Subgroups — #15675652

Order 2944.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625009	C₂	1	4	yes	maximal, complemented
2	#13092797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#493	C₂	1	1	yes	maximal, characteristic
5	C₂×D₈×C₂₃	—	2	1	no	—
6	C₂×D₈×C₂₃	C₂²	1	2	yes	—
7	C₂₃×#127	—	2	1	no	—
8	C₂×Dic₉₂	—	2	1	no	—
9	C₂×Dic₉₂	C₂²	1	2	yes	—
10	#10625040	—	2	1	no	—
11	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	#10625009	—	2	8	no	—
13	C₂×C₂₃⋊C₁₆	C₂²	1	2	yes	—
14	C₂×D₄×C₂₃	—	2	2	no	—
15	C₂×D₄×C₂₃	—	4	2	no	—
16	C₂×Dic₄₆	—	2	2	no	—
17	D₈×C₂₃	—	2	4	no	—
18	D₈×C₂₃	—	4	2	no	—
19	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
21	C₄²×C₂₃	D₄	1	1	yes	characteristic
22	C₄⋊Dic₂₃	—	4	2	no	—
23	Dic₉₂	—	2	4	no	—
24	Dic₉₂	—	4	2	no	—
25	C₂₃⋊C₁₆	D₄	1	4	yes	complemented
26	C₂³×C₂₃	—	4	2	no	—
27	D₄×C₂₃	—	4	2	no	—
28	D₄×C₂₃	—	4	2	no	—
29	D₄×C₂₃	—	8	4	no	—
30	C₂×C₄×C₂₃	D₈	1	2	yes	—
31	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₂₃	—	4	2	no	—
33	Dic₄₆	—	4	2	no	—
34	Dic₄₆	—	4	2	no	—
35	C₈×C₂₃	D₈	1	2	yes	—
36	C₈×C₂₃	C₂×D₄	1	2	yes	—
37	#2248	—	23	1	no	maximal, Sylow
38	C₂²×C₂₃	—	8	2	no	—
39	C₂²×C₂₃	—	8	4	no	—
40	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
41	C₄×C₂₃	SD₃₂	1	4	yes	complemented
42	C₄×C₂₃	#127	1	1	yes	characteristic
43	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
44	Dic₂₃	—	8	2	no	—
45	C₂×SD₃₂	—	23	4	no	—
46	#494	—	23	1	no	—
47	#493	D₂₃	1	1	yes	characteristic
48	C₄×C₁₆	—	23	1	no	—
49	C₂×C₂₃	—	16	2	no	—
50	C₂×C₂₃	#493	1	1	yes	characteristic
51	C₂×C₂₃	C₂×SD₃₂	1	2	yes	—
52	C₂×Q₁₆	—	23	2	no	—
53	C₂×Q₁₆	—	46	1	no	—
54	C₂×D₈	—	2	1	no	—
55	C₂×D₈	C₂×D₂₃	1	2	yes	—
56	C₄⋊Q₈	—	46	1	no	—
57	#127	—	2	1	no	—
58	SD₃₂	—	46	8	no	—
59	C₂×C₁₆	—	23	2	no	—
60	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
61	C₂₃	#2248	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	46	2	no	—
63	C₂×D₄	—	2	2	no	—
64	C₂×D₄	—	4	2	no	—
65	Q₁₆	—	46	4	no	—
66	Q₁₆	—	92	2	no	—
67	D₈	—	2	4	no	—
68	D₈	—	4	2	no	—
69	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
70	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
71	C₄⋊C₄	—	92	2	no	—
72	C₄²	C₂²⋊D₂₃	1	1	yes	characteristic
73	C₁₆	—	23	4	no	—
74	C₂³	—	4	2	no	—
75	Q₈	—	92	2	no	—
76	Q₈	—	92	2	no	—
77	D₄	—	4	2	no	—
78	D₄	—	4	2	no	—
79	D₄	—	8	4	no	—
80	C₂×C₄	—	92	2	no	—
81	C₂×C₄	#67272	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
83	C₈	#67272	1	2	yes	—
84	C₈	D₄×D₂₃	1	2	yes	—
85	C₂²	—	8	2	no	—
86	C₂²	—	8	4	no	—
87	C₂²	C₂×#67272	1	1	yes	characteristic
88	C₄	—	184	2	no	—
89	C₄	#10625009	1	4	yes	complemented
90	C₄	C₂×#67272	1	1	yes	characteristic
91	C₄	#10625111	1	1	yes	characteristic
92	C₂	—	16	2	no	—
93	C₂	#13092793	1	1	yes	characteristic
94	C₂	C₂×#10625009	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#67272
commutator, cosocle	C₂×C₈×C₂₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₃
Fitting, prime radical	C₂₃×#493	C₂
socle	C₂²×C₂₃	C₂×D₈
hypercenter	#493	D₂₃
hypocenter	C₂₃	#2248
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
1. C₂×#10625009	C₂	semidirect
2. #13092797	C₂	semidirect
3. C₄×C₂₃⋊C₁₆	C₂	semidirect
25. C₂₃⋊C₁₆	D₄	semidirect
41. C₄×C₂₃	SD₃₂	semidirect
61. C₂₃	#2248	semidirect
89. C₄	#10625009	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625009	2
#13092797	2
C₄×C₂₃⋊C₁₆	2
C₂₃×#493	2
#2248	23