Subgroups — #15675684

Order 2944.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092822	C₂	1	1	yes	maximal, characteristic
2	#13092244	C₂	1	2	yes	maximal
3	#13092242	C₂	1	2	yes	maximal
4	#13092193	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#499	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#125	—	2	1	no	—
7	#10625040	—	2	1	no	—
8	C₂₃×#107	C₂²	1	1	yes	characteristic
9	C₂₃×#107	C₂²	1	1	yes	characteristic
10	C₂₃×#106	—	2	1	no	—
11	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	#10625000	—	2	1	no	—
13	#10625000	C₂²	1	2	yes	—
14	C₂×C₂₃⋊C₁₆	C₂²	1	2	yes	—
15	C₂×Dic₄₆	—	4	1	no	—
16	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₂₃	—	2	1	no	—
19	C₄⋊C₄×C₂₃	—	2	1	no	—
20	C₄⋊C₄×C₂₃	—	4	1	no	—
21	C₄⋊C₄×C₂₃	—	4	1	no	—
22	C₄²×C₂₃	D₄	1	1	yes	characteristic
23	C₄⋊Dic₂₃	—	2	2	no	—
24	C₄⋊Dic₂₃	—	4	1	no	—
25	C₂₃⋊C₁₆	Q₈	1	4	yes	complemented
26	C₂×C₄×C₂₃	—	4	1	no	—
27	C₂×C₄×C₂₃	—	4	1	no	—
28	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₂₃	—	4	2	no	—
32	Dic₄₆	—	8	2	no	—
33	C₈×C₂₃	Q₁₆	1	2	yes	—
34	C₈×C₂₃	C₂×Q₈	1	2	yes	—
35	#2255	—	23	1	no	maximal, Sylow
36	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
37	C₄×C₂₃	—	2	1	no	—
38	C₄×C₂₃	—	2	1	no	—
39	C₄×C₂₃	—	8	1	no	—
40	C₄×C₂₃	—	8	1	no	—
41	C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
42	C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
43	Dic₂₃	—	8	2	no	—
44	#500	—	23	1	no	—
45	#499	D₂₃	1	1	yes	characteristic
46	#367	—	23	2	no	—
47	#366	—	23	2	no	—
48	#346	—	23	1	no	—
49	C₂×C₂₃	#500	1	1	yes	characteristic
50	C₂×C₂₃	#509	1	1	yes	characteristic
51	C₂×C₂₃	#510	1	1	yes	characteristic
52	C₄⋊Q₈	—	46	1	no	—
53	#125	—	2	1	no	—
54	C₂×C₁₆	—	23	2	no	—
55	#107	—	23	2	no	—
56	#107	—	46	1	no	—
57	#107	C₂×D₂₃	1	1	yes	characteristic
58	#107	C₂×D₂₃	1	1	yes	characteristic
59	#106	—	2	1	no	—
60	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
61	C₂₃	#2255	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	92	1	no	—
63	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
65	C₄⋊C₄	—	2	1	no	—
66	C₄⋊C₄	—	2	1	no	—
67	C₄⋊C₄	—	4	1	no	—
68	C₄⋊C₄	—	4	1	no	—
69	C₄⋊C₄	—	46	2	no	—
70	C₄⋊C₄	—	92	1	no	—
71	C₄²	C₂²⋊D₂₃	1	1	yes	characteristic
72	C₁₆	—	23	4	no	—
73	Q₈	—	184	2	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	92	2	no	—
77	C₂×C₄	#67272	1	1	yes	characteristic
78	C₂×C₄	#67272	1	1	yes	characteristic
79	C₂×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
80	C₈	#67275	1	2	yes	—
81	C₈	Q₈×D₂₃	1	2	yes	—
82	C₂²	C₂×#67272	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	8	1	no	—
87	C₄	—	184	2	no	—
88	C₄	C₂×#67275	1	1	yes	characteristic
89	C₄	#10625115	1	1	yes	characteristic
90	C₂	#13092820	1	1	yes	characteristic
91	C₂	#13092852	1	1	yes	characteristic
92	C₂	#13092857	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#67272
commutator, cosocle	C₂×C₈×C₂₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂₃×#499	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₈
hypercenter	#499	D₂₃
hypocenter	C₂₃	#2255
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
25. C₂₃⋊C₁₆	Q₈	semidirect
61. C₂₃	#2255	semidirect

Maximal subgroups

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

subgroup	index
#13092822	2
#13092244	2
#13092242	2
#13092193	2
C₂₃×#499	2
#2255	23