Finite Group Databasebeta

← #27179981

Subgroups — #27179981

Order 12928.

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×D101C211yesmaximal, characteristic
2#20265649C212yesmaximal, complemented
3#20265290C211yesmaximal, characteristic, complemented
4#20265289C211yesmaximal, characteristic, complemented
5#20265288C211yesmaximal, characteristic, complemented
6C4×#13108059C212yesmaximal, complemented
7#20265257C212yesmaximal, complemented
8#20265212C211yesmaximal, characteristic, complemented
9#20265180C212yesmaximal, complemented
10#20265134C211yesmaximal, characteristic, complemented
11#442×C101C211yesmaximal, characteristic, complemented
12C2×D4×D101C2212yes—
13C2×D808C2211yescharacteristic
14C2×#13108059C2212yes—
15D8×D101C418yescomplemented
16C2×#13108057C2211yescharacteristic
17C2×C8×D101C2211yescharacteristic
18C4×D404C2212yescomplemented
19D4×Dic101C2212yescomplemented
20#15692217C2212yescomplemented
21C4×C22⋊D101—22no—
22#15692215—22no—
23#15692213C2212yes—
24#15692212C2211yescharacteristic
25C2×#13108051—22no—
26C22⋊C4×D101—22no—
27#15692188C2212yescomplemented
28#15692187C2211yescharacteristic, complemented
29#15692177C2212yescomplemented
30#15692176C2212yescomplemented
31#15692175C2212yescomplemented
32#15692165C2211yescharacteristic, complemented
33C4×#11717579C2211yescharacteristic, complemented
34C8×Dic101C2211yescharacteristic, complemented
35C2×D8×C101C2211yescharacteristic
36C4×D4×C101C2212yescomplemented
37#106×C101C2211yescharacteristic, complemented
38#102×C101C2212yescomplemented
39#97×C101C2211yescharacteristic, complemented
40C23×D101—22no—
41C2×D404C2312yes—
42C2×C22⋊D101—22no—
43D4×D101—24no—
44D4×D101C2×C418yescomplemented
45C22×Dic101—22no—
46C2×C4×D101—22no—
47C2×C4×D101—22no—
48C2×C4×D101C2311yescharacteristic
49D808C2×C414yescomplemented
50#13108059C2×C418yescomplemented
51#13108057—22no—
52C2×#11717579C2311yescharacteristic
53C2×#11717579C2311yescharacteristic
54C8×D101C2×C414yescomplemented
55C4⋊Dic101C2312yes—
56#13108053D412yes—
57C22⋊Dic101—22no—
58#13108051—22no—
59#13108051—22no—
60#13108051—22no—
61#13108051D412yes—
62C4×Dic101—22no—
63C4×Dic101C2311yescharacteristic
64C2×D4×C101C2312yes—
65C22×C4×C101—22no—
66D8×C101C2×C414yescomplemented
67C2×C8×C101C2311yescharacteristic
68C2×C8×C101C2311yescharacteristic
69C4⋊C4×C101C2312yes—
70C22⋊C4×C101—22no—
71C42×C101C2311yescharacteristic
72C23×C101—22no—
73C22×D101—22no—
74C22×D101—28no—
75C22×D101—82no—
76C22×D101—82no—
77C22×D101C2×D411yescharacteristic
78D4×C101—22no—
79D4×C101C22×C414yes—
80C2×C4×C101—22no—
81C2×C4×C101—82no—
82C2×C4×C101C2×D412yes—
83C2×C4×C101C2411yescharacteristic
84C22⋊D101—28no—
85C2×Dic101—22no—
86C2×Dic101—82no—
87C2×Dic101C2×D412yes—
88C2×Dic101C2×D411yescharacteristic
89D404—22no—
90D404C22×C414yes—
91C4×D101—82no—
92C4×D101—82no—
93C4×D101C22×C412yes—
94C4×D101#4112yes—
95C8×C101—21no—
96C8×C101C22×C412yes—
97#11717579—21no—
98#11717579C22×C412yes—
99C22×C101—24no—
100C22×C101—42no—
101C22×C101—42no—
102C22×C101C22×D411yescharacteristic
103C2×D101—22no—
104C2×D101—24no—
105C2×D101—42no—
106C2×D101—42no—
107C2×D101—88no—
108C2×D101C4×D412yes—
109C4×C101—22no—
110C4×C101—42no—
111C4×C101C23×C411yescharacteristic
112C4×C101C2×#4111yescharacteristic
113Dic101—22no—
114Dic101—42no—
115Dic101C4×D412yes—
116C2×C101—44no—
117C2×C101C2×C4×D411yescharacteristic
118C2×C101#57612yes—
119D101—22no—
120D101—44no—
121#2948—1011nomaximal, Sylow
122C101#294811yescharacteristic, complemented, Sylow
123C22×D8—1011no—
124#518—1012no—
125#442—1011no—
126#442—1011no—
127#442—1011no—
128#442D10111yescharacteristic, complemented
129C4×D8—1012no—
130C4×D8—1012no—
131#427—1011no—
132#418—1012no—
133#405—1011no—
134C22×D4—1012no—
135C2×D8—1012no—
136C2×D8—1018no—
137C2×D8—1011no—
138C2×D8C2×D10111yescharacteristic
139C2×M16—1011no—
140C22×C8—1011no—
141C4×D4—1012no—
142C4×D4—1012no—
143C4×D4—1012no—
144C4×D4—2022no—
145C4×D4—2022no—
146C4×D4C2×D10112yescomplemented
147#117—1011no—
148#117—1012no—
149C2×C22⋊C4—2022no—
150C2×C22⋊C4—2022no—
151#107—1012no—
152#106—1011no—
153#106C2×D10111yescharacteristic, complemented
154#102—1012no—
155#102—1012no—
156#102—1012no—
157#102C2×D10112yescomplemented
158#97—1011no—
159#97C2×D10111yescharacteristic, complemented
160C4×C8—1011no—
161C4×C8—1011no—
162C24—2022no—
163C2×D4—1018no—
164C2×D4—1012no—
165C2×D4—2024no—
166C2×D4—2022no—
167C2×D4C22×D10112yes—
168C22×C4—22no—
169C22×C4—1011no—
170C22×C4—2022no—
171C22×C4—2022no—
172C22×C4—2022no—
173D8—1018no—
174D8—1014no—
175D8C4×D10114yescomplemented
176M16—2022no—
177C2×C8—1011no—
178C2×C8—1014no—
179C2×C8—1011no—
180C2×C8C22×D10111yescharacteristic
181C2×C8C22×D10111yescharacteristic
182C4⋊C4—1012no—
183C4⋊C4—1012no—
184C4⋊C4C22×D10112yes—
185C22⋊C4—22no—
186C22⋊C4—1012no—
187C22⋊C4—2022no—
188C22⋊C4—2022no—
189C22⋊C4—2022no—
190C22⋊C4—2022no—
191C42—1011no—
192C42—2022no—
193C42C22×D10111yescharacteristic
194C23—22no—
195C23—8082no—
196C23—8082no—
197C23—1011no—
198C23—2028no—
199C23—2022no—
200D4—22no—
201D4—1014no—
202D4—2028no—
203D4—2022no—
204D4C2×C4×D10114yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—8082no—
208C2×C4—8082no—
209C2×C4—8082no—
210C2×C4—1011no—
211C2×C4—1012no—
212C2×C4—1012no—
213C2×C4—1012no—
214C2×C4—2022no—
215C2×C4D4×D10112yes—
216C2×C4C23×D10111yescharacteristic
217C8—21no—
218C8—1012no—
219C8—2021no—
220C8C2×C4×D10112yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—8088no—
225C22—1012no—
226C22—4042no—
227C22—4042no—
228C22—2024no—
229C22—2022no—
230C22C2×D4×D10111yescharacteristic
231C4—22no—
232C4—42no—
233C4—1012no—
234C4—4042no—
235C4—2022no—
236C4C22×C4×D10111yescharacteristic
237C4#41×D10111yescharacteristic
238C2—44no—
239C2—4044no—
240C2—2022no—
241C2C4×D4×D10111yescharacteristic
242C2#2026598112yes—
subgroupG/H
centerC22C2×D4×D101
commutatorC4×C101C23×C4
FrattiniC2×C4C23×D101
Fitting#442×C101C2
socleC22×C101C22×D4
prime radicalC2×D8×D101C2
cosocleC2×C4×C101C24
hypercenter#442D101
hypocenterC101#2948
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #20265649C2semidirect
3. #20265290C2semidirect
4. #20265289C2semidirect
5. #20265288C2semidirect
6. C4×#13108059C2semidirect
7. #20265257C2semidirect
8. #20265212C2semidirect
9. #20265180C2semidirect
10. #20265134C2semidirect
11. #442×C101C2semidirect
15. D8×D101C4semidirect
18. C4×D404C22semidirect
19. D4×Dic101C22semidirect
20. #15692217C22semidirect
27. #15692188C22semidirect
28. #15692187C22semidirect
29. #15692177C22semidirect
30. #15692176C22semidirect
31. #15692175C22semidirect
32. #15692165C22semidirect
33. C4×#11717579C22semidirect
34. C8×Dic101C22semidirect
36. C4×D4×C101C22semidirect
37. #106×C101C22semidirect
38. #102×C101C22semidirect
39. #97×C101C22semidirect
44. D4×D101C2×C4semidirect
49. D808C2×C4semidirect
50. #13108059C2×C4semidirect
54. C8×D101C2×C4semidirect
66. D8×C101C2×C4semidirect
122. C101#2948semidirect
128. #442D101semidirect
146. C4×D4C2×D101semidirect
153. #106C2×D101semidirect
157. #102C2×D101semidirect
159. #97C2×D101semidirect
175. D8C4×D101semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1012
#202656492
#202652902
#202652892
#202652882
C4×#131080592
#202652572
#202652122
#202651802
#202651342
#442×C1012
#2948101