Subgroups — #37548673

Order 23168.

100 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, complemented
2	#26042167	C₂	1	1	yes	maximal, characteristic, complemented
3	#26041357	C₂	1	1	yes	maximal, characteristic
4	C₂×#15668452	—	2	1	no	—
5	C₂×#15668452	—	2	1	no	—
6	C₂×#15668433	—	2	1	no	—
7	C₄⋊#13089678	C₄	1	1	yes	characteristic
8	C₂²⋊#13089678	—	2	1	no	—
9	C₄×#13089678	C₂²	1	1	yes	characteristic
10	C₄×D₄×C₁₈₁	C₄	1	1	yes	characteristic
11	#15668452	—	2	2	no	—
12	#15668452	—	4	1	no	—
13	#15668433	—	4	1	no	—
14	#15668433	—	4	1	no	—
15	C₂×#13089678	—	2	1	no	—
16	C₂×#13089678	D₄	1	1	yes	characteristic
17	C₂×#13089678	D₄	1	1	yes	characteristic
18	C₂×D₄×C₁₈₁	C₈	1	1	yes	characteristic
19	C₂²×C₄×C₁₈₁	—	2	1	no	—
20	C₄⋊C₄×C₁₈₁	C₈	1	1	yes	characteristic
21	C₂²⋊C₄×C₁₈₁	—	2	1	no	—
22	C₄²×C₁₈₁	C₂×C₄	1	1	yes	characteristic
23	#13089678	—	2	1	no	—
24	#13089678	—	4	1	no	—
25	#13089678	D₈	1	1	yes	characteristic
26	#13089678	SD₁₆	1	1	yes	characteristic
27	C₂³×C₁₈₁	—	2	1	no	—
28	D₄×C₁₈₁	—	4	1	no	—
29	C₂×C₄×C₁₈₁	—	2	1	no	—
30	C₂×C₄×C₁₈₁	—	4	1	no	—
31	C₂×C₄×C₁₈₁	—	4	1	no	—
32	C₂×C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
35	C₂²×C₁₈₁	—	4	1	no	—
36	C₂²×C₁₈₁	—	4	1	no	—
37	C₂²×C₁₈₁	—	4	1	no	—
38	C₂²×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₁₈₁	—	2	1	no	—
40	C₄×C₁₈₁	—	2	1	no	—
41	C₄×C₁₈₁	—	4	1	no	—
42	C₄×C₁₈₁	#102	1	1	yes	characteristic
43	C₄×C₁₈₁	#104	1	1	yes	characteristic
44	C₂×C₁₈₁	—	8	1	no	—
45	C₂×C₁₈₁	D₄⋊C₈	1	1	yes	characteristic
46	C₂×C₁₈₁	#349	1	1	yes	characteristic
47	C₂×C₁₈₁	#350	1	1	yes	characteristic
48	C₁₈₁	#1330	1	1	yes	characteristic, complemented, Sylow
49	#1330	—	181	1	no	maximal, Sylow
50	#436	—	181	1	no	—
51	C₄⋊C₁₆	—	181	1	no	—
52	#346	—	181	1	no	—
53	C₂×M₁₆	—	362	1	no	—
54	C₄×D₄	#10624382	1	1	yes	characteristic
55	C₂×C₁₆	—	362	1	no	—
56	C₂×C₁₆	—	362	1	no	—
57	C₄⋊C₈	—	181	1	no	—
58	C₂²⋊C₈	—	362	1	no	—
59	C₄×C₈	—	181	1	no	—
60	C₂×D₄	#13089685	1	1	yes	characteristic
61	C₂²×C₄	—	2	1	no	—
62	M₁₆	—	724	1	no	—
63	M₁₆	—	724	1	no	—
64	C₂×C₈	—	362	1	no	—
65	C₂×C₈	—	181	1	no	—
66	C₂×C₈	—	181	1	no	—
67	C₄⋊C₄	#13089685	1	1	yes	characteristic
68	C₂²⋊C₄	—	2	1	no	—
69	C₄²	C₂×#10624382	1	1	yes	characteristic
70	C₁₆	—	362	2	no	—
71	C₁₆	—	724	1	no	—
72	C₂³	—	2	1	no	—
73	D₄	—	4	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	C₂²⋊#10624382	1	1	yes	characteristic
78	C₂×C₄	C₂×#13089685	1	1	yes	characteristic
79	C₂×C₄	#15668458	1	1	yes	characteristic
80	C₈	—	362	1	no	—
81	C₈	—	181	1	no	—
82	C₈	—	181	1	no	—
83	C₈	—	724	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	C₂²⋊#13089685	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	#19153878	1	1	yes	characteristic
92	C₄	#19153880	1	1	yes	characteristic
93	C₂	—	8	1	no	—
94	C₂	D₄⋊#13089685	1	1	yes	characteristic
95	C₂	#26042175	1	1	yes	characteristic
96	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×D₄×C₁₈₁	C₄
socle	C₂²×C₁₈₁	C₂²⋊C₈
prime radical	C₂×D₄×C₁₈₁	C₈
cosocle	C₄×#13089678	C₂²
hypercenter	C₄×D₄	#10624382
hypocenter	C₁₈₁	#1330
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊#15668452	C₂	semidirect
2. #26042167	C₂	semidirect
48. C₁₈₁	#1330	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
#26041357	2
#1330	181