Finite Group Databasebeta

← #22608355

Subgroups — #22608355

Order 9344.

312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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×C4×D292C211yesmaximal, characteristic
2#17988640C211yesmaximal, characteristic, complemented
3#17988314C214yesmaximal, complemented
4#423×C73C211yesmaximal, characteristic, complemented
5C22×D292C411yescharacteristic
6C22×C4×D73—21no—
7C4×D292—21no—
8C4×D292—21no—
9C4×D292C412yes—
10C4×D292C2212yes—
11C2×C4⋊Dic73C411yescharacteristic
12C2×#11924005—21no—
13C4⋊#10596831—21no—
14C22⋊#10596831—21no—
15C4×#10596831C2212yescomplemented
16C2×M16×C73—21no—
17C2×C42×C73C2211yescharacteristic
18C4⋊C8×C73—21no—
19C4⋊C8×C73C2212yescomplemented
20C23×D73—21no—
21C2×D292—21no—
22C2×D292—24no—
23C2×D292C2×C412yes—
24C22×Dic73—21no—
25C2×C4×D73—22no—
26C2×C4×D73—22no—
27C2×C4×D73—42no—
28C2×C4×D73—42no—
29C2×#10596831—22no—
30C4⋊Dic73—21no—
31C4⋊Dic73C2×C412yes—
32#11924005—22no—
33#11924005—22no—
34C22×C4×C73C2×C411yescharacteristic
35C22×C4×C73D411yescharacteristic
36C22×C4×C73D411yescharacteristic
37M16×C73—42no—
38C2×C8×C73—22no—
39C42×C73C2×C411yescharacteristic
40C42×C73D411yescharacteristic
41C42×C73D411yescharacteristic
42C42×C73C2311yescharacteristic
43C23×C73C22⋊C411yescharacteristic
44C22×D73—24no—
45C22×D73—22no—
46C22×D73—42no—
47C22×D73—42no—
48C2×C4×C73—22no—
49C2×C4×C73—41no—
50C2×C4×C73C22⋊C411yescharacteristic
51C2×C4×C73C22⋊C411yescharacteristic
52C2×C4×C73C22⋊C411yescharacteristic
53C2×C4×C73D812yes—
54C2×C4×C73SD1612yes—
55C2×C4×C73C22×C411yescharacteristic
56C2×C4×C73C2×D411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×Dic73—22no—
59C2×Dic73—42no—
60D292—24no—
61D292—22no—
62D292M1614yescomplemented
63C4×D73—44no—
64C4×D73—42no—
65C4×D73—42no—
66C8×C73—42no—
67#10596831—42no—
68C22×C73—21no—
69C22×C73—21no—
70C22×C73#10212yes—
71C22×C73C2×C22⋊C411yescharacteristic
72C2×D73—24no—
73C2×D73—48no—
74C2×D73—42no—
75C2×D73—42no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—21no—
79C4×C73#10212yes—
80C4×C73C2×M1612yes—
81C4×C73C2×D811yescharacteristic
82C4×C73C2×SD1611yescharacteristic
83Dic73—42no—
84C2×C73—22no—
85C2×C73#40711yescharacteristic
86C2×C73C2×#10211yescharacteristic
87C2×C73#42111yescharacteristic
88D73—44no—
89#1486—731nomaximal, Sylow
90C73#148611yescharacteristic, complemented, Sylow
91C2×C4×D4—731no—
92#431—731no—
93#423D7311yescharacteristic, complemented
94D4⋊C8—734no—
95C22×D4—731no—
96C23×C4—1461no—
97C2×M16—21no—
98C4×D4—732no—
99C4×D4—732no—
100C4×D4—1461no—
101C4×D4—1461no—
102C2×C4⋊C4—731no—
103C2×C22⋊C4—1461no—
104C2×C42C2×D7311yescharacteristic
105C4⋊C8—21no—
106C4⋊C8—1461no—
107C4⋊C8C2×D7312yescomplemented
108C22⋊C8—1461no—
109C4×C8—732no—
110C24—1461no—
111C2×D4—732no—
112C2×D4—1464no—
113C2×D4—1461no—
114C22×C4—2922no—
115C22×C4—2922no—
116C22×C4—1461no—
117C22×C4—1462no—
118C22×C4—1462no—
119C22×C4C4×D7311yescharacteristic
120C22×C4D29211yescharacteristic
121C22×C4C22⋊D7311yescharacteristic
122M16—42no—
123C2×C8—22no—
124C2×C8—1462no—
125C4⋊C4—732no—
126C4⋊C4—1461no—
127C22⋊C4—1462no—
128C22⋊C4—1462no—
129C42C4×D7311yescharacteristic
130C42D29211yescharacteristic
131C42C22⋊D7311yescharacteristic
132C42C22×D7311yescharacteristic
133C23—2922no—
134C23—2922no—
135C23—1464no—
136C23—1462no—
137C23#1192400511yescharacteristic
138D4—734no—
139D4—1464no—
140D4—1462no—
141C2×C4—22no—
142C2×C4—41no—
143C2×C4—2922no—
144C2×C4—2924no—
145C2×C4—2922no—
146C2×C4—2922no—
147C2×C4—1462no—
148C2×C4#1192400511yescharacteristic
149C2×C4#1192400511yescharacteristic
150C2×C4#1192400511yescharacteristic
151C2×C4#1192401312yes—
152C2×C4#1192401512yes—
153C2×C4C2×C4×D7311yescharacteristic
154C2×C4C2×C22⋊D7311yescharacteristic
155C2×C4C2×D29211yescharacteristic
156C8—42no—
157C8—2922no—
158C22—21no—
159C22—21no—
160C22—2928no—
161C22—2922no—
162C22—2922no—
163C22—1464no—
164C22#1455651112yes—
165C22C2×#1192400511yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—2922no—
170C4#1455651112yes—
171C4M16×D7312yes—
172C4C2×#1192401311yescharacteristic
173C4C2×#1192401511yescharacteristic
174C2—22no—
175C2—2924no—
176C2#1798855011yescharacteristic
177C2C2×#1455651111yescharacteristic
178C2#1798860311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#423×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#423D73
hypocenterC73#1486
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #17988640C2semidirect
3. #17988314C2semidirect
4. #423×C73C2semidirect
15. C4×#10596831C22semidirect
19. C4⋊C8×C73C22semidirect
62. D292M16semidirect
90. C73#1486semidirect
93. #423D73semidirect
107. C4⋊C8C2×D73semidirect