Subgroups — #49093488

Order 35968.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823895	C₂	1	1	yes	maximal, characteristic
2	#31823293	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#22582901	—	2	1	no	—
5	Dic₂₂₄₈	C₄	1	1	yes	characteristic
6	#22582824	—	2	1	no	—
7	D₄₄₉₆	C₄	1	1	yes	characteristic
8	#22582815	—	2	1	no	—
9	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
10	C₃₂×C₂₈₁	—	2	1	no	—
11	#17985138	—	4	1	no	—
12	Dic₁₁₂₄	—	2	1	no	—
13	#17985127	—	4	1	no	—
14	D₂₂₄₈	—	2	1	no	—
15	#17985122	—	4	1	no	—
16	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
17	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₂₈₁	D₄	1	1	yes	characteristic
19	Dic₅₆₂	—	4	1	no	—
20	D₁₁₂₄	—	4	1	no	—
21	C₂²⋊D₂₈₁	—	8	1	no	—
22	C₄×D₂₈₁	—	8	1	no	—
23	#14555886	—	8	1	no	—
24	C₂×C₄×C₂₈₁	D₈	1	1	yes	characteristic
25	C₈×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
27	C₂²×C₂₈₁	SD₃₂	1	1	yes	characteristic
28	C₂×D₂₈₁	—	8	1	no	—
29	C₄×C₂₈₁	#102	1	1	yes	characteristic
30	C₄×C₂₈₁	D₁₆	1	1	yes	characteristic
31	Dic₂₈₁	—	8	1	no	—
32	C₂×C₂₈₁	—	2	1	no	—
33	C₂×C₂₈₁	#357	1	1	yes	characteristic
34	D₂₈₁	—	16	1	no	—
35	C₂₈₁	#1417	1	1	yes	characteristic, complemented, Sylow
36	#1417	—	281	1	no	maximal, Sylow
37	#508	—	281	1	no	—
38	C₂×C₃₂	D₂₈₁	1	1	yes	characteristic, complemented
39	#368	—	281	1	no	—
40	#135	—	562	1	no	—
41	Q₃₂	—	281	1	no	—
42	SD₃₂	—	562	1	no	—
43	D₁₆	—	281	1	no	—
44	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
45	#108	—	562	1	no	—
46	C₃₂	—	2	1	no	—
47	#41	—	1124	1	no	—
48	Q₁₆	—	562	1	no	—
49	SD₁₆	—	1124	1	no	—
50	D₈	—	562	1	no	—
51	M₁₆	—	1124	1	no	—
52	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
53	C₁₆	C₄×D₂₈₁	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₂₈₁	1	1	yes	characteristic
55	Q₈	—	1124	1	no	—
56	D₄	—	1124	1	no	—
57	D₄	—	2248	1	no	—
58	C₂×C₄	—	2248	1	no	—
59	C₂×C₄	D₂₂₄₈	1	1	yes	characteristic
60	C₈	—	2248	1	no	—
61	C₈	#17985115	1	1	yes	characteristic
62	C₈	#17985127	1	1	yes	characteristic
63	C₂²	—	2248	1	no	—
64	C₂²	#22582824	1	1	yes	characteristic
65	C₄	—	2248	1	no	—
66	C₄	#22582801	1	1	yes	characteristic
67	C₄	D₄₄₉₆	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4496	1	no	—
70	C₂	#31823265	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄₄₉₆
commutator	C₁₆×C₂₈₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₈₁
Fitting	C₂×C₃₂×C₂₈₁	C₂
socle	C₂×C₂₈₁	#357
prime radical	#31823895	C₂
cosocle	C₂×C₁₆×C₂₈₁	C₂²
hypercenter	C₂×C₃₂	D₂₈₁
hypocenter	C₂₈₁	#1417
LCS	G ▷ C₁₆×C₂₈₁ ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #31823293	C₂	semidirect
3. C₂×C₃₂×C₂₈₁	C₂	semidirect
35. C₂₈₁	#1417	semidirect
38. C₂×C₃₂	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#31823895	2
#31823293	2
C₂×C₃₂×C₂₈₁	2
#1417	281