Subgroups — #44549996

Order 32128.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632085	C₂	1	1	yes	maximal, characteristic
2	#30632083	C₂	1	2	yes	maximal
3	#30632039	C₂	1	2	yes	maximal
4	#30631408	C₂	1	1	yes	maximal, characteristic
5	#494×C₂₅₁	C₂	1	1	yes	maximal, characteristic
6	#22548715	C₂²	1	2	yes	—
7	#22548647	—	2	2	no	—
8	#22548646	—	2	4	no	—
9	#22548638	—	2	4	no	—
10	C₄×C₂₅₁⋊C₈	C₂²	1	2	yes	—
11	C₂×Q₁₆×C₂₅₁	—	2	2	no	—
12	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
13	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₀₂	—	2	2	no	—
16	C₂×C₂₅₁⋊C₈	D₄	1	4	yes	—
17	C₄⋊Dic₂₅₁	—	2	2	no	—
18	C₄⋊Dic₂₅₁	—	2	2	no	—
19	C₂×Q₈×C₂₅₁	—	2	1	no	—
20	C₂×Q₈×C₂₅₁	—	2	1	no	—
21	Q₁₆×C₂₅₁	—	4	4	no	—
22	C₂×C₈×C₂₅₁	D₄	1	2	yes	—
23	C₄⋊C₄×C₂₅₁	—	2	2	no	—
24	C₄⋊C₄×C₂₅₁	—	2	2	no	—
25	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
26	Dic₅₀₂	—	4	4	no	—
27	C₂×Dic₂₅₁	—	4	2	no	—
28	C₂₅₁⋊C₈	—	2	4	no	—
29	Q₈×C₂₅₁	—	4	2	no	—
30	Q₈×C₂₅₁	—	4	2	no	—
31	C₂×C₄×C₂₅₁	—	4	1	no	—
32	C₂×C₄×C₂₅₁	—	4	1	no	—
33	C₂×C₄×C₂₅₁	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
35	C₈×C₂₅₁	SD₁₆	1	4	yes	—
36	C₂²×C₂₅₁	#127	1	1	yes	characteristic
37	C₄×C₂₅₁	—	8	1	no	—
38	C₄×C₂₅₁	—	8	1	no	—
39	C₄×C₂₅₁	C₂×SD₁₆	1	2	yes	—
40	C₄×C₂₅₁	#137	1	4	yes	—
41	Dic₂₅₁	—	8	2	no	—
42	C₂×C₂₅₁	#492	1	1	yes	characteristic
43	C₂×C₂₅₁	#497	1	2	yes	—
44	C₂₅₁	#1716	1	1	yes	characteristic, complemented, Sylow
45	#1716	—	251	1	no	maximal, Sylow
46	#498	—	251	2	no	—
47	#498	—	251	1	no	—
48	#494	D₂₅₁	1	1	yes	characteristic
49	#487	—	251	2	no	—
50	#322	—	251	1	no	—
51	C₂×Q₁₆	—	2	2	no	—
52	C₄⋊Q₈	—	251	2	no	—
53	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
54	C₄⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
55	#106	—	502	4	no	—
56	#106	—	502	2	no	—
57	#103	—	502	4	no	—
58	C₄×C₈	—	251	2	no	—
59	C₄×C₈	C₂×D₂₅₁	1	1	yes	characteristic
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	2	1	no	—
62	C₂×Q₈	—	502	2	no	—
63	Q₁₆	—	4	4	no	—
64	C₂×C₈	—	251	4	no	—
65	C₂×C₈	C₂²⋊D₂₅₁	1	2	yes	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	502	2	no	—
69	C₄⋊C₄	—	502	2	no	—
70	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	Q₈	—	1004	4	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	1004	2	no	—
77	C₂×C₄	D₄×D₂₅₁	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₂₅₁	1	1	yes	characteristic
79	C₈	—	502	4	no	—
80	C₈	#16860798	1	4	yes	—
81	C₂²	#22548711	1	1	yes	characteristic
82	C₄	—	8	1	no	—
83	C₄	—	8	1	no	—
84	C₄	—	2008	2	no	—
85	C₄	C₂×#16860798	1	2	yes	—
86	C₄	#22548747	1	4	yes	—
87	C₂	#30632059	1	1	yes	characteristic
88	C₂	#30632080	1	2	yes	—

	subgroup	G/H
center	C₂²	#22548711
commutator, cosocle	C₄²×C₂₅₁	C₂³
Frattini	C₄²	C₂²×D₂₅₁
Fitting	#494×C₂₅₁	C₂
socle, prime radical	C₂²×C₂₅₁	#127
hypercenter	#494	D₂₅₁
hypocenter	C₂₅₁	#1716
LCS	G ▷ C₄²×C₂₅₁ ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
44. C₂₅₁	#1716	semidirect

Maximal subgroups

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

subgroup	index
#30632085	2
#30632083	2
#30632039	2
#30631408	2
#494×C₂₅₁	2
#1716	251