Subgroups — #15671391

Order 2944.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092199	C₂	1	1	yes	maximal, characteristic
2	C₂₃⋊#338	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#470	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₂₃	C₄	1	1	yes	characteristic
5	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
6	C₂₃×C₂²⋊Q₈	—	2	1	no	—
7	C₂×#67267	—	2	1	no	—
8	C₂₃×#106	C₄	1	1	yes	characteristic
9	C₂₃×#103	—	2	1	no	—
10	#10624994	—	2	1	no	—
11	C₂×Q₈×C₂₃	—	2	1	no	—
12	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
13	Q₁₆×C₂₃	—	4	1	no	—
14	M₁₆×C₂₃	—	4	1	no	—
15	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₂₃	—	2	1	no	—
18	C₄⋊C₄×C₂₃	—	4	1	no	—
19	C₂²⋊C₄×C₂₃	—	4	1	no	—
20	#67267	—	4	1	no	—
21	#67267	—	4	1	no	—
22	C₂×C₂₃⋊C₈	—	2	2	no	—
23	C₂₃⋊C₁₆	—	4	1	no	—
24	C₂³×C₂₃	SD₁₆	1	1	yes	characteristic
25	Q₈×C₂₃	—	4	1	no	—
26	Q₈×C₂₃	—	4	1	no	—
27	C₂×C₄×C₂₃	—	2	1	no	—
28	C₂×C₄×C₂₃	—	2	1	no	—
29	C₂×C₄×C₂₃	—	4	1	no	—
30	C₂×C₄×C₂₃	—	4	1	no	—
31	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
33	C₈×C₂₃	—	2	1	no	—
34	C₈×C₂₃	—	2	1	no	—
35	C₂₃⋊C₈	—	4	2	no	—
36	#1342	—	23	1	no	maximal, Sylow
37	C₂²×C₂₃	—	2	1	no	—
38	C₂²×C₂₃	—	4	1	no	—
39	C₂²×C₂₃	#102	1	1	yes	characteristic
40	C₄×C₂₃	—	2	1	no	—
41	C₄×C₂₃	—	8	1	no	—
42	C₄×C₂₃	—	8	1	no	—
43	C₄×C₂₃	#99	1	1	yes	characteristic
44	C₄×C₂₃	#104	1	1	yes	characteristic
45	#470	D₂₃	1	1	yes	characteristic
46	#349	—	23	1	no	—
47	#338	—	23	1	no	—
48	C₂×C₂₃	—	2	1	no	—
49	C₂×C₂₃	—	4	1	no	—
50	C₂×C₂₃	#327	1	1	yes	characteristic
51	C₂×Q₁₆	Dic₂₃	1	1	yes	characteristic
52	C₂×M₁₆	—	46	1	no	—
53	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic
54	C₂²⋊Q₈	—	2	1	no	—
55	M₃₂	—	46	1	no	—
56	#106	Dic₂₃	1	1	yes	characteristic
57	#103	—	2	1	no	—
58	C₂₃	#1342	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	2	1	no	—
60	C₂²×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
61	Q₁₆	—	4	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	92	1	no	—
64	M₁₆	—	92	1	no	—
65	C₂×C₈	—	46	2	no	—
66	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₄⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	4	1	no	—
71	C₁₆	—	92	1	no	—
72	C₂³	#67273	1	1	yes	characteristic
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	#67272	1	1	yes	characteristic
80	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	92	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#10625014	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	8	1	no	—
89	C₄	—	8	1	no	—
90	C₄	#10625016	1	1	yes	characteristic
91	C₄	#10625019	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#13092151	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092151
commutator	C₂×C₈×C₂₃	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₂₃
Fitting	C₂₃×#470	C₂
socle	C₂×C₂₃	#327
prime radical	C₂³×C₂₃	SD₁₆
cosocle	C₂×M₁₆×C₂₃	C₂²
hypercenter	#470	D₂₃
hypocenter	C₂₃	#1342
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

Complements

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

N	H ≅ G/N	type
58. C₂₃	#1342	semidirect

Maximal subgroups

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

subgroup	index
#13092199	2
C₂₃⋊#338	2
C₂₃×#470	2
#1342	23