Subgroups — C₂²×C₂²⋊D₉₇ #15690847

Order 3104.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³	C₂×D₉₇
commutator, cosocle	C₂×C₉₇	C₂⁴
Frattini	C₂	C₂³×D₉₇
Fitting	C₂⁴×C₉₇	C₂
socle	C₂³×C₉₇	C₂²
hypercenter	C₂⁴	D₉₇
hypocenter	C₉₇	C₂²×D₄
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂³×D₉₇	C₂	semidirect
2. C₂×C₂²⋊D₉₇	C₂	direct (N × H)
3. C₂²×Dic₉₇	C₂	semidirect
4. C₂⁴×C₉₇	C₂	semidirect
7. C₂³×C₉₇	C₂²	semidirect
9. C₂²×D₉₇	C₂²	semidirect
10. C₂²⋊D₉₇	C₂²	direct (N × H)
11. C₂×Dic₉₇	C₂²	semidirect
13. C₂²×C₉₇	D₄	semidirect
15. C₂²×C₉₇	C₂³	semidirect
17. C₂×D₉₇	C₂³	semidirect
18. Dic₉₇	C₂³	semidirect
20. C₂×C₉₇	C₂×D₄	semidirect
23. C₉₇	C₂²×D₄	semidirect
26. C₂⁴	D₉₇	semidirect
33. C₂³	C₂×D₉₇	semidirect
39. C₂²	C₂²⋊D₉₇	direct (N × H)
41. C₂²	C₂²×D₉₇	semidirect
45. C₂	C₂×C₂²⋊D₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₉₇	2
C₂×C₂²⋊D₉₇	2
C₂²×Dic₉₇	2
C₂⁴×C₉₇	2
C₂²×D₄	97

Subgroups — C22×C22⋊D97 #15690847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂²⋊D₉₇ #15690847