Subgroups — Q₈×#15691005 #38734225

Order 24896.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15691005	C₂	1	3	yes	maximal
2	C₄×#15691005	C₂	1	3	yes	maximal
3	C₄×Q₈×C₃₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#15691005	C₂²	1	3	yes	—
5	C₂×#15691005	C₂²	1	1	yes	characteristic
6	C₂×Q₈×C₃₈₉	C₄	1	1	yes	characteristic
7	C₄⋊C₄×C₃₈₉	C₄	1	3	yes	—
8	C₄²×C₃₈₉	C₂²	1	3	yes	—
9	#15691005	—	2	3	no	—
10	#15691005	Q₈	1	2	yes	direct product factor
11	Q₈×C₃₈₉	C₈	1	4	yes	complemented
12	C₂×C₄×C₃₈₉	C₂×C₄	1	3	yes	—
13	C₂×C₄×C₃₈₉	C₂×C₄	1	3	yes	—
14	C₂×C₄×C₃₈₉	C₂³	1	1	yes	characteristic
15	C₂²×C₃₈₉	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₃₈₉	—	2	3	no	—
17	C₄×C₃₈₉	C₂×C₈	1	6	yes	—
18	C₄×C₃₈₉	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₃₈₉	#41	1	1	yes	characteristic
20	C₂×C₃₈₉	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₃₈₉	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₃₈₉	#131	1	1	yes	characteristic
23	C₃₈₉	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
24	C₈×Q₈	—	389	1	no	maximal, Sylow
25	C₄×Q₈	D₃₈₉	1	1	yes	characteristic
26	C₄⋊C₈	—	389	3	no	—
27	C₄×C₈	—	389	3	no	—
28	C₂×Q₈	Dic₃₈₉	1	1	yes	characteristic
29	C₂×C₈	—	389	3	no	—
30	C₂×C₈	—	389	1	no	—
31	C₄⋊C₄	Dic₃₈₉	1	3	yes	—
32	C₄²	C₂×D₃₈₉	1	3	yes	—
33	Q₈	#15691005	1	4	yes	direct product factor
34	C₂×C₄	C₂×Dic₃₈₉	1	3	yes	—
35	C₂×C₄	C₂×Dic₃₈₉	1	3	yes	—
36	C₂×C₄	C₂²×D₃₈₉	1	1	yes	characteristic
37	C₈	—	778	3	no	—
38	C₈	—	389	2	no	—
39	C₂²	C₂²×Dic₃₈₉	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×#15691005	1	6	yes	—
42	C₄	Q₈×D₃₈₉	1	1	yes	characteristic
43	C₄	#20261967	1	1	yes	characteristic
44	C₂	Q₈×Dic₃₈₉	1	1	yes	characteristic
45	C₂	C₂²×#15691005	1	1	yes	characteristic
46	C₂	#27159391	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₈₉
commutator	C₂×C₃₈₉	C₂²×C₈
Fitting	C₄×Q₈×C₃₈₉	C₂
socle, prime radical	C₂²×C₃₈₉	C₂²×C₄
cosocle	C₂×C₄×C₃₈₉	C₂³
hypercenter	C₄×Q₈	D₃₈₉
hypocenter	C₃₈₉	C₈×Q₈
LCS	G ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
10. #15691005	Q₈	direct (N × H)
11. Q₈×C₃₈₉	C₈	semidirect
23. C₃₈₉	C₈×Q₈	semidirect
33. Q₈	#15691005	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊#15691005	2
C₄×#15691005	2
C₄×Q₈×C₃₈₉	2
C₈×Q₈	389

Subgroups — Q8×#15691005 #38734225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#15691005 #38734225