteristic
41#16839725C2211yescharacteristic
42#16839725C2211yescharacteristic
43#16839725C2211yescharacteristic
44#16839725C2211yescharacteristic
45#16839725C2211yescharacteristic
46#16839725C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48C2×#14519689C2211yescharacteristic
49C2×#14519689C2211yescharacteristic
50#16839527C2211yescharacteristic
51#16839527C2211yescharacteristic
52#16839526C2211yescharacteristic
53#16839526C2211yescharacteristic
54#16839526C2211yescharacteristic
55#16839526C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×#108×C61C2211yescharacteristic
58C2×#108×C61C2211yescharacteristic
59C61×#407C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#341C2211yescharacteristic
62C61×#341C2211yescharacteristic
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C411yescharacteristic
68C2×#11758222C2×C411yescharacteristic
69C2×#11758222C2×C411yescharacteristic
70C2×#11758222C2×C411yescharacteristic
71C2×#11758222D411yescharacteristic
72C2×#11758222D411yescharacteristic
73C2×#11758222D411yescharacteristic
74C2×#11758222D411yescharacteristic
75C22×Dic122Q811yescharacteristic
76C22×D244Q811yescharacteristic
77C22×C22⋊D61Q811yescharacteristic
78C22×C22⋊D61Q811yescharacteristic
79C22×C4×D61C2311yescharacteristic
80C22×C4×D61C2311yescharacteristic
81C2×#11758194—21no—
82C2×#11758194—41no—
83C2×#11758194—41no—
84C2×#11758194C2311yescharacteristic
85C2×#11758194C2311yescharacteristic
86C2×#11758194C2311yescharacteristic
87C2×#11758194C2311yescharacteristic
88C2×#11758189—21no—
89C2×#11758189—21no—
90C2×#11758189—41no—
91C2×#11758189—41no—
92C2×#11758189C2×C412yes—
93C2×#11758189C2×C412yes—
94M16×D61—41no—
95M16×D61—41no—
96M16×D61—41no—
97M16×D61—41no—
98C22×#92418—21no—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C2×C8×D61—21no—
102C2×C8×D61—21no—
103C2×C8×D61—41no—
104C2×C8×D61—41no—
105C2×C8×D61C2×C412yes—
106C2×C8×D61C2×C412yes—
107#14519713—41no—
108#14519713—41no—
109#14519712—41no—
110#14519712—41no—
111#14519712—41no—
112#14519712—41no—
113C22⋊#92418—21no—
114C22⋊#92418—21no—
115C22⋊#92418C2×C412yes—
116C22⋊#92418C2×C412yes—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689—21no—
124#14519689—21no—
125#14519689—21no—
126#14519689—21no—
127#14519689—21no—
128#14519689—21no—
129#14519689C2×C412yes—
130#14519689C2×C412yes—
131#14519689C2×C412yes—
132#14519689C2×C412yes—
133C23×C4×C61C2311yescharacteristic
134C2×M16×C61—21no—
135C2×M16×C61—41no—
136C2×M16×C61—41no—
137C2×M16×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C2×M16×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141C22×C8×C61—21no—
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144#108×C61—41no—
145#108×C61—41no—
146C22⋊C8×C61—21no—
147C22⋊C8×C61—21no—
148C22⋊C8×C61C2×C412yes—
149C22⋊C8×C61C2×C412yes—
150C24×C61C2×Q811yescharacteristic
151C23×D61C2×Q811yescharacteristic
152C23×D61C2×Q811yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×Q811yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C2×C22⋊D61—41no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—41no—
166C2×C22⋊D61—41no—
167C2×C22⋊D61C4⋊C411yescharacteristic
168C2×C22⋊D61C4⋊C411yescharacteristic
169C2×C22⋊D61C4⋊C411yescharacteristic
170C2×C22⋊D61C4⋊C411yescharacteristic
171C2×C22⋊D61C4⋊C411yescharacteristic
172C2×C22⋊D61C4⋊C411yescharacteristic
173C2×C22⋊D61C4⋊C411yescharacteristic
174C2×C22⋊D61C4⋊C411yescharacteristic
175C22×Dic61C2×Q811yescharacteristic
176C22×Dic61C2×Q811yescharacteristic
177#11758222—41no—
178#11758222—41no—
179#11758222—41no—
180#11758222—41no—
181#11758222—41no—
182#11758222—41no—
183#11758222—41no—
184#11758222—41no—
185#11758222—41no—
186#11758222—41no—
187#11758222—41no—
188#11758222—41no—
189#11758222—41no—
190#11758222—41no—
191#11758222—41no—
192#11758222—41no—
193C2×D244—41no—
194C2×D244—41no—
195C2×D244C4⋊C411yescharacteristic
196C2×D244C4⋊C411yescharacteristic
197C2×D244C4⋊C411yescharacteristic
198C2×D244C4⋊C411yescharacteristic
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61C22×C411yescharacteristic
208C2×C4×D61C22×C411yescharacteristic
209C2×C4×D61C22×C411yescharacteristic
210C2×C4×D61C22×C411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×Dic122—41no—
216C2×Dic122—41no—
217C2×Dic122C4⋊C411yescharacteristic
218C2×Dic122C4⋊C411yescharacteristic
219C2×Dic122C4⋊C411yescharacteristic
220C2×Dic122C4⋊C411yescharacteristic
221M16×C61—21no—
222M16×C61—21no—
223M16×C61—21no—
224M16×C61—21no—
225M16×C61—21no—
226M16×C61—21no—
227M16×C61—21no—
228M16×C61—21no—
229M16×C61—42no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—42no—
239C2×C8×C61C22×C412yes—
240C2×C8×C61C22×C412yes—
241#11758194—21no—
242#11758194—21no—
243#11758194—21no—
244#11758194—21no—
245#11758194—21no—
246#11758194—21no—
247#11758194—21no—
248#11758194—21no—
249#11758194—42no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—42no—
259C2×#92418C22×C412yes—
260C2×#92418C22×C412yes—
261#11758189—42no—
262#11758189—42no—
263#11758189—42no—
264#11758189—42no—
265C8×D61—42no—
266C8×D61—42no—
267C8×D61—42no—
268C8×D61—42no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61C2×C4⋊C411yescharacteristic
274C23×C61C2×C4⋊C411yescharacteristic
275C23×C61C22×Q811yescharacteristic
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61C2×C4⋊C411yescharacteristic
285C22×D61C2×C4⋊C411yescharacteristic
286C22×D61C2×C4⋊C411yescharacteristic
287C22×D61C2×C4⋊C411yescharacteristic
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61C2×C4⋊C411yescharacteristic
299C2×C4×C61C2×C4⋊C411yescharacteristic
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C22⋊D61—41no—
307C22⋊D61—41no—
308C22⋊D61—41no—
309C22⋊D61—41no—
310C22⋊D61—41no—
311C22⋊D61—41no—
312C22⋊D61—41no—
313C22⋊D61—41no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61C2×C4⋊C411yescharacteristic
319C2×Dic61C2×C4⋊C411yescharacteristic
320C2×Dic61C2×C4⋊C411yescharacteristic
321C2×Dic61C2×C4⋊C411yescharacteristic
322D244—41no—
323D244—41no—
324D244—41no—
325D244—41no—
326C4×D61—21no—
327C4×D61—21no—
328C4×D61—21no—
329C4×D61—21no—
330C4×D61—21no—
331C4×D61—21no—
332C4×D61—21no—
333C4×D61—21no—
334C4×D61—21no—
335C4×D61—21no—
336C4×D61—21no—
337C4×D61—21no—
338C4×D61—21no—
339C4×D61—21no—
340C4×D61—21no—
341C4×D61—21no—
342Dic122—41no—
343Dic122—41no—
344Dic122—41no—
345Dic122—41no—
346C8×C61—22no—
347C8×C61—22no—
348C8×C61—41no—
349C8×C61—41no—
350C8×C61—41no—
351C8×C61—41no—
352#92418—22no—
353#92418—22no—
354#92418—41no—
355#92418—41no—
356#92418—41no—
357#92418—41no—
358#21950—611nomaximal, Sylow
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61C22×C4⋊C411yescharacteristic
370C22×C61#54311yescharacteristic
371C22×C61#54311yescharacteristic
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—81no—
387C2×D61—81no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61#51811yescharacteristic
391C4×C61#51811yescharacteristic
392C4×C61#53411yescharacteristic
393C4×C61#53411yescharacteristic
394Dic61—21no—
395Dic61—21no—
396Dic61—21no—
397Dic61—21no—
398#2879—611no—
399#2879—611no—
400C2×#408—611no—
401#1855—611no—
402#1855—611no—
403#1855—611no—
404#1855—611no—
405#1855—611no—
406#1855—611no—
407#1855—611no—
408#1855D6111yescharacteristic, complemented
409#1811—611no—
410#1811—611no—
411#1810—611no—
412#1810—611no—
413C2×C61—21no—
414C2×C61—21no—
415C2×C61—41no—
416C2×C61—41no—
417C2×C61#231511yescharacteristic
418C2×C61#291611yescharacteristic
419C2×C61#291611yescharacteristic
420D61—41no—
421D61—41no—
422D61—41no—
423D61—41no—
424C22×#41—611no—
425C22×M16—611no—
426C22×M16—611no—
427C22×M16—611no—
428C22×M16—611no—
429C22×M16C2×D6111yescharacteristic
430C23×C8—611no—
431C2×#108—611no—
432C2×#108—611no—
433C2×#108—611no—
434C2×#108—611no—
435C2×#108—611no—
436C2×#108—611no—
437C2×#108C2×D6111yescharacteristic
438C2×#108C2×D6111yescharacteristic
439#408—612no—
440#408—612no—
441#408—612no—
442#408—612no—
443#408—1221no—
444#408—1221no—
445#408—1221no—
446#408—1221no—
447#408—1221no—
448#408—1221no—
449#408—1221no—
450#408—1221no—
451#407—611no—
452#407—611no—
453#407—611no—
454#407—611no—
455#407—611no—
456#407—611no—
457#407—611no—
458#407C2×D6111yescharacteristic
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8C2×D6111yescharacteristic
463#341—611no—
464#341—611no—
465#341—611no—
466#341—611no—
467#341—611no—
468#341—611no—
469#341C2×D6111yescharacteristic
470#341C2×D6111yescharacteristic
471C61#2195011yescharacteristic, complemented, Sylow
472C2×#41—611no—
473C2×#41—611no—
474C2×#41—611no—
475C2×#41—611no—
476C2×#41—611no—
477C2×#41—611no—
478C2×#41—611no—
479C2×#41—611no—
480C2×#41—2441no—
481C2×#41—2441no—
482C2×#41—2441no—
483C2×#41—2441no—
484C22×Q8—611no—
485C22×D4—611no—
486C22×D4—611no—
487C22×D4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4C22×D6111yescharacteristic
491C2×M16—21no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—612no—
495C2×M16—612no—
496C2×M16—611no—
497C2×M16—611no—
498C2×M16—611no—
499C2×M16—611no—
500C2×M16—1221no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16—2441no—
504C2×M16—2441no—
505C2×M16—2441no—
506C2×M16—2441no—
507C2×M16—2441no—
508C2×M16—2441no—
509C2×M16—2441no—
510C2×M16—2441no—
511C2×M16C22×D6111yescharacteristic
512C2×M16C22×D6111yescharacteristic
513C2×M16C22×D6111yescharacteristic
514C2×M16C22×D6111yescharacteristic
515C22×C8—21no—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8—612no—
519C22×C8—612no—
520C22×C8—1221no—
521C22×C8—1221no—
522C22×C8—1221no—
523C22×C8—2441no—
524C22×C8—2441no—
525C22×C8C22×D6111yescharacteristic
526C22×C8C22×D6111yescharacteristic
527#108—41no—
528#108—41no—
529#108—2441no—
530#108—2441no—
531#108—2441no—
532#108—2441no—
533#108—2441no—
534#108—2441no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—612no—
538C22⋊C8—612no—
539C22⋊C8—612no—
540C22⋊C8—612no—
541C22⋊C8—612no—
542C22⋊C8—612no—
543C22⋊C8—1221no—
544C22⋊C8—1221no—
545C22⋊C8—1221no—
546C22⋊C8—1221no—
547C22⋊C8—1221no—
548C22⋊C8—1221no—
549C22⋊C8—1221no—
550C22⋊C8—1221no—
551C22⋊C8—1221no—
552C22⋊C8—1221no—
553C22⋊C8—1221no—
554C22⋊C8—1221no—
555C22⋊C8—1221no—
556C22⋊C8—1221no—
557C22⋊C8C4×D6112yes—
558C22⋊C8C4×D6112yes—
559C24—611no—
560C24—611no—
561C24Q8×D6111yescharacteristic
562#41—2441no—
563#41—2441no—
564#41—2441no—
565#41—2441no—
566#41—2441no—
567#41—2441no—
568#41—2441no—
569#41—2441no—
570#41—2441no—
571#41—2441no—
572#41—2441no—
573#41—2441no—
574#41—2441no—
575#41—2441no—
576#41—2441no—
577#41—2441no—
578C2×Q8—611no—
579C2×Q8—611no—
580C2×Q8—611no—
581C2×Q8—611no—
582C2×Q8—2441no—
583C2×Q8—2441no—
584C2×D4—611no—
585C2×D4—611no—
586C2×D4—611no—
587C2×D4—611no—
588C2×D4—611no—
589C2×D4—611no—
590C2×D4—611no—
591C2×D4—611no—
592C2×D4—611no—
593C2×D4—611no—
594C2×D4—611no—
595C2×D4—611no—
596C2×D4—2441no—
597C2×D4—2441no—
598C2×D4—2441no—
599C2×D4—2441no—
600C2×D4—2441no—
601C2×D4—2441no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4C2×C4×D6111yescharacteristic
625C22×C4C2×C4×D6111yescharacteristic
626C22×C4D4×D6111yescharacteristic
627C22×C4D4×D6111yescharacteristic
628C22×C4Q8×D6111yescharacteristic
629C22×C4C23×D6111yescharacteristic
630M16—21no—
631M16—21no—
632M16—21no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—42no—
639M16—1221no—
640M16—1221no—
641M16—1221no—
642M16—1221no—
643M16—1221no—
644M16—1221no—
645M16—1221no—
646M16—1221no—
647M16—2442no—
648M16—2442no—
649M16—2442no—
650M16—2442no—
651M16—2442no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—42no—
661C2×C8—612no—
662C2×C8—612no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—2442no—
672C2×C8—2442no—
673C2×C8—2442no—
674C2×C8—2442no—
675C2×C8—2442no—
676C2×C8C2×C4×D6112yes—
677C2×C8C2×C4×D6112yes—
678C23—21no—
679C23—21no—
680C23—41no—
681C23—41no—
682C23—611no—
683C23—611no—
684C23—611no—
685C23—611no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—2441no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23C4⋊C4×D6111yescharacteristic
695C23C4⋊C4×D6111yescharacteristic
696C23C2×Q8×D6111yescharacteristic
697Q8—2441no—
698Q8—2441no—
699Q8—2441no—
700Q8—2441no—
701D4—2441no—
702D4—2441no—
703D4—2441no—
704D4—2441no—
705D4—2441no—
706D4—2441no—
707D4—2441no—
708D4—2441no—
709D4—2441no—
710D4—2441no—
711D4—2441no—
712D4—2441no—
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—21no—
722C2×C4—21no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4C4⋊C4×D6111yescharacteristic
748C2×C4C4⋊C4×D6111yescharacteristic
749C2×C4C22×C4×D6111yescharacteristic
750C2×C4C2×D4×D6111yescharacteristic
751C2×C4#1451982211yescharacteristic
752C2×C4#1451982211yescharacteristic
753C2×C4#1451982311yescharacteristic
754C2×C4#1451982311yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—1222no—
762C8—1222no—
763C8—2441no—
764C8—2441no—
765C8—2441no—
766C8—2441no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—81no—
776C22—81no—
777C22—1221no—
778C22—1221no—
779C22—1221no—
780C22—1221no—
781C22—1221no—
782C22—1221no—
783C22—1221no—
784C22—1221no—
785C22—1221no—
786C22—1221no—
787C22—1221no—
788C22—1221no—
789C22—4881no—
790C22—4881no—
791C22—2442no—
792C22—2442no—
793C22C2×C4⋊C4×D6111yescharacteristic
794C22#1684038711yescharacteristic
795C22#1684038711yescharacteristic
796C4—21no—
797C4—21no—
798C4—1221no—
799C4—1221no—
800C4—1221no—
801C4—1221no—
802C4#1684023411yescharacteristic
803C4#1684023411yescharacteristic
804C4#1684032211yescharacteristic
805C4#1684032311yescharacteristic
806C2—21no—
807C2—21no—
808C2—41no—
809C2—41no—
810C2—2441no—
811C2—2441no—
812C2—2441no—
813C2—2441no—
814C2#2144843011yescharacteristic
815C2#2145442711yescharacteristic
816C2#2145442911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1855C2
socleC22×C61C22×C4⋊C4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1855D61
hypocenterC61#21950
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
4. #21446026C2semidirect
5. #21446025C2semidirect
6. #21446025C2semidirect
7. #21446024C2semidirect
8. #21446023C2semidirect
9. #21446022C2semidirect
10. #21446022C2semidirect
11. #21445860C2semidirect
12. #21445858C2semidirect
13. #21445856C2semidirect
14. #21445854C2semidirect
15. C61×#1855C2semidirect
408. #1855D61semidirect
471. C61#21950semidirect

Maximal subgroups

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

subgroupindex
#214542632
#214542622
C2×#168397272
#214460262
#214460252
#214460242
#214460232
#214460222
#214458602
#214458582
#214458562
#214458542
C61×#18552
#2195061