Finite Group Databasebeta

← #22613591

Subgroups — #22613591

Order 9344.

780 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14556567C212yesmaximal, complemented
2C2×C22⋊C4×D73C212yesmaximal
3#17988523C211yesmaximal, characteristic, complemented
4#17988510C212yesmaximal, complemented
5#17988461C212yesmaximal, complemented
6#17988461C212yesmaximal, complemented
7#17988446C212yesmaximal, complemented
8#17988442C211yesmaximal, characteristic
9#393×C73C211yesmaximal, characteristic, complemented
10C24×D73C2211yescharacteristic
11C22×C4×D73C2212yes—
12C22×C4×D73C2212yes—
13#14556567—28no—
14C2×C4⋊Dic73C2212yescomplemented
15C2×C4⋊Dic73C2211yescharacteristic, complemented
16C2×#11924007C2212yescomplemented
17C2×#11924007C2212yescomplemented
18C2×#11924007C2212yescomplemented
19C2×C22⋊Dic73C2212yes—
20C2×C22⋊Dic73C2211yescharacteristic
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23C2×#11924005C2212yes—
24C2×#11924005C2212yes—
25C22⋊C4×D73—28no—
26#14556498C2212yescomplemented
27#14556498C2211yescharacteristic, complemented
28C22×Q8×C73C2211yescharacteristic, complemented
29C2×C22⋊C4×C73C2212yes—
30C2×C22⋊C4×C73C2211yescharacteristic
31#95×C73C2211yescharacteristic, complemented
32#95×C73C2212yescomplemented
33C23×D73—24no—
34C23×D73—24no—
35C23×D73—41no—
36C23×D73—41no—
37C23×D73Q814yescomplemented
38C23×D73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C22×Dic73C2312yes—
42C2×C4×D73—24no—
43C2×C4×D73—24no—
44C2×C4×D73—24no—
45C2×C4×D73—24no—
46C2×C4×D73—42no—
47C2×C4×D73—42no—
48C4⋊Dic73—24no—
49C4⋊Dic73—41no—
50#11924007—24no—
51#11924007—24no—
52#11924007—42no—
53C22⋊Dic73—24no—
54C22⋊Dic73—41no—
55#11924005—24no—
56#11924005—24no—
57#11924005—24no—
58#11924005D418yes—
59C24×C73C2311yescharacteristic
60C2×Q8×C73—24no—
61C2×Q8×C73—41no—
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2312yes—
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2312yes—
66C22⋊C4×C73—24no—
67C22⋊C4×C73—41no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73—21no—
71C23×C73—21no—
72C23×C73C2×Q812yes—
73C23×C73C2411yescharacteristic
74C22×D73—22no—
75C22×D73—22no—
76C22×D73—22no—
77C22×D73—22no—
78C22×D73—216no—
79C22×D73—44no—
80C22×D73—44no—
81C22×D73—48no—
82C22×D73—44no—
83C22×D73C2×D414yes—
84C22×D73C2×Q814yes—
85C22×D73#4114yes—
86Q8×C73—44no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—22no—
96C2×C4×C73C2×D414yes—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73C2×D414yes—
106C4×D73—48no—
107C4×D73—48no—
108C22×C73—24no—
109C22×C73—22no—
110C22×C73—41no—
111C22×C73—42no—
112C22×C73—41no—
113C22×C73C22×D412yes—
114C22×C73C22×Q811yescharacteristic
115C22×C73C2×#4112yes—
116C22×C73H(5,𝔽2)11yescharacteristic
117C22×C73H(5,𝔽2)11yescharacteristic
118C2×D73—24no—
119C2×D73—24no—
120C2×D73—24no—
121C2×D73—24no—
122C2×D73—24no—
123C2×D73—24no—
124C2×D73—416no—
125C2×D73C22⋊Q818yescomplemented
126C4×C73—24no—
127C4×C73—41no—
128C4×C73—42no—
129C4×C73—41no—
130Dic73—24no—
131Dic73—42no—
132Dic73—42no—
133C2×C73—42no—
134C2×C73C2×C22⋊Q812yes—
135C2×C73#54311yescharacteristic
136C2×C73D4211yescharacteristic
137C2×C73#54612yes—
138C2×C73#55111yescharacteristic
139D73—28no—
140#2437—731nomaximal, Sylow
141C73#243711yescharacteristic, complemented, Sylow
142C2×C22⋊Q8—732no—
143C22×C22⋊C4—732no—
144#399—731no—
145#396—732no—
146#393D7311yescharacteristic, complemented
147#385—732no—
148#385—732no—
149#380—732no—
150#379—731no—
151C25—731no—
152C22×Q8C2×D7311yescharacteristic, complemented
153C23×C4—732no—
154C23×C4—732no—
155C22⋊Q8—1468no—
156C2×C4⋊C4—732no—
157C2×C4⋊C4—731no—
158C2×C4⋊C4—732no—
159C2×C4⋊C4—732no—
160C2×C4⋊C4—732no—
161C2×C22⋊C4—731no—
162C2×C22⋊C4—732no—
163C2×C22⋊C4—732no—
164C2×C22⋊C4—732no—
165C2×C22⋊C4—732no—
166C2×C22⋊C4—732no—
167C2×C22⋊C4—1468no—
168C2×C22⋊C4C2×D7312yes—
169C2×C22⋊C4C2×D7311yescharacteristic
170#95—732no—
171#95—731no—
172#95C2×D7311yescharacteristic, complemented
173#95C2×D7312yescomplemented
174C24—2921no—
175C24—2921no—
176C24—734no—
177C24—732no—
178C24—1464no—
179C24—1464no—
180C24C22×D7311yescharacteristic
181C2×Q8—24no—
182C2×Q8—41no—
183C22×C4—2922no—
184C22×C4—2922no—
185C22×C4—732no—
186C22×C4—732no—
187C22×C4—732no—
188C22×C4—1464no—
189C22×C4—1464no—
190C22×C4—1464no—
191C22×C4—1464no—
192C22×C4C22×D7311yescharacteristic
193C22×C4C22×D7312yes—
194C22×C4C22×D7311yescharacteristic
195C22×C4C22×D7312yes—
196C4⋊C4—2922no—
197C4⋊C4—2921no—
198C4⋊C4—1464no—
199C4⋊C4—1464no—
200C4⋊C4—1464no—
201C22⋊C4—24no—
202C22⋊C4—41no—
203C22⋊C4—2921no—
204C22⋊C4—738no—
205C22⋊C4—1464no—
206C22⋊C4—1464no—
207C22⋊C4—1464no—
208C22⋊C4—1464no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—21no—
213C23—2924no—
214C23—2924no—
215C23—2928no—
216C23—2924no—
217C23—734no—
218C23—734no—
219C23—734no—
220C23—14616no—
221C23—1462no—
222C23—1462no—
223C23—1462no—
224C23—1462no—
225C23Q8×D7312yes—
226C23C23×D7311yescharacteristic
227Q8—44no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—2928no—
238C2×C4—2928no—
239C2×C4—734no—
240C2×C4—1462no—
241C2×C4—1462no—
242C2×C4—1462no—
243C2×C4—1462no—
244C2×C4—1462no—
245C2×C4—1462no—
246C2×C4—1462no—
247C2×C4—1462no—
248C2×C4D4×D7314yes—
249C22—22no—
250C22—24no—
251C22—41no—
252C22—42no—
253C22—41no—
254C22—29216no—
255C22—738no—
256C22—1464no—
257C22—1464no—
258C22—1464no—
259C22—1464no—
260C22—1464no—
261C22—1464no—
262C22C2×D4×D7312yes—
263C22C2×Q8×D7311yescharacteristic
264C22#41×D7312yes—
265C22#1455663611yescharacteristic
266C22#1455663711yescharacteristic
267C4—24no—
268C4—41no—
269C4—42no—
270C4—41no—
271C4—2922no—
272C4—2922no—
273C4—1464no—
274C2—42no—
275C2—1468no—
276C2C22⋊Q8×D7312yes—
277C2#1798921211yescharacteristic
278C2#1798921911yescharacteristic
279C2#1798923012yes—
280C2#1798926711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#393×C73C2
hypercenter#393D73
hypocenterC73#2437
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#14556567C2semidirect
3. #17988523C2semidirect
4. #17988510C2semidirect
5. #17988461C2semidirect
6. #17988461C2semidirect
7. #17988446C2semidirect
9. #393×C73C2semidirect
14. C2×C4⋊Dic73C22semidirect
15. C2×C4⋊Dic73C22semidirect
16. C2×#11924007C22semidirect
17. C2×#11924007C22semidirect
18. C2×#11924007C22semidirect
26. #14556498C22semidirect
27. #14556498C22semidirect
28. C22×Q8×C73C22semidirect
31. #95×C73C22semidirect
32. #95×C73C22semidirect
37. C23×D73Q8semidirect
125. C2×D73C22⋊Q8semidirect
141. C73#2437semidirect
146. #393D73semidirect
152. C22×Q8C2×D73semidirect
172. #95C2×D73semidirect
173. #95C2×D73semidirect