Finite Group Databasebeta

← #27181505

Subgroups — #27181505

Order 12928.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#20265733C211yesmaximal, characteristic, complemented
2#127×D101C211yesmaximal, characteristic
3#20265543C211yesmaximal, characteristic, complemented
4#20265542C211yesmaximal, characteristic, complemented
5#20265541C211yesmaximal, characteristic, complemented
6#20265522C214yesmaximal, complemented
7#20265180C214yesmaximal, complemented
8#20265129C211yesmaximal, characteristic, complemented
9#490×C101C211yesmaximal, characteristic, complemented
10C2×D4×D101—22no—
11C2×D4×D101C2212yes—
12C2×#13108057C2212yes—
13#15692254C2212yescomplemented
14#15692252C2211yescharacteristic
15#15692251—22no—
16#15692251C2212yes—
17#15692247C2211yescharacteristic, complemented
18#15692233—22no—
19#15692220—22no—
20#15692213C2212yes—
21C42×D101C2211yescharacteristic
22#15692177C2214yescomplemented
23#15692176C2214yescomplemented
24#15692175C2214yescomplemented
25#15692166C2211yescharacteristic, complemented
26C8×Dic101C2212yescomplemented
27#127×C101C2211yescharacteristic
28#125×C101C2211yescharacteristic, complemented
29#102×C101C2214yescomplemented
30#97×C101C2211yescharacteristic, complemented
31C23×D101—22no—
32C2×Dic202—22no—
33C2×D404—22no—
34C2×D404C2312yes—
35C2×C22⋊D101—24no—
36C2×C22⋊D101—22no—
37D4×D101—28no—
38D4×D101—48no—
39C2×C4×D101D412yes—
40C2×C4×D101C2311yescharacteristic
41#13108057—24no—
42C2×#11717579C2312yes—
43C4⋊Dic101C2312yes—
44#13108053—22no—
45#13108053—22no—
46#13108051—22no—
47C4×Dic101—22no—
48C4×Dic101D412yes—
49C4×Dic101C2311yescharacteristic
50C2×D4×C101—22no—
51C2×D4×C101C2312yes—
52C2×C8×C101C2312yes—
53C4⋊C4×C101—22no—
54C4⋊C4×C101C2312yes—
55C42×C101C2311yescharacteristic
56C23×C101—22no—
57C22×D101—22no—
58C22×D101—48no—
59C22×D101—44no—
60C22×D101C2×D411yescharacteristic
61D4×C101—24no—
62D4×C101—44no—
63C2×C4×C101—22no—
64C2×C4×C101C2×D412yes—
65C2×C4×C101C2411yescharacteristic
66C22⋊D101—44no—
67C22⋊D101—48no—
68C2×Dic101—22no—
69C2×Dic101C2×D411yescharacteristic
70C2×Dic101C2×D412yes—
71D404—24no—
72D404—44no—
73C4×D101—24no—
74C4×D101#4114yes—
75Dic202—44no—
76C8×C101—22no—
77#11717579—22no—
78C22×C101—42no—
79C22×C101—44no—
80C22×C101C22×D411yescharacteristic
81C2×D101—22no—
82C2×D101—42no—
83C2×D101—44no—
84C2×D101—88no—
85C2×D101#12412yes—
86C4×C101—22no—
87C4×C101—42no—
88C4×C101C2×#4112yes—
89Dic101—42no—
90Dic101#12412yes—
91Dic101AGL(1,ℤ/8)14yes—
92C2×C101—82no—
93C2×C101C2×#12411yescharacteristic
94C2×C101C2×AGL(1,ℤ/8)12yes—
95D101—22no—
96D101—82no—
97#3138—1011nomaximal, Sylow
98C101#313811yescharacteristic, complemented, Sylow
99#533—1011no—
100C2×#127—1011no—
101#490—1011no—
102#490—1011no—
103#490—1011no—
104#490D10111yescharacteristic, complemented
105#486—1014no—
106#418—1014no—
107C4×M16—1011no—
108C22×D4—1012no—
109C22×D4—2022no—
110C2×M16—1012no—
111C4⋊Q8—1012no—
112#127—1012no—
113#127—1011no—
114#127—2022no—
115#127C2×D10111yescharacteristic
116#125—1011no—
117#125C2×D10111yescharacteristic, complemented
118C22⋊Q8—2022no—
119C4×Q8—2022no—
120#117—1012no—
121C2×C42—1011no—
122#102—1014no—
123#102—1014no—
124#102—1014no—
125#102C2×D10114yescomplemented
126#97—1011no—
127#97C2×D10111yescharacteristic, complemented
128C4×C8—1012no—
129C24—2022no—
130C2×Q8—2022no—
131C2×D4—22no—
132C2×D4—1012no—
133C2×D4—4048no—
134C2×D4—2028no—
135C2×D4—2024no—
136C2×D4—2022no—
137C2×D4—2022no—
138C2×D4C22×D10112yes—
139C22×C4—1011no—
140C22×C4—1012no—
141M16—2024no—
142C2×C8—1012no—
143C2×C8C22×D10112yes—
144C4⋊C4—22no—
145C4⋊C4—1012no—
146C4⋊C4—2022no—
147C4⋊C4—2022no—
148C4⋊C4C22×D10112yes—
149C22⋊C4—2022no—
150C42—1012no—
151C42—1011no—
152C42—2022no—
153C42C22×D10111yescharacteristic
154C23—22no—
155C23—1011no—
156C23—4044no—
157C23—4048no—
158C23—2022no—
159Q8—4044no—
160D4—24no—
161D4—44no—
162D4—4044no—
163D4—4048no—
164D4—4044no—
165D4—2024no—
166C2×C4—22no—
167C2×C4—1011no—
168C2×C4—1012no—
169C2×C4—1014no—
170C2×C4—2024no—
171C2×C4—2022no—
172C2×C4D4×D10112yes—
173C2×C4C23×D10111yescharacteristic
174C8—22no—
175C8—2022no—
176C22—42no—
177C22—44no—
178C22—8088no—
179C22—1012no—
180C22—4042no—
181C22—4044no—
182C22—2022no—
183C22C2×D4×D10111yescharacteristic
184C4—22no—
185C4—42no—
186C4—1012no—
187C4—1014no—
188C4—4042no—
189C4#41×D10112yes—
190C2—82no—
191C2—8082no—
192C2—2022no—
193C2#124×D10111yescharacteristic
194C2AGL(1,ℤ/8)×D10112yes—
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#490×C101C2
socleC22×C101C22×D4
prime radical#127×D101C2
hypercenter#490D101
hypocenterC101#3138
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #20265733C2semidirect
3. #20265543C2semidirect
4. #20265542C2semidirect
5. #20265541C2semidirect
6. #20265522C2semidirect
7. #20265180C2semidirect
8. #20265129C2semidirect
9. #490×C101C2semidirect
13. #15692254C22semidirect
17. #15692247C22semidirect
22. #15692177C22semidirect
23. #15692176C22semidirect
24. #15692175C22semidirect
25. #15692166C22semidirect
26. C8×Dic101C22semidirect
28. #125×C101C22semidirect
29. #102×C101C22semidirect
30. #97×C101C22semidirect
98. C101#3138semidirect
104. #490D101semidirect
117. #125C2×D101semidirect
125. #102C2×D101semidirect
127. #97C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202657332
#127×D1012
#202655432
#202655422
#202655412
#202655222
#202651802
#202651292
#490×C1012
#3138101