Subgroups — #37550090

Order 23168.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042202	C₂	1	2	yes	maximal, complemented
2	#26042175	C₂	1	2	yes	maximal
3	#26042171	C₂	1	2	yes	maximal, complemented
4	C₄×#15668433	C₂	1	1	yes	maximal, characteristic
5	#19153890	C₂²	1	4	yes	—
6	C₂×#15668433	C₄	1	1	yes	characteristic
7	C₂×#15668433	C₂²	1	1	yes	characteristic
8	#19153727	C₄	1	1	yes	characteristic
9	#19153727	C₂²	1	1	yes	characteristic
10	C₄×#13089678	C₄	1	1	yes	characteristic
11	C₄×#13089678	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₁₈₁	C₄	1	1	yes	characteristic
13	#15668452	—	2	4	no	—
14	#15668433	—	2	2	no	—
15	#15668433	—	2	2	no	—
16	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
17	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
18	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
19	C₂×#13089678	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₁₈₁	—	2	1	no	—
21	C₂²×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₁₈₁	—	2	1	no	—
23	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
25	#13089678	—	2	1	no	—
26	#13089678	—	2	1	no	—
27	#13089678	M₁₆	1	2	yes	—
28	#13089678	#41	1	2	yes	—
29	C₂³×C₁₈₁	M₁₆	1	1	yes	characteristic
30	C₂×C₄×C₁₈₁	—	2	1	no	—
31	C₂×C₄×C₁₈₁	—	2	1	no	—
32	C₂×C₄×C₁₈₁	—	2	1	no	—
33	C₂×C₄×C₁₈₁	—	2	1	no	—
34	C₂×C₄×C₁₈₁	—	4	2	no	—
35	C₂×C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
36	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₁₈₁	—	2	1	no	—
38	C₂²×C₁₈₁	—	4	1	no	—
39	C₂²×C₁₈₁	C₂×M₁₆	1	1	yes	characteristic
40	C₄×C₁₈₁	—	2	2	no	—
41	C₄×C₁₈₁	—	2	1	no	—
42	C₄×C₁₈₁	—	4	1	no	—
43	C₄×C₁₈₁	#117	1	1	yes	characteristic
44	C₄×C₁₈₁	C₂×M₁₆	1	1	yes	characteristic
45	C₂×C₁₈₁	—	2	1	no	—
46	C₂×C₁₈₁	—	4	1	no	—
47	C₂×C₁₈₁	#432	1	1	yes	characteristic
48	C₁₈₁	#2165	1	1	yes	characteristic, complemented, Sylow
49	#2165	—	181	1	no	maximal, Sylow
50	C₄×M₁₆	—	181	1	no	—
51	#364	—	181	2	no	—
52	#349	—	181	2	no	—
53	#347	—	181	2	no	—
54	C₂×M₁₆	—	181	1	no	—
55	C₂×M₁₆	—	181	1	no	—
56	C₂×C₄²	#10624382	1	1	yes	characteristic
57	M₃₂	—	181	4	no	—
58	#97	—	181	1	no	—
59	#97	—	181	1	no	—
60	C₄×C₈	—	181	1	no	—
61	C₄×C₈	—	181	1	no	—
62	C₂²×C₄	—	2	1	no	—
63	C₂²×C₄	C₂×#10624382	1	1	yes	characteristic
64	M₁₆	—	362	2	no	—
65	M₁₆	—	362	2	no	—
66	C₂×C₈	—	181	1	no	—
67	C₂×C₈	—	181	1	no	—
68	C₂×C₈	—	181	1	no	—
69	C₂×C₈	—	181	1	no	—
70	C₄²	—	2	1	no	—
71	C₄²	C₂×#10624382	1	1	yes	characteristic
72	C₄²	C₂×#10624382	1	1	yes	characteristic
73	C₁₆	—	362	4	no	—
74	C₂³	#15668458	1	1	yes	characteristic
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	#15668458	1	1	yes	characteristic
81	C₂×C₄	C₂²×#10624382	1	1	yes	characteristic
82	C₈	—	362	1	no	—
83	C₈	—	362	1	no	—
84	C₈	—	181	2	no	—
85	C₈	—	181	2	no	—
86	C₂²	—	2	1	no	—
87	C₂²	—	4	1	no	—
88	C₂²	C₂×#15668458	1	1	yes	characteristic
89	C₄	—	2	2	no	—
90	C₄	—	2	1	no	—
91	C₄	—	4	1	no	—
92	C₄	#19153895	1	1	yes	characteristic
93	C₄	D₁₈₁⋊M₁₆	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#26042299	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19153895
commutator	C₂×C₄×C₁₈₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#10624382
Fitting	C₂×C₄²×C₁₈₁	C₄
socle	C₂×C₁₈₁	#432
prime radical	C₂³×C₁₈₁	M₁₆
cosocle	C₂×#13089678	C₂³
hypercenter	C₂×C₄²	#10624382
hypocenter	C₁₈₁	#2165
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #26042202	C₂	semidirect
3. #26042171	C₂	semidirect
48. C₁₈₁	#2165	semidirect

Maximal subgroups

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

subgroup	index
#26042202	2
#26042175	2
#26042171	2
C₄×#15668433	2
#2165	181