Subgroups — #15675649

Order 2944.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625011	C₂	1	4	yes	maximal
2	#13092797	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#494	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₂₃	—	2	1	no	—
6	C₂×Q₁₆×C₂₃	C₂²	1	2	yes	—
7	C₂₃×C₄⋊Q₈	—	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	#10625011	—	2	8	no	—
13	C₂×C₂₃⋊C₁₆	C₂²	1	2	yes	—
14	C₂×Q₈×C₂₃	—	2	2	no	—
15	C₂×Dic₄₆	—	2	2	no	—
16	Q₁₆×C₂₃	—	2	4	no	—
17	Q₁₆×C₂₃	—	4	2	no	—
18	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₂₃	—	4	2	no	—
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	—
26	Q₈×C₂₃	—	4	2	no	—
27	Q₈×C₂₃	—	4	2	no	—
28	C₂×C₄×C₂₃	—	4	2	no	—
29	C₂×C₄×C₂₃	D₈	1	2	yes	—
30	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₂₃	—	4	2	no	—
32	Dic₄₆	—	4	2	no	—
33	Dic₄₆	—	4	2	no	—
34	C₈×C₂₃	D₈	1	2	yes	—
35	C₈×C₂₃	C₂×D₄	1	2	yes	—
36	#2247	—	23	1	no	maximal, Sylow
37	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
38	C₄×C₂₃	—	8	2	no	—
39	C₄×C₂₃	Q₃₂	1	4	yes	complemented
40	C₄×C₂₃	#127	1	1	yes	characteristic
41	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
42	Dic₂₃	—	8	2	no	—
43	C₂×Q₃₂	—	23	4	no	—
44	#494	—	23	1	no	—
45	#494	D₂₃	1	1	yes	characteristic
46	C₄×C₁₆	—	23	1	no	—
47	C₂×C₂₃	#493	1	1	yes	characteristic
48	C₂×C₂₃	C₂×Q₃₂	1	2	yes	—
49	C₂×Q₁₆	—	2	1	no	—
50	C₂×Q₁₆	—	23	2	no	—
51	C₂×Q₁₆	—	46	1	no	—
52	C₂×Q₁₆	C₂×D₂₃	1	2	yes	—
53	C₄⋊Q₈	—	2	1	no	—
54	C₄⋊Q₈	—	46	1	no	—
55	Q₃₂	—	46	8	no	—
56	C₂×C₁₆	—	23	2	no	—
57	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
58	C₂₃	#2247	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	2	2	no	—
60	C₂×Q₈	—	46	2	no	—
61	Q₁₆	—	2	4	no	—
62	Q₁₆	—	4	2	no	—
63	Q₁₆	—	46	4	no	—
64	Q₁₆	—	92	2	no	—
65	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
67	C₄⋊C₄	—	4	2	no	—
68	C₄⋊C₄	—	92	2	no	—
69	C₄²	C₂²⋊D₂₃	1	1	yes	characteristic
70	C₁₆	—	23	4	no	—
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	Q₈	—	92	2	no	—
74	Q₈	—	92	2	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	92	2	no	—
77	C₂×C₄	#67272	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
79	C₈	#67272	1	2	yes	—
80	C₈	D₄×D₂₃	1	2	yes	—
81	C₂²	C₂×#67272	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	184	2	no	—
84	C₄	#10625011	1	4	yes	complemented
85	C₄	C₂×#67272	1	1	yes	characteristic
86	C₄	#10625111	1	1	yes	characteristic
87	C₂	#13092793	1	1	yes	characteristic
88	C₂	C₂×#10625011	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#67272
commutator, cosocle	C₂×C₈×C₂₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂₃×#494	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₈
hypercenter	#494	D₂₃
hypocenter	C₂₃	#2247
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
39. C₄×C₂₃	Q₃₂	semidirect
58. C₂₃	#2247	semidirect
84. C₄	#10625011	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625011	2
#13092797	2
C₄×C₂₃⋊C₁₆	2
C₂₃×#494	2
#2247	23