Group #21445868 — subgroups

Subgroups — #21445868

Order 7808.

252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14519785	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519712	C₂	1	2	yes	maximal, complemented
3	#16839744	C₂	1	2	yes	maximal
4	#16839520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758222	C₂²	1	1	yes	characteristic
7	#14519785	—	2	4	no	—
8	C₂×#11758194	C₂²	1	2	yes	—
9	C₂×#11758189	C₄	1	2	yes	—
10	C₂²×#92418	C₂²	1	1	yes	characteristic
11	C₂×C₈×D₆₁	C₄	1	2	yes	—
12	#14519712	—	2	4	no	—
13	#14519695	—	2	2	no	—
14	#14519693	—	2	2	no	—
15	C₂×M₁₆×C₆₁	C₂²	1	2	yes	—
16	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
18	C₂×C₂²⋊D₆₁	Q₈	1	2	yes	—
19	#11758222	—	2	2	no	—
20	#11758222	—	2	2	no	—
21	C₂×D₂₄₄	D₄	1	1	yes	characteristic
22	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
23	C₂×Dic₁₂₂	D₄	1	1	yes	characteristic
24	M₁₆×C₆₁	—	2	2	no	—
25	M₁₆×C₆₁	—	2	2	no	—
26	M₁₆×C₆₁	—	2	2	no	—
27	C₂×C₈×C₆₁	—	2	2	no	—
28	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
29	#11758194	—	2	2	no	—
30	#11758194	—	2	2	no	—
31	C₂×#92418	—	2	2	no	—
32	C₂×#92418	C₂×C₄	1	1	yes	characteristic
33	C₂×#92418	C₂×C₄	1	1	yes	characteristic
34	C₂×#92418	D₄	1	4	yes	—
35	#11758189	—	2	4	no	—
36	C₈×D₆₁	—	2	4	no	—
37	C₂³×C₆₁	C₂×Q₈	1	1	yes	characteristic
38	C₂²×D₆₁	C₄⋊C₄	1	2	yes	—
39	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₆₁	#41	1	2	yes	—
43	C₂²⋊D₆₁	—	2	4	no	—
44	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
45	D₂₄₄	—	2	2	no	—
46	C₄×D₆₁	—	2	2	no	—
47	C₄×D₆₁	—	2	2	no	—
48	Dic₁₂₂	—	2	2	no	—
49	C₈×C₆₁	—	2	2	no	—
50	C₈×C₆₁	—	4	2	no	—
51	#92418	—	4	2	no	—
52	#92418	C₂²⋊C₄	1	2	yes	—
53	#92418	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₆₁	—	4	1	no	—
55	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₆₁	C₂²⋊Q₈	1	2	yes	—
57	C₂×D₆₁	—	2	2	no	—
58	C₂×D₆₁	—	4	2	no	—
59	C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₄×C₆₁	#117	1	1	yes	characteristic
61	C₄×C₆₁	#121	1	2	yes	—
62	Dic₆₁	—	2	2	no	—
63	#1813	—	61	1	no	maximal, Sylow
64	C₂×C₆₁	—	2	1	no	—
65	C₂×C₆₁	—	2	2	no	—
66	C₂×C₆₁	#380	1	1	yes	characteristic
67	D₆₁	—	4	2	no	—
68	C₂×#131	—	61	1	no	—
69	C₂×#108	—	61	2	no	—
70	#413	—	61	2	no	—
71	#338	—	61	1	no	—
72	#338	D₆₁	1	1	yes	characteristic, complemented
73	C₆₁	#1813	1	1	yes	characteristic, complemented, Sylow
74	C₂×#41	—	61	1	no	—
75	#131	—	122	4	no	—
76	C₂×M₁₆	—	61	2	no	—
77	C₂×M₁₆	—	61	2	no	—
78	C₂×M₁₆	C₂×D₆₁	1	2	yes	—
79	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
80	C₂²×C₈	—	61	1	no	—
81	C₂²×C₈	—	61	2	no	—
82	#108	—	122	4	no	—
83	#101	—	122	2	no	—
84	#100	—	122	2	no	—
85	#41	—	122	2	no	—
86	#41	—	122	2	no	—
87	C₂×Q₈	—	61	1	no	—
88	C₂×D₄	—	61	2	no	—
89	C₂×D₄	—	61	1	no	—
90	C₂²×C₄	—	61	2	no	—
91	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
92	M₁₆	—	2	2	no	—
93	M₁₆	—	2	2	no	—
94	M₁₆	—	2	2	no	—
95	M₁₆	—	122	4	no	—
96	M₁₆	—	122	2	no	—
97	M₁₆	—	122	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	61	1	no	—
100	C₂×C₈	—	61	1	no	—
101	C₂×C₈	—	61	4	no	—
102	C₂×C₈	—	122	4	no	—
103	C₂×C₈	—	122	2	no	—
104	C₂×C₈	C₄×D₆₁	1	2	yes	—
105	C₂³	—	61	2	no	—
106	C₂³	Q₈×D₆₁	1	1	yes	characteristic
107	Q₈	—	122	2	no	—
108	D₄	—	122	4	no	—
109	D₄	—	122	2	no	—
110	C₂×C₄	—	61	2	no	—
111	C₂×C₄	—	122	2	no	—
112	C₂×C₄	—	122	2	no	—
113	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
114	C₂×C₄	#11758222	1	2	yes	—
115	C₂×C₄	D₄×D₆₁	1	2	yes	—
116	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
117	C₈	—	2	2	no	—
118	C₈	—	4	2	no	—
119	C₈	—	61	2	no	—
120	C₈	—	61	2	no	—
121	C₈	—	244	2	no	—
122	C₂²	—	4	1	no	—
123	C₂²	—	122	2	no	—
124	C₂²	—	244	2	no	—
125	C₂²	C₄⋊C₄×D₆₁	1	1	yes	characteristic
126	C₂²	#14519755	1	2	yes	—
127	C₄	—	122	2	no	—
128	C₄	C₂²⋊C₄×D₆₁	1	1	yes	characteristic
129	C₄	#14519734	1	1	yes	characteristic
130	C₄	#14519750	1	2	yes	—
131	C₂	—	2	1	no	—
132	C₂	—	2	2	no	—
133	C₂	—	244	2	no	—
134	C₂	#16839621	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519785

C₂

yes

maximal, characteristic

C₂×#14519712

C₂

yes

maximal, complemented

#16839744

C₂

yes

maximal

#16839520

C₂

yes

maximal, characteristic, complemented

C₆₁×#338

C₂

yes

maximal, characteristic, complemented

C₂×#11758222

C₂²

yes

characteristic

#14519785

—

C₂×#11758194

C₂²

yes

—

C₂×#11758189

C₄

yes

—

C₂²×#92418

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₄

yes

—

#14519712

—

#14519695

—

#14519693

—

C₂×M₁₆×C₆₁

C₂²

yes

—

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂×C₂²⋊D₆₁

Q₈

yes

—

#11758222

—

#11758222

—

C₂×D₂₄₄

D₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

—

C₂×Dic₁₂₂

D₄

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

D₄

yes

—

#11758189

—

C₈×D₆₁

—

C₂³×C₆₁

C₂×Q₈

yes

characteristic

C₂²×D₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂²⋊D₆₁

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

D₂₄₄

—

C₄×D₆₁

—

C₄×D₆₁

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

—

#92418

—

#92418

C₂²⋊C₄

yes

—

#92418

C₂²⋊C₄

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

C₂²⋊Q₈

yes

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

C₂×C₂²⋊C₄

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

Dic₆₁

—

#1813

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#380

yes

characteristic

D₆₁

—

—

—

—

—

D₆₁

yes

characteristic, complemented

C₆₁

#1813

yes

characteristic, complemented, Sylow

C₂×#41

—

#131

—

122

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

#108

—

122

—

#101

—

122

—

#100

—

122

—

#41

—

122

—

#41

—

122

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

122

—

103

C₂×C₈

—

122

—

104

C₂×C₈

C₄×D₆₁

yes

—

105

C₂³

—

106

C₂³

Q₈×D₆₁

yes

characteristic

107

Q₈

—

122

—

108

D₄

—

122

—

109

D₄

—

122

—

110

C₂×C₄

—

111

C₂×C₄

—

122

—

112

C₂×C₄

—

122

—

113

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

114

C₂×C₄

#11758222

yes

—

115

C₂×C₄

D₄×D₆₁

yes

—

116

C₂×C₄

D₄×D₆₁

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

—

244

—

122

C₂²

—

123

C₂²

—

122

—

124

C₂²

—

244

—

125

C₂²

C₄⋊C₄×D₆₁

yes

characteristic

126

C₂²

#14519755

yes

—

127

C₄

—

122

—

128

C₄

C₂²⋊C₄×D₆₁

yes

characteristic

129

C₄

#14519734

yes

characteristic

130

C₄

#14519750

yes

—

131

C₂

—

132

C₂

—

133

C₂

—

244

—

134

C₂

#16839621

yes

characteristic

	subgroup	G/H
center	C₄	#14519734
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#338	C₂
socle	C₂×C₆₁	#380
hypercenter	#338	D₆₁
hypocenter	C₆₁	#1813
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

subgroup

G/H

center

C₄

#14519734

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#338

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

N	H ≅ G/N	type
2. C₂×#14519712	C₂	semidirect
4. #16839520	C₂	semidirect
5. C₆₁×#338	C₂	semidirect
72. #338	D₆₁	semidirect
73. C₆₁	#1813	semidirect

H ≅ G/N

type

2. C₂×#14519712

C₂

semidirect

4. #16839520

C₂

semidirect

5. C₆₁×#338

C₂

semidirect

72. #338

D₆₁

semidirect

73. C₆₁

#1813

semidirect

Subgroups — #21445868

Conjugacy classes of subgroups

Complements