Finite Group Databasebeta

← #30617205

Subgroups — #30617205

Order 15616.

900 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462307C211yesmaximal, characteristic
2#21462256C211yesmaximal, characteristic, complemented
3#21461896C211yesmaximal, characteristic, complemented
4#21461896C211yesmaximal, characteristic, complemented
5#21461883C211yesmaximal, characteristic, complemented
6#21461881C211yesmaximal, characteristic, complemented
7#21461806C211yesmaximal, characteristic
8#21461768C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic, complemented
10#21461635C211yesmaximal, characteristic, complemented
11#107×#6923C211yesmaximal, characteristic, complemented
12#21461590C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic, complemented
15#482×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×#14519856C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20C2×#14519846C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23D61⋊(C22⋊C8)C2211yescharacteristic
24C2×#14519831C2211yescharacteristic
25C2×C8×#6923C2211yescharacteristic
26#16840714—21no—
27#16840714C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840712—21no—
30#16840710—21no—
31#16840709—21no—
32#16840704C2211yescharacteristic
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4⋊C4×#6923C2211yescharacteristic
38C4×C4⋊#6923—21no—
39C4×C4⋊#6923—21no—
40C22⋊C4×#6923—21no—
41C22⋊C4×#6923—21no—
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#121×D61C2211yescharacteristic
53#117×D61C2211yescharacteristic
54#16840089C411yescharacteristic, complemented
55#16840088C411yescharacteristic, complemented
56#16840087C411yescharacteristic, complemented
57#16840086C411yescharacteristic, complemented
58#16840085C411yescharacteristic, complemented
59#16840084C411yescharacteristic, complemented
60#16840083C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63#102×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65C22⋊C8×D61C2211yescharacteristic
66C61×#482C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73#14519856—22no—
74#14519856—22no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—22no—
77C2×C4⋊#6923—22no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923D411yescharacteristic
80C2×C4⋊#6923D411yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923D411yescharacteristic
90C2×C22⋊#6923D411yescharacteristic
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923C2311yescharacteristic
97C2×C4×#6923C2311yescharacteristic
98#14519846—22no—
99#14519846—22no—
100#14519839—22no—
101#14519839—22no—
102#14519834—21no—
103C22⋊#92420—21no—
104#14519831—22no—
105C8×#6923—22no—
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—
113C2×D4×D61—21no—
114C2×D4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C2×C8×D61C2311yescharacteristic
117C2×C8×D61C2311yescharacteristic
118#14519752C2×C411yescharacteristic
119#14519751C2×C411yescharacteristic
120#14519750—21no—
121#14519749—21no—
122#14519748C2×C411yescharacteristic
123#14519736C2×C411yescharacteristic, complemented
124#14519735C2×C411yescharacteristic, complemented
125#14519735C2×C411yescharacteristic, complemented
126#14519734—21no—
127#14519733—21no—
128C4⋊C4×D61C2311yescharacteristic
129C4⋊C4×D61C2311yescharacteristic
130C4⋊C4×D61C2311yescharacteristic
131C22⋊C4×D61—21no—
132C22⋊C4×D61—21no—
133C42×D61—21no—
134#14519711C2×C411yescharacteristic, complemented
135#14519710C2×C411yescharacteristic, complemented
136#14519710C2×C411yescharacteristic, complemented
137#14519709C2×C411yescharacteristic, complemented
138#14519708C2×C411yescharacteristic, complemented
139#14519708C2×C411yescharacteristic, complemented
140#14519699C2×C411yescharacteristic, complemented
141#14519699C2×C411yescharacteristic, complemented
142#14519698C2×C411yescharacteristic, complemented
143#14519698C2×C411yescharacteristic, complemented
144#14519697C2×C411yescharacteristic, complemented
145#14519697C2×C411yescharacteristic, complemented
146C22⋊#92418C2×C411yescharacteristic, complemented
147#14519689C2×C411yescharacteristic, complemented
148#14519689C2×C411yescharacteristic, complemented
149#121×C61C2×C411yescharacteristic
150#117×C61C2×C411yescharacteristic, complemented
151#107×C61C2×C411yescharacteristic, complemented
152#106×C61C2×C411yescharacteristic, complemented
153#102×C61C2×C411yescharacteristic, complemented
154#102×C61C2×C411yescharacteristic, complemented
155C22⋊C8×C61C2×C411yescharacteristic, complemented
156C23×D61—21no—
157C23×D61C2×D411yescharacteristic
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—24no—
161C22×#6923—21no—
162C22×#6923—21no—
163C22×#6923—42no—
164C22×#6923—81no—
165C22×#6923—81no—
166C22×#6923—81no—
167C22×#6923—81no—
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C22×#6923C2×D411yescharacteristic
171C22×#6923C2×D411yescharacteristic
172C2×D4×C61—21no—
173C2×D4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C411yescharacteristic
175C2×C22⋊D61—21no—
176C2×C22⋊D61—21no—
177C2×C22⋊D61—21no—
178C22×Dic61#4111yescharacteristic
179D4×D61—21no—
180D4×D61—21no—
181D4×D61—21no—
182D4×D61—21no—
183D4×D61—81no—
184D4×D61—81no—
185C2×D244—21no—
186C2×D244C22×C411yescharacteristic
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61C22×C411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61#4111yescharacteristic
197C2×C4×D61C2411yescharacteristic
198C22⋊#6923—22no—
199C22⋊#6923—22no—
200C22⋊#6923—42no—
201C22⋊#6923—81no—
202C22⋊#6923—81no—
203C22⋊#6923—81no—
204C2×#92420—21no—
205C2×#92420—21no—
206C4⋊#6923—24no—
207C4⋊#6923—22no—
208C4⋊#6923—22no—
209C4⋊#6923—21no—
210C4⋊#6923—21no—
211C4⋊#6923—21no—
212C4⋊#6923—21no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923—81no—
216C4⋊#6923#4112yes—
217C4⋊#6923#4112yes—
218C4×#6923—21no—
219C4×#6923—21no—
220C4×#6923—81no—
221C4×#6923—81no—
222C4×#6923—81no—
223C4×#6923—81no—
224C4×#6923—81no—
225C4×#6923#4112yes—
226C4×#6923#4112yes—
227D61⋊C8—21no—
228D61⋊C8—21no—
229D61⋊C8—21no—
230D61⋊C8—21no—
231C2×C8×C61C22×C411yescharacteristic
232C2×C8×C61C22×C411yescharacteristic
233C4⋊C4×C61C22×C411yescharacteristic
234C4⋊C4×C61C22×C411yescharacteristic
235C4⋊C4×C61C22×C411yescharacteristic
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C42×C61—21no—
239C22⋊Dic61—21no—
240C22⋊Dic61—21no—
241#11758198—21no—
242#11758198—21no—
243#11758198—21no—
244#11758198—21no—
245C4⋊Dic61C22×C411yescharacteristic
246C4⋊Dic61C22×C411yescharacteristic
247C4⋊Dic61C22×C411yescharacteristic
248#11758196—21no—
249#11758196—21no—
250#11758196—21no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61—21no—
254C2×#92418C22×C411yescharacteristic
255C2×#92418C22×C411yescharacteristic
256C8×D61—21no—
257C8×D61—21no—
258C8×D61—21no—
259C8×D61—21no—
260C23×C61—21no—
261C23×C61C4×D411yescharacteristic
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61C4×D411yescharacteristic
276C22×D61C22×D411yescharacteristic
277C2×#6923—21no—
278C2×#6923—21no—
279C2×#6923—21no—
280C2×#6923—21no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—22no—
284C2×#6923—22no—
285C2×#6923—21no—
286C2×#6923—21no—
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—41no—
290C2×#6923—41no—
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—84no—
300C2×#6923—84no—
301C2×#6923#12312yes—
302C2×#6923#12312yes—
303D4×C61—21no—
304D4×C61—21no—
305D4×C61—81no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61C4×D411yescharacteristic
312C2×C4×C61C23×C411yescharacteristic
313C22⋊D61—41no—
314C22⋊D61—41no—
315C22⋊D61—81no—
316C22⋊D61—81no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61C4×D411yescharacteristic
323C2×Dic61C2×#4111yescharacteristic
324D244—21no—
325D244—21no—
326D244—81no—
327C4×D61—21no—
328C4×D61—21no—
329C4×D61—21no—
330C4×D61—21no—
331C4×D61—21no—
332C4×D61—21no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61C2×#4111yescharacteristic
340C4×D61C2×#4111yescharacteristic
341C4×D61C2×#4111yescharacteristic
342C4×D61C2×#4111yescharacteristic
343#92420—41no—
344#92420—41no—
345C8×C61—21no—
346C8×C61—21no—
347#92418—21no—
348#92418—21no—
349#21590—611nomaximal, Sylow
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61C2×C4×D411yescharacteristic
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—41no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61C2×#12311yescharacteristic
372C2×D61#52511yescharacteristic
373C2×D61#57611yescharacteristic
374C2×D61#57611yescharacteristic
375C2×D61#57711yescharacteristic
376C2×D61#57811yescharacteristic
377#6923—22no—
378#6923—22no—
379#6923—41no—
380#6923—41no—
381#6923—42no—
382#6923—42no—
383#6923—81no—
384#6923—81no—
385C4×C61—21no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61—41no—
389C4×C61C4×#4111yescharacteristic
390C4×C61C4×#4111yescharacteristic
391Dic61—21no—
392Dic61—41no—
393Dic61—41no—
394Dic61—41no—
395Dic61#52911yescharacteristic
396Dic61#52911yescharacteristic
397C2×#482—611no—
398#2324—611no—
399#2274—611no—
400#1925—611no—
401#1925—611no—
402#1921—611no—
403#1919—611no—
404#1874—611no—
405#1852—611no—
406#1825—611no—
407#1776—611no—
408C4×#107—611no—
409#1762—611no—
410C4×#102—611no—
411#1750—611no—
412C2×C61—41no—
413C2×C61—81no—
414C2×C61C4×#12311yescharacteristic
415C2×C61#294611yescharacteristic
416C2×C61#295111yescharacteristic
417D61—41no—
418D61—81no—
419D61#309611yescharacteristic
420D61#309811yescharacteristic
421D61#312111yescharacteristic
422D61#312211yescharacteristic
423C2×#121—611no—
424C2×C4×D4—611no—
425C2×#117—611no—
426C2×#117—611no—
427C22×C4⋊C4—611no—
428#482—611no—
429#482—611no—
430#482—611no—
431#482—611no—
432#482—611no—
433#482—611no—
434#482—611no—
435#482#692311yescharacteristic, complemented
436C2×#107—611no—
437C2×#107—611no—
438C2×#107—611no—
439C2×#106—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×#97—611no—
447C2×C4×C8—611no—
448#390—611no—
449#390—1221no—
450#389—611no—
451#388—1221no—
452#386—1221no—
453#385—1221no—
454#380—611no—
455C4×C4⋊C4—611no—
456C4×C4⋊C4—611no—
457C4×C4⋊C4—611no—
458C4×C4⋊C4—611no—
459C4×C4⋊C4—611no—
460C4×C4⋊C4—1221no—
461C4×C4⋊C4—1221no—
462C4×C22⋊C4—1221no—
463C4×C22⋊C4—1221no—
464#340—611no—
465#340—611no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470#340—611no—
471#340—611no—
472#336—611no—
473#336—611no—
474C61#2159011yescharacteristic, complemented, Sylow
475C22×D4—611no—
476C22×D4—1221no—
477C23×C4—611no—
478C23×C4—1221no—
479C23×C4—1221no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—611no—
484#121—611no—
485#121—611no—
486#121—611no—
487#121—1221no—
488#121—1221no—
489#121C2×#692311yescharacteristic
490C4×D4—1222no—
491C4×D4—1222no—
492#117—611no—
493#117—611no—
494#117—611no—
495#117—1221no—
496#117—1222no—
497#117—1222no—
498#117—1221no—
499#117C2×#692311yescharacteristic, complemented
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C42—611no—
522C2×C42—611no—
523C2×C42—1221no—
524C2×C42—1221no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42—1221no—
528C2×C42—1221no—
529#107—611no—
530#107—611no—
531#107—611no—
532#107—1222no—
533#107—1222no—
534#107C2×#692311yescharacteristic, complemented
535#106—611no—
536#106—611no—
537#106—611no—
538#106C2×#692311yescharacteristic, complemented
539#102—611no—
540#102—611no—
541#102—611no—
542#102—611no—
543#102—611no—
544#102—611no—
545#102—1222no—
546#102—1222no—
547#102C2×#692311yescharacteristic, complemented
548#102C2×#692311yescharacteristic, complemented
549C22⋊C8—611no—
550C22⋊C8—611no—
551C22⋊C8—611no—
552C22⋊C8—1221no—
553C22⋊C8—1221no—
554C22⋊C8C2×#692311yescharacteristic, complemented
555#97—1222no—
556C4×C8—1222no—
557#95—1221no—
558#95—1221no—
559#95—1221no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564C24—611no—
565C24—1221no—
566C2×D4—21no—
567C2×D4—611no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—4881no—
577C2×D4—4881no—
578C2×D4C22×#692311yescharacteristic
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1224no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—4881no—
601C22×C4—4881no—
602C22×C4—4881no—
603C22×C4—4881no—
604C22×C4—2442no—
605C22×C4C22×#692311yescharacteristic
606C2×C8—611no—
607C2×C8—611no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8C22×#692311yescharacteristic
619C2×C8C22×#692311yescharacteristic
620C4⋊C4—612no—
621C4⋊C4—612no—
622C4⋊C4—611no—
623C4⋊C4—611no—
624C4⋊C4—611no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1222no—
631C4⋊C4—1222no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1224no—
637C4⋊C4—4881no—
638C4⋊C4C22×#692311yescharacteristic
639C4⋊C4C22×#692311yescharacteristic
640C4⋊C4C22×#692311yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—1221no—
644C22⋊C4—1221no—
645C22⋊C4—1221no—
646C22⋊C4—1221no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1221no—
650C22⋊C4—1221no—
651C22⋊C4—4881no—
652C22⋊C4—4881no—
653C22⋊C4—4881no—
654C22⋊C4—2442no—
655C42—21no—
656C42—612no—
657C42—612no—
658C42—1221no—
659C42—1221no—
660C42—1221no—
661C42—1221no—
662C42—1221no—
663C42—4881no—
664C42—4881no—
665C42—4881no—
666C42—4881no—
667C42—4881no—
668C23—21no—
669C23—611no—
670C23—611no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23D4×#692311yescharacteristic
685D4—21no—
686D4—21no—
687D4—81no—
688D4—1221no—
689D4—1221no—
690D4—4881no—
691D4—4881no—
692D4—4881no—
693D4—2441no—
694D4—2441no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—611no—
701C2×C4—611no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—611no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
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—1222no—
725C2×C4—1222no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—4884no—
732C2×C4—4884no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
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×C4D4×#692311yescharacteristic
750C2×C4C23×#692311yescharacteristic
751C8—21no—
752C8—21no—
753C8—1221no—
754C8—1221no—
755C8—2441no—
756C8—2441no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—611no—
764C22—611no—
765C22—611no—
766C22—611no—
767C22—611no—
768C22—611no—
769C22—1221no—
770C22—1221no—
771C22—1221no—
772C22—4881no—
773C22—4881no—
774C22—4881no—
775C22—4881no—
776C22—2441no—
777C22—2441no—
778C22—2441no—
779C22—2441no—
780C22—2441no—
781C22—2441no—
782C22—2441no—
783C22C2×D4×#692311yescharacteristic
784C4—21no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—611no—
789C4—611no—
790C4—1222no—
791C4—1222no—
792C4—1221no—
793C4—4881no—
794C4—4881no—
795C4—2441no—
796C4—2441no—
797C4—2442no—
798C4—2442no—
799C4—2441no—
800C4—2441no—
801C4—2441no—
802C4#41×#692311yescharacteristic
803C4#41×#692311yescharacteristic
804C2—41no—
805C2—81no—
806C2—611no—
807C2—611no—
808C2—611no—
809C2—611no—
810C2—4881no—
811C2—2441no—
812C2#123×#692311yescharacteristic
813C2#2146257611yescharacteristic
814C2#2146258111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#482C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#482#6923
hypocenterC61#21590
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #21462256C2semidirect
3. #21461896C2semidirect
4. #21461896C2semidirect
5. #21461883C2semidirect
6. #21461881C2semidirect
8. #21461768C2semidirect
9. #21461724C2semidirect
10. #21461635C2semidirect
11. #107×#6923C2semidirect
12. #21461590C2semidirect
13. #102×#6923C2semidirect
14. #21461550C2semidirect
54. #16840089C4semidirect
55. #16840088C4semidirect
56. #16840087C4semidirect
57. #16840086C4semidirect
58. #16840085C4semidirect
59. #16840084C4semidirect
60. #16840083C4semidirect
66. C61×#482C4semidirect
123. #14519736C2×C4semidirect
124. #14519735C2×C4semidirect
125. #14519735C2×C4semidirect
134. #14519711C2×C4semidirect
135. #14519710C2×C4semidirect
136. #14519710C2×C4semidirect
137. #14519709C2×C4semidirect
138. #14519708C2×C4semidirect
139. #14519708C2×C4semidirect
140. #14519699C2×C4semidirect
141. #14519699C2×C4semidirect
142. #14519698C2×C4semidirect
143. #14519698C2×C4semidirect
144. #14519697C2×C4semidirect
145. #14519697C2×C4semidirect
146. C22⋊#92418C2×C4semidirect
147. #14519689C2×C4semidirect
148. #14519689C2×C4semidirect
150. #117×C61C2×C4semidirect
151. #107×C61C2×C4semidirect
152. #106×C61C2×C4semidirect
153. #102×C61C2×C4semidirect
154. #102×C61C2×C4semidirect
155. C22⋊C8×C61C2×C4semidirect
435. #482#6923semidirect
474. C61#21590semidirect
499. #117C2×#6923semidirect
534. #107C2×#6923semidirect
538. #106C2×#6923semidirect
547. #102C2×#6923semidirect
548. #102C2×#6923semidirect
554. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623072
#214622562
#214618962
#214618832
#214618812
#214618062
#214617682
#214617242
#214616352
#107×#69232
#214615902
#102×#69232
#214615502
#482×D612
#2159061