Subgroups — #13092221

Order 1472.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625000	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₂₃	—	2	1	no	—
5	Q₁₆×C₂₃	—	2	1	no	—
6	Q₁₆×C₂₃	C₄	1	2	yes	complemented
7	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₂₃	—	2	1	no	—
9	C₂₃⋊C₁₆	—	2	1	no	—
10	Q₈×C₂₃	—	2	2	no	—
11	Q₈×C₂₃	—	4	1	no	—
12	C₂×C₄×C₂₃	—	4	1	no	—
13	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
14	C₂×Dic₂₃	—	4	1	no	—
15	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₂²×C₂₃	D₈	1	1	yes	characteristic
18	C₄×C₂₃	—	4	2	no	—
19	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₂₃	SD₁₆	1	1	yes	characteristic
21	Dic₂₃	—	8	1	no	—
22	#358	—	23	1	no	maximal, Sylow
23	C₂×C₂₃	#102	1	1	yes	characteristic
24	C₂×C₂₃	SD₃₂	1	1	yes	characteristic
25	C₂×C₂₃	Q₃₂	1	1	yes	characteristic
26	C₂×Q₁₆	D₂₃	1	1	yes	characteristic
27	C₂×C₁₆	—	23	1	no	—
28	#107	—	23	1	no	—
29	C₂₃	#358	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₈	—	2	1	no	—
31	Q₁₆	—	2	1	no	—
32	Q₁₆	Dic₂₃	1	2	yes	complemented
33	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
34	C₄⋊C₄	—	46	1	no	—
35	C₁₆	—	46	1	no	—
36	Q₈	—	2	2	no	—
37	Q₈	—	4	1	no	—
38	C₂×C₄	—	4	1	no	—
39	C₂×C₄	—	92	1	no	—
40	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
41	C₈	C₂×Dic₂₃	1	1	yes	characteristic
42	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
43	C₂²	#67272	1	1	yes	characteristic
44	C₄	—	4	2	no	—
45	C₄	—	184	1	no	—
46	C₄	#67273	1	1	yes	characteristic
47	C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
48	C₂	#10625010	1	1	yes	characteristic
49	C₂	#10625011	1	1	yes	characteristic
50	C₂	#10625014	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#67272
commutator	C₈×C₂₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₂₃
Fitting	C₂×Q₁₆×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	D₈
cosocle	C₂×C₈×C₂₃	C₂²
hypercenter	C₂×Q₁₆	D₂₃
hypocenter	C₂₃	#358
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
6. Q₁₆×C₂₃	C₄	semidirect
29. C₂₃	#358	semidirect
32. Q₁₆	Dic₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₂₃	2
#10625000	2
C₂×C₂₃⋊C₁₆	2
#358	23