Subgroups — #15671444

Order 2944.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092794	C₂	1	1	yes	maximal, characteristic
2	#13092170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₈₄	—	2	1	no	—
5	C₂×D₁₈₄	C₄	1	2	yes	—
6	#10625045	—	2	1	no	—
7	C₂×C₁₆×C₂₃	—	2	1	no	—
8	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₄⋊(C₂₃⋊C₈)	—	2	1	no	—
10	C₂×D₉₂	—	2	2	no	—
11	C₂×D₉₂	—	4	1	no	—
12	C₂×D₉₂	—	4	1	no	—
13	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
15	C₄²×C₂₃	D₄	1	1	yes	characteristic
16	C₂×C₂₃⋊C₈	—	4	1	no	—
17	D₁₈₄	—	4	2	no	—
18	D₁₈₄	—	4	1	no	—
19	D₁₈₄	—	4	1	no	—
20	C₁₆×C₂₃	—	4	1	no	—
21	C₂²×D₂₃	—	4	2	no	—
22	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
24	C₂×C₄×C₂₃	SD₁₆	1	1	yes	characteristic
25	D₉₂	—	4	2	no	—
26	D₉₂	—	4	2	no	—
27	D₉₂	—	8	2	no	—
28	D₉₂	—	8	1	no	—
29	D₉₂	—	8	1	no	—
30	C₈×C₂₃	—	2	1	no	—
31	C₈×C₂₃	D₈	1	1	yes	characteristic
32	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
33	C₂₃⋊C₈	—	8	1	no	—
34	#1361	—	23	1	no	maximal, Sylow
35	C₂²×C₂₃	#102	1	1	yes	characteristic
36	C₂×D₂₃	—	8	2	no	—
37	C₂×D₂₃	—	8	2	no	—
38	C₂×D₂₃	—	8	2	no	—
39	C₄×C₂₃	—	2	1	no	—
40	C₄×C₂₃	#100	1	1	yes	characteristic
41	C₄×C₂₃	#102	1	1	yes	characteristic
42	C₄×C₂₃	D₁₆	1	1	yes	characteristic
43	C₄×C₂₃	SD₃₂	1	1	yes	characteristic
44	#493	—	23	1	no	—
45	C₄⋊C₁₆	D₂₃	1	1	yes	characteristic, complemented
46	#335	—	23	1	no	—
47	C₂×C₂₃	#331	1	1	yes	characteristic
48	C₂×C₂₃	#357	1	1	yes	characteristic
49	C₂×C₂₃	#361	1	1	yes	characteristic
50	D₂₃	—	16	2	no	—
51	C₂×D₈	—	23	2	no	—
52	C₂×D₈	—	46	1	no	—
53	#127	—	46	1	no	—
54	C₂×C₁₆	—	2	1	no	—
55	C₄⋊C₈	—	46	1	no	—
56	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
57	C₂₃	#1361	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₄	—	46	2	no	—
59	C₂×D₄	—	92	1	no	—
60	C₂×D₄	—	92	1	no	—
61	D₈	—	92	2	no	—
62	D₈	—	92	1	no	—
63	D₈	—	92	1	no	—
64	C₂×C₈	—	92	1	no	—
65	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
67	C₄²	D₉₂	1	1	yes	characteristic
68	C₁₆	—	4	1	no	—
69	C₂³	—	92	2	no	—
70	D₄	—	92	2	no	—
71	D₄	—	92	2	no	—
72	D₄	—	184	2	no	—
73	D₄	—	184	1	no	—
74	D₄	—	184	1	no	—
75	C₂×C₄	#67263	1	1	yes	characteristic
76	C₂×C₄	D₁₈₄	1	1	yes	characteristic
77	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	184	1	no	—
80	C₈	#67272	1	1	yes	characteristic
81	C₈	#67274	1	1	yes	characteristic
82	C₂²	—	184	2	no	—
83	C₂²	—	184	2	no	—
84	C₂²	—	184	2	no	—
85	C₂²	#10625003	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	D₃₆₈	1	1	yes	characteristic
88	C₄	#10624982	1	1	yes	characteristic
89	C₄	#10624991	1	1	yes	characteristic
90	C₄	#10625005	1	1	yes	characteristic
91	C₂	—	368	2	no	—
92	C₂	#13092160	1	1	yes	characteristic
93	C₂	#13092219	1	1	yes	characteristic
94	C₂	#13092231	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10625003
commutator	C₂×C₈×C₂₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₃
Fitting	C₂₃×C₄⋊C₁₆	C₂
socle	C₂²×C₂₃	#102
prime radical	#13092794	C₂
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	C₄⋊C₁₆	D₂₃
hypocenter	C₂₃	#1361
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. #13092170	C₂	semidirect
3. C₂₃×C₄⋊C₁₆	C₂	semidirect
45. C₄⋊C₁₆	D₂₃	semidirect
57. C₂₃	#1361	semidirect

Maximal subgroups

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

subgroup	index
#13092794	2
#13092170	2
C₂₃×C₄⋊C₁₆	2
#1361	23