Subgroups — #1368×C₁₉₁ #37568110

Order 24448.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#346×C₁₉₁	C₂	1	1	yes	maximal, characteristic
2	#334×C₁₉₁	C₂	1	2	yes	maximal
3	C₂×C₁₆×C₁₉₁	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₁₉₁	C₄	1	1	yes	characteristic
5	C₄⋊C₈×C₁₉₁	—	2	2	no	—
6	C₄×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₉₁	—	4	2	no	—
8	C₂×C₈×C₁₉₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₉₁	Q₈	1	1	yes	characteristic
10	C₄²×C₁₉₁	D₄	1	1	yes	characteristic
11	C₁₆×C₁₉₁	—	2	1	no	—
12	C₁₆×C₁₉₁	C₈	1	2	yes	complemented
13	C₂×C₄×C₁₉₁	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₉₁	SD₁₆	1	2	yes	—
15	C₈×C₁₉₁	—	2	1	no	—
16	C₈×C₁₉₁	—	8	2	no	—
17	C₈×C₁₉₁	C₂×C₈	1	1	yes	characteristic
18	C₈×C₁₉₁	M₁₆	1	1	yes	characteristic
19	C₂²×C₁₉₁	#106	1	1	yes	characteristic
20	C₄×C₁₉₁	—	2	2	no	—
21	C₄×C₁₉₁	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₁₉₁	#108	1	1	yes	characteristic
23	C₂×C₁₉₁	#334	1	1	yes	characteristic
24	C₂×C₁₉₁	#365	1	2	yes	—
25	C₁₉₁	#1368	1	1	yes	characteristic, direct product factor, Sylow
26	#1368	C₁₉₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	#346	C₂×C₁₉₁	1	1	yes	characteristic
28	#334	C₂×C₁₉₁	1	2	yes	—
29	C₂×C₁₆	C₄×C₁₉₁	1	1	yes	characteristic
30	C₂×C₁₆	C₄×C₁₉₁	1	1	yes	characteristic
31	C₄⋊C₈	—	2	2	no	—
32	C₄×C₈	C₂²×C₁₉₁	1	1	yes	characteristic
33	C₂×C₈	—	4	2	no	—
34	C₂×C₈	C₂×C₄×C₁₉₁	1	1	yes	characteristic
35	C₂×C₈	Q₈×C₁₉₁	1	1	yes	characteristic
36	C₄²	D₄×C₁₉₁	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	C₈×C₁₉₁	1	2	yes	complemented
39	C₂×C₄	C₄⋊C₄×C₁₉₁	1	1	yes	characteristic
40	C₂×C₄	SD₁₆×C₁₉₁	1	2	yes	—
41	C₈	—	2	1	no	—
42	C₈	—	8	2	no	—
43	C₈	C₂×C₈×C₁₉₁	1	1	yes	characteristic
44	C₈	M₁₆×C₁₉₁	1	1	yes	characteristic
45	C₂²	#106×C₁₉₁	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊C₈×C₁₉₁	1	1	yes	characteristic
48	C₄	#108×C₁₉₁	1	1	yes	characteristic
49	C₂	#334×C₁₉₁	1	1	yes	characteristic
50	C₂	#365×C₁₉₁	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉₁	#106
commutator	C₈	C₂×C₈×C₁₉₁
Frattini, cosocle	C₄×C₈	C₂²×C₁₉₁
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉₁ ◁ C₄²×C₁₉₁ ◁ C₄×C₈×C₁₉₁ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₁₉₁	C₈	semidirect
25. C₁₉₁	#1368	direct (N × H)
26. #1368	C₁₉₁	direct (N × H)
38. C₁₆	C₈×C₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
#346×C₁₉₁	2
#334×C₁₉₁	2
#1368	191

Subgroups — #1368×C191 #37568110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1368×C₁₉₁ #37568110