Finite Group Databasebeta

← #22621553

Subgroups — #22621553

Order 9344.

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

normal subgroups only

This group has 556 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#17989258C211yesmaximal, characteristic, complemented
3D4×D292C211yesmaximal, characteristic, complemented
4#17988964C211yesmaximal, characteristic, complemented
5#17988840C212yesmaximal, complemented
6#17988788C211yesmaximal, characteristic, complemented
7#17988783C211yesmaximal, characteristic, complemented
8#17988734C212yesmaximal, complemented
9#17988723C212yesmaximal, complemented
10C4×#11924017C211yesmaximal, characteristic, complemented
11#436×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2212yescomplemented
13C22×D292C2212yes—
14C2×D4×D73—21no—
15#14556619—28no—
16C2×#11924017C2211yescharacteristic
17C2×#11924017C2212yescomplemented
18C2×D584C2212yes—
19C2×D584C2212yescomplemented
20C2×D584C2212yescomplemented
21#14556588C2211yescharacteristic
22#14556588C2211yescharacteristic, complemented
23#14556587—21no—
24#14556566—21no—
25#14556565C2212yes—
26#14556565C2212yescomplemented
27#14556564—22no—
28#14556561—22no—
29C4×Dic146C2211yescharacteristic, complemented
30C4×D292C2211yescharacteristic
31#14556553—21no—
32#14556523C2211yescharacteristic, complemented
33#14556516C2211yescharacteristic, complemented
34#14556513C2211yescharacteristic
35#14556513C2212yescomplemented
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×Dic146C2311yescharacteristic
46C2×D292—24no—
47C2×D292—21no—
48C2×D292—22no—
49C2×D292—21no—
50C2×D292—21no—
51C2×D292—21no—
52C2×D292—42no—
53C2×D292C2312yes—
54C2×D292C2312yes—
55C2×D292C2311yescharacteristic
56C2×C22⋊D73—22no—
57C2×C22⋊D73—22no—
58C2×C22⋊D73—22no—
59D4×D73—44no—
60C2×C4×D73—22no—
61C2×C4×D73—21no—
62#11924017—24no—
63#11924017D414yescomplemented
64D584—24no—
65D584—24no—
66D584—42no—
67C4⋊Dic73C2311yescharacteristic
68C4⋊Dic73C2311yescharacteristic
69#11924007—21no—
70#11924005—22no—
71#11924005—21no—
72#11924005—22no—
73C4×Dic73—21no—
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—22no—
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—
99C22⋊D73—82no—
100C2×Dic73—21no—
101C2×Dic73—21no—
102C2×Dic73—21no—
103D292—22no—
104D292—22no—
105D292—21no—
106D292—22no—
107D292—22no—
108D292—44no—
109D292—42no—
110D292—42no—
111D292—81no—
112D292—81no—
113D292C2×D412yes—
114C4×D73—44no—
115C4×D73—42no—
116Dic146—21no—
117Dic146C2×D412yescomplemented
118C8×C73—22no—
119C8×C73—21no—
120C8×C73C2×D412yescomplemented
121C22×C73—22no—
122C22×C73—22no—
123C22×C73—22no—
124C22×C73C22×D411yescharacteristic
125C2×D73—22no—
126C2×D73—41no—
127C2×D73—41no—
128C2×D73—42no—
129C2×D73—42no—
130C2×D73—42no—
131C2×D73—42no—
132C2×D73—42no—
133C2×D73—42no—
134C2×D73—88no—
135C4×C73—22no—
136C4×C73—21no—
137C4×C73AGL(1,ℤ/8)12yescomplemented
138C4×C73C22×D411yescharacteristic
139C4×C73H(5,𝔽2)11yescharacteristic
140Dic73—22no—
141Dic73—41no—
142Dic73—41no—
143C2×C73—42no—
144C2×C73D4211yescharacteristic
145C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C73#57611yescharacteristic
147D73—42no—
148D73—82no—
149D73—82no—
150#3274—731nomaximal, Sylow
151C73#327411yescharacteristic, complemented, Sylow
152C2×AGL(1,ℤ/8)—732no—
153#550—731no—
154D42—731no—
155#493—731no—
156#469—732no—
157#460—731no—
158#459—731no—
159#449—732no—
160#447—732no—
161C4×SD16—731no—
162#436D7311yescharacteristic, complemented
163C2×#41—732no—
164C22×D4—732no—
165C22×D4—1461no—
166AGL(1,ℤ/8)—1468no—
167C2×SD16—731no—
168C2×SD16—732no—
169C2×D8—732no—
170C2×D8—732no—
171C2×D8—732no—
172C2×M16C2×D7312yescomplemented
173#127—731no—
174#127—731no—
175#127—1461no—
176#121—732no—
177#121—732no—
178#121—1461no—
179#121—1462no—
180#120—1462no—
181C4×Q8—731no—
182C4×D4—731no—
183C4×D4—1461no—
184C4×D4C2×D7311yescharacteristic
185#106—731no—
186C4⋊C8C2×D7311yescharacteristic, complemented
187#103—731no—
188#102—731no—
189#102—732no—
190#102—732no—
191C22⋊C8C2×D7312yescomplemented
192C4×C8C2×D7311yescharacteristic, complemented
193C24—1462no—
194#41—2922no—
195#41—1464no—
196C2×Q8—731no—
197C2×D4—2922no—
198C2×D4—2924no—
199C2×D4—731no—
200C2×D4—732no—
201C2×D4—732no—
202C2×D4—1464no—
203C2×D4—1462no—
204C2×D4—1462no—
205C2×D4—1462no—
206C2×D4—1461no—
207C2×D4—1462no—
208C2×D4—1461no—
209C2×D4—1461no—
210C2×D4—1461no—
211C2×D4D29211yescharacteristic
212C22×C4—1461no—
213C22×C4—1462no—
214C22×C4C22×D7312yes—
215SD16—734no—
216SD16—1464no—
217D8—2922no—
218D8—1464no—
219D8—1464no—
220M16—24no—
221C2×C8C22×D7311yescharacteristic
222C2×C8C22×D7312yes—
223C2×C8C22×D7311yescharacteristic
224C4⋊C4—731no—
225C4⋊C4—731no—
226C4⋊C4—1461no—
227C4⋊C4D29211yescharacteristic
228C22⋊C4—1461no—
229C22⋊C4—1462no—
230C22⋊C4—1462no—
231C22⋊C4D29212yes—
232C42—1461no—
233C42C22×D7311yescharacteristic
234C23—2924no—
235C23—2924no—
236C23—5842no—
237C23—1462no—
238C23—1462no—
239C23—1461no—
240C23C2×D29212yes—
241Q8—732no—
242Q8—1461no—
243D4—22no—
244D4—2924no—
245D4—2924no—
246D4—2924no—
247D4—2922no—
248D4—2922no—
249D4—5841no—
250D4—5841no—
251D4—5842no—
252D4—732no—
253D4—1462no—
254D4—1462no—
255D4—1462no—
256D4—1462no—
257D4—1461no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—2924no—
261C2×C4—2922no—
262C2×C4—1461no—
263C2×C4—1461no—
264C2×C4—1461no—
265C2×C4C2×D29211yescharacteristic
266C2×C4C2×D29212yes—
267C2×C4C2×D29211yescharacteristic
268C2×C4C23×D7311yescharacteristic
269C8—22no—
270C8—21no—
271C8D4×D7312yescomplemented
272C22—22no—
273C22—22no—
274C22—22no—
275C22—2921no—
276C22—2921no—
277C22—2922no—
278C22—2922no—
279C22—2922no—
280C22—2922no—
281C22—2922no—
282C22—2922no—
283C22—5848no—
284C22—1462no—
285C22C22×D29211yescharacteristic
286C4—21no—
287C4—22no—
288C4—2921no—
289C4—2921no—
290C4—1462no—
291C4#1455661912yescomplemented
292C4C2×D4×D7311yescharacteristic
293C4#1455663711yescharacteristic
294C2—42no—
295C2—2922no—
296C2—5842no—
297C2—5842no—
298C2D4×D29211yescharacteristic
299C2C2×#1455661911yescharacteristic
300C2#1798939211yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#436×C73C2
socleC22×C73C22×D4
hypercenter#436D73
hypocenterC73#3274
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. #17989258C2semidirect
3. D4×D292C2semidirect
4. #17988964C2semidirect
5. #17988840C2semidirect
6. #17988788C2semidirect
7. #17988783C2semidirect
8. #17988734C2semidirect
9. #17988723C2semidirect
10. C4×#11924017C2semidirect
11. #436×C73C2semidirect
12. C2×#11924028C22semidirect
17. C2×#11924017C22semidirect
19. C2×D584C22semidirect
20. C2×D584C22semidirect
22. #14556588C22semidirect
26. #14556565C22semidirect
29. C4×Dic146C22semidirect
32. #14556523C22semidirect
33. #14556516C22semidirect
35. #14556513C22semidirect
36. #14556513C22semidirect
37. C2×M16×C73C22semidirect
39. C4⋊C8×C73C22semidirect
40. C22⋊C8×C73C22semidirect
41. C4×C8×C73C22semidirect
63. #11924017D4semidirect
117. Dic146C2×D4semidirect
120. C8×C73C2×D4semidirect
137. C4×C73AGL(1,ℤ/8)semidirect
151. C73#3274semidirect
162. #436D73semidirect
172. C2×M16C2×D73semidirect
186. C4⋊C8C2×D73semidirect
191. C22⋊C8C2×D73semidirect
192. C4×C8C2×D73semidirect
271. C8D4×D73semidirect
291. C4#14556619semidirect