Subgroups — #15671374

Order 2944.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092535	C₂	1	1	yes	maximal, characteristic
2	#13092238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625075	C₄	1	1	yes	characteristic
5	#10625072	—	2	1	no	—
6	C₄×C₈×C₂₃	—	2	1	no	—
7	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	#10625001	C₄	1	1	yes	characteristic
9	#10624994	—	2	1	no	—
10	#10624987	—	2	1	no	—
11	#67288	—	2	1	no	—
12	C₂×C₈×C₂₃	—	2	2	no	—
13	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
15	C₄²×C₂₃	D₄	1	1	yes	characteristic
16	#67267	—	2	1	no	—
17	Dic₉₂	C₈	1	1	yes	characteristic, complemented
18	D₁₈₄	C₈	1	1	yes	characteristic, complemented
19	#67263	—	2	1	no	—
20	#67262	—	4	1	no	—
21	C₈×D₂₃	—	4	1	no	—
22	C₂₃⋊C₁₆	—	4	1	no	—
23	C₂×C₄×C₂₃	—	2	1	no	—
24	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₂₃	—	4	1	no	—
26	D₉₂	—	2	1	no	—
27	C₄×D₂₃	—	4	1	no	—
28	Dic₄₆	—	2	1	no	—
29	C₈×C₂₃	—	4	2	no	—
30	C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
31	C₈×C₂₃	M₁₆	1	1	yes	characteristic
32	C₈×C₂₃	D₈	1	1	yes	characteristic
33	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
34	C₂₃⋊C₈	—	4	1	no	—
35	#1336	—	23	1	no	maximal, Sylow
36	C₂²×C₂₃	#104	1	1	yes	characteristic
37	C₂×D₂₃	—	4	1	no	—
38	C₄×C₂₃	—	2	2	no	—
39	C₄×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₂₃	#102	1	1	yes	characteristic
41	Dic₂₃	—	4	1	no	—
42	#443	—	23	1	no	—
43	#364	—	23	1	no	—
44	#322	D₂₃	1	1	yes	characteristic, complemented
45	C₂×C₂₃	—	2	1	no	—
46	C₂×C₂₃	D₄⋊C₈	1	1	yes	characteristic
47	D₂₃	—	8	1	no	—
48	#135	—	23	1	no	—
49	#131	—	46	1	no	—
50	M₃₂	—	46	1	no	—
51	#108	—	23	1	no	—
52	#104	—	46	1	no	—
53	C₄×C₈	—	2	1	no	—
54	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
55	C₂₃	#1336	1	1	yes	characteristic, complemented, Sylow
56	#41	—	46	1	no	—
57	Q₁₆	—	23	1	no	—
58	SD₁₆	—	46	1	no	—
59	D₈	—	23	1	no	—
60	M₁₆	—	46	1	no	—
61	M₁₆	—	92	1	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	92	1	no	—
64	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
65	C₂×C₈	D₉₂	1	1	yes	characteristic
66	C₄²	C₂²⋊D₂₃	1	1	yes	characteristic
67	C₁₆	—	92	1	no	—
68	Q₈	—	46	1	no	—
69	D₄	—	46	1	no	—
70	D₄	—	92	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	92	1	no	—
73	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	92	1	no	—
76	C₈	C₈×D₂₃	1	1	yes	characteristic
77	C₈	#67262	1	1	yes	characteristic
78	C₈	#67263	1	1	yes	characteristic
79	C₈	D₁₈₄	1	1	yes	characteristic
80	C₂²	—	92	1	no	—
81	C₂²	#10624987	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	92	1	no	—
84	C₄	(C₂×D₂₃)⋊C₈	1	1	yes	characteristic
85	C₄	#10625003	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	184	1	no	—
88	C₂	#13092146	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10625003
commutator	C₈×C₂₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₃
Fitting	C₂₃×#322	C₂
socle	C₂×C₂₃	D₄⋊C₈
prime radical	#10625075	C₄
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	#322	D₂₃
hypocenter	C₂₃	#1336
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #322

Complements

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

N	H ≅ G/N	type
2. #13092238	C₂	semidirect
3. C₂₃×#322	C₂	semidirect
17. Dic₉₂	C₈	semidirect
18. D₁₈₄	C₈	semidirect
44. #322	D₂₃	semidirect
55. C₂₃	#1336	semidirect

Maximal subgroups

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

subgroup	index
#13092535	2
#13092238	2
C₂₃×#322	2
#1336	23