Group #21444933 — subgroups

Subgroups — #21444933

Order 7808.

314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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	#16840397	C₂	1	1	yes	maximal, characteristic
2	#16840049	C₂	1	2	yes	maximal, complemented
3	#16839506	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839491	C₂	1	2	yes	maximal, complemented
5	C₆₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×D₆₁	—	2	2	no	—
7	#14519748	—	2	2	no	—
8	#14519745	—	2	2	no	—
9	C₄×D₂₄₄	C₂²	1	2	yes	—
10	#14519708	—	2	2	no	—
11	C₄⋊#92418	C₂²	1	2	yes	complemented
12	#14519697	—	2	2	no	—
13	C₂×SD₁₆×C₆₁	—	2	2	no	—
14	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
15	#127×C₆₁	C₂²	1	1	yes	characteristic
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₆₁	—	2	2	no	—
18	C₂×Q₈×C₆₁	—	2	1	no	—
19	C₂×D₄×C₆₁	—	2	2	no	—
20	C₂×D₄×C₆₁	D₄	1	2	yes	—
21	C₂×C₂²⋊D₆₁	—	2	4	no	—
22	D₄×D₆₁	—	4	4	no	—
23	D₄×D₆₁	—	4	4	no	—
24	C₂×D₂₄₄	D₄	1	2	yes	—
25	C₂×C₄×D₆₁	—	2	2	no	—
26	SD₁₆×C₆₁	—	4	4	no	—
27	C₂×C₈×C₆₁	—	2	1	no	—
28	C₄⋊C₄×C₆₁	—	2	2	no	—
29	C₄²×C₆₁	C₂³	1	1	yes	characteristic
30	C₂²⋊Dic₆₁	—	2	2	no	—
31	#11758198	—	2	2	no	—
32	C₄⋊Dic₆₁	D₄	1	2	yes	—
33	C₂×#92418	—	2	2	no	—
34	C₂³×C₆₁	—	2	2	no	—
35	C₂²×D₆₁	—	2	2	no	—
36	C₂²×D₆₁	—	4	8	no	—
37	C₂²×D₆₁	—	8	2	no	—
38	Q₈×C₆₁	—	4	2	no	—
39	D₄×C₆₁	—	4	2	no	—
40	D₄×C₆₁	—	4	2	no	—
41	D₄×C₆₁	—	4	2	no	—
42	C₂×C₄×C₆₁	—	4	1	no	—
43	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
45	C₂²⋊D₆₁	—	4	8	no	—
46	C₂×Dic₆₁	—	2	2	no	—
47	D₂₄₄	—	2	2	no	—
48	D₂₄₄	SD₁₆	1	4	yes	complemented
49	C₄×D₆₁	—	4	2	no	—
50	C₄×D₆₁	—	4	2	no	—
51	C₈×C₆₁	—	2	2	no	—
52	#92418	—	4	2	no	—
53	C₂²×C₆₁	—	4	4	no	—
54	C₂²×C₆₁	—	4	2	no	—
55	C₂²×C₆₁	#120	1	1	yes	characteristic
56	C₂×D₆₁	—	2	4	no	—
57	C₂×D₆₁	—	4	2	no	—
58	C₂×D₆₁	—	4	2	no	—
59	C₂×D₆₁	—	8	8	no	—
60	C₄×C₆₁	—	2	1	no	—
61	C₄×C₆₁	—	8	1	no	—
62	C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
63	C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
64	Dic₆₁	—	4	2	no	—
65	#1629	—	61	1	no	maximal, Sylow
66	C₂×C₆₁	—	8	2	no	—
67	C₂×C₆₁	#450	1	2	yes	—
68	C₂×C₆₁	#453	1	1	yes	characteristic
69	D₆₁	—	4	4	no	—
70	D₄²	—	61	1	no	—
71	#492	D₆₁	1	1	yes	characteristic, complemented
72	#476	—	61	2	no	—
73	#331	—	61	1	no	—
74	D₄⋊C₈	—	61	2	no	—
75	C₆₁	#1629	1	1	yes	characteristic, complemented, Sylow
76	C₂²×D₄	—	122	2	no	—
77	C₂×SD₁₆	—	2	2	no	—
78	C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
79	#127	C₂×D₆₁	1	1	yes	characteristic
80	#121	—	122	2	no	—
81	#120	—	122	2	no	—
82	C₄×D₄	—	61	2	no	—
83	#106	—	122	2	no	—
84	C₄⋊C₈	—	61	2	no	—
85	#102	—	122	2	no	—
86	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic, complemented
87	C₂⁴	—	122	2	no	—
88	C₂×Q₈	—	2	1	no	—
89	C₂×D₄	—	2	2	no	—
90	C₂×D₄	—	61	2	no	—
91	C₂×D₄	—	122	4	no	—
92	C₂×D₄	—	244	4	no	—
93	C₂×D₄	—	244	4	no	—
94	C₂×D₄	C₂²⋊D₆₁	1	2	yes	—
95	C₂²×C₄	—	122	2	no	—
96	SD₁₆	—	4	4	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	122	2	no	—
99	C₄⋊C₄	—	2	2	no	—
100	C₄⋊C₄	—	61	2	no	—
101	C₂²⋊C₄	—	122	2	no	—
102	C₂²⋊C₄	—	122	2	no	—
103	C₄²	C₂²×D₆₁	1	1	yes	characteristic
104	C₂³	—	2	2	no	—
105	C₂³	—	122	2	no	—
106	C₂³	—	488	2	no	—
107	C₂³	—	244	8	no	—
108	Q₈	—	4	2	no	—
109	D₄	—	4	2	no	—
110	D₄	—	4	2	no	—
111	D₄	—	4	2	no	—
112	D₄	—	61	4	no	—
113	D₄	—	122	2	no	—
114	D₄	—	244	8	no	—
115	C₂×C₄	—	4	1	no	—
116	C₂×C₄	—	122	2	no	—
117	C₂×C₄	—	244	2	no	—
118	C₂×C₄	—	244	2	no	—
119	C₂×C₄	D₄×D₆₁	1	2	yes	—
120	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
121	C₈	—	2	2	no	—
122	C₈	—	244	2	no	—
123	C₂²	—	4	4	no	—
124	C₂²	—	4	2	no	—
125	C₂²	—	122	4	no	—
126	C₂²	—	488	8	no	—
127	C₂²	—	244	2	no	—
128	C₂²	—	244	2	no	—
129	C₂²	#14519745	1	1	yes	characteristic
130	C₄	—	2	1	no	—
131	C₄	—	8	1	no	—
132	C₄	—	244	2	no	—
133	C₄	SD₁₆×D₆₁	1	2	yes	—
134	C₄	#14519804	1	2	yes	—
135	C₂	—	8	2	no	—
136	C₂	—	244	4	no	—
137	C₂	#16839911	1	2	yes	—
138	C₂	#16839929	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840397

C₂

yes

maximal, characteristic

#16840049

C₂

yes

maximal, complemented

#16839506

C₂

yes

maximal, characteristic, complemented

#16839491

C₂

yes

maximal, complemented

C₆₁×#492

C₂

yes

maximal, characteristic, complemented

C₂×D₄×D₆₁

—

#14519748

—

#14519745

—

C₄×D₂₄₄

C₂²

yes

—

#14519708

—

C₄⋊#92418

C₂²

yes

complemented

#14519697

—

C₂×SD₁₆×C₆₁

—

C₄⋊Q₈×C₆₁

C₂²

yes

characteristic, complemented

#127×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic, complemented

C₂³×D₆₁

—

C₂×Q₈×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

D₄

yes

—

C₂×C₂²⋊D₆₁

—

D₄×D₆₁

—

D₄×D₆₁

—

C₂×D₂₄₄

D₄

yes

—

C₂×C₄×D₆₁

—

SD₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

C₂³

yes

characteristic

C₂²⋊Dic₆₁

—

#11758198

—

C₄⋊Dic₆₁

D₄

yes

—

C₂×#92418

—

C₂³×C₆₁

—

C₂²×D₆₁

—

C₂²×D₆₁

—

C₂²×D₆₁

—

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂²⋊D₆₁

—

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

SD₁₆

yes

complemented

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#120

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×SD₁₆

yes

—

C₄×C₆₁

AGL(1,ℤ/8)

yes

—

Dic₆₁

—

#1629

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#450

yes

—

C₂×C₆₁

#453

yes

characteristic

D₆₁

—

D₄²

—

#492

D₆₁

yes

characteristic, complemented

#476

—

#331

—

D₄⋊C₈

—

C₆₁

#1629

yes

characteristic, complemented, Sylow

C₂²×D₄

—

122

—

C₂×SD₁₆

—

C₄⋊Q₈

C₂×D₆₁

yes

characteristic, complemented

#127

C₂×D₆₁

yes

characteristic

#121

—

122

—

#120

—

122

—

C₄×D₄

—

#106

—

122

—

C₄⋊C₈

—

#102

—

122

—

C₄×C₈

C₂×D₆₁

yes

characteristic, complemented

C₂⁴

—

122

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

122

—

C₂×D₄

—

244

—

C₂×D₄

—

244

—

C₂×D₄

C₂²⋊D₆₁

yes

—

C₂²×C₄

—

122

—

SD₁₆

—

C₂×C₈

—

C₂×C₈

—

122

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

122

—

102

C₂²⋊C₄

—

122

—

103

C₄²

C₂²×D₆₁

yes

characteristic

104

C₂³

—

105

C₂³

—

122

—

106

C₂³

—

488

—

107

C₂³

—

244

—

108

Q₈

—

109

D₄

—

110

D₄

—

111

D₄

—

112

D₄

—

113

D₄

—

122

—

114

D₄

—

244

—

115

C₂×C₄

—

116

C₂×C₄

—

122

—

117

C₂×C₄

—

244

—

118

C₂×C₄

—

244

—

119

C₂×C₄

D₄×D₆₁

yes

—

120

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

121

C₈

—

122

C₈

—

244

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

122

—

126

C₂²

—

488

—

127

C₂²

—

244

—

128

C₂²

—

244

—

129

C₂²

#14519745

yes

characteristic

130

C₄

—

131

C₄

—

132

C₄

—

244

—

133

C₄

SD₁₆×D₆₁

yes

—

134

C₄

#14519804

yes

—

135

C₂

—

136

C₂

—

244

—

137

C₂

#16839911

yes

—

138

C₂

#16839929

yes

characteristic

	subgroup	G/H
center	C₂²	#14519745
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#492	C₂
socle	C₂²×C₆₁	#120
hypercenter	#492	D₆₁
hypocenter	C₆₁	#1629
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

#14519745

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#492

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
2. #16840049	C₂	semidirect
3. #16839506	C₂	semidirect
4. #16839491	C₂	semidirect
5. C₆₁×#492	C₂	semidirect
11. C₄⋊#92418	C₂²	semidirect
14. C₄⋊Q₈×C₆₁	C₂²	semidirect
16. C₄×C₈×C₆₁	C₂²	semidirect
48. D₂₄₄	SD₁₆	semidirect
71. #492	D₆₁	semidirect
75. C₆₁	#1629	semidirect
78. C₄⋊Q₈	C₂×D₆₁	semidirect
86. C₄×C₈	C₂×D₆₁	semidirect

H ≅ G/N

type

2. #16840049

C₂

semidirect

3. #16839506

C₂

semidirect

4. #16839491

C₂

semidirect

5. C₆₁×#492

C₂

semidirect

11. C₄⋊#92418

C₂²

semidirect

14. C₄⋊Q₈×C₆₁

C₂²

semidirect

16. C₄×C₈×C₆₁

C₂²

semidirect

48. D₂₄₄

SD₁₆

semidirect

71. #492

D₆₁

semidirect

75. C₆₁

#1629

semidirect

78. C₄⋊Q₈

C₂×D₆₁

semidirect

86. C₄×C₈

C₂×D₆₁

semidirect

Subgroups — #21444933

Conjugacy classes of subgroups

Complements