Subgroups — #20261601

Order 6208.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11715897	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11715897	—	2	2	no	—
4	C₂×#11715897	—	2	2	no	—
5	C₂×#11715897	C₄	1	4	yes	complemented
6	C₂²×Dic₉₇	C₄	1	1	yes	characteristic
7	C₂²×Dic₉₇	C₂²	1	1	yes	characteristic
8	C₄×Dic₉₇	—	2	2	no	—
9	C₂²×C₄×C₉₇	C₄	1	1	yes	characteristic
10	C₂³×C₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₉₇	—	2	1	no	—
12	C₂×C₄×C₉₇	—	2	1	no	—
13	C₂×C₄×C₉₇	C₈	1	2	yes	complemented
14	C₂×Dic₉₇	—	2	1	no	—
15	C₂×Dic₉₇	—	2	1	no	—
16	C₂×Dic₉₇	C₈	1	2	yes	complemented
17	C₂×Dic₉₇	C₂×C₄	1	2	yes	—
18	C₂×Dic₉₇	D₄	1	1	yes	characteristic
19	C₂×Dic₉₇	D₄	1	2	yes	—
20	C₂×Dic₉₇	Q₈	1	1	yes	characteristic
21	#11715897	—	2	4	no	—
22	C₂²×C₉₇	C₄²	1	1	yes	characteristic
23	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂²×C₉₇	C₂×C₈	1	1	yes	characteristic
26	C₂²×C₉₇	C₂×C₈	1	1	yes	characteristic
27	C₂²×C₉₇	M₁₆	1	1	yes	characteristic
28	C₂²×C₉₇	M₁₆	1	1	yes	characteristic
29	C₄×C₉₇	—	2	2	no	—
30	Dic₉₇	—	2	2	no	—
31	Dic₉₇	C₂²⋊C₄	1	2	yes	—
32	Dic₉₇	C₄⋊C₄	1	2	yes	—
33	C₂×C₉₇	#95	1	1	yes	characteristic
34	C₂×C₉₇	C₄×C₈	1	1	yes	characteristic
35	C₂×C₉₇	#97	1	1	yes	characteristic
36	C₂×C₉₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×C₉₇	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×C₉₇	C₄⋊C₈	1	1	yes	characteristic
39	C₂×C₉₇	C₄⋊C₈	1	1	yes	characteristic
40	C₉₇	#336	1	1	yes	characteristic, complemented, Sylow
41	#336	—	97	1	no	maximal, Sylow
42	C₂²×C₈	—	97	2	no	—
43	C₂×C₄²	—	97	1	no	—
44	C₂²×C₄	—	97	1	no	—
45	C₂²×C₄	—	97	1	no	—
46	C₂²×C₄	#87604	1	1	yes	characteristic
47	C₂×C₈	—	97	4	no	—
48	C₂×C₈	—	194	2	no	—
49	C₂×C₈	—	194	2	no	—
50	C₄²	—	194	2	no	—
51	C₂³	C₂×#87604	1	1	yes	characteristic
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	—	97	2	no	—
55	C₂×C₄	—	97	2	no	—
56	C₂×C₄	—	97	1	no	—
57	C₂×C₄	—	97	1	no	—
58	C₂×C₄	—	97	2	no	—
59	C₂×C₄	—	194	1	no	—
60	C₂×C₄	—	194	1	no	—
61	C₂×C₄	#11715897	1	2	yes	complemented
62	C₈	—	194	4	no	—
63	C₂²	C₄×#87604	1	1	yes	characteristic
64	C₂²	C₂²⋊#87604	1	1	yes	characteristic
65	C₂²	C₄⋊#87604	1	1	yes	characteristic
66	C₂²	C₂×#11715897	1	1	yes	characteristic
67	C₂²	#13095519	1	1	yes	characteristic
68	C₂²	#13095520	1	1	yes	characteristic
69	C₂²	#13095521	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	97	2	no	—
72	C₄	—	97	2	no	—
73	C₄	—	194	2	no	—
74	C₂	(C₂×#87604)⋊C₄	1	1	yes	characteristic
75	C₂	C₄×#11715897	1	1	yes	characteristic
76	C₂	#15690865	1	1	yes	characteristic
77	C₂	C₂²⋊#11715897	1	1	yes	characteristic
78	C₂	#15690867	1	1	yes	characteristic
79	C₂	C₄⋊#11715897	1	1	yes	characteristic
80	C₂	#15690877	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂×#87604
commutator	C₂×C₉₇	C₄×C₈
Fitting	C₂²×C₄×C₉₇	C₄
socle	C₂³×C₉₇	C₂×C₄
hypercenter	C₂²×C₄	#87604
hypocenter	C₉₇	#336
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
5. C₂×#11715897	C₄	semidirect
13. C₂×C₄×C₉₇	C₈	semidirect
16. C₂×Dic₉₇	C₈	semidirect
40. C₉₇	#336	semidirect
61. C₂×C₄	#11715897	semidirect