Group #21461384 — subgroups

Subgroups — #21461384

Order 7808.

166 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 68 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	#16840784	C₂	1	1	yes	maximal, characteristic
2	#16840766	C₂	1	1	yes	maximal, characteristic
3	#16840625	C₂	1	2	yes	maximal, complemented
4	#16840623	C₂	1	2	yes	maximal, complemented
5	#16839714	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758213	—	2	1	no	—
7	C₄⋊#92420	—	2	1	no	—
8	C₄⋊#92420	C₂²	1	2	yes	—
9	C₄⋊#92420	C₂²	1	1	yes	characteristic
10	C₄⋊#92420	C₂²	1	1	yes	characteristic
11	#14519834	—	2	1	no	—
12	#14519832	—	2	1	no	—
13	C₂×#11758189	C₄	1	2	yes	—
14	C₄²×D₆₁	C₂²	1	1	yes	characteristic
15	#14519688	C₄	1	1	yes	characteristic
16	C₈×Dic₆₁	C₂²	1	2	yes	—
17	#97×C₆₁	C₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
20	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
21	C₂×#92420	—	2	1	no	—
22	C₂×#92420	—	2	1	no	—
23	C₂×#92420	—	2	2	no	—
24	#11758213	—	4	2	no	—
25	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
26	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₆₁	D₄	1	1	yes	characteristic
28	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
29	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
30	C₂×#92418	C₂×C₄	1	2	yes	—
31	#11758189	—	2	4	no	—
32	C₂²×D₆₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
39	C₄×D₆₁	—	2	2	no	—
40	C₄×D₆₁	—	2	1	no	—
41	C₄×D₆₁	—	2	1	no	—
42	C₄×D₆₁	—	4	1	no	—
43	#92420	—	4	2	no	—
44	#92420	—	4	1	no	—
45	#92420	—	4	1	no	—
46	C₈×C₆₁	M₁₆	1	4	yes	complemented
47	#92418	—	2	2	no	—
48	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×D₆₁	—	2	1	no	—
50	C₂×D₆₁	—	2	1	no	—
51	C₂×D₆₁	—	2	1	no	—
52	C₄×C₆₁	—	2	1	no	—
53	C₄×C₆₁	—	2	1	no	—
54	C₄×C₆₁	C₂×M₁₆	1	2	yes	—
55	Dic₆₁	—	2	1	no	—
56	Dic₆₁	—	2	1	no	—
57	Dic₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
58	Dic₆₁	#137	1	1	yes	characteristic
59	#1569	—	61	1	no	maximal, Sylow
60	C₂×C₆₁	#423	1	1	yes	characteristic
61	C₂×C₆₁	#428	1	1	yes	characteristic
62	C₂×C₆₁	#430	1	1	yes	characteristic
63	D₆₁	—	4	1	no	—
64	#432	—	61	1	no	—
65	#423	—	61	1	no	—
66	C₄×M₁₆	—	61	1	no	—
67	#335	—	61	2	no	—
68	#334	—	61	2	no	—
69	C₆₁	#1569	1	1	yes	characteristic, complemented, Sylow
70	C₂×M₁₆	—	61	2	no	—
71	C₂×M₁₆	—	122	1	no	—
72	C₂×C₄²	—	61	1	no	—
73	C₄⋊C₈	—	61	1	no	—
74	C₄⋊C₈	—	61	2	no	—
75	C₄⋊C₈	—	61	1	no	—
76	C₄⋊C₈	—	122	1	no	—
77	C₂²⋊C₈	—	122	1	no	—
78	#97	—	61	1	no	—
79	#97	—	122	1	no	—
80	#97	#6923	1	1	yes	characteristic
81	C₄×C₈	—	61	2	no	—
82	C₂²×C₄	—	61	1	no	—
83	C₂²×C₄	—	61	1	no	—
84	C₂²×C₄	—	61	1	no	—
85	M₁₆	—	122	4	no	—
86	M₁₆	—	244	2	no	—
87	C₂×C₈	—	61	2	no	—
88	C₂×C₈	—	122	1	no	—
89	C₂×C₈	—	122	1	no	—
90	C₂×C₈	—	122	2	no	—
91	C₂×C₈	C₂×#6923	1	2	yes	—
92	C₄²	—	61	1	no	—
93	C₄²	—	61	1	no	—
94	C₄²	—	61	1	no	—
95	C₄²	C₂×#6923	1	1	yes	characteristic
96	C₂³	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	122	1	no	—
101	C₂×C₄	—	122	1	no	—
102	C₂×C₄	—	122	2	no	—
103	C₂×C₄	—	244	1	no	—
104	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
105	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
106	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
107	C₈	—	122	2	no	—
108	C₈	—	244	1	no	—
109	C₈	—	244	1	no	—
110	C₈	—	244	2	no	—
111	C₈	#11758213	1	4	yes	complemented
112	C₂²	—	122	1	no	—
113	C₂²	—	122	1	no	—
114	C₂²	—	122	1	no	—
115	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
116	C₄	—	2	1	no	—
117	C₄	—	2	1	no	—
118	C₄	—	61	1	no	—
119	C₄	—	61	1	no	—
120	C₄	—	122	1	no	—
121	C₄	—	122	1	no	—
122	C₄	C₂×#11758213	1	2	yes	—
123	C₂	—	244	1	no	—
124	C₂	#16840766	1	1	yes	characteristic
125	C₂	#16840773	1	1	yes	characteristic
126	C₂	#16840777	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840784

C₂

yes

maximal, characteristic

#16840766

C₂

yes

maximal, characteristic

#16840625

C₂

yes

maximal, complemented

#16840623

C₂

yes

maximal, complemented

#16839714

C₂

yes

maximal, characteristic

C₂×#11758213

—

C₄⋊#92420

—

C₄⋊#92420

C₂²

yes

—

C₄⋊#92420

C₂²

yes

characteristic

C₄⋊#92420

C₂²

yes

—

—

C₄

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#14519688

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

—

#97×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

—

—

—

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

—

#11758189

—

C₂²×D₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

C₂×Q₈

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

#92420

—

#92420

—

#92420

—

C₈×C₆₁

M₁₆

yes

complemented

#92418

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#432

—

#423

—

C₄×M₁₆

—

#335

—

#334

—

C₆₁

#1569

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

122

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

#97

—

#97

—

122

—

#97

#6923

yes

characteristic

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

122

—

101

C₂×C₄

—

122

—

102

C₂×C₄

—

122

—

103

C₂×C₄

—

244

—

104

C₂×C₄

C₄⋊#6923

yes

characteristic

105

C₂×C₄

C₄⋊#6923

yes

characteristic

106

C₂×C₄

C₂²×#6923

yes

characteristic

107

C₈

—

122

—

108

C₈

—

244

—

109

C₈

—

244

—

110

C₈

—

244

—

111

C₈

#11758213

yes

complemented

112

C₂²

—

122

—

113

C₂²

—

122

—

114

C₂²

—

122

—

115

C₂²

C₂×C₄⋊#6923

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

122

—

121

C₄

—

122

—

122

C₄

C₂×#11758213

yes

—

123

C₂

—

244

—

124

C₂

#16840766

yes

characteristic

125

C₂

#16840773

yes

characteristic

126

C₂

#16840777

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#97×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	#97	#6923
hypocenter	C₆₁	#1569
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

#97×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
3. #16840625	C₂	semidirect
4. #16840623	C₂	semidirect
46. C₈×C₆₁	M₁₆	semidirect
69. C₆₁	#1569	semidirect
111. C₈	#11758213	semidirect

H ≅ G/N

type

3. #16840625

C₂

semidirect

4. #16840623

C₂

semidirect

46. C₈×C₆₁

M₁₆

semidirect

69. C₆₁

#1569

semidirect

111. C₈

#11758213

semidirect

Subgroups — #21461384

Conjugacy classes of subgroups

Complements