Subgroups — #37548689

Order 23168.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15668452	C₂	1	1	yes	maximal, characteristic
2	#26042167	C₂	1	1	yes	maximal, characteristic
3	#26041410	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668452	—	2	1	no	—
5	C₂×#15668452	—	2	1	no	—
6	C₄⋊#13089678	—	2	1	no	—
7	C₄⋊#13089678	C₄	1	1	yes	characteristic
8	#19153727	—	2	1	no	—
9	C₄×#13089678	C₂²	1	1	yes	characteristic
10	C₄×Q₈×C₁₈₁	C₄	1	1	yes	characteristic
11	#15668452	—	2	2	no	—
12	#15668452	—	4	1	no	—
13	C₂×#13089678	—	2	1	no	—
14	C₂×#13089678	D₄	1	1	yes	characteristic
15	C₂×#13089678	D₄	1	1	yes	characteristic
16	C₂×Q₈×C₁₈₁	C₈	1	1	yes	characteristic
17	C₄⋊C₄×C₁₈₁	—	2	1	no	—
18	C₄⋊C₄×C₁₈₁	C₈	1	1	yes	characteristic
19	C₄²×C₁₈₁	—	2	1	no	—
20	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
21	#13089678	—	2	1	no	—
22	#13089678	—	4	1	no	—
23	#13089678	SD₁₆	1	1	yes	characteristic
24	#13089678	Q₁₆	1	1	yes	characteristic
25	Q₈×C₁₈₁	—	4	1	no	—
26	C₂×C₄×C₁₈₁	—	2	1	no	—
27	C₂×C₄×C₁₈₁	—	2	1	no	—
28	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
31	C₂²×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₁₈₁	—	2	1	no	—
33	C₄×C₁₈₁	—	2	1	no	—
34	C₄×C₁₈₁	—	4	1	no	—
35	C₄×C₁₈₁	—	4	1	no	—
36	C₄×C₁₈₁	#103	1	1	yes	characteristic
37	C₄×C₁₈₁	#104	1	1	yes	characteristic
38	C₂×C₁₈₁	Q₈⋊C₈	1	1	yes	characteristic
39	C₂×C₁₈₁	#349	1	1	yes	characteristic
40	C₂×C₁₈₁	#350	1	1	yes	characteristic
41	C₁₈₁	#1338	1	1	yes	characteristic, complemented, Sylow
42	#1338	—	181	1	no	maximal, Sylow
43	#446	—	181	1	no	—
44	C₄⋊C₁₆	—	181	1	no	—
45	#346	—	181	1	no	—
46	C₄×Q₈	#10624382	1	1	yes	characteristic
47	C₂×C₁₆	—	362	1	no	—
48	C₂×C₁₆	—	362	1	no	—
49	C₄⋊C₈	—	362	1	no	—
50	C₄⋊C₈	—	181	1	no	—
51	#97	—	362	1	no	—
52	C₄×C₈	—	181	1	no	—
53	C₂×Q₈	#13089685	1	1	yes	characteristic
54	C₂×C₈	—	362	1	no	—
55	C₂×C₈	—	181	1	no	—
56	C₂×C₈	—	181	1	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	#13089685	1	1	yes	characteristic
59	C₄²	—	2	1	no	—
60	C₄²	C₂×#10624382	1	1	yes	characteristic
61	C₁₆	—	362	2	no	—
62	C₁₆	—	724	1	no	—
63	Q₈	—	4	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
67	C₂×C₄	C₂×#13089685	1	1	yes	characteristic
68	C₂×C₄	#15668458	1	1	yes	characteristic
69	C₈	—	362	1	no	—
70	C₈	—	181	1	no	—
71	C₈	—	181	1	no	—
72	C₈	—	724	1	no	—
73	C₂²	C₂²⋊#13089685	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	#19153879	1	1	yes	characteristic
79	C₄	#19153881	1	1	yes	characteristic
80	C₂	Q₈⋊#13089685	1	1	yes	characteristic
81	C₂	#26042175	1	1	yes	characteristic
82	C₂	#26042177	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#10624382
commutator	C₂×C₄×C₁₈₁	C₂×C₈
Frattini	C₄²	C₂×#10624382
Fitting	C₄×Q₈×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	C₂²⋊C₈
cosocle	C₄×#13089678	C₂²
hypercenter	C₄×Q₈	#10624382
hypocenter	C₁₈₁	#1338
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
41. C₁₈₁	#1338	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#15668452	2
#26042167	2
#26041410	2
#1338	181