Subgroups — #1342×C₁₉₁ #37568084

Order 24448.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#470×C₁₉₁	C₂	1	1	yes	maximal, characteristic
2	#349×C₁₉₁	C₂	1	1	yes	maximal, characteristic
3	#338×C₁₉₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₉₁	C₄	1	1	yes	characteristic
5	C₂×M₁₆×C₁₉₁	—	2	1	no	—
6	C₂×M₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
7	C₂²⋊Q₈×C₁₉₁	—	2	1	no	—
8	M₃₂×C₁₉₁	—	2	1	no	—
9	#106×C₁₉₁	C₄	1	1	yes	characteristic
10	#103×C₁₉₁	—	2	1	no	—
11	C₂×Q₈×C₁₉₁	—	2	1	no	—
12	C₂²×C₄×C₁₉₁	D₄	1	1	yes	characteristic
13	Q₁₆×C₁₉₁	—	4	1	no	—
14	M₁₆×C₁₉₁	—	4	1	no	—
15	M₁₆×C₁₉₁	—	4	1	no	—
16	M₁₆×C₁₉₁	—	4	1	no	—
17	C₂×C₈×C₁₉₁	—	2	2	no	—
18	C₂×C₈×C₁₉₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
20	C₄⋊C₄×C₁₉₁	—	2	1	no	—
21	C₄⋊C₄×C₁₉₁	—	4	1	no	—
22	C₂²⋊C₄×C₁₉₁	—	4	1	no	—
23	C₁₆×C₁₉₁	—	4	1	no	—
24	C₂³×C₁₉₁	SD₁₆	1	1	yes	characteristic
25	Q₈×C₁₉₁	—	4	1	no	—
26	Q₈×C₁₉₁	—	4	1	no	—
27	C₂×C₄×C₁₉₁	—	2	1	no	—
28	C₂×C₄×C₁₉₁	—	2	1	no	—
29	C₂×C₄×C₁₉₁	—	4	1	no	—
30	C₂×C₄×C₁₉₁	—	4	1	no	—
31	C₂×C₄×C₁₉₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉₁	D₈	1	1	yes	characteristic
33	C₈×C₁₉₁	—	2	1	no	—
34	C₈×C₁₉₁	—	2	1	no	—
35	C₈×C₁₉₁	—	4	2	no	—
36	C₂²×C₁₉₁	—	2	1	no	—
37	C₂²×C₁₉₁	—	4	1	no	—
38	C₂²×C₁₉₁	#102	1	1	yes	characteristic
39	C₄×C₁₉₁	—	2	1	no	—
40	C₄×C₁₉₁	—	8	1	no	—
41	C₄×C₁₉₁	—	8	1	no	—
42	C₄×C₁₉₁	#99	1	1	yes	characteristic
43	C₄×C₁₉₁	#104	1	1	yes	characteristic
44	C₂×C₁₉₁	—	2	1	no	—
45	C₂×C₁₉₁	—	4	1	no	—
46	C₂×C₁₉₁	#327	1	1	yes	characteristic
47	C₁₉₁	#1342	1	1	yes	characteristic, direct product factor, Sylow
48	#1342	C₁₉₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	#470	C₂×C₁₉₁	1	1	yes	characteristic
50	#349	C₂×C₁₉₁	1	1	yes	characteristic
51	#338	C₂×C₁₉₁	1	1	yes	characteristic
52	C₂×Q₁₆	C₄×C₁₉₁	1	1	yes	characteristic
53	C₂×M₁₆	—	2	1	no	—
54	C₂×M₁₆	C₂²×C₁₉₁	1	1	yes	characteristic
55	C₂²⋊Q₈	—	2	1	no	—
56	M₃₂	—	2	1	no	—
57	#106	C₄×C₁₉₁	1	1	yes	characteristic
58	#103	—	2	1	no	—
59	C₂×Q₈	—	2	1	no	—
60	C₂²×C₄	D₄×C₁₉₁	1	1	yes	characteristic
61	Q₁₆	—	4	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	4	1	no	—
64	M₁₆	—	4	1	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	C₂×C₄×C₁₉₁	1	1	yes	characteristic
67	C₂×C₈	D₄×C₁₉₁	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₄⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	4	1	no	—
71	C₁₆	—	4	1	no	—
72	C₂³	SD₁₆×C₁₉₁	1	1	yes	characteristic
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	C₂²⋊C₄×C₁₉₁	1	1	yes	characteristic
80	C₂×C₄	D₈×C₁₉₁	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	4	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#102×C₁₉₁	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	8	1	no	—
89	C₄	—	8	1	no	—
90	C₄	#99×C₁₉₁	1	1	yes	characteristic
91	C₄	#104×C₁₉₁	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#327×C₁₉₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉₁	#327
commutator	C₂×C₈	C₂×C₄×C₁₉₁
Frattini, cosocle	C₂×M₁₆	C₂²×C₁₉₁
prime radical	C₂³×C₁₉₁	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉₁ ◁ C₂×C₄×C₁₉₁ ◁ C₂×M₁₆×C₁₉₁ ◁ G

Complements

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

N	H ≅ G/N	type
47. C₁₉₁	#1342	direct (N × H)
48. #1342	C₁₉₁	direct (N × H)

Maximal subgroups

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

subgroup	index
#470×C₁₉₁	2
#349×C₁₉₁	2
#338×C₁₉₁	2
#1342	191

Subgroups — #1342×C191 #37568084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1342×C₁₉₁ #37568084