Subgroups — #37570719

Order 24448.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#27132489	C₂	1	1	yes	maximal, characteristic
3	#366×C₁₉₁	C₂	1	1	yes	maximal, characteristic
4	#20259256	—	2	1	no	—
5	C₁₉₁⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
7	#107×C₁₉₁	—	2	1	no	—
8	C₄⋊Dic₁₉₁	—	4	1	no	—
9	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₁₉₁	—	4	1	no	—
11	C₁₆×C₁₉₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₉₁	Q₈	1	1	yes	characteristic
13	C₂×Dic₁₉₁	—	8	1	no	—
14	C₂×C₄×C₁₉₁	—	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	D₁₆	1	1	yes	characteristic
19	C₄×C₁₉₁	—	16	1	no	—
20	C₄×C₁₉₁	#107	1	1	yes	characteristic
21	C₄×C₁₉₁	Q₃₂	1	1	yes	characteristic
22	Dic₁₉₁	—	16	1	no	—
23	C₂×C₁₉₁	#366	1	1	yes	characteristic
24	C₂×C₁₉₁	D₃₂	1	1	yes	characteristic
25	C₂×C₁₉₁	Q₆₄	1	1	yes	characteristic
26	C₁₉₁	#1423	1	1	yes	characteristic, complemented, Sylow
27	#1423	—	191	1	no	maximal, Sylow
28	C₂×C₃₂	—	191	1	no	—
29	#366	—	191	1	no	—
30	#366	D₁₉₁	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₁₉₁	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	382	1	no	—
34	C₃₂	—	191	2	no	—
35	C₂×C₈	C₂²⋊D₁₉₁	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	764	1	no	—
38	C₁₆	C₄×D₁₉₁	1	1	yes	characteristic
39	C₁₆	Dic₃₈₂	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	1528	1	no	—
42	C₂×C₄	#15690272	1	1	yes	characteristic
43	C₈	Dic₁₉₁⋊C₄	1	1	yes	characteristic
44	C₈	#15690277	1	1	yes	characteristic
45	C₂²	#20259263	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	3056	1	no	—
48	C₄	#20259255	1	1	yes	characteristic
49	C₄	#20259268	1	1	yes	characteristic
50	C₂	#27132488	1	1	yes	characteristic
51	C₂	#27132498	1	1	yes	characteristic
52	C₂	#27132503	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#20259263
commutator	C₁₆×C₁₉₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₉₁
Fitting	#366×C₁₉₁	C₂
socle, prime radical	C₂²×C₁₉₁	D₁₆
cosocle	C₂×C₁₆×C₁₉₁	C₂²
hypercenter	#366	D₁₉₁
hypocenter	C₁₉₁	#1423
LCS	G ▷ C₁₆×C₁₉₁ ▷ C₈×C₁₉₁ ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. C₁₉₁⋊C₃₂	C₄	semidirect
26. C₁₉₁	#1423	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉₁⋊C₃₂	2
#27132489	2
#366×C₁₉₁	2
#1423	191