Finite Group Databasebeta

← #44408583

Subgroups — #44408583

Order 29056.

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×D227C211yesmaximal, characteristic
2#28409504C212yesmaximal, complemented
3#28409145C211yesmaximal, characteristic, complemented
4#28409144C211yesmaximal, characteristic, complemented
5#28409143C211yesmaximal, characteristic, complemented
6C4×#16813869C212yesmaximal, complemented
7#28409112C212yesmaximal, complemented
8#28409067C211yesmaximal, characteristic, complemented
9#28409035C212yesmaximal, complemented
10#28408989C211yesmaximal, characteristic, complemented
11#442×C227C211yesmaximal, characteristic, complemented
12C2×D4×D227C2212yes—
13C2×D1816C2211yescharacteristic
14C2×#16813869C2212yes—
15D8×D227C418yescomplemented
16C2×#16813867C2211yescharacteristic
17C2×C8×D227C2211yescharacteristic
18C4×D908C2212yescomplemented
19D4×Dic227C2212yescomplemented
20#20300250C2212yescomplemented
21C4×C22⋊D227—22no—
22(C22⋊D227)⋊C4—22no—
23#20300246C2212yes—
24#20300245C2211yescharacteristic
25C2×(C2×D227)⋊C4—22no—
26C22⋊C4×D227—22no—
27#20300221C2212yescomplemented
28#20300220C2211yescharacteristic, complemented
29#20300210C2212yescomplemented
30#20300209C2212yescomplemented
31#20300208C2212yescomplemented
32#20300198C2211yescharacteristic, complemented
33C4×C227⋊C8C2211yescharacteristic, complemented
34C8×Dic227C2211yescharacteristic, complemented
35C2×D8×C227C2211yescharacteristic
36C4×D4×C227C2212yescomplemented
37#106×C227C2211yescharacteristic, complemented
38#102×C227C2212yescomplemented
39#97×C227C2211yescharacteristic, complemented
40C23×D227—22no—
41C2×D908C2312yes—
42C2×C22⋊D227—22no—
43D4×D227—24no—
44D4×D227C2×C418yescomplemented
45C22×Dic227—22no—
46C2×C4×D227—22no—
47C2×C4×D227—22no—
48C2×C4×D227C2311yescharacteristic
49D1816C2×C414yescomplemented
50#16813869C2×C418yescomplemented
51#16813867—22no—
52C2×C227⋊C8C2311yescharacteristic
53C2×C227⋊C8C2311yescharacteristic
54C8×D227C2×C414yescomplemented
55C4⋊Dic227C2312yes—
56Dic227⋊C4D412yes—
57C22⋊Dic227—22no—
58(C2×D227)⋊C4—22no—
59(C2×D227)⋊C4—22no—
60(C2×D227)⋊C4—22no—
61(C2×D227)⋊C4D412yes—
62C4×Dic227—22no—
63C4×Dic227C2311yescharacteristic
64C2×D4×C227C2312yes—
65C22×C4×C227—22no—
66D8×C227C2×C414yescomplemented
67C2×C8×C227C2311yescharacteristic
68C2×C8×C227C2311yescharacteristic
69C4⋊C4×C227C2312yes—
70C22⋊C4×C227—22no—
71C42×C227C2311yescharacteristic
72C22×D227—22no—
73C22×D227—28no—
74C22×D227—82no—
75C22×D227—82no—
76C22×D227C2×D411yescharacteristic
77D908—22no—
78D908C22×C414yes—
79C22⋊D227—28no—
80C2×Dic227—22no—
81C2×Dic227—82no—
82C2×Dic227C2×D412yes—
83C2×Dic227C2×D411yescharacteristic
84C4×D227—82no—
85C4×D227—82no—
86C4×D227C22×C412yes—
87C4×D227#4112yes—
88C227⋊C8—21no—
89C227⋊C8C22×C412yes—
90C23×C227—22no—
91D4×C227—22no—
92D4×C227C22×C414yes—
93C2×C4×C227—22no—
94C2×C4×C227—82no—
95C2×C4×C227C2×D412yes—
96C2×C4×C227C2411yescharacteristic
97C8×C227—21no—
98C8×C227C22×C412yes—
99C22×C227—24no—
100C22×C227—42no—
101C22×C227—42no—
102C22×C227C22×D411yescharacteristic
103C2×D227—22no—
104C2×D227—24no—
105C2×D227—42no—
106C2×D227—42no—
107C2×D227—88no—
108C2×D227C4×D412yes—
109C4×C227—22no—
110C4×C227—42no—
111C4×C227C23×C411yescharacteristic
112C4×C227C2×#4111yescharacteristic
113Dic227—22no—
114Dic227—42no—
115Dic227C4×D412yes—
116C2×C227—44no—
117C2×C227C2×C4×D411yescharacteristic
118C2×C227#57612yes—
119D227—22no—
120D227—44no—
121C227#294811yescharacteristic, complemented, Sylow
122#2948—2271nomaximal, Sylow
123C22×D8—2271no—
124#518—2272no—
125#442—2271no—
126#442—2271no—
127#442—2271no—
128#442D22711yescharacteristic, complemented
129C4×D8—2272no—
130C4×D8—2272no—
131#427—2271no—
132#418—2272no—
133#405—2271no—
134C22×D4—2272no—
135C2×D8—2272no—
136C2×D8—2278no—
137C2×D8—2271no—
138C2×D8C2×D22711yescharacteristic
139C2×M16—2271no—
140C22×C8—2271no—
141C4×D4—4542no—
142C4×D4—4542no—
143C4×D4—2272no—
144C4×D4—2272no—
145C4×D4—2272no—
146C4×D4C2×D22712yescomplemented
147#117—2272no—
148#117—2271no—
149C2×C22⋊C4—4542no—
150C2×C22⋊C4—4542no—
151#107—2272no—
152#106—2271no—
153#106C2×D22711yescharacteristic, complemented
154#102—2272no—
155#102—2272no—
156#102—2272no—
157#102C2×D22712yescomplemented
158#97—2271no—
159#97C2×D22711yescharacteristic, complemented
160C4×C8—2271no—
161C4×C8—2271no—
162C24—4542no—
163C2×D4—4544no—
164C2×D4—4542no—
165C2×D4—2278no—
166C2×D4—2272no—
167C2×D4C22×D22712yes—
168C22×C4—22no—
169C22×C4—4542no—
170C22×C4—4542no—
171C22×C4—4542no—
172C22×C4—2271no—
173D8—2278no—
174D8—2274no—
175D8C4×D22714yescomplemented
176M16—4542no—
177C2×C8—2271no—
178C2×C8—2271no—
179C2×C8—2274no—
180C2×C8C22×D22711yescharacteristic
181C2×C8C22×D22711yescharacteristic
182C4⋊C4—2272no—
183C4⋊C4—2272no—
184C4⋊C4C22×D22712yes—
185C22⋊C4—22no—
186C22⋊C4—4542no—
187C22⋊C4—4542no—
188C22⋊C4—4542no—
189C22⋊C4—4542no—
190C22⋊C4—2272no—
191C42—4542no—
192C42—2271no—
193C42C22×D22711yescharacteristic
194C23—22no—
195C23—18162no—
196C23—18162no—
197C23—4548no—
198C23—4542no—
199C23—2271no—
200D4—22no—
201D4—4548no—
202D4—4542no—
203D4—2274no—
204D4C2×C4×D22714yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—18162no—
208C2×C4—18162no—
209C2×C4—18162no—
210C2×C4—4542no—
211C2×C4—2272no—
212C2×C4—2271no—
213C2×C4—2272no—
214C2×C4—2272no—
215C2×C4D4×D22712yes—
216C2×C4C23×D22711yescharacteristic
217C8—21no—
218C8—4541no—
219C8—2272no—
220C8C2×C4×D22712yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—18168no—
225C22—9082no—
226C22—9082no—
227C22—4544no—
228C22—4542no—
229C22—2272no—
230C22C2×D4×D22711yescharacteristic
231C4—22no—
232C4—42no—
233C4—9082no—
234C4—4542no—
235C4—2272no—
236C4C22×C4×D22711yescharacteristic
237C4#41×D22711yescharacteristic
238C2—44no—
239C2—9084no—
240C2—4542no—
241C2C4×D4×D22711yescharacteristic
242C2#2840983612yes—
subgroupG/H
centerC22C2×D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
Fitting#442×C227C2
socleC22×C227C22×D4
prime radicalC2×D8×D227C2
cosocleC2×C4×C227C24
hypercenter#442D227
hypocenterC227#2948
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #28409504C2semidirect
3. #28409145C2semidirect
4. #28409144C2semidirect
5. #28409143C2semidirect
6. C4×#16813869C2semidirect
7. #28409112C2semidirect
8. #28409067C2semidirect
9. #28409035C2semidirect
10. #28408989C2semidirect
11. #442×C227C2semidirect
15. D8×D227C4semidirect
18. C4×D908C22semidirect
19. D4×Dic227C22semidirect
20. #20300250C22semidirect
27. #20300221C22semidirect
28. #20300220C22semidirect
29. #20300210C22semidirect
30. #20300209C22semidirect
31. #20300208C22semidirect
32. #20300198C22semidirect
33. C4×C227⋊C8C22semidirect
34. C8×Dic227C22semidirect
36. C4×D4×C227C22semidirect
37. #106×C227C22semidirect
38. #102×C227C22semidirect
39. #97×C227C22semidirect
44. D4×D227C2×C4semidirect
49. D1816C2×C4semidirect
50. #16813869C2×C4semidirect
54. C8×D227C2×C4semidirect
66. D8×C227C2×C4semidirect
121. C227#2948semidirect
128. #442D227semidirect
146. C4×D4C2×D227semidirect
153. #106C2×D227semidirect
157. #102C2×D227semidirect
159. #97C2×D227semidirect
175. D8C4×D227semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D8×D2272
#284095042
#284091452
#284091442
#284091432
C4×#168138692
#284091122
#284090672
#284090352
#284089892
#442×C2272
#2948227