Subgroups — #13092174

Order 1472.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625097	C₂	1	2	yes	maximal
3	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
4	M₁₆×C₂₃	—	2	2	no	—
5	C₂×C₈×C₂₃	C₄	1	2	yes	complemented
6	C₂²⋊Dic₂₃	—	2	2	no	—
7	C₄⋊Dic₂₃	—	2	2	no	—
8	C₄×Dic₂₃	C₄	1	4	yes	complemented
9	C₂³×C₂₃	D₄	1	1	yes	characteristic
10	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
11	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₂₃	D₄	1	2	yes	—
13	C₂×C₄×C₂₃	Q₈	1	1	yes	characteristic
14	C₂×Dic₂₃	—	2	4	no	—
15	C₈×C₂₃	—	2	2	no	—
16	C₂²×C₂₃	—	4	1	no	—
17	C₂²×C₂₃	C₂²⋊C₄	1	2	yes	—
18	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₂₃	C₄²	1	1	yes	characteristic
20	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₂₃	C₄⋊C₄	1	2	yes	—
22	Dic₂₃	—	4	4	no	—
23	H(3,ℤ/4)	—	23	1	no	maximal, Sylow
24	C₂×C₂₃	—	2	2	no	—
25	C₂×C₂₃	—	2	1	no	—
26	C₂×C₂₃	#95	1	1	yes	characteristic
27	C₂×M₁₆	D₂₃	1	1	yes	characteristic
28	#117	—	23	2	no	—
29	C₂₃	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
31	M₁₆	—	2	2	no	—
32	C₂×C₈	Dic₂₃	1	2	yes	complemented
33	C₄⋊C₄	—	46	2	no	—
34	C₂²⋊C₄	—	46	2	no	—
35	C₄²	—	23	4	no	—
36	C₂³	D₉₂	1	1	yes	characteristic
37	C₂×C₄	—	46	4	no	—
38	C₂×C₄	Dic₄₆	1	1	yes	characteristic
39	C₂×C₄	C₄×D₂₃	1	2	yes	—
40	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
41	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
42	C₈	—	2	2	no	—
43	C₂²	—	4	1	no	—
44	C₂²	C₄⋊Dic₂₃	1	1	yes	characteristic
45	C₂²	(C₂×D₂₃)⋊C₄	1	2	yes	—
46	C₄	—	92	4	no	—
47	C₄	C₄×Dic₂₃	1	1	yes	characteristic
48	C₄	Dic₂₃⋊C₄	1	2	yes	—
49	C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₂₃⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₂₃
commutator	C₄×C₂₃	C₄²
Frattini	C₂²×C₄	C₂×D₂₃
Fitting	C₂×M₁₆×C₂₃	C₂
socle	C₂×C₂₃	#95
prime radical	C₂³×C₂₃	D₄
cosocle	C₂²×C₄×C₂₃	C₂²
hypercenter	C₂×M₁₆	D₂₃
hypocenter	C₂₃	H(3,ℤ/4)
LCS	G ▷ C₄×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
5. C₂×C₈×C₂₃	C₄	semidirect
8. C₄×Dic₂₃	C₄	semidirect
29. C₂₃	H(3,ℤ/4)	semidirect
32. C₂×C₈	Dic₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₂₃	2
#10625097	2
H(3,ℤ/4)	23