Finite Group Databasebeta

← #22617925

Subgroups — #22617925

Order 9344.

712 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556559C212yesmaximal, complemented
2#17988516C212yesmaximal, complemented
3#17988512C211yesmaximal, characteristic, complemented
4#17988503C212yesmaximal, complemented
5#17988502C212yesmaximal, complemented
6#17988501C212yesmaximal, complemented
7#17988495C212yesmaximal, complemented
8#17988442C211yesmaximal, characteristic, complemented
9#392×C73C211yesmaximal, characteristic, complemented
10C24×D73C2211yescharacteristic
11C22×C22⋊D73C2212yes—
12C22×C22⋊D73C2212yes—
13#14556559—28no—
14C2×C4⋊Dic73C2211yescharacteristic, complemented
15C2×#11924007C2212yescomplemented
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2211yescharacteristic
18C2×C22⋊Dic73C2212yescomplemented
19C2×C22⋊Dic73C2212yescomplemented
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23C2×#11924005C2212yes—
24#14556498C2212yescomplemented
25#14556498C2212yescomplemented
26#14556498C2211yescharacteristic, complemented
27C22×D4×C73C2212yes—
28C22×D4×C73C2211yescharacteristic, complemented
29C2×C22⋊C4×C73C2211yescharacteristic
30C2×C22⋊C4×C73C2212yescomplemented
31#95×C73C2211yescharacteristic, complemented
32C23×D73—42no—
33C23×D73—42no—
34C23×D73—41no—
35C23×D73—41no—
36C23×D73D414yescomplemented
37C23×D73C2312yes—
38C2×C22⋊D73—24no—
39C2×C22⋊D73—24no—
40C2×C22⋊D73—42no—
41C2×C22⋊D73—42no—
42C2×C22⋊D73—42no—
43C2×C22⋊D73—42no—
44C22×Dic73C2312yes—
45C22×Dic73C2312yes—
46C22×Dic73C2312yes—
47C4⋊Dic73—41no—
48#11924007—42no—
49C22⋊Dic73—24no—
50C22⋊Dic73—41no—
51C22⋊Dic73—42no—
52C22⋊Dic73—42no—
53#11924005—24no—
54#11924005—24no—
55#11924005—42no—
56#11924005—42no—
57C24×C73C2312yes—
58C24×C73C2311yescharacteristic
59C2×D4×C73—24no—
60C2×D4×C73—42no—
61C2×D4×C73—42no—
62C2×D4×C73—41no—
63C2×D4×C73—42no—
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2312yes—
66C22×C4×C73C2311yescharacteristic
67C22⋊C4×C73—41no—
68C22⋊C4×C73—42no—
69C23×C73—21no—
70C23×C73—22no—
71C23×C73—22no—
72C23×C73—21no—
73C23×C73—22no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73—22no—
77C23×C73—22no—
78C23×C73—22no—
79C23×C73—22no—
80C23×C73C2×D412yes—
81C23×C73C2411yescharacteristic
82C22×D73—22no—
83C22×D73—22no—
84C22×D73—22no—
85C22×D73—22no—
86C22×D73—22no—
87C22×D73—22no—
88C22×D73—44no—
89C22×D73—48no—
90C22×D73—44no—
91C22×D73—48no—
92C22×D73—44no—
93C22×D73C2×D414yes—
94D4×C73—48no—
95D4×C73—44no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—21no—
99C2×C4×C73—22no—
100C2×C4×C73—21no—
101C2×C4×C73—22no—
102C2×C4×C73—22no—
103C22⋊D73—48no—
104C22⋊D73—48no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C22×C73—24no—
115C22×C73—22no—
116C22×C73—41no—
117C22×C73—42no—
118C22×C73—41no—
119C22×C73—42no—
120C22×C73—42no—
121C22×C73—42no—
122C22×C73—42no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73—42no—
126C22×C73C22×D411yescharacteristic
127C22×C73H(5,𝔽2)12yes—
128C22×C73H(5,𝔽2)11yescharacteristic
129C22×C73H(5,𝔽2)12yes—
130C22×C73H(5,𝔽2)11yescharacteristic
131C2×D73—24no—
132C2×D73—24no—
133C2×D73—24no—
134C2×D73—416no—
135C2×D73—42no—
136C2×D73—42no—
137C2×D73—42no—
138C2×D73—42no—
139C4×C73—42no—
140C4×C73—41no—
141C4×C73—41no—
142Dic73—42no—
143Dic73—42no—
144Dic73—42no—
145C2×C73—42no—
146C2×C73—82no—
147C2×C73#53411yescharacteristic
148C2×C73#53412yes—
149C2×C73#56011yescharacteristic
150C2×C73#56012yes—
151C2×C73H(3,𝔽4)11yescharacteristic
152D73—44no—
153#2812—731nomaximal, Sylow
154C73#281211yescharacteristic, complemented, Sylow
155C2×#120—732no—
156#397—731no—
157#397—732no—
158#394—732no—
159#394—732no—
160#394—732no—
161#392—732no—
162#392D7311yescharacteristic, complemented
163#379—731no—
164C25—731no—
165C22×D4—732no—
166C22×D4—732no—
167C22×D4C2×D7312yes—
168C22×D4C2×D7311yescharacteristic, complemented
169#120—1468no—
170C2×C4⋊C4—732no—
171C2×C4⋊C4—731no—
172C2×C22⋊C4—731no—
173C2×C22⋊C4—732no—
174C2×C22⋊C4—732no—
175C2×C22⋊C4—732no—
176C2×C22⋊C4—732no—
177C2×C22⋊C4—732no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4C2×D7311yescharacteristic
181C2×C22⋊C4C2×D7312yescomplemented
182#95—732no—
183#95—731no—
184#95—732no—
185#95C2×D7311yescharacteristic, complemented
186C24—2921no—
187C24—2922no—
188C24—2922no—
189C24—2921no—
190C24—734no—
191C24—732no—
192C24C22×D7312yes—
193C24C22×D7311yescharacteristic
194C2×D4—24no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—41no—
198C2×D4—42no—
199C2×D4—2922no—
200C2×D4—2922no—
201C2×D4—2922no—
202C2×D4—2922no—
203C2×D4—1464no—
204C2×D4—1464no—
205C22×C4—732no—
206C22×C4—732no—
207C22×C4—732no—
208C22×C4C22×D7311yescharacteristic
209C22×C4C22×D7312yes—
210C22×C4C22×D7311yescharacteristic
211C4⋊C4—2922no—
212C4⋊C4—2921no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—2922no—
216C22⋊C4—2922no—
217C22⋊C4—2922no—
218C22⋊C4—2921no—
219C22⋊C4—2922no—
220C22⋊C4—1464no—
221C22⋊C4—1464no—
222C22⋊C4—1464no—
223C23—21no—
224C23—22no—
225C23—22no—
226C23—21no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—2924no—
235C23—2928no—
236C23—2924no—
237C23—2928no—
238C23—2924no—
239C23—734no—
240C23—1462no—
241C23—1462no—
242C23—1462no—
243C23—1462no—
244C23—1462no—
245C23—1462no—
246C23D4×D7312yes—
247C23C23×D7311yescharacteristic
248D4—48no—
249D4—44no—
250D4—2928no—
251D4—2928no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—1462no—
260C2×C4—1462no—
261C2×C4—1462no—
262C2×C4—1462no—
263C2×C4—1462no—
264C2×C4—1462no—
265C2×C4—1462no—
266C2×C4—1462no—
267C2×C4—1462no—
268C22—22no—
269C22—24no—
270C22—41no—
271C22—42no—
272C22—41no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—29216no—
281C22—2922no—
282C22—2922no—
283C22—2922no—
284C22—2922no—
285C22—1464no—
286C22—1464no—
287C22—1464no—
288C22C2×D4×D7311yescharacteristic
289C22#1455663611yescharacteristic
290C22#1455663612yes—
291C22#1455663612yes—
292C22#1455663711yescharacteristic
293C4—42no—
294C4—41no—
295C4—41no—
296C4—2922no—
297C4—2922no—
298C4—2922no—
299C2—42no—
300C2—82no—
301C2—2924no—
302C2#1798914511yescharacteristic
303C2#1798914712yes—
304C2#1798932411yescharacteristic
305C2#1798932512yes—
306C2#1798933011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2812
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14556559C2semidirect
2. #17988516C2semidirect
3. #17988512C2semidirect
4. #17988503C2semidirect
5. #17988502C2semidirect
6. #17988501C2semidirect
7. #17988495C2semidirect
8. #17988442C2semidirect
9. #392×C73C2semidirect
14. C2×C4⋊Dic73C22semidirect
15. C2×#11924007C22semidirect
18. C2×C22⋊Dic73C22semidirect
19. C2×C22⋊Dic73C22semidirect
24. #14556498C22semidirect
25. #14556498C22semidirect
26. #14556498C22semidirect
28. C22×D4×C73C22semidirect
30. C2×C22⋊C4×C73C22semidirect
31. #95×C73C22semidirect
36. C23×D73D4semidirect
154. C73#2812semidirect
162. #392D73semidirect
168. C22×D4C2×D73semidirect
181. C2×C22⋊C4C2×D73semidirect
185. #95C2×D73semidirect