Subgroups — #15673149

Order 2944.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10624985	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13092172	C₂	1	4	yes	maximal
4	C₂₃×#376	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄²×C₂₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×C₂₃⋊C₈	C₂²	1	2	yes	—
8	C₂²×C₂₃⋊C₈	C₂²	1	2	yes	—
9	C₂₃×#95	C₄	1	4	yes	—
10	#10624985	C₄	1	4	yes	complemented
11	C₄×C₂₃⋊C₈	C₄	1	4	yes	complemented
12	C₂²×C₄×C₂₃	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
15	C₄²×C₂₃	—	2	4	no	—
16	C₄²×C₂₃	C₂×C₄	1	2	yes	—
17	C₄²×C₂₃	C₂×C₄	1	2	yes	—
18	C₂×C₂₃⋊C₈	—	2	4	no	—
19	C₂×C₂₃⋊C₈	—	2	4	no	—
20	C₂×C₂₃⋊C₈	C₂×C₄	1	4	yes	—
21	C₂×C₂₃⋊C₈	C₂×C₄	1	4	yes	—
22	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₃	—	2	4	no	—
24	C₂×C₄×C₂₃	—	2	4	no	—
25	C₂×C₄×C₂₃	—	2	8	no	—
26	C₂×C₄×C₂₃	C₄²	1	4	yes	—
27	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₃	#41	1	4	yes	—
30	C₂₃⋊C₈	—	2	4	no	—
31	C₂₃⋊C₈	—	2	4	no	—
32	#1746	—	23	1	no	maximal, Sylow
33	C₂²×C₂₃	C₂×C₄²	1	1	yes	characteristic
34	C₂²×C₂₃	#117	1	2	yes	—
35	C₂²×C₂₃	#131	1	4	yes	—
36	C₄×C₂₃	—	2	4	no	—
37	C₄×C₂₃	—	4	4	no	—
38	C₄×C₂₃	#117	1	2	yes	—
39	C₄×C₂₃	#117	1	2	yes	—
40	C₂×#97	—	23	1	no	—
41	C₂×C₄×C₈	—	23	1	no	—
42	#376	D₂₃	1	1	yes	characteristic
43	#336	—	23	4	no	—
44	C₂×C₂₃	#376	1	1	yes	characteristic
45	C₂×C₂₃	#405	1	2	yes	—
46	C₂×C₂₃	#433	1	4	yes	—
47	C₂²×C₈	—	23	2	no	—
48	C₂²×C₈	—	23	2	no	—
49	C₂×C₄²	C₂×D₂₃	1	2	yes	—
50	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
51	#97	—	23	4	no	—
52	C₄×C₈	—	23	4	no	—
53	#95	Dic₂₃	1	4	yes	—
54	C₂₃	#1746	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₄	C₂×Dic₂₃	1	4	yes	—
56	C₂²×C₄	C₂×Dic₂₃	1	2	yes	—
57	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
58	C₂×C₈	—	23	4	no	—
59	C₂×C₈	—	23	4	no	—
60	C₂×C₈	—	46	4	no	—
61	C₂×C₈	—	46	4	no	—
62	C₄²	—	2	4	no	—
63	C₄²	C₄×D₂₃	1	2	yes	—
64	C₄²	C₄×D₂₃	1	2	yes	—
65	C₂³	C₂²×Dic₂₃	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	4	no	—
68	C₂×C₄	—	2	8	no	—
69	C₂×C₄	C₄×Dic₂₃	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
71	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
72	C₂×C₄	#67288	1	4	yes	—
73	C₈	—	46	4	no	—
74	C₈	—	46	4	no	—
75	C₂²	C₂×C₄×Dic₂₃	1	1	yes	characteristic
76	C₂²	#10625097	1	2	yes	—
77	C₂²	#10625119	1	4	yes	—
78	C₄	—	2	4	no	—
79	C₄	—	4	4	no	—
80	C₄	#10625043	1	2	yes	—
81	C₄	#10625043	1	2	yes	—
82	C₂	#13092263	1	1	yes	characteristic
83	C₂	#13092373	1	2	yes	—
84	C₂	#13092478	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₃
commutator	C₂²×C₂₃	C₂×C₄²
Fitting	C₂₃×#376	C₂
socle, prime radical	C₂³×C₂₃	C₂²×C₄
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	#376	D₂₃
hypocenter	C₂₃	#1746
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
10. #10624985	C₄	semidirect
11. C₄×C₂₃⋊C₈	C₄	semidirect
54. C₂₃	#1746	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10624985	2
C₂×C₄×C₂₃⋊C₈	2
#13092172	2
C₂₃×#376	2
#1746	23