Finite Group Databasebeta

← #22620739

Subgroups — #22620739

Order 9344.

462 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14556571C211yesmaximal, characteristic, complemented
2#121×D73C211yesmaximal, characteristic
3#17988924C212yesmaximal, complemented
4#17988900C211yesmaximal, characteristic, complemented
5#17988834C212yesmaximal, complemented
6#17988832C212yesmaximal, complemented
7#17988739C212yesmaximal, complemented
8#17988728C211yesmaximal, characteristic, complemented
9#17988725C211yesmaximal, characteristic, complemented
10#17988549C211yesmaximal, characteristic, complemented
11#480×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic, complemented
13C2×D4×D73—21no—
14C2×D4×D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16C2×#11924017C2212yescomplemented
17C2×#11924016C2212yescomplemented
18C2×#11924011C2212yescomplemented
19#14556571—21no—
20#14556571—21no—
21#14556571C2212yes—
22#14556571C2212yescomplemented
23#14556566C2211yescharacteristic
24#14556565C2211yescharacteristic
25#14556564—21no—
26#14556563—21no—
27#14556562C2211yescharacteristic
28C2×C4⋊Dic73—21no—
29C4⋊C4×D73C2211yescharacteristic
30C2×#11924005—21no—
31C22⋊C4×D73—21no—
32#14556524C2212yescomplemented
33#14556516C2212yescomplemented
34#14556514C2212yescomplemented
35#14556511C2212yescomplemented
36C22⋊#10596831C2211yescharacteristic, complemented
37#14556503C2212yes—
38#121×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic, complemented
40#107×C73C2212yescomplemented
41#102×C73C2212yescomplemented
42C22⋊C8×C73C2211yescharacteristic, complemented
43C23×D73—21no—
44C23×D73D411yescharacteristic
45C2×Dic146—21no—
46C2×Dic146—42no—
47C2×Dic146C2312yes—
48C2×D292—21no—
49C2×D292C2311yescharacteristic
50C2×C22⋊D73—21no—
51C2×C22⋊D73—21no—
52C2×C22⋊D73—21no—
53D4×D73—42no—
54D4×D73—44no—
55C22×Dic73—21no—
56C22×Dic73D411yescharacteristic
57C2×C4×D73—21no—
58C2×C4×D73—42no—
59C2×C4×D73D411yescharacteristic
60C2×C4×D73D411yescharacteristic
61C2×C4×D73C2311yescharacteristic
62C2×C4×D73C2311yescharacteristic
63#11924017—42no—
64#11924016—42no—
65#11924011—42no—
66C2×#10596831C2312yes—
67C4⋊Dic73—22no—
68C4⋊Dic73—22no—
69C4⋊Dic73C2311yescharacteristic
70#11924007—21no—
71C22⋊Dic73—21no—
72#11924005—22no—
73#11924005—22no—
74#11924005—21no—
75#11924005—21no—
76C2×D4×C73—21no—
77C2×D4×C73C2311yescharacteristic
78C22×C4×C73—21no—
79C22×C4×C73C2311yescharacteristic
80C2×C8×C73C2312yes—
81C4⋊C4×C73—21no—
82C4⋊C4×C73C2312yes—
83C4⋊C4×C73C2311yescharacteristic
84C22⋊C4×C73—21no—
85C23×C73—21no—
86C23×C73C2×D411yescharacteristic
87C22×D73—22no—
88C22×D73—22no—
89C22×D73—21no—
90C22×D73—41no—
91C22×D73—42no—
92C22×D73—42no—
93C22×D73—42no—
94C22×D73C2×D411yescharacteristic
95C22×D73C2×D411yescharacteristic
96D4×C73—22no—
97D4×C73—42no—
98C2×C4×C73—22no—
99C2×C4×C73—21no—
100C2×C4×C73—22no—
101C2×C4×C73—42no—
102C2×C4×C73C2×D411yescharacteristic
103C2×C4×C73C2411yescharacteristic
104C22⋊D73—42no—
105C22⋊D73—42no—
106C22⋊D73—42no—
107C2×Dic73—22no—
108C2×Dic73—21no—
109C2×Dic73—41no—
110C2×Dic73—42no—
111C2×Dic73C2×D411yescharacteristic
112C2×Dic73C2×D411yescharacteristic
113D292—22no—
114D292—42no—
115C4×D73—22no—
116C4×D73—22no—
117C4×D73—41no—
118C4×D73—41no—
119C4×D73—42no—
120Dic146—22no—
121Dic146—22no—
122Dic146—42no—
123C8×C73—22no—
124#10596831—22no—
125C22×C73—21no—
126C22×C73—21no—
127C22×C73—41no—
128C22×C73—41no—
129C22×C73—41no—
130C22×C73AGL(1,ℤ/8)12yes—
131C22×C73C22×D411yescharacteristic
132C2×D73—21no—
133C2×D73—21no—
134C2×D73—21no—
135C2×D73—21no—
136C2×D73—21no—
137C2×D73—44no—
138C2×D73—41no—
139C2×D73—41no—
140C2×D73—41no—
141C2×D73—84no—
142C2×D73#13712yes—
143C4×C73—21no—
144C4×C73—41no—
145C4×C73—42no—
146C4×C73H(5,𝔽2)12yes—
147Dic73—21no—
148Dic73—21no—
149Dic73—42no—
150Dic73—41no—
151C2×C73—22no—
152C2×C73—81no—
153C2×C73#53411yescharacteristic
154C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
155C2×C73C2×#13711yescharacteristic
156D73—22no—
157D73—41no—
158D73—81no—
159#3193—731nomaximal, Sylow
160C73#319311yescharacteristic, complemented, Sylow
161C2×C22⋊Q8—731no—
162C2×#121—731no—
163#484—732no—
164#480—731no—
165#480D7311yescharacteristic, complemented
166#468—732no—
167#468—732no—
168#450—732no—
169#448—731no—
170#448—731no—
171#407—731no—
172C22×Q8—731no—
173C22×D4—731no—
174C22×D4—1461no—
175C23×C4—731no—
176C2×SD16—732no—
177C2×SD16—732no—
178C2×M16—732no—
179C22⋊Q8—732no—
180C22⋊Q8—732no—
181C22⋊Q8—1461no—
182C22⋊Q8—1461no—
183#121—731no—
184#121—731no—
185#121—731no—
186#121—1461no—
187#121—1461no—
188#121C2×D7311yescharacteristic
189C2×C4⋊C4—731no—
190C2×C4⋊C4—1461no—
191C2×C4⋊C4C2×D7311yescharacteristic, complemented
192C2×C22⋊C4—1461no—
193C2×C22⋊C4—1461no—
194#107—732no—
195#107C2×D7312yescomplemented
196#103—732no—
197#103—732no—
198#102—732no—
199#102C2×D7312yescomplemented
200C22⋊C8—731no—
201C22⋊C8—732no—
202C22⋊C8C2×D7311yescharacteristic, complemented
203C24—731no—
204C24—1461no—
205C2×Q8—2922no—
206C2×Q8—732no—
207C2×Q8—1461no—
208C2×D4—21no—
209C2×D4—2924no—
210C2×D4—2922no—
211C2×D4—731no—
212C2×D4—1461no—
213C2×D4—1461no—
214C2×D4—1461no—
215C2×D4—1461no—
216C2×D4C22×D7311yescharacteristic
217C22×C4—21no—
218C22×C4—2922no—
219C22×C4—731no—
220C22×C4—731no—
221C22×C4—731no—
222C22×C4—731no—
223C22×C4—731no—
224C22×C4—1461no—
225C22×C4—1461no—
226C22×C4C22×D7311yescharacteristic
227SD16—2922no—
228SD16—2922no—
229M16—2922no—
230C2×C8—732no—
231C2×C8C22×D7312yes—
232C4⋊C4—21no—
233C4⋊C4—731no—
234C4⋊C4—1461no—
235C4⋊C4—1462no—
236C4⋊C4—1462no—
237C4⋊C4C22×D7312yes—
238C4⋊C4C22×D7311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—1461no—
241C22⋊C4—1462no—
242C22⋊C4—1462no—
243C22⋊C4—1461no—
244C22⋊C4—1461no—
245C23—21no—
246C23—2921no—
247C23—2922no—
248C23—2922no—
249C23—2922no—
250C23—731no—
251C23—731no—
252C23—1462no—
253C23—1461no—
254C23—1462no—
255C23D4×D7311yescharacteristic
256Q8—2922no—
257Q8—1462no—
258Q8—1462no—
259D4—22no—
260D4—42no—
261D4—2922no—
262D4—2922no—
263D4—2922no—
264D4—2922no—
265D4—1462no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—2921no—
271C2×C4—2921no—
272C2×C4—2922no—
273C2×C4—2922no—
274C2×C4—2921no—
275C2×C4—731no—
276C2×C4—731no—
277C2×C4—1461no—
278C2×C4—1462no—
279C2×C4—1462no—
280C2×C4—1462no—
281C2×C4D4×D7311yescharacteristic
282C2×C4C23×D7311yescharacteristic
283C8—22no—
284C8—1462no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—2924no—
291C22—2921no—
292C22—2921no—
293C22—2921no—
294C22—5844no—
295C22—732no—
296C22—1461no—
297C22—1461no—
298C22—1461no—
299C22—1461no—
300C22—1461no—
301C22#1455661512yes—
302C22C2×D4×D7311yescharacteristic
303C4—21no—
304C4—42no—
305C4—41no—
306C4—2922no—
307C4—2921no—
308C4—1461no—
309C4—1461no—
310C4#1455663712yes—
311C2—22no—
312C2—81no—
313C2—2921no—
314C2—5841no—
315C2—1462no—
316C2#1798914811yescharacteristic
317C2C2×#1455661511yescharacteristic
318C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#480×C73C2
socleC22×C73C22×D4
hypercenter#480D73
hypocenterC73#3193
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. C2×#14556571C2semidirect
3. #17988924C2semidirect
4. #17988900C2semidirect
5. #17988834C2semidirect
6. #17988832C2semidirect
7. #17988739C2semidirect
8. #17988728C2semidirect
9. #17988725C2semidirect
10. #17988549C2semidirect
11. #480×C73C2semidirect
12. C22×Dic146C22semidirect
16. C2×#11924017C22semidirect
17. C2×#11924016C22semidirect
18. C2×#11924011C22semidirect
22. #14556571C22semidirect
32. #14556524C22semidirect
33. #14556516C22semidirect
34. #14556514C22semidirect
35. #14556511C22semidirect
36. C22⋊#10596831C22semidirect
39. C2×C4⋊C4×C73C22semidirect
40. #107×C73C22semidirect
41. #102×C73C22semidirect
42. C22⋊C8×C73C22semidirect
160. C73#3193semidirect
165. #480D73semidirect
191. C2×C4⋊C4C2×D73semidirect
195. #107C2×D73semidirect
199. #102C2×D73semidirect
202. C22⋊C8C2×D73semidirect