Finite Group Databasebeta

← #30613693

Subgroups — #30613693

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462652C211yesmaximal, characteristic, complemented
2#21462561C211yesmaximal, characteristic, complemented
3#21461467C211yesmaximal, characteristic, complemented
4#21461453C211yesmaximal, characteristic, complemented
5#21461448C211yesmaximal, characteristic, complemented
6#21461439C211yesmaximal, characteristic, complemented
7#21461424C211yesmaximal, characteristic, complemented
8#21461419C211yesmaximal, characteristic, complemented
9#21461409C211yesmaximal, characteristic, complemented
10#21461399C211yesmaximal, characteristic, complemented
11#21461372C211yesmaximal, characteristic, complemented
12#21461138C211yesmaximal, characteristic, complemented
13#21461136C211yesmaximal, characteristic, complemented
14#21461042C211yesmaximal, characteristic, complemented
15#21456407C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840813C2211yescharacteristic
18Q8×#92420C2211yescharacteristic
19#16840797C2211yescharacteristic
20#16840796C2211yescharacteristic
21#16840796C2211yescharacteristic
22#16840795—21no—
23#16840794—21no—
24#16840794—21no—
25#16840791—21no—
26#16840790C2211yescharacteristic
27#16840790C2211yescharacteristic
28D4×#92420C2211yescharacteristic
29#16840787—21no—
30#16840778C2211yescharacteristic
31C2×C4⋊#92420C2211yescharacteristic
32#16840735—21no—
33#16840727—21no—
34C4×#11758217C2211yescharacteristic
35C4×#11758217C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840626C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840624C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840307C2211yescharacteristic
53#16840298C2211yescharacteristic
54#16840170C411yescharacteristic
55#16840148C411yescharacteristic
56#16840125C411yescharacteristic
57#16840123C411yescharacteristic
58#16840015C411yescharacteristic
59#16840013C411yescharacteristic
60#16840010C411yescharacteristic
61SD16×Dic61C2211yescharacteristic
62#16839847C2211yescharacteristic
63#16839844C2211yescharacteristic
64#16839842C2211yescharacteristic
65M16×Dic61C2211yescharacteristic
66C61×#468C411yescharacteristic
67#14519864—44no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758217—21no—
71C2×#11758217—21no—
72C2×#11758217D411yescharacteristic
73C2×#11758217D411yescharacteristic
74C2×D61⋊C8—21no—
75C2×D61⋊C8—21no—
76C22×#92420—21no—
77C22×#92420—21no—
78#14519844—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92#14519832—21no—
93#14519832—21no—
94#14519832D411yescharacteristic
95#14519832D411yescharacteristic
96C4×#92420—21no—
97C4×#92420—21no—
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C4×#92420C2311yescharacteristic
102C2×#11758224—21no—
103C2×#11758201C2×C411yescharacteristic
104C2×D488C2×C411yescharacteristic
105C2×#11758199C2×C411yescharacteristic
106C2×#11758194C2×C411yescharacteristic
107#14519776C2×C411yescharacteristic
108#14519773C2×C411yescharacteristic
109#14519772—21no—
110#14519768C2×C411yescharacteristic
111#14519766C2×C411yescharacteristic
112#14519763—21no—
113#14519761—21no—
114#14519751C2×C411yescharacteristic
115#14519751C2×C411yescharacteristic
116#14519749—21no—
117Q8×Dic61C2311yescharacteristic
118D4×Dic61C2311yescharacteristic
119#14519739C2311yescharacteristic
120#14519739C2311yescharacteristic
121#14519737—21no—
122#14519737—21no—
123#14519735—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519709C2×C411yescharacteristic
127#14519708C2×C411yescharacteristic
128#14519701C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134#14519687C2×C411yescharacteristic
135#14519687C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139C2×M16×C61C2×C411yescharacteristic
140C22⋊Q8×C61C2×C411yescharacteristic
141#121×C61C2×C411yescharacteristic
142#107×C61C2×C411yescharacteristic
143#103×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C22×Dic61—21no—
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61#4111yescharacteristic
156#11758224—42no—
157#11758224—42no—
158C2×D244C22×C411yescharacteristic
159C2×D244C22×C411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×Dic122—21no—
163#11758217—22no—
164#11758217—41no—
165#11758217—42no—
166#11758217—42no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—42no—
174C2×#92420—42no—
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178C2×#92420C2×D411yescharacteristic
179#11758213—42no—
180#11758213—42no—
181D61⋊C8—42no—
182D61⋊C8—42no—
183SD16×C61—41no—
184M16×C61—41no—
185C2×C8×C61C22×C411yescharacteristic
186C2×C8×C61C22×C411yescharacteristic
187C4⋊C4×C61—21no—
188C4⋊C4×C61C22×C411yescharacteristic
189C4⋊C4×C61C22×C411yescharacteristic
190C22⋊C4×C61—21no—
191C22⋊C4×C61—21no—
192C22⋊Dic61—21no—
193#11758201—22no—
194#11758199—22no—
195#11758198—21no—
196#11758198—21no—
197#11758198—21no—
198#11758198—21no—
199#11758198—21no—
200#11758198—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61C22×C411yescharacteristic
204C4⋊Dic61C22×C411yescharacteristic
205#11758196—21no—
206#11758196—21no—
207C4×Dic61—21no—
208C4×Dic61C22×C411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61#4111yescharacteristic
211C4×Dic61C2411yescharacteristic
212#11758194—22no—
213C2×#92418C22×C411yescharacteristic
214C2×#92418C22×C411yescharacteristic
215D488—41no—
216C23×C61—21no—
217C23×C61C4×D411yescharacteristic
218C22×D61—21no—
219C22×D61—21no—
220Q8×C61—21no—
221Q8×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—42no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C22⋊D61—42no—
233C22⋊D61—42no—
234C22⋊D61—81no—
235C22⋊D61—81no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61C4×D411yescharacteristic
244C2×Dic61C4×D411yescharacteristic
245C2×Dic61C22×D411yescharacteristic
246C2×Dic61C2×#4111yescharacteristic
247D244—21no—
248D244—21no—
249D244—21no—
250D244—21no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—41no—
255Dic122—42no—
256#92420—22no—
257#92420—21no—
258#92420—21no—
259#92420—21no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264#92420—41no—
265#92420AGL(1,ℤ/8)12yes—
266C8×C61—21no—
267C8×C61—21no—
268#92418—21no—
269#92418#13112yescomplemented
270#18076—611nomaximal, Sylow
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61C2×C4×D411yescharacteristic
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C4×C61—21no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61C2×#13111yescharacteristic
289C4×C61#56811yescharacteristic
290Dic61—21no—
291Dic61—21no—
292Dic61—21no—
293Dic61—41no—
294Dic61—41no—
295Dic61C2×AGL(1,ℤ/8)11yescharacteristic
296Dic61#57511yescharacteristic
297#3171—611no—
298#2969—611no—
299#2935—611no—
300#1594—611no—
301#1590—611no—
302#1588—611no—
303#1586—611no—
304#1582—611no—
305#1581—611no—
306SD16⋊C8—611no—
307C8×D8—611no—
308#1565—611no—
309#1484—611no—
310#1483—611no—
311#1455—611no—
312C2×C61—41no—
313C2×C61—81no—
314C2×C61#293511yescharacteristic
315C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
316C2×C61#295611yescharacteristic
317D61—81no—
318D61—81no—
319C2×#131—1221no—
320#532—611no—
321#529—611no—
322#501—611no—
323#496—611no—
324#490—611no—
325#489—611no—
326#469—611no—
327#469—611no—
328#468—611no—
329#468#692311yescharacteristic
330#446—611no—
331C8×Q8—611no—
332C4×SD16—611no—
333C4×SD16—611no—
334C4×D8—611no—
335C4×D8—611no—
336#436—611no—
337#436—611no—
338#436—611no—
339#436—1221no—
340#435—1221no—
341#435—1221no—
342#435—1221no—
343C8×D4—611no—
344C8×D4—611no—
345C8×D4—611no—
346#433—1221no—
347#431—611no—
348C2×C4⋊C8—611no—
349#408—1221no—
350#405—1221no—
351C4×M16—611no—
352C4×M16—611no—
353C4×M16—611no—
354#335—611no—
355#335—611no—
356#334—611no—
357#334—611no—
358Q8⋊C8—611no—
359Q8⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366#322—611no—
367#322—611no—
368#322—611no—
369C82—611no—
370C61#1807611yescharacteristic, complemented, Sylow
371C2×#41—1221no—
372C2×SD16—611no—
373C2×SD16C2×#692311yescharacteristic
374C2×D8—611no—
375C2×D8—611no—
376#131—2444no—
377C2×M16—611no—
378C2×M16—611no—
379C2×M16—611no—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16C2×#692311yescharacteristic
385C22×C8—1221no—
386C22×C8—1221no—
387C22×C8—1221no—
388C22×C8—1221no—
389C4⋊Q8—611no—
390#127—611no—
391#126—1221no—
392#125—611no—
393#124—611no—
394#124—1221no—
395#123—1221no—
396C22⋊Q8C2×#692311yescharacteristic
397#121—611no—
398#121—611no—
399#121—1221no—
400#121C2×#692311yescharacteristic
401C4×Q8—611no—
402C4×D4—611no—
403C4×D4—611no—
404C4×D4—611no—
405C4×D4—1221no—
406C4×D4—1221no—
407#117—1221no—
408C2×C42—611no—
409#107—611no—
410#107C2×#692311yescharacteristic
411#106—611no—
412#106—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8—1221no—
420#103—611no—
421#103C2×#692311yescharacteristic
422#102—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427#102C2×#692311yescharacteristic
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435#97—611no—
436#97—611no—
437#97—611no—
438#97—611no—
439#97—1221no—
440#97—1221no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—1221no—
448C4×C8—1221no—
449#41—2442no—
450#41—2442no—
451C2×Q8—1221no—
452C2×Q8C22×#692311yescharacteristic
453C2×D4—21no—
454C2×D4—611no—
455C2×D4—611no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4C22×#692311yescharacteristic
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4C22×#692311yescharacteristic
467SD16—41no—
468SD16—1222no—
469D8—1222no—
470D8—2441no—
471M16—41no—
472M16—1222no—
473M16—1222no—
474M16—2442no—
475M16—2441no—
476M16—2442no—
477M16—2442no—
478M16—2442no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—2442no—
492C2×C8—2442no—
493C2×C8—2442no—
494C2×C8—2442no—
495C2×C8C22×#692311yescharacteristic
496C2×C8C22×#692311yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—611no—
499C4⋊C4—611no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4C22×#692311yescharacteristic
505C4⋊C4C22×#692311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C22⋊C4—1221no—
513C22⋊C4—1221no—
514C22⋊C4—1221no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—1221no—
520C23—21no—
521C23—1221no—
522C23—1221no—
523C23D4×#692311yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—2442no—
527D4—21no—
528D4—21no—
529D4—42no—
530D4—1221no—
531D4—1221no—
532D4—1221no—
533D4—1221no—
534D4—4881no—
535D4—4881no—
536D4—2442no—
537D4—2442no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—611no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4D4×#692311yescharacteristic
559C2×C4C23×#692311yescharacteristic
560C8—21no—
561C8—21no—
562C8—612no—
563C8—612no—
564C8—1221no—
565C8—1221no—
566C8—1221no—
567C8—1222no—
568C8—1221no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C8—2441no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22C2×D4×#692311yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—611no—
592C4—611no—
593C4—1221no—
594C4—1221no—
595C4—1221no—
596C4—2441no—
597C4—2441no—
598C4D61⋊#13111yescharacteristic
599C4#1684084011yescharacteristic
600C2—41no—
601C2—81no—
602C2—4881no—
603C2—4881no—
604C2#2146256311yescharacteristic
605C2AGL(1,ℤ/8)×#692311yescharacteristic
606C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#468C4
socleC22×C61C2×C4×D4
prime radical#21456407C2
cosocleC4×Dic61C24
hypercenter#468#6923
hypocenterC61#18076
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #21462652C2semidirect
2. #21462561C2semidirect
3. #21461467C2semidirect
4. #21461453C2semidirect
5. #21461448C2semidirect
6. #21461439C2semidirect
7. #21461424C2semidirect
8. #21461419C2semidirect
9. #21461409C2semidirect
10. #21461399C2semidirect
11. #21461372C2semidirect
12. #21461138C2semidirect
13. #21461136C2semidirect
14. #21461042C2semidirect
269. #92418#131semidirect
370. C61#18076semidirect

Maximal subgroups

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

subgroupindex
#214626522
#214625612
#214614672
#214614532
#214614482
#214614392
#214614242
#214614192
#214614092
#214613992
#214613722
#214611382
#214611362
#214610422
#214564072
#1807661