Subgroups — #38740804

Order 25216.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263260	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₁₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₁₉₇	—	2	2	no	—
4	#20263260	—	2	2	no	—
5	#20263260	C₄	1	4	yes	complemented
6	C₂²×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉₇	—	2	2	no	—
8	C₂×C₁₆×C₁₉₇	C₄	1	2	yes	complemented
9	C₂²×Dic₁₉₇	—	4	2	no	—
10	C₄⋊Dic₁₉₇	—	2	4	no	—
11	C₄⋊Dic₁₉₇	—	4	2	no	—
12	C₂²×C₄×C₁₉₇	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₉₇	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₁₉₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₉₇	D₄	1	2	yes	—
16	C₂×C₈×C₁₉₇	Q₈	1	1	yes	characteristic
17	C₁₆×C₁₉₇	—	2	2	no	—
18	C₂×Dic₁₉₇	—	4	4	no	—
19	C₂×Dic₁₉₇	—	8	2	no	—
20	C₂×Dic₁₉₇	—	8	2	no	—
21	C₂³×C₁₉₇	D₈	1	1	yes	characteristic
22	C₂×C₄×C₁₉₇	C₂²⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₉₇	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₉₇	SD₁₆	1	2	yes	—
25	C₂×C₄×C₁₉₇	Q₁₆	1	1	yes	characteristic
26	C₈×C₁₉₇	C₄²	1	1	yes	characteristic
27	C₈×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₁₉₇	C₄⋊C₄	1	2	yes	—
29	C₂²×C₁₉₇	#102	1	2	yes	—
30	C₂²×C₁₉₇	#107	1	1	yes	characteristic
31	C₂²×C₁₉₇	D₁₆	1	1	yes	characteristic
32	C₂²×C₁₉₇	SD₃₂	1	2	yes	—
33	C₂²×C₁₉₇	Q₃₂	1	1	yes	characteristic
34	C₄×C₁₉₇	#95	1	1	yes	characteristic
35	C₄×C₁₉₇	#103	1	2	yes	—
36	C₄×C₁₉₇	#106	1	1	yes	characteristic
37	Dic₁₉₇	—	8	4	no	—
38	C₂×C₁₉₇	#340	1	1	yes	characteristic
39	C₂×C₁₉₇	#357	1	2	yes	—
40	C₂×C₁₉₇	#358	1	2	yes	—
41	C₂×C₁₉₇	#366	1	1	yes	characteristic
42	C₂×C₁₉₇	#367	1	1	yes	characteristic
43	C₁₉₇	#1380	1	1	yes	characteristic, complemented, Sylow
44	#1380	—	197	1	no	maximal, Sylow
45	C₂²×C₁₆	D₁₉₇	1	1	yes	characteristic
46	C₂×#107	—	197	2	no	—
47	C₂²×C₈	C₂×D₁₉₇	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	394	2	no	—
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	Dic₁₉₇	1	2	yes	complemented
51	#107	—	394	2	no	—
52	#107	—	197	4	no	—
53	C₂²×C₄	—	788	2	no	—
54	C₂²×C₄	D₇₈₈	1	1	yes	characteristic
55	C₂×C₈	C₄×D₁₉₇	1	2	yes	—
56	C₂×C₈	C₂×Dic₁₉₇	1	1	yes	characteristic
57	C₂×C₈	C₂²⋊D₁₉₇	1	2	yes	—
58	C₂×C₈	Dic₃₉₄	1	1	yes	characteristic
59	C₄⋊C₄	—	788	2	no	—
60	C₄⋊C₄	—	394	4	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₁₅₇₆	1	1	yes	characteristic
63	C₂×C₄	—	788	4	no	—
64	C₂×C₄	—	1576	2	no	—
65	C₂×C₄	—	1576	2	no	—
66	C₂×C₄	#15691335	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₁₉₇	1	1	yes	characteristic
68	C₂×C₄	#15691347	1	2	yes	—
69	C₂×C₄	Dic₇₈₈	1	1	yes	characteristic
70	C₈	C₄×Dic₁₉₇	1	1	yes	characteristic
71	C₈	C₂²⋊Dic₁₉₇	1	1	yes	characteristic
72	C₈	#15691337	1	2	yes	—
73	C₂²	#20263248	1	2	yes	—
74	C₂²	#20263260	1	1	yes	characteristic
75	C₂²	D₃₁₅₂	1	1	yes	characteristic
76	C₂²	#20263271	1	2	yes	—
77	C₂²	Dic₁₅₇₆	1	1	yes	characteristic
78	C₄	—	1576	4	no	—
79	C₄	#20263233	1	1	yes	characteristic
80	C₄	#20263251	1	2	yes	—
81	C₄	#20263258	1	1	yes	characteristic
82	C₂	#27160842	1	1	yes	characteristic
83	C₂	#27160881	1	2	yes	—
84	C₂	#27160884	1	2	yes	—
85	C₂	#27160905	1	1	yes	characteristic
86	C₂	#27160907	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₅₇₆
commutator	C₈×C₁₉₇	C₄²
Frattini	C₂²×C₈	C₂×D₁₉₇
Fitting	C₂²×C₁₆×C₁₉₇	C₂
socle, prime radical	C₂³×C₁₉₇	D₈
cosocle	C₂²×C₈×C₁₉₇	C₂²
hypercenter	C₂²×C₁₆	D₁₉₇
hypocenter	C₁₉₇	#1380
LCS	G ▷ C₈×C₁₉₇ ▷ C₄×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
5. #20263260	C₄	semidirect
8. C₂×C₁₆×C₁₉₇	C₄	semidirect
43. C₁₉₇	#1380	semidirect
50. C₂×C₁₆	Dic₁₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20263260	2
C₂²×C₁₆×C₁₉₇	2
#1380	197