Finite Group Databasebeta

← #22621533

Subgroups — #22621533

Order 9344.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556619C212yesmaximal, complemented
2#17989242C211yesmaximal, characteristic, complemented
3D4×D292C211yesmaximal, characteristic, complemented
4#17988960C211yesmaximal, characteristic, complemented
5#17988833C212yesmaximal, complemented
6#17988793C211yesmaximal, characteristic, complemented
7#17988783C211yesmaximal, characteristic, complemented
8#17988740C212yesmaximal, complemented
9#17988734C212yesmaximal, complemented
10C4×D584C211yesmaximal, characteristic, complemented
11#436×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2212yescomplemented
13C22×D292C2212yes—
14C2×D4×D73—21no—
15#14556619—28no—
16C2×#11924017C2212yes—
17C2×#11924017C2212yescomplemented
18C2×#11924017C2212yescomplemented
19C2×D584C2211yescharacteristic
20C2×D584C2212yescomplemented
21#14556591C2211yescharacteristic, complemented
22#14556588C2211yescharacteristic
23#14556573—22no—
24#14556570C2212yescomplemented
25#14556566—21no—
26#14556565C2212yes—
27#14556562—21no—
28#14556561—22no—
29C4×D292C2211yescharacteristic
30C4×D292C2211yescharacteristic, complemented
31C4⋊C4×D73—21no—
32#14556525C2211yescharacteristic, complemented
33#14556516C2212yescomplemented
34#14556513C2211yescharacteristic
35#14556513C2211yescharacteristic, complemented
36#14556513C2212yescomplemented
37C2×M16×C73C2212yescomplemented
38C4×D4×C73C2211yescharacteristic
39C4⋊C8×C73C2211yescharacteristic, complemented
40C22⋊C8×C73C2212yescomplemented
41C4×C8×C73C2211yescharacteristic, complemented
42C23×D73—22no—
43#11924028—24no—
44#11924028—42no—
45C2×Dic146C2312yes—
46C2×D292—24no—
47C2×D292—22no—
48C2×D292—21no—
49C2×D292—21no—
50C2×D292—42no—
51C2×D292C2312yes—
52C2×D292C2311yescharacteristic
53C2×D292C2311yescharacteristic
54C2×C22⋊D73—22no—
55C2×C22⋊D73—22no—
56D4×D73—44no—
57C2×C4×D73—21no—
58C2×C4×D73—22no—
59C2×C4×D73—21no—
60#11924017—24no—
61#11924017—24no—
62#11924017—42no—
63D584—24no—
64D584D414yescomplemented
65C4⋊Dic73—21no—
66C4⋊Dic73—21no—
67C4⋊Dic73C2311yescharacteristic
68C4⋊Dic73C2311yescharacteristic
69#11924007—22no—
70C22⋊Dic73—22no—
71#11924005—21no—
72#11924005—21no—
73#11924005—22no—
74C2×D4×C73D411yescharacteristic
75C22×C4×C73C2312yes—
76M16×C73—24no—
77C2×C8×C73C2311yescharacteristic
78C2×C8×C73C2312yes—
79C2×C8×C73C2311yescharacteristic
80C4⋊C4×C73D411yescharacteristic
81C22⋊C4×C73D412yes—
82C42×C73C2311yescharacteristic
83C23×C73C2×D412yes—
84C22×D73—21no—
85C22×D73—21no—
86C22×D73—22no—
87C22×D73—44no—
88C22×D73—44no—
89C22×D73—82no—
90D4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73C2×D411yescharacteristic
94C2×C4×C73C2×D412yes—
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2411yescharacteristic
97C22⋊D73—44no—
98C22⋊D73—44no—
99C2×Dic73—21no—
100C2×Dic73—21no—
101C2×Dic73—22no—
102D292—22no—
103D292—21no—
104D292—21no—
105D292—22no—
106D292—44no—
107D292—42no—
108D292—81no—
109D292C2×D412yes—
110D292C2×D412yescomplemented
111C4×D73—44no—
112C4×D73—42no—
113C4×D73—42no—
114Dic146—22no—
115Dic146—22no—
116C8×C73—22no—
117C8×C73—21no—
118C8×C73C2×D412yescomplemented
119C22×C73—22no—
120C22×C73—22no—
121C22×C73—22no—
122C22×C73C22×D411yescharacteristic
123C2×D73—22no—
124C2×D73—22no—
125C2×D73—41no—
126C2×D73—41no—
127C2×D73—41no—
128C2×D73—41no—
129C2×D73—42no—
130C2×D73—42no—
131C2×D73—42no—
132C2×D73—88no—
133C4×C73—22no—
134C4×C73—21no—
135C4×C73AGL(1,ℤ/8)12yescomplemented
136C4×C73C22×D411yescharacteristic
137C4×C73H(5,𝔽2)11yescharacteristic
138Dic73—42no—
139Dic73—41no—
140Dic73—41no—
141C2×C73—42no—
142C2×C73D4211yescharacteristic
143C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C73#57711yescharacteristic
145D73—42no—
146D73—42no—
147D73—82no—
148#3272—731nomaximal, Sylow
149C73#327211yescharacteristic, complemented, Sylow
150C2×AGL(1,ℤ/8)—732no—
151#547—731no—
152D42—731no—
153#492—731no—
154#468—732no—
155#461—731no—
156#459—731no—
157#450—732no—
158#449—732no—
159C4×D8—731no—
160#436D7311yescharacteristic, complemented
161C2×#41—732no—
162C22×D4—732no—
163C22×D4—1461no—
164AGL(1,ℤ/8)—1468no—
165C2×SD16—732no—
166C2×SD16—732no—
167C2×SD16—732no—
168C2×D8—731no—
169C2×D8—732no—
170C2×M16C2×D7312yescomplemented
171C4⋊Q8—731no—
172#127—731no—
173#123—1462no—
174C22⋊Q8—732no—
175#121—732no—
176#121—1461no—
177#121—1461no—
178#120—1462no—
179C4×D4—731no—
180C4×D4—731no—
181C4×D4C2×D7311yescharacteristic
182C2×C4⋊C4—1461no—
183#107—731no—
184C4⋊C8C2×D7311yescharacteristic, complemented
185#103—732no—
186#102—731no—
187#102—731no—
188#102—732no—
189C22⋊C8C2×D7312yescomplemented
190C4×C8C2×D7311yescharacteristic, complemented
191C24—1462no—
192#41—2922no—
193#41—1464no—
194C2×Q8—732no—
195C2×D4—2922no—
196C2×D4—2924no—
197C2×D4—731no—
198C2×D4—731no—
199C2×D4—732no—
200C2×D4—1464no—
201C2×D4—1462no—
202C2×D4—1462no—
203C2×D4—1462no—
204C2×D4—1461no—
205C2×D4—1461no—
206C2×D4D29211yescharacteristic
207C22×C4—1461no—
208C22×C4—1462no—
209C22×C4—1461no—
210C22×C4C22×D7312yes—
211SD16—2922no—
212SD16—1464no—
213SD16—1464no—
214D8—734no—
215D8—1464no—
216M16—24no—
217C2×C8C22×D7311yescharacteristic
218C2×C8C22×D7312yes—
219C2×C8C22×D7311yescharacteristic
220C4⋊C4—731no—
221C4⋊C4—731no—
222C4⋊C4—1462no—
223C4⋊C4—1461no—
224C4⋊C4—1461no—
225C4⋊C4D29211yescharacteristic
226C22⋊C4—1462no—
227C22⋊C4—1461no—
228C22⋊C4—1461no—
229C22⋊C4—1462no—
230C22⋊C4D29212yes—
231C42C22×D7311yescharacteristic
232C23—2924no—
233C23—2924no—
234C23—5842no—
235C23—1462no—
236C23—1461no—
237C23—1461no—
238C23C2×D29212yes—
239Q8—1462no—
240Q8—1462no—
241D4—22no—
242D4—2924no—
243D4—2924no—
244D4—2924no—
245D4—2922no—
246D4—5841no—
247D4—732no—
248D4—732no—
249D4—1462no—
250D4—1462no—
251D4—1461no—
252D4—1461no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—2924no—
256C2×C4—2922no—
257C2×C4—2922no—
258C2×C4—1461no—
259C2×C4—1461no—
260C2×C4—1462no—
261C2×C4C2×D29211yescharacteristic
262C2×C4C2×D29212yes—
263C2×C4C2×D29211yescharacteristic
264C2×C4C23×D7311yescharacteristic
265C8—22no—
266C8—21no—
267C8D4×D7312yescomplemented
268C22—22no—
269C22—22no—
270C22—22no—
271C22—2921no—
272C22—2921no—
273C22—2921no—
274C22—2921no—
275C22—2922no—
276C22—2922no—
277C22—2922no—
278C22—5848no—
279C22—1462no—
280C22—1462no—
281C22C22×D29211yescharacteristic
282C4—21no—
283C4—22no—
284C4—2921no—
285C4—2921no—
286C4—2922no—
287C4#1455661912yescomplemented
288C4C2×D4×D7311yescharacteristic
289C4#1455663711yescharacteristic
290C2—42no—
291C2—2922no—
292C2—2922no—
293C2—5842no—
294C2D4×D29211yescharacteristic
295C2C2×#1455661911yescharacteristic
296C2#1798939911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#436×C73C2
socleC22×C73C22×D4
hypercenter#436D73
hypocenterC73#3272
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#14556619C2semidirect
2. #17989242C2semidirect
3. D4×D292C2semidirect
4. #17988960C2semidirect
5. #17988833C2semidirect
6. #17988793C2semidirect
7. #17988783C2semidirect
8. #17988740C2semidirect
9. #17988734C2semidirect
10. C4×D584C2semidirect
11. #436×C73C2semidirect
12. C2×#11924028C22semidirect
17. C2×#11924017C22semidirect
18. C2×#11924017C22semidirect
20. C2×D584C22semidirect
21. #14556591C22semidirect
24. #14556570C22semidirect
30. C4×D292C22semidirect
32. #14556525C22semidirect
33. #14556516C22semidirect
35. #14556513C22semidirect
36. #14556513C22semidirect
37. C2×M16×C73C22semidirect
39. C4⋊C8×C73C22semidirect
40. C22⋊C8×C73C22semidirect
41. C4×C8×C73C22semidirect
64. D584D4semidirect
110. D292C2×D4semidirect
118. C8×C73C2×D4semidirect
135. C4×C73AGL(1,ℤ/8)semidirect
149. C73#3272semidirect
160. #436D73semidirect
170. C2×M16C2×D73semidirect
184. C4⋊C8C2×D73semidirect
189. C22⋊C8C2×D73semidirect
190. C4×C8C2×D73semidirect
267. C8D4×D73semidirect
287. C4#14556619semidirect