Subgroups — #13092337

Order 1472.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₂₃⋊C₄	C₂	1	2	yes	maximal
4	C₂₃⋊#95	C₂	1	2	yes	maximal
5	C₂₃⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×Dic₂₃	C₂²	1	2	yes	—
10	C₂²×Dic₂₃	C₂²	1	2	yes	—
11	C₂×Dic₄₆	—	2	2	no	—
12	C₂×Dic₄₆	—	2	4	no	—
13	C₄⋊C₄×C₂₃	—	2	2	no	—
14	Dic₂₃⋊C₄	—	2	4	no	—
15	C₂³×C₂₃	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₂₃	—	2	1	no	—
17	C₂×C₄×C₂₃	—	2	2	no	—
18	C₂×C₄×C₂₃	—	2	1	no	—
19	C₂×C₄×C₂₃	—	2	2	no	—
20	C₂×C₄×C₂₃	—	2	1	no	—
21	C₂×C₄×C₂₃	D₄	1	2	yes	—
22	C₂×C₄×C₂₃	Q₈	1	2	yes	complemented
23	C₂×Dic₂₃	—	2	2	no	—
24	C₂×Dic₂₃	—	2	2	no	—
25	C₂×Dic₂₃	—	2	2	no	—
26	C₂×Dic₂₃	—	2	2	no	—
27	C₂×Dic₂₃	D₄	1	4	yes	—
28	C₂×Dic₂₃	Q₈	1	4	yes	complemented
29	Dic₄₆	—	2	8	no	—
30	C₂²×C₂₃	C₂×D₄	1	2	yes	—
31	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₂₃	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₂₃	C₂×Q₈	1	2	yes	—
34	C₂²×C₂₃	#41	1	1	yes	characteristic
35	C₄×C₂₃	—	2	2	no	—
36	C₄×C₂₃	—	2	2	no	—
37	C₄×C₂₃	—	4	1	no	—
38	Dic₂₃	—	2	4	no	—
39	Dic₂₃	—	2	4	no	—
40	#395	—	23	1	no	maximal, Sylow
41	C₂×C₂₃	#120	1	1	yes	characteristic
42	C₂×C₂₃	C₂²⋊Q₈	1	2	yes	—
43	C₂×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
44	C₂×C₂₃	C₄⋊Q₈	1	2	yes	—
45	C₂×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
46	C₂²×Q₈	—	23	1	no	—
47	C₂×C₄⋊C₄	—	23	2	no	—
48	C₂×C₄⋊C₄	D₂₃	1	1	yes	characteristic
49	#95	—	23	1	no	—
50	#95	—	23	2	no	—
51	C₂₃	#395	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₈	—	46	4	no	—
53	C₂×Q₈	—	46	2	no	—
54	C₂²×C₄	—	23	2	no	—
55	C₂²×C₄	—	23	2	no	—
56	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
57	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
58	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
59	C₄⋊C₄	—	2	2	no	—
60	C₄⋊C₄	—	46	4	no	—
61	C₂³	C₂²×D₂₃	1	1	yes	characteristic
62	Q₈	—	46	8	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	23	4	no	—
69	C₂×C₄	—	23	4	no	—
70	C₂×C₄	—	46	2	no	—
71	C₂×C₄	—	46	2	no	—
72	C₂×C₄	—	46	2	no	—
73	C₂×C₄	—	46	2	no	—
74	C₂×C₄	Dic₄₆	1	2	yes	complemented
75	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
76	C₂²	C₂×Dic₄₆	1	1	yes	characteristic
77	C₂²	#67288	1	1	yes	characteristic
78	C₂²	D₄×D₂₃	1	2	yes	—
79	C₂²	Q₈×D₂₃	1	2	yes	—
80	C₂²	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	2	2	no	—
83	C₄	—	4	1	no	—
84	C₄	—	46	4	no	—
85	C₄	—	46	4	no	—
86	C₂	#10625059	1	2	yes	—
87	C₂	#10625067	1	2	yes	—
88	C₂	#10625095	1	1	yes	characteristic
89	C₂	#10625108	1	1	yes	characteristic
90	C₂	#10625115	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₂₃
commutator, socle, prime radical, cosocle	C₂³×C₂₃	C₂³
Fitting	C₂×C₄⋊C₄×C₂₃	C₂
hypercenter	C₂×C₄⋊C₄	D₂₃
hypocenter	C₂₃	#395
LCS	G ▷ C₂³×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
22. C₂×C₄×C₂₃	Q₈	semidirect
28. C₂×Dic₂₃	Q₈	semidirect
51. C₂₃	#395	semidirect
74. C₂×C₄	Dic₄₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₄₆	2
C₂×C₄⋊C₄×C₂₃	2
C₂×Dic₂₃⋊C₄	2
C₂₃⋊#95	2
#395	23