Subgroups — #37548684

Order 23168.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042201	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈×#13089685	C₂	1	1	yes	maximal, characteristic, complemented
3	#26041395	C₂	1	1	yes	maximal, characteristic
4	#19153890	—	2	1	no	—
5	C₄×#13089685	—	2	1	no	—
6	#19153838	C₄	1	1	yes	characteristic
7	#19153824	—	2	1	no	—
8	#19153742	—	2	1	no	—
9	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
10	#108×C₁₈₁	C₄	1	1	yes	characteristic
11	C₂×#13089685	—	2	2	no	—
12	#15668452	—	4	1	no	—
13	#15668449	—	2	1	no	—
14	Dic₇₂₄	C₈	1	1	yes	characteristic, complemented
15	#15668438	—	2	1	no	—
16	D₁₄₄₈	C₈	1	1	yes	characteristic, complemented
17	#15668432	—	4	1	no	—
18	C₂×#13089678	D₄	1	1	yes	characteristic
19	C₈×D₁₈₁	—	4	1	no	—
20	C₄×Dic₁₈₁	D₄	1	1	yes	characteristic
21	M₁₆×C₁₈₁	—	2	1	no	—
22	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
23	#13089685	—	2	4	no	—
24	Dic₃₆₂	—	2	1	no	—
25	D₇₂₄	—	2	1	no	—
26	C₂²⋊D₁₈₁	—	4	1	no	—
27	C₂×Dic₁₈₁	—	2	1	no	—
28	C₄×D₁₈₁	—	4	1	no	—
29	#13089678	D₈	1	1	yes	characteristic
30	#13089678	SD₁₆	1	1	yes	characteristic
31	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₈×C₁₈₁	—	4	1	no	—
33	C₈×C₁₈₁	C₂×C₈	1	1	yes	characteristic
34	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
35	C₂²×C₁₈₁	#104	1	1	yes	characteristic
36	C₂×D₁₈₁	—	4	1	no	—
37	C₄×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
38	C₄×C₁₈₁	#102	1	1	yes	characteristic
39	Dic₁₈₁	—	2	2	no	—
40	Dic₁₈₁	—	4	1	no	—
41	C₂×C₁₈₁	—	2	1	no	—
42	C₂×C₁₈₁	D₄⋊C₈	1	1	yes	characteristic
43	D₁₈₁	—	8	1	no	—
44	C₁₈₁	#1335	1	1	yes	characteristic, complemented, Sylow
45	#1335	—	181	1	no	maximal, Sylow
46	#443	—	181	1	no	—
47	#364	—	181	1	no	—
48	C₈²	—	181	1	no	—
49	#135	—	181	1	no	—
50	#131	—	362	1	no	—
51	M₃₂	—	362	1	no	—
52	#108	#10624382	1	1	yes	characteristic
53	#104	—	362	1	no	—
54	C₄×C₈	—	362	1	no	—
55	C₄×C₈	—	181	1	no	—
56	#41	—	362	1	no	—
57	Q₁₆	—	181	1	no	—
58	SD₁₆	—	362	1	no	—
59	D₈	—	181	1	no	—
60	M₁₆	—	2	1	no	—
61	M₁₆	—	724	1	no	—
62	C₂×C₈	—	362	2	no	—
63	C₂×C₈	—	181	1	no	—
64	C₂×C₈	—	724	1	no	—
65	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
66	C₄²	—	181	1	no	—
67	C₁₆	—	724	1	no	—
68	Q₈	—	362	1	no	—
69	D₄	—	362	1	no	—
70	D₄	—	724	1	no	—
71	C₂×C₄	—	362	1	no	—
72	C₂×C₄	—	724	1	no	—
73	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
74	C₈	—	4	1	no	—
75	C₈	—	362	4	no	—
76	C₈	—	181	1	no	—
77	C₈	—	181	1	no	—
78	C₈	D₁₈₁⋊C₈	1	1	yes	characteristic
79	C₈	#15668459	1	1	yes	characteristic
80	C₂²	—	724	1	no	—
81	C₂²	#19153881	1	1	yes	characteristic
82	C₄	—	362	2	no	—
83	C₄	—	724	1	no	—
84	C₄	#19153873	1	1	yes	characteristic
85	C₄	#19153878	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	1448	1	no	—
88	C₂	#26042127	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19153878
commutator	C₈×C₁₈₁	C₂×C₈
Frattini	C₂×C₈	C₂×#10624382
Fitting	#108×C₁₈₁	C₄
socle	C₂×C₁₈₁	D₄⋊C₈
prime radical	#19153838	C₄
cosocle	C₈×Dic₁₈₁	C₂²
hypercenter	#108	#10624382
hypocenter	C₁₈₁	#1335
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
1. #26042201	C₂	semidirect
2. C₈×#13089685	C₂	semidirect
14. Dic₇₂₄	C₈	semidirect
16. D₁₄₄₈	C₈	semidirect
44. C₁₈₁	#1335	semidirect

Maximal subgroups

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

subgroup	index
#26042201	2
C₈×#13089685	2
#26041395	2
#1335	181