Subgroups — #15675648

Order 2944.

176 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	C₂×#10625011	C₂	1	2	yes	maximal
3	#13092795	C₂	1	2	yes	maximal
4	C₁₆×Dic₂₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₂₃	C₂²	1	2	yes	—
7	#10625115	—	2	2	no	—
8	C₂×#67275	—	2	2	no	—
9	C₂×Dic₉₂	C₂²	1	2	yes	—
10	C₂₃×Q₃₂	—	2	2	no	—
11	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	#10625011	—	2	4	no	—
13	C₈×Dic₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃⋊C₁₆	C₂²	1	1	yes	characteristic
15	Dic₁₈₄	—	2	2	no	—
16	C₂×Q₈×C₂₃	—	2	2	no	—
17	C₂×Dic₄₆	—	2	2	no	—
18	Q₁₆×C₂₃	—	2	2	no	—
19	Q₁₆×C₂₃	—	2	2	no	—
20	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
21	#67275	—	4	4	no	—
22	Dic₂₃⋊C₄	—	4	4	no	—
23	C₄×Dic₂₃	D₄	1	1	yes	characteristic
24	C₂×C₂₃⋊C₈	D₄	1	1	yes	characteristic
25	Dic₉₂	—	2	2	no	—
26	Dic₉₂	—	2	2	no	—
27	C₁₆×C₂₃	D₄	1	2	yes	—
28	C₂₃⋊C₁₆	D₄	1	2	yes	—
29	Q₈×C₂₃	—	4	2	no	—
30	Q₈×C₂₃	—	4	2	no	—
31	C₂×C₄×C₂₃	—	4	2	no	—
32	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₂₃	—	4	2	no	—
34	C₂×Dic₂₃	D₈	1	2	yes	—
35	Dic₄₆	—	4	2	no	—
36	Dic₄₆	—	4	2	no	—
37	C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
38	C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
39	C₂₃⋊C₈	D₈	1	2	yes	—
40	#2247	—	23	1	no	maximal, Sylow
41	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
42	C₄×C₂₃	—	8	2	no	—
43	C₄×C₂₃	#127	1	1	yes	characteristic
44	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
45	Dic₂₃	—	8	2	no	—
46	Dic₂₃	Q₃₂	1	4	yes	complemented
47	C₂×Q₃₂	—	23	2	no	—
48	C₂×Q₃₂	—	23	1	no	—
49	C₂×Q₃₂	D₂₃	1	1	yes	characteristic
50	#494	—	23	2	no	—
51	C₄×C₁₆	—	23	1	no	—
52	C₂×C₂₃	#493	1	1	yes	characteristic
53	C₂×C₂₃	C₂×Q₃₂	1	2	yes	—
54	C₂×Q₁₆	—	23	2	no	—
55	C₂×Q₁₆	—	46	2	no	—
56	C₂×Q₁₆	C₂×D₂₃	1	2	yes	—
57	C₄⋊Q₈	—	46	2	no	—
58	Q₃₂	—	2	2	no	—
59	Q₃₂	—	46	4	no	—
60	Q₃₂	—	46	2	no	—
61	C₂×C₁₆	—	23	1	no	—
62	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
63	C₄×C₈	—	23	1	no	—
64	C₂₃	#2247	1	1	yes	characteristic, complemented, Sylow
65	C₂×Q₈	—	2	2	no	—
66	C₂×Q₈	—	46	2	no	—
67	Q₁₆	—	2	2	no	—
68	Q₁₆	—	2	2	no	—
69	Q₁₆	—	46	2	no	—
70	Q₁₆	—	46	2	no	—
71	Q₁₆	—	92	4	no	—
72	C₂×C₈	—	23	1	no	—
73	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
74	C₄⋊C₄	—	92	4	no	—
75	C₄²	—	23	1	no	—
76	C₁₆	—	23	2	no	—
77	C₁₆	C₂²⋊D₂₃	1	2	yes	—
78	Q₈	—	4	2	no	—
79	Q₈	—	4	2	no	—
80	Q₈	—	92	2	no	—
81	Q₈	—	92	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	23	2	no	—
84	C₂×C₄	—	92	2	no	—
85	C₂×C₄	D₄×D₂₃	1	1	yes	characteristic
86	C₈	—	23	2	no	—
87	C₈	D₄×D₂₃	1	1	yes	characteristic
88	C₈	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
89	C₂²	D₈×D₂₃	1	1	yes	characteristic
90	C₄	—	8	2	no	—
91	C₄	—	23	4	no	—
92	C₄	—	184	2	no	—
93	C₄	D₈×D₂₃	1	1	yes	characteristic
94	C₄	#10625111	1	1	yes	characteristic
95	C₂	#13092792	1	1	yes	characteristic
96	C₂	Q₃₂×D₂₃	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₂₃
commutator, cosocle	C₂×C₈×C₂₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂×C₂₃×Q₃₂	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₈
hypercenter	C₂×Q₃₂	D₂₃
hypocenter	C₂₃	#2247
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
46. Dic₂₃	Q₃₂	semidirect
64. C₂₃	#2247	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
C₂×#10625011	2
#13092795	2
C₁₆×Dic₂₃	2
C₂×C₂₃×Q₃₂	2
#2247	23