Group #22611490 — subgroups

Subgroups — #22611490

Order 9344.

214 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 87 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	#17988485	C₂	1	1	yes	maximal, characteristic
2	#17988457	C₂	1	1	yes	maximal, characteristic
3	#17988350	C₂	1	2	yes	maximal
4	#17988350	C₂	1	2	yes	maximal
5	#336×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₇₃	—	2	1	no	—
7	C₂×C₄⋊Dic₇₃	—	2	1	no	—
8	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
11	C₂×#11924007	—	2	1	no	—
12	#14556498	—	2	1	no	—
13	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×Dic₇₃	—	2	1	no	—
16	C₂²×Dic₇₃	—	2	1	no	—
17	C₂²×Dic₇₃	—	2	2	no	—
18	C₄⋊Dic₇₃	—	2	1	no	—
19	C₄⋊Dic₇₃	—	2	2	no	—
20	C₄⋊Dic₇₃	—	2	4	no	—
21	C₄⋊Dic₇₃	—	4	2	no	—
22	C₄⋊Dic₇₃	—	4	2	no	—
23	C₄⋊Dic₇₃	Q₈	1	2	yes	—
24	#11924007	—	4	2	no	—
25	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₂×C₈×C₇₃	—	2	2	no	—
30	C₂×C₈×C₇₃	—	2	2	no	—
31	C₄²×C₇₃	—	2	2	no	—
32	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	—	2	1	no	—
34	C₂×C₄×C₇₃	—	2	1	no	—
35	C₂×C₄×C₇₃	—	2	1	no	—
36	C₂×C₄×C₇₃	—	2	1	no	—
37	C₂×C₄×C₇₃	D₈	1	2	yes	—
38	C₂×C₄×C₇₃	SD₁₆	1	2	yes	—
39	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₇₃	#41	1	2	yes	—
41	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
42	C₂×C₄×C₇₃	#41	1	2	yes	—
43	C₂×Dic₇₃	—	2	2	no	—
44	C₂×Dic₇₃	—	4	1	no	—
45	C₂×Dic₇₃	—	4	1	no	—
46	C₂×Dic₇₃	—	4	1	no	—
47	C₂×Dic₇₃	—	4	2	no	—
48	C₂×Dic₇₃	—	4	1	no	—
49	C₂×Dic₇₃	—	4	2	no	—
50	C₂×Dic₇₃	—	4	2	no	—
51	C₂×Dic₇₃	—	4	1	no	—
52	C₈×C₇₃	—	4	2	no	—
53	C₂²×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
54	C₂²×C₇₃	#123	1	1	yes	characteristic
55	C₂²×C₇₃	#124	1	1	yes	characteristic
56	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
57	C₂²×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
58	C₂²×C₇₃	#137	1	1	yes	characteristic
59	C₂²×C₇₃	#137	1	1	yes	characteristic
60	C₄×C₇₃	—	2	2	no	—
61	C₄×C₇₃	—	2	2	no	—
62	C₄×C₇₃	#125	1	2	yes	—
63	C₄×C₇₃	#126	1	2	yes	—
64	Dic₇₃	—	4	2	no	—
65	Dic₇₃	—	8	1	no	—
66	Dic₇₃	—	8	2	no	—
67	C₂×C₇₃	#400	1	1	yes	characteristic
68	C₂×C₇₃	#474	1	1	yes	characteristic
69	C₂×C₇₃	#475	1	1	yes	characteristic
70	C₂×C₇₃	#480	1	1	yes	characteristic
71	C₂×C₇₃	#483	1	1	yes	characteristic
72	C₂×C₇₃	#486	1	1	yes	characteristic
73	C₂×C₇₃	#491	1	1	yes	characteristic
74	#2099	—	73	1	no	maximal, Sylow
75	C₇₃	#2099	1	1	yes	characteristic, complemented, Sylow
76	#389	—	73	1	no	—
77	#384	—	73	1	no	—
78	#340	—	73	2	no	—
79	#340	—	73	2	no	—
80	#336	D₇₃	1	1	yes	characteristic
81	C₂²×C₈	C₂×D₇₃	1	2	yes	—
82	C₂×C₄⋊C₄	—	73	1	no	—
83	C₂×C₄⋊C₄	—	73	2	no	—
84	C₂×C₄⋊C₄	—	73	1	no	—
85	C₂×C₄⋊C₄	—	146	1	no	—
86	C₂×C₄⋊C₄	—	146	1	no	—
87	C₂×C₄⋊C₄	—	146	1	no	—
88	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
89	#95	—	146	1	no	—
90	C₂²×C₄	—	146	1	no	—
91	C₂²×C₄	—	146	2	no	—
92	C₂²×C₄	—	146	1	no	—
93	C₂²×C₄	D₂₉₂	1	1	yes	characteristic
94	C₂²×C₄	D₂₉₂	1	1	yes	characteristic
95	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₄⋊C₄	—	292	2	no	—
100	C₄⋊C₄	—	292	2	no	—
101	C₄⋊C₄	—	292	2	no	—
102	C₄⋊C₄	—	73	2	no	—
103	C₄⋊C₄	—	146	2	no	—
104	C₄⋊C₄	—	146	4	no	—
105	C₄⋊C₄	—	146	1	no	—
106	C₄²	—	2	2	no	—
107	C₂³	C₂×D₂₉₂	1	1	yes	characteristic
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	292	1	no	—
113	C₂×C₄	—	292	1	no	—
114	C₂×C₄	—	292	1	no	—
115	C₂×C₄	—	292	2	no	—
116	C₂×C₄	—	292	1	no	—
117	C₂×C₄	—	292	2	no	—
118	C₂×C₄	—	292	2	no	—
119	C₂×C₄	—	292	1	no	—
120	C₂×C₄	—	146	2	no	—
121	C₂×C₄	D₅₈₄	1	2	yes	—
122	C₂×C₄	#11924017	1	2	yes	—
123	C₂×C₄	Q₈×D₇₃	1	1	yes	characteristic
124	C₂×C₄	#11924027	1	2	yes	—
125	C₂×C₄	#11924027	1	1	yes	characteristic
126	C₂×C₄	#11924028	1	2	yes	—
127	C₈	—	4	2	no	—
128	C₂²	#14556571	1	1	yes	characteristic
129	C₂²	#14556575	1	1	yes	characteristic
130	C₂²	#14556579	1	1	yes	characteristic
131	C₂²	C₂×D₅₈₄	1	1	yes	characteristic
132	C₂²	C₂×#11924017	1	1	yes	characteristic
133	C₂²	#14556624	1	1	yes	characteristic
134	C₂²	#14556624	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	2	2	no	—
137	C₄	—	292	2	no	—
138	C₄	—	584	1	no	—
139	C₄	—	584	2	no	—
140	C₄	#14556581	1	2	yes	—
141	C₄	#14556584	1	2	yes	—
142	C₂	#17988527	1	1	yes	characteristic
143	C₂	#17988868	1	1	yes	characteristic
144	C₂	#17988873	1	1	yes	characteristic
145	C₂	#17988901	1	1	yes	characteristic
146	C₂	#17988918	1	1	yes	characteristic
147	C₂	#17988934	1	1	yes	characteristic
148	C₂	#17988956	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988485

C₂

yes

maximal, characteristic

#17988457

C₂

yes

maximal, characteristic

#17988350

C₂

yes

maximal

#17988350

C₂

yes

maximal

#336×C₇₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

characteristic

C₂×#11924007

—

#14556498

—

C₂²×C₈×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

Q₈

yes

—

#11924007

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

D₈

yes

—

C₂×C₄×C₇₃

SD₁₆

yes

—

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

C₂²×C₇₃

C₂²⋊Q₈

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₂²×C₇₃

C₂×SD₁₆

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#125

yes

—

C₄×C₇₃

#126

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₃

yes

characteristic

C₂²×C₈

C₂×D₇₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#95

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

D₂₉₂

yes

characteristic

C₂²×C₄

D₂₉₂

yes

characteristic

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

292

—

100

C₄⋊C₄

—

292

—

101

C₄⋊C₄

—

292

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

146

—

104

C₄⋊C₄

—

146

—

105

C₄⋊C₄

—

146

—

106

C₄²

—

107

C₂³

C₂×D₂₉₂

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

292

—

113

C₂×C₄

—

292

—

114

C₂×C₄

—

292

—

115

C₂×C₄

—

292

—

116

C₂×C₄

—

292

—

117

C₂×C₄

—

292

—

118

C₂×C₄

—

292

—

119

C₂×C₄

—

292

—

120

C₂×C₄

—

146

—

121

C₂×C₄

D₅₈₄

yes

—

122

C₂×C₄

#11924017

yes

—

123

C₂×C₄

Q₈×D₇₃

yes

characteristic

124

C₂×C₄

#11924027

yes

—

125

C₂×C₄

#11924027

yes

characteristic

126

C₂×C₄

#11924028

yes

—

127

C₈

—

128

C₂²

#14556571

yes

characteristic

129

C₂²

#14556575

yes

characteristic

130

C₂²

#14556579

yes

characteristic

131

C₂²

C₂×D₅₈₄

yes

characteristic

132

C₂²

C₂×#11924017

yes

characteristic

133

C₂²

#14556624

yes

characteristic

134

C₂²

#14556624

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

292

—

138

C₄

—

584

—

139

C₄

—

584

—

140

C₄

#14556581

yes

—

141

C₄

#14556584

yes

—

142

C₂

#17988527

yes

characteristic

143

C₂

#17988868

yes

characteristic

144

C₂

#17988873

yes

characteristic

145

C₂

#17988901

yes

characteristic

146

C₂

#17988918

yes

characteristic

147

C₂

#17988934

yes

characteristic

148

C₂

#17988956

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₂₉₂
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#336×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	#336	D₇₃
hypocenter	C₇₃	#2099
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₂₉₂

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#336×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
75. C₇₃	#2099	semidirect

H ≅ G/N

type

75. C₇₃

#2099

semidirect

Subgroups — #22611490

Conjugacy classes of subgroups

Complements