Subgroups — #31823581

Order 17984.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582901	C₂	1	1	yes	maximal, characteristic
2	#22582885	C₂	1	2	yes	maximal, complemented
3	#22582815	C₂	1	1	yes	maximal, characteristic, complemented
4	#22582807	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#17985138	C₂²	1	2	yes	—
7	Dic₁₁₂₄	C₄	1	1	yes	characteristic, complemented
8	#17985127	C₄	1	2	yes	complemented
9	D₂₂₄₈	C₄	1	1	yes	characteristic, complemented
10	#17985122	C₂²	1	2	yes	—
11	#17985121	—	2	2	no	—
12	C₈×D₂₈₁	—	2	2	no	—
13	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
15	C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
16	Dic₅₆₂	C₂×C₄	1	2	yes	—
17	D₁₁₂₄	C₂×C₄	1	2	yes	—
18	C₂²⋊D₂₈₁	—	2	2	no	—
19	C₄×D₂₈₁	—	2	2	no	—
20	#14555886	—	2	2	no	—
21	C₂×C₄×C₂₈₁	—	2	1	no	—
22	C₂×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
23	C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
24	C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
25	C₈×C₂₈₁	D₄	1	1	yes	characteristic
26	C₈×C₂₈₁	D₄	1	1	yes	characteristic
27	C₂²×C₂₈₁	#41	1	1	yes	characteristic
28	C₂×D₂₈₁	—	2	2	no	—
29	C₄×C₂₈₁	—	2	2	no	—
30	C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
32	Dic₂₈₁	—	2	2	no	—
33	C₂×C₂₈₁	—	2	1	no	—
34	C₂×C₂₈₁	C₄×D₄	1	1	yes	characteristic
35	D₂₈₁	—	4	2	no	—
36	C₂₈₁	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	281	1	no	maximal, Sylow
38	#135	—	281	1	no	—
39	#131	—	281	2	no	—
40	#108	—	281	1	no	—
41	#104	—	281	2	no	—
42	C₄×C₈	D₂₈₁	1	1	yes	characteristic, complemented
43	#41	—	281	2	no	—
44	Q₁₆	—	281	1	no	—
45	SD₁₆	—	281	2	no	—
46	D₈	—	281	1	no	—
47	M₁₆	—	281	2	no	—
48	M₁₆	—	562	2	no	—
49	C₂×C₈	—	562	2	no	—
50	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
51	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
52	C₄²	C₂×D₂₈₁	1	1	yes	characteristic
53	Q₈	—	281	2	no	—
54	D₄	—	281	2	no	—
55	D₄	—	562	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	562	2	no	—
58	C₂×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
59	C₈	—	562	2	no	—
60	C₈	C₄×D₂₈₁	1	1	yes	characteristic
61	C₈	C₄×D₂₈₁	1	1	yes	characteristic
62	C₈	D₁₁₂₄	1	1	yes	characteristic
63	C₈	D₁₁₂₄	1	1	yes	characteristic
64	C₂²	—	562	2	no	—
65	C₂²	#17985138	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	562	2	no	—
68	C₄	C₂×C₄×D₂₈₁	1	1	yes	characteristic
69	C₄	C₂×D₁₁₂₄	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	1124	2	no	—
72	C₂	C₄×D₁₁₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₁₁₂₄
commutator	C₄×C₂₈₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₈₁
Fitting	C₄×C₈×C₂₈₁	C₂
socle	C₂×C₂₈₁	C₄×D₄
prime radical	#22582901	C₂
cosocle	C₂×C₄×C₂₈₁	C₂³
hypercenter	C₄×C₈	D₂₈₁
hypocenter	C₂₈₁	#443
LCS	G ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #22582885	C₂	semidirect
3. #22582815	C₂	semidirect
4. #22582807	C₂	semidirect
5. C₄×C₈×C₂₈₁	C₂	semidirect
7. Dic₁₁₂₄	C₄	semidirect
8. #17985127	C₄	semidirect
9. D₂₂₄₈	C₄	semidirect
36. C₂₈₁	#443	semidirect
42. C₄×C₈	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#22582901	2
#22582885	2
#22582815	2
#22582807	2
C₄×C₈×C₂₈₁	2
#443	281