Finite Group Databasebeta

← #30611980

Subgroups — #30611980

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462752C211yesmaximal, characteristic
2#21462748C211yesmaximal, characteristic
3#21461359C211yesmaximal, characteristic, complemented
4#21461355C211yesmaximal, characteristic, complemented
5#21461354C211yesmaximal, characteristic, complemented
6#21461345C211yesmaximal, characteristic, complemented
7#21461344C211yesmaximal, characteristic, complemented
8#21461337C211yesmaximal, characteristic, complemented
9#21461336C211yesmaximal, characteristic, complemented
10#21461333C211yesmaximal, characteristic, complemented
11#21461333C211yesmaximal, characteristic, complemented
12#21461325C211yesmaximal, characteristic, complemented
13#21461321C211yesmaximal, characteristic, complemented
14#21461320C211yesmaximal, characteristic, complemented
15#21459701C211yesmaximal, characteristic
16#16840814—21no—
17#16840811—21no—
18#16840796—21no—
19#16840795—21no—
20#16840795—21no—
21#16840792—21no—
22#16840791—21no—
23#16840789—21no—
24#16840785C2211yescharacteristic
25#16840782C2211yescharacteristic
26#16840780C2211yescharacteristic
27#16840780C2211yescharacteristic
28#16840780C2211yescharacteristic
29#16840779C2211yescharacteristic
30#16840767C2211yescharacteristic
31#16840767C2211yescharacteristic
32#16840767C2211yescharacteristic
33#16840765C2211yescharacteristic
34C2×#14519844C2211yescharacteristic
35D61⋊(C4⋊C8)C2211yescharacteristic
36#16840622C2211yescharacteristic
37#16840622C2211yescharacteristic
38#16840622C2211yescharacteristic
39#16840622C2211yescharacteristic
40#16840622C2211yescharacteristic
41#16840622C2211yescharacteristic
42#16840622C2211yescharacteristic
43#16840622C2211yescharacteristic
44#16840621C2211yescharacteristic
45#16840621C2211yescharacteristic
46#16840621C2211yescharacteristic
47#16840621C2211yescharacteristic
48#16840621C2211yescharacteristic
49#16840621C2211yescharacteristic
50#16840621C2211yescharacteristic
51#16840621C2211yescharacteristic
52#16840489—21no—
53#16840489—21no—
54#16840479—21no—
55#16840479—21no—
56#16840448—21no—
57#16840448—21no—
58#16840444—21no—
59#16840444—21no—
60#16840375C411yescharacteristic
61#16840374C411yescharacteristic
62#16840373C411yescharacteristic
63#16840335C411yescharacteristic
64#16840335C411yescharacteristic
65#16840318C2211yescharacteristic
66#16840316C2211yescharacteristic
67#16840316C2211yescharacteristic
68#16840314C2211yescharacteristic
69#16840314C2211yescharacteristic
70C4⋊Q8×D61C2211yescharacteristic
71#16840238C411yescharacteristic
72#16840238C411yescharacteristic
73#16840230C2211yescharacteristic
74C61×#541C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C22×#92420—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84#14519844—21no—
85#14519844C2311yescharacteristic
86#14519844C2311yescharacteristic
87#14519844C2311yescharacteristic
88#14519844C2311yescharacteristic
89#14519844C2311yescharacteristic
90#14519844C2311yescharacteristic
91#14519844C2311yescharacteristic
92#14519844C2311yescharacteristic
93C4⋊#92420—21no—
94C4⋊#92420—21no—
95#14519834—21no—
96#14519834—21no—
97#14519834—21no—
98#14519834—21no—
99C22⋊#92420—21no—
100C22⋊#92420—21no—
101#14519832—21no—
102#14519832—21no—
103C4×#92420—21no—
104C4×#92420—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758222C2×C411yescharacteristic
108C2×Q8×D61C2×C411yescharacteristic
109C2×Q8×D61C2×C411yescharacteristic
110#14519777C2×C411yescharacteristic
111#14519776—21no—
112#14519776—21no—
113#14519776—21no—
114#14519776—21no—
115#14519776C2311yescharacteristic
116#14519776C2311yescharacteristic
117#14519775C2311yescharacteristic
118#14519775C2311yescharacteristic
119#14519772—21no—
120#14519772—21no—
121#14519772—21no—
122#14519772—21no—
123#14519770—21no—
124#14519770—21no—
125#14519769C2×C411yescharacteristic
126#14519768—21no—
127#14519768—21no—
128#14519767—21no—
129#14519767—21no—
130#14519767—21no—
131#14519767—21no—
132#14519767—21no—
133#14519767—21no—
134#14519767—21no—
135#14519767—21no—
136#14519763—21no—
137#14519763—21no—
138#14519762—21no—
139#14519762—21no—
140#14519759—21no—
141#14519759—21no—
142#14519757C2×C411yescharacteristic
143#14519757C2×C411yescharacteristic
144#14519756C2×C411yescharacteristic
145#14519756C2×C411yescharacteristic
146#14519755—21no—
147#14519755—21no—
148#14519755—21no—
149#14519755—21no—
150#14519754—21no—
151#14519754—21no—
152#14519753C2×C411yescharacteristic
153#14519753C2×C411yescharacteristic
154Q8×Dic61C2×C411yescharacteristic
155Q8×Dic61C2×C411yescharacteristic
156C4×Dic122—21no—
157C4×Dic122—21no—
158C4×Dic122—21no—
159C4×Dic122—21no—
160C4×Dic122C2×C411yescharacteristic
161C4×Dic122C2×C411yescharacteristic
162#14519742—21no—
163#14519742—21no—
164#14519742—21no—
165#14519742—21no—
166#14519742—21no—
167#14519742—21no—
168#14519742C2×C411yescharacteristic
169#14519742C2×C411yescharacteristic
170#14519742D411yescharacteristic
171#14519742D411yescharacteristic
172#14519739D411yescharacteristic
173#14519739D411yescharacteristic
174#14519737D411yescharacteristic
175#14519737D411yescharacteristic
176#14519737D411yescharacteristic
177#14519737D411yescharacteristic
178#14519735—21no—
179#14519735—21no—
180#14519735C2×C411yescharacteristic
181#14519735C2×C411yescharacteristic
182#14519734—21no—
183#14519734—21no—
184#14519734—21no—
185#14519734—21no—
186#14519734C2×C411yescharacteristic
187#14519734C2×C411yescharacteristic
188#14519733—21no—
189#14519733—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#126×C61—21no—
197#126×C61—21no—
198#125×C61—21no—
199#125×C61—21no—
200#125×C61C2×C411yescharacteristic
201C22⋊Q8×C61C2×C411yescharacteristic
202C22⋊Q8×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×Q8×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C2×Q8×C61C22×C411yescharacteristic
207C2×Q8×C61C22×C411yescharacteristic
208C22×C4×C61C22×C411yescharacteristic
209C2×C22⋊D61C22⋊C411yescharacteristic
210C2×C22⋊D61C22⋊C411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213Q8×D61—42no—
214Q8×D61—42no—
215#11758222—42no—
216C2×D244C22⋊C411yescharacteristic
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61C22×C411yescharacteristic
220C2×C4×D61C22×C411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122C22⋊C411yescharacteristic
230C2×Dic122C22×C411yescharacteristic
231C2×Dic122C22×C411yescharacteristic
232#11758217—81no—
233C2×#92420—21no—
234C2×#92420—21no—
235C2×#92420—21no—
236C2×#92420—21no—
237C2×#92420—21no—
238C2×#92420—21no—
239C2×#92420—21no—
240C2×#92420—21no—
241C2×#92420—81no—
242#11758213—81no—
243#11758213—81no—
244#11758213—81no—
245D61⋊C8—81no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C22⋊C411yescharacteristic
255C4⋊C4×C61C22⋊C411yescharacteristic
256C4⋊C4×C61C22×C411yescharacteristic
257C4⋊C4×C61C22×C411yescharacteristic
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61C22⋊C411yescharacteristic
261C22⋊C4×C61C22⋊C411yescharacteristic
262C42×C61—21no—
263C42×C61—21no—
264C42×C61C22×C411yescharacteristic
265C42×C61C22×C411yescharacteristic
266C22⋊Dic61—21no—
267C22⋊Dic61—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198C22⋊C411yescharacteristic
275#11758198C22⋊C411yescharacteristic
276#11758198C22⋊C411yescharacteristic
277#11758198C22⋊C411yescharacteristic
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61C22×C411yescharacteristic
285C4⋊Dic61C22×C411yescharacteristic
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196C22⋊C411yescharacteristic
303#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
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×C61C2×C22⋊C411yescharacteristic
323C22×D61C2×C22⋊C411yescharacteristic
324C22×D61C2×C22⋊C411yescharacteristic
325Q8×C61—41no—
326Q8×C61—41no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—41no—
332C2×C4×C61C2×C22⋊C411yescharacteristic
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C2×C4×C61C2×C22⋊C411yescharacteristic
337C2×C4×C61C23×C411yescharacteristic
338C22⋊D61—22no—
339C22⋊D61—41no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C22×D411yescharacteristic
353C2×Dic61C22×D411yescharacteristic
354D244—41no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—22no—
364C4×D61—41no—
365C4×D61—42no—
366C4×D61—42no—
367Dic122—22no—
368Dic122—41no—
369Dic122—41no—
370Dic122—41no—
371Dic122—41no—
372Dic122—42no—
373Dic122—42no—
374Dic122—41no—
375Dic122—41no—
376#92420—41no—
377#92420—41no—
378#92420—41no—
379#92420—41no—
380#92420—41no—
381#92420—41no—
382#92420—41no—
383#92420—41no—
384#17778—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61C22×C22⋊C411yescharacteristic
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—41no—
405Dic61—21no—
406Dic61—21no—
407Dic61—21no—
408Dic61—41no—
409Dic61—41no—
410Dic61—41no—
411Dic61—41no—
412Dic61#41312yes—
413Dic61#57711yescharacteristic
414Dic61#57711yescharacteristic
415Dic61#57811yescharacteristic
416Dic61#57811yescharacteristic
417#3509—611no—
418#2991—611no—
419#2990—611no—
420#1561—611no—
421#1559—611no—
422#1559—611no—
423#1554—611no—
424#1554—611no—
425#1550—611no—
426#1550—611no—
427#1548—611no—
428#1548—611no—
429#1544—611no—
430#1542—611no—
431#1542—611no—
432C2×C61—41no—
433C2×C61C2×#41311yescharacteristic
434C2×C61#289811yescharacteristic
435C2×C61#289811yescharacteristic
436D61—41no—
437D61—41no—
438#557—1221no—
439#557—1221no—
440#556—1221no—
441#556—1221no—
442#552—1221no—
443#552—1221no—
444#552—1221no—
445#552—1221no—
446#541—611no—
447#541—611no—
448#541—611no—
449#541#692311yescharacteristic
450#536—611no—
451#536—611no—
452#533—611no—
453#533—611no—
454#533—611no—
455#533—611no—
456#533—611no—
457C2×C4⋊Q8—611no—
458#519—611no—
459#519—611no—
460C4×#41—611no—
461#446—1221no—
462C8×Q8—1221no—
463#436—1221no—
464#436—1221no—
465#436—1221no—
466#435—1221no—
467#435—1221no—
468C8×D4—1221no—
469#432—611no—
470#432—611no—
471#431—611no—
472#431—611no—
473#431—611no—
474#431—611no—
475#423—611no—
476#423—611no—
477#423—611no—
478#423—611no—
479C2×C4⋊C8—611no—
480C2×C4⋊C8—611no—
481#333—611no—
482#333—611no—
483#333—611no—
484#333—611no—
485#333—611no—
486#333—611no—
487#333—611no—
488#333—611no—
489#332—611no—
490#332—611no—
491#332—611no—
492#332—611no—
493#332—611no—
494#332—611no—
495#332—611no—
496#332—611no—
497C61#1777811yescharacteristic, complemented, Sylow
498C2×#41—611no—
499C22×Q8—611no—
500C22×Q8—611no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C22×C8—1221no—
506C22×C8—1221no—
507C4⋊Q8—611no—
508C4⋊Q8—611no—
509C4⋊Q8—611no—
510C4⋊Q8—611no—
511C4⋊Q8—611no—
512C4⋊Q8—1221no—
513C4⋊Q8—1221no—
514C4⋊Q8—1221no—
515C4⋊Q8—1221no—
516C4⋊Q8C2×#692311yescharacteristic
517#126—21no—
518#126—21no—
519#126—1221no—
520#126—1221no—
521#126—1221no—
522#126—1221no—
523#126—1221no—
524#126—1221no—
525#125—21no—
526#125—21no—
527#125—611no—
528#125—1221no—
529#125—1221no—
530#125—1221no—
531#125—1221no—
532#125—1221no—
533#125—1221no—
534#125—1221no—
535#125—1221no—
536#125—1221no—
537#125—1221no—
538#125C2×#692311yescharacteristic
539#124—1221no—
540#124—1221no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545C22⋊Q8—611no—
546C22⋊Q8—611no—
547C22⋊Q8—611no—
548C22⋊Q8—611no—
549C22⋊Q8—611no—
550C22⋊Q8—611no—
551C22⋊Q8—1221no—
552C22⋊Q8—1221no—
553C22⋊Q8—1221no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8C2×#692311yescharacteristic
558C22⋊Q8C2×#692311yescharacteristic
559C4×Q8—611no—
560C4×Q8—611no—
561C4×Q8—611no—
562C4×Q8—611no—
563C4×Q8—611no—
564C4×Q8—611no—
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—1221no—
568C4×Q8—1221no—
569C4×Q8—1221no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8C2×#692311yescharacteristic
578C4×Q8C2×#692311yescharacteristic
579C4×D4—611no—
580C4×D4—611no—
581C4×D4—611no—
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—611no—
585#117—611no—
586#117—611no—
587#117—611no—
588#117—611no—
589#117—1221no—
590#117—1221no—
591#117—1221no—
592#117—1221no—
593#117—1221no—
594#117—1221no—
595#117—1221no—
596#117—1221no—
597#117C2×#692311yescharacteristic
598C2×C4⋊C4—1221no—
599C2×C4⋊C4—1221no—
600C2×C42—611no—
601C2×C42—611no—
602C2×C42—611no—
603C4⋊C8—611no—
604C4⋊C8—611no—
605C4⋊C8—611no—
606C4⋊C8—611no—
607C4⋊C8—611no—
608C4⋊C8—611no—
609C4⋊C8—611no—
610C4⋊C8—611no—
611C4⋊C8—1221no—
612C4⋊C8—1221no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C4⋊C8—1221no—
616C4⋊C8—1221no—
617C22⋊C8—1221no—
618C22⋊C8—1221no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621C22⋊C8—1221no—
622C22⋊C8—1221no—
623#97—1221no—
624#97—1221no—
625C4×C8—1221no—
626C4×C8—1221no—
627C4×C8—1221no—
628C4×C8—1221no—
629#41—2442no—
630C2×Q8—611no—
631C2×Q8—611no—
632C2×Q8—611no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×Q8—2442no—
638C2×Q8—2442no—
639C2×Q8C22×#692311yescharacteristic
640C2×Q8C22×#692311yescharacteristic
641C2×D4—611no—
642C2×D4—611no—
643C2×D4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4C22×#692311yescharacteristic
655M16—4881no—
656M16—4881no—
657M16—4881no—
658M16—4881no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—4881no—
668C2×C8—4881no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—611no—
678C4⋊C4—611no—
679C4⋊C4—611no—
680C4⋊C4—611no—
681C4⋊C4—611no—
682C4⋊C4—611no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
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⋊C4C22⋊#692311yescharacteristic
706C4⋊C4C22⋊#692311yescharacteristic
707C4⋊C4C22×#692311yescharacteristic
708C4⋊C4C22×#692311yescharacteristic
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—611no—
712C22⋊C4—611no—
713C22⋊C4—611no—
714C22⋊C4—611no—
715C22⋊C4—1221no—
716C22⋊C4—1221no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4C22⋊#692311yescharacteristic
724C22⋊C4C22⋊#692311yescharacteristic
725C42—21no—
726C42—21no—
727C42—611no—
728C42—611no—
729C42—611no—
730C42—611no—
731C42—611no—
732C42—611no—
733C42—611no—
734C42—611no—
735C42—1221no—
736C42—1221no—
737C42—1221no—
738C42—1221no—
739C42—1221no—
740C42—1221no—
741C42—1221no—
742C42—1221no—
743C42C22×#692311yescharacteristic
744C42C22×#692311yescharacteristic
745C23—611no—
746C23—611no—
747C23C2×C22⋊#692311yescharacteristic
748Q8—41no—
749Q8—41no—
750Q8—1222no—
751Q8—2441no—
752Q8—2441no—
753Q8—2441no—
754Q8—2441no—
755Q8—2441no—
756Q8—2441no—
757Q8—2442no—
758Q8—2442no—
759D4—1222no—
760D4—2441no—
761D4—2441no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—41no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—611no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1222no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—2441no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4C2×C22⋊#692311yescharacteristic
794C2×C4C2×C22⋊#692311yescharacteristic
795C2×C4C2×C22⋊#692311yescharacteristic
796C2×C4C2×C22⋊#692311yescharacteristic
797C2×C4C2×C22⋊#692311yescharacteristic
798C2×C4C23×#692311yescharacteristic
799C8—2441no—
800C8—2441no—
801C8—2441no—
802C8—2441no—
803C8—2441no—
804C8—2441no—
805C8—2441no—
806C8—2441no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—1221no—
811C22—1221no—
812C22—1221no—
813C22—1221no—
814C22—1221no—
815C22—1221no—
816C22C22×C22⋊#692311yescharacteristic
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—612no—
828C4—611no—
829C4—611no—
830C4—611no—
831C4—611no—
832C4—1221no—
833C4—1221no—
834C4—1221no—
835C4—2441no—
836C4—2441no—
837C4—2441no—
838C4—2441no—
839C2—41no—
840C2—2441no—
841C2—2441no—
842C2D61⋊#41311yescharacteristic
843C2#2146244111yescharacteristic
844C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#541C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222C2×C4
cosocleC4×Dic61C24
hypercenter#541#6923
hypocenterC61#17778
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
3. #21461359C2semidirect
4. #21461355C2semidirect
5. #21461354C2semidirect
6. #21461345C2semidirect
7. #21461344C2semidirect
8. #21461337C2semidirect
9. #21461336C2semidirect
10. #21461333C2semidirect
11. #21461333C2semidirect
12. #21461325C2semidirect
13. #21461321C2semidirect
14. #21461320C2semidirect
497. C61#17778semidirect

Maximal subgroups

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

subgroupindex
#214627522
#214627482
#214613592
#214613552
#214613542
#214613452
#214613442
#214613372
#214613362
#214613332
#214613252
#214613212
#214613202
#214597012
#1777861