Subgroups — #38740543

Order 25216.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27161132	C₂	1	2	yes	maximal
2	C₂×#97×C₁₉₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#13096802	—	2	2	no	—
4	C₂²⋊#13096802	—	2	2	no	—
5	C₄×#13096802	C₄	1	4	yes	—
6	C₂²×C₈×C₁₉₇	C₄	1	2	yes	—
7	C₂×C₄²×C₁₉₇	C₂²	1	1	yes	characteristic
8	#97×C₁₉₇	—	2	2	no	—
9	C₂×#13096802	—	2	4	no	—
10	C₂²×C₄×C₁₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄×C₁₉₇	D₄	1	1	yes	characteristic
12	C₂²×C₄×C₁₉₇	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₁₉₇	—	2	2	no	—
14	C₂×C₈×C₁₉₇	—	2	2	no	—
15	C₂×C₈×C₁₉₇	C₈	1	4	yes	complemented
16	C₄²×C₁₉₇	C₂×C₄	1	2	yes	—
17	C₄²×C₁₉₇	D₄	1	2	yes	—
18	#13096802	—	4	4	no	—
19	C₂³×C₁₉₇	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₉₇	—	4	1	no	—
21	C₂×C₄×C₁₉₇	—	4	1	no	—
22	C₂×C₄×C₁₉₇	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₁₉₇	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₉₇	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₁₉₇	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₉₇	M₁₆	1	2	yes	—
28	C₈×C₁₉₇	—	2	4	no	—
29	C₂²×C₁₉₇	—	2	1	no	—
30	C₂²×C₁₉₇	—	2	1	no	—
31	C₂²×C₁₉₇	#95	1	1	yes	characteristic
32	C₂²×C₁₉₇	C₄⋊C₈	1	2	yes	—
33	C₄×C₁₉₇	—	2	2	no	—
34	C₄×C₁₉₇	—	2	2	no	—
35	C₄×C₁₉₇	C₄×C₈	1	1	yes	characteristic
36	C₄×C₁₉₇	#97	1	1	yes	characteristic
37	C₄×C₁₉₇	C₂²⋊C₈	1	2	yes	—
38	C₂×C₁₉₇	—	2	2	no	—
39	C₂×C₁₉₇	#336	1	1	yes	characteristic
40	C₂×C₁₉₇	H(3,ℤ/4)	1	1	yes	characteristic
41	C₂×C₁₉₇	#338	1	1	yes	characteristic
42	C₁₉₇	#1275	1	1	yes	characteristic, complemented, Sylow
43	#1275	—	197	1	no	maximal, Sylow
44	#431	—	197	2	no	—
45	C₂×#97	D₁₉₇	1	1	yes	characteristic
46	C₂²×C₈	Dic₁₉₇	1	2	yes	—
47	C₂×C₄²	C₂×D₁₉₇	1	1	yes	characteristic
48	C₄⋊C₈	—	394	2	no	—
49	C₂²⋊C₈	—	394	2	no	—
50	#97	—	2	2	no	—
51	C₄×C₈	—	197	4	no	—
52	C₂²×C₄	C₂×Dic₁₉₇	1	1	yes	characteristic
53	C₂²×C₄	D₇₈₈	1	1	yes	characteristic
54	C₂²×C₄	Dic₃₉₄	1	1	yes	characteristic
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	—	2	2	no	—
57	C₂×C₈	—	394	4	no	—
58	C₂×C₈	#13096802	1	4	yes	complemented
59	C₄²	C₄×D₁₉₇	1	2	yes	—
60	C₄²	C₂²⋊D₁₉₇	1	2	yes	—
61	C₂³	C₄⋊Dic₁₉₇	1	1	yes	characteristic
62	C₂×C₄	—	4	1	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	C₄×Dic₁₉₇	1	1	yes	characteristic
65	C₂×C₄	#15691335	1	2	yes	—
66	C₂×C₄	C₂²⋊Dic₁₉₇	1	1	yes	characteristic
67	C₂×C₄	#15691337	1	2	yes	—
68	C₂×C₄	C₂×#13096802	1	2	yes	—
69	C₂×C₄	#15691342	1	2	yes	—
70	C₈	—	2	4	no	—
71	C₈	—	788	4	no	—
72	C₂²	—	2	1	no	—
73	C₂²	—	2	1	no	—
74	C₂²	#20263233	1	1	yes	characteristic
75	C₂²	C₄⋊#13096802	1	2	yes	—
76	C₄	—	2	2	no	—
77	C₄	—	2	2	no	—
78	C₄	C₄×#13096802	1	1	yes	characteristic
79	C₄	#20263237	1	1	yes	characteristic
80	C₄	C₂²⋊#13096802	1	2	yes	—
81	C₂	—	2	2	no	—
82	C₂	#27160834	1	1	yes	characteristic
83	C₂	#27160836	1	1	yes	characteristic
84	C₂	#27160837	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×Dic₁₉₇
commutator	C₄×C₁₉₇	C₄×C₈
Frattini	C₂×C₄²	C₂×D₁₉₇
Fitting	C₂×#97×C₁₉₇	C₂
socle	C₂²×C₁₉₇	#95
prime radical	C₂³×C₁₉₇	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉₇	C₂²
hypercenter	C₂×#97	D₁₉₇
hypocenter	C₁₉₇	#1275
LCS	G ▷ C₄×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
15. C₂×C₈×C₁₉₇	C₈	semidirect
42. C₁₉₇	#1275	semidirect
58. C₂×C₈	#13096802	semidirect

Maximal subgroups

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

subgroup	index
#27161132	2
C₂×#97×C₁₉₇	2
#1275	197