Subgroups — #37550124

Order 23168.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042323	C₂	1	2	yes	maximal, complemented
2	#26042208	C₂	1	1	yes	maximal, characteristic, complemented
3	#26042194	C₂	1	2	yes	maximal, complemented
4	#26042166	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041712	C₂	1	1	yes	maximal, characteristic
6	#19153904	—	2	2	no	—
7	D₁₈₁⋊C₁₆	C₂²	1	1	yes	characteristic
8	#19153887	C₂²	1	2	yes	—
9	#19153881	—	2	2	no	—
10	C₈×#10624382	C₂²	1	1	yes	characteristic
11	#19153839	C₂²	1	2	yes	—
12	#19153759	C₄	1	2	yes	complemented
13	D₂₈₉₆	C₄	1	1	yes	characteristic, complemented
14	C₁₆×D₁₈₁	C₂²	1	1	yes	characteristic
15	Q₃₂×C₁₈₁	C₄	1	1	yes	characteristic, complemented
16	#15668459	—	2	2	no	—
17	#15668459	—	4	2	no	—
18	D₁₈₁⋊C₈	—	4	2	no	—
19	D₁₈₁⋊C₈	D₄	1	1	yes	characteristic
20	C₄×#10624382	D₄	1	1	yes	characteristic
21	#15668452	—	2	1	no	—
22	#15668450	—	2	2	no	—
23	#15668436	—	2	2	no	—
24	D₁₄₄₈	C₂×C₄	1	2	yes	—
25	C₈×D₁₈₁	C₂³	1	1	yes	characteristic
26	#15668424	C₂×C₄	1	1	yes	characteristic
27	Q₁₆×C₁₈₁	C₂×C₄	1	2	yes	—
28	C₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic
29	C₂×#10624382	—	2	1	no	—
30	#13089685	—	4	2	no	—
31	#13089685	D₈	1	2	yes	—
32	D₇₂₄	—	2	2	no	—
33	D₇₂₄	—	4	2	no	—
34	C₄×D₁₈₁	—	4	2	no	—
35	C₄×D₁₈₁	C₂×D₄	1	1	yes	characteristic
36	#13089678	#41	1	1	yes	characteristic
37	Q₈×C₁₈₁	—	2	2	no	—
38	C₈×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×D₁₈₁	—	4	2	no	—
40	C₂×D₁₈₁	#135	1	1	yes	characteristic
41	#10624382	—	4	1	no	—
42	C₄×C₁₈₁	—	4	2	no	—
43	C₄×C₁₈₁	C₄×D₄	1	1	yes	characteristic
44	Dic₁₈₁	C₂×D₈	1	1	yes	characteristic
45	C₂×C₁₈₁	C₄×D₈	1	1	yes	characteristic
46	D₁₈₁	—	2	1	no	—
47	D₁₈₁	—	8	2	no	—
48	C₁₈₁	#2179	1	1	yes	characteristic, complemented, Sylow
49	#2179	—	181	1	no	maximal, Sylow
50	#508	—	181	1	no	—
51	#443	—	181	2	no	—
52	#368	—	181	1	no	—
53	#359	—	181	2	no	—
54	#346	—	181	1	no	—
55	#135	—	181	2	no	—
56	#131	—	362	2	no	—
57	Q₃₂	#10624382	1	1	yes	characteristic, complemented
58	SD₃₂	—	181	2	no	—
59	D₁₆	—	181	1	no	—
60	C₂×C₁₆	—	181	1	no	—
61	C₂×C₁₆	—	181	1	no	—
62	#108	—	181	2	no	—
63	#104	—	362	2	no	—
64	C₄×C₈	—	181	1	no	—
65	#41	—	362	2	no	—
66	Q₁₆	C₂×#10624382	1	2	yes	—
67	SD₁₆	—	362	2	no	—
68	D₈	—	181	2	no	—
69	M₁₆	—	362	2	no	—
70	M₁₆	—	724	2	no	—
71	C₂×C₈	—	181	1	no	—
72	C₂×C₈	—	181	1	no	—
73	C₂×C₈	—	724	2	no	—
74	C₄²	—	181	1	no	—
75	C₁₆	—	362	1	no	—
76	C₁₆	—	181	1	no	—
77	C₁₆	C₂×#10624382	1	1	yes	characteristic
78	Q₈	—	2	2	no	—
79	D₄	—	362	2	no	—
80	D₄	—	724	2	no	—
81	C₂×C₄	—	362	1	no	—
82	C₂×C₄	—	181	1	no	—
83	C₂×C₄	—	724	2	no	—
84	C₈	—	181	2	no	—
85	C₈	—	181	1	no	—
86	C₈	—	724	2	no	—
87	C₈	C₂²×#10624382	1	1	yes	characteristic
88	C₂²	—	181	1	no	—
89	C₂²	—	724	2	no	—
90	C₄	—	4	2	no	—
91	C₄	—	181	1	no	—
92	C₄	—	724	1	no	—
93	C₄	D₄×#10624382	1	1	yes	characteristic
94	C₂	—	362	1	no	—
95	C₂	—	1448	2	no	—
96	C₂	D₈×#10624382	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×#10624382
commutator	C₈×C₁₈₁	C₂²×C₄
Frattini	C₈	C₂²×#10624382
Fitting	Q₃₂×C₁₈₁	C₄
socle	C₂×C₁₈₁	C₄×D₈
prime radical	#26041712	C₂
cosocle	C₈×D₁₈₁	C₂³
hypercenter	Q₃₂	#10624382
hypocenter	C₁₈₁	#2179
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #26042323	C₂	semidirect
2. #26042208	C₂	semidirect
3. #26042194	C₂	semidirect
4. #26042166	C₂	semidirect
12. #19153759	C₄	semidirect
13. D₂₈₉₆	C₄	semidirect
15. Q₃₂×C₁₈₁	C₄	semidirect
48. C₁₈₁	#2179	semidirect
57. Q₃₂	#10624382	semidirect

Maximal subgroups

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

subgroup	index
#26042323	2
#26042208	2
#26042194	2
#26042166	2
#26041712	2
#2179	181