Subgroups — #13092228

Order 1472.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625075	C₂	1	1	yes	maximal, characteristic
2	C₂₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#10624999	C₂	1	1	yes	maximal, characteristic, complemented
4	#67288	—	2	1	no	—
5	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₂₃	—	2	1	no	—
7	Dic₉₂	C₄	1	1	yes	characteristic, complemented
8	D₁₈₄	C₄	1	1	yes	characteristic, complemented
9	#67263	—	2	1	no	—
10	C₁₆×C₂₃	—	2	1	no	—
11	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
12	C₂²⋊D₂₃	—	4	1	no	—
13	C₂×Dic₂₃	—	4	1	no	—
14	D₉₂	—	2	1	no	—
15	C₄×D₂₃	—	4	1	no	—
16	Dic₄₆	—	2	1	no	—
17	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₈×C₂₃	D₄	1	1	yes	characteristic
19	C₂²×C₂₃	D₈	1	1	yes	characteristic
20	C₂×D₂₃	—	4	1	no	—
21	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₂₃	SD₁₆	1	1	yes	characteristic
23	Dic₂₃	—	4	1	no	—
24	Dic₂₃	—	8	1	no	—
25	#360	—	23	1	no	maximal, Sylow
26	C₂×C₂₃	—	2	1	no	—
27	C₂×C₂₃	#102	1	1	yes	characteristic
28	D₂₃	—	8	1	no	—
29	#135	—	23	1	no	—
30	M₃₂	D₂₃	1	1	yes	characteristic, complemented
31	#106	—	23	1	no	—
32	C₂₃	#360	1	1	yes	characteristic, complemented, Sylow
33	#41	—	46	1	no	—
34	Q₁₆	—	23	1	no	—
35	SD₁₆	—	46	1	no	—
36	D₈	—	23	1	no	—
37	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
38	C₄⋊C₄	—	46	1	no	—
39	C₁₆	—	2	1	no	—
40	Q₈	—	46	1	no	—
41	D₄	—	46	1	no	—
42	D₄	—	92	1	no	—
43	C₂×C₄	—	92	1	no	—
44	C₂×C₄	—	92	1	no	—
45	C₂×C₄	D₉₂	1	1	yes	characteristic
46	C₈	C₄×D₂₃	1	1	yes	characteristic
47	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
48	C₂²	—	92	1	no	—
49	C₂²	D₁₈₄	1	1	yes	characteristic
50	C₄	—	92	1	no	—
51	C₄	—	184	1	no	—
52	C₄	#67263	1	1	yes	characteristic
53	C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	184	1	no	—
56	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	#10625075	C₂
cosocle	C₂×C₈×C₂₃	C₂²
hypercenter	M₃₂	D₂₃
hypocenter	C₂₃	#360
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. #10624999	C₂	semidirect
7. Dic₉₂	C₄	semidirect
8. D₁₈₄	C₄	semidirect
30. M₃₂	D₂₃	semidirect
32. C₂₃	#360	semidirect

Maximal subgroups

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

subgroup	index
#10625075	2
C₂₃×M₃₂	2
#10624999	2
#360	23