Subgroups — #15673031

Order 2944.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092813	C₂	1	2	yes	maximal
2	#13092797	C₂	1	1	yes	maximal, characteristic
3	#13092767	C₂	1	2	yes	maximal
4	#13092138	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#498	C₂	1	1	yes	maximal, characteristic
6	C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×Dic₉₂	—	2	2	no	—
8	#10625040	C₂²	1	1	yes	characteristic
9	#10625040	C₂²	1	1	yes	characteristic
10	C₂₃×#106	—	2	2	no	—
11	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	#10625017	—	2	4	no	—
13	#10624990	—	2	4	no	—
14	C₄×C₂₃⋊C₈	C₂²	1	2	yes	—
15	C₂×Q₈×C₂₃	—	2	2	no	—
16	C₂×Dic₄₆	—	2	1	no	—
17	C₂×Dic₄₆	—	2	1	no	—
18	C₂×C₈×C₂₃	D₄	1	2	yes	—
19	C₄⋊C₄×C₂₃	—	2	2	no	—
20	C₄⋊C₄×C₂₃	—	2	2	no	—
21	C₄²×C₂₃	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₂₃	—	2	2	no	—
23	C₄⋊Dic₂₃	—	2	2	no	—
24	C₂×C₂₃⋊C₈	D₄	1	4	yes	—
25	Dic₉₂	—	4	4	no	—
26	Q₈×C₂₃	—	4	4	no	—
27	C₂×C₄×C₂₃	—	4	2	no	—
28	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
29	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₂₃	—	4	1	no	—
31	C₂×Dic₂₃	—	4	1	no	—
32	Dic₄₆	—	4	2	no	—
33	Dic₄₆	—	4	2	no	—
34	C₈×C₂₃	SD₁₆	1	4	yes	—
35	C₂₃⋊C₈	—	2	4	no	—
36	#1716	—	23	1	no	maximal, Sylow
37	C₂²×C₂₃	#127	1	1	yes	characteristic
38	C₄×C₂₃	—	8	2	no	—
39	C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
40	C₄×C₂₃	#137	1	4	yes	—
41	Dic₂₃	—	8	1	no	—
42	Dic₂₃	—	8	1	no	—
43	#498	—	23	2	no	—
44	#498	D₂₃	1	1	yes	characteristic
45	#494	—	23	1	no	—
46	#487	—	23	2	no	—
47	#322	—	23	1	no	—
48	C₂×C₂₃	#492	1	1	yes	characteristic
49	C₂×C₂₃	#497	1	2	yes	—
50	C₂×Q₁₆	—	46	2	no	—
51	C₄⋊Q₈	—	23	1	no	—
52	C₄⋊Q₈	—	23	1	no	—
53	C₄⋊Q₈	C₂×D₂₃	1	2	yes	—
54	#106	—	2	2	no	—
55	#106	—	46	4	no	—
56	#103	—	46	4	no	—
57	C₄×C₈	—	23	2	no	—
58	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
59	C₂₃	#1716	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	2	2	no	—
61	C₂×Q₈	—	46	1	no	—
62	C₂×Q₈	—	46	1	no	—
63	Q₁₆	—	92	4	no	—
64	C₂×C₈	—	23	4	no	—
65	C₂×C₈	C₂²⋊D₂₃	1	2	yes	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	46	2	no	—
69	C₄⋊C₄	—	46	2	no	—
70	C₄²	C₂²×D₂₃	1	1	yes	characteristic
71	Q₈	—	4	4	no	—
72	Q₈	—	92	2	no	—
73	Q₈	—	92	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	92	1	no	—
76	C₂×C₄	—	92	1	no	—
77	C₂×C₄	D₄×D₂₃	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
79	C₈	—	46	4	no	—
80	C₈	#67274	1	4	yes	—
81	C₂²	#10625111	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	184	1	no	—
84	C₄	—	184	1	no	—
85	C₄	#10625086	1	4	yes	—
86	C₄	C₂×#67274	1	2	yes	—
87	C₂	#13092791	1	1	yes	characteristic
88	C₂	#13092808	1	2	yes	—

	subgroup	G/H
center	C₂²	#10625111
commutator, cosocle	C₄²×C₂₃	C₂³
Frattini	C₄²	C₂²×D₂₃
Fitting	C₂₃×#498	C₂
socle, prime radical	C₂²×C₂₃	#127
hypercenter	#498	D₂₃
hypocenter	C₂₃	#1716
LCS	G ▷ C₄²×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

Complements

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

N	H ≅ G/N	type
59. C₂₃	#1716	semidirect

Maximal subgroups

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

subgroup	index
#13092813	2
#13092797	2
#13092767	2
#13092138	2
C₂₃×#498	2
#1716	23