Subgroups — C₂×#13095511 #15690853

Order 3104.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095511	C₂	1	8	yes	maximal, direct product factor
2	C₂×Dic₁₉₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₈₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂²⋊D₉₇	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₉₇	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×C₉₇	C₂²	1	1	yes	characteristic
8	C₂²×D₉₇	C₂²	1	2	yes	—
9	C₂×C₄×C₉₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₉₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₉₇	C₂²	1	4	yes	complemented
12	C₂²⋊D₉₇	C₂²	1	8	yes	complemented
13	C₂×Dic₉₇	C₂²	1	2	yes	—
14	D₃₈₈	C₂²	1	4	yes	complemented
15	C₄×D₉₇	C₂²	1	8	yes	complemented
16	Dic₁₉₄	C₂²	1	4	yes	complemented
17	C₂²×C₉₇	—	2	2	no	—
18	C₂²×C₉₇	C₂³	1	2	yes	—
19	C₂²×C₉₇	C₂³	1	1	yes	characteristic
20	C₂×D₉₇	—	2	4	no	—
21	C₂×D₉₇	C₂³	1	4	yes	—
22	C₄×C₉₇	C₂³	1	2	yes	—
23	C₄×C₉₇	C₂³	1	2	yes	—
24	Dic₉₇	C₂³	1	4	yes	—
25	C₂×C₉₇	—	2	2	no	—
26	C₂×C₉₇	#41	1	2	yes	complemented
27	C₂×C₉₇	C₂⁴	1	1	yes	characteristic
28	D₉₇	—	2	4	no	—
29	C₉₇	C₂×#41	1	1	yes	characteristic, complemented, Sylow
30	C₂×#41	—	97	1	no	maximal, Sylow
31	#41	—	97	8	no	—
32	C₂×Q₈	—	97	1	no	—
33	C₂×D₄	—	97	2	no	—
34	C₂×D₄	—	97	1	no	—
35	C₂²×C₄	—	97	2	no	—
36	C₂²×C₄	D₉₇	1	1	yes	characteristic, complemented
37	C₂³	—	97	2	no	—
38	C₂³	C₂×D₉₇	1	1	yes	characteristic
39	Q₈	—	97	4	no	—
40	D₄	—	97	8	no	—
41	D₄	—	97	4	no	—
42	C₂×C₄	—	97	2	no	—
43	C₂×C₄	—	97	8	no	—
44	C₂×C₄	C₂×D₉₇	1	1	yes	characteristic
45	C₂×C₄	C₂×D₉₇	1	1	yes	characteristic
46	C₂×C₄	C₂×D₉₇	1	4	yes	complemented
47	C₂²	—	2	2	no	—
48	C₂²	—	97	4	no	—
49	C₂²	—	194	4	no	—
50	C₂²	C₂²×D₉₇	1	2	yes	—
51	C₂²	C₂²×D₉₇	1	1	yes	characteristic
52	C₄	—	97	4	no	—
53	C₄	C₂²×D₉₇	1	2	yes	—
54	C₄	C₂²×D₉₇	1	2	yes	—
55	C₂	—	2	2	no	—
56	C₂	—	194	4	no	—
57	C₂	#13095511	1	2	yes	direct product factor
58	C₂	C₂³×D₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₉₇
commutator, cosocle	C₂×C₉₇	C₂⁴
Frattini	C₂	C₂³×D₉₇
Fitting	C₂²×C₄×C₉₇	C₂
socle	C₂²×C₉₇	C₂³
hypercenter	C₂²×C₄	D₉₇
hypocenter	C₉₇	C₂×#41
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #13095511	C₂	direct (N × H)
2. C₂×Dic₁₉₄	C₂	semidirect
3. C₂×D₃₈₈	C₂	semidirect
4. C₂×C₂²⋊D₉₇	C₂	semidirect
5. C₂×C₄×D₉₇	C₂	semidirect
6. C₂²×C₄×C₉₇	C₂	semidirect
11. C₂×C₄×C₉₇	C₂²	semidirect
12. C₂²⋊D₉₇	C₂²	semidirect
14. D₃₈₈	C₂²	semidirect
15. C₄×D₉₇	C₂²	semidirect
16. Dic₁₉₄	C₂²	semidirect
26. C₂×C₉₇	#41	semidirect
29. C₉₇	C₂×#41	semidirect
36. C₂²×C₄	D₉₇	semidirect
46. C₂×C₄	C₂×D₉₇	semidirect
57. C₂	#13095511	direct (N × H)

Maximal subgroups

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

subgroup	index
#13095511	2
C₂×Dic₁₉₄	2
C₂×D₃₈₈	2
C₂×C₂²⋊D₉₇	2
C₂×C₄×D₉₇	2
C₂²×C₄×C₉₇	2
C₂×#41	97

Subgroups — C2×#13095511 #15690853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13095511 #15690853