Subgroups — #13092219

Order 1472.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₈₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#10625000	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₉₂	—	2	1	no	—
5	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₂₃	—	2	1	no	—
7	D₁₈₄	—	2	1	no	—
8	D₁₈₄	C₄	1	2	yes	complemented
9	C₁₆×C₂₃	—	2	1	no	—
10	C₂²×D₂₃	—	4	1	no	—
11	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
12	C₂×Dic₂₃	—	4	1	no	—
13	D₉₂	—	2	2	no	—
14	D₉₂	—	4	1	no	—
15	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₂²×C₂₃	D₈	1	1	yes	characteristic
18	C₂×D₂₃	—	4	2	no	—
19	C₂×D₂₃	—	8	1	no	—
20	C₂×D₂₃	—	8	1	no	—
21	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₂₃	SD₁₆	1	1	yes	characteristic
23	Dic₂₃	—	8	1	no	—
24	#357	—	23	1	no	maximal, Sylow
25	C₂×C₂₃	#102	1	1	yes	characteristic
26	C₂×C₂₃	D₁₆	1	1	yes	characteristic
27	C₂×C₂₃	SD₃₂	1	1	yes	characteristic
28	D₂₃	—	8	2	no	—
29	C₂×D₈	—	23	1	no	—
30	C₂×C₁₆	D₂₃	1	1	yes	characteristic, complemented
31	#107	—	23	1	no	—
32	C₂₃	#357	1	1	yes	characteristic, complemented, Sylow
33	C₂×D₄	—	46	1	no	—
34	D₈	—	23	2	no	—
35	D₈	—	46	1	no	—
36	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
37	C₄⋊C₄	—	46	1	no	—
38	C₁₆	—	2	1	no	—
39	C₂³	—	92	1	no	—
40	D₄	—	46	2	no	—
41	D₄	—	92	1	no	—
42	C₂×C₄	—	92	1	no	—
43	C₂×C₄	D₉₂	1	1	yes	characteristic
44	C₈	C₄×D₂₃	1	1	yes	characteristic
45	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
46	C₂²	—	92	2	no	—
47	C₂²	—	184	1	no	—
48	C₂²	—	184	1	no	—
49	C₂²	D₁₈₄	1	1	yes	characteristic
50	C₄	—	184	1	no	—
51	C₄	#67263	1	1	yes	characteristic
52	C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
53	C₂	—	184	2	no	—
54	C₂	D₃₆₈	1	1	yes	characteristic
55	C₂	#10624982	1	1	yes	characteristic
56	C₂	#10625003	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₈₄
commutator	C₈×C₂₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₂₃
Fitting	C₂×C₁₆×C₂₃	C₂
socle	C₂²×C₂₃	D₈
prime radical	C₂×D₁₈₄	C₂
cosocle	C₂×C₈×C₂₃	C₂²
hypercenter	C₂×C₁₆	D₂₃
hypocenter	C₂₃	#357
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₆×C₂₃	C₂	semidirect
3. #10625000	C₂	semidirect
8. D₁₈₄	C₄	semidirect
30. C₂×C₁₆	D₂₃	semidirect
32. C₂₃	#357	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₈₄	2
C₂×C₁₆×C₂₃	2
#10625000	2
#357	23