Subgroups — #37570723

Order 24448.

50 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	#27132493	C₂	1	1	yes	maximal, characteristic
3	#368×C₁₉₁	C₂	1	1	yes	maximal, characteristic
4	#20259258	—	2	1	no	—
5	C₁₉₁⋊C₃₂	C₄	1	2	yes	—
6	C₂×C₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
7	#108×C₁₉₁	—	2	1	no	—
8	#15690271	—	4	1	no	—
9	M₁₆×C₁₉₁	—	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	C₁₉₁⋊C₈	—	8	1	no	—
14	C₂×C₄×C₁₉₁	D₈	1	1	yes	characteristic
15	C₈×C₁₉₁	—	8	1	no	—
16	C₈×C₁₉₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₉₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₉₁	Q₃₂	1	1	yes	characteristic
19	C₄×C₁₉₁	#107	1	1	yes	characteristic
20	C₄×C₁₉₁	D₁₆	1	1	yes	characteristic
21	C₂×C₁₉₁	—	2	1	no	—
22	C₂×C₁₉₁	#366	1	1	yes	characteristic
23	C₁₉₁	#1425	1	1	yes	characteristic, complemented, Sylow
24	#1425	—	191	1	no	maximal, Sylow
25	C₂×C₃₂	—	191	1	no	—
26	#368	—	191	1	no	—
27	#368	D₁₉₁	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₁₉₁	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	382	1	no	—
31	C₃₂	—	191	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	764	1	no	—
34	C₂×C₈	C₂²⋊D₁₉₁	1	1	yes	characteristic
35	C₁₆	C₄×D₁₉₁	1	1	yes	characteristic
36	C₁₆	Dic₃₈₂	1	1	yes	characteristic
37	C₂×C₄	#15690272	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	1528	1	no	—
40	C₈	Dic₁₉₁⋊C₄	1	1	yes	characteristic
41	C₈	#15690277	1	1	yes	characteristic
42	C₂²	#20259268	1	1	yes	characteristic
43	C₄	#20259255	1	1	yes	characteristic
44	C₄	#20259263	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#27132488	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#20259263
commutator	C₁₆×C₁₉₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₉₁
Fitting	#368×C₁₉₁	C₂
socle	C₂×C₁₉₁	#366
prime radical	C₂²×C₁₉₁	Q₃₂
cosocle	C₂×C₁₆×C₁₉₁	C₂²
hypercenter	#368	D₁₉₁
hypocenter	C₁₉₁	#1425
LCS	G ▷ C₁₆×C₁₉₁ ▷ C₈×C₁₉₁ ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
23. C₁₉₁	#1425	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
#27132493	2
#368×C₁₉₁	2
#1425	191