Subgroups — #15675284

Order 2944.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092849	C₂	1	1	yes	maximal, characteristic
2	#13092535	C₂	1	2	yes	maximal, complemented
3	#13092247	C₂	1	1	yes	maximal, characteristic, complemented
4	#13092225	C₂	1	2	yes	maximal, complemented
5	C₂₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	#10625075	C₂²	1	2	yes	—
7	#10625072	—	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	#10625001	C₂²	1	2	yes	—
12	#10624987	—	2	2	no	—
13	Dic₁₈₄	C₄	1	1	yes	characteristic, complemented
14	#10624982	C₄	1	2	yes	complemented
15	D₃₆₈	C₄	1	1	yes	characteristic, complemented
16	#67288	—	2	2	no	—
17	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
19	C₄²×C₂₃	D₄	1	1	yes	characteristic
20	#67267	—	2	2	no	—
21	Dic₉₂	C₂×C₄	1	2	yes	—
22	D₁₈₄	C₂×C₄	1	2	yes	—
23	#67263	—	2	2	no	—
24	#67262	—	4	2	no	—
25	C₈×D₂₃	—	4	2	no	—
26	C₁₆×C₂₃	—	2	1	no	—
27	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₃	—	2	1	no	—
30	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₂₃	—	4	2	no	—
32	D₉₂	—	2	2	no	—
33	C₄×D₂₃	—	4	2	no	—
34	Dic₄₆	—	2	2	no	—
35	C₈×C₂₃	D₈	1	2	yes	—
36	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₂₃	#41	1	1	yes	characteristic
38	C₂₃⋊C₈	—	4	2	no	—
39	#2179	—	23	1	no	maximal, Sylow
40	C₂²×C₂₃	#135	1	1	yes	characteristic
41	C₂×D₂₃	—	4	2	no	—
42	C₄×C₂₃	—	4	1	no	—
43	C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
44	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
45	Dic₂₃	—	4	2	no	—
46	#508	—	23	1	no	—
47	#443	—	23	2	no	—
48	#368	—	23	1	no	—
49	#359	—	23	2	no	—
50	#346	D₂₃	1	1	yes	characteristic, complemented
51	C₂×C₂₃	—	2	1	no	—
52	C₂×C₂₃	C₄×D₈	1	1	yes	characteristic
53	D₂₃	—	8	2	no	—
54	#135	—	23	2	no	—
55	#131	—	46	2	no	—
56	Q₃₂	—	23	1	no	—
57	SD₃₂	—	23	2	no	—
58	D₁₆	—	23	1	no	—
59	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
60	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
61	#108	—	23	2	no	—
62	#104	—	46	2	no	—
63	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
64	C₂₃	#2179	1	1	yes	characteristic, complemented, Sylow
65	#41	—	46	2	no	—
66	Q₁₆	—	23	2	no	—
67	SD₁₆	—	46	2	no	—
68	D₈	—	23	2	no	—
69	M₁₆	—	46	2	no	—
70	M₁₆	—	92	2	no	—
71	C₂×C₈	—	92	2	no	—
72	C₂×C₈	D₉₂	1	1	yes	characteristic
73	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
74	C₄²	D₉₂	1	1	yes	characteristic
75	C₁₆	—	2	1	no	—
76	C₁₆	C₄×D₂₃	1	1	yes	characteristic
77	C₁₆	C₄×D₂₃	1	1	yes	characteristic
78	Q₈	—	46	2	no	—
79	D₄	—	46	2	no	—
80	D₄	—	92	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	92	2	no	—
83	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
84	C₈	—	92	2	no	—
85	C₈	D₁₈₄	1	2	yes	—
86	C₈	C₂×C₄×D₂₃	1	1	yes	characteristic
87	C₈	#67288	1	1	yes	characteristic
88	C₂²	—	92	2	no	—
89	C₂²	#10625075	1	1	yes	characteristic
90	C₄	—	4	1	no	—
91	C₄	—	92	2	no	—
92	C₄	C₄×D₉₂	1	1	yes	characteristic
93	C₄	C₂×D₁₈₄	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	184	2	no	—
96	C₂	C₄×D₁₈₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₁₈₄
commutator	C₈×C₂₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂₃×#346	C₂
socle	C₂×C₂₃	C₄×D₈
prime radical	#13092849	C₂
cosocle	C₂×C₈×C₂₃	C₂³
hypercenter	#346	D₂₃
hypocenter	C₂₃	#2179
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #13092535	C₂	semidirect
3. #13092247	C₂	semidirect
4. #13092225	C₂	semidirect
5. C₂₃×#346	C₂	semidirect
13. Dic₁₈₄	C₄	semidirect
14. #10624982	C₄	semidirect
15. D₃₆₈	C₄	semidirect
50. #346	D₂₃	semidirect
64. C₂₃	#2179	semidirect

Maximal subgroups

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

subgroup	index
#13092849	2
#13092535	2
#13092247	2
#13092225	2
C₂₃×#346	2
#2179	23