Subgroups — #44548405

Order 32128.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632060	C₂	1	1	yes	maximal, characteristic
2	#30631508	C₂	1	1	yes	maximal, characteristic, complemented
3	#364×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16860799	—	2	1	no	—
5	C₂×#16860799	—	2	1	no	—
6	#22548715	C₄	1	1	yes	characteristic
7	#22548712	C₄	1	1	yes	characteristic
8	#22548655	—	2	1	no	—
9	M₃₂×C₂₅₁	—	2	1	no	—
10	C₄×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₅₀₂	—	2	1	no	—
12	C₂×D₁₀₀₄	—	2	1	no	—
13	C₂×D₁₀₀₄	—	4	1	no	—
14	#16860799	—	4	1	no	—
15	#16860799	—	4	1	no	—
16	#16860799	—	4	1	no	—
17	#16860799	—	4	1	no	—
18	C₄⋊Dic₂₅₁	—	4	1	no	—
19	C₂₅₁⋊C₁₆	—	4	1	no	—
20	C₂×C₈×C₂₅₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₂₅₁	D₄	1	1	yes	characteristic
22	C₄²×C₂₅₁	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₂₅₁	—	4	1	no	—
24	C₂²×D₂₅₁	—	4	1	no	—
25	Dic₅₀₂	—	4	1	no	—
26	Dic₅₀₂	—	4	1	no	—
27	D₁₀₀₄	—	4	1	no	—
28	D₁₀₀₄	—	4	1	no	—
29	D₁₀₀₄	—	8	2	no	—
30	C₂×Dic₂₅₁	—	4	1	no	—
31	C₂×C₄×C₂₅₁	—	2	1	no	—
32	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₈×C₂₅₁	D₈	1	1	yes	characteristic
34	C₈×C₂₅₁	D₈	1	1	yes	characteristic
35	C₈×C₂₅₁	SD₁₆	1	1	yes	characteristic
36	C₈×C₂₅₁	SD₁₆	1	1	yes	characteristic
37	C₂²×C₂₅₁	#100	1	1	yes	characteristic
38	C₂×D₂₅₁	—	8	2	no	—
39	C₂×D₂₅₁	—	8	1	no	—
40	C₄×C₂₅₁	—	2	2	no	—
41	C₄×C₂₅₁	#102	1	1	yes	characteristic
42	C₄×C₂₅₁	#102	1	1	yes	characteristic
43	Dic₂₅₁	—	8	1	no	—
44	C₂×C₂₅₁	—	2	1	no	—
45	C₂×C₂₅₁	#331	1	1	yes	characteristic
46	D₂₅₁	—	16	1	no	—
47	C₂₅₁	#1359	1	1	yes	characteristic, complemented, Sylow
48	#1359	—	251	1	no	maximal, Sylow
49	#492	—	251	1	no	—
50	#364	—	251	1	no	—
51	#364	D₂₅₁	1	1	yes	characteristic, complemented
52	C₂×SD₁₆	—	502	1	no	—
53	C₂×SD₁₆	—	502	1	no	—
54	C₄⋊Q₈	—	251	1	no	—
55	#127	—	251	1	no	—
56	M₃₂	—	2	1	no	—
57	M₃₂	—	502	1	no	—
58	C₄×C₈	C₂×D₂₅₁	1	1	yes	characteristic
59	C₂×Q₈	—	502	1	no	—
60	C₂×D₄	—	1004	1	no	—
61	C₂×D₄	—	502	1	no	—
62	SD₁₆	—	1004	1	no	—
63	SD₁₆	—	1004	1	no	—
64	SD₁₆	—	1004	1	no	—
65	SD₁₆	—	1004	1	no	—
66	C₂×C₈	C₂²⋊D₂₅₁	1	1	yes	characteristic
67	C₂×C₈	D₁₀₀₄	1	1	yes	characteristic
68	C₄⋊C₄	—	1004	1	no	—
69	C₄²	C₄×D₂₅₁	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	1004	1	no	—
72	C₂³	—	1004	1	no	—
73	Q₈	—	1004	1	no	—
74	Q₈	—	1004	1	no	—
75	D₄	—	2008	2	no	—
76	D₄	—	1004	1	no	—
77	D₄	—	1004	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	1004	1	no	—
80	C₂×C₄	(C₂×D₂₅₁)⋊C₄	1	1	yes	characteristic
81	C₈	#16860795	1	1	yes	characteristic
82	C₈	D₂₀₀₈	1	1	yes	characteristic
83	C₈	#16860797	1	1	yes	characteristic
84	C₈	#16860799	1	1	yes	characteristic
85	C₂²	—	2008	2	no	—
86	C₂²	—	2008	1	no	—
87	C₂²	#22548631	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	2008	1	no	—
90	C₄	#22548635	1	1	yes	characteristic
91	C₄	#22548637	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4016	1	no	—
94	C₂	#30631430	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#30631430
commutator	C₄²×C₂₅₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₅₁
Fitting	#364×C₂₅₁	C₂
socle	C₂×C₂₅₁	#331
prime radical	#22548712	C₄
cosocle	C₄×C₈×C₂₅₁	C₂²
hypercenter	#364	D₂₅₁
hypocenter	C₂₅₁	#1359
LCS	G ▷ C₄²×C₂₅₁ ▷ C₂×C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #30631508	C₂	semidirect
3. #364×C₂₅₁	C₂	semidirect
47. C₂₅₁	#1359	semidirect
51. #364	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632060	2
#30631508	2
#364×C₂₅₁	2
#1359	251