Subgroups — #41×D₉₇ #15690851

Order 3104.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095512	C₂	1	1	yes	maximal, characteristic, complemented
2	#13095511	C₂	1	3	yes	maximal, complemented
3	#13095510	C₂	1	3	yes	maximal, complemented
4	Q₈×D₉₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×D₉₇	C₂	1	3	yes	maximal, complemented
6	C₂×C₄×D₉₇	C₂	1	3	yes	maximal, complemented
7	#41×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₉₇	C₂²	1	3	yes	—
9	Q₈×C₉₇	C₂²	1	1	yes	characteristic, complemented
10	D₄×C₉₇	C₂²	1	3	yes	complemented
11	C₂×C₄×C₉₇	C₂²	1	3	yes	complemented
12	C₂²⋊D₉₇	C₂²	1	6	yes	complemented
13	C₂×Dic₉₇	C₂²	1	3	yes	complemented
14	D₃₈₈	C₂²	1	3	yes	complemented
15	C₄×D₉₇	C₂²	1	1	yes	characteristic
16	C₄×D₉₇	C₂²	1	3	yes	—
17	C₄×D₉₇	C₂²	1	3	yes	complemented
18	C₄×D₉₇	C₂²	1	3	yes	complemented
19	Dic₁₉₄	C₂²	1	3	yes	complemented
20	C₂²×C₉₇	C₂³	1	3	yes	—
21	C₂×D₉₇	—	2	6	no	—
22	C₂×D₉₇	C₂³	1	3	yes	—
23	C₂×D₉₇	C₂³	1	1	yes	characteristic
24	C₄×C₉₇	C₂³	1	3	yes	—
25	C₄×C₉₇	C₂³	1	1	yes	characteristic
26	Dic₉₇	C₂³	1	3	yes	—
27	Dic₉₇	C₂³	1	1	yes	characteristic
28	C₂×C₉₇	—	2	3	no	—
29	C₂×C₉₇	C₂⁴	1	1	yes	characteristic
30	D₉₇	—	2	3	no	—
31	D₉₇	#41	1	2	yes	direct product factor
32	C₉₇	C₂×#41	1	1	yes	characteristic, complemented, Sylow
33	C₂×#41	—	97	1	no	maximal, Sylow
34	#41	—	97	1	no	—
35	#41	—	97	3	no	—
36	#41	—	97	3	no	—
37	#41	D₉₇	1	1	yes	characteristic, direct product factor
38	C₂×Q₈	—	97	1	no	—
39	C₂×D₄	—	97	3	no	—
40	C₂²×C₄	—	97	3	no	—
41	C₂³	—	97	3	no	—
42	Q₈	—	97	3	no	—
43	Q₈	C₂×D₉₇	1	1	yes	characteristic, complemented
44	D₄	—	97	6	no	—
45	D₄	—	97	3	no	—
46	D₄	C₂×D₉₇	1	3	yes	complemented
47	C₂×C₄	—	97	3	no	—
48	C₂×C₄	—	97	3	no	—
49	C₂×C₄	—	97	3	no	—
50	C₂×C₄	—	97	1	no	—
51	C₂×C₄	—	97	3	no	—
52	C₂×C₄	C₂×D₉₇	1	3	yes	complemented
53	C₂²	—	97	1	no	—
54	C₂²	—	97	3	no	—
55	C₂²	—	194	6	no	—
56	C₂²	C₂²×D₉₇	1	3	yes	—
57	C₄	—	97	1	no	—
58	C₄	—	97	3	no	—
59	C₄	C₂²×D₉₇	1	3	yes	—
60	C₄	C₂²×D₉₇	1	1	yes	characteristic
61	C₂	—	2	3	no	—
62	C₂	—	97	2	no	—
63	C₂	—	194	3	no	—
64	C₂	C₂³×D₉₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #13095512	C₂	semidirect
2. #13095511	C₂	semidirect
3. #13095510	C₂	semidirect
4. Q₈×D₉₇	C₂	semidirect
5. D₄×D₉₇	C₂	semidirect
6. C₂×C₄×D₉₇	C₂	semidirect
7. #41×C₉₇	C₂	semidirect
9. Q₈×C₉₇	C₂²	semidirect
10. D₄×C₉₇	C₂²	semidirect
11. C₂×C₄×C₉₇	C₂²	semidirect
12. C₂²⋊D₉₇	C₂²	semidirect
13. C₂×Dic₉₇	C₂²	semidirect
14. D₃₈₈	C₂²	semidirect
17. C₄×D₉₇	C₂²	semidirect
18. C₄×D₉₇	C₂²	semidirect
19. Dic₁₉₄	C₂²	semidirect
31. D₉₇	#41	direct (N × H)
32. C₉₇	C₂×#41	semidirect
37. #41	D₉₇	direct (N × H)
43. Q₈	C₂×D₉₇	semidirect
46. D₄	C₂×D₉₇	semidirect
52. C₂×C₄	C₂×D₉₇	semidirect

Maximal subgroups

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

subgroup	index
#13095512	2
#13095511	2
#13095510	2
Q₈×D₉₇	2
D₄×D₉₇	2
C₂×C₄×D₉₇	2
#41×C₉₇	2
C₂×#41	97

Subgroups — #41×D97 #15690851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×D₉₇ #15690851