Group #22626938 — subgroups

Subgroups — #22626938

Order 9344.

172 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 55 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	#17989700	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10596842	C₂	1	1	yes	maximal, characteristic
3	M₁₆×#64408	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10596842	—	2	1	no	—
5	C₄⋊#10596842	C₄	1	2	yes	—
6	C₂²⋊#10596842	—	2	1	no	—
7	C₄×#10596842	—	2	1	no	—
8	C₄×#10596842	—	2	1	no	—
9	C₄×#10596842	C₄	1	2	yes	—
10	D₇₃⋊M₁₆	C₄	1	1	yes	characteristic
11	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
12	#14556645	—	2	1	no	—
13	C₈×#64408	—	2	1	no	—
14	M₁₆×D₇₃	C₄	1	1	yes	characteristic
15	C₂×#10596842	—	2	4	no	—
16	C₂×#10596842	—	2	2	no	—
17	C₂×#10596842	—	2	2	no	—
18	C₂²×#64408	D₄	1	1	yes	characteristic
19	C₂²×#64408	Q₈	1	1	yes	characteristic
20	#11924038	C₈	1	2	yes	complemented
21	#11924037	—	2	1	no	—
22	#11924036	—	2	1	no	—
23	C₄×#64408	C₂×C₄	1	1	yes	characteristic
24	C₄×#64408	C₂×C₄	1	1	yes	characteristic
25	C₄×#64408	D₄	1	1	yes	characteristic
26	C₄×#64408	D₄	1	1	yes	characteristic
27	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
28	#11924012	C₈	1	1	yes	characteristic, complemented
29	#11924011	—	2	1	no	—
30	C₈×D₇₃	—	2	1	no	—
31	M₁₆×C₇₃	C₈	1	1	yes	characteristic, complemented
32	C₂²×D₇₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×#64408	—	2	2	no	—
34	C₂×#64408	—	2	2	no	—
35	C₂×#64408	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×#64408	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×#64408	C₄⋊C₄	1	1	yes	characteristic
38	C₂×#64408	C₄⋊C₄	1	1	yes	characteristic
39	#10596842	—	2	4	no	—
40	#10596842	—	4	2	no	—
41	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
42	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
43	C₄×D₇₃	C₄²	1	1	yes	characteristic
44	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
45	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
46	C₄×D₇₃	M₁₆	1	1	yes	characteristic
47	#10596833	—	2	2	no	—
48	C₈×C₇₃	—	2	1	no	—
49	#10596831	—	2	1	no	—
50	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
51	C₂×D₇₃	—	2	1	no	—
52	C₂×D₇₃	—	2	1	no	—
53	C₂×D₇₃	#95	1	1	yes	characteristic
54	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
55	#64408	—	2	1	no	—
56	#64408	—	2	1	no	—
57	#64408	#104	1	2	yes	—
58	#64408	#108	1	2	yes	—
59	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
60	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
61	Dic₇₃	#97	1	1	yes	characteristic
62	Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
63	C₂×C₇₃	—	2	1	no	—
64	C₂×C₇₃	#336	1	1	yes	characteristic
65	D₇₃	—	2	1	no	—
66	D₇₃	#339	1	1	yes	characteristic
67	D₇₃	#341	1	1	yes	characteristic
68	#1278	—	73	1	no	maximal, Sylow
69	C₇₃	#1278	1	1	yes	characteristic, complemented, Sylow
70	#431	—	73	1	no	—
71	C₄×M₁₆	—	73	1	no	—
72	C₂×C₄×C₈	—	73	1	no	—
73	C₂×M₁₆	—	73	1	no	—
74	C₂×M₁₆	—	73	1	no	—
75	C₂²×C₈	—	146	1	no	—
76	C₂×C₄²	—	73	1	no	—
77	C₄⋊C₈	—	73	2	no	—
78	C₂²⋊C₈	—	146	1	no	—
79	#97	—	146	1	no	—
80	C₄×C₈	—	73	2	no	—
81	C₄×C₈	—	146	1	no	—
82	C₄×C₈	—	146	1	no	—
83	C₄×C₈	—	146	1	no	—
84	C₂²×C₄	—	73	1	no	—
85	C₂²×C₄	—	73	1	no	—
86	C₂²×C₄	—	73	1	no	—
87	M₁₆	—	73	2	no	—
88	M₁₆	—	73	1	no	—
89	M₁₆	—	146	1	no	—
90	M₁₆	—	146	1	no	—
91	M₁₆	#10596842	1	1	yes	characteristic, complemented
92	C₂×C₈	—	146	1	no	—
93	C₂×C₈	—	146	2	no	—
94	C₂×C₈	—	146	1	no	—
95	C₂×C₈	—	146	2	no	—
96	C₂×C₈	—	146	4	no	—
97	C₄²	—	73	1	no	—
98	C₄²	—	73	1	no	—
99	C₄²	—	73	1	no	—
100	C₄²	—	73	1	no	—
101	C₂³	—	73	1	no	—
102	C₂×C₄	—	73	1	no	—
103	C₂×C₄	—	73	1	no	—
104	C₂×C₄	—	73	1	no	—
105	C₂×C₄	—	73	1	no	—
106	C₂×C₄	—	73	1	no	—
107	C₂×C₄	—	73	1	no	—
108	C₂×C₄	—	73	1	no	—
109	C₂×C₄	—	73	1	no	—
110	C₂×C₄	—	73	1	no	—
111	C₂×C₄	—	146	2	no	—
112	C₂×C₄	—	146	2	no	—
113	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
114	C₈	—	2	1	no	—
115	C₈	—	292	2	no	—
116	C₈	—	146	2	no	—
117	C₈	—	146	4	no	—
118	C₈	—	146	1	no	—
119	C₂²	—	73	1	no	—
120	C₂²	—	73	1	no	—
121	C₂²	—	146	1	no	—
122	C₂²	—	146	1	no	—
123	C₂²	C₄⋊#10596842	1	1	yes	characteristic
124	C₄	—	73	2	no	—
125	C₄	—	73	2	no	—
126	C₄	—	73	1	no	—
127	C₄	—	73	1	no	—
128	C₄	—	146	1	no	—
129	C₄	—	146	1	no	—
130	C₄	C₄×#10596842	1	1	yes	characteristic
131	C₄	C₂²⋊#10596842	1	1	yes	characteristic
132	C₂	—	2	1	no	—
133	C₂	—	73	1	no	—
134	C₂	—	73	1	no	—
135	C₂	—	146	1	no	—
136	C₂	(C₂×#10596842)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989700

C₂

yes

maximal, characteristic

C₂×C₄×#10596842

C₂

yes

maximal, characteristic

M₁₆×#64408

C₂

yes

maximal, characteristic

C₂²×#10596842

—

C₄⋊#10596842

C₄

yes

—

—

—

—

C₄

yes

—

D₇₃⋊M₁₆

C₄

yes

characteristic

C₂×C₄×#64408

C₂²

yes

characteristic

#14556645

—

C₈×#64408

—

M₁₆×D₇₃

C₄

yes

—

—

—

C₂²×#64408

D₄

yes

characteristic

C₂²×#64408

Q₈

yes

characteristic

#11924038

C₈

yes

—

—

C₂×C₄

yes

characteristic

C₄×#64408

C₂×C₄

yes

characteristic

C₄×#64408

D₄

yes

characteristic

C₄×#64408

D₄

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

#11924012

C₈

yes

characteristic, complemented

#11924011

—

C₈×D₇₃

—

M₁₆×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₄⋊C₄

yes

—

—

C₂²⋊C₄

yes

characteristic

C₂×#64408

C₂²⋊C₄

yes

characteristic

C₂×#64408

C₄⋊C₄

yes

characteristic

C₂×#64408

C₄⋊C₄

yes

characteristic

#10596842

—

#10596842

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

M₁₆

yes

characteristic

C₄×D₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₄⋊C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

#95

yes

characteristic

C₂×D₇₃

C₄⋊C₈

yes

—

—

yes

—

#64408

#108

yes

—

C₄×C₇₃

C₄×C₈

yes

characteristic

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

Dic₇₃

#97

yes

characteristic

Dic₇₃

C₂²⋊C₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

#336

yes

characteristic

D₇₃

—

D₇₃

yes

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#431

—

C₄×M₁₆

—

C₂×C₄×C₈

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

146

—

#97

—

146

—

C₄×C₈

—

C₄×C₈

—

146

—

C₄×C₈

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

#10596842

yes

characteristic, complemented

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

100

C₄²

—

101

C₂³

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

146

—

112

C₂×C₄

—

146

—

113

C₂×C₄

C₂×#10596842

yes

characteristic

114

C₈

—

115

C₈

—

292

—

116

C₈

—

146

—

117

C₈

—

146

—

118

C₈

—

146

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

146

—

122

C₂²

—

146

—

123

C₂²

C₄⋊#10596842

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

146

—

129

C₄

—

146

—

130

C₄

C₄×#10596842

yes

characteristic

131

C₄

C₂²⋊#10596842

yes

characteristic

132

C₂

—

133

C₂

—

134

C₂

—

135

C₂

—

146

—

136

C₂

(C₂×#10596842)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₄	C₂²⋊#10596842
commutator	C₄×C₇₃	C₄×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	M₁₆×C₇₃	C₈
socle	C₂×C₇₃	#336
hypercenter	M₁₆	#10596842
hypocenter	C₇₃	#1278
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

subgroup

G/H

center

C₄

C₂²⋊#10596842

commutator

C₄×C₇₃

C₄×C₈

Frattini

C₂×C₄

C₂×#10596842

Fitting

M₁₆×C₇₃

C₈

C₂×C₇₃

M₁₆

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

N	H ≅ G/N	type
20. #11924038	C₈	semidirect
28. #11924012	C₈	semidirect
31. M₁₆×C₇₃	C₈	semidirect
69. C₇₃	#1278	semidirect
91. M₁₆	#10596842	semidirect

H ≅ G/N

type

20. #11924038

C₈

semidirect

28. #11924012

C₈

semidirect

31. M₁₆×C₇₃

C₈

semidirect

69. C₇₃

#1278

semidirect

91. M₁₆

#10596842

semidirect

Subgroups — #22626938

Conjugacy classes of subgroups

Complements