Finite Group Databasebeta

← #22598480

Subgroups — #22598480

Order 9088.

450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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#17986533C211yesmaximal, characteristic, complemented
2C2×C4×D284C211yesmaximal, characteristic, complemented
3#17986330C211yesmaximal, characteristic, complemented
4#17986313C211yesmaximal, characteristic, complemented
5#17986300C212yesmaximal, complemented
6#17986215C212yesmaximal, complemented
7#17986152C211yesmaximal, characteristic, complemented
8#17986135C211yesmaximal, characteristic
9#17986112C212yesmaximal, complemented
10#17986101C212yesmaximal, complemented
11#432×C71C211yesmaximal, characteristic, complemented
12C22×D284C2211yescharacteristic
13C22×C4×D71—21no—
14C2×#11765854C2212yes—
15C2×D568C2212yes—
16#14556122—21no—
17#14556120C2211yescharacteristic, complemented
18#14556116C2211yescharacteristic, complemented
19#14556111—21no—
20#14556107C2211yescharacteristic
21#14556102C2211yescharacteristic
22C4×Dic142C2211yescharacteristic, complemented
23C4×D284—21no—
24C4×D284—21no—
25C4×D284C2212yes—
26C4×D284C2212yes—
27C4×D284C2211yescharacteristic, complemented
28C4×C22⋊D71—21no—
29#14556085—21no—
30C2×C4⋊Dic71C2211yescharacteristic
31C2×(C2×D71)⋊C4—21no—
32#14556062C2212yescomplemented
33#14556060C2212yescomplemented
34#14556053C2212yescomplemented
35#14556050C2212yes—
36#14556050C2212yes—
37#14556050C2212yescomplemented
38C2×C42×C71C2211yescharacteristic
39C4⋊C8×C71C2212yescomplemented
40C22⋊C8×C71C2211yescharacteristic
41C22⋊C8×C71C2211yescharacteristic
42#97×C71C2212yescomplemented
43C23×D71—21no—
44C2×Dic142C2311yescharacteristic
45C2×D284—21no—
46C2×D284—24no—
47C2×D284C2311yescharacteristic
48C2×D284C2312yes—
49C2×C22⋊D71—21no—
50C22×Dic71—21no—
51C2×C4×D71—22no—
52C2×C4×D71—22no—
53C2×C4×D71—21no—
54C2×C4×D71—44no—
55#11765854—24no—
56D568—24no—
57C4⋊Dic71—21no—
58C4⋊Dic71C2311yescharacteristic
59C4⋊Dic71C2311yescharacteristic
60C4⋊Dic71C2312yes—
61Dic71⋊C4—21no—
62Dic71⋊C4—21no—
63Dic71⋊C4—21no—
64Dic71⋊C4—21no—
65C22⋊Dic71—21no—
66(C2×D71)⋊C4—22no—
67(C2×D71)⋊C4—22no—
68(C2×D71)⋊C4—21no—
69(C2×D71)⋊C4—21no—
70(C2×D71)⋊C4—21no—
71(C2×D71)⋊C4—21no—
72C4×Dic71—21no—
73C22×C4×C71D411yescharacteristic
74C22×C4×C71D411yescharacteristic
75C22×C4×C71C2311yescharacteristic
76C2×C8×C71C2312yes—
77C2×C8×C71C2312yes—
78C42×C71D411yescharacteristic
79C42×C71D411yescharacteristic
80C42×C71C2311yescharacteristic
81C42×C71C2311yescharacteristic
82C23×C71C2×D411yescharacteristic
83C22×D71—24no—
84C22×D71—22no—
85C22×D71—21no—
86C22×D71—42no—
87C22×D71—42no—
88C2×C4×C71—22no—
89C2×C4×C71—22no—
90C2×C4×C71—41no—
91C2×C4×C71C2×D411yescharacteristic
92C2×C4×C71C2×D411yescharacteristic
93C2×C4×C71C2×D411yescharacteristic
94C2×C4×C71C2×D411yescharacteristic
95C2×C4×C71C2×D411yescharacteristic
96C2×C4×C71C2411yescharacteristic
97C22⋊D71—42no—
98C2×Dic71—21no—
99C2×Dic71—21no—
100C2×Dic71—22no—
101C2×Dic71—21no—
102C2×Dic71—42no—
103D284—24no—
104D284—22no—
105D284—22no—
106D284#4114yes—
107C4×D71—42no—
108C4×D71—44no—
109C4×D71—44no—
110Dic142—22no—
111C8×C71—22no—
112C8×C71—22no—
113C22×C71—21no—
114C22×C71—21no—
115C22×C71AGL(1,ℤ/8)12yes—
116C22×C71C22×D411yescharacteristic
117C2×D71—24no—
118C2×D71—48no—
119C2×D71—42no—
120C2×D71—42no—
121C2×D71—41no—
122C2×D71—41no—
123C2×D71—41no—
124C4×C71—21no—
125C4×C71—21no—
126C4×C71—21no—
127C4×C71—21no—
128C4×C71—21no—
129C4×C71C2×#4112yes—
130Dic71—41no—
131Dic71—42no—
132Dic71—41no—
133Dic71—41no—
134C2×C71—22no—
135C2×C71#52511yescharacteristic
136C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C71#57511yescharacteristic
138D71—44no—
139D71—81no—
140#3114—711nomaximal, Sylow
141C71#311411yescharacteristic, complemented, Sylow
142#529—711no—
143C2×C4×D4—711no—
144#483—711no—
145#480—711no—
146#478—712no—
147#463—712no—
148#450—711no—
149#447—711no—
150#442—712no—
151#440—712no—
152#432D7111yescharacteristic, complemented
153C22×D4—711no—
154C23×C4—1421no—
155C2×SD16—712no—
156C2×D8—712no—
157#126—1421no—
158#125—711no—
159#124—711no—
160#123—1421no—
161C22⋊Q8—711no—
162#121—711no—
163C4×Q8—711no—
164C4×D4—712no—
165C4×D4—712no—
166C4×D4—711no—
167C4×D4—1421no—
168C4×D4—1421no—
169C4×D4—1421no—
170#117—1421no—
171C2×C4⋊C4—711no—
172C2×C22⋊C4—1421no—
173C2×C42C2×D7111yescharacteristic
174#107—712no—
175#106—712no—
176C4⋊C8C2×D7112yescomplemented
177#103—712no—
178#102—712no—
179#102—712no—
180#102—712no—
181C22⋊C8C2×D7111yescharacteristic
182C22⋊C8C2×D7111yescharacteristic
183#97C2×D7112yescomplemented
184C24—1421no—
185C2×Q8—711no—
186C2×D4—712no—
187C2×D4—711no—
188C2×D4—1424no—
189C2×D4—1421no—
190C2×D4—1421no—
191C22×C4—2844no—
192C22×C4—1421no—
193C22×C4—1421no—
194C22×C4—1422no—
195C22×C4—1422no—
196C22×C4D28411yescharacteristic
197C22×C4D28411yescharacteristic
198C22×C4C22×D7111yescharacteristic
199SD16—1424no—
200D8—1424no—
201C2×C8C22×D7112yes—
202C2×C8C22×D7112yes—
203C4⋊C4—711no—
204C4⋊C4—711no—
205C4⋊C4—712no—
206C4⋊C4—1421no—
207C4⋊C4—1421no—
208C4⋊C4—1421no—
209C4⋊C4—1421no—
210C4⋊C4—1421no—
211C22⋊C4—1421no—
212C22⋊C4—1422no—
213C22⋊C4—1422no—
214C22⋊C4—1421no—
215C22⋊C4—1421no—
216C22⋊C4—1421no—
217C22⋊C4—1421no—
218C42—1421no—
219C42D28411yescharacteristic
220C42D28411yescharacteristic
221C42C22×D7111yescharacteristic
222C42C22×D7111yescharacteristic
223C23—2842no—
224C23—2842no—
225C23—1424no—
226C23—1421no—
227C23—1422no—
228C23C2×D28411yescharacteristic
229Q8—1422no—
230D4—2842no—
231D4—714no—
232D4—1424no—
233D4—1422no—
234D4—1422no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—2844no—
239C2×C4—2844no—
240C2×C4—2842no—
241C2×C4—2842no—
242C2×C4—1421no—
243C2×C4—1421no—
244C2×C4—1421no—
245C2×C4—1422no—
246C2×C4C2×D28411yescharacteristic
247C2×C4C2×D28411yescharacteristic
248C2×C4C2×D28411yescharacteristic
249C2×C4C2×D28411yescharacteristic
250C2×C4C2×D28411yescharacteristic
251C2×C4C23×D7111yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—2848no—
257C22—2842no—
258C22—2842no—
259C22—2841no—
260C22—2841no—
261C22—2841no—
262C22—1424no—
263C22#1455615612yes—
264C22C22×D28411yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—2841no—
271C4—2842no—
272C4—2841no—
273C4—2841no—
274C4#41×D7112yes—
275C2—22no—
276C2—2844no—
277C2—5681no—
278C2#1798651111yescharacteristic
279C2C2×#1455615611yescharacteristic
280C2#1798679911yescharacteristic
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#432×C71C2
socleC22×C71C22×D4
hypercenter#432D71
hypocenterC71#3114
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #17986533C2semidirect
2. C2×C4×D284C2semidirect
3. #17986330C2semidirect
4. #17986313C2semidirect
5. #17986300C2semidirect
6. #17986215C2semidirect
7. #17986152C2semidirect
9. #17986112C2semidirect
10. #17986101C2semidirect
11. #432×C71C2semidirect
17. #14556120C22semidirect
18. #14556116C22semidirect
22. C4×Dic142C22semidirect
27. C4×D284C22semidirect
32. #14556062C22semidirect
33. #14556060C22semidirect
34. #14556053C22semidirect
37. #14556050C22semidirect
39. C4⋊C8×C71C22semidirect
42. #97×C71C22semidirect
141. C71#3114semidirect
152. #432D71semidirect
176. C4⋊C8C2×D71semidirect
183. #97C2×D71semidirect