Subgroups — #31826907

Order 18112.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22583633	C₂	1	1	yes	maximal, characteristic
2	Q₁₆×D₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#22583556	C₂	1	1	yes	maximal, characteristic, complemented
4	#22583555	C₂	1	1	yes	maximal, characteristic, complemented
5	#22583553	C₂	1	1	yes	maximal, characteristic, complemented
6	#22583549	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₃₂×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#17985393	—	2	1	no	—
9	Q₈×D₂₈₃	—	2	1	no	—
10	Dic₁₁₃₂	C₂²	1	1	yes	characteristic
11	#17985382	—	2	1	no	—
12	#17985379	—	2	1	no	—
13	D₂₂₆₄	C₂²	1	1	yes	characteristic
14	C₈×D₂₈₃	C₂²	1	1	yes	characteristic
15	C₂₈₃⋊C₁₆	C₂²	1	1	yes	characteristic
16	Q₁₆×C₂₈₃	C₂²	1	1	yes	characteristic
17	Q₁₆×C₂₈₃	C₂²	1	1	yes	characteristic
18	C₁₆×C₂₈₃	C₂²	1	1	yes	characteristic
19	Dic₅₆₆	—	2	1	no	—
20	Dic₅₆₆	—	4	1	no	—
21	D₁₁₃₂	—	2	1	no	—
22	D₁₁₃₂	—	4	1	no	—
23	C₄×D₂₈₃	—	4	1	no	—
24	C₄×D₂₈₃	—	4	1	no	—
25	C₄×D₂₈₃	D₄	1	1	yes	characteristic
26	C₂₈₃⋊C₈	D₄	1	1	yes	characteristic
27	Q₈×C₂₈₃	—	2	1	no	—
28	Q₈×C₂₈₃	—	2	1	no	—
29	C₈×C₂₈₃	C₂³	1	1	yes	characteristic
30	C₂×D₂₈₃	—	4	1	no	—
31	C₂×D₂₈₃	D₈	1	1	yes	characteristic
32	C₄×C₂₈₃	—	4	1	no	—
33	C₄×C₂₈₃	—	4	1	no	—
34	C₄×C₂₈₃	C₂×D₄	1	1	yes	characteristic
35	Dic₂₈₃	—	4	1	no	—
36	Dic₂₈₃	D₈	1	1	yes	characteristic
37	C₂×C₂₈₃	C₂×D₈	1	1	yes	characteristic
38	D₂₈₃	—	2	1	no	—
39	D₂₈₃	—	8	1	no	—
40	C₂₈₃	#510	1	1	yes	characteristic, complemented, Sylow
41	#510	—	283	1	no	maximal, Sylow
42	#135	—	283	1	no	—
43	C₂×Q₁₆	—	283	1	no	—
44	Q₃₂	—	283	1	no	—
45	Q₃₂	D₂₈₃	1	1	yes	characteristic, complemented
46	SD₃₂	—	283	1	no	—
47	SD₃₂	—	283	1	no	—
48	M₃₂	—	283	1	no	—
49	#41	—	566	1	no	—
50	C₂×Q₈	—	566	1	no	—
51	Q₁₆	—	283	1	no	—
52	Q₁₆	—	566	1	no	—
53	Q₁₆	C₂×D₂₈₃	1	1	yes	characteristic
54	Q₁₆	C₂×D₂₈₃	1	1	yes	characteristic
55	SD₁₆	—	566	1	no	—
56	D₈	—	283	1	no	—
57	C₂×C₈	—	283	1	no	—
58	C₁₆	—	283	1	no	—
59	C₁₆	C₂×D₂₈₃	1	1	yes	characteristic
60	Q₈	—	2	1	no	—
61	Q₈	—	2	1	no	—
62	Q₈	—	566	1	no	—
63	Q₈	—	1132	1	no	—
64	D₄	—	566	1	no	—
65	D₄	—	1132	1	no	—
66	C₂×C₄	—	283	1	no	—
67	C₂×C₄	—	1132	1	no	—
68	C₂×C₄	—	1132	1	no	—
69	C₈	—	283	1	no	—
70	C₈	C₂²×D₂₈₃	1	1	yes	characteristic
71	C₂²	—	283	1	no	—
72	C₂²	—	1132	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	4	1	no	—
75	C₄	—	283	1	no	—
76	C₄	—	1132	1	no	—
77	C₄	D₄×D₂₈₃	1	1	yes	characteristic
78	C₂	—	566	1	no	—
79	C₂	—	2264	1	no	—
80	C₂	D₈×D₂₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₂₈₃
commutator, cosocle	C₈×C₂₈₃	C₂³
Frattini	C₈	C₂²×D₂₈₃
Fitting	Q₃₂×C₂₈₃	C₂
socle	C₂×C₂₈₃	C₂×D₈
prime radical	#22583633	C₂
hypercenter	Q₃₂	D₂₈₃
hypocenter	C₂₈₃	#510
LCS	G ▷ C₈×C₂₈₃ ▷ C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Q₁₆×D₂₈₃	C₂	semidirect
3. #22583556	C₂	semidirect
4. #22583555	C₂	semidirect
5. #22583553	C₂	semidirect
6. #22583549	C₂	semidirect
7. Q₃₂×C₂₈₃	C₂	semidirect
40. C₂₈₃	#510	semidirect
45. Q₃₂	D₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
#22583633	2
Q₁₆×D₂₈₃	2
#22583556	2
#22583555	2
#22583553	2
#22583549	2
Q₃₂×C₂₈₃	2
#510	283