Finite Group Databasebeta

← #22614206

Subgroups — #22614206

Order 9344.

672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14556549C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D73C211yesmaximal, characteristic
3#17988522C211yesmaximal, characteristic, complemented
4#17988514C211yesmaximal, characteristic, complemented
5#17988512C211yesmaximal, characteristic, complemented
6#17988481C212yesmaximal, complemented
7#17988477C212yesmaximal, complemented
8#17988458C212yesmaximal, complemented
9#17988449C211yesmaximal, characteristic, complemented
10#17988442C212yesmaximal
11#399×C73C211yesmaximal, characteristic, complemented
12C24×D73C2211yescharacteristic
13C22×C4×D73C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15#14556549—24no—
16C2×C4⋊Dic73C2211yescharacteristic, complemented
17C2×#11924007C2212yescomplemented
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2211yescharacteristic
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C22⋊C4×D73—24no—
27C2×C4×Dic73C2212yescomplemented
28#14556498C2212yescomplemented
29#14556498C2211yescharacteristic, complemented
30#14556498C2212yescomplemented
31#14556498C2212yescomplemented
32C2×C4⋊C4×C73C2211yescharacteristic, complemented
33C2×C4⋊C4×C73C2212yescomplemented
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic, complemented
37C23×D73—22no—
38C23×D73—22no—
39C23×D73—22no—
40C23×D73—24no—
41C23×D73—42no—
42C23×D73C2311yescharacteristic
43C23×D73C2311yescharacteristic
44C22×Dic73C2312yes—
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C2×C4×D73—24no—
49C2×C4×D73—22no—
50C2×C4×D73—42no—
51C2×C4×D73D414yes—
52C4⋊Dic73—22no—
53#11924007—42no—
54C22⋊Dic73—24no—
55C22⋊Dic73—22no—
56#11924005—24no—
57#11924005—24no—
58#11924005—24no—
59#11924005—22no—
60#11924005—22no—
61#11924005—42no—
62C4×Dic73—24no—
63C24×C73C2311yescharacteristic
64C22×C4×C73C2312yes—
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2312yes—
67C22×C4×C73C2311yescharacteristic
68C4⋊C4×C73—22no—
69C4⋊C4×C73—42no—
70C22⋊C4×C73—22no—
71C22⋊C4×C73—42no—
72C23×C73—21no—
73C23×C73—21no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73#4112yes—
77C23×C73C2411yescharacteristic
78C22×D73—21no—
79C22×D73—21no—
80C22×D73—22no—
81C22×D73—28no—
82C22×D73—21no—
83C22×D73—22no—
84C22×D73—21no—
85C22×D73—22no—
86C22×D73—48no—
87C22×D73—48no—
88C22×D73—44no—
89C22×D73—44no—
90C22×D73C2×D412yes—
91C22×D73#4112yes—
92C22×D73#4114yes—
93C2×C4×C73—22no—
94C2×C4×C73—21no—
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×C73C2×D412yes—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—21no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73C2×D412yes—
113C4×D73—28no—
114C4×D73—44no—
115C22×C73—22no—
116C22×C73—24no—
117C22×C73—41no—
118C22×C73—41no—
119C22×C73—42no—
120C22×C73C22×D411yescharacteristic
121C22×C73C2×#4112yes—
122C22×C73C2×#4111yescharacteristic
123C22×C73C2×#4111yescharacteristic
124C22×C73H(5,𝔽2)12yes—
125C2×D73—22no—
126C2×D73—22no—
127C2×D73—24no—
128C2×D73—24no—
129C2×D73—22no—
130C2×D73—24no—
131C2×D73—416no—
132C2×D73—41no—
133C2×D73—41no—
134C2×D73—42no—
135C2×D73#12314yes—
136C4×C73—22no—
137C4×C73—41no—
138C4×C73—42no—
139C4×C73—42no—
140Dic73—22no—
141Dic73—42no—
142Dic73—41no—
143Dic73—42no—
144C2×C73—42no—
145C2×C73C2×#12311yescharacteristic
146C2×C73#52511yescharacteristic
147C2×C73#53511yescharacteristic
148C2×C73#55112yes—
149C2×C73#55112yes—
150D73—24no—
151D73—42no—
152#2482—731nomaximal, Sylow
153C73#248211yescharacteristic, complemented, Sylow
154C2×#117—731no—
155C22×C22⋊C4—731no—
156#399—731no—
157#399D7311yescharacteristic, complemented
158#397—731no—
159#397—731no—
160#388—732no—
161#388—732no—
162#385—732no—
163#381—731no—
164#379—732no—
165C25—731no—
166C23×C4—731no—
167C23×C4—731no—
168#117—1464no—
169C2×C4⋊C4—732no—
170C2×C4⋊C4—731no—
171C2×C4⋊C4C2×D7311yescharacteristic, complemented
172C2×C4⋊C4C2×D7312yescomplemented
173C2×C22⋊C4—732no—
174C2×C22⋊C4—731no—
175C2×C22⋊C4—732no—
176C2×C22⋊C4—731no—
177C2×C22⋊C4—731no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4—732no—
181C2×C22⋊C4—1464no—
182C2×C22⋊C4C2×D7311yescharacteristic
183C2×C22⋊C4C2×D7312yes—
184C2×C42—732no—
185#95—732no—
186#95—731no—
187#95—732no—
188#95—732no—
189#95C2×D7311yescharacteristic, complemented
190C24—2922no—
191C24—731no—
192C24—731no—
193C24—1464no—
194C24—1462no—
195C24—1462no—
196C24—1462no—
197C24C22×D7311yescharacteristic
198C22×C4—2922no—
199C22×C4—731no—
200C22×C4—734no—
201C22×C4—732no—
202C22×C4—732no—
203C22×C4—731no—
204C22×C4—1462no—
205C22×C4—1464no—
206C22×C4C22×D7312yes—
207C22×C4C22×D7311yescharacteristic
208C22×C4C22×D7312yes—
209C22×C4C22×D7311yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—42no—
212C4⋊C4—2922no—
213C4⋊C4—1462no—
214C22⋊C4—22no—
215C22⋊C4—42no—
216C22⋊C4—2922no—
217C22⋊C4—1462no—
218C22⋊C4—1464no—
219C22⋊C4—1464no—
220C22⋊C4—1464no—
221C22⋊C4—1462no—
222C22⋊C4—1464no—
223C22⋊C4—1462no—
224C42—1464no—
225C23—21no—
226C23—22no—
227C23—21no—
228C23—22no—
229C23—2928no—
230C23—2924no—
231C23—2924no—
232C23—2928no—
233C23—732no—
234C23—734no—
235C23—732no—
236C23—1468no—
237C23—1461no—
238C23—1462no—
239C23—1461no—
240C23—1462no—
241C23—1461no—
242C23—1461no—
243C23—1462no—
244C23#1192402912yes—
245C23C23×D7311yescharacteristic
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—2924no—
256C2×C4—732no—
257C2×C4—1468no—
258C2×C4—1462no—
259C2×C4—1461no—
260C2×C4—1462no—
261C2×C4—1462no—
262C2×C4—1462no—
263C2×C4—1462no—
264C2×C4—1462no—
265C2×C4—1462no—
266C2×C4—1462no—
267C2×C4D4×D7312yes—
268C22—24no—
269C22—22no—
270C22—41no—
271C22—42no—
272C22—41no—
273C22—29216no—
274C22—2921no—
275C22—2922no—
276C22—2921no—
277C22—734no—
278C22—1464no—
279C22—1462no—
280C22—1462no—
281C22—1464no—
282C22—1464no—
283C22—1462no—
284C22C2×D4×D7311yescharacteristic
285C22#41×D7312yes—
286C22#41×D7311yescharacteristic
287C22C2×#1192402911yescharacteristic
288C22#1455663612yes—
289C4—22no—
290C4—41no—
291C4—42no—
292C4—42no—
293C4—2921no—
294C4—2922no—
295C4—2922no—
296C4—1462no—
297C2—42no—
298C2—2922no—
299C2—1464no—
300C2#123×D7311yescharacteristic
301C2#1798910011yescharacteristic
302C2#1798915011yescharacteristic
303C2#1798926412yes—
304C2#1798926512yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2482
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14556549C2semidirect
3. #17988522C2semidirect
4. #17988514C2semidirect
5. #17988512C2semidirect
6. #17988481C2semidirect
7. #17988477C2semidirect
8. #17988458C2semidirect
9. #17988449C2semidirect
11. #399×C73C2semidirect
16. C2×C4⋊Dic73C22semidirect
17. C2×#11924007C22semidirect
27. C2×C4×Dic73C22semidirect
28. #14556498C22semidirect
29. #14556498C22semidirect
30. #14556498C22semidirect
31. #14556498C22semidirect
32. C2×C4⋊C4×C73C22semidirect
33. C2×C4⋊C4×C73C22semidirect
36. #95×C73C22semidirect
153. C73#2482semidirect
157. #399D73semidirect
171. C2×C4⋊C4C2×D73semidirect
172. C2×C4⋊C4C2×D73semidirect
189. #95C2×D73semidirect