Subgroups — #27186040

Order 12928.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266180	C₂	1	2	yes	maximal
2	#20265200	C₂	1	1	yes	maximal, characteristic
3	C₂×#13108083	C₄	1	4	yes	—
4	#15692322	—	2	2	no	—
5	C₄⋊#11717581	—	2	2	no	—
6	C₂×#13108058	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
8	#15692184	—	2	2	no	—
9	C₂×M₁₆×C₁₀₁	C₄	1	1	yes	characteristic
10	#13108083	—	4	4	no	—
11	C₂×#11717581	—	2	4	no	—
12	C₂²×Dic₁₀₁	C₂×C₄	1	2	yes	—
13	#13108058	—	4	1	no	—
14	C₂×#11717579	—	2	1	no	—
15	C₄×Dic₁₀₁	D₄	1	1	yes	characteristic
16	C₄×Dic₁₀₁	D₄	1	2	yes	—
17	C₄×Dic₁₀₁	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
19	M₁₆×C₁₀₁	—	4	1	no	—
20	C₂×C₈×C₁₀₁	—	2	1	no	—
21	C₂³×C₁₀₁	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₁₀₁	—	2	1	no	—
23	C₂×C₄×C₁₀₁	—	2	1	no	—
24	C₂×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
26	C₂×Dic₁₀₁	—	2	2	no	—
27	C₂×Dic₁₀₁	—	2	2	no	—
28	C₂×Dic₁₀₁	C₂²⋊C₄	1	2	yes	—
29	C₂×Dic₁₀₁	C₄⋊C₄	1	2	yes	—
30	#11717581	—	4	4	no	—
31	C₈×C₁₀₁	—	4	1	no	—
32	#11717579	—	4	1	no	—
33	C₂²×C₁₀₁	—	2	2	no	—
34	C₂²×C₁₀₁	—	2	1	no	—
35	C₂²×C₁₀₁	#95	1	1	yes	characteristic
36	C₄×C₁₀₁	—	2	1	no	—
37	C₄×C₁₀₁	#100	1	1	yes	characteristic
38	C₄×C₁₀₁	#101	1	1	yes	characteristic
39	Dic₁₀₁	—	2	2	no	—
40	Dic₁₀₁	#100	1	2	yes	—
41	Dic₁₀₁	#101	1	2	yes	—
42	C₂×C₁₀₁	—	4	1	no	—
43	C₂×C₁₀₁	#343	1	2	yes	—
44	C₂×C₁₀₁	#343	1	1	yes	characteristic
45	#1309	—	101	1	no	maximal, Sylow
46	C₁₀₁	#1309	1	1	yes	characteristic, complemented, Sylow
47	#423	—	101	2	no	—
48	#423	—	101	1	no	—
49	C₂×M₁₆	—	101	4	no	—
50	C₂×M₁₆	—	101	1	no	—
51	C₂×M₁₆	#87938	1	1	yes	characteristic
52	C₂×C₄²	—	101	1	no	—
53	C₄⋊C₈	—	202	2	no	—
54	C₄⋊C₈	—	202	2	no	—
55	C₄⋊C₈	—	202	2	no	—
56	C₂²×C₄	—	101	2	no	—
57	C₂²×C₄	C₂×#87938	1	1	yes	characteristic
58	M₁₆	—	4	1	no	—
59	M₁₆	—	404	1	no	—
60	M₁₆	—	404	4	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	202	4	no	—
63	C₂×C₈	—	202	1	no	—
64	C₄²	—	101	2	no	—
65	C₄²	—	101	1	no	—
66	C₄²	—	101	1	no	—
67	C₂³	C₄×#87938	1	1	yes	characteristic
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	101	2	no	—
71	C₂×C₄	—	101	2	no	—
72	C₂×C₄	—	202	2	no	—
73	C₂×C₄	—	202	2	no	—
74	C₂×C₄	C₂²⋊#87938	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#87938	1	1	yes	characteristic
76	C₈	—	4	1	no	—
77	C₈	—	404	4	no	—
78	C₈	—	404	1	no	—
79	C₂²	—	2	2	no	—
80	C₂²	—	2	1	no	—
81	C₂²	(C₂×#87938)⋊C₄	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	101	2	no	—
84	C₄	—	101	2	no	—
85	C₄	—	202	2	no	—
86	C₄	#15692315	1	1	yes	characteristic
87	C₄	#15692316	1	1	yes	characteristic
88	C₂	—	4	1	no	—
89	C₂	#20266056	1	2	yes	—
90	C₂	#20266057	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#87938)⋊C₄
commutator, prime radical	C₂³×C₁₀₁	C₄²
Frattini	C₂²×C₄	C₂×#87938
Fitting	C₂×M₁₆×C₁₀₁	C₄
socle	C₂²×C₁₀₁	#95
cosocle	C₂×C₄×Dic₁₀₁	C₂²
hypercenter	C₂×M₁₆	#87938
hypocenter	C₁₀₁	#1309
LCS	G ▷ C₂³×C₁₀₁ ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
46. C₁₀₁	#1309	semidirect

Maximal subgroups

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

subgroup	index
#20266180	2
#20265200	2
#1309	101