Subgroups — #15671338

Order 2944.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092443	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₂₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₂₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	#10625097	C₄	1	1	yes	characteristic
6	C₂×#67267	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₂₃	—	2	1	no	—
8	Dic₂₃⋊C₈	—	2	1	no	—
9	Dic₂₃⋊C₈	—	2	1	no	—
10	C₂×C₂₃⋊C₁₆	—	2	1	no	—
11	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₂₃	—	4	1	no	—
13	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
15	C₂²⋊Dic₂₃	—	2	1	no	—
16	C₄⋊Dic₂₃	C₈	1	1	yes	characteristic
17	C₄⋊Dic₂₃	C₈	1	1	yes	characteristic
18	C₄×Dic₂₃	—	2	1	no	—
19	#67267	—	4	1	no	—
20	C₂×C₂₃⋊C₈	—	2	1	no	—
21	C₁₆×C₂₃	—	4	1	no	—
22	C₂₃⋊C₁₆	—	4	1	no	—
23	C₂³×C₂₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₂₃	—	2	1	no	—
25	C₂×C₄×C₂₃	—	2	1	no	—
26	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₂₃	—	2	1	no	—
29	C₂×Dic₂₃	—	2	1	no	—
30	C₈×C₂₃	—	2	1	no	—
31	C₈×C₂₃	—	2	1	no	—
32	C₂₃⋊C₈	—	4	1	no	—
33	#1323	—	23	1	no	maximal, Sylow
34	C₂²×C₂₃	—	2	1	no	—
35	C₂²×C₂₃	—	2	1	no	—
36	C₂²×C₂₃	—	2	1	no	—
37	C₂²×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
38	C₄×C₂₃	—	2	1	no	—
39	C₄×C₂₃	#99	1	1	yes	characteristic
40	C₄×C₂₃	#101	1	1	yes	characteristic
41	Dic₂₃	—	4	1	no	—
42	Dic₂₃	—	4	1	no	—
43	#424	—	23	1	no	—
44	C₂²⋊C₁₆	—	23	1	no	—
45	C₂²⋊C₁₆	D₂₃	1	1	yes	characteristic
46	C₂×C₂₃	—	4	1	no	—
47	C₂×C₂₃	#324	1	1	yes	characteristic
48	C₂×C₂₃	#350	1	1	yes	characteristic
49	C₂×C₂₃	#350	1	1	yes	characteristic
50	C₂×M₁₆	—	23	1	no	—
51	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
52	#117	—	23	1	no	—
53	C₂×C₁₆	—	2	1	no	—
54	C₂×C₁₆	—	46	1	no	—
55	C₄⋊C₈	—	46	1	no	—
56	C₄⋊C₈	—	46	1	no	—
57	C₂₃	#1323	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	C₄×D₂₃	1	1	yes	characteristic
59	M₁₆	—	92	1	no	—
60	C₂×C₈	—	4	1	no	—
61	C₂×C₈	—	46	1	no	—
62	C₂×C₈	D₉₂	1	1	yes	characteristic
63	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
64	C₄⋊C₄	—	23	1	no	—
65	C₄⋊C₄	—	23	1	no	—
66	C₂²⋊C₄	—	46	1	no	—
67	C₄²	—	46	1	no	—
68	C₁₆	—	4	1	no	—
69	C₁₆	—	92	1	no	—
70	C₂³	#67262	1	1	yes	characteristic
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	46	1	no	—
74	C₂×C₄	—	46	1	no	—
75	C₂×C₄	C₈×D₂₃	1	1	yes	characteristic
76	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₈	—	92	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	(C₂×D₂₃)⋊C₈	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	92	1	no	—
86	C₄	—	92	1	no	—
87	C₄	#10624988	1	1	yes	characteristic
88	C₄	#10625006	1	1	yes	characteristic
89	C₂	—	4	1	no	—
90	C₂	#13092142	1	1	yes	characteristic
91	C₂	#13092200	1	1	yes	characteristic
92	C₂	#13092202	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₂₃)⋊C₄
commutator	C₂×C₄×C₂₃	C₂×C₈
Frattini	C₂²×C₈	C₂×D₂₃
Fitting	C₂₃×C₂²⋊C₁₆	C₂
socle	C₂²×C₂₃	C₂²⋊C₈
prime radical	C₂³×C₂₃	M₁₆
cosocle	C₂²×C₈×C₂₃	C₂²
hypercenter	C₂²⋊C₁₆	D₂₃
hypocenter	C₂₃	#1323
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
57. C₂₃	#1323	semidirect

Maximal subgroups

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

subgroup	index
#13092443	2
C₂²⋊(C₂₃⋊C₁₆)	2
C₂₃×C₂²⋊C₁₆	2
#1323	23