Subgroups — #15671501

Order 2944.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625001	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	C₂×#67267	—	2	2	no	—
5	C₂₃×M₃₂	—	2	2	no	—
6	C₂×C₁₆×C₂₃	C₄	1	2	yes	—
7	#10625001	—	2	2	no	—
8	#10625001	C₄	1	4	yes	—
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	#67267	—	2	4	no	—
15	#67267	—	4	2	no	—
16	C₂×C₂₃⋊C₈	—	4	2	no	—
17	C₁₆×C₂₃	—	2	2	no	—
18	C₂³×C₂₃	Q₁₆	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	D₈	1	1	yes	characteristic
22	C₂×C₄×C₂₃	SD₁₆	1	2	yes	—
23	C₈×C₂₃	C₄²	1	1	yes	characteristic
24	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
26	C₂₃⋊C₈	—	4	4	no	—
27	#1385	—	23	1	no	maximal, Sylow
28	C₂²×C₂₃	—	4	1	no	—
29	C₂²×C₂₃	#103	1	2	yes	—
30	C₂²×C₂₃	#107	1	1	yes	characteristic
31	C₄×C₂₃	#95	1	1	yes	characteristic
32	C₄×C₂₃	#102	1	2	yes	—
33	C₄×C₂₃	#106	1	1	yes	characteristic
34	C₂×M₃₂	D₂₃	1	1	yes	characteristic
35	C₂×#108	—	23	2	no	—
36	C₂×C₂₃	—	2	2	no	—
37	C₂×C₂₃	—	2	1	no	—
38	C₂×C₂₃	#340	1	1	yes	characteristic
39	C₂×M₁₆	—	46	2	no	—
40	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
41	M₃₂	—	2	2	no	—
42	C₂×C₁₆	Dic₂₃	1	2	yes	—
43	#108	—	23	4	no	—
44	#108	—	46	2	no	—
45	C₂₃	#1385	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	D₉₂	1	1	yes	characteristic
47	M₁₆	—	46	4	no	—
48	M₁₆	—	92	2	no	—
49	C₂×C₈	—	92	2	no	—
50	C₂×C₈	Dic₄₆	1	1	yes	characteristic
51	C₂×C₈	C₄×D₂₃	1	2	yes	—
52	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₂₃	1	2	yes	—
54	C₁₆	—	2	2	no	—
55	C₂³	Dic₉₂	1	1	yes	characteristic
56	C₂×C₄	#67263	1	2	yes	—
57	C₂×C₄	D₁₈₄	1	1	yes	characteristic
58	C₂×C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
59	C₂×C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
60	C₈	—	92	4	no	—
61	C₈	C₄×Dic₂₃	1	1	yes	characteristic
62	C₈	Dic₂₃⋊C₄	1	2	yes	—
63	C₈	C₂²⋊Dic₂₃	1	1	yes	characteristic
64	C₂²	—	4	1	no	—
65	C₂²	#10624998	1	2	yes	—
66	C₂²	#10625000	1	1	yes	characteristic
67	C₄	#10624999	1	1	yes	characteristic
68	C₄	#10625003	1	2	yes	—
69	C₄	C₂₃⋊#95	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	—	2	1	no	—
72	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	Q₁₆
cosocle	C₂²×C₈×C₂₃	C₂²
hypercenter	C₂×M₃₂	D₂₃
hypocenter	C₂₃	#1385
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
45. C₂₃	#1385	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625001	2
C₂×C₂₃×M₃₂	2
#1385	23