Subgroups — #20260489

Order 6208.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11715895	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₉₇	C₄	1	2	yes	—
5	C₂×#11715895	—	2	1	no	—
6	C₂×#11715895	—	2	1	no	—
7	C₂×#11715895	C₄	1	2	yes	complemented
8	C₄×Dic₉₇	—	2	1	no	—
9	C₄×Dic₉₇	—	2	1	no	—
10	C₂²×C₄×C₉₇	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₉₇	—	2	1	no	—
12	C₂×C₈×C₉₇	—	2	1	no	—
13	C₂×C₈×C₉₇	C₄	1	2	yes	complemented
14	C₂³×C₉₇	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	D₄	1	1	yes	characteristic
18	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₉₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₉₇	Q₈	1	1	yes	characteristic
21	C₂×Dic₉₇	—	2	2	no	—
22	C₂×Dic₉₇	—	2	2	no	—
23	C₂×Dic₉₇	C₈	1	4	yes	complemented
24	C₈×C₉₇	—	2	2	no	—
25	#11715895	—	2	2	no	—
26	C₂²×C₉₇	C₄²	1	1	yes	characteristic
27	C₂²×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×C₉₇	C₄⋊C₄	1	1	yes	characteristic
29	C₂²×C₉₇	C₂×C₈	1	2	yes	—
30	C₂²×C₉₇	M₁₆	1	2	yes	—
31	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
33	C₄×C₉₇	C₄⋊C₄	1	1	yes	characteristic
34	C₄×C₉₇	C₄⋊C₄	1	1	yes	characteristic
35	Dic₉₇	—	2	4	no	—
36	C₂×C₉₇	#95	1	1	yes	characteristic
37	C₂×C₉₇	C₄×C₈	1	1	yes	characteristic
38	C₂×C₉₇	#97	1	1	yes	characteristic
39	C₂×C₉₇	C₂²⋊C₈	1	2	yes	—
40	C₂×C₉₇	C₄⋊C₈	1	2	yes	—
41	C₉₇	#336	1	1	yes	characteristic, complemented, Sylow
42	#336	—	97	1	no	maximal, Sylow
43	C₂²×C₈	—	97	1	no	—
44	C₂²×C₈	D₉₇	1	1	yes	characteristic
45	C₂×C₄²	—	97	1	no	—
46	C₂²×C₄	—	97	2	no	—
47	C₂²×C₄	C₂×D₉₇	1	1	yes	characteristic
48	C₂×C₈	—	2	1	no	—
49	C₂×C₈	—	2	1	no	—
50	C₂×C₈	—	97	2	no	—
51	C₂×C₈	—	194	1	no	—
52	C₂×C₈	—	194	1	no	—
53	C₂×C₈	Dic₉₇	1	2	yes	complemented
54	C₄²	—	194	1	no	—
55	C₄²	—	194	1	no	—
56	C₂³	C₄×D₉₇	1	1	yes	characteristic
57	C₂×C₄	—	97	4	no	—
58	C₂×C₄	—	194	2	no	—
59	C₂×C₄	—	194	2	no	—
60	C₂×C₄	Dic₁₉₄	1	1	yes	characteristic
61	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
62	C₂×C₄	D₃₈₈	1	1	yes	characteristic
63	C₂×C₄	C₂×Dic₉₇	1	1	yes	characteristic
64	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊D₉₇	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	194	2	no	—
68	C₂²	C₄×Dic₉₇	1	1	yes	characteristic
69	C₂²	#13095488	1	1	yes	characteristic
70	C₂²	#13095490	1	1	yes	characteristic
71	C₂²	C₈×D₉₇	1	2	yes	—
72	C₂²	#13095494	1	2	yes	—
73	C₄	—	194	4	no	—
74	C₄	#13095488	1	1	yes	characteristic
75	C₄	C₂²⋊Dic₉₇	1	1	yes	characteristic
76	C₄	#13095490	1	1	yes	characteristic
77	C₄	C₄⋊Dic₉₇	1	1	yes	characteristic
78	C₂	#15690717	1	1	yes	characteristic
79	C₂	C₈×Dic₉₇	1	1	yes	characteristic
80	C₂	#15690720	1	1	yes	characteristic
81	C₂	#15690722	1	2	yes	—
82	C₂	#15690739	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₉₇
commutator	C₂×C₉₇	C₄×C₈
Fitting	C₂²×C₈×C₉₇	C₂
socle	C₂³×C₉₇	C₂×C₄
hypercenter	C₂²×C₈	D₉₇
hypocenter	C₉₇	#336
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
7. C₂×#11715895	C₄	semidirect
13. C₂×C₈×C₉₇	C₄	semidirect
23. C₂×Dic₉₇	C₈	semidirect
41. C₉₇	#336	semidirect
53. C₂×C₈	Dic₉₇	semidirect