Subgroups — #15675269

Order 2944.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₈₄	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₉₂	C₂	1	2	yes	maximal
3	#13092245	C₂	1	1	yes	maximal, characteristic
4	#13092222	C₂	1	2	yes	maximal
5	C₂₃×#346	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₂	C₂²	1	2	yes	—
7	C₄×Dic₄₆	—	2	2	no	—
8	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
11	#10625000	C₂²	1	2	yes	—
12	#10624998	—	2	2	no	—
13	Dic₁₈₄	C₄	1	4	yes	complemented
14	C₂×Dic₄₆	—	2	2	no	—
15	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
17	C₄²×C₂₃	D₄	1	1	yes	characteristic
18	C₄⋊Dic₂₃	—	2	2	no	—
19	Dic₂₃⋊C₄	—	4	2	no	—
20	C₄×Dic₂₃	—	4	2	no	—
21	Dic₉₂	—	2	2	no	—
22	Dic₉₂	C₂×C₄	1	4	yes	—
23	C₁₆×C₂₃	—	2	1	no	—
24	C₁₆×C₂₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₂₃	D₈	1	2	yes	—
26	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₂₃	—	4	2	no	—
28	C₂×Dic₂₃	—	4	2	no	—
29	Dic₄₆	—	2	4	no	—
30	Dic₄₆	—	4	2	no	—
31	C₈×C₂₃	—	2	1	no	—
32	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₂₃	#41	1	1	yes	characteristic
34	#2176	—	23	1	no	maximal, Sylow
35	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
36	C₄×C₂₃	—	2	2	no	—
37	C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
38	C₄×C₂₃	#135	1	1	yes	characteristic
39	Dic₂₃	—	4	4	no	—
40	Dic₂₃	—	8	2	no	—
41	C₂×Q₃₂	—	23	1	no	—
42	C₄×Q₁₆	—	23	2	no	—
43	#367	—	23	1	no	—
44	#358	—	23	2	no	—
45	#346	D₂₃	1	1	yes	characteristic
46	C₂×C₂₃	C₄×D₈	1	1	yes	characteristic
47	C₂×C₂₃	#510	1	2	yes	—
48	C₂×Q₁₆	—	23	2	no	—
49	C₄×Q₈	—	46	2	no	—
50	Q₃₂	—	23	4	no	—
51	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
52	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
53	#107	—	23	2	no	—
54	#103	—	46	2	no	—
55	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
56	C₂₃	#2176	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	46	2	no	—
58	Q₁₆	—	23	4	no	—
59	Q₁₆	—	46	2	no	—
60	C₂×C₈	D₉₂	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
62	C₄⋊C₄	—	46	2	no	—
63	C₄⋊C₄	—	92	2	no	—
64	C₄²	—	92	2	no	—
65	C₄²	D₉₂	1	1	yes	characteristic
66	C₁₆	—	2	1	no	—
67	C₁₆	C₄×D₂₃	1	2	yes	—
68	Q₈	—	46	4	no	—
69	Q₈	—	92	2	no	—
70	C₂×C₄	—	92	2	no	—
71	C₂×C₄	—	92	2	no	—
72	C₂×C₄	D₁₈₄	1	2	yes	—
73	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	C₂×C₄×D₂₃	1	1	yes	characteristic
76	C₈	#67288	1	1	yes	characteristic
77	C₂²	C₂×D₁₈₄	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	92	4	no	—
80	C₄	—	184	2	no	—
81	C₄	C₄×D₉₂	1	1	yes	characteristic
82	C₄	#10625075	1	1	yes	characteristic
83	C₂	C₄×D₁₈₄	1	1	yes	characteristic
84	C₂	#13092860	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₈₄
commutator	C₈×C₂₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂₃×#346	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₈
cosocle	C₂×C₈×C₂₃	C₂³
hypercenter	#346	D₂₃
hypocenter	C₂₃	#2176
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
13. Dic₁₈₄	C₄	semidirect
56. C₂₃	#2176	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₈₄	2
C₄×Dic₉₂	2
#13092245	2
#13092222	2
C₂₃×#346	2
#2176	23