Subgroups — #13092540

Order 1472.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625075	C₂	1	1	yes	maximal, characteristic
2	#10625072	C₂	1	2	yes	maximal, complemented
3	C₂₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625001	C₂	1	1	yes	maximal, characteristic, complemented
5	#10624987	C₂	1	2	yes	maximal, complemented
6	#67288	C₂²	1	2	yes	—
7	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₄²×C₂₃	C₂²	1	1	yes	characteristic
10	#67267	C₂²	1	2	yes	—
11	Dic₉₂	C₄	1	1	yes	characteristic, complemented
12	D₁₈₄	C₄	1	1	yes	characteristic, complemented
13	#67263	C₄	1	2	yes	complemented
14	#67262	—	2	2	no	—
15	C₈×D₂₃	—	2	2	no	—
16	C₂×C₄×C₂₃	—	2	1	no	—
17	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
18	C₂²⋊D₂₃	—	2	2	no	—
19	D₉₂	C₂×C₄	1	2	yes	—
20	C₄×D₂₃	—	2	2	no	—
21	Dic₄₆	C₂×C₄	1	2	yes	—
22	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
23	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
24	C₈×C₂₃	D₄	1	2	yes	—
25	C₂₃⋊C₈	—	2	2	no	—
26	C₂²×C₂₃	#41	1	1	yes	characteristic
27	C₂×D₂₃	—	2	2	no	—
28	C₄×C₂₃	—	4	1	no	—
29	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
31	Dic₂₃	—	2	2	no	—
32	#444	—	23	1	no	maximal, Sylow
33	C₂×C₂₃	—	2	1	no	—
34	C₂×C₂₃	C₄×D₄	1	1	yes	characteristic
35	D₂₃	—	4	2	no	—
36	#135	—	23	1	no	—
37	#131	—	23	2	no	—
38	#108	—	23	1	no	—
39	#104	—	23	2	no	—
40	#97	D₂₃	1	1	yes	characteristic, complemented
41	C₂₃	#444	1	1	yes	characteristic, complemented, Sylow
42	#41	—	23	2	no	—
43	Q₁₆	—	23	1	no	—
44	SD₁₆	—	23	2	no	—
45	D₈	—	23	1	no	—
46	M₁₆	—	23	2	no	—
47	M₁₆	—	46	2	no	—
48	C₂×C₈	—	46	2	no	—
49	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
50	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
51	C₄²	C₂×D₂₃	1	1	yes	characteristic
52	Q₈	—	23	2	no	—
53	D₄	—	23	2	no	—
54	D₄	—	46	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	46	2	no	—
57	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
58	C₈	—	46	2	no	—
59	C₈	C₄×D₂₃	1	1	yes	characteristic
60	C₈	C₄×D₂₃	1	1	yes	characteristic
61	C₈	D₉₂	1	2	yes	—
62	C₂²	—	46	2	no	—
63	C₂²	#67288	1	1	yes	characteristic
64	C₄	—	4	1	no	—
65	C₄	—	46	2	no	—
66	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
67	C₄	C₂×D₉₂	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	92	2	no	—
70	C₂	C₄×D₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₉₂
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#97	C₂
socle	C₂×C₂₃	C₄×D₄
prime radical	#10625075	C₂
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#97	D₂₃
hypocenter	C₂₃	#444
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

Complements

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

N	H ≅ G/N	type
2. #10625072	C₂	semidirect
3. C₂₃×#97	C₂	semidirect
4. #10625001	C₂	semidirect
5. #10624987	C₂	semidirect
11. Dic₉₂	C₄	semidirect
12. D₁₈₄	C₄	semidirect
13. #67263	C₄	semidirect
40. #97	D₂₃	semidirect
41. C₂₃	#444	semidirect

Maximal subgroups

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

subgroup	index
#10625075	2
#10625072	2
C₂₃×#97	2
#10625001	2
#10624987	2
#444	23