Subgroups — D₈×D₃₉₇ #27163105

Order 12704.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₃₉₇	C₂	1	2	yes	maximal, complemented
2	D₃₁₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#20263716	C₂	1	2	yes	maximal, complemented
4	C₈×D₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₉₇	—	2	2	no	—
7	D₁₅₈₈	C₂²	1	2	yes	complemented
8	C₂²⋊D₃₉₇	—	2	2	no	—
9	C₄×D₃₉₇	C₂²	1	1	yes	characteristic
10	#15691787	C₂²	1	1	yes	characteristic, complemented
11	D₄×C₃₉₇	C₂²	1	2	yes	complemented
12	C₈×C₃₉₇	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₃₉₇	—	2	2	no	—
14	C₂×D₃₉₇	—	2	2	no	—
15	C₂×D₃₉₇	—	4	4	no	—
16	C₂×D₃₉₇	D₄	1	1	yes	characteristic
17	C₄×C₃₉₇	C₂³	1	1	yes	characteristic
18	Dic₃₉₇	D₄	1	1	yes	characteristic
19	C₂×C₃₉₇	—	4	2	no	—
20	C₂×C₃₉₇	C₂×D₄	1	1	yes	characteristic
21	D₃₉₇	—	4	2	no	—
22	D₃₉₇	D₈	1	2	yes	direct product factor
23	C₃₉₇	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₈	—	397	1	no	maximal, Sylow
25	C₂×D₄	—	397	2	no	—
26	D₈	—	397	2	no	—
27	D₈	—	397	1	no	—
28	D₈	D₃₉₇	1	1	yes	characteristic, direct product factor
29	C₂×C₈	—	397	1	no	—
30	C₂³	—	794	2	no	—
31	D₄	—	794	2	no	—
32	D₄	—	397	2	no	—
33	D₄	C₂×D₃₉₇	1	2	yes	complemented
34	C₂×C₄	—	397	1	no	—
35	C₈	—	397	1	no	—
36	C₈	C₂×D₃₉₇	1	1	yes	characteristic, complemented
37	C₂²	—	2	2	no	—
38	C₂²	—	794	2	no	—
39	C₂²	—	1588	4	no	—
40	C₂²	—	397	1	no	—
41	C₄	—	397	1	no	—
42	C₄	C₂²×D₃₉₇	1	1	yes	characteristic
43	C₂	—	4	2	no	—
44	C₂	—	1588	2	no	—
45	C₂	—	397	2	no	—
46	C₂	D₄×D₃₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₃₉₇
commutator, cosocle	C₄×C₃₉₇	C₂³
Frattini	C₄	C₂²×D₃₉₇
Fitting	D₈×C₃₉₇	C₂
socle	C₂×C₃₉₇	C₂×D₄
hypercenter	D₈	D₃₉₇
hypocenter	C₃₉₇	C₂×D₈
LCS	G ▷ C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×D₃₉₇	C₂	semidirect
2. D₃₁₇₆	C₂	semidirect
3. #20263716	C₂	semidirect
4. C₈×D₃₉₇	C₂	semidirect
5. D₈×C₃₉₇	C₂	semidirect
7. D₁₅₈₈	C₂²	semidirect
10. #15691787	C₂²	semidirect
11. D₄×C₃₉₇	C₂²	semidirect
12. C₈×C₃₉₇	C₂²	semidirect
22. D₃₉₇	D₈	direct (N × H)
23. C₃₉₇	C₂×D₈	semidirect
28. D₈	D₃₉₇	direct (N × H)
33. D₄	C₂×D₃₉₇	semidirect
36. C₈	C₂×D₃₉₇	semidirect

Maximal subgroups

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

subgroup	index
D₄×D₃₉₇	2
D₃₁₇₆	2
#20263716	2
C₈×D₃₉₇	2
D₈×C₃₉₇	2
C₂×D₈	397

Subgroups — D8×D397 #27163105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×D₃₉₇ #27163105