Finite Group Databasebeta

← #22616133

Subgroups — #22616133

Order 9344.

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

normal subgroups only

This group has 816 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×#14556563C212yesmaximal, complemented
2C2×#14556559C212yesmaximal, complemented
3#17988523C211yesmaximal, characteristic, complemented
4#17988516C212yesmaximal, complemented
5#17988503C212yesmaximal, complemented
6#17988467C212yesmaximal, complemented
7#17988464C212yesmaximal, complemented
8#17988442C211yesmaximal, characteristic, complemented
9#392×C73C211yesmaximal, characteristic, complemented
10C24×D73C2211yescharacteristic
11C22×C22⋊D73C2212yes—
12C22×C22⋊D73C2212yes—
13C23×Dic73C2212yescomplemented
14#14556563—28no—
15#14556559—28no—
16C2×C4⋊Dic73C2211yescharacteristic, complemented
17C2×#11924007C2212yescomplemented
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2211yescharacteristic
20C2×C22⋊Dic73C2212yescomplemented
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23C2×#11924005C2212yes—
24C2×#11924005C2212yes—
25#14556498C2211yescharacteristic, complemented
26#14556498C2212yescomplemented
27#14556498C2212yescomplemented
28C22×D4×C73C2212yes—
29C22×D4×C73C2211yescharacteristic, complemented
30C2×C22⋊C4×C73C2211yescharacteristic
31C2×C22⋊C4×C73C2212yescomplemented
32#95×C73C2211yescharacteristic, complemented
33C23×D73—22no—
34C23×D73—24no—
35C23×D73—42no—
36C23×D73—41no—
37C23×D73—41no—
38C23×D73C2312yes—
39C2×C22⋊D73—24no—
40C2×C22⋊D73—24no—
41C2×C22⋊D73—42no—
42C2×C22⋊D73—42no—
43C2×C22⋊D73—42no—
44C2×C22⋊D73D418yescomplemented
45C22×Dic73—24no—
46C22×Dic73—42no—
47C22×Dic73—42no—
48C22×Dic73C2312yes—
49C22×Dic73C2312yes—
50C22×Dic73C2312yes—
51C4⋊Dic73—41no—
52#11924007—24no—
53C22⋊Dic73—24no—
54C22⋊Dic73—24no—
55C22⋊Dic73—41no—
56#11924005—24no—
57#11924005—24no—
58#11924005—24no—
59#11924005—42no—
60C24×C73C2312yes—
61C24×C73C2311yescharacteristic
62C2×D4×C73—24no—
63C2×D4×C73—24no—
64C2×D4×C73—24no—
65C2×D4×C73—42no—
66C2×D4×C73—41no—
67C22×C4×C73C2311yescharacteristic
68C22×C4×C73C2312yes—
69C22×C4×C73C2311yescharacteristic
70C22⋊C4×C73—41no—
71C22⋊C4×C73—42no—
72C23×C73—22no—
73C23×C73—22no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73—21no—
77C23×C73—22no—
78C23×C73—22no—
79C23×C73—22no—
80C23×C73—21no—
81C23×C73—22no—
82C23×C73C2×D414yes—
83C23×C73#4112yes—
84C23×C73C2411yescharacteristic
85C22×D73—22no—
86C22×D73—22no—
87C22×D73—22no—
88C22×D73—22no—
89C22×D73—22no—
90C22×D73—22no—
91C22×D73—44no—
92C22×D73—48no—
93C22×D73—48no—
94C22×D73—44no—
95C22×D73—44no—
96C22×D73C2×D414yes—
97D4×C73—44no—
98D4×C73—48no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73—22no—
104C2×C4×C73—22no—
105C2×C4×C73—21no—
106C22⋊D73—48no—
107C22⋊D73—48no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—22no—
115C2×Dic73—22no—
116C2×Dic73—48no—
117C2×Dic73C2×D414yes—
118C22×C73—24no—
119C22×C73—22no—
120C22×C73—24no—
121C22×C73—24no—
122C22×C73—24no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73—42no—
126C22×C73—41no—
127C22×C73—42no—
128C22×C73—41no—
129C22×C73—42no—
130C22×C73C22×D412yes—
131C22×C73C2×#4111yescharacteristic
132C22×C73H(5,𝔽2)12yes—
133C22×C73H(5,𝔽2)11yescharacteristic
134C22×C73H(5,𝔽2)11yescharacteristic
135C2×D73—24no—
136C2×D73—24no—
137C2×D73—24no—
138C2×D73—416no—
139C2×D73—42no—
140C2×D73—42no—
141C2×D73—42no—
142C2×D73—42no—
143C4×C73—41no—
144C4×C73—42no—
145C4×C73—41no—
146Dic73—24no—
147Dic73—42no—
148Dic73—42no—
149C2×C73—42no—
150C2×C73—44no—
151C2×C73#53412yes—
152C2×C73#53811yescharacteristic
153C2×C73D4211yescharacteristic
154C2×C73#54612yes—
155C2×C73#56011yescharacteristic
156D73—44no—
157#2668—731nomaximal, Sylow
158C73#266811yescharacteristic, complemented, Sylow
159C2×#121—732no—
160C2×#120—732no—
161#399—731no—
162#397—732no—
163#394—732no—
164#392D7311yescharacteristic, complemented
165#386—732no—
166#386—732no—
167#379—731no—
168C25—731no—
169C22×D4—732no—
170C22×D4—732no—
171C22×D4C2×D7312yes—
172C22×D4C2×D7311yescharacteristic, complemented
173C23×C4—732no—
174#121—1468no—
175#120—1468no—
176C2×C4⋊C4—731no—
177C2×C4⋊C4—732no—
178C2×C22⋊C4—731no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4—732no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—732no—
183C2×C22⋊C4—732no—
184C2×C22⋊C4—732no—
185C2×C22⋊C4C2×D7311yescharacteristic
186C2×C22⋊C4C2×D7312yescomplemented
187#95—732no—
188#95—731no—
189#95—732no—
190#95C2×D7311yescharacteristic, complemented
191C24—2921no—
192C24—2922no—
193C24—2921no—
194C24—732no—
195C24—1464no—
196C24—1462no—
197C24C22×D7312yes—
198C24C22×D7311yescharacteristic
199C2×D4—24no—
200C2×D4—24no—
201C2×D4—24no—
202C2×D4—42no—
203C2×D4—41no—
204C2×D4—2922no—
205C2×D4—2922no—
206C2×D4—2922no—
207C2×D4—738no—
208C2×D4—1464no—
209C2×D4—1464no—
210C22×C4—2922no—
211C22×C4—2922no—
212C22×C4—732no—
213C22×C4—732no—
214C22×C4—732no—
215C22×C4—1464no—
216C22×C4C22×D7312yes—
217C22×C4C22×D7311yescharacteristic
218C22×C4C22×D7311yescharacteristic
219C4⋊C4—2921no—
220C4⋊C4—1464no—
221C22⋊C4—41no—
222C22⋊C4—42no—
223C22⋊C4—2922no—
224C22⋊C4—2921no—
225C22⋊C4—1464no—
226C22⋊C4—1464no—
227C22⋊C4—1464no—
228C22⋊C4—1464no—
229C22⋊C4—1464no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—21no—
239C23—22no—
240C23—2924no—
241C23—2928no—
242C23—2924no—
243C23—2928no—
244C23—2924no—
245C23—734no—
246C23—1462no—
247C23—1462no—
248C23—1462no—
249C23—1462no—
250C23—1462no—
251C23—1462no—
252C23D4×D7314yes—
253C23#1192402712yes—
254C23C23×D7311yescharacteristic
255D4—44no—
256D4—48no—
257D4—2928no—
258D4—2928no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—2928no—
267C2×C4—734no—
268C2×C4—1462no—
269C2×C4—1462no—
270C2×C4—1462no—
271C2×C4—1462no—
272C2×C4—1462no—
273C2×C4—1462no—
274C2×C4—1462no—
275C2×C4—1462no—
276C22—24no—
277C22—22no—
278C22—24no—
279C22—24no—
280C22—24no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—42no—
288C22—29216no—
289C22—2922no—
290C22—2922no—
291C22—2922no—
292C22—2922no—
293C22—1464no—
294C22—1464no—
295C22—1464no—
296C22C2×D4×D7312yes—
297C22C2×#1192402711yescharacteristic
298C22#1455663612yes—
299C22#1455663611yescharacteristic
300C22#1455663711yescharacteristic
301C4—41no—
302C4—42no—
303C4—41no—
304C4—2922no—
305C4—2922no—
306C4—1464no—
307C2—42no—
308C2—44no—
309C2—2924no—
310C2#1798914512yes—
311C2#1798917411yescharacteristic
312C2#1798921911yescharacteristic
313C2#1798922412yes—
314C2#1798932411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2668
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14556563C2semidirect
2. C2×#14556559C2semidirect
3. #17988523C2semidirect
4. #17988516C2semidirect
5. #17988503C2semidirect
6. #17988467C2semidirect
7. #17988464C2semidirect
8. #17988442C2semidirect
9. #392×C73C2semidirect
13. C23×Dic73C22semidirect
16. C2×C4⋊Dic73C22semidirect
17. C2×#11924007C22semidirect
20. C2×C22⋊Dic73C22semidirect
25. #14556498C22semidirect
26. #14556498C22semidirect
27. #14556498C22semidirect
29. C22×D4×C73C22semidirect
31. C2×C22⋊C4×C73C22semidirect
32. #95×C73C22semidirect
44. C2×C22⋊D73D4semidirect
158. C73#2668semidirect
164. #392D73semidirect
172. C22×D4C2×D73semidirect
186. C2×C22⋊C4C2×D73semidirect
190. #95C2×D73semidirect