Finite Group Databasebeta

← #30613411

Subgroups — #30613411

Order 15616.

794 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462559C211yesmaximal, characteristic, complemented
2D4×#11758217C211yesmaximal, characteristic, complemented
3#21461450C212yesmaximal, complemented
4#21461421C212yesmaximal, complemented
5#21461418C212yesmaximal, complemented
6#21461399C212yesmaximal, complemented
7#21461376C211yesmaximal, characteristic, complemented
8#21461146C211yesmaximal, characteristic, complemented
9#21461144C211yesmaximal, characteristic, complemented
10C8×#11758217C211yesmaximal, characteristic, complemented
11C2×#16839842C211yesmaximal, characteristic
12C2×D61⋊M16—21no—
13C22×#11758217—21no—
14#16840797C2212yescomplemented
15#16840796C2212yescomplemented
16#16840793—22no—
17#16840792—22no—
18#16840790C2212yescomplemented
19D4×#92420C2212yescomplemented
20#16840779C2211yescharacteristic
21#16840765C2211yescharacteristic
22#16840765C2211yescharacteristic
23#16840734—21no—
24#16840732—21no—
25C4×#11758217C2211yescharacteristic
26#16840626C2212yescomplemented
27#16840625C2212yescomplemented
28#16840610C2212yescomplemented
29#16840610C2212yescomplemented
30D4⋊#92420C2212yescomplemented
31D4⋊#92420C2212yescomplemented
32#92420⋊C8C2212yescomplemented
33C8×#92420C2212yescomplemented
34C22×#11758199C411yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37#16839842C411yescharacteristic
38#16839842C411yescharacteristic
39#16839842C411yescharacteristic
40#16839842C411yescharacteristic
41#16839842C2211yescharacteristic
42#16839842C2211yescharacteristic
43#16839842C2211yescharacteristic
44#16839842C2211yescharacteristic
45C2×#14519710C411yescharacteristic
46C2×#14519699C411yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48C2×#102×C61C411yescharacteristic
49C2×#11758213—22no—
50D61⋊M16—44no—
51C2×#11758217—21no—
52C2×#11758217—21no—
53C2×#11758217—22no—
54C2×#11758217—44no—
55C2×#11758217D411yescharacteristic
56C2×#11758217D411yescharacteristic
57C2×D61⋊C8—22no—
58C22×#92420—22no—
59#14519844—21no—
60#14519844—21no—
61#14519844—21no—
62C4⋊#92420C2312yes—
63C4⋊#92420C2312yes—
64#14519834—22no—
65#14519834—22no—
66C22⋊#92420—21no—
67C22⋊#92420—22no—
68C22⋊#92420—22no—
69#14519832D412yes—
70C4×#92420C2312yes—
71C4×#92420C2312yes—
72C22×D244C2×C411yescharacteristic
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C2×#11758199—24no—
76C2×#11758199C2×C411yescharacteristic
77C2×#11758199C2×C411yescharacteristic
78C2×#11758199C2×C411yescharacteristic
79C2×#11758199C2×C411yescharacteristic
80C22×#92418C2×C411yescharacteristic
81D4×Dic61—21no—
82D4×Dic61—21no—
83D4×Dic61C2×C411yescharacteristic
84D4×Dic61C2×C411yescharacteristic
85D4×Dic61C2311yescharacteristic
86D4×Dic61C2311yescharacteristic
87#14519739—21no—
88#14519739—21no—
89#14519739C2×C411yescharacteristic
90#14519739C2×C411yescharacteristic
91#14519739C2311yescharacteristic
92#14519739C2311yescharacteristic
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C22⋊Dic61—21no—
95C2×#11758198—21no—
96C2×C4×Dic61C2311yescharacteristic
97#14519710C2×C411yescharacteristic
98#14519710C2×C411yescharacteristic
99#14519710C2×C411yescharacteristic
100#14519710C2×C411yescharacteristic
101#14519699C2×C411yescharacteristic
102#14519699C2×C411yescharacteristic
103#14519699C2×C411yescharacteristic
104#14519699C2×C411yescharacteristic
105C8×Dic61C2×C411yescharacteristic
106C8×Dic61C2×C411yescharacteristic
107C8×Dic61C2311yescharacteristic
108C8×Dic61C2311yescharacteristic
109C22×D4×C61C2×C411yescharacteristic
110C22×C8×C61C2×C411yescharacteristic
111C2×C4⋊C4×C61C2×C411yescharacteristic
112#102×C61C2×C411yescharacteristic
113#102×C61C2×C411yescharacteristic
114#102×C61C2×C411yescharacteristic
115#102×C61C2×C411yescharacteristic
116C24×C61—21no—
117C23×D61—21no—
118C2×D4×C61—22no—
119C2×D4×C61—21no—
120C2×D4×C61—41no—
121C2×D4×C61C22×C411yescharacteristic
122C2×D4×C61C22×C411yescharacteristic
123C22×C4×C61—21no—
124C22×C4×C61C22×C411yescharacteristic
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—42no—
131C22×Dic61—42no—
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61#4111yescharacteristic
134C2×D244—22no—
135C2×D244—21no—
136C2×D244—41no—
137C2×D244C22×C411yescharacteristic
138C2×D244C22×C411yescharacteristic
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—42no—
144C2×C4×D61—42no—
145#11758217—22no—
146#11758217—42no—
147#11758217—42no—
148#11758217—44no—
149#11758217D814yescomplemented
150C2×#92420—22no—
151C2×#92420—22no—
152C2×#92420—22no—
153C2×#92420—44no—
154C2×#92420C2×D412yes—
155C2×#92420C2×D412yes—
156#11758213—44no—
157D61⋊C8—44no—
158C2×C8×C61—41no—
159C2×C8×C61C22×C411yescharacteristic
160C2×C8×C61C22×C411yescharacteristic
161C4⋊C4×C61—21no—
162C4⋊C4×C61C22×C411yescharacteristic
163C4⋊C4×C61C22×C411yescharacteristic
164C22⋊Dic61—21no—
165C22⋊Dic61—21no—
166C22⋊Dic61—21no—
167C22⋊Dic61—21no—
168#11758199—22no—
169#11758199—22no—
170#11758199—22no—
171#11758199M1614yescomplemented
172#11758198—21no—
173#11758198—21no—
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61C22×C411yescharacteristic
178C4⋊Dic61C22×C411yescharacteristic
179C4×Dic61C22×C411yescharacteristic
180C4×Dic61C2×D411yescharacteristic
181C4×Dic61#4111yescharacteristic
182C4×Dic61C2411yescharacteristic
183C2×#92418—22no—
184C2×#92418C22×C411yescharacteristic
185C2×#92418C22×C411yescharacteristic
186C23×C61—21no—
187C23×C61—21no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61—81no—
191C23×C61C4×D411yescharacteristic
192C22×D61—21no—
193C22×D61—21no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—81no—
197D4×C61—21no—
198D4×C61—21no—
199D4×C61—21no—
200D4×C61—42no—
201D4×C61C2×M1612yescomplemented
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—42no—
207C2×C4×C61C4×D411yescharacteristic
208C2×C4×C61C23×C411yescharacteristic
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—41no—
212C2×Dic61—42no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61C4×D411yescharacteristic
220C2×Dic61C4×D411yescharacteristic
221C2×Dic61C2×D812yes—
222C2×Dic61#13512yes—
223C2×Dic61C22×D411yescharacteristic
224C2×Dic61C2×#4111yescharacteristic
225D244—21no—
226D244—21no—
227D244—21no—
228D244—42no—
229D244C2×M1612yescomplemented
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—41no—
233C4×D61—41no—
234C4×D61—42no—
235C4×D61—42no—
236#92420—22no—
237#92420—42no—
238#92420—42no—
239#92420—42no—
240#92420C2×D814yescomplemented
241C8×C61—21no—
242C8×C61—21no—
243#92418—21no—
244#92418C2×M1612yescomplemented
245M16×D8—611nomaximal, Sylow
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—22no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61—41no—
254C22×C61—84no—
255C22×C61C4×D812yes—
256C22×C61C2×C4×D411yescharacteristic
257C2×D61—22no—
258C2×D61—41no—
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—41no—
263C2×D61—84no—
264C4×C61—21no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61C22×M1611yescharacteristic
268C4×C61#56811yescharacteristic
269Dic61—21no—
270Dic61—21no—
271Dic61—41no—
272Dic61—41no—
273Dic61C4×D812yes—
274Dic61C22×D811yescharacteristic
275Dic61C2×#13511yescharacteristic
276C2×C4×D8—611no—
277D4×M16—611no—
278D4×M16—611no—
279#1589—612no—
280#1581—612no—
281#1581—612no—
282C8×D8—612no—
283#1567—611no—
284#1486—611no—
285#1486—611no—
286C8×M16—611no—
287C2×C61—22no—
288C2×C61—42no—
289C2×C61—81no—
290C2×C61D4×M1611yescharacteristic
291C2×C61C2×C4×D811yescharacteristic
292C2×C61#295711yescharacteristic
293D61—42no—
294D61—81no—
295C22×D8—611no—
296C22×M16—1221no—
297C22×M16—1221no—
298C2×C4×D4—611no—
299C2×C4×D4—611no—
300C4×D8—611no—
301C4×D8—611no—
302C4×D8—611no—
303C4×D8—611no—
304C4×D8—611no—
305C4×D8—611no—
306C4×D8—611no—
307C4×D8—611no—
308#436—612no—
309#436—612no—
310#435—1222no—
311#435—1222no—
312C8×D4—612no—
313C8×D4—612no—
314#431—611no—
315C2×#107—611no—
316#423—611no—
317#423—611no—
318C2×#102—611no—
319C2×#102#692311yescharacteristic
320#407—1221no—
321#407—1221no—
322C4×M16—611no—
323C2×C4×C8—611no—
324#335—612no—
325#335—612no—
326D4⋊C8—612no—
327D4⋊C8—612no—
328D4⋊C8—612no—
329D4⋊C8—612no—
330#322—612no—
331C82—612no—
332C61M16×D811yescharacteristic, complemented, Sylow
333C22×D4—611no—
334C22×D4C2×#692311yescharacteristic
335C23×C4—1221no—
336C23×C4—1221no—
337C2×D8—611no—
338C2×D8—611no—
339C2×D8—611no—
340C2×D8—611no—
341C2×D8—1224no—
342C2×M16—611no—
343C2×M16—611no—
344C2×M16—1222no—
345C2×M16—1222no—
346C2×M16—1221no—
347C2×M16—1221no—
348C2×M16—2444no—
349C2×M16—2444no—
350C22×C8—611no—
351C22×C8—1222no—
352C22×C8—1222no—
353C22×C8C2×#692311yescharacteristic
354C4×D4—611no—
355C4×D4—611no—
356C4×D4—611no—
357C4×D4—611no—
358C4×D4—611no—
359C4×D4—611no—
360C4×D4—611no—
361C4×D4—611no—
362C4×D4—1221no—
363C4×D4—1221no—
364C4×D4—1221no—
365C4×D4—1221no—
366C2×C4⋊C4—611no—
367C2×C4⋊C4C2×#692311yescharacteristic
368C2×C22⋊C4—1221no—
369C2×C22⋊C4—1221no—
370C2×C42—611no—
371#107—611no—
372#107—611no—
373#107—611no—
374#107—611no—
375C4⋊C8—612no—
376C4⋊C8—612no—
377C4⋊C8—1221no—
378C4⋊C8—1221no—
379C4⋊C8—1221no—
380#102—611no—
381#102—611no—
382#102—611no—
383#102—611no—
384#102C2×#692311yescharacteristic
385#102C2×#692311yescharacteristic
386#102C2×#692311yescharacteristic
387#102C2×#692311yescharacteristic
388C22⋊C8—1222no—
389C22⋊C8—1222no—
390C22⋊C8—1222no—
391C22⋊C8—1222no—
392C22⋊C8—1221no—
393#97—612no—
394C4×C8—612no—
395C4×C8—611no—
396C4×C8—611no—
397C4×C8—611no—
398C4×C8—611no—
399C4×C8—612no—
400C24—21no—
401C24—1221no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—41no—
405C2×D4—611no—
406C2×D4—611no—
407C2×D4—1222no—
408C2×D4—1221no—
409C2×D4—2441no—
410C2×D4C22×#692311yescharacteristic
411C2×D4C22×#692311yescharacteristic
412C22×C4—21no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—1221no—
416C22×C4—1221no—
417C22×C4—1221no—
418C22×C4—1221no—
419C22×C4—1221no—
420C22×C4—1221no—
421C22×C4—1221no—
422C22×C4—1221no—
423C22×C4—1221no—
424C22×C4—2442no—
425C22×C4—2442no—
426C22×C4—2442no—
427C22×C4—2442no—
428C22×C4C22×#692311yescharacteristic
429D8—614no—
430D8—1222no—
431D8—1222no—
432D8—1222no—
433M16—614no—
434M16—1222no—
435M16—2444no—
436M16—2444no—
437M16—2442no—
438M16—2442no—
439C2×C8—41no—
440C2×C8—612no—
441C2×C8—611no—
442C2×C8—612no—
443C2×C8—611no—
444C2×C8—1222no—
445C2×C8—1222no—
446C2×C8—1222no—
447C2×C8—1222no—
448C2×C8—2444no—
449C2×C8—2444no—
450C2×C8C22×#692311yescharacteristic
451C2×C8C22×#692311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—611no—
454C4⋊C4—611no—
455C4⋊C4—1221no—
456C4⋊C4C22×#692311yescharacteristic
457C4⋊C4C22×#692311yescharacteristic
458C22⋊C4—1221no—
459C22⋊C4—1221no—
460C22⋊C4—1221no—
461C22⋊C4—1221no—
462C22⋊C4—1221no—
463C22⋊C4—1221no—
464C22⋊C4—1221no—
465C22⋊C4—1221no—
466C42—611no—
467C42—611no—
468C42—611no—
469C42—611no—
470C23—21no—
471C23—21no—
472C23—42no—
473C23—42no—
474C23—81no—
475C23—1221no—
476C23—1221no—
477C23—4881no—
478C23—2442no—
479C23—2442no—
480C23D4×#692311yescharacteristic
481D4—21no—
482D4—21no—
483D4—21no—
484D4—42no—
485D4—612no—
486D4—1221no—
487D4—1221no—
488D4—1221no—
489D4—2442no—
490D4D61⋊M1612yescomplemented
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—42no—
496C2×C4—612no—
497C2×C4—612no—
498C2×C4—611no—
499C2×C4—611no—
500C2×C4—611no—
501C2×C4—611no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2442no—
509C2×C4—2442no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2442no—
515C2×C4—2442no—
516C2×C4—2441no—
517C2×C4—2442no—
518C2×C4D4×#692311yescharacteristic
519C2×C4C23×#692311yescharacteristic
520C8—21no—
521C8—21no—
522C8—614no—
523C8—612no—
524C8—1222no—
525C8—1221no—
526C8—2442no—
527C8—2442no—
528C8—2442no—
529C22—21no—
530C22—21no—
531C22—22no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—84no—
538C22—1222no—
539C22—4884no—
540C22—2441no—
541C22—2441no—
542C22—2441no—
543C22—2441no—
544C22—2441no—
545C22D8×#692312yes—
546C22C2×D4×#692311yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—611no—
551C4—611no—
552C4—612no—
553C4—1221no—
554C4—1221no—
555C4—2441no—
556C4—2441no—
557C4C2×D61⋊M1611yescharacteristic
558C4#1684084011yescharacteristic
559C2—22no—
560C2—42no—
561C2—81no—
562C2—4881no—
563C2—2442no—
564C2#2146255711yescharacteristic
565C2C2×D8×#692311yescharacteristic
566C2#2146259711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#102×C61C4
socleC22×C61C2×C4×D4
prime radicalC22×#11758199C4
cosocleC4×Dic61C24
hypercenterC2×#102#6923
hypocenterC61M16×D8
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #21462559C2semidirect
2. D4×#11758217C2semidirect
3. #21461450C2semidirect
4. #21461421C2semidirect
5. #21461418C2semidirect
6. #21461399C2semidirect
7. #21461376C2semidirect
8. #21461146C2semidirect
9. #21461144C2semidirect
10. C8×#11758217C2semidirect
14. #16840797C22semidirect
15. #16840796C22semidirect
18. #16840790C22semidirect
19. D4×#92420C22semidirect
26. #16840626C22semidirect
27. #16840625C22semidirect
28. #16840610C22semidirect
29. #16840610C22semidirect
30. D4⋊#92420C22semidirect
31. D4⋊#92420C22semidirect
32. #92420⋊C8C22semidirect
33. C8×#92420C22semidirect
149. #11758217D8semidirect
171. #11758199M16semidirect
201. D4×C61C2×M16semidirect
229. D244C2×M16semidirect
240. #92420C2×D8semidirect
244. #92418C2×M16semidirect
332. C61M16×D8semidirect
490. D4D61⋊M16semidirect

Maximal subgroups

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

subgroupindex
#214625592
D4×#117582172
#214614502
#214614212
#214614182
#214613992
#214613762
#214611462
#214611442
C8×#117582172
C2×#168398422
M16×D861