Finite Group Databasebeta

← #29648147

Subgroups — #29648147

Order 15616.

976 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2C2×#16839817C211yesmaximal, characteristic, complemented
3#432×D61C211yesmaximal, characteristic, complemented
4#21444455C212yesmaximal, complemented
5#21444452C212yesmaximal, complemented
6#21444440C211yesmaximal, characteristic, complemented
7#21444439C211yesmaximal, characteristic, complemented
8#21444438C212yesmaximal, complemented
9#21444437C211yesmaximal, characteristic, complemented
10#21444436C212yesmaximal, complemented
11C61×#1532C211yesmaximal, characteristic, complemented
12#16840318C2211yescharacteristic
13#16840316C411yescharacteristic
14#16840314C411yescharacteristic
15#16840311C2211yescharacteristic
16#16840309C411yescharacteristic
17#16840307C411yescharacteristic
18#16840297C2211yescharacteristic
19#16840296C2211yescharacteristic
20#16840295—21no—
21#16840295—21no—
22#16840291C2211yescharacteristic
23#16840290—21no—
24#16840289—21no—
25#16840275C411yescharacteristic
26#16840272C411yescharacteristic
27#16840271—21no—
28#16840270—21no—
29C4×#11758226C411yescharacteristic
30#16840230—21no—
31C4×#11758224—21no—
32C4×#11758224C411yescharacteristic
33C2×C42×D61C2211yescharacteristic
34#16839819C2211yescharacteristic
35#16839818—21no—
36#16839817—21no—
37#16839817—21no—
38#16839817C2212yes—
39#16839817C2212yes—
40#16839817C2212yes—
41#16839816—21no—
42C2×#14519706—21no—
43C4⋊C8×D61—21no—
44C2×#14519689—21no—
45C22⋊C8×D61—21no—
46C2×#14519688C2211yescharacteristic
47#97×D61C2212yes—
48#16839504C2212yescomplemented
49#16839503C2212yescomplemented
50#16839503C2212yescomplemented
51#16839502C2212yescomplemented
52#16839501C2212yescomplemented
53#16839501C2212yescomplemented
54C61×#529C2211yescharacteristic
55C61×#432C2211yescharacteristic
56C2×#97×C61C2211yescharacteristic
57C61×#330C2212yescomplemented
58C61×#329C2212yescomplemented
59C2×#11758226C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758224—21no—
62C2×#11758224C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×#92418—21no—
67C2×C8×D61—22no—
68#14519776C2×C411yescharacteristic
69#14519776C2×C411yescharacteristic
70#14519775C2×C411yescharacteristic
71#14519773C2×C411yescharacteristic
72#14519772—21no—
73#14519771—21no—
74#14519770—21no—
75#14519769C2311yescharacteristic
76#14519767—21no—
77#14519767—21no—
78#14519765C2311yescharacteristic
79#14519763—21no—
80#14519763—21no—
81#14519762—21no—
82#14519762—21no—
83#14519760—21no—
84#14519759—21no—
85#14519759—21no—
86#14519757C2×C411yescharacteristic
87#14519756C2×C411yescharacteristic
88#14519755—21no—
89#14519755—21no—
90#14519755—21no—
91#14519754—21no—
92#14519753C2×C411yescharacteristic
93#14519752C2×C411yescharacteristic
94#14519751C2×C411yescharacteristic
95#14519750—21no—
96#14519750—21no—
97#14519750—21no—
98#14519749—21no—
99#14519748C2×C411yescharacteristic
100#14519747—21no—
101#14519745—21no—
102Q8×Dic61C2×C411yescharacteristic
103C4×Dic122—21no—
104C4×Dic122C2×C411yescharacteristic
105#14519742—21no—
106#14519742—21no—
107#14519742—21no—
108#14519742C2×C411yescharacteristic
109C4×D244—21no—
110C4×D244C2×C411yescharacteristic
111D4×Dic61—21no—
112D4×Dic61C2×C411yescharacteristic
113#14519739—21no—
114#14519739—21no—
115#14519739—21no—
116#14519739C2×C411yescharacteristic
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C4×C22⋊D61—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519735—21no—
128#14519735—21no—
129#14519735C2×C411yescharacteristic
130#14519735C2×C411yescharacteristic
131#14519734—21no—
132#14519734—21no—
133#14519733—21no—
134#14519733—21no—
135#14519733—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61D411yescharacteristic
139C2×C4×Dic61D411yescharacteristic
140C42×D61—21no—
141C42×D61C2×C411yescharacteristic
142C42×D61C2×C411yescharacteristic
143C42×D61D411yescharacteristic
144C42×D61D411yescharacteristic
145C42×D61D411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61C2311yescharacteristic
148C42×D61C2311yescharacteristic
149C4⋊#92418—21no—
150#14519706—22no—
151#14519706—22no—
152#14519706—22no—
153C22⋊#92418—21no—
154#14519689—22no—
155#14519689—22no—
156#14519689—22no—
157#14519688—21no—
158#14519688C2312yes—
159#14519688C2312yes—
160#14519687—22no—
161C22×C8×C61—21no—
162#126×C61—21no—
163#125×C61C2311yescharacteristic
164#124×C61C2311yescharacteristic
165#123×C61—21no—
166C22⋊Q8×C61C2×C411yescharacteristic
167#121×C61C2×C411yescharacteristic
168C4×Q8×C61C2×C411yescharacteristic
169C4×D4×C61—21no—
170C4×D4×C61C2×C411yescharacteristic
171#117×C61—21no—
172C2×C42×C61C2311yescharacteristic
173C4⋊C8×C61—21no—
174C22⋊C8×C61—21no—
175#97×C61—21no—
176#97×C61C2312yes—
177#97×C61C2312yes—
178C23×D61C22⋊C411yescharacteristic
179C2×Q8×C61C22×C411yescharacteristic
180C2×D4×C61—21no—
181C2×D4×C61C22×C411yescharacteristic
182C22×C4×C61—21no—
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61C22⋊C411yescharacteristic
194C22×Dic61C22⋊C411yescharacteristic
195C22×Dic61C22⋊C411yescharacteristic
196#11758226—42no—
197#11758224—42no—
198#11758224—44no—
199#11758222—44no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244C22×C411yescharacteristic
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22×C411yescharacteristic
216C2×C4×D61C22×C411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122C22×C411yescharacteristic
224C2×C8×C61—22no—
225C2×C8×C61—22no—
226C2×C8×C61—42no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C22×C411yescharacteristic
232C4⋊C4×C61C22×C411yescharacteristic
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C42×C61—21no—
239C42×C61C22×C411yescharacteristic
240C42×C61C2×D411yescharacteristic
241C42×C61C2×D411yescharacteristic
242C42×C61C2411yescharacteristic
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246#11758198—21no—
247#11758198—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61C22×C411yescharacteristic
259C4⋊Dic61C22×C411yescharacteristic
260#11758196—21no—
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61C22⋊C411yescharacteristic
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22×C411yescharacteristic
282C4×Dic61C22×C411yescharacteristic
283C4×Dic61C2×D411yescharacteristic
284C4×Dic61C2×D411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C2×#92418—22no—
288C2×#92418—22no—
289C2×#92418—42no—
290C8×D61—44no—
291C23×C61—21no—
292C23×C61C2×C22⋊C411yescharacteristic
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—21no—
296C22×D61—41no—
297C22×D61C2×C22⋊C411yescharacteristic
298C22×D61C2×C22⋊C411yescharacteristic
299Q8×C61—41no—
300D4×C61—41no—
301D4×C61—42no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—42no—
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C2×C22⋊C411yescharacteristic
311C2×C4×C61C2×C22⋊C411yescharacteristic
312C2×C4×C61C23×C411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C22⋊D61—42no—
316C22⋊D61—42no—
317C22⋊D61—42no—
318C22⋊D61—42no—
319C22⋊D61—42no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—41no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61C2×C22⋊C411yescharacteristic
329C2×Dic61C2×C22⋊C411yescharacteristic
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C2×C22⋊C411yescharacteristic
332C2×Dic61C2×C22⋊C411yescharacteristic
333C2×Dic61C2×C22⋊C411yescharacteristic
334D244—41no—
335D244—42no—
336D244—42no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—42no—
350C4×D61—42no—
351C4×D61—42no—
352Dic122—42no—
353Dic122—42no—
354Dic122—41no—
355C8×C61—42no—
356C8×C61—42no—
357#92418—42no—
358#92418—42no—
359#17678—611nomaximal, Sylow
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61#42112yes—
366C22×C61C22×C22⋊C411yescharacteristic
367C2×D61—21no—
368C2×D61—21no—
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—44no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61#42112yes—
377C4×C61—21no—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—21no—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—41no—
384C4×C61—41no—
385C4×C61—41no—
386Dic61—21no—
387Dic61—21no—
388Dic61—21no—
389Dic61—21no—
390Dic61—21no—
391Dic61—41no—
392Dic61—41no—
393Dic61—41no—
394Dic61#41312yes—
395#3444—611no—
396C2×#432—611no—
397C2×#432—611no—
398#1537—612no—
399#1536—612no—
400#1532—611no—
401#1532—611no—
402#1532—612no—
403#1532—612no—
404#1532—611no—
405#1532D6111yescharacteristic, complemented
406C2×C61—22no—
407C2×C61—81no—
408C2×C61C2×#41311yescharacteristic
409C2×C61C2×#42111yescharacteristic
410C2×C61C2×#42111yescharacteristic
411D61—22no—
412D61—41no—
413D61—81no—
414#533—611no—
415#533—611no—
416#533—611no—
417#532—611no—
418#532—611no—
419#532—611no—
420#529—611no—
421#529—611no—
422#529—611no—
423#529—1221no—
424#529—1221no—
425#529—1221no—
426#529—1221no—
427#529C2×D6111yescharacteristic
428#525—611no—
429#525—611no—
430#525—1221no—
431#525—1221no—
432C4×#41—611no—
433C4×#41—611no—
434C4×#41—1221no—
435C4×#41—1221no—
436C22×C42—611no—
437#432—611no—
438#432—612no—
439#432—612no—
440#432—612no—
441#432—1221no—
442#432—1221no—
443#432—1221no—
444#432—1221no—
445#432C2×D6111yescharacteristic
446C2×C4⋊C8—1221no—
447C2×C4⋊C8—1221no—
448C2×C22⋊C8—1221no—
449C2×C22⋊C8—1221no—
450C2×#97—611no—
451C2×#97—612no—
452C2×#97C2×D6111yescharacteristic
453#330—612no—
454#330—612no—
455#330—612no—
456#330C2×D6112yescomplemented
457#329—612no—
458#329—612no—
459#329—612no—
460#329C2×D6112yescomplemented
461C61#1767811yescharacteristic, complemented, Sylow
462C2×#41—611no—
463C2×#41—611no—
464C2×#41—1221no—
465C2×#41—1221no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C22×C8—21no—
470C22×C8—1222no—
471C22×C8—1221no—
472C4⋊Q8—611no—
473C4⋊Q8—611no—
474C4⋊Q8—611no—
475#127—611no—
476#126—21no—
477#126—1221no—
478#126—1221no—
479#126—1221no—
480#125—611no—
481#125—1221no—
482#125—1221no—
483#125C22×D6111yescharacteristic
484#124—611no—
485#124—1221no—
486#124—1221no—
487#124C22×D6111yescharacteristic
488#123—21no—
489#123—1221no—
490#123—1221no—
491#123—1221no—
492#123—1221no—
493#123—1221no—
494C22⋊Q8—611no—
495C22⋊Q8—611no—
496C22⋊Q8—611no—
497C22⋊Q8—1221no—
498C22⋊Q8—1221no—
499C22⋊Q8—1221no—
500C22⋊Q8—1221no—
501C22⋊Q8C4×D6111yescharacteristic
502#121—611no—
503#121—611no—
504#121—611no—
505#121—1221no—
506#121—1221no—
507#121—1221no—
508#121—1221no—
509#121C4×D6111yescharacteristic
510#120—1221no—
511#120—1221no—
512C4×Q8—611no—
513C4×Q8—611no—
514C4×Q8—611no—
515C4×Q8—1221no—
516C4×Q8—1221no—
517C4×Q8—1221no—
518C4×Q8—1221no—
519C4×Q8C4×D6111yescharacteristic
520C4×D4—21no—
521C4×D4—611no—
522C4×D4—611no—
523C4×D4—611no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1221no—
527C4×D4—1221no—
528C4×D4—1221no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4C4×D6111yescharacteristic
540#117—21no—
541#117—611no—
542#117—611no—
543#117—1221no—
544#117—1221no—
545#117—1221no—
546#117—1221no—
547#117—1221no—
548#117—1221no—
549#117—1221no—
550C2×C42—611no—
551C2×C42—611no—
552C2×C42—611no—
553C2×C42—611no—
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—611no—
557C2×C42—611no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—611no—
561C2×C42—1221no—
562C2×C42—1221no—
563C2×C42C22×D6111yescharacteristic
564C4⋊C8—21no—
565C4⋊C8—1222no—
566C4⋊C8—1222no—
567C4⋊C8—1222no—
568C4⋊C8—1221no—
569C22⋊C8—21no—
570C22⋊C8—1222no—
571C22⋊C8—1222no—
572C22⋊C8—1222no—
573C22⋊C8—1221no—
574#97—21no—
575#97—612no—
576#97—612no—
577#97—1222no—
578#97—1221no—
579#97C22×D6112yes—
580#97C22×D6112yes—
581C24—611no—
582#41—2444no—
583#41—2444no—
584#41—2442no—
585#41—2442no—
586C2×Q8—611no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8C2×C4×D6111yescharacteristic
590C2×D4—21no—
591C2×D4—611no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—1221no—
599C2×D4C2×C4×D6111yescharacteristic
600C22×C4—21no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
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—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4C2×C4×D6111yescharacteristic
625C22×C4D4×D6111yescharacteristic
626C22×C4D4×D6111yescharacteristic
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—42no—
630C2×C8—1222no—
631C2×C8—1222no—
632C2×C8—2444no—
633C2×C8—2442no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—611no—
639C4⋊C4—611no—
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—1221no—
651C4⋊C4—1221no—
652C4⋊C4C2×C4×D6111yescharacteristic
653C4⋊C4C2×C4×D6111yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—1221no—
660C22⋊C4—1221no—
661C22⋊C4—1221no—
662C22⋊C4—1221no—
663C22⋊C4—1221no—
664C22⋊C4—1221no—
665C22⋊C4—1221no—
666C22⋊C4—1221no—
667C22⋊C4—1221no—
668C22⋊C4—1221no—
669C22⋊C4—1221no—
670C22⋊C4—1221no—
671C22⋊C4—1221no—
672C42—21no—
673C42—611no—
674C42—611no—
675C42—611no—
676C42—611no—
677C42—611no—
678C42—611no—
679C42—611no—
680C42—611no—
681C42—611no—
682C42—611no—
683C42—611no—
684C42—611no—
685C42—1221no—
686C42—1221no—
687C42—1221no—
688C42—1221no—
689C42—1221no—
690C42C2×C4×D6111yescharacteristic
691C42D4×D6111yescharacteristic
692C42D4×D6111yescharacteristic
693C42C23×D6111yescharacteristic
694C23—21no—
695C23—611no—
696C23—611no—
697C23—1222no—
698C23—1222no—
699C23—1221no—
700C23—2441no—
701C23C22⋊C4×D6111yescharacteristic
702Q8—41no—
703Q8—2441no—
704Q8—2442no—
705Q8—2442no—
706D4—41no—
707D4—42no—
708D4—2441no—
709D4—2442no—
710D4—2442no—
711D4—2442no—
712D4—2442no—
713D4—2442no—
714D4—2442no—
715D4—2442no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
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—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2441no—
751C2×C4—2442no—
752C2×C4C22⋊C4×D6111yescharacteristic
753C2×C4C22⋊C4×D6111yescharacteristic
754C2×C4C22⋊C4×D6111yescharacteristic
755C2×C4C22×C4×D6111yescharacteristic
756C2×C4C2×D4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C8—42no—
759C8—42no—
760C8—2442no—
761C8—2442no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—612no—
768C22—1221no—
769C22—1221no—
770C22—1221no—
771C22—1221no—
772C22—1221no—
773C22—2444no—
774C22—2441no—
775C22—2441no—
776C22—2441no—
777C22#1683977712yes—
778C22C2×C22⋊C4×D6111yescharacteristic
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—612no—
789C4—1221no—
790C4—1221no—
791C4—1221no—
792C4—1221no—
793C4—1221no—
794C4—2441no—
795C4—2441no—
796C4—2441no—
797C2—22no—
798C2—81no—
799C2—1222no—
800C2—4881no—
801C2—2441no—
802C2#413×D6111yescharacteristic
803C2#421×D6111yescharacteristic
804C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1532C2
socleC22×C61C22×C22⋊C4
prime radical#21459113C2
cosocleC42×C61C24
hypercenter#1532D61
hypocenterC61#17678
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1532

Complements

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

NH ≅ G/Ntype
2. C2×#16839817C2semidirect
3. #432×D61C2semidirect
4. #21444455C2semidirect
5. #21444452C2semidirect
6. #21444440C2semidirect
7. #21444439C2semidirect
8. #21444438C2semidirect
9. #21444437C2semidirect
10. #21444436C2semidirect
11. C61×#1532C2semidirect
48. #16839504C22semidirect
49. #16839503C22semidirect
50. #16839503C22semidirect
51. #16839502C22semidirect
52. #16839501C22semidirect
53. #16839501C22semidirect
57. C61×#330C22semidirect
58. C61×#329C22semidirect
405. #1532D61semidirect
456. #330C2×D61semidirect
460. #329C2×D61semidirect
461. C61#17678semidirect

Maximal subgroups

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

subgroupindex
#214591132
C2×#168398172
#432×D612
#214444552
#214444522
#214444402
#214444392
#214444382
#214444372
#214444362
C61×#15322
#1767861