Subgroups — #13092687

Order 1472.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	#10625120	C₂	1	2	yes	maximal, complemented
3	C₂×D₁₈₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625005	C₂	1	2	yes	maximal, complemented
5	#10625001	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×D₉₂	C₂²	1	2	yes	—
8	M₁₆×C₂₃	—	2	1	no	—
9	M₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₃	—	2	1	no	—
11	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	#67274	—	2	2	no	—
13	#67272	—	2	2	no	—
14	#67267	C₂²	1	2	yes	—
15	D₁₈₄	—	2	1	no	—
16	D₁₈₄	—	2	1	no	—
17	C₂²×D₂₃	—	2	2	no	—
18	Q₈×C₂₃	D₄	1	1	yes	characteristic
19	D₄×C₂₃	—	2	1	no	—
20	D₄×C₂₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₃	—	2	1	no	—
22	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
23	D₉₂	—	2	2	no	—
24	D₉₂	—	2	2	no	—
25	C₈×C₂₃	—	2	1	no	—
26	C₈×C₂₃	D₄	1	1	yes	characteristic
27	C₈×C₂₃	D₄	1	1	yes	characteristic
28	C₂₃⋊C₈	—	2	2	no	—
29	C₂²×C₂₃	—	2	1	no	—
30	C₂²×C₂₃	#41	1	1	yes	characteristic
31	C₂×D₂₃	—	4	2	no	—
32	C₂×D₂₃	—	8	2	no	—
33	C₄×C₂₃	—	2	1	no	—
34	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
35	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
36	#472	—	23	1	no	maximal, Sylow
37	C₂×C₂₃	—	2	1	no	—
38	C₂×C₂₃	—	4	1	no	—
39	C₂×C₂₃	#121	1	1	yes	characteristic
40	D₂₃	—	8	2	no	—
41	AGL(1,ℤ/8)	—	23	2	no	—
42	C₂×D₈	—	23	1	no	—
43	#131	D₂₃	1	1	yes	characteristic, complemented
44	#108	—	23	1	no	—
45	#100	—	23	2	no	—
46	C₂₃	#472	1	1	yes	characteristic, complemented, Sylow
47	#41	C₂×D₂₃	1	1	yes	characteristic
48	C₂×D₄	—	23	2	no	—
49	SD₁₆	—	46	2	no	—
50	D₈	—	46	2	no	—
51	D₈	—	46	1	no	—
52	D₈	—	46	1	no	—
53	M₁₆	—	2	1	no	—
54	M₁₆	—	23	2	no	—
55	M₁₆	C₂×D₂₃	1	1	yes	characteristic
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
58	C₂³	—	46	2	no	—
59	Q₈	D₉₂	1	1	yes	characteristic
60	D₄	—	2	1	no	—
61	D₄	—	46	2	no	—
62	D₄	—	46	2	no	—
63	D₄	D₉₂	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
66	C₈	—	2	1	no	—
67	C₈	—	46	2	no	—
68	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
69	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
70	C₂²	—	2	1	no	—
71	C₂²	—	92	2	no	—
72	C₂²	—	184	2	no	—
73	C₂²	#67288	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	C₂×D₉₂	1	1	yes	characteristic
76	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	4	1	no	—
79	C₂	—	184	2	no	—
80	C₂	#10625101	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10625101
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#131	C₂
socle	C₂×C₂₃	#121
hypercenter	#131	D₂₃
hypocenter	C₂₃	#472
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
1. C₂₃×#131	C₂	semidirect
2. #10625120	C₂	semidirect
3. C₂×D₁₈₄	C₂	semidirect
4. #10625005	C₂	semidirect
5. #10625001	C₂	semidirect
43. #131	D₂₃	semidirect
46. C₂₃	#472	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#131	2
#10625120	2
C₂×D₁₈₄	2
#10625005	2
#10625001	2
#472	23