Finite Group Databasebeta

← #22616271

Subgroups — #22616271

Order 9344.

568 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556576C212yesmaximal
2C2×#14556569C212yesmaximal, complemented
3#17988518C212yesmaximal, complemented
4#17988513C212yesmaximal, complemented
5#17988507C211yesmaximal, characteristic, complemented
6#17988504C211yesmaximal, characteristic
7#17988478C212yesmaximal, complemented
8#17988458C212yesmaximal, complemented
9#384×C73C211yesmaximal, characteristic, complemented
10C22×Dic146C2211yescharacteristic
11C22×D292C2211yescharacteristic
12C22×C4×D73C2212yes—
13#14556576—28no—
14#14556569—28no—
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C2×#11924007C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26#14556498C2211yescharacteristic
27#14556498C2211yescharacteristic
28C2×C4⋊C4×C73C2212yes—
29C2×C4⋊C4×C73C2212yes—
30C2×C4⋊C4×C73C2211yescharacteristic
31C2×C4⋊C4×C73C2211yescharacteristic
32C2×C42×C73C2211yescharacteristic
33C23×D73C2312yes—
34C2×Dic146—24no—
35C2×Dic146—41no—
36C2×D292—24no—
37C2×D292—41no—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C2×C4×D73—24no—
42C2×C4×D73—24no—
43C2×C4×D73—42no—
44#11924007—24no—
45#11924007—24no—
46#11924007—24no—
47#11924005—24no—
48#11924005—24no—
49#11924005—24no—
50#11924005—24no—
51#11924005D418yes—
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2312yes—
54C22×C4×C73C2311yescharacteristic
55C22×C4×C73C2312yes—
56C22×C4×C73C2311yescharacteristic
57C4⋊C4×C73—24no—
58C4⋊C4×C73—24no—
59C4⋊C4×C73—41no—
60C4⋊C4×C73—41no—
61C42×C73—22no—
62C23×C73C2411yescharacteristic
63C22×D73—22no—
64C22×D73—22no—
65C22×D73—22no—
66C22×D73—22no—
67C22×D73—22no—
68C22×D73—22no—
69C22×D73C2×D414yes—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73C2×D414yes—
82C2×C4×C73#4112yes—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73C2×D414yes—
92D292—44no—
93C4×D73—48no—
94Dic146—44no—
95C22×C73C22×D412yes—
96C22×C73C2×#4111yescharacteristic
97C22×C73H(5,𝔽2)11yescharacteristic
98C22×C732−1+411yescharacteristic
99C22×C732−1+412yes—
100C2×D73—24no—
101C2×D73—24no—
102C2×D73—24no—
103C2×D73—42no—
104C2×D73—42no—
105C2×D73—42no—
106C2×D73—42no—
107C4×C73—22no—
108C4×C73—24no—
109C4×C73—41no—
110C4×C73—42no—
111C4×C73—41no—
112Dic73—24no—
113Dic73—42no—
114Dic73—42no—
115C2×C73#53612yes—
116C2×C73#53911yescharacteristic
117C2×C73D4211yescharacteristic
118C2×C73#54712yes—
119C2×C73#56311yescharacteristic
120D73—44no—
121#2680—731nomaximal, Sylow
122C73#268011yescharacteristic, complemented, Sylow
123C2×#123—732no—
124C2×C22⋊Q8—732no—
125#398—732no—
126#397—732no—
127#395—731no—
128#394—731no—
129#388—732no—
130#385—732no—
131#384D7311yescharacteristic, complemented
132C22×Q8—731no—
133C22×D4—731no—
134C23×C4—732no—
135#123—1468no—
136C22⋊Q8—1468no—
137C2×C4⋊C4—732no—
138C2×C4⋊C4—732no—
139C2×C4⋊C4—732no—
140C2×C4⋊C4C2×D7312yes—
141C2×C4⋊C4C2×D7312yes—
142C2×C4⋊C4C2×D7311yescharacteristic
143C2×C4⋊C4C2×D7311yescharacteristic
144C2×C22⋊C4—732no—
145C2×C22⋊C4—732no—
146C2×C22⋊C4—732no—
147C2×C22⋊C4—732no—
148C2×C22⋊C4—732no—
149C2×C42C2×D7311yescharacteristic
150#95—732no—
151#95—732no—
152#95—732no—
153#95—731no—
154#95—731no—
155C24—732no—
156C2×Q8—2921no—
157C2×Q8—1464no—
158C2×D4—2921no—
159C2×D4—1464no—
160C22×C4—2922no—
161C22×C4—732no—
162C22×C4—732no—
163C22×C4—732no—
164C22×C4—1464no—
165C22×C4—1464no—
166C22×C4C22×D7311yescharacteristic
167C22×C4C22×D7312yes—
168C22×C4C22×D7311yescharacteristic
169C22×C4C22×D7312yes—
170C22×C4C22×D7311yescharacteristic
171C4⋊C4—24no—
172C4⋊C4—24no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—1464no—
176C4⋊C4—1464no—
177C4⋊C4—1464no—
178C22⋊C4—738no—
179C22⋊C4—1464no—
180C22⋊C4—1464no—
181C22⋊C4—1464no—
182C22⋊C4—1464no—
183C42—22no—
184C23—734no—
185C23—1462no—
186C23—1462no—
187C23—1462no—
188C23—1462no—
189C23—1462no—
190C23—1462no—
191C23C23×D7311yescharacteristic
192Q8—2924no—
193D4—2924no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—2928no—
206C2×C4—734no—
207C2×C4—1462no—
208C2×C4—1462no—
209C2×C4—1462no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4—1462no—
213C2×C4—1462no—
214C2×C4—1462no—
215C2×C4D4×D7314yes—
216C2×C4#1192402812yes—
217C22—2922no—
218C22—2922no—
219C22—2922no—
220C22—2922no—
221C22—1464no—
222C22—1464no—
223C22—1464no—
224C22C2×D4×D7312yes—
225C22C2×#1192402811yescharacteristic
226C22#1455663611yescharacteristic
227C22#1455663911yescharacteristic
228C22#1455663912yes—
229C4—22no—
230C4—24no—
231C4—42no—
232C4—41no—
233C4—41no—
234C4—2922no—
235C4—2922no—
236C4—1464no—
237C2—2924no—
238C2#1798916212yes—
239C2#1798918411yescharacteristic
240C2#1798922211yescharacteristic
241C2#1798923812yes—
242C2#1798933611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#384×C73C2
hypercenter#384D73
hypocenterC73#2680
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#14556569C2semidirect
3. #17988518C2semidirect
4. #17988513C2semidirect
5. #17988507C2semidirect
7. #17988478C2semidirect
8. #17988458C2semidirect
9. #384×C73C2semidirect
122. C73#2680semidirect
131. #384D73semidirect