Subgroups — #13092801

Order 1472.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₈₄	C₂	1	1	yes	maximal, characteristic
3	C₂×#67263	C₂	1	2	yes	maximal, complemented
4	#10625046	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₉₂	C₂²	1	2	yes	—
7	C₂×Dic₄₆	C₂²	1	2	yes	—
8	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₄²×C₂₃	C₂²	1	1	yes	characteristic
11	(C₂×D₂₃)⋊C₄	—	2	4	no	—
12	Dic₉₂	—	2	2	no	—
13	D₁₈₄	—	2	2	no	—
14	#67263	—	2	4	no	—
15	C₂²×D₂₃	—	2	2	no	—
16	C₂×C₄×C₂₃	D₄	1	2	yes	—
17	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₂₃	—	2	2	no	—
19	D₉₂	—	2	2	no	—
20	D₉₂	—	2	2	no	—
21	Dic₄₆	—	2	2	no	—
22	Dic₄₆	—	2	2	no	—
23	C₈×C₂₃	D₄	1	2	yes	—
24	C₈×C₂₃	D₄	1	2	yes	—
25	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
26	C₂×D₂₃	—	4	2	no	—
27	C₂×D₂₃	—	4	4	no	—
28	C₄×C₂₃	—	2	2	no	—
29	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
30	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
31	Dic₂₃	—	4	2	no	—
32	#495	—	23	1	no	maximal, Sylow
33	C₂×C₂₃	#127	1	1	yes	characteristic
34	C₂×C₂₃	#135	1	2	yes	—
35	D₂₃	—	8	2	no	—
36	C₂×Q₁₆	—	23	1	no	—
37	C₂×SD₁₆	—	23	2	no	—
38	C₂×D₈	—	23	1	no	—
39	#124	—	23	2	no	—
40	C₄×C₈	D₂₃	1	1	yes	characteristic, complemented
41	C₂₃	#495	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₈	—	23	2	no	—
43	C₂×D₄	—	23	2	no	—
44	Q₁₆	—	46	2	no	—
45	SD₁₆	—	46	4	no	—
46	D₈	—	46	2	no	—
47	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
48	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
49	C₂²⋊C₄	—	46	4	no	—
50	C₄²	C₂×D₂₃	1	1	yes	characteristic
51	C₂³	—	46	2	no	—
52	Q₈	—	46	2	no	—
53	Q₈	—	46	2	no	—
54	D₄	—	46	2	no	—
55	D₄	—	46	2	no	—
56	C₂×C₄	—	46	2	no	—
57	C₂×C₄	D₉₂	1	2	yes	—
58	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
59	C₈	D₉₂	1	2	yes	—
60	C₈	D₉₂	1	2	yes	—
61	C₂²	—	92	2	no	—
62	C₂²	—	92	4	no	—
63	C₂²	C₂×D₉₂	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	92	2	no	—
66	C₄	C₂×D₉₂	1	1	yes	characteristic
67	C₄	C₂×D₉₂	1	1	yes	characteristic
68	C₂	—	184	2	no	—
69	C₂	#10625045	1	1	yes	characteristic
70	C₂	#10625075	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₉₂
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₄×C₈×C₂₃	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂×D₁₈₄	C₂
hypercenter	C₄×C₈	D₂₃
hypocenter	C₂₃	#495
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₉₂	C₂	semidirect
3. C₂×#67263	C₂	semidirect
4. #10625046	C₂	semidirect
5. C₄×C₈×C₂₃	C₂	semidirect
40. C₄×C₈	D₂₃	semidirect
41. C₂₃	#495	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₉₂	2
C₂×D₁₈₄	2
C₂×#67263	2
#10625046	2
C₄×C₈×C₂₃	2
#495	23