Subgroups — #15671565

Order 2944.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092796	C₂	1	1	yes	maximal, characteristic
2	#13092216	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#356	C₂	1	1	yes	maximal, characteristic
4	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
5	C₂×#67275	—	2	1	no	—
6	C₂×#67275	—	2	1	no	—
7	#10625040	C₄	1	1	yes	characteristic
8	C₂₃×#101	—	2	1	no	—
9	#10625018	—	2	1	no	—
10	C₄×C₂₃⋊C₈	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₂₃	D₄	1	1	yes	characteristic
12	C₂×Q₈×C₂₃	D₄	1	1	yes	characteristic
13	C₂×Dic₄₆	—	2	1	no	—
14	M₁₆×C₂₃	—	4	1	no	—
15	C₄⋊C₄×C₂₃	—	4	1	no	—
16	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
17	#67275	—	4	2	no	—
18	#67275	—	4	2	no	—
19	C₄⋊Dic₂₃	—	4	1	no	—
20	#67267	—	4	1	no	—
21	C₂×C₂₃⋊C₈	—	2	1	no	—
22	Q₈×C₂₃	—	4	1	no	—
23	Q₈×C₂₃	—	4	1	no	—
24	C₂×C₄×C₂₃	—	2	1	no	—
25	C₂×C₄×C₂₃	—	2	1	no	—
26	C₂×C₄×C₂₃	—	2	1	no	—
27	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₂₃	—	4	1	no	—
29	Dic₄₆	—	4	1	no	—
30	Dic₄₆	—	4	1	no	—
31	C₈×C₂₃	—	8	1	no	—
32	C₂₃⋊C₈	—	2	2	no	—
33	C₂₃⋊C₈	—	8	1	no	—
34	#1411	—	23	1	no	maximal, Sylow
35	C₂²×C₂₃	#99	1	1	yes	characteristic
36	C₄×C₂₃	—	2	2	no	—
37	C₄×C₂₃	—	2	1	no	—
38	C₄×C₂₃	—	4	1	no	—
39	C₄×C₂₃	—	4	1	no	—
40	Dic₂₃	—	8	1	no	—
41	#494	—	23	1	no	—
42	#356	—	23	1	no	—
43	#356	D₂₃	1	1	yes	characteristic
44	C₂×C₂₃	—	2	1	no	—
45	C₂×C₂₃	#353	1	1	yes	characteristic
46	C₂×Q₁₆	—	46	1	no	—
47	C₂×Q₁₆	—	46	1	no	—
48	C₄⋊Q₈	—	23	1	no	—
49	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
50	#101	—	2	1	no	—
51	#101	—	46	1	no	—
52	C₄×C₈	—	23	1	no	—
53	C₂₃	#1411	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	46	1	no	—
55	C₂×Q₈	D₉₂	1	1	yes	characteristic
56	C₂×Q₈	C₂²⋊D₂₃	1	1	yes	characteristic
57	Q₁₆	—	92	2	no	—
58	Q₁₆	—	92	2	no	—
59	M₁₆	—	4	1	no	—
60	M₁₆	—	92	1	no	—
61	C₂×C₈	—	46	1	no	—
62	C₄⋊C₄	—	4	1	no	—
63	C₄⋊C₄	—	92	1	no	—
64	C₄²	C₄×D₂₃	1	1	yes	characteristic
65	Q₈	—	4	1	no	—
66	Q₈	—	4	1	no	—
67	Q₈	—	92	1	no	—
68	Q₈	—	92	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	92	1	no	—
73	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
74	C₈	—	8	1	no	—
75	C₈	—	46	2	no	—
76	C₈	—	184	1	no	—
77	C₂²	#10624988	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	1	no	—
80	C₄	—	4	1	no	—
81	C₄	—	4	1	no	—
82	C₄	—	184	1	no	—
83	C₂	—	2	1	no	—
84	C₂	#13092209	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092209
commutator	C₄²×C₂₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₂₃
Fitting	C₂₃×#356	C₂
socle	C₂×C₂₃	#353
prime radical	C₂²×C₂₃	#99
cosocle	C₂₃×C₄⋊Q₈	C₂²
hypercenter	#356	D₂₃
hypocenter	C₂₃	#1411
LCS	G ▷ C₄²×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
53. C₂₃	#1411	semidirect

Maximal subgroups

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

subgroup	index
#13092796	2
#13092216	2
C₂₃×#356	2
#1411	23