Group #21460697 — subgroups

Subgroups — #21460697

Order 7808.

188 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519844	C₂	1	2	yes	maximal
2	#16839631	C₂	1	1	yes	maximal, characteristic
3	C₂²×#92420	—	2	2	no	—
4	#14519844	—	2	2	no	—
5	#14519844	C₄	1	4	yes	complemented
6	C₂×C₄⋊Dic₆₁	C₄	1	1	yes	characteristic
7	C₂×#11758196	—	2	2	no	—
8	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	—	2	1	no	—
11	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₆₁	—	2	1	no	—
13	C₂²×Dic₆₁	D₄	1	2	yes	—
14	C₂×#92420	—	2	4	no	—
15	C₂×#92420	—	4	2	no	—
16	C₂×#92420	—	4	2	no	—
17	C₄⋊C₄×C₆₁	—	4	1	no	—
18	C₄⋊Dic₆₁	—	4	1	no	—
19	#11758196	—	4	2	no	—
20	#11758196	—	4	2	no	—
21	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
22	C₄×Dic₆₁	D₄	1	1	yes	characteristic
23	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
24	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	—	2	1	no	—
26	C₂×C₄×C₆₁	—	2	1	no	—
27	C₂×C₄×C₆₁	—	4	1	no	—
28	C₂×C₄×C₆₁	—	4	2	no	—
29	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×Dic₆₁	—	4	1	no	—
32	C₂×Dic₆₁	—	4	2	no	—
33	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
34	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
35	C₂×Dic₆₁	D₈	1	2	yes	—
36	C₂×Dic₆₁	SD₁₆	1	2	yes	—
37	C₂×Dic₆₁	SD₁₆	1	2	yes	—
38	C₂×Dic₆₁	Q₁₆	1	2	yes	—
39	#92420	—	4	4	no	—
40	C₂²×C₆₁	#95	1	1	yes	characteristic
41	C₂²×C₆₁	#100	1	1	yes	characteristic
42	C₂²×C₆₁	#101	1	1	yes	characteristic
43	C₂²×C₆₁	#102	1	2	yes	—
44	C₂²×C₆₁	#103	1	2	yes	—
45	C₄×C₆₁	—	2	1	no	—
46	C₄×C₆₁	—	2	1	no	—
47	C₄×C₆₁	—	8	1	no	—
48	Dic₆₁	—	8	1	no	—
49	Dic₆₁	#102	1	2	yes	—
50	Dic₆₁	#103	1	2	yes	—
51	Dic₆₁	#106	1	2	yes	—
52	Dic₆₁	#107	1	2	yes	—
53	#1296	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	#331	1	1	yes	characteristic
55	C₂×C₆₁	#332	1	2	yes	—
56	C₂×C₆₁	#333	1	1	yes	characteristic
57	C₂×C₆₁	#340	1	2	yes	—
58	C₂×C₆₁	#343	1	1	yes	characteristic
59	C₂×C₄⋊C₈	—	61	2	no	—
60	#384	—	61	1	no	—
61	C₆₁	#1296	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	122	2	no	—
63	C₂×C₄⋊C₄	—	61	1	no	—
64	C₂×C₄⋊C₄	—	122	2	no	—
65	C₂×C₄⋊C₄	#6923	1	1	yes	characteristic
66	C₂×C₄²	—	61	1	no	—
67	C₄⋊C₈	—	61	4	no	—
68	C₄⋊C₈	—	122	2	no	—
69	C₂²×C₄	—	2	1	no	—
70	C₂²×C₄	—	61	2	no	—
71	C₂²×C₄	—	122	1	no	—
72	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
73	C₂×C₈	—	122	4	no	—
74	C₂×C₈	—	244	2	no	—
75	C₂×C₈	—	244	2	no	—
76	C₄⋊C₄	—	4	1	no	—
77	C₄⋊C₄	—	244	1	no	—
78	C₄⋊C₄	—	244	2	no	—
79	C₄⋊C₄	—	244	2	no	—
80	C₄²	—	61	2	no	—
81	C₄²	—	61	1	no	—
82	C₄²	—	61	1	no	—
83	C₂³	C₂²⋊#6923	1	1	yes	characteristic
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	—	4	2	no	—
88	C₂×C₄	—	61	2	no	—
89	C₂×C₄	—	61	2	no	—
90	C₂×C₄	—	61	2	no	—
91	C₂×C₄	—	61	2	no	—
92	C₂×C₄	—	61	2	no	—
93	C₂×C₄	—	61	2	no	—
94	C₂×C₄	—	244	1	no	—
95	C₂×C₄	—	244	2	no	—
96	C₂×C₄	C₄×#6923	1	1	yes	characteristic
97	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
98	C₈	—	244	4	no	—
99	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
100	C₂²	#14519837	1	1	yes	characteristic
101	C₂²	#14519838	1	1	yes	characteristic
102	C₂²	#14519839	1	2	yes	—
103	C₂²	#14519840	1	2	yes	—
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	8	1	no	—
107	C₄	—	61	2	no	—
108	C₄	—	61	2	no	—
109	C₄	—	61	2	no	—
110	C₄	—	61	2	no	—
111	C₄	—	488	1	no	—
112	C₂	#16840620	1	1	yes	characteristic
113	C₂	#16840621	1	2	yes	—
114	C₂	#16840622	1	1	yes	characteristic
115	C₂	#16840635	1	2	yes	—
116	C₂	#16840642	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519844

C₂

yes

maximal

#16839631

C₂

yes

maximal, characteristic

C₂²×#92420

—

#14519844

—

#14519844

C₄

yes

complemented

C₂×C₄⋊Dic₆₁

C₄

yes

characteristic

C₂×#11758196

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

D₄

yes

—

C₂×#92420

—

C₂×#92420

—

C₂×#92420

—

C₄⋊C₄×C₆₁

—

C₄⋊Dic₆₁

—

#11758196

—

#11758196

—

C₄×Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₂³×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

D₈

yes

—

C₂×Dic₆₁

SD₁₆

yes

—

C₂×Dic₆₁

SD₁₆

yes

—

C₂×Dic₆₁

Q₁₆

yes

—

#92420

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

—

C₂²×C₆₁

#103

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

#102

yes

—

Dic₆₁

#103

yes

—

Dic₆₁

#106

yes

—

Dic₆₁

#107

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

#333

yes

characteristic

C₂×C₆₁

#340

yes

—

C₂×C₆₁

#343

yes

characteristic

C₂×C₄⋊C₈

—

#384

—

C₆₁

#1296

yes

characteristic, complemented, Sylow

C₂²×C₈

—

122

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄⋊C₄

#6923

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₄⋊C₄

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²⋊#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

244

—

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

100

C₂²

#14519837

yes

characteristic

101

C₂²

#14519838

yes

characteristic

102

C₂²

#14519839

yes

—

103

C₂²

#14519840

yes

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

488

—

112

C₂

#16840620

yes

characteristic

113

C₂

#16840621

yes

—

114

C₂

#16840622

yes

characteristic

115

C₂

#16840635

yes

—

116

C₂

#16840642

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×C₄⋊C₄×C₆₁	C₄
socle	C₂³×C₆₁	C₂²⋊C₄
hypercenter	C₂×C₄⋊C₄	#6923
hypocenter	C₆₁	#1296
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂²⋊#6923

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂×C₄⋊C₄×C₆₁

C₄

socle

C₂³×C₆₁

C₂²⋊C₄

C₂×C₄⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
5. #14519844	C₄	semidirect
61. C₆₁	#1296	semidirect

H ≅ G/N

type

5. #14519844

C₄

semidirect

61. C₆₁

#1296

semidirect

Subgroups — #21460697

Conjugacy classes of subgroups

Complements