Finite Group Databasebeta

← #22614204

Subgroups — #22614204

Order 9344.

672 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14556547C211yesmaximal, characteristic, complemented
2C22×#11924005C211yesmaximal, characteristic
3#17988522C212yesmaximal, complemented
4#17988516C212yesmaximal, complemented
5#17988477C212yesmaximal, complemented
6#17988476C212yesmaximal, complemented
7#17988460C211yesmaximal, characteristic, complemented
8#17988448C211yesmaximal, characteristic, complemented
9#17988442C211yesmaximal, characteristic
10#17988442C211yesmaximal, characteristic
11#385×C73C211yesmaximal, characteristic, complemented
12C24×D73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14#14556547—24no—
15C2×#11924007C2211yescharacteristic, complemented
16C2×#11924007C2211yescharacteristic, complemented
17C2×#11924007C2212yescomplemented
18C2×C22⋊Dic73C2211yescharacteristic
19C2×C22⋊Dic73C2211yescharacteristic
20C2×#11924005—24no—
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23C2×#11924005C2212yes—
24C2×#11924005C2212yes—
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27C2×C4×Dic73C2211yescharacteristic, complemented
28C2×C4×Dic73C2211yescharacteristic, complemented
29#14556498C2212yescomplemented
30#14556498C2212yescomplemented
31#14556498C2212yescomplemented
32C23×C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yescomplemented
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2211yescharacteristic
36#95×C73C2212yescomplemented
37C23×D73—22no—
38C23×D73—24no—
39C23×D73—22no—
40C23×D73—22no—
41C23×D73—42no—
42C23×D73C2312yes—
43C22×Dic73—22no—
44C22×Dic73—22no—
45C22×Dic73D414yes—
46C22×Dic73C2312yes—
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C22×Dic73C2311yescharacteristic
50C22×Dic73C2311yescharacteristic
51#11924007—22no—
52#11924007—22no—
53#11924007—42no—
54C22⋊Dic73—22no—
55C22⋊Dic73—22no—
56#11924005—24no—
57#11924005—24no—
58#11924005—24no—
59#11924005—24no—
60#11924005—42no—
61#11924005—42no—
62C4×Dic73—22no—
63C4×Dic73—22no—
64C24×C73C2311yescharacteristic
65C22×C4×C73—22no—
66C22×C4×C73—42no—
67C22×C4×C73C2311yescharacteristic
68C22×C4×C73C2312yes—
69C22×C4×C73C2312yes—
70C22×C4×C73C2311yescharacteristic
71C4⋊C4×C73—42no—
72C22⋊C4×C73—22no—
73C22⋊C4×C73—22no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73C2×D412yes—
77C23×C73#4112yes—
78C23×C73#4112yes—
79C23×C73C2411yescharacteristic
80C22×D73—28no—
81C22×D73—22no—
82C22×D73—22no—
83C22×D73—22no—
84C22×D73—22no—
85C22×D73—22no—
86C22×D73—22no—
87C22×D73—48no—
88C22×D73—48no—
89C22×D73—44no—
90C22×D73—44no—
91C22×D73#4114yes—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73—44no—
103C2×Dic73—28no—
104C2×Dic73—21no—
105C2×Dic73—21no—
106C2×Dic73—21no—
107C2×Dic73—21no—
108C2×Dic73—21no—
109C2×Dic73—21no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—22no—
115C2×Dic73C2×D412yes—
116C2×Dic73C2×D412yes—
117C22×C73—22no—
118C22×C73—22no—
119C22×C73—24no—
120C22×C73—24no—
121C22×C73#12314yes—
122C22×C73C22×D411yescharacteristic
123C22×C73C2×#4112yes—
124C22×C73C2×#4111yescharacteristic
125C22×C73C2×#4111yescharacteristic
126C22×C73H(5,𝔽2)12yes—
127C2×D73—24no—
128C2×D73—24no—
129C2×D73—24no—
130C2×D73—416no—
131C2×D73—42no—
132C2×D73—42no—
133C2×D73—42no—
134C2×D73—42no—
135C4×C73—41no—
136C4×C73—41no—
137C4×C73—42no—
138C4×C73—42no—
139Dic73—22no—
140Dic73—22no—
141Dic73—41no—
142Dic73—41no—
143Dic73—42no—
144C2×C73—24no—
145C2×C73C2×#12311yescharacteristic
146C2×C73#52511yescharacteristic
147C2×C73#53511yescharacteristic
148C2×C73#55112yes—
149C2×C73#55112yes—
150D73—44no—
151#2482—731nomaximal, Sylow
152C73#248211yescharacteristic, complemented, Sylow
153C2×#117—731no—
154C22×C22⋊C4—731no—
155#399—732no—
156#397—732no—
157#388—732no—
158#388—732no—
159#385—731no—
160#385D7311yescharacteristic, complemented
161#381—731no—
162#379—731no—
163#379—731no—
164C25—731no—
165C23×C4—731no—
166C23×C4C2×D7311yescharacteristic
167#117—1464no—
168C2×C4⋊C4—732no—
169C2×C4⋊C4—731no—
170C2×C4⋊C4—731no—
171C2×C4⋊C4C2×D7312yescomplemented
172C2×C22⋊C4—732no—
173C2×C22⋊C4—732no—
174C2×C22⋊C4—731no—
175C2×C22⋊C4—731no—
176C2×C22⋊C4—732no—
177C2×C22⋊C4—732no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4—1464no—
181C2×C22⋊C4C2×D7311yescharacteristic
182C2×C22⋊C4C2×D7311yescharacteristic
183C2×C42—731no—
184C2×C42—731no—
185#95—732no—
186#95—732no—
187#95—732no—
188#95C2×D7312yescomplemented
189C24—2922no—
190C24—732no—
191C24—1464no—
192C24—1462no—
193C24—1462no—
194C24—1462no—
195C24C22×D7311yescharacteristic
196C22×C4—22no—
197C22×C4—42no—
198C22×C4—734no—
199C22×C4—731no—
200C22×C4—731no—
201C22×C4—732no—
202C22×C4—731no—
203C22×C4—731no—
204C22×C4—1462no—
205C22×C4—1462no—
206C22×C4C22×D7312yes—
207C22×C4C22×D7312yes—
208C22×C4C22×D7311yescharacteristic
209C22×C4C22×D7311yescharacteristic
210C4⋊C4—42no—
211C4⋊C4—2922no—
212C4⋊C4—1462no—
213C4⋊C4—1462no—
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—2922no—
217C22⋊C4—2922no—
218C22⋊C4—1464no—
219C22⋊C4—1464no—
220C22⋊C4—1464no—
221C22⋊C4—1464no—
222C22⋊C4—1462no—
223C22⋊C4—1462no—
224C42—1462no—
225C42—1462no—
226C23—22no—
227C23—22no—
228C23—2924no—
229C23—2928no—
230C23—2928no—
231C23—2924no—
232C23—734no—
233C23—1468no—
234C23—1462no—
235C23—1462no—
236C23—1462no—
237C23—1462no—
238C23—1462no—
239C23—1462no—
240C23D4×D7312yes—
241C23#1192402812yes—
242C23#1192402912yes—
243C23C23×D7311yescharacteristic
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—44no—
255C2×C4—732no—
256C2×C4—732no—
257C2×C4—1461no—
258C2×C4—1461no—
259C2×C4—1462no—
260C2×C4—1462no—
261C2×C4—1462no—
262C2×C4—1462no—
263C2×C4—1462no—
264C2×C4—1468no—
265C2×C4—1461no—
266C2×C4—1461no—
267C2×C4—1461no—
268C2×C4—1461no—
269C22—22no—
270C22—24no—
271C22—24no—
272C22—22no—
273C22—29216no—
274C22—2922no—
275C22—2922no—
276C22—2922no—
277C22—2922no—
278C22—1464no—
279C22—1464no—
280C22—1464no—
281C22#1455657614yes—
282C22C2×D4×D7311yescharacteristic
283C22#41×D7312yes—
284C22C2×#1192402811yescharacteristic
285C22C2×#1192402911yescharacteristic
286C22#1455663612yes—
287C4—42no—
288C4—41no—
289C4—42no—
290C4—41no—
291C4—2921no—
292C4—2922no—
293C4—2921no—
294C4—1462no—
295C4—1462no—
296C2—24no—
297C2—2924no—
298C2C2×#1455657611yescharacteristic
299C2#1798909511yescharacteristic
300C2#1798915211yescharacteristic
301C2#1798926412yes—
302C2#1798926612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2482
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14556547C2semidirect
3. #17988522C2semidirect
4. #17988516C2semidirect
5. #17988477C2semidirect
6. #17988476C2semidirect
7. #17988460C2semidirect
8. #17988448C2semidirect
11. #385×C73C2semidirect
15. C2×#11924007C22semidirect
16. C2×#11924007C22semidirect
17. C2×#11924007C22semidirect
27. C2×C4×Dic73C22semidirect
28. C2×C4×Dic73C22semidirect
29. #14556498C22semidirect
30. #14556498C22semidirect
31. #14556498C22semidirect
33. C2×C4⋊C4×C73C22semidirect
36. #95×C73C22semidirect
152. C73#2482semidirect
160. #385D73semidirect
171. C2×C4⋊C4C2×D73semidirect
188. #95C2×D73semidirect