Finite Group Databasebeta

← #30622591

Subgroups — #30622591

Order 15616.

870 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462345C211yesmaximal, characteristic
2#21462343C211yesmaximal, characteristic
3#21461910C211yesmaximal, characteristic, complemented
4#21461908C211yesmaximal, characteristic, complemented
5#21461882C211yesmaximal, characteristic, complemented
6#21461882C211yesmaximal, characteristic, complemented
7#21461813C211yesmaximal, characteristic, complemented
8#21461813C211yesmaximal, characteristic, complemented
9#21461805C211yesmaximal, characteristic
10#21461804C211yesmaximal, characteristic
11#21461592C211yesmaximal, characteristic, complemented
12#103×#6923C211yesmaximal, characteristic, complemented
13#21461559C211yesmaximal, characteristic
14#21461507C211yesmaximal, characteristic
15#470×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519840C2211yescharacteristic
24D61⋊(C22⋊C8)C2211yescharacteristic
25C2×#14519831C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27(C2×#6923)⋊Q8C2211yescharacteristic
28(C2×#6923)⋊Q8C2211yescharacteristic
29#16840713—21no—
30#16840713C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840712—21no—
33#16840712—21no—
34#16840711—21no—
35#16840711—21no—
36#16840709—21no—
37C4⋊C4×#6923—21no—
38C4⋊C4×#6923C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C22⋊C4×#6923—21no—
41C4×C22⋊#6923C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×Q16×D61C2211yescharacteristic
53C2×M16×D61C2211yescharacteristic
54C22⋊Q8×D61C2211yescharacteristic
55C22⋊Q8×D61C2211yescharacteristic
56#16840021C411yescharacteristic, complemented
57#16840020C411yescharacteristic, complemented
58#16840019C411yescharacteristic, complemented
59#16840019C411yescharacteristic, complemented
60#16840018C411yescharacteristic, complemented
61#16840018C411yescharacteristic, complemented
62#16840017C411yescharacteristic, complemented
63#106×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#103×D61C2211yescharacteristic
66C61×#470C411yescharacteristic, complemented
67C23×#6923—21no—
68C2×D61⋊C8C2311yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70Q8×#6923—22no—
71Q8×#6923—22no—
72Q8×#6923—41no—
73Q8×#6923—41no—
74#14519856—22no—
75#14519856—41no—
76C2×C4⋊#6923—22no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—41no—
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
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×#6923C2311yescharacteristic
96C2×C4×#6923C2311yescharacteristic
97#14519840—22no—
98#14519840—22no—
99#14519840—41no—
100#14519840—41no—
101#14519834—21no—
102C22⋊#92420—21no—
103#14519831—41no—
104C8×#6923—41no—
105(C2×#6923)⋊C4—21no—
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—
113(C2×#6923)⋊C4D411yescharacteristic
114(C2×#6923)⋊C4D411yescharacteristic
115C2×Q8×D61C2311yescharacteristic
116C2×Q8×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C2×Dic244C2×C411yescharacteristic, complemented
119C2×#11758202C2×C411yescharacteristic, complemented
120C2×#11758202C2×C411yescharacteristic, complemented
121Q16×D61—41no—
122Q16×D61—41no—
123C2×#11758194C2×C411yescharacteristic
124C2×#11758189C2×C411yescharacteristic
125C2×#11758189C2×C411yescharacteristic
126M16×D61—41no—
127M16×D61—41no—
128C2×C8×D61C2311yescharacteristic
129C2×C8×D61C2311yescharacteristic
130#14519757C2×C411yescharacteristic
131#14519757C2×C411yescharacteristic
132#14519756C2×C411yescharacteristic
133#14519756C2×C411yescharacteristic
134#14519755—21no—
135#14519755—21no—
136#14519754—21no—
137#14519754—21no—
138#14519753C2×C411yescharacteristic
139#14519753C2×C411yescharacteristic
140C4⋊C4×D61—21no—
141C4⋊C4×D61—21no—
142C4⋊C4×D61C2311yescharacteristic
143C4⋊C4×D61C2311yescharacteristic
144C22⋊C4×D61—21no—
145C22⋊C4×D61—21no—
146#14519709C2×C411yescharacteristic, complemented
147#14519708C2×C411yescharacteristic, complemented
148#14519708C2×C411yescharacteristic, complemented
149#14519702C2×C411yescharacteristic, complemented
150#14519702C2×C411yescharacteristic, complemented
151#14519701C2×C411yescharacteristic, complemented
152#14519701C2×C411yescharacteristic, complemented
153#14519700C2×C411yescharacteristic, complemented
154#14519700C2×C411yescharacteristic, complemented
155C2×Q16×C61C2×C411yescharacteristic, complemented
156C2×M16×C61C2×C411yescharacteristic
157C22⋊Q8×C61C2×C411yescharacteristic
158C22⋊Q8×C61C2×C411yescharacteristic
159#106×C61C2×C411yescharacteristic, complemented
160#103×C61C2×C411yescharacteristic, complemented
161#103×C61C2×C411yescharacteristic, complemented
162C23×D61C2×D411yescharacteristic
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—42no—
168C22×#6923—42no—
169C22×#6923—81no—
170C22×#6923C2×D411yescharacteristic
171C22×#6923C2×D411yescharacteristic
172C22×#6923C2×D411yescharacteristic
173C22×#6923C2×D411yescharacteristic
174C2×Q8×C61C22×C411yescharacteristic
175C2×Q8×C61C22×C411yescharacteristic
176C22×C4×C61C22×C411yescharacteristic
177C22×Dic61#4111yescharacteristic
178Q8×D61—21no—
179Q8×D61—21no—
180Q8×D61—21no—
181Q8×D61—21no—
182Q8×D61—21no—
183Q8×D61—21no—
184Q8×D61—21no—
185Q8×D61—21no—
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×D61C22×C411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61#4111yescharacteristic
197C2×C4×D61C2411yescharacteristic
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122C22×C411yescharacteristic
201C2×Dic122C22×C411yescharacteristic
202C22⋊#6923—22no—
203C22⋊#6923—41no—
204C22⋊#6923—42no—
205C2×#92420—21no—
206C2×#92420—21no—
207C4⋊#6923—21no—
208C4⋊#6923—21no—
209C4⋊#6923—21no—
210C4⋊#6923—21no—
211C4⋊#6923—21no—
212C4⋊#6923—21no—
213C4⋊#6923—42no—
214C4⋊#6923—42no—
215C4⋊#6923—42no—
216C4⋊#6923—42no—
217C4⋊#6923—81no—
218C4⋊#6923#4112yes—
219C4⋊#6923#4112yes—
220C4×#6923—21no—
221C4×#6923—21no—
222C4×#6923—21no—
223C4×#6923—21no—
224C4×#6923—42no—
225C4×#6923—42no—
226C4×#6923—42no—
227C4×#6923—42no—
228C4×#6923—81no—
229D61⋊C8—21no—
230D61⋊C8—21no—
231D61⋊C8—21no—
232D61⋊C8—21no—
233Q16×C61—41no—
234M16×C61—41no—
235C2×C8×C61C22×C411yescharacteristic
236C2×C8×C61C22×C411yescharacteristic
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61C22×C411yescharacteristic
240C4⋊C4×C61C22×C411yescharacteristic
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245#11758202—41no—
246#11758202—41no—
247#11758198—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61C22×C411yescharacteristic
254C4⋊Dic61C22×C411yescharacteristic
255#11758196—21no—
256#11758196—21no—
257#11758196—21no—
258#11758196—21no—
259#11758196—21no—
260#11758196—21no—
261#11758194—41no—
262C2×#92418C22×C411yescharacteristic
263C2×#92418C22×C411yescharacteristic
264Dic244—41no—
265#11758189—41no—
266#11758189—41no—
267C8×D61—21no—
268C8×D61—21no—
269C8×D61—21no—
270C8×D61—21no—
271C23×C61C4×D411yescharacteristic
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61C4×D411yescharacteristic
279C22×D61C22×D411yescharacteristic
280C2×#6923—21no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—21no—
284C2×#6923—21no—
285C2×#6923—22no—
286C2×#6923—22no—
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—21no—
292C2×#6923—21no—
293C2×#6923—41no—
294C2×#6923—41no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923—41no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923—41no—
303C2×#6923—84no—
304C2×#6923#13712yes—
305Q8×C61—21no—
306Q8×C61—21no—
307Q8×C61—21no—
308Q8×C61—21no—
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×C61C4×D411yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61C4×D411yescharacteristic
324C2×Dic61C2×#4111yescharacteristic
325C4×D61—21no—
326C4×D61—21no—
327C4×D61—21no—
328C4×D61—21no—
329C4×D61—21no—
330C4×D61—21no—
331C4×D61—41no—
332C4×D61—41no—
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×D61H(5,𝔽2)11yescharacteristic
342C4×D61H(5,𝔽2)11yescharacteristic
343Dic122—21no—
344Dic122—21no—
345Dic122—21no—
346Dic122—21no—
347Dic122—41no—
348Dic122—41no—
349Dic122—41no—
350Dic122—41no—
351#92420—41no—
352#92420—41no—
353C8×C61—21no—
354C8×C61—21no—
355#92418—21no—
356#92418—21no—
357#23144—611nomaximal, Sylow
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61C2×C4×D411yescharacteristic
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61#54611yescharacteristic
370C2×D61#54611yescharacteristic
371C2×D61C2×#13711yescharacteristic
372C2×D61#57511yescharacteristic
373C2×D61#57711yescharacteristic
374C2×D61#57811yescharacteristic
375#6923—22no—
376#6923—41no—
377#6923—42no—
378#6923—41no—
379#6923—42no—
380#6923—41no—
381#6923—81no—
382#6923—81no—
383C4×C61—21no—
384C4×C61—41no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61C4×#4111yescharacteristic
389C4×C61#51811yescharacteristic
390Dic61—21no—
391Dic61—41no—
392Dic61—41no—
393Dic61—41no—
394Dic61—41no—
395Dic61#55311yescharacteristic
396Dic61#55311yescharacteristic
397C2×#470—611no—
398#2362—611no—
399#2360—611no—
400#1935—611no—
401#1933—611no—
402#1920—611no—
403#1920—611no—
404#1878—611no—
405#1878—611no—
406#1873—611no—
407#1872—611no—
408#1763—611no—
409C4×#103—611no—
410#1753—611no—
411#1736—611no—
412C2×C61—41no—
413C2×C61#236411yescharacteristic
414C2×C61C4×#13711yescharacteristic
415C2×C61#294711yescharacteristic
416D61—41no—
417D61#331111yescharacteristic
418D61#331211yescharacteristic
419D61#332711yescharacteristic
420D61#333111yescharacteristic
421C22×Q16—611no—
422C22×M16—611no—
423C2×C22⋊Q8—611no—
424C2×C22⋊Q8—611no—
425C2×C4×Q8—611no—
426C2×C4×Q8—611no—
427C2×#117—611no—
428C22×C4⋊C4—611no—
429#470—611no—
430#470—611no—
431#470—611no—
432#470—611no—
433#470—611no—
434#470—611no—
435#470—611no—
436#470#692311yescharacteristic, complemented
437C2×#106—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×C22⋊C8—611no—
445C2×#97—611no—
446C2×C4×C8—611no—
447#391—611no—
448#391—611no—
449#389—611no—
450#389—611no—
451#389—1221no—
452#388—1221no—
453#388—1221no—
454#387—1221no—
455#387—1221no—
456#385—1221no—
457C4×C4⋊C4—611no—
458C4×C4⋊C4—611no—
459C4×C4⋊C4—1221no—
460C4×C22⋊C4—611no—
461C4×C22⋊C4—1221no—
462#340—611no—
463#340—611no—
464#340—611no—
465#340—611no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470#336—611no—
471#336—611no—
472C61#2314411yescharacteristic, complemented, Sylow
473C22×Q8—611no—
474C22×Q8—611no—
475C23×C4—611no—
476C23×C4—1221no—
477C2×Q16—611no—
478C2×Q16—611no—
479C2×Q16—611no—
480C2×Q16—2441no—
481C2×Q16—2441no—
482C2×Q16C2×#692311yescharacteristic, complemented
483C2×M16—611no—
484C2×M16—611no—
485C2×M16—611no—
486C2×M16—2441no—
487C2×M16—2441no—
488C2×M16C2×#692311yescharacteristic
489C22×C8—611no—
490C22×C8—611no—
491C22×C8—611no—
492C22×C8—611no—
493C22⋊Q8—611no—
494C22⋊Q8—611no—
495C22⋊Q8—611no—
496C22⋊Q8—611no—
497C22⋊Q8—611no—
498C22⋊Q8—611no—
499C22⋊Q8—1221no—
500C22⋊Q8—1221no—
501C22⋊Q8—1221no—
502C22⋊Q8—1221no—
503C22⋊Q8C2×#692311yescharacteristic
504C22⋊Q8C2×#692311yescharacteristic
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×Q8—2441no—
508C4×Q8—2441no—
509#117—1222no—
510#117—2441no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—2441no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C42—611no—
532C2×C42—611no—
533C2×C42—1221no—
534C2×C42—1221no—
535C2×C42—1221no—
536C2×C42—1221no—
537C2×C42—1221no—
538#106—611no—
539#106—611no—
540#106—611no—
541#106C2×#692311yescharacteristic, complemented
542#103—611no—
543#103—611no—
544#103—611no—
545#103—611no—
546#103—611no—
547#103—611no—
548#103—1222no—
549#103—1222no—
550#103—2441no—
551#103—2441no—
552#103C2×#692311yescharacteristic, complemented
553#103C2×#692311yescharacteristic, complemented
554C22⋊C8—1221no—
555C22⋊C8—1221no—
556#97—2441no—
557C4×C8—2441no—
558#95—611no—
559#95—611no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566#95—1221no—
567#95—1221no—
568C24—611no—
569C2×Q8—611no—
570C2×Q8—611no—
571C2×Q8—1221no—
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8C22×#692311yescharacteristic
582C2×Q8C22×#692311yescharacteristic
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—4881no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4C22×#692311yescharacteristic
608Q16—41no—
609Q16—2441no—
610Q16—2441no—
611Q16—2441no—
612M16—41no—
613M16—2441no—
614M16—2441no—
615M16—2441no—
616C2×C8—611no—
617C2×C8—611no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8C22×#692311yescharacteristic
629C2×C8C22×#692311yescharacteristic
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—612no—
633C4⋊C4—612no—
634C4⋊C4—611no—
635C4⋊C4—611no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—4881no—
651C4⋊C4—2442no—
652C4⋊C4—2442no—
653C4⋊C4—2442no—
654C4⋊C4—2442no—
655C4⋊C4C22×#692311yescharacteristic
656C4⋊C4C22×#692311yescharacteristic
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—1221no—
660C22⋊C4—1221no—
661C22⋊C4—1221no—
662C22⋊C4—1221no—
663C22⋊C4—1222no—
664C22⋊C4—1221no—
665C22⋊C4—1221no—
666C22⋊C4—2441no—
667C22⋊C4—2442no—
668C42—1221no—
669C42—1221no—
670C42—1221no—
671C42—1221no—
672C42—4881no—
673C42—2442no—
674C42—2442no—
675C42—2442no—
676C42—2442no—
677C23—611no—
678C23—611no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23—1221no—
684C23—1221no—
685C23D4×#692311yescharacteristic
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—1221no—
691Q8—1221no—
692Q8—1221no—
693Q8—1221no—
694Q8—2441no—
695Q8—2441no—
696Q8—2441no—
697Q8—2441no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—611no—
709C2×C4—612no—
710C2×C4—611no—
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—1221no—
725C2×C4—1222no—
726C2×C4—1222no—
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—4884no—
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×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—611no—
767C22—611no—
768C22—611no—
769C22—611no—
770C22—611no—
771C22—611no—
772C22—1221no—
773C22—1221no—
774C22—1221no—
775C22—2441no—
776C22—2441no—
777C22—2441no—
778C22—2441no—
779C22C2×D4×#692311yescharacteristic
780C4—21no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—611no—
786C4—611no—
787C4—1222no—
788C4—1221no—
789C4—4881no—
790C4—4881no—
791C4—2441no—
792C4—2441no—
793C4—2441no—
794C4—2442no—
795C4—2442no—
796C4—2441no—
797C4—2441no—
798C4—2441no—
799C4—2441no—
800C4#41×#692311yescharacteristic
801C4#1684082911yescharacteristic
802C2—41no—
803C2—611no—
804C2—611no—
805C2—611no—
806C2—611no—
807C2—2441no—
808C2#2146234711yescharacteristic
809C2#137×#692311yescharacteristic
810C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#470C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#470#6923
hypocenterC61#23144
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
3. #21461910C2semidirect
4. #21461908C2semidirect
5. #21461882C2semidirect
6. #21461882C2semidirect
7. #21461813C2semidirect
8. #21461813C2semidirect
11. #21461592C2semidirect
12. #103×#6923C2semidirect
56. #16840021C4semidirect
57. #16840020C4semidirect
58. #16840019C4semidirect
59. #16840019C4semidirect
60. #16840018C4semidirect
61. #16840018C4semidirect
62. #16840017C4semidirect
66. C61×#470C4semidirect
118. C2×Dic244C2×C4semidirect
119. C2×#11758202C2×C4semidirect
120. C2×#11758202C2×C4semidirect
146. #14519709C2×C4semidirect
147. #14519708C2×C4semidirect
148. #14519708C2×C4semidirect
149. #14519702C2×C4semidirect
150. #14519702C2×C4semidirect
151. #14519701C2×C4semidirect
152. #14519701C2×C4semidirect
153. #14519700C2×C4semidirect
154. #14519700C2×C4semidirect
155. C2×Q16×C61C2×C4semidirect
159. #106×C61C2×C4semidirect
160. #103×C61C2×C4semidirect
161. #103×C61C2×C4semidirect
436. #470#6923semidirect
472. C61#23144semidirect
482. C2×Q16C2×#6923semidirect
541. #106C2×#6923semidirect
552. #103C2×#6923semidirect
553. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623452
#214623432
#214619102
#214619082
#214618822
#214618132
#214618052
#214618042
#214615922
#103×#69232
#214615592
#214615072
#470×D612
#2314461