Subgroups — #20261736

Order 6208.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095519	C₂	1	2	yes	maximal
2	#15690877	C₂	1	2	yes	maximal, complemented
3	C₄⋊#11715897	C₂	1	2	yes	maximal, complemented
4	C₄²×D₉₇	C₂	1	1	yes	maximal, characteristic
5	#13095519	—	2	4	no	—
6	C₂×#11715897	C₂²	1	4	yes	—
7	C₂×C₄×D₉₇	C₄	1	1	yes	characteristic
8	C₂×C₄×D₉₇	C₄	1	1	yes	characteristic
9	C₂×C₄×D₉₇	C₂²	1	1	yes	characteristic
10	C₄×Dic₉₇	C₄	1	1	yes	characteristic
11	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
12	C₄×Dic₉₇	C₂²	1	1	yes	characteristic
13	C₄²×C₉₇	C₄	1	1	yes	characteristic
14	C₂²×D₉₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₉₇	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₉₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₉₇	C₂³	1	1	yes	characteristic
21	C₄×D₉₇	—	2	2	no	—
22	C₄×D₉₇	C₈	1	4	yes	complemented
23	C₄×D₉₇	D₄	1	2	yes	—
24	C₄×D₉₇	Q₈	1	2	yes	—
25	#11715897	—	2	4	no	—
26	C₂²×C₉₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₉₇	C₄⋊C₄	1	2	yes	—
28	C₂×D₉₇	C₂×C₈	1	2	yes	—
29	C₂×D₉₇	M₁₆	1	2	yes	—
30	C₄×C₉₇	—	2	1	no	—
31	C₄×C₉₇	C₄⋊C₄	1	2	yes	—
32	C₄×C₉₇	C₂×C₈	1	2	yes	complemented
33	Dic₉₇	—	2	1	no	—
34	Dic₉₇	C₂×C₈	1	2	yes	complemented
35	Dic₉₇	C₂×D₄	1	1	yes	characteristic
36	Dic₉₇	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₉₇	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₉₇	C₂²×C₈	1	1	yes	characteristic
39	C₂×C₉₇	C₂×M₁₆	1	1	yes	characteristic
40	D₉₇	C₄⋊C₈	1	4	yes	complemented
41	C₉₇	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₄⋊C₈	—	97	1	no	maximal, Sylow
43	C₂²×C₈	—	97	2	no	—
44	C₂×C₄²	—	97	1	no	—
45	C₄⋊C₈	—	97	2	no	—
46	C₄⋊C₈	—	97	2	no	—
47	C₂²×C₄	—	97	1	no	—
48	C₂²×C₄	—	97	1	no	—
49	C₂²×C₄	—	97	1	no	—
50	C₂×C₈	—	97	4	no	—
51	C₂×C₈	—	194	4	no	—
52	C₄²	—	97	1	no	—
53	C₄²	—	97	1	no	—
54	C₄²	—	97	1	no	—
55	C₄²	#87604	1	1	yes	characteristic
56	C₂³	—	97	1	no	—
57	C₂×C₄	—	97	1	no	—
58	C₂×C₄	—	97	1	no	—
59	C₂×C₄	—	97	2	no	—
60	C₂×C₄	—	97	2	no	—
61	C₂×C₄	—	97	4	no	—
62	C₂×C₄	—	97	1	no	—
63	C₂×C₄	—	194	2	no	—
64	C₂×C₄	C₂×#87604	1	1	yes	characteristic
65	C₂×C₄	C₂×#87604	1	1	yes	characteristic
66	C₂×C₄	C₂×#87604	1	1	yes	characteristic
67	C₈	—	194	4	no	—
68	C₂²	—	97	2	no	—
69	C₂²	—	97	2	no	—
70	C₂²	—	97	2	no	—
71	C₂²	C₂²×#87604	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	—	97	1	no	—
74	C₄	—	97	1	no	—
75	C₄	—	97	2	no	—
76	C₄	—	194	1	no	—
77	C₄	C₄⋊#87604	1	2	yes	—
78	C₄	#13095519	1	2	yes	complemented
79	C₂	—	97	4	no	—
80	C₂	C₂×C₄⋊#87604	1	1	yes	characteristic
81	C₂	C₂×#13095519	1	1	yes	characteristic
82	C₂	D₉₇⋊M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#87604
commutator	C₂×C₉₇	C₂²×C₈
Frattini	C₂²	C₂²×#87604
Fitting	C₄²×C₉₇	C₄
socle	C₂²×C₉₇	C₂²×C₄
hypercenter	C₄²	#87604
hypocenter	C₉₇	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #15690877	C₂	semidirect
3. C₄⋊#11715897	C₂	semidirect
22. C₄×D₉₇	C₈	semidirect
32. C₄×C₉₇	C₂×C₈	semidirect
34. Dic₉₇	C₂×C₈	semidirect
40. D₉₇	C₄⋊C₈	semidirect
41. C₉₇	C₂×C₄⋊C₈	semidirect
78. C₄	#13095519	semidirect