Subgroups — #13092476

Order 1472.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625043	C₂	1	1	yes	maximal, characteristic
2	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₂₃)⋊C₈	C₂	1	2	yes	maximal
4	Dic₂₃⋊C₈	C₂	1	2	yes	maximal, complemented
5	#10624985	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₂₃	C₂²	1	2	yes	—
8	C₄²×C₂₃	C₂²	1	1	yes	characteristic
9	(C₂×D₂₃)⋊C₄	C₄	1	2	yes	—
10	Dic₂₃⋊C₄	C₄	1	2	yes	—
11	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
13	C₂²×D₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
16	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
17	C₂×Dic₂₃	C₂×C₄	1	1	yes	characteristic
18	C₄×D₂₃	—	2	2	no	—
19	C₈×C₂₃	—	2	2	no	—
20	C₂₃⋊C₈	—	2	2	no	—
21	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
22	C₂×D₂₃	—	2	1	no	—
23	C₂×D₂₃	—	2	2	no	—
24	C₄×C₂₃	—	2	2	no	—
25	C₄×C₂₃	#41	1	2	yes	—
26	Dic₂₃	—	2	1	no	—
27	Dic₂₃	—	2	2	no	—
28	#433	—	23	1	no	maximal, Sylow
29	C₂×C₂₃	#117	1	1	yes	characteristic
30	C₂×C₂₃	#131	1	2	yes	—
31	D₂₃	—	4	1	no	—
32	#117	—	23	1	no	—
33	C₄⋊C₈	—	23	2	no	—
34	C₂²⋊C₈	—	23	2	no	—
35	#97	—	23	1	no	—
36	C₄×C₈	D₂₃	1	1	yes	characteristic, complemented
37	C₂₃	#433	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₄	—	23	1	no	—
39	C₂×C₈	—	23	2	no	—
40	C₂×C₈	C₂×D₂₃	1	2	yes	—
41	C₄⋊C₄	—	23	2	no	—
42	C₂²⋊C₄	—	23	2	no	—
43	C₄²	—	23	1	no	—
44	C₄²	C₂×D₂₃	1	1	yes	characteristic
45	C₂³	—	23	1	no	—
46	C₂×C₄	—	23	2	no	—
47	C₂×C₄	—	23	1	no	—
48	C₂×C₄	—	46	2	no	—
49	C₂×C₄	C₄×D₂₃	1	2	yes	—
50	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	46	2	no	—
53	C₂²	—	46	1	no	—
54	C₂²	—	46	2	no	—
55	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	46	1	no	—
58	C₄	—	46	2	no	—
59	C₄	#67288	1	2	yes	—
60	C₂	—	92	1	no	—
61	C₂	#10625043	1	1	yes	characteristic
62	C₂	#10625072	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₃
commutator, socle	C₂²×C₂₃	C₂²×C₄
Fitting	C₄×C₈×C₂₃	C₂
prime radical	C₂²×D₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₄×C₈	D₂₃
hypocenter	C₂₃	#433
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×C₈×C₂₃	C₂	semidirect
4. Dic₂₃⋊C₈	C₂	semidirect
5. #10624985	C₂	semidirect
36. C₄×C₈	D₂₃	semidirect
37. C₂₃	#433	semidirect

Maximal subgroups

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

subgroup	index
#10625043	2
C₄×C₈×C₂₃	2
(C₂×D₂₃)⋊C₈	2
Dic₂₃⋊C₈	2
#10624985	2
#433	23