Subgroups — #15671447

Order 2944.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092797	C₂	1	1	yes	maximal, characteristic
2	#13092170	C₂	1	1	yes	maximal, characteristic
3	C₂₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₉₂	—	2	1	no	—
5	C₂×Dic₉₂	C₄	1	2	yes	—
6	#10625040	—	2	1	no	—
7	C₂×C₁₆×C₂₃	—	2	1	no	—
8	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₄⋊(C₂₃⋊C₈)	—	2	1	no	—
10	C₂×Dic₄₆	—	2	2	no	—
11	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
13	C₄²×C₂₃	D₄	1	1	yes	characteristic
14	C₄⋊Dic₂₃	—	4	1	no	—
15	C₄⋊Dic₂₃	—	4	1	no	—
16	C₂×C₂₃⋊C₈	—	4	1	no	—
17	Dic₉₂	—	4	2	no	—
18	Dic₉₂	—	4	1	no	—
19	Dic₉₂	—	4	1	no	—
20	C₁₆×C₂₃	—	4	1	no	—
21	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
23	C₂×C₄×C₂₃	SD₁₆	1	1	yes	characteristic
24	C₂×Dic₂₃	—	4	2	no	—
25	Dic₄₆	—	4	2	no	—
26	Dic₄₆	—	4	2	no	—
27	C₈×C₂₃	—	2	1	no	—
28	C₈×C₂₃	D₈	1	1	yes	characteristic
29	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
30	C₂₃⋊C₈	—	8	1	no	—
31	#1362	—	23	1	no	maximal, Sylow
32	C₂²×C₂₃	#102	1	1	yes	characteristic
33	C₄×C₂₃	—	2	1	no	—
34	C₄×C₂₃	#100	1	1	yes	characteristic
35	C₄×C₂₃	#102	1	1	yes	characteristic
36	C₄×C₂₃	SD₃₂	1	1	yes	characteristic
37	C₄×C₂₃	Q₃₂	1	1	yes	characteristic
38	Dic₂₃	—	8	2	no	—
39	#494	—	23	1	no	—
40	C₄⋊C₁₆	D₂₃	1	1	yes	characteristic
41	#335	—	23	1	no	—
42	C₂×C₂₃	#331	1	1	yes	characteristic
43	C₂×C₂₃	#358	1	1	yes	characteristic
44	C₂×C₂₃	#362	1	1	yes	characteristic
45	C₂×Q₁₆	—	23	2	no	—
46	C₂×Q₁₆	—	46	1	no	—
47	C₄⋊Q₈	—	46	1	no	—
48	C₂×C₁₆	—	2	1	no	—
49	C₄⋊C₈	—	46	1	no	—
50	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
51	C₂₃	#1362	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₈	—	46	2	no	—
53	Q₁₆	—	92	2	no	—
54	Q₁₆	—	92	1	no	—
55	Q₁₆	—	92	1	no	—
56	C₂×C₈	—	92	1	no	—
57	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
59	C₄⋊C₄	—	92	1	no	—
60	C₄⋊C₄	—	92	1	no	—
61	C₄²	D₉₂	1	1	yes	characteristic
62	C₁₆	—	4	1	no	—
63	Q₈	—	92	2	no	—
64	Q₈	—	92	2	no	—
65	C₂×C₄	—	92	2	no	—
66	C₂×C₄	#67263	1	1	yes	characteristic
67	C₂×C₄	D₁₈₄	1	1	yes	characteristic
68	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	184	1	no	—
71	C₈	#67272	1	1	yes	characteristic
72	C₈	#67274	1	1	yes	characteristic
73	C₂²	#10625003	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	184	2	no	—
76	C₄	#10624982	1	1	yes	characteristic
77	C₄	Dic₁₈₄	1	1	yes	characteristic
78	C₄	#10624991	1	1	yes	characteristic
79	C₄	#10625005	1	1	yes	characteristic
80	C₂	#13092160	1	1	yes	characteristic
81	C₂	#13092222	1	1	yes	characteristic
82	C₂	#13092234	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10625003
commutator	C₂×C₈×C₂₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₃
Fitting	C₂₃×C₄⋊C₁₆	C₂
socle, prime radical	C₂²×C₂₃	#102
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	C₄⋊C₁₆	D₂₃
hypocenter	C₂₃	#1362
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
51. C₂₃	#1362	semidirect

Maximal subgroups

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

subgroup	index
#13092797	2
#13092170	2
C₂₃×C₄⋊C₁₆	2
#1362	23