Subgroups — #1357×C₁₉₁ #37568099

Order 24448.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#493×C₁₉₁	C₂	1	1	yes	maximal, characteristic
2	#364×C₁₉₁	C₂	1	2	yes	maximal, complemented
3	C₂×D₈×C₁₉₁	—	2	2	no	—
4	#127×C₁₉₁	C₄	1	2	yes	—
5	M₃₂×C₁₉₁	—	2	2	no	—
6	C₄×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₁₉₁	—	2	2	no	—
8	C₂×D₄×C₁₉₁	—	4	2	no	—
9	D₈×C₁₉₁	—	4	2	no	—
10	D₈×C₁₉₁	—	4	2	no	—
11	C₂×C₈×C₁₉₁	D₄	1	2	yes	—
12	C₄²×C₁₉₁	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₁₉₁	—	4	2	no	—
14	C₂³×C₁₉₁	—	4	2	no	—
15	D₄×C₁₉₁	—	4	4	no	—
16	D₄×C₁₉₁	—	8	4	no	—
17	C₂×C₄×C₁₉₁	—	2	1	no	—
18	C₂×C₄×C₁₉₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₈×C₁₉₁	D₈	1	2	yes	—
20	C₈×C₁₉₁	SD₁₆	1	2	yes	—
21	C₂²×C₁₉₁	—	8	4	no	—
22	C₂²×C₁₉₁	—	8	2	no	—
23	C₂²×C₁₉₁	#100	1	1	yes	characteristic
24	C₄×C₁₉₁	—	2	2	no	—
25	C₄×C₁₉₁	#102	1	2	yes	—
26	C₂×C₁₉₁	—	2	1	no	—
27	C₂×C₁₉₁	—	16	2	no	—
28	C₂×C₁₉₁	#331	1	1	yes	characteristic
29	C₁₉₁	#1357	1	1	yes	characteristic, direct product factor, Sylow
30	#1357	C₁₉₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	#493	C₂×C₁₉₁	1	1	yes	characteristic
32	#364	C₂×C₁₉₁	1	2	yes	complemented
33	C₂×D₈	—	2	2	no	—
34	#127	C₄×C₁₉₁	1	2	yes	—
35	M₃₂	—	2	2	no	—
36	C₄×C₈	C₂²×C₁₉₁	1	1	yes	characteristic
37	C₂×D₄	—	2	2	no	—
38	C₂×D₄	—	4	2	no	—
39	D₈	—	4	2	no	—
40	D₈	—	4	2	no	—
41	C₂×C₈	D₄×C₁₉₁	1	2	yes	—
42	C₄²	C₂×C₄×C₁₉₁	1	1	yes	characteristic
43	C₁₆	—	4	2	no	—
44	C₂³	—	4	2	no	—
45	D₄	—	4	4	no	—
46	D₄	—	8	4	no	—
47	C₂×C₄	—	2	1	no	—
48	C₂×C₄	C₂²⋊C₄×C₁₉₁	1	1	yes	characteristic
49	C₈	D₈×C₁₉₁	1	2	yes	—
50	C₈	SD₁₆×C₁₉₁	1	2	yes	—
51	C₂²	—	8	4	no	—
52	C₂²	—	8	2	no	—
53	C₂²	#100×C₁₉₁	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	#102×C₁₉₁	1	2	yes	—
56	C₂	—	2	1	no	—
57	C₂	—	16	2	no	—
58	C₂	#331×C₁₉₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉₁	#331
commutator	C₄²	C₂×C₄×C₁₉₁
Frattini, cosocle	C₄×C₈	C₂²×C₁₉₁
prime radical	#493×C₁₉₁	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉₁ ◁ C₂×C₄×C₁₉₁ ◁ C₄×C₈×C₁₉₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #364×C₁₉₁	C₂	semidirect
29. C₁₉₁	#1357	direct (N × H)
30. #1357	C₁₉₁	direct (N × H)
32. #364	C₂×C₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
#493×C₁₉₁	2
#364×C₁₉₁	2
#1357	191

Subgroups — #1357×C191 #37568099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1357×C₁₉₁ #37568099