Finite Group Databasebeta

← #30617201

Subgroups — #30617201

Order 15616.

900 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462307C211yesmaximal, characteristic
2#21462257C211yesmaximal, characteristic, complemented
3#21461897C211yesmaximal, characteristic, complemented
4#21461896C211yesmaximal, characteristic, complemented
5#21461883C211yesmaximal, characteristic, complemented
6#21461880C211yesmaximal, characteristic, complemented
7#21461807C211yesmaximal, characteristic
8#21461770C211yesmaximal, characteristic, complemented
9#21461723C211yesmaximal, characteristic, complemented
10#21461634C211yesmaximal, characteristic, complemented
11#107×#6923C211yesmaximal, characteristic, complemented
12#21461590C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic, complemented
15#480×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×#14519856C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
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×#6923—21no—
34C4⋊C4×#6923—21no—
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4⋊C4×#6923C2211yescharacteristic
38C4⋊C4×#6923C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C4×C22⋊#6923—21no—
41C4×C22⋊#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
53C2×C4⋊C4×D61C2211yescharacteristic
54#16840077C411yescharacteristic, complemented
55#16840077C411yescharacteristic, complemented
56#16840076C411yescharacteristic, complemented
57#16840075C411yescharacteristic, complemented
58#16840074C411yescharacteristic, complemented
59#16840074C411yescharacteristic, complemented
60#16840073C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#107×D61C2211yescharacteristic
63#102×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65C22⋊C8×D61C2211yescharacteristic
66C61×#480C411yescharacteristic, complemented
67C23×#6923—21no—
68C2×D61⋊C8C2311yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70D4×#6923—22no—
71D4×#6923—22no—
72#14519856—22no—
73#14519856—22no—
74#14519856—22no—
75#14519856—22no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923D411yescharacteristic
78C2×C4⋊#6923D411yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923D411yescharacteristic
89C2×C22⋊#6923D411yescharacteristic
90C2×C4×#6923—21no—
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#14519845—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×D61—21no—
116C22×C4×D61C2311yescharacteristic
117C2×C8×D61C2311yescharacteristic
118C2×C8×D61C2311yescharacteristic
119#14519752C2×C411yescharacteristic
120#14519751C2×C411yescharacteristic
121#14519750—21no—
122#14519749—21no—
123#14519748C2×C411yescharacteristic
124C2×C4⋊Dic61C2×C411yescharacteristic, complemented
125C2×#11758196—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61C2×C411yescharacteristic, complemented
129C4⋊C4×D61C2×C411yescharacteristic, complemented
130C4⋊C4×D61C2311yescharacteristic
131C4⋊C4×D61C2311yescharacteristic
132C4⋊C4×D61C2311yescharacteristic
133C22⋊C4×D61—21no—
134#14519711C2×C411yescharacteristic, complemented
135#14519711C2×C411yescharacteristic, complemented
136#14519710C2×C411yescharacteristic, complemented
137#14519710C2×C411yescharacteristic, complemented
138#14519710C2×C411yescharacteristic, complemented
139#14519710C2×C411yescharacteristic, complemented
140#14519699C2×C411yescharacteristic
141#14519699C2×C411yescharacteristic
142#14519698C2×C411yescharacteristic
143#14519698C2×C411yescharacteristic
144#14519697C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146C22⋊#92418C2×C411yescharacteristic, complemented
147#14519689C2×C411yescharacteristic, complemented
148#14519689C2×C411yescharacteristic, complemented
149#121×C61C2×C411yescharacteristic
150C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
151#107×C61C2×C411yescharacteristic, complemented
152#107×C61C2×C411yescharacteristic, complemented
153#102×C61C2×C411yescharacteristic
154#102×C61C2×C411yescharacteristic
155C22⋊C8×C61C2×C411yescharacteristic, complemented
156C23×D61—21no—
157C23×D61C2×D411yescharacteristic
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—42no—
163C22×#6923—81no—
164C22×#6923—81no—
165C22×#6923C2×D411yescharacteristic
166C22×#6923C2×D411yescharacteristic
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C2×D4×C61—21no—
170C2×D4×C61C22×C411yescharacteristic
171C22×C4×C61—21no—
172C22×C4×C61C22×C411yescharacteristic
173C2×C22⋊D61—21no—
174C2×C22⋊D61—21no—
175C2×C22⋊D61—21no—
176C22×Dic61—21no—
177C22×Dic61#4111yescharacteristic
178D4×D61—21no—
179D4×D61—21no—
180D4×D61—21no—
181D4×D61—21no—
182D4×D61—81no—
183D4×D61—81no—
184C2×D244—21no—
185C2×D244C22×C411yescharacteristic
186C2×C4×D61—21no—
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×D61—21no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C2×C4×D61C22×C411yescharacteristic
198C2×C4×D61C2×D411yescharacteristic
199C2×C4×D61#4111yescharacteristic
200C2×C4×D61C2411yescharacteristic
201C22⋊#6923—24no—
202C22⋊#6923—22no—
203C22⋊#6923—22no—
204C22⋊#6923—42no—
205C22⋊#6923—81no—
206C22⋊#6923—81no—
207C22⋊#6923—81no—
208C2×#92420—21no—
209C2×#92420—21no—
210C4⋊#6923—22no—
211C4⋊#6923—22no—
212C4⋊#6923—21no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923—21no—
216C4⋊#6923—21no—
217C4⋊#6923—21no—
218C4⋊#6923—81no—
219C4⋊#6923#4112yes—
220C4⋊#6923#4112yes—
221C4×#6923—24no—
222C4×#6923—21no—
223C4×#6923—21no—
224C4×#6923—81no—
225C4×#6923—81no—
226C4×#6923—81no—
227C4×#6923—81no—
228C4×#6923—81no—
229C4×#6923#4112yes—
230C4×#6923#4112yes—
231D61⋊C8—21no—
232D61⋊C8—21no—
233D61⋊C8—21no—
234D61⋊C8—21no—
235C2×C8×C61C22×C411yescharacteristic
236C2×C8×C61C22×C411yescharacteristic
237C4⋊C4×C61—21no—
238C4⋊C4×C61C22×C411yescharacteristic
239C4⋊C4×C61C22×C411yescharacteristic
240C4⋊C4×C61C22×C411yescharacteristic
241C22⋊C4×C61—21no—
242C22⋊Dic61—21no—
243#11758198—21no—
244#11758198—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61C22×C411yescharacteristic
247C4⋊Dic61C22×C411yescharacteristic
248C4⋊Dic61C22×C411yescharacteristic
249#11758196—21no—
250#11758196—21no—
251#11758196—21no—
252#11758196—21no—
253#11758196—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#12312yes—
301C2×#6923#12312yes—
302D4×C61—21no—
303D4×C61—21no—
304D4×C61—81no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—81no—
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×Dic61—81no—
323C2×Dic61C4×D411yescharacteristic
324C2×Dic61C2×#4111yescharacteristic
325D244—21no—
326D244—21no—
327D244—81no—
328C4×D61—21no—
329C4×D61—21no—
330C4×D61—21no—
331C4×D61—21no—
332C4×D61—21no—
333C4×D61—21no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—81no—
341C4×D61—81no—
342C4×D61C2×#4111yescharacteristic
343C4×D61C2×#4111yescharacteristic
344C4×D61C2×#4111yescharacteristic
345C4×D61C2×#4111yescharacteristic
346#92420—41no—
347#92420—41no—
348C8×C61—21no—
349C8×C61—21no—
350#92418—21no—
351#92418—21no—
352#21586—611nomaximal, Sylow
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61C2×C4×D411yescharacteristic
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61C2×#12311yescharacteristic
375C2×D61#52511yescharacteristic
376C2×D61#57611yescharacteristic
377C2×D61#57611yescharacteristic
378C2×D61#57711yescharacteristic
379C2×D61#57811yescharacteristic
380#6923—22no—
381#6923—22no—
382#6923—41no—
383#6923—41no—
384#6923—42no—
385#6923—42no—
386#6923—81no—
387#6923—81no—
388C4×C61—21no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61C4×#4111yescharacteristic
393C4×C61C4×#4111yescharacteristic
394Dic61—21no—
395Dic61—41no—
396Dic61—41no—
397Dic61—41no—
398Dic61#52911yescharacteristic
399Dic61#52911yescharacteristic
400C2×#480—611no—
401#2324—611no—
402#2274—611no—
403#1926—611no—
404#1925—611no—
405#1921—611no—
406#1918—611no—
407#1875—611no—
408#1854—611no—
409#1824—611no—
410#1776—611no—
411C4×#107—611no—
412#1762—611no—
413C4×#102—611no—
414#1750—611no—
415C2×C61—41no—
416C2×C61—81no—
417C2×C61C4×#12311yescharacteristic
418C2×C61#294711yescharacteristic
419C2×C61#294811yescharacteristic
420D61—41no—
421D61—81no—
422D61#309611yescharacteristic
423D61#309811yescharacteristic
424D61#311911yescharacteristic
425D61#312411yescharacteristic
426C2×#121—611no—
427C2×C4×D4—611no—
428C2×#117—611no—
429C2×#117—611no—
430C22×C4⋊C4—611no—
431#480—611no—
432#480—611no—
433#480—611no—
434#480—611no—
435#480—611no—
436#480—611no—
437#480—611no—
438#480#692311yescharacteristic, complemented
439C2×#107—611no—
440C2×#107—611no—
441C2×#107—611no—
442C2×#106—611no—
443C2×#102—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×#97—611no—
450C2×C4×C8—611no—
451#390—611no—
452#390—1221no—
453#389—611no—
454#388—1221no—
455#386—1221no—
456#385—1221no—
457#380—611no—
458C4×C4⋊C4—611no—
459C4×C4⋊C4—611no—
460C4×C4⋊C4—611no—
461C4×C4⋊C4—611no—
462C4×C4⋊C4—611no—
463C4×C4⋊C4—1221no—
464C4×C4⋊C4—1221no—
465C4×C22⋊C4—1221no—
466C4×C22⋊C4—1221no—
467#340—611no—
468#340—611no—
469#340—611no—
470#340—611no—
471#340—611no—
472#340—611no—
473#340—611no—
474#340—611no—
475#336—611no—
476#336—611no—
477C61#2158611yescharacteristic, complemented, Sylow
478C22×D4—611no—
479C22×D4—1221no—
480C23×C4—611no—
481C23×C4—1221no—
482C23×C4—1221no—
483C22×C8—611no—
484C22×C8—611no—
485C22×C8—611no—
486C22×C8—611no—
487#121—611no—
488#121—611no—
489#121—611no—
490#121—1221no—
491#121—1221no—
492#121C2×#692311yescharacteristic
493C4×D4—1222no—
494C4×D4—1222no—
495#117—1222no—
496#117—1222no—
497#117—1222no—
498#117—1222no—
499C2×C4⋊C4—611no—
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—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4C2×#692311yescharacteristic, complemented
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C42—611no—
525C2×C42—611no—
526C2×C42—1221no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532#107—611no—
533#107—611no—
534#107—611no—
535#107—611no—
536#107—611no—
537#107—611no—
538#107—1222no—
539#107C2×#692311yescharacteristic, complemented
540#107C2×#692311yescharacteristic, complemented
541#106—1222no—
542#102—611no—
543#102—611no—
544#102—611no—
545#102—611no—
546#102—611no—
547#102—611no—
548#102—1222no—
549#102—1222no—
550#102C2×#692311yescharacteristic
551#102C2×#692311yescharacteristic
552C22⋊C8—611no—
553C22⋊C8—611no—
554C22⋊C8—611no—
555C22⋊C8—1221no—
556C22⋊C8—1221no—
557C22⋊C8C2×#692311yescharacteristic, complemented
558#97—1222no—
559C4×C8—1222no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566#95—1221no—
567C24—611no—
568C24—1221no—
569C2×D4—21no—
570C2×D4—611no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—4881no—
580C2×D4—4881no—
581C2×D4C22×#692311yescharacteristic
582C22×C4—21no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
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—4881no—
607C22×C4—4881no—
608C22×C4—4881no—
609C22×C4—4881no—
610C22×C4—2442no—
611C22×C4C22×#692311yescharacteristic
612C2×C8—611no—
613C2×C8—611no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8C22×#692311yescharacteristic
625C2×C8C22×#692311yescharacteristic
626C4⋊C4—21no—
627C4⋊C4—612no—
628C4⋊C4—612no—
629C4⋊C4—611no—
630C4⋊C4—611no—
631C4⋊C4—611no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1222no—
640C4⋊C4—1222no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—4881no—
647C4⋊C4C22×#692311yescharacteristic
648C4⋊C4C22×#692311yescharacteristic
649C4⋊C4C22×#692311yescharacteristic
650C22⋊C4—21no—
651C22⋊C4—1221no—
652C22⋊C4—1221no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1224no—
656C22⋊C4—1221no—
657C22⋊C4—4881no—
658C22⋊C4—4881no—
659C22⋊C4—4881no—
660C22⋊C4—2442no—
661C42—612no—
662C42—612no—
663C42—1221no—
664C42—1221no—
665C42—1224no—
666C42—4881no—
667C42—4881no—
668C42—4881no—
669C42—4881no—
670C42—4881no—
671C23—21no—
672C23—611no—
673C23—611no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23D4×#692311yescharacteristic
688D4—21no—
689D4—21no—
690D4—81no—
691D4—1221no—
692D4—1221no—
693D4—4881no—
694D4—4881no—
695D4—4881no—
696D4—2441no—
697D4—2441no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—81no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—611no—
709C2×C4—612no—
710C2×C4—612no—
711C2×C4—611no—
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—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—4881no—
736C2×C4—4881no—
737C2×C4—4884no—
738C2×C4—4881no—
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×C4—2441no—
755C2×C4D4×#692311yescharacteristic
756C2×C4C23×#692311yescharacteristic
757C8—21no—
758C8—21no—
759C8—1221no—
760C8—1221no—
761C8—2441no—
762C8—2441no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—611no—
770C22—611no—
771C22—611no—
772C22—611no—
773C22—611no—
774C22—611no—
775C22—1221no—
776C22—1221no—
777C22—1221no—
778C22—4881no—
779C22—4881no—
780C22—4881no—
781C22—4881no—
782C22—2441no—
783C22—2441no—
784C22—2441no—
785C22—2441no—
786C22—2441no—
787C22—2441no—
788C22—2441no—
789C22C2×D4×#692311yescharacteristic
790C4—21no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—611no—
795C4—611no—
796C4—1222no—
797C4—1222no—
798C4—1221no—
799C4—4881no—
800C4—4881no—
801C4—2441no—
802C4—2441no—
803C4—2442no—
804C4—2442no—
805C4—2441no—
806C4—2441no—
807C4—2441no—
808C4#41×#692311yescharacteristic
809C4#41×#692311yescharacteristic
810C2—41no—
811C2—81no—
812C2—611no—
813C2—611no—
814C2—611no—
815C2—611no—
816C2—4881no—
817C2—2441no—
818C2#123×#692311yescharacteristic
819C2#2146257711yescharacteristic
820C2#2146257811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#480C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#480#6923
hypocenterC61#21586
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #21462257C2semidirect
3. #21461897C2semidirect
4. #21461896C2semidirect
5. #21461883C2semidirect
6. #21461880C2semidirect
8. #21461770C2semidirect
9. #21461723C2semidirect
10. #21461634C2semidirect
11. #107×#6923C2semidirect
12. #21461590C2semidirect
13. #102×#6923C2semidirect
14. #21461550C2semidirect
54. #16840077C4semidirect
55. #16840077C4semidirect
56. #16840076C4semidirect
57. #16840075C4semidirect
58. #16840074C4semidirect
59. #16840074C4semidirect
60. #16840073C4semidirect
66. C61×#480C4semidirect
124. C2×C4⋊Dic61C2×C4semidirect
128. C4⋊C4×D61C2×C4semidirect
129. C4⋊C4×D61C2×C4semidirect
134. #14519711C2×C4semidirect
135. #14519711C2×C4semidirect
136. #14519710C2×C4semidirect
137. #14519710C2×C4semidirect
138. #14519710C2×C4semidirect
139. #14519710C2×C4semidirect
146. C22⋊#92418C2×C4semidirect
147. #14519689C2×C4semidirect
148. #14519689C2×C4semidirect
150. C2×C4⋊C4×C61C2×C4semidirect
151. #107×C61C2×C4semidirect
152. #107×C61C2×C4semidirect
155. C22⋊C8×C61C2×C4semidirect
438. #480#6923semidirect
477. C61#21586semidirect
515. C2×C4⋊C4C2×#6923semidirect
539. #107C2×#6923semidirect
540. #107C2×#6923semidirect
557. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623072
#214622572
#214618972
#214618962
#214618832
#214618802
#214618072
#214617702
#214617232
#214616342
#107×#69232
#214615902
#102×#69232
#214615502
#480×D612
#2158661