Finite Group Databasebeta

← #22597189

Subgroups — #22597189

Order 9088.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D71C211yesmaximal, characteristic
2#17986471C212yesmaximal, complemented
3#17986112C211yesmaximal, characteristic, complemented
4#17986111C211yesmaximal, characteristic, complemented
5#17986110C211yesmaximal, characteristic, complemented
6C4×#11765850C212yesmaximal, complemented
7#17986079C212yesmaximal, complemented
8#17986034C211yesmaximal, characteristic, complemented
9#17986002C212yesmaximal, complemented
10#17985956C211yesmaximal, characteristic, complemented
11#442×C71C211yesmaximal, characteristic, complemented
12C2×D4×D71C2212yes—
13C2×D568C2211yescharacteristic
14C2×#11765850C2212yes—
15D8×D71C418yescomplemented
16C2×#11765848C2211yescharacteristic
17C2×C8×D71C2211yescharacteristic
18C4×D284C2212yescomplemented
19D4×Dic71C2212yescomplemented
20#14556090C2212yescomplemented
21C4×C22⋊D71—22no—
22(C22⋊D71)⋊C4—22no—
23#14556086C2212yes—
24#14556085C2211yescharacteristic
25C2×(C2×D71)⋊C4—22no—
26C22⋊C4×D71—22no—
27#14556061C2212yescomplemented
28#14556060C2211yescharacteristic, complemented
29#14556050C2212yescomplemented
30#14556049C2212yescomplemented
31#14556048C2212yescomplemented
32#14556038C2211yescharacteristic, complemented
33C4×C71⋊C8C2211yescharacteristic, complemented
34C8×Dic71C2211yescharacteristic, complemented
35C2×D8×C71C2211yescharacteristic
36C4×D4×C71C2212yescomplemented
37#106×C71C2211yescharacteristic, complemented
38#102×C71C2212yescomplemented
39#97×C71C2211yescharacteristic, complemented
40C23×D71—22no—
41C2×D284C2312yes—
42C2×C22⋊D71—22no—
43D4×D71—24no—
44D4×D71C2×C418yescomplemented
45C22×Dic71—22no—
46C2×C4×D71—22no—
47C2×C4×D71—22no—
48C2×C4×D71C2311yescharacteristic
49D568C2×C414yescomplemented
50#11765850C2×C418yescomplemented
51#11765848—22no—
52C2×C71⋊C8C2311yescharacteristic
53C2×C71⋊C8C2311yescharacteristic
54C8×D71C2×C414yescomplemented
55C4⋊Dic71C2312yes—
56Dic71⋊C4D412yes—
57C22⋊Dic71—22no—
58(C2×D71)⋊C4—22no—
59(C2×D71)⋊C4—22no—
60(C2×D71)⋊C4—22no—
61(C2×D71)⋊C4D412yes—
62C4×Dic71—22no—
63C4×Dic71C2311yescharacteristic
64C2×D4×C71C2312yes—
65C22×C4×C71—22no—
66D8×C71C2×C414yescomplemented
67C2×C8×C71C2311yescharacteristic
68C2×C8×C71C2311yescharacteristic
69C4⋊C4×C71C2312yes—
70C22⋊C4×C71—22no—
71C42×C71C2311yescharacteristic
72C23×C71—22no—
73C22×D71—22no—
74C22×D71—28no—
75C22×D71—82no—
76C22×D71—82no—
77C22×D71C2×D411yescharacteristic
78D4×C71—22no—
79D4×C71C22×C414yes—
80C2×C4×C71—22no—
81C2×C4×C71—82no—
82C2×C4×C71C2×D412yes—
83C2×C4×C71C2411yescharacteristic
84C22⋊D71—28no—
85C2×Dic71—22no—
86C2×Dic71—82no—
87C2×Dic71C2×D412yes—
88C2×Dic71C2×D411yescharacteristic
89D284—22no—
90D284C22×C414yes—
91C4×D71—82no—
92C4×D71—82no—
93C4×D71C22×C412yes—
94C4×D71#4112yes—
95C8×C71—21no—
96C8×C71C22×C412yes—
97C71⋊C8—21no—
98C71⋊C8C22×C412yes—
99C22×C71—24no—
100C22×C71—42no—
101C22×C71—42no—
102C22×C71C22×D411yescharacteristic
103C2×D71—22no—
104C2×D71—24no—
105C2×D71—42no—
106C2×D71—42no—
107C2×D71—88no—
108C2×D71C4×D412yes—
109C4×C71—22no—
110C4×C71—42no—
111C4×C71C23×C411yescharacteristic
112C4×C71C2×#4111yescharacteristic
113Dic71—22no—
114Dic71—42no—
115Dic71C4×D412yes—
116C2×C71—44no—
117C2×C71C2×C4×D411yescharacteristic
118C2×C71#57612yes—
119D71—22no—
120D71—44no—
121#2948—711nomaximal, Sylow
122C71#294811yescharacteristic, complemented, Sylow
123C22×D8—711no—
124#518—712no—
125#442—711no—
126#442—711no—
127#442—711no—
128#442D7111yescharacteristic, complemented
129C4×D8—712no—
130C4×D8—712no—
131#427—711no—
132#418—712no—
133#405—711no—
134C22×D4—712no—
135C2×D8—712no—
136C2×D8—718no—
137C2×D8—711no—
138C2×D8C2×D7111yescharacteristic
139C2×M16—711no—
140C22×C8—711no—
141C4×D4—712no—
142C4×D4—712no—
143C4×D4—712no—
144C4×D4—1422no—
145C4×D4—1422no—
146C4×D4C2×D7112yescomplemented
147#117—711no—
148#117—712no—
149C2×C22⋊C4—1422no—
150C2×C22⋊C4—1422no—
151#107—712no—
152#106—711no—
153#106C2×D7111yescharacteristic, complemented
154#102—712no—
155#102—712no—
156#102—712no—
157#102C2×D7112yescomplemented
158#97—711no—
159#97C2×D7111yescharacteristic, complemented
160C4×C8—711no—
161C4×C8—711no—
162C24—1422no—
163C2×D4—718no—
164C2×D4—712no—
165C2×D4—1424no—
166C2×D4—1422no—
167C2×D4C22×D7112yes—
168C22×C4—22no—
169C22×C4—711no—
170C22×C4—1422no—
171C22×C4—1422no—
172C22×C4—1422no—
173D8—718no—
174D8—714no—
175D8C4×D7114yescomplemented
176M16—1422no—
177C2×C8—711no—
178C2×C8—714no—
179C2×C8—711no—
180C2×C8C22×D7111yescharacteristic
181C2×C8C22×D7111yescharacteristic
182C4⋊C4—712no—
183C4⋊C4—712no—
184C4⋊C4C22×D7112yes—
185C22⋊C4—22no—
186C22⋊C4—712no—
187C22⋊C4—1422no—
188C22⋊C4—1422no—
189C22⋊C4—1422no—
190C22⋊C4—1422no—
191C42—711no—
192C42—1422no—
193C42C22×D7111yescharacteristic
194C23—22no—
195C23—5682no—
196C23—5682no—
197C23—711no—
198C23—1428no—
199C23—1422no—
200D4—22no—
201D4—714no—
202D4—1428no—
203D4—1422no—
204D4C2×C4×D7114yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—5682no—
208C2×C4—5682no—
209C2×C4—5682no—
210C2×C4—711no—
211C2×C4—712no—
212C2×C4—712no—
213C2×C4—712no—
214C2×C4—1422no—
215C2×C4D4×D7112yes—
216C2×C4C23×D7111yescharacteristic
217C8—21no—
218C8—712no—
219C8—1421no—
220C8C2×C4×D7112yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—2842no—
225C22—2842no—
226C22—5688no—
227C22—712no—
228C22—1424no—
229C22—1422no—
230C22C2×D4×D7111yescharacteristic
231C4—22no—
232C4—42no—
233C4—2842no—
234C4—712no—
235C4—1422no—
236C4C22×C4×D7111yescharacteristic
237C4#41×D7111yescharacteristic
238C2—44no—
239C2—2844no—
240C2—1422no—
241C2C4×D4×D7111yescharacteristic
242C2#1798680312yes—
subgroupG/H
centerC22C2×D4×D71
commutatorC4×C71C23×C4
FrattiniC2×C4C23×D71
Fitting#442×C71C2
socleC22×C71C22×D4
hypercenter#442D71
hypocenterC71#2948
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #17986471C2semidirect
3. #17986112C2semidirect
4. #17986111C2semidirect
5. #17986110C2semidirect
6. C4×#11765850C2semidirect
7. #17986079C2semidirect
8. #17986034C2semidirect
9. #17986002C2semidirect
10. #17985956C2semidirect
11. #442×C71C2semidirect
15. D8×D71C4semidirect
18. C4×D284C22semidirect
19. D4×Dic71C22semidirect
20. #14556090C22semidirect
27. #14556061C22semidirect
28. #14556060C22semidirect
29. #14556050C22semidirect
30. #14556049C22semidirect
31. #14556048C22semidirect
32. #14556038C22semidirect
33. C4×C71⋊C8C22semidirect
34. C8×Dic71C22semidirect
36. C4×D4×C71C22semidirect
37. #106×C71C22semidirect
38. #102×C71C22semidirect
39. #97×C71C22semidirect
44. D4×D71C2×C4semidirect
49. D568C2×C4semidirect
50. #11765850C2×C4semidirect
54. C8×D71C2×C4semidirect
66. D8×C71C2×C4semidirect
122. C71#2948semidirect
128. #442D71semidirect
146. C4×D4C2×D71semidirect
153. #106C2×D71semidirect
157. #102C2×D71semidirect
159. #97C2×D71semidirect
175. D8C4×D71semidirect