Finite Group Databasebeta

← #442×D101 #27179921

Subgroups — #442×D101 #27179921

Order 12928.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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
2C4×D4×D101C212yesmaximal, complemented
3#20265290C211yesmaximal, characteristic, complemented
4#20265289C211yesmaximal, characteristic, complemented
5#20265288C211yesmaximal, characteristic, complemented
6#20265287C212yesmaximal, complemented
7#20265286C212yesmaximal, complemented
8#106×D101C211yesmaximal, characteristic, complemented
9#102×D101C212yesmaximal, complemented
10#97×D101C211yesmaximal, characteristic, complemented
11#442×C101C211yesmaximal, characteristic, complemented
12C2×D4×D101C2212yes—
13C22×C4×D101—22no—
14C2×D808C2211yescharacteristic
15C2×#13108059C2212yes—
16D8×D101C418yescomplemented
17C2×C8×D101C2211yescharacteristic
18C2×C8×D101C2211yescharacteristic
19C4×D404C2212yescomplemented
20D4×Dic101C2212yescomplemented
21#15692217C2212yescomplemented
22C4×C22⋊D101—22no—
23#15692215—22no—
24C4⋊C4×D101C2212yes—
25C22⋊C4×D101—22no—
26C42×D101C2211yescharacteristic
27#15692187C2211yescharacteristic, complemented
28#15692186C2212yescomplemented
29#15692177C2212yescomplemented
30#15692176C2212yescomplemented
31#15692175C2212yescomplemented
32#15692166C2211yescharacteristic, complemented
33#15692165C2211yescharacteristic, complemented
34#15692165C2211yescharacteristic, 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×D101—22no—
49C2×C4×D101—48no—
50C2×C4×D101D412yes—
51C2×C4×D101C2311yescharacteristic
52D808C2×C414yescomplemented
53#13108059C2×C418yescomplemented
54C2×#11717579C2311yescharacteristic
55C2×#11717579C2311yescharacteristic
56C8×D101—22no—
57C8×D101C2×C414yescomplemented
58C4⋊Dic101C2312yes—
59#13108053—22no—
60C22⋊Dic101—22no—
61#13108051—22no—
62#13108051—22no—
63C4×Dic101D412yes—
64C4×Dic101C2311yescharacteristic
65C2×D4×C101C2312yes—
66C22×C4×C101—22no—
67D8×C101C2×C414yescomplemented
68C2×C8×C101C2311yescharacteristic
69C2×C8×C101C2311yescharacteristic
70C4⋊C4×C101C2312yes—
71C22⋊C4×C101—22no—
72C42×C101C2311yescharacteristic
73C23×C101—22no—
74C22×D101—22no—
75C22×D101—28no—
76C22×D101—44no—
77C22×D101—44no—
78C22×D101C2×D411yescharacteristic
79D4×C101—22no—
80D4×C101C22×C414yescomplemented
81C2×C4×C101—22no—
82C2×C4×C101—44no—
83C2×C4×C101C2×D412yes—
84C2×C4×C101C2411yescharacteristic
85C22⋊D101—28no—
86C2×Dic101—22no—
87C2×Dic101—44no—
88C2×Dic101C2×D412yes—
89C2×Dic101C2×D411yescharacteristic
90D404—22no—
91D404C22×C414yescomplemented
92C4×D101—24no—
93C4×D101—44no—
94C4×D101—44no—
95C4×D101—44no—
96C4×D101C22×C412yes—
97C4×D101#4112yes—
98C8×C101—21no—
99C8×C101C22×C412yescomplemented
100#11717579—21no—
101#11717579C22×C412yescomplemented
102C22×C101—24no—
103C22×C101—42no—
104C22×C101—42no—
105C22×C101C22×D411yescharacteristic
106C2×D101—24no—
107C2×D101—42no—
108C2×D101—42no—
109C2×D101—416no—
110C2×D101C4×D412yes—
111C2×D101AGL(1,ℤ/8)14yes—
112C4×C101—22no—
113C4×C101—42no—
114C4×C101C23×C411yescharacteristic
115C4×C101C2×#4111yescharacteristic
116Dic101—22no—
117Dic101—42no—
118Dic101C4×D412yes—
119C2×C101—44no—
120C2×C101C2×C4×D411yescharacteristic
121C2×C101C2×AGL(1,ℤ/8)12yes—
122D101—44no—
123D101#44214yesdirect product factor
124C2×#442—1011nomaximal, Sylow
125C101C2×#44211yescharacteristic, complemented, Sylow
126C22×D8—1011no—
127C2×C4×D4—1012no—
128#442—1011no—
129#442—1012no—
130#442—1011no—
131#442—1012no—
132#442—1011no—
133#442D10111yescharacteristic, direct product factor
134C2×#106—1011no—
135C2×#102—1012no—
136C2×#97—1011no—
137C22×D4—1012no—
138C23×C4—2022no—
139C2×D8—1012no—
140C2×D8—1018no—
141C2×D8—1011no—
142C2×D8C2×D10111yescharacteristic
143C22×C8—1011no—
144C22×C8—1011no—
145C4×D4—1012no—
146C4×D4—1012no—
147C4×D4—1012no—
148C4×D4—2022no—
149C4×D4—2022no—
150C4×D4C2×D10112yescomplemented
151C2×C4⋊C4—1012no—
152C2×C22⋊C4—2022no—
153C2×C42—1011no—
154#106—1011no—
155#106—1012no—
156#106C2×D10111yescharacteristic, complemented
157#102—1012no—
158#102—1012no—
159#102—1012no—
160#102C2×D10112yescomplemented
161#97—1011no—
162#97—1011no—
163#97—1011no—
164#97C2×D10111yescharacteristic, complemented
165C24—2022no—
166C2×D4—1018no—
167C2×D4—1012no—
168C2×D4—2024no—
169C2×D4—2022no—
170C2×D4C22×D10112yes—
171C22×C4—22no—
172C22×C4—1011no—
173C22×C4—1012no—
174C22×C4—4048no—
175C22×C4—2022no—
176C22×C4—2022no—
177C22×C4—2022no—
178C22×C4—2022no—
179D8—1018no—
180D8—1014no—
181D8C4×D10114yescomplemented
182C2×C8—1011no—
183C2×C8—1014no—
184C2×C8—1011no—
185C2×C8—2022no—
186C2×C8C22×D10111yescharacteristic
187C2×C8C22×D10111yescharacteristic
188C4⋊C4—1012no—
189C4⋊C4—2022no—
190C4⋊C4C22×D10112yes—
191C22⋊C4—22no—
192C22⋊C4—2022no—
193C22⋊C4—2022no—
194C22⋊C4—2022no—
195C42—1012no—
196C42—1011no—
197C42C22×D10111yescharacteristic
198C23—22no—
199C23—1011no—
200C23—4044no—
201C23—4044no—
202C23—2028no—
203C23—2022no—
204D4—22no—
205D4—1014no—
206D4—2028no—
207D4—2022no—
208D4C2×C4×D10114yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—1011no—
212C2×C4—1012no—
213C2×C4—1012no—
214C2×C4—1012no—
215C2×C4—4044no—
216C2×C4—4044no—
217C2×C4—4044no—
218C2×C4—4044no—
219C2×C4—2024no—
220C2×C4—2022no—
221C2×C4D4×D10112yes—
222C2×C4C23×D10111yescharacteristic
223C8—21no—
224C8—1012no—
225C8—2021no—
226C8C2×C4×D10112yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—1012no—
231C22—1014no—
232C22—40416no—
233C22—4042no—
234C22—4042no—
235C22—2024no—
236C22C2×D4×D10111yescharacteristic
237C4—22no—
238C4—42no—
239C4—1012no—
240C4—4042no—
241C4—2022no—
242C4C22×C4×D10111yescharacteristic
243C4#41×D10111yescharacteristic
244C2—44no—
245C2—1014no—
246C2—4044no—
247C2C4×D4×D10111yescharacteristic
248C2AGL(1,ℤ/8)×D10112yes—
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
hypocenterC101C2×#442
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. C4×D4×D101C2semidirect
3. #20265290C2semidirect
4. #20265289C2semidirect
5. #20265288C2semidirect
6. #20265287C2semidirect
7. #20265286C2semidirect
8. #106×D101C2semidirect
9. #102×D101C2semidirect
10. #97×D101C2semidirect
11. #442×C101C2semidirect
16. D8×D101C4semidirect
19. C4×D404C22semidirect
20. D4×Dic101C22semidirect
21. #15692217C22semidirect
27. #15692187C22semidirect
28. #15692186C22semidirect
29. #15692177C22semidirect
30. #15692176C22semidirect
31. #15692175C22semidirect
32. #15692166C22semidirect
33. #15692165C22semidirect
34. #15692165C22semidirect
36. C4×D4×C101C22semidirect
37. #106×C101C22semidirect
38. #102×C101C22semidirect
39. #97×C101C22semidirect
44. D4×D101C2×C4semidirect
52. D808C2×C4semidirect
53. #13108059C2×C4semidirect
57. C8×D101C2×C4semidirect
67. D8×C101C2×C4semidirect
80. D4×C101C22×C4semidirect
91. D404C22×C4semidirect
99. C8×C101C22×C4semidirect
101. #11717579C22×C4semidirect
123. D101#442direct (N × H)
125. C101C2×#442semidirect
133. #442D101direct (N × H)
150. C4×D4C2×D101semidirect
156. #106C2×D101semidirect
160. #102C2×D101semidirect
164. #97C2×D101semidirect
181. D8C4×D101semidirect
208. D4C2×C4×D101semidirect
226. C8C2×C4×D101semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1012
C4×D4×D1012
#202652902
#202652892
#202652882
#202652872
#202652862
#106×D1012
#102×D1012
#97×D1012
#442×C1012
C2×#442101