Subgroups — #15671392

Order 2944.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092675	C₂	1	1	yes	maximal, characteristic
2	C₂₃⋊#338	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#349	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
5	#10625095	—	2	1	no	—
6	C₂×#67267	—	2	1	no	—
7	C₂×Dic₉₂	C₄	1	1	yes	characteristic
8	C₂₃×M₃₂	—	2	1	no	—
9	#10624999	C₄	1	1	yes	characteristic
10	#10624998	—	2	1	no	—
11	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
12	C₂×Dic₄₆	—	2	1	no	—
13	M₁₆×C₂₃	—	4	1	no	—
14	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
16	C₂²⋊Dic₂₃	—	4	1	no	—
17	C₄⋊Dic₂₃	—	2	1	no	—
18	Dic₂₃⋊C₄	—	4	1	no	—
19	#67267	—	4	1	no	—
20	#67267	—	4	1	no	—
21	C₂×C₂₃⋊C₈	—	2	2	no	—
22	Dic₉₂	—	4	1	no	—
23	C₁₆×C₂₃	—	4	1	no	—
24	C₂³×C₂₃	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₂₃	—	2	1	no	—
26	C₂×C₄×C₂₃	—	2	1	no	—
27	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
29	C₂×Dic₂₃	—	4	1	no	—
30	C₂×Dic₂₃	—	4	1	no	—
31	Dic₄₆	—	4	1	no	—
32	Dic₄₆	—	4	1	no	—
33	C₈×C₂₃	—	2	1	no	—
34	C₈×C₂₃	—	2	1	no	—
35	C₂₃⋊C₈	—	4	2	no	—
36	#1342	—	23	1	no	maximal, Sylow
37	C₂²×C₂₃	—	2	1	no	—
38	C₂²×C₂₃	—	4	1	no	—
39	C₂²×C₂₃	#102	1	1	yes	characteristic
40	C₄×C₂₃	—	2	1	no	—
41	C₄×C₂₃	#99	1	1	yes	characteristic
42	C₄×C₂₃	#104	1	1	yes	characteristic
43	Dic₂₃	—	8	1	no	—
44	Dic₂₃	—	8	1	no	—
45	#470	—	23	1	no	—
46	#349	D₂₃	1	1	yes	characteristic
47	#338	—	23	1	no	—
48	C₂×C₂₃	—	2	1	no	—
49	C₂×C₂₃	—	4	1	no	—
50	C₂×C₂₃	#327	1	1	yes	characteristic
51	C₂×Q₁₆	—	23	1	no	—
52	C₂×M₁₆	—	46	1	no	—
53	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic
54	C₂²⋊Q₈	—	46	1	no	—
55	M₃₂	—	2	1	no	—
56	#106	—	23	1	no	—
57	#103	—	46	1	no	—
58	C₂₃	#1342	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	46	1	no	—
60	C₂²×C₄	D₉₂	1	1	yes	characteristic
61	Q₁₆	—	92	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	92	1	no	—
64	M₁₆	—	92	1	no	—
65	C₂×C₈	—	46	2	no	—
66	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
68	C₄⋊C₄	—	46	1	no	—
69	C₄⋊C₄	—	92	1	no	—
70	C₂²⋊C₄	—	92	1	no	—
71	C₁₆	—	4	1	no	—
72	C₂³	#67263	1	1	yes	characteristic
73	Q₈	—	92	1	no	—
74	Q₈	—	92	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	92	1	no	—
78	C₂×C₄	—	92	1	no	—
79	C₂×C₄	D₁₈₄	1	1	yes	characteristic
80	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	92	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#10625003	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	184	1	no	—
89	C₄	—	184	1	no	—
90	C₄	#10624988	1	1	yes	characteristic
91	C₄	#10625007	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#13092152	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092152
commutator	C₂×C₈×C₂₃	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₂₃
Fitting	C₂₃×#349	C₂
socle	C₂×C₂₃	#327
prime radical	C₂³×C₂₃	SD₁₆
cosocle	C₂×M₁₆×C₂₃	C₂²
hypercenter	#349	D₂₃
hypocenter	C₂₃	#1342
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
58. C₂₃	#1342	semidirect

Maximal subgroups

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

subgroup	index
#13092675	2
C₂₃⋊#338	2
C₂₃×#349	2
#1342	23