Subgroups — #13092280

Order 1472.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊Dic₂₃	C₂	1	2	yes	maximal
3	C₂₃⋊#95	C₂	1	4	yes	maximal, complemented
4	C₂⁴×C₂₃	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₂₃	—	2	4	no	—
6	C₂²×C₄×C₂₃	C₄	1	4	yes	complemented
7	C₂²×C₄×C₂₃	C₂²	1	2	yes	—
8	C₂²×Dic₂₃	C₂²	1	4	yes	—
9	C₂²⋊Dic₂₃	—	2	4	no	—
10	C₂³×C₂₃	—	2	4	no	—
11	C₂³×C₂₃	C₂×C₄	1	2	yes	—
12	C₂³×C₂₃	D₄	1	4	yes	—
13	C₂³×C₂₃	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₂₃	—	2	8	no	—
15	C₂×C₄×C₂₃	—	2	4	no	—
16	C₂×C₄×C₂₃	C₂×C₄	1	4	yes	—
17	C₂×Dic₂₃	—	2	4	no	—
18	C₂×Dic₂₃	—	2	8	no	—
19	C₂²×C₂₃	—	2	4	no	—
20	C₂²×C₂₃	—	2	8	no	—
21	C₂²×C₂₃	C₂²⋊C₄	1	4	yes	—
22	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₂₃	C₂×D₄	1	2	yes	—
24	C₂²×C₂₃	#41	1	4	yes	—
25	C₄×C₂₃	—	2	4	no	—
26	Dic₂₃	—	4	4	no	—
27	#381	—	23	1	no	maximal, Sylow
28	C₂×C₂₃	—	2	4	no	—
29	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₂₃	#117	1	2	yes	—
31	C₂×C₂₃	#123	1	4	yes	—
32	C₂³×C₄	D₂₃	1	1	yes	characteristic
33	C₂×C₂²⋊C₄	—	23	2	no	—
34	#95	—	23	4	no	—
35	C₂₃	#381	1	1	yes	characteristic, complemented, Sylow
36	C₂⁴	C₂×D₂₃	1	1	yes	characteristic
37	C₂²×C₄	—	2	4	no	—
38	C₂²×C₄	—	23	4	no	—
39	C₂²×C₄	Dic₂₃	1	4	yes	complemented
40	C₂²×C₄	C₂×D₂₃	1	2	yes	—
41	C₂²⋊C₄	—	46	4	no	—
42	C₂³	—	2	4	no	—
43	C₂³	C₂×Dic₂₃	1	2	yes	—
44	C₂³	C₂²⋊D₂₃	1	4	yes	—
45	C₂³	C₂²×D₂₃	1	1	yes	characteristic
46	C₂×C₄	—	2	8	no	—
47	C₂×C₄	—	2	4	no	—
48	C₂×C₄	—	46	8	no	—
49	C₂×C₄	—	46	4	no	—
50	C₂×C₄	C₂×Dic₂₃	1	4	yes	—
51	C₂²	—	2	4	no	—
52	C₂²	—	2	8	no	—
53	C₂²	C₂²⋊Dic₂₃	1	4	yes	—
54	C₂²	#67288	1	4	yes	—
55	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
56	C₂²	C₂×C₂²⋊D₂₃	1	2	yes	—
57	C₄	—	2	4	no	—
58	C₄	—	92	4	no	—
59	C₂	—	2	4	no	—
60	C₂	#10625097	1	2	yes	—
61	C₂	#10625100	1	4	yes	—
62	C₂	C₂×C₂²⋊Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₂₃
commutator	C₂²×C₂₃	C₂²×C₄
Fitting	C₂³×C₄×C₂₃	C₂
socle, cosocle	C₂³×C₂₃	C₂³
prime radical	C₂⁴×C₂₃	C₂²
hypercenter	C₂³×C₄	D₂₃
hypocenter	C₂₃	#381
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₂₃⋊#95	C₂	semidirect
6. C₂²×C₄×C₂₃	C₄	semidirect
35. C₂₃	#381	semidirect
39. C₂²×C₄	Dic₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₂₃	2
C₂×C₂²⋊Dic₂₃	2
C₂₃⋊#95	2
#381	23