Subgroups — #27187061

Order 12928.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266043	C₂	1	6	yes	maximal
2	#20265022	C₂	1	1	yes	maximal, characteristic
3	C₂²×#11717581	C₂²	1	4	yes	—
4	C₂×C₄×Dic₁₀₁	C₂²	1	3	yes	—
5	#15692162	C₄	1	3	yes	—
6	#95×C₁₀₁	C₄	1	1	yes	characteristic
7	C₂×#11717581	—	2	12	no	—
8	C₂²×Dic₁₀₁	C₂×C₄	1	3	yes	—
9	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
10	C₄×Dic₁₀₁	—	2	6	no	—
11	C₂²×C₄×C₁₀₁	C₂×C₄	1	3	yes	—
12	C₂³×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₀₁	—	2	3	no	—
14	C₂×C₄×C₁₀₁	—	2	6	no	—
15	C₂×Dic₁₀₁	—	2	3	no	—
16	C₂×Dic₁₀₁	—	2	3	no	—
17	C₂×Dic₁₀₁	—	2	3	no	—
18	C₂×Dic₁₀₁	#41	1	6	yes	—
19	#11717581	—	4	4	no	—
20	C₂²×C₁₀₁	#117	1	3	yes	—
21	C₂²×C₁₀₁	#131	1	3	yes	—
22	C₂²×C₁₀₁	#131	1	1	yes	characteristic
23	C₄×C₁₀₁	—	4	3	no	—
24	Dic₁₀₁	—	4	3	no	—
25	Dic₁₀₁	#126	1	4	yes	—
26	C₂×C₁₀₁	#383	1	1	yes	characteristic
27	C₂×C₁₀₁	#433	1	3	yes	—
28	C₂×C₁₀₁	#433	1	3	yes	—
29	#1840	—	101	1	no	maximal, Sylow
30	C₁₀₁	#1840	1	1	yes	characteristic, complemented, Sylow
31	#376	—	101	1	no	—
32	#336	—	101	6	no	—
33	C₂²×C₈	—	101	4	no	—
34	C₂×C₄²	—	101	3	no	—
35	#95	—	101	3	no	—
36	#95	#87938	1	1	yes	characteristic
37	C₂²×C₄	—	101	1	no	—
38	C₂²×C₄	—	101	3	no	—
39	C₂²×C₄	C₂×#87938	1	3	yes	—
40	C₂×C₈	—	202	12	no	—
41	C₄²	—	202	6	no	—
42	C₂³	C₂²×#87938	1	1	yes	characteristic
43	C₂×C₄	—	2	3	no	—
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	101	6	no	—
46	C₂×C₄	—	202	3	no	—
47	C₂×C₄	—	202	3	no	—
48	C₂×C₄	—	202	3	no	—
49	C₈	—	404	4	no	—
50	C₂²	#15692334	1	3	yes	—
51	C₂²	#15692342	1	3	yes	—
52	C₂²	#15692343	1	1	yes	characteristic
53	C₄	—	4	3	no	—
54	C₄	—	101	4	no	—
55	C₄	—	404	3	no	—
56	C₂	#20266122	1	1	yes	characteristic
57	C₂	#20266201	1	3	yes	—
58	C₂	#20266202	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#87938
commutator, socle, prime radical	C₂³×C₁₀₁	C₂²×C₄
Fitting	#95×C₁₀₁	C₄
cosocle	C₂²×Dic₁₀₁	C₂³
hypercenter	#95	#87938
hypocenter	C₁₀₁	#1840
LCS	G ▷ C₂³×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
30. C₁₀₁	#1840	semidirect

Maximal subgroups

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

subgroup	index
#20266043	2
#20265022	2
#1840	101