Subgroups — #15674563

Order 2944.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092278	C₂	1	3	yes	maximal
2	#13092184	C₂	1	3	yes	maximal
3	C₂₃×#543	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic
5	C₂₃×C₂²⋊Q₈	—	2	6	no	—
6	C₂×C₂²⋊C₄×C₂₃	C₂²	1	3	yes	—
7	C₂×C₂²⋊Dic₂₃	C₂²	1	3	yes	—
8	C₂₃⋊#95	—	2	6	no	—
9	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
10	C₂×Q₈×C₂₃	—	2	2	no	—
11	C₂²×C₄×C₂₃	D₄	1	6	yes	—
12	C₂²×Dic₂₃	—	2	3	no	—
13	C₂²×Dic₂₃	—	2	3	no	—
14	C₂²×Dic₂₃	—	2	3	no	—
15	C₂²×Dic₂₃	Q₈	1	2	yes	complemented
16	C₄⋊C₄×C₂₃	—	2	6	no	—
17	C₂²⋊C₄×C₂₃	—	2	6	no	—
18	C₂²⋊Dic₂₃	—	2	6	no	—
19	C₂³×C₂₃	—	4	2	no	—
20	C₂³×C₂₃	C₂×D₄	1	3	yes	—
21	C₂³×C₂₃	C₂×Q₈	1	1	yes	characteristic
22	C₂³×C₂₃	#41	1	3	yes	—
23	Q₈×C₂₃	—	8	2	no	—
24	C₂×C₄×C₂₃	—	2	6	no	—
25	C₂×C₄×C₂₃	—	4	6	no	—
26	C₂×Dic₂₃	—	2	6	no	—
27	C₂×Dic₂₃	—	4	1	no	—
28	C₂×Dic₂₃	—	4	3	no	—
29	C₂×Dic₂₃	—	4	6	no	—
30	C₂×Dic₂₃	—	4	3	no	—
31	#2030	—	23	1	no	maximal, Sylow
32	C₂²×C₂₃	—	2	6	no	—
33	C₂²×C₂₃	—	4	1	no	—
34	C₂²×C₂₃	—	4	3	no	—
35	C₂²×C₂₃	#120	1	1	yes	characteristic
36	C₂²×C₂₃	C₂²⋊Q₈	1	3	yes	—
37	C₂²×C₂₃	#124	1	3	yes	—
38	C₄×C₂₃	—	4	6	no	—
39	Dic₂₃	—	4	2	no	—
40	Dic₂₃	—	8	3	no	—
41	#543	D₂₃	1	1	yes	characteristic
42	#381	—	23	3	no	—
43	#342	—	23	3	no	—
44	C₂×C₂₃	—	2	3	no	—
45	C₂×C₂₃	—	2	3	no	—
46	C₂×C₂₃	#393	1	1	yes	characteristic
47	C₂×C₂₃	#458	1	2	yes	—
48	C₂³×C₄	—	23	1	no	—
49	C₂²⋊Q₈	—	2	6	no	—
50	C₂×C₂²⋊C₄	—	23	3	no	—
51	C₂×C₂²⋊C₄	C₂×D₂₃	1	3	yes	—
52	#95	—	46	6	no	—
53	C₂₃	#2030	1	1	yes	characteristic, complemented, Sylow
54	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
55	C₂×Q₈	—	2	2	no	—
56	C₂²×C₄	—	23	2	no	—
57	C₂²×C₄	—	46	3	no	—
58	C₂²×C₄	—	46	3	no	—
59	C₂²×C₄	—	46	3	no	—
60	C₂²×C₄	C₂²⋊D₂₃	1	6	yes	—
61	C₄⋊C₄	—	2	6	no	—
62	C₂²⋊C₄	—	2	6	no	—
63	C₂²⋊C₄	—	46	6	no	—
64	C₂³	—	4	2	no	—
65	C₂³	Q₈×D₂₃	1	1	yes	characteristic
66	C₂³	#67292	1	3	yes	—
67	C₂³	C₂×C₂²⋊D₂₃	1	3	yes	—
68	Q₈	—	8	2	no	—
69	C₂×C₄	—	2	6	no	—
70	C₂×C₄	—	4	6	no	—
71	C₂×C₄	—	46	6	no	—
72	C₂×C₄	—	92	3	no	—
73	C₂×C₄	—	92	1	no	—
74	C₂×C₄	—	92	6	no	—
75	C₂×C₄	—	92	3	no	—
76	C₂²	—	2	6	no	—
77	C₂²	—	4	1	no	—
78	C₂²	—	4	3	no	—
79	C₂²	#10625117	1	3	yes	—
80	C₂²	#10625118	1	3	yes	—
81	C₂²	#10625124	1	1	yes	characteristic
82	C₄	—	4	6	no	—
83	C₄	—	92	2	no	—
84	C₄	—	184	3	no	—
85	C₂	—	2	3	no	—
86	C₂	—	2	3	no	—
87	C₂	#13092328	1	1	yes	characteristic
88	C₂	#13092607	1	2	yes	—

	subgroup	G/H
center	C₂²	#10625124
commutator, prime radical, cosocle	C₂⁴×C₂₃	C₂³
Frattini	C₂⁴	C₂²×D₂₃
Fitting	C₂₃×#543	C₂
socle	C₂²×C₂₃	#120
hypercenter	#543	D₂₃
hypocenter	C₂₃	#2030
LCS	G ▷ C₂⁴×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

Complements

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

N	H ≅ G/N	type
15. C₂²×Dic₂₃	Q₈	semidirect
53. C₂₃	#2030	semidirect

Maximal subgroups

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

subgroup	index
#13092278	2
#13092184	2
C₂₃×#543	2
#2030	23