Finite Group Databasebeta

← #22625167

Subgroups — #22625167

Order 9344.

332 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊#10596833C212yesmaximal, complemented
2#17989432C212yesmaximal, complemented
3#17989430C212yesmaximal, complemented
4C2×D4×Dic73C211yesmaximal, characteristic
5C22×#10596833—22no—
6C22⋊#10596833—22no—
7C22⋊#10596833C2214yes—
8C23×Dic73C411yescharacteristic
9C23×Dic73C2211yescharacteristic
10D4×Dic73—22no—
11D4×Dic73—22no—
12C2×C4⋊Dic73C2211yescharacteristic
13C2×C22⋊Dic73C411yescharacteristic
14C2×C22⋊Dic73C2211yescharacteristic
15C2×C4×Dic73C411yescharacteristic
16C22×D4×C73C411yescharacteristic
17C2×#10596833—24no—
18C2×#10596833—44no—
19C22×Dic73—21no—
20C22×Dic73—21no—
21C22×Dic73—42no—
22C22×Dic73—42no—
23C22×Dic73C2×C411yescharacteristic
24C22×Dic73C2×C411yescharacteristic
25C22×Dic73C2×C411yescharacteristic
26C22×Dic73D412yes—
27C22×Dic73D412yes—
28C22×Dic73C2311yescharacteristic
29C4⋊Dic73—22no—
30C22⋊Dic73—22no—
31C22⋊Dic73—22no—
32C4×Dic73—21no—
33C4×Dic73—21no—
34C24×C73C2×C411yescharacteristic
35C24×C73C2×C411yescharacteristic
36C2×D4×C73—22no—
37C2×D4×C73—22no—
38C2×D4×C73C814yescomplemented
39C22×C4×C73C2×C411yescharacteristic
40C23×C73—21no—
41C23×C73—21no—
42C23×C73—41no—
43C23×C73—41no—
44C23×C73—41no—
45C23×C73—41no—
46C23×C73C22⋊C412yes—
47C23×C73C2×C812yes—
48C23×C73C2×C812yescomplemented
49C23×C73M1612yes—
50C23×C73C22×C411yescharacteristic
51D4×C73—28no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73C2×C812yescomplemented
55C2×Dic73—22no—
56C2×Dic73—24no—
57C2×Dic73—21no—
58C2×Dic73—21no—
59C2×Dic73—42no—
60C2×Dic73—41no—
61C2×Dic73—42no—
62C2×Dic73—42no—
63C2×Dic73—41no—
64C2×Dic73—41no—
65C2×Dic73C22⋊C411yescharacteristic
66C2×Dic73C22⋊C411yescharacteristic
67C2×Dic73C2×D412yes—
68#10596833—44no—
69C22×C73—21no—
70C22×C73—22no—
71C22×C73—21no—
72C22×C73—22no—
73C22×C73—22no—
74C22×C73—42no—
75C22×C73—42no—
76C22×C73—42no—
77C22×C73—42no—
78C22×C73—41no—
79C22×C73—41no—
80C22×C73C22⋊C814yes—
81C22×C73C2×C22⋊C411yescharacteristic
82C22×C73C22×C811yescharacteristic
83C22×C73C2×M1611yescharacteristic
84C4×C73—22no—
85Dic73—22no—
86Dic73—21no—
87Dic73—41no—
88Dic73—41no—
89Dic73#9912yes—
90C2×C73—21no—
91C2×C73—21no—
92C2×C73—24no—
93C2×C73—42no—
94C2×C73C2×C22⋊C811yescharacteristic
95C2×C73C2×#9911yescharacteristic
96C2×C73#41311yescharacteristic
97#1459—731nomaximal, Sylow
98C73#145911yescharacteristic, complemented, Sylow
99C2×C4×D4—731no—
100C2×C22⋊C8—732no—
101#324—732no—
102#323—732no—
103C22×D4#6440811yescharacteristic
104C23×C4—731no—
105C23×C4—731no—
106C22×C8—1462no—
107C4×D4—1462no—
108C4×D4—1462no—
109C2×C4⋊C4—731no—
110C2×C22⋊C4—731no—
111C2×C22⋊C4—731no—
112C2×C42—731no—
113C22⋊C8—734no—
114C22⋊C8—1462no—
115C24C2×#6440811yescharacteristic
116C24C2×#6440811yescharacteristic
117C2×D4—22no—
118C2×D4—22no—
119C2×D4#1059683314yescomplemented
120C22×C4—2922no—
121C22×C4—2922no—
122C22×C4—732no—
123C22×C4—731no—
124C22×C4—731no—
125C22×C4—731no—
126C22×C4—732no—
127C22×C4—731no—
128C22×C4—1461no—
129C22×C4—1461no—
130C22×C4C2×#6440811yescharacteristic
131C2×C8—2924no—
132C2×C8—1464no—
133C4⋊C4—1462no—
134C22⋊C4—1462no—
135C22⋊C4—1462no—
136C42—1461no—
137C42—1461no—
138C23—21no—
139C23—21no—
140C23—41no—
141C23—41no—
142C23—41no—
143C23—41no—
144C23C22⋊#6440812yes—
145C23C2×#1059683312yes—
146C23C2×#1059683312yescomplemented
147C23#1192403712yes—
148C23C22×#6440811yescharacteristic
149D4—28no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—2922no—
153C2×C4—2922no—
154C2×C4—2921no—
155C2×C4—2921no—
156C2×C4—2921no—
157C2×C4—2922no—
158C2×C4—731no—
159C2×C4—731no—
160C2×C4—732no—
161C2×C4—1461no—
162C2×C4—1461no—
163C2×C4—1464no—
164C2×C4—1462no—
165C2×C4C2×#1059683312yescomplemented
166C8—2924no—
167C22—21no—
168C22—22no—
169C22—21no—
170C22—22no—
171C22—22no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22C22⋊#1059683314yes—
179C22C2×C22⋊#6440811yescharacteristic
180C22C22×#1059683311yescharacteristic
181C22C2×#1192403711yescharacteristic
182C4—22no—
183C4—2921no—
184C4—2921no—
185C4—732no—
186C4—1462no—
187C4—1461no—
188C2—21no—
189C2—21no—
190C2—24no—
191C2—42no—
192C2C2×C22⋊#1059683311yescharacteristic
193C2D73⋊#9911yescharacteristic
194C2#1798957411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC22×C73C22×C8
FrattiniC23C22×#64408
FittingC22×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×D4#64408
hypocenterC73#1459
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C22⋊#10596833C2semidirect
2. #17989432C2semidirect
3. #17989430C2semidirect
38. C2×D4×C73C8semidirect
48. C23×C73C2×C8semidirect
54. C2×C4×C73C2×C8semidirect
98. C73#1459semidirect
119. C2×D4#10596833semidirect
146. C23C2×#10596833semidirect
165. C2×C4C2×#10596833semidirect