Finite Group Databasebeta

← #27182932

Subgroups — #27182932

Order 12928.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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#20265982C212yesmaximal, complemented
2#20265979C212yesmaximal, complemented
3#20265554C211yesmaximal, characteristic, complemented
4#20265448C212yesmaximal, complemented
5#20265447C212yesmaximal, complemented
6#20265346C214yesmaximal, complemented
7#20265295C211yesmaximal, characteristic, complemented
8#443×C101C211yesmaximal, characteristic, complemented
9#15692301C2214yescomplemented
10#15692283—24no—
11#15692283C2214yescomplemented
12#15692282—24no—
13#15692280C2214yescomplemented
14#15692278—22no—
15#15692277—22no—
16#15692277C2211yescharacteristic
17C2×D808—22no—
18C2×D808C2212yescomplemented
19C2×D808C2212yescomplemented
20D8×D101—22no—
21#15692261C2212yescomplemented
22#15692252C2212yescomplemented
23#15692191C2211yescharacteristic, complemented
24#15692183C2212yescomplemented
25#15692171C2214yescomplemented
26#135×C101C2211yescharacteristic
27#131×C101C2212yescomplemented
28#108×C101C2211yescharacteristic, complemented
29#104×C101C2212yescomplemented
30C4×C8×C101C2211yescharacteristic, complemented
31#13108075—24no—
32#13108074—24no—
33#13108074C2312yes—
34C2×D404—24no—
35C2×D404—42no—
36C2×D404C2314yes—
37D4×D101—24no—
38D4×D101—44no—
39Dic404D411yescharacteristic, complemented
40#13108063—24no—
41#13108063D412yescomplemented
42#13108061—24no—
43D808—24no—
44D808—22no—
45D808—22no—
46D808—22no—
47D808—22no—
48D808D411yescharacteristic, complemented
49#13108059—24no—
50#13108058C2312yes—
51#13108057—22no—
52C8×D101—22no—
53#41×C101C2312yes—
54Q16×C101D411yescharacteristic, complemented
55SD16×C101D412yescomplemented
56D8×C101D411yescharacteristic, complemented
57M16×C101—22no—
58M16×C101C2312yes—
59C2×C8×C101—22no—
60C2×C8×C101C2311yescharacteristic
61C2×C8×C101C2311yescharacteristic
62C42×C101C2311yescharacteristic
63C22×D101—24no—
64C22×D101—44no—
65Q8×C101C2×D412yes—
66D4×C101—22no—
67D4×C101C2×D412yes—
68C2×C4×C101—21no—
69C2×C4×C101—22no—
70C2×C4×C101C2411yescharacteristic
71C22⋊D101—22no—
72C22⋊D101—44no—
73D404—24no—
74D404—24no—
75D404—44no—
76D404—84no—
77D404C2×D412yes—
78C4×D101—22no—
79C4×D101—44no—
80Dic202C2×D412yes—
81C8×C101—22no—
82C8×C101C2×D411yescharacteristic
83C8×C101C2×D411yescharacteristic
84C8×C101C2×D411yescharacteristic
85C8×C101C2×D411yescharacteristic
86#11717579—22no—
87C22×C101—22no—
88C22×C101H(5,𝔽2)11yescharacteristic
89C2×D101—22no—
90C2×D101—44no—
91C2×D101—84no—
92C2×D101—164no—
93C4×C101—22no—
94C4×C101—22no—
95C4×C101C22×D411yescharacteristic
96C4×C101C22×D411yescharacteristic
97Dic101—22no—
98C2×C101—21no—
99C2×C101—42no—
100C2×C101D4211yescharacteristic
101D101—42no—
102D101—84no—
103#3292—1011nomaximal, Sylow
104C101#329211yescharacteristic, complemented, Sylow
105#576—1012no—
106#576—1012no—
107#493—1011no—
108#472—1012no—
109#472—1012no—
110#453—1014no—
111#443—1011no—
112#443D10111yescharacteristic, complemented
113H(5,𝔽2)—1014no—
114AGL(1,ℤ/8)—1014no—
115AGL(1,ℤ/8)—1014no—
116AGL(1,ℤ/8)—2024no—
117AGL(1,ℤ/8)—2024no—
118#135—1011no—
119#135—2022no—
120#135—2022no—
121#135C2×D10111yescharacteristic
122C2×D8—1012no—
123C2×D8—1012no—
124C2×D8—2022no—
125C2×D8—2022no—
126#131—1012no—
127#131C2×D10112yescomplemented
128#127—1012no—
129#108—1011no—
130#108C2×D10111yescharacteristic, complemented
131#104—1012no—
132#104C2×D10112yescomplemented
133#100—1014no—
134C4×C8C2×D10111yescharacteristic, complemented
135#41—1012no—
136#41—2024no—
137#41—2024no—
138#41C22×D10112yes—
139C2×D4—1014no—
140C2×D4—4042no—
141C2×D4—4044no—
142C2×D4—2024no—
143C2×D4—2024no—
144Q16—1011no—
145Q16D40411yescharacteristic, complemented
146SD16—1012no—
147SD16—2024no—
148SD16—2024no—
149SD16D40412yescomplemented
150D8—1011no—
151D8—2024no—
152D8—2024no—
153D8—2022no—
154D8—2022no—
155D8—2022no—
156D8—2022no—
157D8D40411yescharacteristic, complemented
158M16—22no—
159M16—1012no—
160M16—2022no—
161M16C22×D10112yes—
162C2×C8—22no—
163C2×C8—2022no—
164C2×C8C22×D10111yescharacteristic
165C2×C8C22×D10111yescharacteristic
166C42C22×D10111yescharacteristic
167C23—4044no—
168C23—2024no—
169Q8—1012no—
170Q8C2×D40412yes—
171D4—22no—
172D4—8084no—
173D4—1012no—
174D4—4044no—
175D4—4044no—
176D4—2022no—
177D4—2024no—
178D4—2024no—
179D4C2×D40412yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—4044no—
183C2×C4—2022no—
184C2×C4C23×D10111yescharacteristic
185C8—22no—
186C8—2022no—
187C8D4×D10111yescharacteristic
188C8D4×D10111yescharacteristic
189C8C2×D40411yescharacteristic
190C8C2×D40411yescharacteristic
191C22—22no—
192C22—8084no—
193C22—16164no—
194C22—4044no—
195C22—2022no—
196C22#1569230111yescharacteristic
197C4—22no—
198C4—22no—
199C4—2022no—
200C4C2×D4×D10111yescharacteristic
201C4C22×D40411yescharacteristic
202C2—21no—
203C2—42no—
204C2—8084no—
205C2—4042no—
206C2D4×D40411yescharacteristic
subgroupG/H
centerC2D4×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#443×C101C2
socleC2×C101D42
hypercenter#443D101
hypocenterC101#3292
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #20265982C2semidirect
2. #20265979C2semidirect
3. #20265554C2semidirect
4. #20265448C2semidirect
5. #20265447C2semidirect
6. #20265346C2semidirect
7. #20265295C2semidirect
8. #443×C101C2semidirect
9. #15692301C22semidirect
11. #15692283C22semidirect
13. #15692280C22semidirect
18. C2×D808C22semidirect
19. C2×D808C22semidirect
21. #15692261C22semidirect
22. #15692252C22semidirect
23. #15692191C22semidirect
24. #15692183C22semidirect
25. #15692171C22semidirect
27. #131×C101C22semidirect
28. #108×C101C22semidirect
29. #104×C101C22semidirect
30. C4×C8×C101C22semidirect
39. Dic404D4semidirect
41. #13108063D4semidirect
48. D808D4semidirect
54. Q16×C101D4semidirect
55. SD16×C101D4semidirect
56. D8×C101D4semidirect
104. C101#3292semidirect
112. #443D101semidirect
127. #131C2×D101semidirect
130. #108C2×D101semidirect
132. #104C2×D101semidirect
134. C4×C8C2×D101semidirect
145. Q16D404semidirect
149. SD16D404semidirect
157. D8D404semidirect

Maximal subgroups

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

subgroupindex
#202659822
#202659792
#202655542
#202654482
#202654472
#202653462
#202652952
#443×C1012
#3292101