Finite Group Databasebeta

← #22610857

Subgroups — #22610857

Order 9344.

428 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14556588C211yesmaximal, characteristic
2C2×#14556513C214yesmaximal, complemented
3C4×C4⋊Dic73C211yesmaximal, characteristic, complemented
4C2×C4⋊C8×C73C211yesmaximal, characteristic, complemented
5C22×D292—21no—
6C22×D292—21no—
7C22×D292C2212yes—
8#14556588—22no—
9#14556588C414yescomplemented
10C2×C4⋊Dic73C2212yes—
11C2×C4×Dic73—21no—
12#14556513—28no—
13#14556498—21no—
14C22×C8×C73C2212yes—
15C2×C42×C73C2211yescharacteristic
16C4⋊C8×C73—22no—
17C23×D73—22no—
18C2×D292—24no—
19C2×D292—24no—
20C2×D292—24no—
21C2×D292—24no—
22C2×D292—22no—
23C2×D292—44no—
24C2×D292—42no—
25C2×D292—42no—
26C2×D292C2×C414yes—
27C22×Dic73—22no—
28C4⋊Dic73—22no—
29C4⋊Dic73D414yescomplemented
30C4×Dic73—42no—
31C22×C4×C73D411yescharacteristic
32C22×C4×C73D411yescharacteristic
33C22×C4×C73C2311yescharacteristic
34C2×C8×C73—22no—
35C2×C8×C73—24no—
36C42×C73C2×C412yes—
37C42×C73D412yes—
38C23×C73C2×D411yescharacteristic
39C22×D73—24no—
40C22×D73—44no—
41C22×D73—42no—
42C22×D73—42no—
43C22×D73—44no—
44C2×C4×C73—22no—
45C2×C4×C73C22⋊C412yes—
46C2×C4×C73C22⋊C412yes—
47C2×C4×C73D812yes—
48C2×C4×C73SD1612yes—
49C2×C4×C73C22×C411yescharacteristic
50C2×C4×C73C2×D412yes—
51C2×C4×C73C2×D411yescharacteristic
52C2×C4×C73#4112yes—
53C2×Dic73—24no—
54C2×Dic73—42no—
55C2×Dic73—42no—
56D292—28no—
57D292—48no—
58D292—48no—
59D292—42no—
60D292—42no—
61C8×C73—42no—
62C22×C73C2×C22⋊C411yescharacteristic
63C22×C73#12112yes—
64C22×C73C2×D811yescharacteristic
65C22×C73C2×SD1611yescharacteristic
66C22×C73AGL(1,ℤ/8)12yes—
67C2×D73—44no—
68C2×D73—44no—
69C2×D73—44no—
70C2×D73—84no—
71C2×D73—84no—
72C4×C73—22no—
73C4×C73#10214yescomplemented
74C4×C73C4×D412yes—
75C4×C73#12411yescharacteristic
76C4×C73#12711yescharacteristic
77Dic73—44no—
78C2×C73#39011yescharacteristic
79C2×C73C2×#10211yescharacteristic
80C2×C73#41811yescharacteristic
81C2×C73#45912yes—
82C2×C73#46012yes—
83D73—84no—
84#1982—731nomaximal, Sylow
85C73#198211yescharacteristic, complemented, Sylow
86C2×#127—731no—
87C2×C4⋊C8D7311yescharacteristic, complemented
88C2×#102—734no—
89C4×C4⋊C4—731no—
90C22×D4—732no—
91C22×D4—1461no—
92C22×D4—1461no—
93C22×C8C2×D7312yes—
94#127—734no—
95#127—1462no—
96C2×C4⋊C4—732no—
97C2×C42—1461no—
98C2×C42C2×D7311yescharacteristic
99C4⋊C8—22no—
100#102—1468no—
101#95—1461no—
102C24—1462no—
103C2×D4—2924no—
104C2×D4—2922no—
105C2×D4—2922no—
106C2×D4—734no—
107C2×D4—1464no—
108C2×D4—1464no—
109C2×D4—1464no—
110C2×D4—1462no—
111C2×D4—1464no—
112C22×C4—1462no—
113C22×C4D29211yescharacteristic
114C22×C4D29211yescharacteristic
115C22×C4C22×D7311yescharacteristic
116C2×C8—24no—
117C2×C8—22no—
118C4⋊C4—734no—
119C4⋊C4—1462no—
120C42—2922no—
121C42C4×D7312yes—
122C42C22⋊D7312yes—
123C23—2924no—
124C23—2922no—
125C23—2922no—
126C23—2924no—
127C23—1464no—
128C23C2×D29211yescharacteristic
129D4—2928no—
130D4—2928no—
131D4—2922no—
132D4—2922no—
133D4—1468no—
134C2×C4—22no—
135C2×C4—2922no—
136C2×C4—2922no—
137C2×C4—1464no—
138C2×C4#1192400512yes—
139C2×C4#1192400512yes—
140C2×C4D58412yes—
141C2×C4#1192401712yes—
142C2×C4C2×C4×D7311yescharacteristic
143C2×C4D4×D7312yes—
144C2×C4C2×C22⋊D7311yescharacteristic
145C2×C4#1192402912yes—
146C8—42no—
147C22—2924no—
148C22—2924no—
149C22—2924no—
150C22—5844no—
151C22—5844no—
152C22C2×#1192400511yescharacteristic
153C22#1455656612yes—
154C22C2×D58411yescharacteristic
155C22C2×#1192401711yescharacteristic
156C22#1455661912yes—
157C4—22no—
158C4—2924no—
159C4#1455651314yescomplemented
160C4#1455655312yes—
161C4#1455658011yescharacteristic
162C4#1455658711yescharacteristic
163C2—5844no—
164C2#1798848811yescharacteristic
165C2C2×#1455651311yescharacteristic
166C2#1798859311yescharacteristic
167C2#1798878312yes—
168C2#1798878812yes—
subgroupG/H
centerC23C2×D292
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×C4⋊C8×C73C2
socleC23×C73C2×D4
hypercenterC2×C4⋊C8D73
hypocenterC73#1982
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14556513C2semidirect
3. C4×C4⋊Dic73C2semidirect
4. C2×C4⋊C8×C73C2semidirect
9. #14556588C4semidirect
29. C4⋊Dic73D4semidirect
73. C4×C73#102semidirect
85. C73#1982semidirect
87. C2×C4⋊C8D73semidirect
159. C4#14556513semidirect