Finite Group Databasebeta

← #22607809

Subgroups — #22607809

Order 9344.

276 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 89 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⋊#10596831C211yesmaximal, characteristic
2C2×#14556498C211yesmaximal, characteristic
3#380×C73C211yesmaximal, characteristic
4C23×Dic73—21no—
5C22×#10596831—21no—
6C22⋊#10596831—21no—
7C22⋊#10596831C412yescomplemented
8#14556498—21no—
9#14556498C412yescomplemented
10C23×C4×C73C2211yescharacteristic
11C2×C4⋊C4×C73C412yescomplemented
12C2×C22⋊C4×C73—21no—
13#95×C73—21no—
14C22×Dic73—24no—
15C22×Dic73—22no—
16C22×Dic73—42no—
17C22×Dic73—41no—
18C22×Dic73—41no—
19C2×#10596831—22no—
20C2×#10596831—42no—
21C24×C73D411yescharacteristic
22C22×C4×C73—22no—
23C22×C4×C73—42no—
24C22×C4×C73C2×C411yescharacteristic
25C22×C4×C73C2×C411yescharacteristic
26C22×C4×C73C2×C411yescharacteristic
27C22×C4×C73D411yescharacteristic
28C22×C4×C73D411yescharacteristic
29C22×C4×C73Q811yescharacteristic
30C4⋊C4×C73—42no—
31C22⋊C4×C73—41no—
32C22⋊C4×C73—41no—
33C23×C73—22no—
34C23×C73—22no—
35C23×C73C22⋊C411yescharacteristic
36C23×C73C22⋊C411yescharacteristic
37C23×C73C4⋊C411yescharacteristic
38C23×C73D811yescharacteristic
39C23×C73SD1611yescharacteristic
40C23×C73SD1611yescharacteristic
41C23×C73Q1611yescharacteristic
42C2×C4×C73—22no—
43C2×C4×C73—22no—
44C2×C4×C73—41no—
45C2×C4×C73—41no—
46C2×C4×C73—41no—
47C2×C4×C73—41no—
48C2×C4×C73—42no—
49C2×C4×C73—42no—
50C2×C4×C73—42no—
51C2×C4×C73C4211yescharacteristic
52C2×C4×C73C22⋊C411yescharacteristic
53C2×C4×C73C4⋊C411yescharacteristic
54C2×C4×C73C4⋊C411yescharacteristic
55C2×Dic73—24no—
56C2×Dic73—44no—
57C2×Dic73—44no—
58C2×Dic73—42no—
59C2×Dic73—42no—
60#10596831—42no—
61C22×C73—22no—
62C22×C73—22no—
63C22×C73—22no—
64C22×C73—22no—
65C22×C73—21no—
66C22×C73—21no—
67C22×C73—21no—
68C22×C73—21no—
69C22×C73#9511yescharacteristic
70C22×C73#9912yes—
71C22×C73#10211yescharacteristic
72C22×C73#10211yescharacteristic
73C22×C73#10311yescharacteristic
74C22×C73#10311yescharacteristic
75C22×C73#10412yes—
76C22×C73#10611yescharacteristic
77C22×C73#10711yescharacteristic
78C4×C73—21no—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—21no—
82C4×C73—82no—
83Dic73—44no—
84C2×C73—21no—
85C2×C73—21no—
86C2×C73—21no—
87C2×C73—21no—
88C2×C73#32712yes—
89C2×C73#32812yes—
90C2×C73#33911yescharacteristic
91C2×C73#34011yescharacteristic
92C2×C73#34211yescharacteristic
93#1294—731nomaximal, Sylow
94C73#129411yescharacteristic, complemented, Sylow
95C2×C22⋊C8—731no—
96#380D7311yescharacteristic
97C2×#95—731no—
98C23×C4—1461no—
99C23×C4C2×D7311yescharacteristic
100C22×C8—1461no—
101C2×C4⋊C4Dic7312yescomplemented
102C2×C22⋊C4—21no—
103C22⋊C8—732no—
104C22⋊C8—1461no—
105#95—21no—
106#95—732no—
107#95—1461no—
108C24C22⋊D7311yescharacteristic
109C22×C4—22no—
110C22×C4—42no—
111C22×C4—2922no—
112C22×C4—2921no—
113C22×C4—2921no—
114C22×C4—1464no—
115C22×C4—1462no—
116C22×C4Dic14611yescharacteristic
117C22×C4C4×D7311yescharacteristic
118C22×C4C4×D7311yescharacteristic
119C22×C4D29211yescharacteristic
120C22×C4C2×Dic7311yescharacteristic
121C22×C4C22⋊D7311yescharacteristic
122C2×C8—2922no—
123C2×C8—1462no—
124C4⋊C4—42no—
125C22⋊C4—41no—
126C22⋊C4—41no—
127C23—22no—
128C23—22no—
129C23#1192400511yescharacteristic
130C23C22⋊Dic7311yescharacteristic
131C23#1192400711yescharacteristic
132C23#1192401311yescharacteristic
133C23#1192401511yescharacteristic
134C23#1192401611yescharacteristic
135C23#1192401811yescharacteristic
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—2922no—
146C2×C4—2924no—
147C2×C4—2924no—
148C2×C4—2922no—
149C2×C4—1464no—
150C2×C4C4×Dic7311yescharacteristic
151C2×C4#1192400511yescharacteristic
152C2×C4#1192400711yescharacteristic
153C2×C4C4⋊Dic7311yescharacteristic
154C8—2922no—
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—22no—
161C22—21no—
162C22—21no—
163C22#1455649811yescharacteristic
164C22#1455650612yes—
165C22#1455651111yescharacteristic
166C22#1455651211yescharacteristic
167C22#1455651411yescharacteristic
168C22#1455651511yescharacteristic
169C22#1455651812yes—
170C22#1455652211yescharacteristic
171C22#1455652411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—2924no—
178C2—21no—
179C2—21no—
180C2—21no—
181C2—21no—
182C2#1798832112yes—
183C2#1798832412yes—
184C2#1798834611yescharacteristic
185C2#1798834911yescharacteristic
186C2#1798835411yescharacteristic
subgroupG/H
centerC23C22⋊Dic73
commutatorC2×C4×C73C42
FrattiniC23×C4C2×D73
Fitting#380×C73C2
socleC23×C73C22⋊C4
hypercenter#380D73
hypocenterC73#1294
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
7. C22⋊#10596831C4semidirect
9. #14556498C4semidirect
11. C2×C4⋊C4×C73C4semidirect
94. C73#1294semidirect
101. C2×C4⋊C4Dic73semidirect