Subgroups — #38740693

Order 25216.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27161209	C₂	1	1	yes	maximal, characteristic
2	#27160855	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₁₉₇	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₃₉₄	C₄	1	1	yes	characteristic
5	C₂×#15691333	—	2	1	no	—
6	C₄⋊#13096802	C₄	1	1	yes	characteristic
7	#20263255	—	2	1	no	—
8	#20263236	—	2	1	no	—
9	C₂×C₁₆×C₁₉₇	—	2	1	no	—
10	C₄×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₃₉₄	C₈	1	1	yes	characteristic
12	C₂×#13096802	—	2	1	no	—
13	C₄⋊Dic₁₉₇	C₈	1	1	yes	characteristic
14	#15691337	—	2	1	no	—
15	C₄×Dic₁₉₇	—	2	1	no	—
16	#15691333	—	2	2	no	—
17	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
19	C₄²×C₁₉₇	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₁₉₇	—	4	1	no	—
21	Dic₃₉₄	—	4	1	no	—
22	C₂×Dic₁₉₇	—	2	1	no	—
23	C₂×Dic₁₉₇	—	2	1	no	—
24	#13096802	—	4	1	no	—
25	C₂×C₄×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₉₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₉₇	M₁₆	1	1	yes	characteristic
28	C₈×C₁₉₇	—	2	1	no	—
29	C₈×C₁₉₇	SD₁₆	1	1	yes	characteristic
30	C₈×C₁₉₇	Q₁₆	1	1	yes	characteristic
31	C₂²×C₁₉₇	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₁₉₇	—	2	1	no	—
33	C₄×C₁₉₇	—	2	1	no	—
34	C₄×C₁₉₇	#103	1	1	yes	characteristic
35	C₄×C₁₉₇	#104	1	1	yes	characteristic
36	Dic₁₉₇	—	4	1	no	—
37	Dic₁₉₇	—	4	1	no	—
38	C₂×C₁₉₇	Q₈⋊C₈	1	1	yes	characteristic
39	C₂×C₁₉₇	#349	1	1	yes	characteristic
40	C₂×C₁₉₇	#350	1	1	yes	characteristic
41	C₁₉₇	#1338	1	1	yes	characteristic, complemented, Sylow
42	#1338	—	197	1	no	maximal, Sylow
43	#446	—	197	1	no	—
44	C₄⋊C₁₆	D₁₉₇	1	1	yes	characteristic
45	#346	—	197	1	no	—
46	C₄×Q₈	—	197	1	no	—
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	394	1	no	—
49	C₄⋊C₈	—	394	1	no	—
50	C₄⋊C₈	—	197	1	no	—
51	#97	—	394	1	no	—
52	C₄×C₈	C₂×D₁₉₇	1	1	yes	characteristic
53	C₂×Q₈	—	197	1	no	—
54	C₂×C₈	—	394	1	no	—
55	C₂×C₈	C₂²⋊D₁₉₇	1	1	yes	characteristic
56	C₂×C₈	D₇₈₈	1	1	yes	characteristic
57	C₄⋊C₄	—	394	1	no	—
58	C₄⋊C₄	—	197	1	no	—
59	C₄²	—	394	1	no	—
60	C₄²	C₄×D₁₉₇	1	1	yes	characteristic
61	C₁₆	—	4	1	no	—
62	C₁₆	—	394	2	no	—
63	Q₈	—	788	1	no	—
64	C₂×C₄	—	394	1	no	—
65	C₂×C₄	—	394	1	no	—
66	C₂×C₄	#15691335	1	1	yes	characteristic
67	C₂×C₄	C₈×D₁₉₇	1	1	yes	characteristic
68	C₂×C₄	#15691341	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	788	1	no	—
71	C₈	#15691346	1	1	yes	characteristic
72	C₈	#15691348	1	1	yes	characteristic
73	C₂²	#20263238	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	788	1	no	—
77	C₄	—	788	1	no	—
78	C₄	#20263249	1	1	yes	characteristic
79	C₄	#20263252	1	1	yes	characteristic
80	C₂	#27160809	1	1	yes	characteristic
81	C₂	#27160860	1	1	yes	characteristic
82	C₂	#27160862	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15691335
commutator	C₂×C₄×C₁₉₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₉₇
Fitting	C₄⋊C₁₆×C₁₉₇	C₂
socle, prime radical	C₂²×C₁₉₇	C₂²⋊C₈
cosocle	C₄×C₈×C₁₉₇	C₂²
hypercenter	C₄⋊C₁₆	D₁₉₇
hypocenter	C₁₉₇	#1338
LCS	G ▷ C₂×C₄×C₁₉₇ ▷ C₂²×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
41. C₁₉₇	#1338	semidirect

Maximal subgroups

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

subgroup	index
#27161209	2
#27160855	2
C₄⋊C₁₆×C₁₉₇	2
#1338	197