Subgroups — #37570726

Order 24448.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27132493	C₂	1	1	yes	maximal, characteristic
2	#27132491	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₁₉₁	C₂	1	1	yes	maximal, characteristic
4	#20259258	—	2	1	no	—
5	#20259256	—	2	1	no	—
6	C₂×C₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
7	C₃₂×C₁₉₁	C₄	1	2	yes	complemented
8	#15690271	—	4	1	no	—
9	C₄⋊Dic₁₉₁	—	4	1	no	—
10	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
11	C₁₆×C₁₉₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₉₁	Q₈	1	1	yes	characteristic
13	C₂×Dic₁₉₁	—	8	1	no	—
14	C₁₉₁⋊C₈	—	8	1	no	—
15	C₂×C₄×C₁₉₁	D₈	1	1	yes	characteristic
16	C₈×C₁₉₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₉₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₉₁	SD₃₂	1	1	yes	characteristic
19	C₄×C₁₉₁	#107	1	1	yes	characteristic
20	C₄×C₁₉₁	SD₃₂	1	1	yes	characteristic
21	Dic₁₉₁	—	16	1	no	—
22	C₂×C₁₉₁	—	2	1	no	—
23	C₂×C₁₉₁	#367	1	1	yes	characteristic
24	C₁₉₁	#1426	1	1	yes	characteristic, complemented, Sylow
25	#1426	—	191	1	no	maximal, Sylow
26	M₆₄	D₁₉₁	1	1	yes	characteristic
27	#368	—	191	1	no	—
28	#367	—	191	1	no	—
29	C₂×C₁₆	C₂×D₁₉₁	1	1	yes	characteristic
30	#108	—	382	1	no	—
31	#107	—	382	1	no	—
32	C₃₂	Dic₁₉₁	1	2	yes	complemented
33	M₁₆	—	764	1	no	—
34	C₂×C₈	D₇₆₄	1	1	yes	characteristic
35	C₄⋊C₄	—	764	1	no	—
36	C₁₆	C₂×Dic₁₉₁	1	1	yes	characteristic
37	C₁₆	Dic₃₈₂	1	1	yes	characteristic
38	C₂×C₄	—	1528	1	no	—
39	C₂×C₄	D₁₅₂₈	1	1	yes	characteristic
40	C₈	—	1528	1	no	—
41	C₈	C₄⋊Dic₁₉₁	1	1	yes	characteristic
42	C₈	Dic₇₆₄	1	1	yes	characteristic
43	C₂²	#20259267	1	1	yes	characteristic
44	C₄	—	3056	1	no	—
45	C₄	#20259256	1	1	yes	characteristic
46	C₄	#20259267	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#27132491	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27132491
commutator	C₁₆×C₁₉₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₉₁
Fitting	M₆₄×C₁₉₁	C₂
socle	C₂×C₁₉₁	#367
prime radical	C₂²×C₁₉₁	SD₃₂
cosocle	C₂×C₁₆×C₁₉₁	C₂²
hypercenter	M₆₄	D₁₉₁
hypocenter	C₁₉₁	#1426
LCS	G ▷ C₁₆×C₁₉₁ ▷ C₈×C₁₉₁ ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
7. C₃₂×C₁₉₁	C₄	semidirect
24. C₁₉₁	#1426	semidirect
32. C₃₂	Dic₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
#27132493	2
#27132491	2
M₆₄×C₁₉₁	2
#1426	191