Group #22626040 — subgroups

Subgroups — #22626040

Order 9344.

200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 70 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×#14556661	C₂	1	1	yes	maximal, characteristic
2	#17989594	C₂	1	2	yes	maximal
3	C₂×#14556645	C₂	1	1	yes	maximal, characteristic
4	#17989457	C₂	1	2	yes	maximal
5	#17988624	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924038	C₂²	1	2	yes	—
7	C₂×#11924036	C₂²	1	1	yes	characteristic
8	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
9	#14556661	—	2	2	no	—
10	#14556658	—	2	2	no	—
11	C₄⋊#10596833	—	2	2	no	—
12	#14556645	—	2	2	no	—
13	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
14	#14556549	C₂²	1	2	yes	—
15	#14556525	C₄	1	1	yes	characteristic, complemented
16	#14556522	C₄	1	2	yes	complemented
17	#107×C₇₃	C₄	1	1	yes	characteristic, complemented
18	C₂²×#64408	—	2	1	no	—
19	#11924038	—	2	2	no	—
20	#11924038	—	2	2	no	—
21	#11924036	—	2	1	no	—
22	#11924036	—	2	1	no	—
23	C₂×#10596833	—	2	2	no	—
24	C₂×#10596833	D₄	1	2	yes	—
25	C₄×#64408	—	2	1	no	—
26	C₄×#64408	Q₈	1	2	yes	—
27	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
28	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
29	C₈×D₇₃	D₄	1	2	yes	—
30	C₈×D₇₃	Q₈	1	2	yes	—
31	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
32	#11924005	—	2	2	no	—
33	C₄×Dic₇₃	—	2	2	no	—
34	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
36	C₂²×D₇₃	#41	1	1	yes	characteristic
37	C₂×#64408	—	2	2	no	—
38	C₂×#64408	—	4	1	no	—
39	C₂×#64408	—	4	1	no	—
40	C₂×C₄×C₇₃	—	2	2	no	—
41	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×Dic₇₃	—	2	2	no	—
43	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
44	C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
45	C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
46	C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
47	C₄×D₇₃	#41	1	1	yes	characteristic
48	#10596833	—	2	2	no	—
49	#10596833	—	4	2	no	—
50	C₈×C₇₃	C₄⋊C₄	1	2	yes	—
51	#10596831	C₄⋊C₄	1	2	yes	—
52	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
53	C₂×D₇₃	—	2	1	no	—
54	C₂×D₇₃	—	2	1	no	—
55	C₂×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
56	C₂×D₇₃	#125	1	1	yes	characteristic
57	#64408	—	4	2	no	—
58	C₄×C₇₃	—	4	2	no	—
59	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
61	Dic₇₃	—	4	2	no	—
62	Dic₇₃	#121	1	1	yes	characteristic
63	Dic₇₃	C₄⋊Q₈	1	1	yes	characteristic
64	C₂×C₇₃	#389	1	1	yes	characteristic
65	C₂×C₇₃	#444	1	1	yes	characteristic
66	C₂×C₇₃	#444	1	1	yes	characteristic
67	D₇₃	—	2	1	no	—
68	D₇₃	—	2	1	no	—
69	#1946	—	73	1	no	maximal, Sylow
70	C₇₃	#1946	1	1	yes	characteristic, complemented, Sylow
71	C₂×#108	—	73	1	no	—
72	#427	—	73	1	no	—
73	#424	—	73	2	no	—
74	C₂×#97	—	73	1	no	—
75	#339	—	73	2	no	—
76	C₂×M₁₆	—	73	2	no	—
77	C₂²×C₈	—	73	1	no	—
78	C₂²×C₈	—	73	1	no	—
79	#117	—	73	2	no	—
80	C₂×C₄²	—	73	1	no	—
81	#108	—	146	2	no	—
82	#107	—	73	1	no	—
83	#107	#64408	1	1	yes	characteristic, complemented
84	#106	—	73	2	no	—
85	C₄⋊C₈	—	146	2	no	—
86	C₄⋊C₈	—	146	2	no	—
87	#97	—	146	2	no	—
88	C₂²×C₄	—	73	1	no	—
89	C₂²×C₄	—	146	1	no	—
90	M₁₆	—	146	2	no	—
91	M₁₆	—	146	2	no	—
92	C₂×C₈	—	73	1	no	—
93	C₂×C₈	—	73	2	no	—
94	C₂×C₈	—	73	2	no	—
95	C₂×C₈	—	73	2	no	—
96	C₂×C₈	—	146	2	no	—
97	C₂×C₈	—	146	1	no	—
98	C₂×C₈	—	146	1	no	—
99	C₂×C₈	C₂×#64408	1	1	yes	characteristic
100	C₄⋊C₄	—	73	2	no	—
101	C₄⋊C₄	C₂×#64408	1	2	yes	—
102	C₂²⋊C₄	—	146	2	no	—
103	C₄²	—	73	2	no	—
104	C₄²	—	146	2	no	—
105	C₄²	—	146	1	no	—
106	C₂³	—	73	1	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	292	1	no	—
109	C₂×C₄	—	292	1	no	—
110	C₂×C₄	—	73	1	no	—
111	C₂×C₄	—	73	1	no	—
112	C₂×C₄	—	73	1	no	—
113	C₂×C₄	—	73	1	no	—
114	C₂×C₄	—	73	1	no	—
115	C₂×C₄	—	146	2	no	—
116	C₂×C₄	—	146	2	no	—
117	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
118	C₈	—	292	2	no	—
119	C₈	—	73	2	no	—
120	C₈	—	146	2	no	—
121	C₈	C₄⋊#64408	1	2	yes	—
122	C₂²	—	73	1	no	—
123	C₂²	—	73	1	no	—
124	C₂²	—	146	1	no	—
125	C₂²	—	146	1	no	—
126	C₂²	D₄×#64408	1	1	yes	characteristic
127	C₄	—	4	2	no	—
128	C₄	—	292	2	no	—
129	C₄	—	292	2	no	—
130	C₄	—	73	1	no	—
131	C₄	—	73	1	no	—
132	C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
133	C₄	Q₈×#64408	1	1	yes	characteristic
134	C₂	—	146	1	no	—
135	C₂	—	146	1	no	—
136	C₂	#17989538	1	1	yes	characteristic
137	C₂	#17989633	1	1	yes	characteristic
138	C₂	#17989634	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556661

C₂

yes

maximal, characteristic

#17989594

C₂

yes

maximal

C₂×#14556645

C₂

yes

maximal, characteristic

#17989457

C₂

yes

maximal

#17988624

C₂

yes

maximal, characteristic

C₂×#11924038

C₂²

yes

—

C₂×#11924036

C₂²

yes

characteristic

C₂×C₄×#64408

C₂²

yes

—

—

—

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556549

C₂²

yes

—

#14556525

C₄

yes

characteristic, complemented

#14556522

C₄

yes

complemented

#107×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

—

—

—

—

—

D₄

yes

—

C₄×#64408

—

C₄×#64408

Q₈

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

D₄

yes

—

C₈×D₇₃

Q₈

yes

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924005

—

C₄×Dic₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂²×D₇₃

yes

—

—

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₄×D₇₃

C₂×D₄

yes

characteristic

C₄×D₇₃

C₂×Q₈

yes

characteristic

C₄×D₇₃

C₂×Q₈

yes

C₄×D₇₃

yes

—

—

C₈×C₇₃

C₄⋊C₄

yes

—

#10596831

C₄⋊C₄

yes

—

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂²⋊Q₈

yes

C₂×D₇₃

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₄×Q₈

yes

characteristic

Dic₇₃

—

Dic₇₃

#121

yes

characteristic

Dic₇₃

C₄⋊Q₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

D₇₃

—

#1946

—

maximal, Sylow

C₇₃

#1946

yes

characteristic, complemented, Sylow

C₂×#108

—

#427

—

#424

—

C₂×#97

—

#339

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

#108

—

146

—

#107

—

#107

#64408

yes

characteristic, complemented

#106

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

#97

—

146

—

C₂²×C₄

—

C₂²×C₄

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

characteristic

100

C₄⋊C₄

—

101

C₄⋊C₄

C₂×#64408

yes

—

102

C₂²⋊C₄

—

146

—

103

C₄²

—

104

C₄²

—

146

—

105

C₄²

—

146

—

106

C₂³

—

107

C₂×C₄

—

108

C₂×C₄

—

292

—

109

C₂×C₄

—

292

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

146

—

116

C₂×C₄

—

146

—

117

C₂×C₄

C₂²×#64408

yes

characteristic

118

C₈

—

292

—

119

C₈

—

120

C₈

—

146

—

121

C₈

C₄⋊#64408

yes

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

146

—

125

C₂²

—

146

—

126

C₂²

D₄×#64408

yes

characteristic

127

C₄

—

128

C₄

—

292

—

129

C₄

—

292

—

130

C₄

—

131

C₄

—

132

C₄

C₂×C₄⋊#64408

yes

characteristic

133

C₄

Q₈×#64408

yes

characteristic

134

C₂

—

146

—

135

C₂

—

146

—

136

C₂

#17989538

yes

characteristic

137

C₂

#17989633

yes

characteristic

138

C₂

#17989634

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#107×C₇₃	C₄
socle	C₂²×C₇₃	C₄×D₄
hypercenter	#107	#64408
hypocenter	C₇₃	#1946
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

subgroup

G/H

center

C₂²

D₄×#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#107×C₇₃

C₄

socle

C₂²×C₇₃

C₄×D₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

N	H ≅ G/N	type
15. #14556525	C₄	semidirect
16. #14556522	C₄	semidirect
17. #107×C₇₃	C₄	semidirect
70. C₇₃	#1946	semidirect
83. #107	#64408	semidirect

H ≅ G/N

type

15. #14556525

C₄

semidirect

16. #14556522

C₄

semidirect

17. #107×C₇₃

C₄

semidirect

70. C₇₃

#1946

semidirect

83. #107

#64408

semidirect

Subgroups — #22626040

Conjugacy classes of subgroups

Complements