Finite Group Databasebeta

← #22608331

Subgroups — #22608331

Order 9344.

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

normal subgroups only

This group has 260 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
1#17989137C211yesmaximal, characteristic
2C2×C4⋊#10596831C211yesmaximal, characteristic, complemented
3#17988316C214yesmaximal, complemented
4#431×C73C211yesmaximal, characteristic, complemented
5C2×#11924028—21no—
6C22×#10596831—21no—
7#14556591C411yescharacteristic
8#14556588C411yescharacteristic
9#14556579—21no—
10#14556565—21no—
11#14556565C412yes—
12C4×D292—21no—
13C4×D292C2212yes—
14C4⋊#10596831—21no—
15C4⋊#10596831C2212yes—
16C2×C42×C73C2211yescharacteristic
17C4⋊C8×C73—21no—
18C22⋊C8×C73—21no—
19C4×C8×C73C2212yes—
20#11924028—42no—
21#11924028—42no—
22C2×Dic146—21no—
23C2×D292—21no—
24C2×D292—21no—
25C2×D292C2×C412yes—
26C2×C22⋊D73—22no—
27C2×C4×D73—22no—
28C2×#10596831—22no—
29C2×#10596831—42no—
30C4⋊Dic73—21no—
31C4⋊Dic73C2×C412yes—
32#11924005—22no—
33#11924005—22no—
34C22×C4×C73C2×C411yescharacteristic
35C22×C4×C73D411yescharacteristic
36C22×C4×C73D411yescharacteristic
37C2×C8×C73—22no—
38C42×C73C2×C411yescharacteristic
39C42×C73D411yescharacteristic
40C42×C73D411yescharacteristic
41C42×C73C2311yescharacteristic
42C23×C73C22⋊C411yescharacteristic
43C22×D73—22no—
44C2×C4×C73—22no—
45C2×C4×C73—41no—
46C2×C4×C73C22⋊C411yescharacteristic
47C2×C4×C73C22⋊C411yescharacteristic
48C2×C4×C73C22⋊C411yescharacteristic
49C2×C4×C73D812yes—
50C2×C4×C73SD1612yes—
51C2×C4×C73C22×C411yescharacteristic
52C2×C4×C73C2×D411yescharacteristic
53C2×C4×C73C2×D411yescharacteristic
54C22⋊D73—44no—
55C2×Dic73—22no—
56D292—24no—
57D292—42no—
58D292—42no—
59C4×D73—42no—
60C4×D73—42no—
61Dic146—42no—
62C8×C73—42no—
63#10596831—42no—
64C22×C73—21no—
65C22×C73—21no—
66C22×C73#10212yes—
67C22×C73C2×C22⋊C411yescharacteristic
68C2×D73—42no—
69C2×D73—42no—
70C2×D73—42no—
71C4×C73—21no—
72C4×C73—21no—
73C4×C73—21no—
74C4×C73#10212yes—
75C4×C73#13112yes—
76C4×C73C2×D811yescharacteristic
77C4×C73C2×SD1611yescharacteristic
78Dic73—42no—
79C2×C73—22no—
80C2×C73#40811yescharacteristic
81C2×C73C2×#10211yescharacteristic
82C2×C73#42111yescharacteristic
83D73—82no—
84#1480—731nomaximal, Sylow
85C73#148011yescharacteristic, complemented, Sylow
86#532—731no—
87#431D7311yescharacteristic, complemented
88C2×C4⋊C8—731no—
89D4⋊C8—734no—
90C2×#41—1461no—
91C22×C8—1461no—
92C4⋊Q8—731no—
93#127—731no—
94#124—1461no—
95#121—732no—
96#121—1461no—
97C4×D4—732no—
98C4×D4—1461no—
99C2×C42C2×D7311yescharacteristic
100C4⋊C8—21no—
101C4⋊C8—732no—
102C4⋊C8—1461no—
103C22⋊C8—21no—
104C4×C8C2×D7312yes—
105#41—2922no—
106#41—2922no—
107C2×Q8—1461no—
108C2×D4—732no—
109C2×D4—1462no—
110C2×D4—1461no—
111C2×D4—1461no—
112C22×C4—1462no—
113C22×C4C4×D7311yescharacteristic
114C22×C4D29211yescharacteristic
115C22×C4C22⋊D7311yescharacteristic
116C2×C8—22no—
117C2×C8—2922no—
118C2×C8—1462no—
119C4⋊C4—732no—
120C4⋊C4—1461no—
121C22⋊C4—1462no—
122C22⋊C4—1462no—
123C42C4×D7311yescharacteristic
124C42D29211yescharacteristic
125C42C22⋊D7311yescharacteristic
126C42C22×D7311yescharacteristic
127C23—1462no—
128C23#1192400511yescharacteristic
129Q8—2922no—
130D4—2922no—
131D4—2924no—
132D4—2922no—
133D4—1464no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—2922no—
137C2×C4—2922no—
138C2×C4—1462no—
139C2×C4#1192400511yescharacteristic
140C2×C4#1192400511yescharacteristic
141C2×C4#1192400511yescharacteristic
142C2×C4D58412yes—
143C2×C4#1192401712yes—
144C2×C4C2×C4×D7311yescharacteristic
145C2×C4C2×C22⋊D7311yescharacteristic
146C2×C4C2×D29211yescharacteristic
147C8—42no—
148C8—2922no—
149C22—21no—
150C22—21no—
151C22—2922no—
152C22—2922no—
153C22—2922no—
154C22#1455651312yes—
155C22C2×#1192400511yescharacteristic
156C4—21no—
157C4—21no—
158C4—21no—
159C4—2922no—
160C4#1455651312yes—
161C4#1455659912yes—
162C4C2×D58411yescharacteristic
163C4C2×#1192401711yescharacteristic
164C2—22no—
165C2—5842no—
166C2#1798855511yescharacteristic
167C2C2×#1455651311yescharacteristic
168C2#1798860511yescharacteristic
subgroupG/H
centerC2×C4C2×D292
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#431×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#431D73
hypocenterC73#1480
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#10596831C2semidirect
3. #17988316C2semidirect
4. #431×C73C2semidirect
85. C73#1480semidirect
87. #431D73semidirect