Finite Group Databasebeta

← #22620730

Subgroups — #22620730

Order 9344.

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

normal subgroups only

This group has 514 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×#14556566C211yesmaximal, characteristic, complemented
2#121×D73C211yesmaximal, characteristic, complemented
3#17988907C212yesmaximal, complemented
4#17988905C211yesmaximal, characteristic, complemented
5#17988841C212yesmaximal, complemented
6#17988839C212yesmaximal, complemented
7#17988723C211yesmaximal, characteristic, complemented
8#17988722C212yesmaximal, complemented
9#17988720C211yesmaximal, characteristic, complemented
10#17988549C211yesmaximal, characteristic, complemented
11#481×C73C211yesmaximal, characteristic, complemented
12C22×D292—21no—
13C22×D292C2211yescharacteristic, complemented
14C2×D4×D73—21no—
15C2×D4×D73C2211yescharacteristic, complemented
16C22×C4×D73C2211yescharacteristic
17C2×D584C2212yescomplemented
18C2×#11924013C2212yescomplemented
19C2×#11924011C2212yescomplemented
20#14556566—21no—
21#14556566—21no—
22#14556566C2212yes—
23#14556566C2211yescharacteristic, complemented
24#14556566C2212yescomplemented
25#14556565C2211yescharacteristic
26#14556564—21no—
27#14556563—21no—
28#14556562C2211yescharacteristic, complemented
29C4⋊C4×D73C2211yescharacteristic, complemented
30C2×#11924005—21no—
31C22⋊C4×D73—21no—
32#14556522C2212yescomplemented
33#14556513C2212yescomplemented
34#14556511C2212yescomplemented
35#14556511C2212yescomplemented
36C22⋊#10596831C2211yescharacteristic, complemented
37#14556503C2212yescomplemented
38#121×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic, complemented
40#106×C73C2212yescomplemented
41#102×C73C2212yescomplemented
42C22⋊C8×C73C2211yescharacteristic, complemented
43C23×D73—21no—
44C23×D73—21no—
45C23×D73D411yescharacteristic
46C2×D292—21no—
47C2×D292—22no—
48C2×D292—22no—
49C2×D292—21no—
50C2×D292—42no—
51C2×D292—44no—
52C2×D292C2311yescharacteristic
53C2×D292C2312yes—
54C2×C22⋊D73—21no—
55C2×C22⋊D73—21no—
56C2×C22⋊D73—21no—
57D4×D73—42no—
58D4×D73—44no—
59C22×Dic73D411yescharacteristic
60C2×C4×D73—21no—
61C2×C4×D73—42no—
62C2×C4×D73D411yescharacteristic
63C2×C4×D73D411yescharacteristic
64C2×C4×D73C2311yescharacteristic
65C2×C4×D73C2311yescharacteristic
66D584—42no—
67#11924013—42no—
68#11924011—42no—
69C2×#10596831C2312yes—
70C4⋊Dic73C2311yescharacteristic
71#11924007—21no—
72C22⋊Dic73—21no—
73#11924005—21no—
74#11924005—21no—
75#11924005—22no—
76#11924005—22no—
77C2×D4×C73—21no—
78C2×D4×C73C2311yescharacteristic
79C22×C4×C73—21no—
80C22×C4×C73C2311yescharacteristic
81C2×C8×C73C2312yes—
82C4⋊C4×C73—21no—
83C4⋊C4×C73C2312yes—
84C4⋊C4×C73C2311yescharacteristic
85C22⋊C4×C73—21no—
86C23×C73—21no—
87C23×C73C2×D411yescharacteristic
88C22×D73—22no—
89C22×D73—22no—
90C22×D73—21no—
91C22×D73—22no—
92C22×D73—41no—
93C22×D73—42no—
94C22×D73—42no—
95C22×D73—42no—
96C22×D73—42no—
97C22×D73—42no—
98C22×D73—42no—
99C22×D73C2×D411yescharacteristic
100C22×D73C2×D411yescharacteristic
101D4×C73—22no—
102D4×C73—42no—
103C2×C4×C73—22no—
104C2×C4×C73—21no—
105C2×C4×C73—22no—
106C2×C4×C73—42no—
107C2×C4×C73C2×D411yescharacteristic
108C2×C4×C73C2411yescharacteristic
109C22⋊D73—42no—
110C22⋊D73—42no—
111C22⋊D73—42no—
112C2×Dic73—21no—
113C2×Dic73—41no—
114C2×Dic73C2×D411yescharacteristic
115C2×Dic73C2×D411yescharacteristic
116D292—22no—
117D292—22no—
118D292—22no—
119D292—42no—
120D292—42no—
121D292—44no—
122D292—44no—
123C4×D73—22no—
124C4×D73—22no—
125C4×D73—41no—
126C4×D73—41no—
127C4×D73—42no—
128C8×C73—22no—
129#10596831—22no—
130C22×C73—21no—
131C22×C73—21no—
132C22×C73—41no—
133C22×C73—41no—
134C22×C73—41no—
135C22×C73AGL(1,ℤ/8)12yes—
136C22×C73C22×D411yescharacteristic
137C2×D73—21no—
138C2×D73—21no—
139C2×D73—21no—
140C2×D73—21no—
141C2×D73—21no—
142C2×D73—44no—
143C2×D73—42no—
144C2×D73—41no—
145C2×D73—42no—
146C2×D73—41no—
147C2×D73—41no—
148C2×D73—42no—
149C2×D73—84no—
150C2×D73—84no—
151C2×D73AGL(1,ℤ/8)12yes—
152C4×C73—21no—
153C4×C73—41no—
154C4×C73—42no—
155C4×C73H(5,𝔽2)12yes—
156Dic73—21no—
157Dic73—21no—
158Dic73—41no—
159C2×C73—22no—
160C2×C73—81no—
161C2×C73#53411yescharacteristic
162C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
163C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
164D73—22no—
165D73—41no—
166D73—82no—
167D73—81no—
168#3192—731nomaximal, Sylow
169C73#319211yescharacteristic, complemented, Sylow
170C2×#121—731no—
171C2×#121—731no—
172#481—731no—
173#481—732no—
174#481D7311yescharacteristic, complemented
175#469—732no—
176#469—732no—
177#447—731no—
178#447—732no—
179#447—731no—
180#407—731no—
181C22×D4—731no—
182C22×D4—731no—
183C22×D4—1461no—
184C22×D4—1461no—
185C23×C4—731no—
186C2×D8—732no—
187C2×D8—732no—
188C2×M16—732no—
189#121—731no—
190#121—731no—
191#121—732no—
192#121—731no—
193#121—732no—
194#121—1461no—
195#121—1461no—
196#121—1461no—
197#121—1461no—
198#121C2×D7311yescharacteristic
199C2×C4⋊C4—731no—
200C2×C4⋊C4C2×D7311yescharacteristic, complemented
201C2×C22⋊C4—1461no—
202C2×C22⋊C4—1461no—
203#106—732no—
204#106C2×D7312yescomplemented
205#102—732no—
206#102—732no—
207#102—732no—
208#102C2×D7312yescomplemented
209C22⋊C8—731no—
210C22⋊C8—732no—
211C22⋊C8C2×D7311yescharacteristic, complemented
212C24—731no—
213C24—1461no—
214C24—1461no—
215C2×D4—21no—
216C2×D4—2922no—
217C2×D4—2924no—
218C2×D4—2924no—
219C2×D4—2922no—
220C2×D4—731no—
221C2×D4—732no—
222C2×D4—1461no—
223C2×D4—1462no—
224C2×D4—1462no—
225C2×D4—1461no—
226C2×D4—1461no—
227C2×D4—1461no—
228C2×D4—1461no—
229C2×D4C22×D7311yescharacteristic
230C22×C4—21no—
231C22×C4—2922no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—731no—
235C22×C4—731no—
236C22×C4—731no—
237C22×C4—1461no—
238C22×C4C22×D7311yescharacteristic
239D8—2922no—
240D8—2922no—
241M16—2922no—
242C2×C8—732no—
243C2×C8C22×D7312yes—
244C4⋊C4—21no—
245C4⋊C4—731no—
246C4⋊C4—1461no—
247C4⋊C4C22×D7311yescharacteristic
248C4⋊C4C22×D7312yes—
249C22⋊C4—21no—
250C22⋊C4—1461no—
251C22⋊C4—1462no—
252C22⋊C4—1462no—
253C22⋊C4—1461no—
254C22⋊C4—1461no—
255C23—21no—
256C23—2921no—
257C23—2922no—
258C23—2922no—
259C23—2922no—
260C23—2922no—
261C23—2922no—
262C23—2922no—
263C23—731no—
264C23—731no—
265C23—1462no—
266C23—1462no—
267C23—1461no—
268C23—1462no—
269C23D4×D7311yescharacteristic
270D4—22no—
271D4—42no—
272D4—2922no—
273D4—2924no—
274D4—2924no—
275D4—2922no—
276D4—2922no—
277D4—2922no—
278D4—2922no—
279D4—1462no—
280D4—1462no—
281D4—1462no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—2921no—
287C2×C4—2921no—
288C2×C4—2922no—
289C2×C4—2921no—
290C2×C4—731no—
291C2×C4—731no—
292C2×C4—1461no—
293C2×C4—1462no—
294C2×C4—1462no—
295C2×C4D4×D7311yescharacteristic
296C2×C4C23×D7311yescharacteristic
297C8—22no—
298C8—1462no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—2924no—
305C22—2922no—
306C22—2921no—
307C22—2922no—
308C22—2921no—
309C22—2921no—
310C22—2922no—
311C22—5844no—
312C22—5844no—
313C22—732no—
314C22—1461no—
315C22—1461no—
316C22—1461no—
317C22—1461no—
318C22—1461no—
319C22#1455661812yes—
320C22C2×D4×D7311yescharacteristic
321C4—21no—
322C4—42no—
323C4—41no—
324C4—2921no—
325C4—1461no—
326C4—1461no—
327C4#1455663712yes—
328C2—22no—
329C2—81no—
330C2—2921no—
331C2—5842no—
332C2—5841no—
333C2—1462no—
334C2#1798914811yescharacteristic
335C2AGL(1,ℤ/8)×D7311yescharacteristic
336C2C2×#1455661811yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#481×C73C2
socleC22×C73C22×D4
hypercenter#481D73
hypocenterC73#3192
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. C2×#14556566C2semidirect
2. #121×D73C2semidirect
3. #17988907C2semidirect
4. #17988905C2semidirect
5. #17988841C2semidirect
6. #17988839C2semidirect
7. #17988723C2semidirect
8. #17988722C2semidirect
9. #17988720C2semidirect
10. #17988549C2semidirect
11. #481×C73C2semidirect
13. C22×D292C22semidirect
15. C2×D4×D73C22semidirect
17. C2×D584C22semidirect
18. C2×#11924013C22semidirect
19. C2×#11924011C22semidirect
23. #14556566C22semidirect
24. #14556566C22semidirect
28. #14556562C22semidirect
29. C4⋊C4×D73C22semidirect
32. #14556522C22semidirect
33. #14556513C22semidirect
34. #14556511C22semidirect
35. #14556511C22semidirect
36. C22⋊#10596831C22semidirect
37. #14556503C22semidirect
39. C2×C4⋊C4×C73C22semidirect
40. #106×C73C22semidirect
41. #102×C73C22semidirect
42. C22⋊C8×C73C22semidirect
169. C73#3192semidirect
174. #481D73semidirect
200. C2×C4⋊C4C2×D73semidirect
204. #106C2×D73semidirect
208. #102C2×D73semidirect
211. C22⋊C8C2×D73semidirect