Group #21445208 — subgroups

Subgroups — #21445208

Order 7808.

172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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	#16840167	C₂	1	1	yes	maximal, characteristic, complemented
2	#16839967	C₂	1	2	yes	maximal
3	#16839515	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839507	C₂	1	2	yes	maximal, complemented
5	C₈×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758200	—	2	2	no	—
7	#14519777	C₂²	1	2	yes	—
8	#14519711	—	2	1	no	—
9	#14519711	—	2	1	no	—
10	C₄⋊#92418	C₂²	1	2	yes	—
11	#14519700	—	2	2	no	—
12	C₂²×C₈×C₆₁	—	2	1	no	—
13	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²⋊C₈×C₆₁	—	2	1	no	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₆₁	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₆₁	—	2	1	no	—
19	C₂×Dic₁₂₂	—	2	2	no	—
20	C₂×C₈×C₆₁	—	2	1	no	—
21	C₂×C₈×C₆₁	—	4	2	no	—
22	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
23	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
25	C₂²⋊C₄×C₆₁	—	2	1	no	—
26	C₄²×C₆₁	C₂³	1	1	yes	characteristic
27	#11758200	—	4	4	no	—
28	C₄⋊Dic₆₁	—	2	2	no	—
29	C₄⋊Dic₆₁	—	2	2	no	—
30	C₂×#92418	—	2	2	no	—
31	C₂³×C₆₁	—	2	1	no	—
32	D₄×C₆₁	—	2	1	no	—
33	D₄×C₆₁	D₈	1	2	yes	—
34	C₂×C₄×C₆₁	—	2	1	no	—
35	C₂×C₄×C₆₁	—	4	1	no	—
36	C₂×C₄×C₆₁	—	4	1	no	—
37	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
40	C₂×Dic₆₁	—	4	2	no	—
41	Dic₁₂₂	—	4	2	no	—
42	Dic₁₂₂	—	4	2	no	—
43	C₈×C₆₁	—	2	1	no	—
44	C₈×C₆₁	—	4	1	no	—
45	C₈×C₆₁	SD₁₆	1	2	yes	complemented
46	#92418	—	4	2	no	—
47	C₂²×C₆₁	—	2	2	no	—
48	C₂²×C₆₁	—	4	1	no	—
49	C₂²×C₆₁	—	4	1	no	—
50	C₂²×C₆₁	#121	1	1	yes	characteristic
51	C₄×C₆₁	—	2	1	no	—
52	C₄×C₆₁	—	4	1	no	—
53	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
54	C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
55	C₄×C₆₁	#135	1	1	yes	characteristic
56	C₄×C₆₁	#137	1	1	yes	characteristic
57	Dic₆₁	—	8	2	no	—
58	#1673	—	61	1	no	maximal, Sylow
59	C₂×C₆₁	—	4	2	no	—
60	C₂×C₆₁	#461	1	1	yes	characteristic
61	C₂×C₆₁	#466	1	1	yes	characteristic
62	C₂×C₆₁	#473	1	1	yes	characteristic
63	#500	—	61	1	no	—
64	#461	—	61	2	no	—
65	C₈×D₄	D₆₁	1	1	yes	characteristic
66	#335	—	61	1	no	—
67	#332	—	61	2	no	—
68	C₆₁	#1673	1	1	yes	characteristic, complemented, Sylow
69	C₂×SD₁₆	—	122	2	no	—
70	C₂²×C₈	—	2	1	no	—
71	C₄⋊Q₈	—	61	2	no	—
72	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
73	#107	—	122	1	no	—
74	#107	—	122	1	no	—
75	C₄⋊C₈	—	61	2	no	—
76	C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
77	#103	—	122	2	no	—
78	C₂²⋊C₈	—	2	1	no	—
79	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
80	C₂×Q₈	—	122	2	no	—
81	C₂×D₄	D₂₄₄	1	1	yes	characteristic
82	C₂²×C₄	—	2	1	no	—
83	SD₁₆	—	244	4	no	—
84	C₂×C₈	—	2	1	no	—
85	C₂×C₈	—	4	2	no	—
86	C₂×C₈	—	122	2	no	—
87	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
88	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
89	C₄⋊C₄	—	122	2	no	—
90	C₄⋊C₄	—	122	2	no	—
91	C₄⋊C₄	D₂₄₄	1	1	yes	characteristic
92	C₂²⋊C₄	—	2	1	no	—
93	C₄²	C₂²×D₆₁	1	1	yes	characteristic
94	C₂³	—	2	1	no	—
95	Q₈	—	244	2	no	—
96	Q₈	—	244	2	no	—
97	D₄	—	2	1	no	—
98	D₄	D₄₈₈	1	2	yes	—
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	244	2	no	—
103	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
104	C₂×C₄	#11758222	1	1	yes	characteristic
105	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
106	C₈	—	2	1	no	—
107	C₈	—	4	1	no	—
108	C₈	—	244	2	no	—
109	C₈	#11758200	1	2	yes	complemented
110	C₂²	—	2	2	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	4	1	no	—
113	C₂²	#14519751	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	4	1	no	—
116	C₄	—	488	2	no	—
117	C₄	C₂×D₄₈₈	1	1	yes	characteristic
118	C₄	C₂×#11758200	1	1	yes	characteristic
119	C₄	#14519799	1	1	yes	characteristic
120	C₄	#14519807	1	1	yes	characteristic
121	C₂	—	4	2	no	—
122	C₂	#16839967	1	1	yes	characteristic
123	C₂	#16839998	1	1	yes	characteristic
124	C₂	#16840037	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840167

C₂

yes

maximal, characteristic, complemented

#16839967

C₂

yes

maximal

#16839515

C₂

yes

maximal, characteristic, complemented

#16839507

C₂

yes

maximal, complemented

C₈×D₄×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758200

—

#14519777

C₂²

yes

—

#14519711

—

#14519711

—

C₄⋊#92418

C₂²

yes

—

#14519700

—

C₂²×C₈×C₆₁

—

C₄×D₄×C₆₁

C₂²

yes

characteristic

C₄⋊C₈×C₆₁

C₂²

yes

characteristic

C₂²⋊C₈×C₆₁

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₄×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₄⋊C₄×C₆₁

D₄

yes

characteristic

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

C₂³

yes

characteristic

#11758200

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₂×#92418

—

C₂³×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

D₈

yes

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

SD₁₆

yes

complemented

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#121

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×D₈

yes

characteristic

C₄×C₆₁

C₂×SD₁₆

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

#1673

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

C₈×D₄

D₆₁

yes

characteristic

#335

—

#332

—

C₆₁

#1673

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

122

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄×D₄

C₂×D₆₁

yes

characteristic

#107

—

122

—

#107

—

122

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₆₁

yes

characteristic

#103

—

122

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

C₂×D₄

D₂₄₄

yes

characteristic

C₂²×C₄

—

SD₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

D₂₄₄

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

Q₈

—

244

—

Q₈

—

244

—

D₄

—

D₄

D₄₈₈

yes

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

244

—

103

C₂×C₄

C₂×D₂₄₄

yes

characteristic

104

C₂×C₄

#11758222

yes

characteristic

105

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

106

C₈

—

107

C₈

—

108

C₈

—

244

—

109

C₈

#11758200

yes

complemented

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

#14519751

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

488

—

117

C₄

C₂×D₄₈₈

yes

characteristic

118

C₄

C₂×#11758200

yes

characteristic

119

C₄

#14519799

yes

characteristic

120

C₄

#14519807

yes

characteristic

121

C₂

—

122

C₂

#16839967

yes

characteristic

123

C₂

#16839998

yes

characteristic

124

C₂

#16840037

yes

characteristic

	subgroup	G/H
center	C₂²	#14519751
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₈×D₄×C₆₁	C₂
socle	C₂²×C₆₁	#121
hypercenter	C₈×D₄	D₆₁
hypocenter	C₆₁	#1673
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₄

subgroup

G/H

center

C₂²

#14519751

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₈×D₄×C₆₁

C₂

socle

C₂²×C₆₁

#121

hypercenter

C₈×D₄

D₆₁

hypocenter

C₆₁

#1673

LCS

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₄

N	H ≅ G/N	type
1. #16840167	C₂	semidirect
3. #16839515	C₂	semidirect
4. #16839507	C₂	semidirect
45. C₈×C₆₁	SD₁₆	semidirect
68. C₆₁	#1673	semidirect
109. C₈	#11758200	semidirect

H ≅ G/N

type

1. #16840167

C₂

semidirect

3. #16839515

C₂

semidirect

4. #16839507

C₂

semidirect

45. C₈×C₆₁

SD₁₆

semidirect

68. C₆₁

#1673

semidirect

109. C₈

#11758200

semidirect

Subgroups — #21445208

Conjugacy classes of subgroups

Complements