Group #21447984 — subgroups

Subgroups — #21447984

Order 7808.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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	#16840164	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₂₄₄	C₂	1	1	yes	maximal, characteristic
3	#16839590	C₂	1	1	yes	maximal, characteristic
4	#16839588	C₂	1	1	yes	maximal, characteristic
5	#16839567	C₂	1	1	yes	maximal, characteristic
6	#16839567	C₂	1	1	yes	maximal, characteristic
7	C₆₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₄₄	C₂²	1	1	yes	characteristic
9	#14519769	—	2	1	no	—
10	C₄×Dic₁₂₂	—	2	1	no	—
11	#14519711	C₂²	1	1	yes	characteristic
12	#14519711	C₂²	1	1	yes	characteristic
13	#14519711	C₂²	1	1	yes	characteristic
14	#14519709	—	2	1	no	—
15	#14519702	—	2	1	no	—
16	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₂₂	—	2	1	no	—
20	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
22	C₄²×C₆₁	D₄	1	1	yes	characteristic
23	C₄⋊Dic₆₁	—	2	1	no	—
24	C₄⋊Dic₆₁	—	2	1	no	—
25	C₄⋊Dic₆₁	—	2	1	no	—
26	#11758196	—	4	1	no	—
27	#11758196	—	4	1	no	—
28	#11758196	—	4	1	no	—
29	C₄×Dic₆₁	—	4	1	no	—
30	Dic₂₄₄	—	2	1	no	—
31	Dic₂₄₄	Q₈	1	2	yes	—
32	C₁₆×C₆₁	—	2	1	no	—
33	C₁₆×C₆₁	—	2	1	no	—
34	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
35	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₆₁	—	4	1	no	—
38	C₂×Dic₆₁	—	4	1	no	—
39	C₂×Dic₆₁	—	4	1	no	—
40	C₂×Dic₆₁	—	4	1	no	—
41	Dic₁₂₂	—	2	2	no	—
42	Dic₁₂₂	—	4	1	no	—
43	C₈×C₆₁	—	2	1	no	—
44	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₆₁	#41	1	1	yes	characteristic
46	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
47	C₄×C₆₁	—	2	1	no	—
48	C₄×C₆₁	—	2	1	no	—
49	C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
50	C₄×C₆₁	#137	1	1	yes	characteristic
51	Dic₆₁	—	4	2	no	—
52	Dic₆₁	—	8	1	no	—
53	Dic₆₁	—	8	1	no	—
54	Dic₆₁	—	8	1	no	—
55	#2229	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	#474	1	1	yes	characteristic
57	C₂×C₆₁	#508	1	1	yes	characteristic
58	C₂×C₆₁	#510	1	1	yes	characteristic
59	#499	—	61	1	no	—
60	C₄×Q₁₆	—	61	1	no	—
61	#367	—	61	1	no	—
62	#366	—	61	1	no	—
63	C₄⋊C₁₆	D₆₁	1	1	yes	characteristic
64	#358	—	61	1	no	—
65	#358	—	61	1	no	—
66	C₆₁	#2229	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₁₆	—	61	1	no	—
68	#125	—	122	1	no	—
69	C₄×Q₈	—	122	1	no	—
70	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
71	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
72	#107	—	61	1	no	—
73	#107	—	61	1	no	—
74	#107	—	61	1	no	—
75	#106	—	122	1	no	—
76	#103	—	122	1	no	—
77	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
78	C₂×Q₈	—	122	1	no	—
79	Q₁₆	—	61	2	no	—
80	Q₁₆	—	122	1	no	—
81	C₂×C₈	D₂₄₄	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
83	C₄⋊C₄	—	122	1	no	—
84	C₄⋊C₄	—	122	1	no	—
85	C₄⋊C₄	—	122	1	no	—
86	C₄⋊C₄	—	244	1	no	—
87	C₄⋊C₄	—	244	1	no	—
88	C₄⋊C₄	—	244	1	no	—
89	C₄²	—	244	1	no	—
90	C₄²	D₂₄₄	1	1	yes	characteristic
91	C₁₆	—	2	1	no	—
92	C₁₆	—	2	1	no	—
93	Q₈	—	122	2	no	—
94	Q₈	—	244	1	no	—
95	C₂×C₄	—	244	1	no	—
96	C₂×C₄	—	244	1	no	—
97	C₂×C₄	—	244	1	no	—
98	C₂×C₄	—	244	1	no	—
99	C₂×C₄	D₄₈₈	1	1	yes	characteristic
100	C₂×C₄	D₄₈₈	1	1	yes	characteristic
101	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	#11758224	1	1	yes	characteristic
104	C₈	Q₈×D₆₁	1	1	yes	characteristic
105	C₂²	C₂×D₄₈₈	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	488	1	no	—
109	C₄	—	488	1	no	—
110	C₄	—	488	1	no	—
111	C₄	—	244	2	no	—
112	C₄	#14519757	1	1	yes	characteristic
113	C₄	#14519810	1	1	yes	characteristic
114	C₂	#16840043	1	1	yes	characteristic
115	C₂	#16840194	1	1	yes	characteristic
116	C₂	#16840205	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840164

C₂

yes

maximal, characteristic

C₄×Dic₂₄₄

C₂

yes

maximal, characteristic

#16839590

C₂

yes

maximal, characteristic

#16839588

C₂

yes

maximal, characteristic

#16839567

C₂

yes

maximal, characteristic

#16839567

C₂

yes

maximal, characteristic

C₆₁×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂×Dic₂₄₄

C₂²

yes

characteristic

#14519769

—

C₄×Dic₁₂₂

—

#14519711

C₂²

yes

characteristic

#14519711

C₂²

yes

characteristic

#14519711

C₂²

yes

characteristic

#14519709

—

#14519702

—

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

D₄

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758196

—

#11758196

—

#11758196

—

C₄×Dic₆₁

—

Dic₂₄₄

—

Dic₂₄₄

Q₈

yes

—

C₁₆×C₆₁

—

C₁₆×C₆₁

—

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

C₂×Q₈

yes

characteristic

C₈×C₆₁

#41

yes

characteristic

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂²⋊Q₈

yes

characteristic

C₄×C₆₁

#137

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₄×Q₁₆

—

#367

—

#366

—

C₄⋊C₁₆

D₆₁

yes

characteristic

#358

—

#358

—

C₆₁

#2229

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

#125

—

122

—

C₄×Q₈

—

122

—

C₂×C₁₆

C₂×D₆₁

yes

characteristic

C₂×C₁₆

C₂×D₆₁

yes

—

—

—

—

122

—

#103

—

122

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

Q₁₆

—

Q₁₆

—

122

—

C₂×C₈

D₂₄₄

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₄²

—

244

—

C₄²

D₂₄₄

yes

characteristic

C₁₆

—

C₁₆

—

Q₈

—

122

—

Q₈

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

D₄₈₈

yes

characteristic

100

C₂×C₄

D₄₈₈

yes

characteristic

101

C₂×C₄

C₂×D₂₄₄

yes

characteristic

102

C₈

—

103

C₈

#11758224

yes

characteristic

104

C₈

Q₈×D₆₁

yes

characteristic

105

C₂²

C₂×D₄₈₈

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

488

—

109

C₄

—

488

—

110

C₄

—

488

—

111

C₄

—

244

—

112

C₄

#14519757

yes

characteristic

113

C₄

#14519810

yes

characteristic

114

C₂

#16840043

yes

characteristic

115

C₂

#16840194

yes

characteristic

116

C₂

#16840205

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₈₈
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×C₄⋊C₁₆	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	C₄⋊C₁₆	D₆₁
hypocenter	C₆₁	#2229
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂²

C₂×D₄₈₈

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×C₄⋊C₁₆

C₂

socle

C₂²×C₆₁

C₂×D₈

hypercenter

C₄⋊C₁₆

D₆₁

hypocenter

C₆₁

#2229

LCS

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
66. C₆₁	#2229	semidirect

H ≅ G/N

type

66. C₆₁

#2229

semidirect

Subgroups — #21447984

Conjugacy classes of subgroups

Complements