Finite Group Databasebeta

← #22618219

Subgroups — #22618219

Order 9344.

1068 conjugacy classes of subgroups; only the 201 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 201 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
1C23×C4×D73C211yesmaximal, characteristic
2C2×#14556571C212yesmaximal, complemented
3C2×#14556570C211yesmaximal, characteristic, complemented
4#17988462C212yesmaximal, complemented
5#17988461C214yesmaximal, complemented
6#17988444C212yesmaximal, complemented
7#17988442C212yesmaximal
8#380×C73C211yesmaximal, characteristic, complemented
9C24×D73C2211yescharacteristic
10C22×Dic146C2211yescharacteristic, complemented
11C23×Dic73C2211yescharacteristic
12C22×C4×D73—28no—
13C22×C4×D73—24no—
14C22×C4×D73C2212yes—
15C22×C4×D73C2212yes—
16#14556571—28no—
17#14556570—24no—
18C2×C4⋊Dic73C2211yescharacteristic, complemented
19C2×C4⋊Dic73C2214yescomplemented
20C2×#11924007C2212yescomplemented
21C2×C22⋊Dic73C2212yes—
22C2×#11924005C2214yes—
23C2×#11924005C2214yes—
24#14556498C2214yescomplemented
25C23×C4×C73C2211yescharacteristic
26C2×C4⋊C4×C73C2212yescomplemented
27C2×C22⋊C4×C73C2212yes—
28#95×C73C2212yescomplemented
29C23×D73—22no—
30C23×D73—22no—
31C23×D73—24no—
32C23×D73—24no—
33C23×D73Q814yescomplemented
34C23×D73C2312yes—
35C2×Dic146—22no—
36C2×Dic146—24no—
37C22×Dic73—22no—
38C22×Dic73—24no—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C22×Dic73C2312yes—
42C2×C4×D73—232no—
43C2×C4×D73—24no—
44C2×C4×D73—24no—
45C2×C4×D73—24no—
46C2×C4×D73—24no—
47C2×C4×D73—24no—
48C2×C4×D73D418yes—
49C4⋊Dic73—22no—
50C4⋊Dic73—28no—
51#11924007—24no—
52C22⋊Dic73—24no—
53#11924005—28no—
54#11924005—28no—
55C24×C73C2311yescharacteristic
56C22×C4×C73—24no—
57C22×C4×C73D414yes—
58C22×C4×C73C2314yes—
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2311yescharacteristic
61C4⋊C4×C73—24no—
62C22⋊C4×C73—24no—
63C23×C73—22no—
64C23×C73—22no—
65C23×C73C2×D412yes—
66C23×C73C2×Q812yes—
67C23×C73#4112yes—
68C23×C73C2411yescharacteristic
69C22×D73—28no—
70C22×D73—216no—
71C22×D73—28no—
72C22×D73—28no—
73C22×D73—22no—
74C22×D73—22no—
75C22×D73—22no—
76C22×D73—22no—
77C22×D73—216no—
78C22×D73C2×D414yes—
79C22×D73C2×Q814yes—
80C22×D73#4114yes—
81C2×C4×C73—22no—
82C2×C4×C73—28no—
83C2×C4×C73—24no—
84C2×C4×C73—24no—
85C2×C4×C73—24no—
86C2×C4×C73C2×D414yes—
87C2×C4×C73C2×D412yes—
88C2×C4×C73C2×D412yes—
89C2×Dic73—28no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—24no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—24no—
96C2×Dic73C2×D414yes—
97C4×D73—216no—
98C4×D73—216no—
99Dic146—44no—
100C22×C73—22no—
101C22×C73—24no—
102C22×C73—22no—
103C22×C73—24no—
104C22×C73C22⋊Q814yescomplemented
105C22×C73C22×D412yes—
106C22×C73C22×D411yescharacteristic
107C22×C73C22×Q811yescharacteristic
108C22×C73C2×#4112yes—
109C22×C73C2×#4111yescharacteristic
110C2×D73—232no—
111C2×D73—24no—
112C2×D73—24no—
113C2×D73—24no—
114C2×D73—24no—
115C2×D73—24no—
116C2×D73—24no—
117C2×D73C22⋊Q818yescomplemented
118C4×C73—22no—
119C4×C73—44no—
120C4×C73#12014yes—
121Dic73—24no—
122Dic73—42no—
123Dic73—42no—
124C2×C73—24no—
125C2×C73C2×#12011yescharacteristic
126C2×C73C2×C22⋊Q812yes—
127C2×C73C2×C22⋊Q811yescharacteristic
128C2×C73#52512yes—
129C2×C73#52511yescharacteristic
130D73—28no—
131#2848—731nomaximal, Sylow
132C73#284811yescharacteristic, complemented, Sylow
133C24×C4—731no—
134C2×C22⋊Q8—731no—
135C2×C22⋊Q8—732no—
136#385—732no—
137#385—734no—
138#380—732no—
139#380D7311yescharacteristic, complemented
140#379—732no—
141C25—731no—
142C22×Q8—731no—
143C23×C4—732no—
144C23×C4—731no—
145C23×C4—732no—
146C23×C4—1468no—
147C23×C4—1464no—
148C23×C4C2×D7311yescharacteristic
149C22⋊Q8—1468no—
150C22⋊Q8—1464no—
151C2×C4⋊C4—731no—
152C2×C4⋊C4—732no—
153C2×C4⋊C4—734no—
154C2×C4⋊C4C2×D7312yescomplemented
155C2×C22⋊C4—732no—
156C2×C22⋊C4—734no—
157C2×C22⋊C4—734no—
158C2×C22⋊C4C2×D7312yes—
159#95—734no—
160#95C2×D7312yescomplemented
161C24—732no—
162C24—734no—
163C24—1464no—
164C24—1464no—
165C24—1462no—
166C24—1462no—
167C24C22×D7311yescharacteristic
168C2×Q8—1464no—
169C2×Q8—1462no—
170C22×C4—24no—
171C22×C4—732no—
172C22×C4—738no—
173C22×C4—732no—
174C22×C4—732no—
175C22×C4—1464no—
176C22×C4—1464no—
177C22×C4—14632no—
178C22×C4—1464no—
179C22×C4—1462no—
180C22×C4—1464no—
181C22×C4—1464no—
182C22×C4—1464no—
183C22×C4D29214yes—
184C22×C4C22×D7314yes—
185C22×C4C22×D7311yescharacteristic
186C22×C4C22×D7311yescharacteristic
187C4⋊C4—24no—
188C4⋊C4—1468no—
189C4⋊C4—1464no—
190C4⋊C4—1462no—
191C22⋊C4—24no—
192C22⋊C4—1468no—
193C22⋊C4—1468no—
194C22⋊C4—1464no—
195C23—22no—
196C23—22no—
197C23—734no—
198C23—734no—
199C23—734no—
200C23—14616no—
201C23—1468no—
202C23—14616no—
203C23—1468no—
204C23—1468no—
205C23—1462no—
206C23—1462no—
207C23—1462no—
208C23—1462no—
209C23C2×D29212yes—
210C23Q8×D7312yes—
211C23#1192402712yes—
212C23C23×D7311yescharacteristic
213Q8—2924no—
214C2×C4—22no—
215C2×C4—28no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—24no—
219C2×C4—734no—
220C2×C4—14616no—
221C2×C4—1464no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1464no—
225C2×C4—1468no—
226C2×C4—1462no—
227C2×C4—1462no—
228C2×C4—14616no—
229C2×C4D4×D7314yes—
230C2×C4C2×D29212yes—
231C2×C4C2×D29212yes—
232C22—22no—
233C22—24no—
234C22—24no—
235C22—22no—
236C22—738no—
237C22—14632no—
238C22—1464no—
239C22—1464no—
240C22—1464no—
241C22—1464no—
242C22—1464no—
243C22—1464no—
244C22#1455657114yescomplemented
245C22C2×D4×D7312yes—
246C22C22×D29211yescharacteristic
247C22C2×Q8×D7311yescharacteristic
248C22#41×D7312yes—
249C22C2×#1192402711yescharacteristic
250C4—22no—
251C4—44no—
252C4—2922no—
253C4—2922no—
254C4—1464no—
255C4#1455656114yes—
256C2—24no—
257C2—1468no—
258C2C2×#1455656111yescharacteristic
259C2C22⋊Q8×D7312yes—
260C2C2×#1455657111yescharacteristic
261C2#1798909712yes—
262C2#1798909911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#380×C73C2
hypercenter#380D73
hypocenterC73#2848
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#14556571C2semidirect
3. C2×#14556570C2semidirect
4. #17988462C2semidirect
5. #17988461C2semidirect
6. #17988444C2semidirect
8. #380×C73C2semidirect
10. C22×Dic146C22semidirect
18. C2×C4⋊Dic73C22semidirect
19. C2×C4⋊Dic73C22semidirect
20. C2×#11924007C22semidirect
24. #14556498C22semidirect
26. C2×C4⋊C4×C73C22semidirect
28. #95×C73C22semidirect
33. C23×D73Q8semidirect
104. C22×C73C22⋊Q8semidirect
117. C2×D73C22⋊Q8semidirect
132. C73#2848semidirect
139. #380D73semidirect
154. C2×C4⋊C4C2×D73semidirect
160. #95C2×D73semidirect
244. C22#14556571semidirect