Subgroups — #15674977

Order 2944.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092466	C₂	1	1	yes	maximal, characteristic
2	#13092187	C₂	1	2	yes	maximal
3	#13092182	C₂	1	2	yes	maximal
4	C₂₃⋊#338	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#424	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#117	C₂²	1	1	yes	characteristic
9	C₂×#67267	C₂²	1	2	yes	—
10	C₂×#67267	C₂²	1	2	yes	—
11	C₂₃×C₄⋊C₈	—	2	2	no	—
12	#10625001	—	2	2	no	—
13	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
14	M₁₆×C₂₃	—	2	2	no	—
15	C₂×C₈×C₂₃	—	2	1	no	—
16	C₂×C₈×C₂₃	—	2	2	no	—
17	C₂×C₈×C₂₃	D₄	1	2	yes	—
18	C₄⋊C₄×C₂₃	—	2	1	no	—
19	C₂²⋊C₄×C₂₃	Q₈	1	2	yes	—
20	C₄²×C₂₃	—	2	1	no	—
21	#67267	—	2	2	no	—
22	#67267	—	2	2	no	—
23	#67267	—	2	2	no	—
24	#67267	—	2	2	no	—
25	C₂×C₂₃⋊C₈	—	2	2	no	—
26	C₂×C₂₃⋊C₈	—	2	2	no	—
27	C₂³×C₂₃	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₂₃	—	2	2	no	—
29	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₂₃	#41	1	1	yes	characteristic
31	C₂×C₄×C₂₃	#41	1	2	yes	—
32	C₂×C₄×C₂₃	#41	1	2	yes	—
33	C₈×C₂₃	—	2	2	no	—
34	C₈×C₂₃	—	4	1	no	—
35	C₂₃⋊C₈	—	4	2	no	—
36	C₂₃⋊C₈	—	4	2	no	—
37	#2103	—	23	1	no	maximal, Sylow
38	C₂²×C₂₃	—	4	1	no	—
39	C₂²×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂²×C₂₃	#125	1	2	yes	—
41	C₄×C₂₃	—	4	2	no	—
42	C₄×C₂₃	#123	1	1	yes	characteristic
43	C₄×C₂₃	#124	1	1	yes	characteristic
44	C₄×C₂₃	#126	1	2	yes	—
45	#430	—	23	1	no	—
46	#424	D₂₃	1	1	yes	characteristic
47	#344	—	23	2	no	—
48	#341	—	23	2	no	—
49	#338	—	23	1	no	—
50	C₂×C₂₃	—	2	1	no	—
51	C₂×C₂₃	—	2	2	no	—
52	C₂×C₂₃	#400	1	1	yes	characteristic
53	C₂×M₁₆	—	23	2	no	—
54	C₂×M₁₆	—	23	2	no	—
55	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic
56	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
57	#117	C₂×D₂₃	1	1	yes	characteristic
58	#108	—	46	2	no	—
59	C₄⋊C₈	—	2	2	no	—
60	C₂₃	#2103	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	46	2	no	—
64	M₁₆	—	46	2	no	—
65	M₁₆	—	46	2	no	—
66	M₁₆	—	46	2	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	46	2	no	—
70	C₂×C₈	—	46	2	no	—
71	C₂×C₈	C₂²⋊D₂₃	1	2	yes	—
72	C₄⋊C₄	—	2	1	no	—
73	C₂²⋊C₄	Dic₄₆	1	2	yes	—
74	C₄²	—	2	1	no	—
75	C₂³	C₂×Dic₄₆	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	#67288	1	1	yes	characteristic
78	C₂×C₄	#67290	1	2	yes	—
79	C₂×C₄	#67292	1	2	yes	—
80	C₂×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	1	no	—
83	C₈	—	92	2	no	—
84	C₈	—	92	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#10625061	1	2	yes	—
87	C₂²	#10625095	1	1	yes	characteristic
88	C₄	—	4	2	no	—
89	C₄	#10625069	1	2	yes	—
90	C₄	#10625106	1	1	yes	characteristic
91	C₄	#10625118	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#13092356	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10625118
commutator, cosocle	C₂²×C₄×C₂₃	C₂³
Frattini	C₂²×C₄	C₂²×D₂₃
Fitting	C₂₃×#424	C₂
socle	C₂×C₂₃	#400
prime radical	C₂³×C₂₃	C₂×Q₈
hypercenter	#424	D₂₃
hypocenter	C₂₃	#2103
LCS	G ▷ C₂²×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #424

Complements

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

N	H ≅ G/N	type
60. C₂₃	#2103	semidirect

Maximal subgroups

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

subgroup	index
#13092466	2
#13092187	2
#13092182	2
C₂₃⋊#338	2
C₂₃×#424	2
#2103	23