Subgroups — #13092857

Order 1472.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#10625011	C₂	1	2	yes	maximal, complemented
4	#10625009	C₂	1	2	yes	maximal, complemented
5	#10624994	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₂₃	—	2	1	no	—
7	C₂×Dic₄₆	—	2	1	no	—
8	Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
9	SD₁₆×C₂₃	—	2	1	no	—
10	D₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	Dic₉₂	—	2	1	no	—
13	Dic₉₂	C₂²	1	2	yes	—
14	C₂₃⋊C₁₆	C₂²	1	2	yes	—
15	Q₈×C₂₃	—	2	1	no	—
16	D₄×C₂₃	—	2	1	no	—
17	D₄×C₂₃	—	4	1	no	—
18	C₂×C₄×C₂₃	—	4	1	no	—
19	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
20	C₂×Dic₂₃	—	4	1	no	—
21	Dic₄₆	—	2	2	no	—
22	Dic₄₆	—	4	1	no	—
23	C₈×C₂₃	D₄	1	1	yes	characteristic
24	C₈×C₂₃	C₂³	1	1	yes	characteristic
25	C₂²×C₂₃	—	4	1	no	—
26	C₂²×C₂₃	D₈	1	1	yes	characteristic
27	C₄×C₂₃	—	4	1	no	—
28	C₄×C₂₃	D₈	1	1	yes	characteristic
29	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
30	Dic₂₃	—	4	2	no	—
31	#510	—	23	1	no	maximal, Sylow
32	C₂×C₂₃	—	2	1	no	—
33	C₂×C₂₃	—	8	1	no	—
34	C₂×C₂₃	C₂×D₈	1	1	yes	characteristic
35	#135	D₂₃	1	1	yes	characteristic
36	C₂×Q₁₆	—	23	1	no	—
37	Q₃₂	—	23	2	no	—
38	SD₃₂	—	23	2	no	—
39	M₃₂	—	23	1	no	—
40	C₂₃	#510	1	1	yes	characteristic, complemented, Sylow
41	#41	—	2	1	no	—
42	C₂×Q₈	—	46	1	no	—
43	Q₁₆	—	23	2	no	—
44	Q₁₆	—	46	1	no	—
45	Q₁₆	C₂×D₂₃	1	1	yes	characteristic
46	SD₁₆	—	2	1	no	—
47	D₈	C₂×D₂₃	1	1	yes	characteristic
48	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
49	C₁₆	—	23	2	no	—
50	Q₈	—	2	1	no	—
51	Q₈	—	46	2	no	—
52	Q₈	—	92	1	no	—
53	D₄	—	2	1	no	—
54	D₄	—	4	1	no	—
55	C₂×C₄	—	4	1	no	—
56	C₂×C₄	—	92	1	no	—
57	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
58	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
59	C₈	C₂²×D₂₃	1	1	yes	characteristic
60	C₂²	—	4	1	no	—
61	C₂²	#67272	1	1	yes	characteristic
62	C₄	—	4	1	no	—
63	C₄	—	92	2	no	—
64	C₄	#67272	1	1	yes	characteristic
65	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
66	C₂	—	2	1	no	—
67	C₂	—	8	1	no	—
68	C₂	C₂×#67272	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#67272
commutator, cosocle	C₈×C₂₃	C₂³
Frattini	C₈	C₂²×D₂₃
Fitting, prime radical	C₂₃×#135	C₂
socle	C₂×C₂₃	C₂×D₈
hypercenter	#135	D₂₃
hypocenter	C₂₃	#510
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₉₂	C₂	semidirect
3. #10625011	C₂	semidirect
4. #10625009	C₂	semidirect
5. #10624994	C₂	semidirect
40. C₂₃	#510	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#135	2
C₂×Dic₉₂	2
#10625011	2
#10625009	2
#10624994	2
#510	23