Subgroups — #13092231

Order 1472.

62 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	C₂₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#10625001	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₉₂	—	2	1	no	—
5	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	#67267	—	2	1	no	—
7	D₁₈₄	—	2	1	no	—
8	D₁₈₄	C₄	1	2	yes	—
9	C₁₆×C₂₃	—	2	1	no	—
10	C₂²×D₂₃	—	4	1	no	—
11	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
12	D₉₂	—	2	2	no	—
13	D₉₂	—	4	1	no	—
14	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₈×C₂₃	D₄	1	1	yes	characteristic
16	C₂₃⋊C₈	—	4	1	no	—
17	C₂²×C₂₃	SD₁₆	1	1	yes	characteristic
18	C₂×D₂₃	—	4	2	no	—
19	C₂×D₂₃	—	8	2	no	—
20	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₂₃	D₈	1	1	yes	characteristic
22	#361	—	23	1	no	maximal, Sylow
23	C₂×C₂₃	—	2	1	no	—
24	C₂×C₂₃	#102	1	1	yes	characteristic
25	D₂₃	—	8	2	no	—
26	C₂×D₈	—	23	1	no	—
27	M₃₂	D₂₃	1	1	yes	characteristic, complemented
28	#108	—	23	1	no	—
29	C₂₃	#361	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₄	—	46	1	no	—
31	D₈	—	23	2	no	—
32	D₈	—	46	1	no	—
33	M₁₆	—	46	1	no	—
34	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₂³	—	92	1	no	—
37	D₄	—	46	2	no	—
38	D₄	—	92	1	no	—
39	C₂×C₄	D₉₂	1	1	yes	characteristic
40	C₈	—	92	1	no	—
41	C₈	C₄×D₂₃	1	1	yes	characteristic
42	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
43	C₂²	—	92	2	no	—
44	C₂²	—	184	2	no	—
45	C₂²	#67263	1	1	yes	characteristic
46	C₄	D₁₈₄	1	1	yes	characteristic
47	C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	184	2	no	—
50	C₂	#10625003	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10625003
commutator	C₈×C₂₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₂₃
Fitting	C₂₃×M₃₂	C₂
socle	C₂×C₂₃	#102
prime radical	C₂×D₁₈₄	C₂
cosocle	C₂×C₈×C₂₃	C₂²
hypercenter	M₃₂	D₂₃
hypocenter	C₂₃	#361
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂₃×M₃₂	C₂	semidirect
3. #10625001	C₂	semidirect
27. M₃₂	D₂₃	semidirect
29. C₂₃	#361	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
C₂₃×M₃₂	2
#10625001	2
#361	23