Subgroups — #391×C₁₈₁ #26040802

Order 11584.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₁₈₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₁₈₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₁₈₁	C₂	1	1	yes	maximal, characteristic
4	#95×C₁₈₁	C₂	1	4	yes	maximal
5	C₂×Q₈×C₁₈₁	—	2	2	no	—
6	C₂×Q₈×C₁₈₁	—	2	2	no	—
7	C₂×Q₈×C₁₈₁	C₄	1	4	yes	complemented
8	C₂²×C₄×C₁₈₁	C₂²	1	2	yes	—
9	C₂²×C₄×C₁₈₁	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₈₁	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₈₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₈₁	—	2	2	no	—
13	C₄²×C₁₈₁	—	2	2	no	—
14	C₂³×C₁₈₁	C₂³	1	1	yes	characteristic
15	Q₈×C₁₈₁	—	2	8	no	—
16	C₂×C₄×C₁₈₁	—	2	2	no	—
17	C₂×C₄×C₁₈₁	—	2	2	no	—
18	C₂×C₄×C₁₈₁	—	2	2	no	—
19	C₂×C₄×C₁₈₁	—	2	2	no	—
20	C₂×C₄×C₁₈₁	—	2	2	no	—
21	C₂×C₄×C₁₈₁	—	2	4	no	—
22	C₂×C₄×C₁₈₁	C₂×C₄	1	4	yes	—
23	C₂×C₄×C₁₈₁	C₂×C₄	1	2	yes	—
24	C₂×C₄×C₁₈₁	D₄	1	2	yes	—
25	C₂×C₄×C₁₈₁	D₄	1	2	yes	—
26	C₂×C₄×C₁₈₁	Q₈	1	4	yes	complemented
27	C₂²×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₁₈₁	C₂×D₄	1	1	yes	characteristic
29	C₂²×C₁₈₁	C₂×D₄	1	1	yes	characteristic
30	C₂²×C₁₈₁	C₂×Q₈	1	2	yes	—
31	C₂²×C₁₈₁	#41	1	2	yes	—
32	C₄×C₁₈₁	—	2	4	no	—
33	C₄×C₁₈₁	—	2	4	no	—
34	C₄×C₁₈₁	—	4	2	no	—
35	C₄×C₁₈₁	C₂²⋊C₄	1	4	yes	—
36	C₂×C₁₈₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₁₈₁	C₄×Q₈	1	2	yes	—
38	C₂×C₁₈₁	C₂²⋊Q₈	1	2	yes	—
39	C₂×C₁₈₁	#124	1	1	yes	characteristic
40	C₂×C₁₈₁	C₄⋊Q₈	1	1	yes	characteristic
41	C₁₈₁	#391	1	1	yes	characteristic, direct product factor, Sylow
42	#391	C₁₈₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×Q₈	C₂×C₁₈₁	1	1	yes	characteristic
44	C₂×C₄⋊C₄	C₂×C₁₈₁	1	1	yes	characteristic
45	C₂×C₄²	C₂×C₁₈₁	1	1	yes	characteristic
46	#95	C₂×C₁₈₁	1	4	yes	—
47	C₂×Q₈	—	2	2	no	—
48	C₂×Q₈	—	2	2	no	—
49	C₂×Q₈	C₄×C₁₈₁	1	4	yes	complemented
50	C₂²×C₄	C₂²×C₁₈₁	1	2	yes	—
51	C₂²×C₄	C₂²×C₁₈₁	1	2	yes	—
52	C₂²×C₄	C₂²×C₁₈₁	1	2	yes	—
53	C₂²×C₄	C₂²×C₁₈₁	1	1	yes	characteristic
54	C₄⋊C₄	—	2	2	no	—
55	C₄²	—	2	2	no	—
56	C₂³	C₂³×C₁₈₁	1	1	yes	characteristic
57	Q₈	—	2	8	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	4	no	—
64	C₂×C₄	C₂×C₄×C₁₈₁	1	4	yes	—
65	C₂×C₄	C₂×C₄×C₁₈₁	1	2	yes	—
66	C₂×C₄	D₄×C₁₈₁	1	2	yes	—
67	C₂×C₄	D₄×C₁₈₁	1	2	yes	—
68	C₂×C₄	Q₈×C₁₈₁	1	4	yes	complemented
69	C₂²	C₂²×C₄×C₁₈₁	1	1	yes	characteristic
70	C₂²	C₂×D₄×C₁₈₁	1	1	yes	characteristic
71	C₂²	C₂×D₄×C₁₈₁	1	1	yes	characteristic
72	C₂²	C₂×Q₈×C₁₈₁	1	2	yes	—
73	C₂²	#41×C₁₈₁	1	2	yes	—
74	C₄	—	2	4	no	—
75	C₄	—	2	4	no	—
76	C₄	—	4	2	no	—
77	C₄	C₂²⋊C₄×C₁₈₁	1	4	yes	—
78	C₂	C₂×C₂²⋊C₄×C₁₈₁	1	1	yes	characteristic
79	C₂	C₄×Q₈×C₁₈₁	1	2	yes	—
80	C₂	C₂²⋊Q₈×C₁₈₁	1	2	yes	—
81	C₂	#124×C₁₈₁	1	1	yes	characteristic
82	C₂	C₄⋊Q₈×C₁₈₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₈₁	C₂³
commutator	C₂²	C₂²×C₄×C₁₈₁
Frattini, cosocle	C₂³	C₂³×C₁₈₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₈₁ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₂×Q₈×C₁₈₁	C₄	semidirect
26. C₂×C₄×C₁₈₁	Q₈	semidirect
41. C₁₈₁	#391	direct (N × H)
42. #391	C₁₈₁	direct (N × H)
49. C₂×Q₈	C₄×C₁₈₁	semidirect
68. C₂×C₄	Q₈×C₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₁₈₁	2
C₂×C₄⋊C₄×C₁₈₁	2
C₂×C₄²×C₁₈₁	2
#95×C₁₈₁	2
#391	181

Subgroups — #391×C181 #26040802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #391×C₁₈₁ #26040802