Subgroups — #13092466

Order 1472.

102 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	C₂×#67267	C₂	1	2	yes	maximal
3	#10625001	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
5	M₁₆×C₂₃	C₄	1	4	yes	—
6	C₂×C₈×C₂₃	C₂²	1	2	yes	—
7	#67267	—	2	2	no	—
8	#67267	C₂²	1	4	yes	—
9	C₂×C₂₃⋊C₈	—	2	2	no	—
10	C₂³×C₂₃	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₂₃	D₄	1	2	yes	—
13	C₂×C₄×C₂₃	Q₈	1	1	yes	characteristic
14	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
15	C₈×C₂₃	C₂×C₄	1	4	yes	—
16	C₂₃⋊C₈	—	2	4	no	—
17	C₂²×C₂₃	—	4	1	no	—
18	C₂²×C₂₃	C₄⋊C₄	1	2	yes	—
19	C₂²×C₂₃	C₂×Q₈	1	1	yes	characteristic
20	C₄×C₂₃	C₄⋊C₄	1	2	yes	—
21	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
22	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
23	#430	—	23	1	no	maximal, Sylow
24	C₂×C₂₃	—	2	2	no	—
25	C₂×C₂₃	—	2	1	no	—
26	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂×M₁₆	—	23	2	no	—
28	C₂×M₁₆	D₂₃	1	1	yes	characteristic
29	#108	—	23	4	no	—
30	C₂₃	#430	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
32	M₁₆	—	23	4	no	—
33	M₁₆	—	46	2	no	—
34	M₁₆	Dic₂₃	1	4	yes	—
35	C₂×C₈	—	46	2	no	—
36	C₂×C₈	C₂×D₂₃	1	2	yes	—
37	C₂³	Dic₄₆	1	1	yes	characteristic
38	C₂×C₄	Dic₄₆	1	1	yes	characteristic
39	C₂×C₄	D₉₂	1	2	yes	—
40	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
41	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
42	C₈	—	46	4	no	—
43	C₈	C₂×Dic₂₃	1	4	yes	—
44	C₂²	—	4	1	no	—
45	C₂²	C₄⋊Dic₂₃	1	2	yes	—
46	C₂²	C₂×Dic₄₆	1	1	yes	characteristic
47	C₄	C₄⋊Dic₂₃	1	2	yes	—
48	C₄	C₂×D₉₂	1	1	yes	characteristic
49	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₉₂
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×M₁₆×C₂₃	C₂
socle	C₂×C₂₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₃	Q₈
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂×M₁₆	D₂₃
hypocenter	C₂₃	#430
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #10625001	C₂	semidirect
30. C₂₃	#430	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
C₂×#67267	2
#10625001	2
#430	23