Finite Group Databasebeta

← #30611691

Subgroups — #30611691

Order 15616.

898 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462658C211yesmaximal, characteristic, complemented
2#21462658C211yesmaximal, characteristic, complemented
3#21461305C211yesmaximal, characteristic, complemented
4#21461303C211yesmaximal, characteristic, complemented
5#21461301C211yesmaximal, characteristic, complemented
6#21461296C211yesmaximal, characteristic, complemented
7#21461294C211yesmaximal, characteristic, complemented
8#21461288C211yesmaximal, characteristic, complemented
9#21461288C211yesmaximal, characteristic, complemented
10#21461286C211yesmaximal, characteristic, complemented
11#21461284C211yesmaximal, characteristic, complemented
12#21461271C211yesmaximal, characteristic, complemented
13#21461269C211yesmaximal, characteristic, complemented
14C2×#16840619C211yesmaximal, characteristic, complemented
15#21459736C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840792—21no—
19#16840792—21no—
20#16840791—21no—
21#16840791—21no—
22#16840789—21no—
23#16840789—21no—
24#16840785C2211yescharacteristic
25#16840785C2211yescharacteristic
26#16840784C2211yescharacteristic
27#16840784C2211yescharacteristic
28#16840782C2211yescharacteristic
29#16840782C2211yescharacteristic
30C4×#11758213C2211yescharacteristic
31C4×#11758213C2211yescharacteristic
32#16840721C2211yescharacteristic
33#16840721C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×#14519832C2211yescharacteristic
36#16840619C2211yescharacteristic
37#16840619C2211yescharacteristic
38#16840619C2211yescharacteristic
39#16840619C2211yescharacteristic
40#16840619C2211yescharacteristic
41#16840619C2211yescharacteristic
42#16840619C2211yescharacteristic
43#16840619C2211yescharacteristic
44#16840618C2211yescharacteristic
45#16840618C2211yescharacteristic
46#16840618C2211yescharacteristic
47#16840618C2211yescharacteristic
48#16840617C2211yescharacteristic
49#16840617C2211yescharacteristic
50#16840617C2211yescharacteristic
51#16840617C2211yescharacteristic
52#16840461—21no—
53#16840461—21no—
54#16840460—21no—
55#16840458—21no—
56#16840458—21no—
57#16840456—21no—
58#16840451—21no—
59#16840447—21no—
60#16840370C411yescharacteristic
61#16840370C411yescharacteristic
62#16840363C411yescharacteristic
63#16840363C411yescharacteristic
64#16840343C411yescharacteristic
65#16840340C411yescharacteristic
66#16840308C2211yescharacteristic
67#16840299C2211yescharacteristic
68#16840299C2211yescharacteristic
69#16840294C2211yescharacteristic
70#16840294C2211yescharacteristic
71C2×#14519768C2211yescharacteristic
72#16840242C411yescharacteristic
73#16840230C2211yescharacteristic
74C61×#520C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C22×#92420—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84#14519844—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832—21no—
95#14519832—21no—
96#14519832—21no—
97#14519832C2311yescharacteristic
98#14519832C2311yescharacteristic
99#14519832C2311yescharacteristic
100#14519832C2311yescharacteristic
101#14519832C2311yescharacteristic
102#14519832C2311yescharacteristic
103#14519832C2311yescharacteristic
104#14519832C2311yescharacteristic
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758222C2×C411yescharacteristic
108C2×#11758222C2×C411yescharacteristic
109#14519775C2×C411yescharacteristic
110#14519773C2×C411yescharacteristic
111#14519772—21no—
112#14519772—21no—
113#14519772—21no—
114#14519772—21no—
115#14519771—21no—
116#14519771—21no—
117#14519770—21no—
118#14519770—21no—
119#14519769—21no—
120#14519769—21no—
121#14519768—21no—
122#14519768—21no—
123#14519768C2×C411yescharacteristic
124#14519768C2×C411yescharacteristic
125#14519768C2311yescharacteristic
126#14519768C2311yescharacteristic
127#14519767—21no—
128#14519767—21no—
129#14519766C2311yescharacteristic
130#14519764C2311yescharacteristic
131#14519762—21no—
132#14519762—21no—
133#14519760—21no—
134#14519760—21no—
135#14519759—21no—
136#14519759—21no—
137#14519759—21no—
138#14519759—21no—
139#14519757—21no—
140#14519757C2×C411yescharacteristic
141#14519757C2×C411yescharacteristic
142#14519756—21no—
143#14519753C2×C411yescharacteristic
144#14519753C2×C411yescharacteristic
145#14519752—21no—
146#14519752C2×C411yescharacteristic
147#14519752C2×C411yescharacteristic
148#14519751—21no—
149#14519751—21no—
150#14519751—21no—
151#14519751—21no—
152#14519751—21no—
153#14519750—21no—
154#14519750—21no—
155#14519749—21no—
156#14519749—21no—
157#14519749—21no—
158#14519749—21no—
159#14519748C2×C411yescharacteristic
160#14519748C2×C411yescharacteristic
161C4×Dic122C2×C411yescharacteristic
162C4×Dic122C2×C411yescharacteristic
163#14519742D411yescharacteristic
164#14519742D411yescharacteristic
165C4×D244—21no—
166C4×D244—21no—
167C4×D244C2×C411yescharacteristic
168C4×D244C2×C411yescharacteristic
169#14519739D411yescharacteristic
170#14519739D411yescharacteristic
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175#14519737—21no—
176#14519737—21no—
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181#14519736—21no—
182#14519736—21no—
183#14519735—21no—
184#14519734—21no—
185#14519734—21no—
186#14519734C2×C411yescharacteristic
187#14519734C2×C411yescharacteristic
188C2×C4⋊Dic61—21no—
189C2×C4⋊Dic61C2×C411yescharacteristic
190C2×#11758196—21no—
191C4⋊C4×D61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C4×Q8×C61C2×C411yescharacteristic
197C4×Q8×C61C2×C411yescharacteristic
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200C4×D4×C61C2×C411yescharacteristic
201C4×D4×C61C2×C411yescharacteristic
202#117×C61—21no—
203#117×C61C2×C411yescharacteristic
204C2×C4⋊C4×C61—21no—
205C2×C4⋊C4×C61C2×C411yescharacteristic
206#41×C61—42no—
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61—21no—
209C2×D4×C61C22×C411yescharacteristic
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C22×C411yescharacteristic
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61C22⋊C411yescharacteristic
221C2×C22⋊D61C22⋊C411yescharacteristic
222C22×Dic61—21no—
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225#11758222—42no—
226#11758222—42no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244C22⋊C411yescharacteristic
230C2×D244C22×C411yescharacteristic
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61C22×C411yescharacteristic
235C2×C4×D61C22×C411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×Dic122C22⋊C411yescharacteristic
241C2×Dic122C22×C411yescharacteristic
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—21no—
250C2×#92420—42no—
251C2×#92420—42no—
252#11758213—42no—
253#11758213—42no—
254D61⋊C8—42no—
255D61⋊C8—42no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C22⋊C411yescharacteristic
260C4⋊C4×C61C22⋊C411yescharacteristic
261C4⋊C4×C61C22×C411yescharacteristic
262C4⋊C4×C61C22×C411yescharacteristic
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61C22⋊C411yescharacteristic
266C22⋊C4×C61C22⋊C411yescharacteristic
267C42×C61—21no—
268C42×C61—21no—
269C42×C61C22×C411yescharacteristic
270C42×C61C22×C411yescharacteristic
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198C22⋊C411yescharacteristic
286#11758198C22⋊C411yescharacteristic
287#11758198C22⋊C411yescharacteristic
288#11758198C22⋊C411yescharacteristic
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61C22×C411yescharacteristic
297C4⋊Dic61C22×C411yescharacteristic
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2411yescharacteristic
322C23×C61—21no—
323C23×C61C2×C22⋊C411yescharacteristic
324C22×D61—21no—
325C22×D61C2×C22⋊C411yescharacteristic
326C22×D61C2×C22⋊C411yescharacteristic
327Q8×C61—41no—
328D4×C61—41no—
329D4×C61—42no—
330C2×C4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—42no—
335C2×C4×C61—81no—
336C2×C4×C61—81no—
337C2×C4×C61—81no—
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C23×C411yescharacteristic
344C22⋊D61—22no—
345C22⋊D61—22no—
346C22⋊D61—42no—
347C22⋊D61—81no—
348C22⋊D61—81no—
349C22⋊D61—81no—
350C22⋊D61—81no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—81no—
357C2×Dic61C2×C22⋊C411yescharacteristic
358C2×Dic61C2×C22⋊C411yescharacteristic
359C2×Dic61C2×C22⋊C411yescharacteristic
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C22×D411yescharacteristic
362C2×Dic61C22×D411yescharacteristic
363D244—41no—
364D244—41no—
365D244—81no—
366D244—81no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—41no—
372C4×D61—41no—
373C4×D61—42no—
374C4×D61—81no—
375C4×D61—81no—
376Dic122—41no—
377Dic122—41no—
378#92420—22no—
379#92420—22no—
380#92420—41no—
381#92420—41no—
382#92420—41no—
383#92420—41no—
384#92420—41no—
385#92420—41no—
386#17690—611nomaximal, Sylow
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61#41312yes—
393C22×C61C22×C22⋊C411yescharacteristic
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—41no—
410C4×C61—41no—
411C4×C61—41no—
412Dic61—21no—
413Dic61—21no—
414Dic61—21no—
415Dic61—21no—
416Dic61—21no—
417Dic61—21no—
418Dic61—41no—
419Dic61—41no—
420Dic61—41no—
421#3512—611no—
422#2970—611no—
423#2970—611no—
424#1535—611no—
425#1535—611no—
426#1534—611no—
427#1532—611no—
428#1532—611no—
429#1530—611no—
430#1530—611no—
431#1529—611no—
432#1529—611no—
433#1524—611no—
434#1524—611no—
435C2×#330—611no—
436C2×C61—22no—
437C2×C61—81no—
438C2×C61C2×#41311yescharacteristic
439C2×C61#290111yescharacteristic
440C2×C61#290111yescharacteristic
441D61—41no—
442D61—41no—
443D61—81no—
444#553—1221no—
445#553—1221no—
446#553—1221no—
447#553—1221no—
448#553—1221no—
449#553—1221no—
450#552—1221no—
451#552—1221no—
452#541—611no—
453#541—611no—
454#540—611no—
455#540—611no—
456#537—611no—
457#537—611no—
458#532—611no—
459#529—611no—
460#529—611no—
461#529—611no—
462#529—611no—
463C2×#125—611no—
464#520—611no—
465#520#692311yescharacteristic
466C4×#41—611no—
467#446—1221no—
468#446—1221no—
469#435—1221no—
470#435—1221no—
471#435—1221no—
472#435—1221no—
473C8×D4—1221no—
474C8×D4—1221no—
475#432—611no—
476#432—611no—
477#432—611no—
478#432—611no—
479#432—611no—
480#432—611no—
481C4×M16—611no—
482C4×M16—611no—
483C2×#97—611no—
484C2×#97—611no—
485C2×#97—611no—
486C2×#97—611no—
487#330—611no—
488#330—611no—
489#330—611no—
490#330—611no—
491#330—611no—
492#330—611no—
493#330—611no—
494#330—611no—
495#329—611no—
496#329—611no—
497#329—611no—
498#329—611no—
499#329—611no—
500#329—611no—
501#329—611no—
502#329—611no—
503C61#1769011yescharacteristic, complemented, Sylow
504C2×#41—611no—
505C2×#41—611no—
506C2×#41C2×#692311yescharacteristic
507C2×M16—1221no—
508C2×M16—1221no—
509C22×C8—1221no—
510C22×C8—1221no—
511C22×C8—1221no—
512C22×C8—1221no—
513C4⋊Q8—611no—
514#127—611no—
515#126—1221no—
516#126—1221no—
517#126—1221no—
518#126—1221no—
519#126—1221no—
520#126—1221no—
521#126—1221no—
522#126—1221no—
523#125—611no—
524#125—611no—
525#125—611no—
526#125—611no—
527#125—1221no—
528#125—1221no—
529#125—1221no—
530#125—1221no—
531#125—1221no—
532#125—1221no—
533#124—611no—
534#124—611no—
535#123—1221no—
536#123—1221no—
537#123—1221no—
538#123—1221no—
539#123—1221no—
540#123—1221no—
541#123—1221no—
542#123—1221no—
543C22⋊Q8—611no—
544C22⋊Q8—611no—
545C22⋊Q8—611no—
546C22⋊Q8—611no—
547C22⋊Q8—1221no—
548C22⋊Q8—1221no—
549#121—611no—
550#121—611no—
551#121—611no—
552#121—611no—
553#121—1221no—
554#121—1221no—
555#121—1221no—
556#121—1221no—
557#121—1221no—
558#121—1221no—
559#121—1221no—
560#121—1221no—
561#121—1221no—
562#121—1221no—
563#121—1221no—
564#121—1221no—
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8C2×#692311yescharacteristic
570C4×Q8C2×#692311yescharacteristic
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—611no—
574C4×D4—611no—
575C4×D4—611no—
576C4×D4—611no—
577C4×D4—611no—
578C4×D4—611no—
579C4×D4—611no—
580C4×D4—611no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4—1221no—
584C4×D4—1221no—
585C4×D4—1221no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4C2×#692311yescharacteristic
590C4×D4C2×#692311yescharacteristic
591#117—21no—
592#117—611no—
593#117—611no—
594#117—1221no—
595#117—1221no—
596#117—1221no—
597#117—1221no—
598#117—1221no—
599#117C2×#692311yescharacteristic
600C2×C4⋊C4—21no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4C2×#692311yescharacteristic
606C2×C42—611no—
607C2×C42—611no—
608C2×C42—611no—
609C4⋊C8—1221no—
610C4⋊C8—1221no—
611C4⋊C8—1221no—
612C4⋊C8—1221no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C22⋊C8—1221no—
616C22⋊C8—1221no—
617C22⋊C8—1221no—
618C22⋊C8—1221no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621#97—611no—
622#97—611no—
623#97—611no—
624#97—611no—
625#97—611no—
626#97—611no—
627#97—611no—
628#97—611no—
629#97—1221no—
630#97—1221no—
631#97—1221no—
632#97—1221no—
633C4×C8—1221no—
634C4×C8—1221no—
635#41—42no—
636#41—2442no—
637#41—2442no—
638C2×Q8—611no—
639C2×Q8—611no—
640C2×Q8C22×#692311yescharacteristic
641C2×D4—21no—
642C2×D4—611no—
643C2×D4—611no—
644C2×D4—611no—
645C2×D4—611no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4C22×#692311yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4C22×#692311yescharacteristic
671M16—2442no—
672M16—2442no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—2442no—
682C2×C8—2442no—
683C2×C8—2442no—
684C2×C8—2442no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—611no—
689C4⋊C4—611no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—611no—
693C4⋊C4—611no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4C22⋊#692311yescharacteristic
712C4⋊C4C22⋊#692311yescharacteristic
713C4⋊C4C22×#692311yescharacteristic
714C4⋊C4C22×#692311yescharacteristic
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—611no—
718C22⋊C4—611no—
719C22⋊C4—611no—
720C22⋊C4—611no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4C22⋊#692311yescharacteristic
736C22⋊C4C22⋊#692311yescharacteristic
737C42—21no—
738C42—21no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—1221no—
748C42—1221no—
749C42C22×#692311yescharacteristic
750C42C22×#692311yescharacteristic
751C23—21no—
752C23—611no—
753C23—611no—
754C23—1221no—
755C23C2×C22⋊#692311yescharacteristic
756Q8—41no—
757Q8—2441no—
758Q8—2441no—
759D4—41no—
760D4—42no—
761D4—1222no—
762D4—1222no—
763D4—4881no—
764D4—4881no—
765D4—4881no—
766D4—4881no—
767D4—4881no—
768D4—4881no—
769D4—2441no—
770D4—2441no—
771D4—2442no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—42no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—611no—
781C2×C4—611no—
782C2×C4—611no—
783C2×C4—611no—
784C2×C4—611no—
785C2×C4—611no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—4881no—
790C2×C4—4881no—
791C2×C4—4881no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2442no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4C2×C22⋊#692311yescharacteristic
802C2×C4C2×C22⋊#692311yescharacteristic
803C2×C4C2×C22⋊#692311yescharacteristic
804C2×C4C2×C22⋊#692311yescharacteristic
805C2×C4C2×C22⋊#692311yescharacteristic
806C2×C4C23×#692311yescharacteristic
807C8—1222no—
808C8—1222no—
809C8—2441no—
810C8—2441no—
811C8—2441no—
812C8—2441no—
813C8—2441no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—1221no—
821C22—1221no—
822C22—1221no—
823C22—1221no—
824C22—1221no—
825C22—1221no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22#1684074812yes—
830C22C22×C22⋊#692311yescharacteristic
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—1221no—
841C4—1221no—
842C4—1221no—
843C4—1221no—
844C4—1221no—
845C4—1221no—
846C4—2441no—
847C4—2441no—
848C4—2441no—
849C2—22no—
850C2—81no—
851C2—4881no—
852C2—2441no—
853C2—2441no—
854C2C2×#1684074811yescharacteristic
855C2#2146244911yescharacteristic
856C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#520C4
socleC22×C61C22×C22⋊C4
prime radical#21459736C2
cosocleC4×Dic61C24
hypercenter#520#6923
hypocenterC61#17690
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #21462658C2semidirect
2. #21462658C2semidirect
3. #21461305C2semidirect
4. #21461303C2semidirect
5. #21461301C2semidirect
6. #21461296C2semidirect
7. #21461294C2semidirect
8. #21461288C2semidirect
9. #21461288C2semidirect
10. #21461286C2semidirect
11. #21461284C2semidirect
12. #21461271C2semidirect
13. #21461269C2semidirect
14. C2×#16840619C2semidirect
503. C61#17690semidirect

Maximal subgroups

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

subgroupindex
#214626582
#214613052
#214613032
#214613012
#214612962
#214612942
#214612882
#214612862
#214612842
#214612712
#214612692
C2×#168406192
#214597362
#1769061