Subgroups — #49097189

Order 35968.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823580	C₂	1	2	yes	maximal, complemented
2	#31823293	C₂	1	1	yes	maximal, characteristic, complemented
3	#31823270	C₂	1	2	yes	maximal, complemented
4	#31823238	C₂	1	1	yes	maximal, characteristic, complemented
5	#508×C₂₈₁	C₂	1	1	yes	maximal, characteristic
6	#22582886	—	2	2	no	—
7	C₂×#17985113	C₂²	1	1	yes	characteristic
8	#22582815	C₂²	1	2	yes	—
9	#22582806	—	2	2	no	—
10	C₈×Dic₂₈₁	C₂²	1	1	yes	characteristic
11	#135×C₂₈₁	C₂²	1	2	yes	—
12	Q₃₂×C₂₈₁	C₄	1	1	yes	characteristic, complemented
13	SD₃₂×C₂₈₁	C₄	1	2	yes	complemented
14	D₁₆×C₂₈₁	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
16	#17985122	—	2	2	no	—
17	#17985122	—	4	2	no	—
18	C₂×#14555886	—	4	2	no	—
19	C₂×#14555886	D₄	1	1	yes	characteristic
20	C₄×Dic₂₈₁	D₄	1	1	yes	characteristic
21	#17985113	—	2	1	no	—
22	#41×C₂₈₁	—	2	2	no	—
23	Q₁₆×C₂₈₁	C₂×C₄	1	2	yes	—
24	SD₁₆×C₂₈₁	—	2	2	no	—
25	D₈×C₂₈₁	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₂₈₁	C₂³	1	1	yes	characteristic
27	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
29	C₂×Dic₂₈₁	—	2	1	no	—
30	#14555886	—	4	2	no	—
31	#14555886	D₈	1	2	yes	—
32	Q₈×C₂₈₁	—	2	2	no	—
33	D₄×C₂₈₁	—	2	2	no	—
34	D₄×C₂₈₁	—	4	2	no	—
35	C₂×C₄×C₂₈₁	—	4	2	no	—
36	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
37	C₈×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₂₈₁	#41	1	1	yes	characteristic
39	C₂²×C₂₈₁	—	4	2	no	—
40	C₂²×C₂₈₁	#135	1	1	yes	characteristic
41	C₄×C₂₈₁	—	4	2	no	—
42	C₄×C₂₈₁	C₄×D₄	1	1	yes	characteristic
43	C₄×C₂₈₁	C₂×D₈	1	1	yes	characteristic
44	Dic₂₈₁	—	4	1	no	—
45	C₂×C₂₈₁	—	2	1	no	—
46	C₂×C₂₈₁	—	8	2	no	—
47	C₂×C₂₈₁	C₄×D₈	1	1	yes	characteristic
48	C₂₈₁	#2179	1	1	yes	characteristic, complemented, Sylow
49	#2179	—	281	1	no	maximal, Sylow
50	#508	D₂₈₁	1	1	yes	characteristic
51	#443	—	281	2	no	—
52	#368	—	281	1	no	—
53	#359	—	281	2	no	—
54	#346	—	281	1	no	—
55	#135	C₂×D₂₈₁	1	2	yes	—
56	#131	—	562	2	no	—
57	Q₃₂	Dic₂₈₁	1	1	yes	characteristic, complemented
58	SD₃₂	Dic₂₈₁	1	2	yes	complemented
59	D₁₆	Dic₂₈₁	1	1	yes	characteristic, complemented
60	C₂×C₁₆	—	281	1	no	—
61	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
62	#108	—	281	2	no	—
63	#104	—	562	2	no	—
64	C₄×C₈	—	281	1	no	—
65	#41	—	2	2	no	—
66	Q₁₆	C₂×Dic₂₈₁	1	2	yes	—
67	SD₁₆	—	2	2	no	—
68	D₈	C₂×Dic₂₈₁	1	2	yes	—
69	M₁₆	—	562	2	no	—
70	M₁₆	—	1124	2	no	—
71	C₂×C₈	—	281	1	no	—
72	C₂×C₈	—	1124	2	no	—
73	C₂×C₈	C₂²×D₂₈₁	1	1	yes	characteristic
74	C₄²	—	281	1	no	—
75	C₁₆	—	562	1	no	—
76	C₁₆	C₂×Dic₂₈₁	1	1	yes	characteristic
77	C₁₆	C₂×Dic₂₈₁	1	1	yes	characteristic
78	Q₈	—	2	2	no	—
79	D₄	—	2	2	no	—
80	D₄	—	4	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	562	1	no	—
83	C₂×C₄	D₄×D₂₈₁	1	1	yes	characteristic
84	C₈	—	281	2	no	—
85	C₈	—	1124	2	no	—
86	C₈	C₂²×Dic₂₈₁	1	1	yes	characteristic
87	C₈	#17985137	1	1	yes	characteristic
88	C₂²	—	4	2	no	—
89	C₂²	#22582898	1	1	yes	characteristic
90	C₄	—	4	2	no	—
91	C₄	—	1124	1	no	—
92	C₄	D₄×Dic₂₈₁	1	1	yes	characteristic
93	C₄	D₈×D₂₈₁	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	8	2	no	—
96	C₂	D₈×Dic₂₈₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₂₈₁
commutator	C₈×C₂₈₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₈₁
Fitting, prime radical	#508×C₂₈₁	C₂
socle	C₂×C₂₈₁	C₄×D₈
cosocle	C₂×C₈×C₂₈₁	C₂³
hypercenter	#508	D₂₈₁
hypocenter	C₂₈₁	#2179
LCS	G ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

Complements

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

N	H ≅ G/N	type
1. #31823580	C₂	semidirect
2. #31823293	C₂	semidirect
3. #31823270	C₂	semidirect
4. #31823238	C₂	semidirect
12. Q₃₂×C₂₈₁	C₄	semidirect
13. SD₃₂×C₂₈₁	C₄	semidirect
14. D₁₆×C₂₈₁	C₄	semidirect
48. C₂₈₁	#2179	semidirect
57. Q₃₂	Dic₂₈₁	semidirect
58. SD₃₂	Dic₂₈₁	semidirect
59. D₁₆	Dic₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#31823580	2
#31823293	2
#31823270	2
#31823238	2
#508×C₂₈₁	2
#2179	281