Subgroups — #27169234

Order 12928.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265215	C₂	1	2	yes	maximal
2	C₂×M₃₂×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#15692214	—	2	2	no	—
4	#15692189	—	2	2	no	—
5	#15692187	C₄	1	4	yes	complemented
6	C₂²×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
7	M₃₂×C₁₀₁	—	2	2	no	—
8	C₂×C₁₆×C₁₀₁	C₄	1	2	yes	complemented
9	C₄⋊Dic₁₀₁	—	2	4	no	—
10	C₂²⋊Dic₁₀₁	—	4	2	no	—
11	C₄×Dic₁₀₁	—	4	2	no	—
12	C₂²×C₄×C₁₀₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₀₁	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₀₁	D₄	1	2	yes	—
16	C₂×C₈×C₁₀₁	Q₈	1	1	yes	characteristic
17	C₁₆×C₁₀₁	—	2	2	no	—
18	C₂³×C₁₀₁	D₈	1	1	yes	characteristic
19	C₂×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₀₁	SD₁₆	1	2	yes	—
22	C₂×C₄×C₁₀₁	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₁₀₁	—	4	4	no	—
24	C₈×C₁₀₁	C₄²	1	1	yes	characteristic
25	C₈×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₀₁	C₄⋊C₄	1	2	yes	—
27	C₂²×C₁₀₁	—	4	1	no	—
28	C₂²×C₁₀₁	#102	1	2	yes	—
29	C₂²×C₁₀₁	#107	1	1	yes	characteristic
30	C₄×C₁₀₁	#95	1	1	yes	characteristic
31	C₄×C₁₀₁	#103	1	2	yes	—
32	C₄×C₁₀₁	#106	1	1	yes	characteristic
33	Dic₁₀₁	—	8	4	no	—
34	C₂×C₁₀₁	—	2	2	no	—
35	C₂×C₁₀₁	—	2	1	no	—
36	C₂×C₁₀₁	#340	1	1	yes	characteristic
37	#1384	—	101	1	no	maximal, Sylow
38	C₁₀₁	#1384	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₃₂	D₁₀₁	1	1	yes	characteristic
40	#427	—	101	2	no	—
41	C₂²×C₈	C₂×D₁₀₁	1	1	yes	characteristic
42	#117	—	202	2	no	—
43	M₃₂	—	2	2	no	—
44	C₂×C₁₆	Dic₁₀₁	1	2	yes	complemented
45	#107	—	202	2	no	—
46	#106	—	101	4	no	—
47	C₂²×C₄	D₄₀₄	1	1	yes	characteristic
48	C₂×C₈	Dic₂₀₂	1	1	yes	characteristic
49	C₂×C₈	C₄×D₁₀₁	1	2	yes	—
50	C₂×C₈	C₂×Dic₁₀₁	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₁₀₁	1	2	yes	—
52	C₄⋊C₄	—	202	4	no	—
53	C₂²⋊C₄	—	404	2	no	—
54	C₄²	—	404	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₈₀₈	1	1	yes	characteristic
57	C₂×C₄	—	404	4	no	—
58	C₂×C₄	#13108051	1	2	yes	—
59	C₂×C₄	C₄⋊Dic₁₀₁	1	1	yes	characteristic
60	C₂×C₄	#13108063	1	2	yes	—
61	C₂×C₄	Dic₄₀₄	1	1	yes	characteristic
62	C₈	C₄×Dic₁₀₁	1	1	yes	characteristic
63	C₈	C₂²⋊Dic₁₀₁	1	1	yes	characteristic
64	C₈	#13108053	1	2	yes	—
65	C₂²	—	4	1	no	—
66	C₂²	#15692177	1	2	yes	—
67	C₂²	#15692189	1	1	yes	characteristic
68	C₄	—	808	4	no	—
69	C₄	#15692162	1	1	yes	characteristic
70	C₄	#15692180	1	2	yes	—
71	C₄	#15692187	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#20264940	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15692187
commutator	C₈×C₁₀₁	C₄²
Frattini	C₂²×C₈	C₂×D₁₀₁
Fitting	C₂×M₃₂×C₁₀₁	C₂
socle	C₂×C₁₀₁	#340
prime radical	C₂³×C₁₀₁	D₈
cosocle	C₂²×C₈×C₁₀₁	C₂²
hypercenter	C₂×M₃₂	D₁₀₁
hypocenter	C₁₀₁	#1384
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
5. #15692187	C₄	semidirect
8. C₂×C₁₆×C₁₀₁	C₄	semidirect
38. C₁₀₁	#1384	semidirect
44. C₂×C₁₆	Dic₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265215	2
C₂×M₃₂×C₁₀₁	2
#1384	101