Subgroups — #15671499

Order 2944.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092455	C₂	1	2	yes	maximal
2	C₂×C₂₃×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
4	#10625097	—	2	2	no	—
5	C₂₃×M₃₂	—	2	2	no	—
6	C₂×C₁₆×C₂₃	C₄	1	2	yes	complemented
7	#10625000	—	2	2	no	—
8	#10624999	C₄	1	4	yes	complemented
9	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
10	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
11	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₂₃	D₄	1	2	yes	—
13	C₂×C₈×C₂₃	Q₈	1	1	yes	characteristic
14	C₂²⋊Dic₂₃	—	4	2	no	—
15	C₄⋊Dic₂₃	—	2	4	no	—
16	C₄×Dic₂₃	—	4	2	no	—
17	C₁₆×C₂₃	—	2	2	no	—
18	C₂³×C₂₃	D₈	1	1	yes	characteristic
19	C₂×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₃	SD₁₆	1	2	yes	—
22	C₂×C₄×C₂₃	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₂₃	—	4	4	no	—
24	C₈×C₂₃	C₄²	1	1	yes	characteristic
25	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
27	#1384	—	23	1	no	maximal, Sylow
28	C₂²×C₂₃	—	4	1	no	—
29	C₂²×C₂₃	#102	1	2	yes	—
30	C₂²×C₂₃	#107	1	1	yes	characteristic
31	C₄×C₂₃	#95	1	1	yes	characteristic
32	C₄×C₂₃	#103	1	2	yes	—
33	C₄×C₂₃	#106	1	1	yes	characteristic
34	Dic₂₃	—	8	4	no	—
35	C₂×M₃₂	D₂₃	1	1	yes	characteristic
36	#427	—	23	2	no	—
37	C₂×C₂₃	—	2	2	no	—
38	C₂×C₂₃	—	2	1	no	—
39	C₂×C₂₃	#340	1	1	yes	characteristic
40	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
41	#117	—	46	2	no	—
42	M₃₂	—	2	2	no	—
43	C₂×C₁₆	Dic₂₃	1	2	yes	complemented
44	#107	—	46	2	no	—
45	#106	—	23	4	no	—
46	C₂₃	#1384	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄	D₉₂	1	1	yes	characteristic
48	C₂×C₈	Dic₄₆	1	1	yes	characteristic
49	C₂×C₈	C₄×D₂₃	1	2	yes	—
50	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₂₃	1	2	yes	—
52	C₄⋊C₄	—	46	4	no	—
53	C₂²⋊C₄	—	92	2	no	—
54	C₄²	—	92	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₁₈₄	1	1	yes	characteristic
57	C₂×C₄	—	92	4	no	—
58	C₂×C₄	#67263	1	2	yes	—
59	C₂×C₄	Dic₉₂	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
61	C₂×C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
62	C₈	C₄×Dic₂₃	1	1	yes	characteristic
63	C₈	Dic₂₃⋊C₄	1	2	yes	—
64	C₈	C₂²⋊Dic₂₃	1	1	yes	characteristic
65	C₂²	—	4	1	no	—
66	C₂²	#10625000	1	1	yes	characteristic
67	C₂²	#10625003	1	2	yes	—
68	C₄	—	184	4	no	—
69	C₄	#10624998	1	2	yes	—
70	C₄	#10624999	1	1	yes	characteristic
71	C₄	C₂₃⋊#95	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#13092180	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10624999
commutator	C₈×C₂₃	C₄²
Frattini	C₂²×C₈	C₂×D₂₃
Fitting	C₂×C₂₃×M₃₂	C₂
socle	C₂×C₂₃	#340
prime radical	C₂³×C₂₃	D₈
cosocle	C₂²×C₈×C₂₃	C₂²
hypercenter	C₂×M₃₂	D₂₃
hypocenter	C₂₃	#1384
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
6. C₂×C₁₆×C₂₃	C₄	semidirect
8. #10624999	C₄	semidirect
43. C₂×C₁₆	Dic₂₃	semidirect
46. C₂₃	#1384	semidirect

Maximal subgroups

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

subgroup	index
#13092455	2
C₂×C₂₃×M₃₂	2
#1384	23