Finite Group Databasebeta

← #22620950

Subgroups — #22620950

Order 9344.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#127×D73C211yesmaximal, characteristic, complemented
2#17989122C211yesmaximal, characteristic, complemented
3#17988976C211yesmaximal, characteristic, complemented
4#17988974C211yesmaximal, characteristic, complemented
5#17988953C211yesmaximal, characteristic, complemented
6#17988786C212yesmaximal, complemented
7#17988781C212yesmaximal, complemented
8#17988739C212yesmaximal, complemented
9#17988722C212yesmaximal, complemented
10#17988642C211yesmaximal, characteristic, complemented
11#490×C73C211yesmaximal, characteristic, complemented
12C2×D4×D73—21no—
13C2×D4×D73—21no—
14C2×D4×D73C2212yes—
15C2×#11924017C2212yescomplemented
16C2×#11924016C2212yescomplemented
17C2×D584C2212yescomplemented
18C2×#11924013C2212yescomplemented
19#14556588C2211yescharacteristic
20#14556587—21no—
21#14556587—21no—
22#14556587C2212yes—
23#14556586—21no—
24#14556579C2211yescharacteristic, complemented
25#14556576—21no—
26#14556571C2211yescharacteristic
27#14556566C2211yescharacteristic
28#14556556C2211yescharacteristic, complemented
29#14556553—21no—
30#14556553C2211yescharacteristic, complemented
31#14556549—21no—
32C42×D73C2211yescharacteristic
33#14556520C2212yescomplemented
34#14556511C2212yescomplemented
35#14556511C2212yescomplemented
36#14556503C2212yes—
37#14556502C2211yescharacteristic, complemented
38#127×C73C2211yescharacteristic
39#125×C73C2211yescharacteristic, complemented
40#102×C73C2212yescomplemented
41#102×C73C2212yescomplemented
42#97×C73C2211yescharacteristic, complemented
43C23×D73—22no—
44C2×Dic146C2311yescharacteristic
45C2×D292—21no—
46C2×D292—21no—
47C2×D292—21no—
48C2×D292C2312yes—
49C2×D292C2311yescharacteristic
50C2×C22⋊D73—22no—
51C2×C22⋊D73—22no—
52C2×C22⋊D73—22no—
53D4×D73—42no—
54D4×D73—42no—
55D4×D73—44no—
56D4×D73—44no—
57C2×C4×D73—21no—
58C2×C4×D73D411yescharacteristic
59C2×C4×D73D411yescharacteristic
60C2×C4×D73C2311yescharacteristic
61#11924017—42no—
62#11924016—42no—
63D584—42no—
64#11924013—42no—
65C2×#10596831C2312yes—
66C4⋊Dic73—21no—
67#11924007—21no—
68#11924005—21no—
69#11924005—21no—
70#11924005—21no—
71#11924005—21no—
72#11924005—21no—
73C4×Dic73—21no—
74C4×Dic73D411yescharacteristic
75C4×Dic73D411yescharacteristic
76C4×Dic73C2311yescharacteristic
77C2×D4×C73—21no—
78C2×D4×C73—21no—
79C2×D4×C73C2312yes—
80C2×C8×C73C2312yes—
81C4⋊C4×C73—21no—
82C4⋊C4×C73—21no—
83C4⋊C4×C73C2311yescharacteristic
84C4⋊C4×C73C2311yescharacteristic
85C42×C73C2311yescharacteristic
86C23×C73—22no—
87C22×D73—21no—
88C22×D73—22no—
89C22×D73—44no—
90C22×D73—44no—
91C22×D73—44no—
92C22×D73C2×D411yescharacteristic
93D4×C73—22no—
94D4×C73—22no—
95D4×C73—42no—
96D4×C73—42no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73C2×D411yescharacteristic
100C2×C4×C73C2×D411yescharacteristic
101C2×C4×C73C2411yescharacteristic
102C22⋊D73—44no—
103C22⋊D73—44no—
104C22⋊D73—44no—
105C2×Dic73—21no—
106C2×Dic73C2×D411yescharacteristic
107C2×Dic73C2×D411yescharacteristic
108C2×Dic73C2×D411yescharacteristic
109D292—22no—
110D292—22no—
111D292—22no—
112D292—42no—
113D292—42no—
114D292—42no—
115C4×D73—22no—
116C4×D73—22no—
117C4×D73—22no—
118C4×D73—42no—
119Dic146—22no—
120C8×C73—22no—
121#10596831—22no—
122C22×C73—42no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73C22×D411yescharacteristic
126C2×D73—21no—
127C2×D73—21no—
128C2×D73—42no—
129C2×D73—41no—
130C2×D73—41no—
131C2×D73—42no—
132C2×D73—42no—
133C2×D73—41no—
134C2×D73—88no—
135C2×D73AGL(1,ℤ/8)12yes—
136C4×C73—21no—
137C4×C73—21no—
138C4×C73—41no—
139C4×C73—41no—
140C4×C73H(5,𝔽2)12yes—
141Dic73—21no—
142Dic73—21no—
143Dic73—41no—
144Dic73AGL(1,ℤ/8)12yes—
145C2×C73—82no—
146C2×C73#53511yescharacteristic
147C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
149D73—22no—
150D73—81no—
151D73—82no—
152#3217—731nomaximal, Sylow
153C73#321711yescharacteristic, complemented, Sylow
154C2×#127—731no—
155#529—731no—
156#496—731no—
157#496—731no—
158#490—731no—
159#490D7311yescharacteristic, complemented
160#460—732no—
161#459—732no—
162#450—732no—
163#447—732no—
164#432—731no—
165C22×D4—732no—
166C22×D4—1461no—
167C22×D4—1461no—
168C2×SD16—732no—
169C2×SD16—732no—
170C2×D8—732no—
171C2×D8—732no—
172#127—732no—
173#127—731no—
174#127—1461no—
175#127—1461no—
176#127C2×D7311yescharacteristic
177#126—1461no—
178#125C2×D7311yescharacteristic, complemented
179#124—731no—
180#123—1461no—
181C22⋊Q8—731no—
182#121—731no—
183C4×Q8—731no—
184C4×D4—731no—
185C4×D4—1461no—
186#117—1461no—
187C2×C42—731no—
188C4⋊C8—732no—
189#102—732no—
190#102—732no—
191#102C2×D7312yescomplemented
192#102C2×D7312yescomplemented
193C22⋊C8—732no—
194#97—731no—
195#97C2×D7311yescharacteristic, complemented
196C24—1462no—
197C2×Q8—731no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—2922no—
201C2×D4—2922no—
202C2×D4—2924no—
203C2×D4—2924no—
204C2×D4—732no—
205C2×D4—731no—
206C2×D4—1461no—
207C2×D4—1462no—
208C2×D4—1462no—
209C2×D4—1462no—
210C2×D4—1461no—
211C2×D4—1461no—
212C2×D4C22×D7312yes—
213C22×C4—731no—
214C22×C4—731no—
215C22×C4—731no—
216C22×C4—1461no—
217SD16—2922no—
218SD16—2922no—
219D8—2922no—
220D8—2922no—
221C2×C8—732no—
222C2×C8C22×D7312yes—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—1461no—
226C4⋊C4—1461no—
227C4⋊C4C22×D7311yescharacteristic
228C4⋊C4C22×D7311yescharacteristic
229C22⋊C4—1461no—
230C22⋊C4—1461no—
231C22⋊C4—1461no—
232C22⋊C4—1461no—
233C22⋊C4—1461no—
234C42—731no—
235C42—731no—
236C42—731no—
237C42—1461no—
238C42C22×D7311yescharacteristic
239C23—22no—
240C23—2924no—
241C23—2924no—
242C23—2924no—
243C23—731no—
244C23—1461no—
245C23—1462no—
246Q8—1462no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—42no—
251D4—2922no—
252D4—2922no—
253D4—2922no—
254D4—2924no—
255D4—2924no—
256D4—2924no—
257D4—1462no—
258D4—1462no—
259D4—1462no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—2922no—
263C2×C4—731no—
264C2×C4—731no—
265C2×C4—731no—
266C2×C4—1462no—
267C2×C4—1462no—
268C2×C4—1461no—
269C2×C4—1462no—
270C2×C4D4×D7311yescharacteristic
271C2×C4D4×D7311yescharacteristic
272C2×C4C23×D7311yescharacteristic
273C8—22no—
274C8—1462no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—2922no—
279C22—2921no—
280C22—2921no—
281C22—2922no—
282C22—2922no—
283C22—2921no—
284C22—5848no—
285C22—732no—
286C22—1461no—
287C22—1461no—
288C22C2×D4×D7311yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—2921no—
294C4—732no—
295C4—1461no—
296C4—1461no—
297C4#1455663712yes—
298C2—82no—
299C2—5842no—
300C2—5841no—
301C2—1462no—
302C2#1798915511yescharacteristic
303C2AGL(1,ℤ/8)×D7311yescharacteristic
304C2AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#490×C73C2
socleC22×C73C22×D4
hypercenter#490D73
hypocenterC73#3217
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #127×D73C2semidirect
2. #17989122C2semidirect
3. #17988976C2semidirect
4. #17988974C2semidirect
5. #17988953C2semidirect
6. #17988786C2semidirect
7. #17988781C2semidirect
8. #17988739C2semidirect
9. #17988722C2semidirect
10. #17988642C2semidirect
11. #490×C73C2semidirect
15. C2×#11924017C22semidirect
16. C2×#11924016C22semidirect
17. C2×D584C22semidirect
18. C2×#11924013C22semidirect
24. #14556579C22semidirect
28. #14556556C22semidirect
30. #14556553C22semidirect
33. #14556520C22semidirect
34. #14556511C22semidirect
35. #14556511C22semidirect
37. #14556502C22semidirect
39. #125×C73C22semidirect
40. #102×C73C22semidirect
41. #102×C73C22semidirect
42. #97×C73C22semidirect
153. C73#3217semidirect
159. #490D73semidirect
178. #125C2×D73semidirect
191. #102C2×D73semidirect
192. #102C2×D73semidirect
195. #97C2×D73semidirect