Subgroups — #15673554

Order 2944.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10624999	C₂	1	4	yes	maximal
2	#13092287	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₃	C₂²	1	2	yes	—
5	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊Dic₂₃	—	2	4	no	—
7	C₂×C₄⋊Dic₂₃	C₂²	1	4	yes	—
8	C₄×C₈×C₂₃	C₄	1	4	yes	complemented
9	#10624999	—	2	8	no	—
10	C₂²×C₄×C₂₃	D₄	1	2	yes	—
11	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
12	C₂²×Dic₂₃	—	2	4	no	—
13	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₂₃	D₄	1	4	yes	—
15	C₂×C₈×C₂₃	Q₈	1	4	yes	—
16	C₄²×C₂₃	C₂×C₄	1	2	yes	—
17	C₄²×C₂₃	Q₈	1	2	yes	—
18	C₄⋊Dic₂₃	—	2	8	no	—
19	C₄⋊Dic₂₃	—	4	8	no	—
20	C₂³×C₂₃	C₂×D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₃	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₂₃	SD₁₆	1	8	yes	—
23	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₂₃	C₂×Q₈	1	2	yes	—
26	C₂×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
27	C₂×Dic₂₃	—	4	4	no	—
28	C₂×Dic₂₃	—	4	8	no	—
29	C₈×C₂₃	C₄⋊C₄	1	8	yes	complemented
30	#1844	—	23	1	no	maximal, Sylow
31	C₂²×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂²×C₂₃	#127	1	1	yes	characteristic
33	C₂²×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
34	C₂²×C₂₃	C₂×SD₁₆	1	4	yes	—
35	C₄×C₂₃	#106	1	8	yes	complemented
36	C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
37	C₄×C₂₃	C₄⋊Q₈	1	2	yes	—
38	Dic₂₃	—	8	4	no	—
39	C₂×#106	—	23	4	no	—
40	C₂×C₄×C₈	D₂₃	1	1	yes	characteristic
41	#384	—	23	2	no	—
42	C₂×C₂₃	#384	1	1	yes	characteristic
43	C₂×C₂₃	C₂×#106	1	2	yes	—
44	C₂×C₂₃	#492	1	2	yes	—
45	C₂×C₂₃	#498	1	2	yes	—
46	C₂²×C₈	C₂×D₂₃	1	2	yes	—
47	C₂×C₄⋊C₄	—	23	4	no	—
48	C₂×C₄⋊C₄	—	46	4	no	—
49	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
50	#106	—	46	8	no	—
51	C₄×C₈	Dic₂₃	1	4	yes	complemented
52	C₂₃	#1844	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₄	—	46	4	no	—
54	C₂²×C₄	D₉₂	1	2	yes	—
55	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
56	C₂×C₈	Dic₄₆	1	4	yes	—
57	C₂×C₈	D₉₂	1	4	yes	—
58	C₂×C₈	C₂×Dic₂₃	1	4	yes	—
59	C₄⋊C₄	—	46	8	no	—
60	C₄⋊C₄	—	92	8	no	—
61	C₄²	Dic₄₆	1	2	yes	—
62	C₄²	C₂×Dic₂₃	1	2	yes	—
63	C₂³	C₂×D₉₂	1	1	yes	characteristic
64	C₂×C₄	—	92	4	no	—
65	C₂×C₄	—	92	8	no	—
66	C₂×C₄	#67263	1	8	yes	—
67	C₂×C₄	C₄⋊Dic₂₃	1	4	yes	—
68	C₂×C₄	C₂×Dic₄₆	1	1	yes	characteristic
69	C₂×C₄	C₂×Dic₄₆	1	2	yes	—
70	C₂×C₄	C₂×D₉₂	1	2	yes	—
71	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
72	C₈	C₄⋊Dic₂₃	1	8	yes	complemented
73	C₂²	#10625040	1	1	yes	characteristic
74	C₂²	#10625045	1	1	yes	characteristic
75	C₂²	C₂×#67263	1	4	yes	—
76	C₂²	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
77	C₄	—	184	4	no	—
78	C₄	#10624999	1	8	yes	complemented
79	C₄	#10625040	1	2	yes	—
80	C₄	C₂×C₄⋊Dic₂₃	1	2	yes	—
81	C₂	#13092287	1	1	yes	characteristic
82	C₂	C₂×#10624999	1	2	yes	—
83	C₂	#13092790	1	2	yes	—
84	C₂	#13092815	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₉₂
commutator	C₂×C₄×C₂₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₃
Fitting	C₂×C₄×C₈×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₂×D₄
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	C₂×C₄×C₈	D₂₃
hypocenter	C₂₃	#1844
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. C₄×C₈×C₂₃	C₄	semidirect
29. C₈×C₂₃	C₄⋊C₄	semidirect
35. C₄×C₂₃	#106	semidirect
51. C₄×C₈	Dic₂₃	semidirect
52. C₂₃	#1844	semidirect
72. C₈	C₄⋊Dic₂₃	semidirect
78. C₄	#10624999	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10624999	2
#13092287	2
C₂×C₄×C₈×C₂₃	2
#1844	23