Finite Group Databasebeta

← #22608609

Subgroups — #22608609

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#17988334C212yesmaximal, complemented
4#17988330C212yesmaximal, complemented
5#423×C73C211yesmaximal, characteristic, complemented
6C2×#11924028—21no—
7C22×#10596831—21no—
8#14556591C2211yescharacteristic
9#14556588C2211yescharacteristic
10#14556579—21no—
11#14556565—21no—
12#14556565C412yes—
13C4×D292—21no—
14C4×D292C412yes—
15C4⋊#10596831—21no—
16C4⋊#10596831C2212yes—
17C2×M16×C73—21no—
18C2×C42×C73C2211yescharacteristic
19C4⋊C8×C73—21no—
20C4⋊C8×C73C2212yes—
21#11924028—42no—
22#11924028—42no—
23C2×Dic146—21no—
24C2×D292—21no—
25C2×D292—21no—
26C2×D292C2×C412yes—
27C2×C22⋊D73—22no—
28C2×C4×D73—22no—
29C2×#10596831—22no—
30C2×#10596831—42no—
31C4⋊Dic73—21no—
32C4⋊Dic73C2×C412yes—
33#11924005—22no—
34#11924005—22no—
35C22×C4×C73C2×C411yescharacteristic
36C22×C4×C73D411yescharacteristic
37C22×C4×C73D411yescharacteristic
38M16×C73—42no—
39C2×C8×C73—22no—
40C42×C73C2×C411yescharacteristic
41C42×C73D411yescharacteristic
42C42×C73D411yescharacteristic
43C42×C73C2311yescharacteristic
44C23×C73C22⋊C411yescharacteristic
45C22×D73—22no—
46C2×C4×C73—21no—
47C2×C4×C73—21no—
48C2×C4×C73—41no—
49C2×C4×C73C22⋊C411yescharacteristic
50C2×C4×C73C22⋊C411yescharacteristic
51C2×C4×C73C22⋊C411yescharacteristic
52C2×C4×C73D812yes—
53C2×C4×C73SD1612yes—
54C2×C4×C73C22×C411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×D411yescharacteristic
57C22⋊D73—44no—
58C2×Dic73—22no—
59D292—42no—
60D292—41no—
61D292—41no—
62D292—41no—
63D292—41no—
64C4×D73—44no—
65Dic146—41no—
66Dic146—41no—
67C8×C73—42no—
68#10596831—42no—
69C22×C73—21no—
70C22×C73—21no—
71C22×C73#10212yes—
72C22×C73C2×C22⋊C411yescharacteristic
73C2×D73—42no—
74C2×D73—42no—
75C2×D73—42no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—21no—
79C4×C73#10212yes—
80C4×C73C2×D811yescharacteristic
81C4×C73C2×SD1611yescharacteristic
82C4×C73AGL(1,ℤ/8)11yescharacteristic
83C4×C73#13711yescharacteristic
84Dic73—42no—
85C2×C73—22no—
86C2×C73#41311yescharacteristic
87C2×C73C2×#10211yescharacteristic
88C2×C73#41711yescharacteristic
89D73—82no—
90#1547—731nomaximal, Sylow
91C73#154711yescharacteristic, complemented, Sylow
92#532—731no—
93#423D7311yescharacteristic, complemented
94C2×C4⋊C8—731no—
95#332—732no—
96#331—732no—
97C2×#41—1461no—
98C2×M16—21no—
99C22×C8—1461no—
100C4⋊Q8—731no—
101#127—731no—
102#124—1461no—
103#121—732no—
104#121—1461no—
105C4×D4—732no—
106C4×D4—1461no—
107C2×C42C2×D7311yescharacteristic
108C4⋊C8—21no—
109C4⋊C8—732no—
110C4⋊C8—1461no—
111C4⋊C8C2×D7312yes—
112#41—2922no—
113#41—2922no—
114C2×Q8—1461no—
115C2×D4—732no—
116C2×D4—1462no—
117C2×D4—1461no—
118C2×D4—1461no—
119C22×C4—1462no—
120C22×C4C4×D7311yescharacteristic
121C22×C4D29211yescharacteristic
122C22×C4C22⋊D7311yescharacteristic
123M16—42no—
124C2×C8—22no—
125C2×C8—2922no—
126C2×C8—1462no—
127C4⋊C4—732no—
128C4⋊C4—1461no—
129C22⋊C4—1462no—
130C22⋊C4—1462no—
131C42C4×D7311yescharacteristic
132C42D29211yescharacteristic
133C42C22⋊D7311yescharacteristic
134C42C22×D7311yescharacteristic
135C23—1462no—
136C23#1192400511yescharacteristic
137Q8—2921no—
138Q8—2921no—
139D4—2922no—
140D4—2924no—
141D4—2921no—
142D4—2921no—
143D4—2921no—
144D4—2921no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—2924no—
149C2×C4—1462no—
150C2×C4#1192400511yescharacteristic
151C2×C4#1192400511yescharacteristic
152C2×C4#1192400511yescharacteristic
153C2×C4#1192401312yes—
154C2×C4#1192401512yes—
155C2×C4C2×C4×D7311yescharacteristic
156C2×C4C2×C22⋊D7311yescharacteristic
157C2×C4C2×D29211yescharacteristic
158C8—42no—
159C8—2922no—
160C22—21no—
161C22—21no—
162C22—2922no—
163C22—2922no—
164C22—2922no—
165C22#1455651112yes—
166C22C2×#1192400511yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—2922no—
171C4#1455651112yes—
172C4C2×#1192401311yescharacteristic
173C4C2×#1192401511yescharacteristic
174C4#1455661911yescharacteristic
175C4#1455662411yescharacteristic
176C2—22no—
177C2—5842no—
178C2#1798856911yescharacteristic
179C2C2×#1455651111yescharacteristic
180C2#1798858911yescharacteristic
subgroupG/H
centerC22C2×#11924005
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#423×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#423D73
hypocenterC73#1547
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#10596831C2semidirect
3. #17988334C2semidirect
4. #17988330C2semidirect
5. #423×C73C2semidirect
91. C73#1547semidirect
93. #423D73semidirect