Subgroups — C₂×C₈×D₃₉₇ #27163097

Order 12704.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₈	D₃₉₇
commutator, hypocenter	C₃₉₇	C₂²×C₈
Frattini	C₄	C₂²×D₃₉₇
Fitting	C₂×C₈×C₃₉₇	C₂
socle	C₂²×C₃₉₇	C₂×C₄
prime radical	C₂²×D₃₉₇	C₄
cosocle	C₄×C₃₉₇	C₂³
LCS	G ▷ C₃₉₇
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#15691787	C₂	semidirect
3. C₈×D₃₉₇	C₂	direct (N × H)
4. C₂×C₈×C₃₉₇	C₂	semidirect
9. #15691787	C₂²	semidirect
11. C₈×C₃₉₇	C₂²	semidirect
13. C₂×D₃₉₇	C₈	direct (N × H)
18. C₂×C₃₉₇	C₂×C₈	semidirect
20. D₃₉₇	C₂×C₈	direct (N × H)
21. C₃₉₇	C₂²×C₈	semidirect
26. C₂×C₈	D₃₉₇	direct (N × H)
33. C₈	C₂×D₃₉₇	direct (N × H)
41. C₂	C₈×D₃₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃₉₇	2
C₂×#15691787	2
C₈×D₃₉₇	2
C₂×C₈×C₃₉₇	2
C₂²×C₈	397

Subgroups — C2×C8×D397 #27163097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×D₃₉₇ #27163097