Subgroups — #38740894

Order 25216.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₇₆	C₂	1	1	yes	maximal, characteristic
2	#27160905	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₁₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₈₈	—	2	1	no	—
5	Dic₁₅₇₆	—	2	1	no	—
6	Dic₁₅₇₆	C₄	1	2	yes	complemented
7	#20263260	—	2	1	no	—
8	C₂×C₁₆×C₁₉₇	C₂²	1	1	yes	characteristic
9	C₃₂×C₁₉₇	—	2	1	no	—
10	C₂×Dic₃₉₄	—	4	1	no	—
11	Dic₇₈₈	—	2	2	no	—
12	Dic₇₈₈	—	4	1	no	—
13	C₄⋊Dic₁₉₇	—	4	1	no	—
14	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
15	C₁₆×C₁₉₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₉₇	D₄	1	1	yes	characteristic
17	Dic₃₉₄	—	4	2	no	—
18	Dic₃₉₄	—	8	1	no	—
19	C₂×Dic₁₉₇	—	8	1	no	—
20	C₂×Dic₁₉₇	—	8	1	no	—
21	C₂×C₄×C₁₉₇	D₈	1	1	yes	characteristic
22	C₈×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₉₇	SD₁₆	1	1	yes	characteristic
24	C₂²×C₁₉₇	D₁₆	1	1	yes	characteristic
25	C₄×C₁₉₇	#102	1	1	yes	characteristic
26	C₄×C₁₉₇	SD₃₂	1	1	yes	characteristic
27	Dic₁₉₇	—	8	2	no	—
28	Dic₁₉₇	—	16	1	no	—
29	C₂×C₁₉₇	#357	1	1	yes	characteristic
30	C₂×C₁₉₇	SD₆₄	1	1	yes	characteristic
31	C₂×C₁₉₇	Q₆₄	1	1	yes	characteristic
32	C₁₉₇	#1416	1	1	yes	characteristic, complemented, Sylow
33	#1416	—	197	1	no	maximal, Sylow
34	C₂×Q₃₂	—	197	1	no	—
35	C₂×C₃₂	D₁₉₇	1	1	yes	characteristic
36	#366	—	197	1	no	—
37	C₂×Q₁₆	—	394	1	no	—
38	Q₃₂	—	394	1	no	—
39	Q₃₂	—	197	2	no	—
40	C₂×C₁₆	C₂×D₁₉₇	1	1	yes	characteristic
41	#107	—	394	1	no	—
42	C₃₂	—	2	1	no	—
43	C₂×Q₈	—	788	1	no	—
44	Q₁₆	—	788	1	no	—
45	Q₁₆	—	394	2	no	—
46	C₂×C₈	D₇₈₈	1	1	yes	characteristic
47	C₄⋊C₄	—	788	1	no	—
48	C₁₆	C₄×D₁₉₇	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₁₉₇	1	1	yes	characteristic
50	Q₈	—	788	2	no	—
51	Q₈	—	1576	1	no	—
52	C₂×C₄	—	1576	1	no	—
53	C₂×C₄	—	1576	1	no	—
54	C₂×C₄	D₁₅₇₆	1	1	yes	characteristic
55	C₈	#15691335	1	1	yes	characteristic
56	C₈	#15691347	1	1	yes	characteristic
57	C₂²	D₃₁₅₂	1	1	yes	characteristic
58	C₄	—	1576	2	no	—
59	C₄	—	3152	1	no	—
60	C₄	#20263248	1	1	yes	characteristic
61	C₄	#20263271	1	1	yes	characteristic
62	C₂	#27160881	1	1	yes	characteristic
63	C₂	#27160918	1	1	yes	characteristic
64	C₂	Dic₃₁₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₁₅₂
commutator	C₁₆×C₁₉₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₉₇
Fitting	C₂×C₃₂×C₁₉₇	C₂
socle, prime radical	C₂²×C₁₉₇	D₁₆
cosocle	C₂×C₁₆×C₁₉₇	C₂²
hypercenter	C₂×C₃₂	D₁₉₇
hypocenter	C₁₉₇	#1416
LCS	G ▷ C₁₆×C₁₉₇ ▷ C₈×C₁₉₇ ▷ C₄×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
6. Dic₁₅₇₆	C₄	semidirect
32. C₁₉₇	#1416	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₅₇₆	2
#27160905	2
C₂×C₃₂×C₁₉₇	2
#1416	197