Finite Group Databasebeta

← #22610367

Subgroups — #22610367

Order 9344.

412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C22×#11924012C211yesmaximal, characteristic, complemented
2C2×#14556565C211yesmaximal, characteristic
3C2×#14556511C212yesmaximal, complemented
4#17988349C212yesmaximal, complemented
5#380×C73C211yesmaximal, characteristic, complemented
6C22×D292C2211yescharacteristic
7C22×C22⋊D73—21no—
8C2×#11924012—24no—
9C2×#11924012—22no—
10C22×#10596831C2212yes—
11#14556565—22no—
12#14556565C414yescomplemented
13C2×C4⋊Dic73C2211yescharacteristic
14C2×#11924005—21no—
15#14556511—24no—
16C23×C4×C73C2211yescharacteristic
17C2×C4⋊C4×C73C2212yes—
18C2×C22⋊C4×C73—21no—
19#95×C73—21no—
20C23×D73—21no—
21C2×D292—22no—
22C2×D292—22no—
23C2×D292—21no—
24C2×D292C2×C412yes—
25C2×C22⋊D73—24no—
26C2×C22⋊D73—44no—
27C22×Dic73—21no—
28#11924012—28no—
29C2×#10596831—22no—
30C2×#10596831—22no—
31C2×#10596831D414yescomplemented
32C4⋊Dic73—21no—
33C4⋊Dic73C2×C412yes—
34#11924005—24no—
35C24×C73D411yescharacteristic
36C22×C4×C73—22no—
37C22×C4×C73—22no—
38C22×C4×C73—22no—
39C22×C4×C73C2×C412yes—
40C22×C4×C73D412yes—
41C22×C4×C73D411yescharacteristic
42C22×C4×C73C2311yescharacteristic
43C4⋊C4×C73—22no—
44C4⋊C4×C73—22no—
45C22⋊C4×C73—42no—
46C23×C73—22no—
47C23×C73—21no—
48C23×C73—22no—
49C23×C73—21no—
50C23×C73C22⋊C412yes—
51C23×C73C2×D411yescharacteristic
52C22×D73—22no—
53C22×D73—42no—
54C22×D73—42no—
55C22×D73—41no—
56C22×D73—41no—
57C2×C4×C73—22no—
58C2×C4×C73—24no—
59C2×C4×C73—22no—
60C2×C4×C73—22no—
61C2×C4×C73—42no—
62C2×C4×C73—42no—
63C2×C4×C73—42no—
64C2×C4×C73C22⋊C412yes—
65C2×C4×C73C22×C411yescharacteristic
66C2×C4×C73C2×D412yes—
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73#4112yes—
69C22⋊D73—48no—
70C2×Dic73—22no—
71C2×Dic73—42no—
72D292—24no—
73D292—41no—
74D292—41no—
75#10596831—24no—
76C22×C73—22no—
77C22×C73—22no—
78C22×C73—22no—
79C22×C73—42no—
80C22×C73—42no—
81C22×C73C2×C22⋊C411yescharacteristic
82C22×C73#12112yes—
83C22×C73AGL(1,ℤ/8)12yes—
84C22×C73AGL(1,ℤ/8)11yescharacteristic
85C22×C73#13711yescharacteristic
86C2×D73—42no—
87C2×D73—42no—
88C2×D73—42no—
89C2×D73—82no—
90C2×D73—82no—
91C4×C73—22no—
92C4×C73—82no—
93C4×C73C4×D412yes—
94C4×C73#12011yescharacteristic
95C4×C73#12311yescharacteristic
96Dic73—42no—
97C2×C73—42no—
98C2×C73#38611yescharacteristic
99C2×C73#41711yescharacteristic
100C2×C73#41811yescharacteristic
101C2×C73#46812yes—
102C2×C73#46912yes—
103D73—82no—
104#1895—731nomaximal, Sylow
105C73#189511yescharacteristic, complemented, Sylow
106C22×M16—731no—
107C2×#121—731no—
108C2×#102—732no—
109#380D7311yescharacteristic, complemented
110#340—732no—
111C22×D4—731no—
112C22×D4—1461no—
113C23×C4C2×D7311yescharacteristic
114C2×M16—1464no—
115C2×M16—1462no—
116C22×C8—732no—
117#121—734no—
118#121—1462no—
119C2×C4⋊C4—731no—
120C2×C4⋊C4C2×D7312yes—
121C2×C22⋊C4—21no—
122C2×C22⋊C4—1461no—
123#102—1464no—
124#95—21no—
125C24—1461no—
126C24C22⋊D7311yescharacteristic
127C2×D4—2924no—
128C2×D4—732no—
129C2×D4—1464no—
130C2×D4—1462no—
131C2×D4—1461no—
132C2×D4—1462no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—1461no—
137C22×C4C4×D7312yes—
138C22×C4D29212yes—
139C22×C4C22⋊D7311yescharacteristic
140C22×C4C22×D7311yescharacteristic
141M16—1468no—
142C2×C8—734no—
143C2×C8—1462no—
144C2×C8—1462no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C4⋊C4—732no—
148C4⋊C4—1461no—
149C22⋊C4—42no—
150C22⋊C4—1464no—
151C23—22no—
152C23—22no—
153C23—21no—
154C23—21no—
155C23—2922no—
156C23—2922no—
157C23—2921no—
158C23—2921no—
159C23—1462no—
160C23#1192400512yes—
161C23C2×C22⋊D7311yescharacteristic
162D4—2928no—
163D4—2921no—
164D4—2921no—
165D4—1464no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—2922no—
174C2×C4—1462no—
175C2×C4#1192400512yes—
176C2×C4C2×C4×D7311yescharacteristic
177C2×C4D4×D7312yes—
178C2×C4C2×D29211yescharacteristic
179C2×C4#1192402712yes—
180C8—1464no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—2922no—
187C22—2922no—
188C22—2922no—
189C22—5842no—
190C22—5842no—
191C22C2×#1192400511yescharacteristic
192C22#1455656312yes—
193C22#1455661612yes—
194C22#1455661711yescharacteristic
195C22#1455662211yescharacteristic
196C4—22no—
197C4—82no—
198C4—2922no—
199C4#1455655112yes—
200C4#1455656111yescharacteristic
201C4#1455657511yescharacteristic
202C2—42no—
203C2—5842no—
204C2#1798846411yescharacteristic
205C2#1798858611yescharacteristic
206C2#1798859111yescharacteristic
207C2#1798883512yes—
208C2#1798883812yes—
subgroupG/H
centerC23C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#380×C73C2
socleC23×C73C2×D4
hypercenter#380D73
hypocenterC73#1895
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C22×#11924012C2semidirect
3. C2×#14556511C2semidirect
4. #17988349C2semidirect
5. #380×C73C2semidirect
12. #14556565C4semidirect
31. C2×#10596831D4semidirect
105. C73#1895semidirect
109. #380D73semidirect