Finite Group Databasebeta

← #24919263

Subgroups — #24919263

Order 10624.

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#19128506C212yesmaximal, complemented
2#19128503C212yesmaximal, complemented
3#19128078C211yesmaximal, characteristic, complemented
4#19127972C212yesmaximal, complemented
5#19127971C212yesmaximal, complemented
6#19127870C214yesmaximal, complemented
7#19127819C211yesmaximal, characteristic, complemented
8#443×C83C211yesmaximal, characteristic, complemented
9#14581838C2214yescomplemented
10#14581820—24no—
11#14581820C2214yescomplemented
12#14581819—24no—
13#14581817C2214yescomplemented
14#14581815—22no—
15#14581814—22no—
16#14581814C2211yescharacteristic
17C2×D664—22no—
18C2×D664C2212yescomplemented
19C2×D664C2212yescomplemented
20D8×D83—22no—
21#14581798C2212yescomplemented
22#14581789C2212yescomplemented
23#14581728C2211yescharacteristic, complemented
24#14581720C2212yescomplemented
25#14581708C2214yescomplemented
26#135×C83C2211yescharacteristic
27#131×C83C2212yescomplemented
28#108×C83C2211yescharacteristic, complemented
29#104×C83C2212yescomplemented
30C4×C8×C83C2211yescharacteristic, complemented
31#13050591—24no—
32#13050590—24no—
33#13050590C2312yes—
34C2×D332—24no—
35C2×D332—42no—
36C2×D332C2314yes—
37D4×D83—24no—
38D4×D83—44no—
39Dic332D411yescharacteristic, complemented
40#13050579—24no—
41#13050579D412yescomplemented
42#13050577—24no—
43D664—24no—
44D664—22no—
45D664—22no—
46D664—22no—
47D664—22no—
48D664D411yescharacteristic, complemented
49#13050575—24no—
50#13050574C2312yes—
51#13050573—22no—
52C8×D83—22no—
53#41×C83C2312yes—
54Q16×C83D411yescharacteristic, complemented
55SD16×C83D412yescomplemented
56D8×C83D411yescharacteristic, complemented
57M16×C83—22no—
58M16×C83C2312yes—
59C2×C8×C83—22no—
60C2×C8×C83C2311yescharacteristic
61C2×C8×C83C2311yescharacteristic
62C42×C83C2311yescharacteristic
63C22×D83—24no—
64C22×D83—44no—
65Q8×C83C2×D412yes—
66D4×C83—22no—
67D4×C83C2×D412yes—
68C2×C4×C83—21no—
69C2×C4×C83—22no—
70C2×C4×C83C2411yescharacteristic
71C22⋊D83—22no—
72C22⋊D83—44no—
73D332—24no—
74D332—24no—
75D332—44no—
76D332—84no—
77D332C2×D412yes—
78C4×D83—22no—
79C4×D83—44no—
80Dic166C2×D412yes—
81C8×C83—22no—
82C8×C83C2×D411yescharacteristic
83C8×C83C2×D411yescharacteristic
84C8×C83C2×D411yescharacteristic
85C8×C83C2×D411yescharacteristic
86C83⋊C8—22no—
87C22×C83—22no—
88C22×C83H(5,𝔽2)11yescharacteristic
89C2×D83—22no—
90C2×D83—44no—
91C2×D83—84no—
92C2×D83—164no—
93C4×C83—22no—
94C4×C83—22no—
95C4×C83C22×D411yescharacteristic
96C4×C83C22×D411yescharacteristic
97Dic83—22no—
98C2×C83—21no—
99C2×C83—42no—
100C2×C83D4211yescharacteristic
101D83—42no—
102D83—84no—
103#3292—831nomaximal, Sylow
104C83#329211yescharacteristic, complemented, Sylow
105#576—832no—
106#576—832no—
107#493—831no—
108#472—832no—
109#472—832no—
110#453—834no—
111#443—831no—
112#443D8311yescharacteristic, complemented
113H(5,𝔽2)—834no—
114AGL(1,ℤ/8)—834no—
115AGL(1,ℤ/8)—834no—
116AGL(1,ℤ/8)—1664no—
117AGL(1,ℤ/8)—1664no—
118#135—831no—
119#135—1662no—
120#135—1662no—
121#135C2×D8311yescharacteristic
122C2×D8—832no—
123C2×D8—832no—
124C2×D8—1662no—
125C2×D8—1662no—
126#131—832no—
127#131C2×D8312yescomplemented
128#127—832no—
129#108—831no—
130#108C2×D8311yescharacteristic, complemented
131#104—832no—
132#104C2×D8312yescomplemented
133#100—834no—
134C4×C8C2×D8311yescharacteristic, complemented
135#41—832no—
136#41—1664no—
137#41—1664no—
138#41C22×D8312yes—
139C2×D4—3322no—
140C2×D4—3324no—
141C2×D4—834no—
142C2×D4—1664no—
143C2×D4—1664no—
144Q16—831no—
145Q16D33211yescharacteristic, complemented
146SD16—832no—
147SD16—1664no—
148SD16—1664no—
149SD16D33212yescomplemented
150D8—831no—
151D8—1664no—
152D8—1664no—
153D8—1662no—
154D8—1662no—
155D8—1662no—
156D8—1662no—
157D8D33211yescharacteristic, complemented
158M16—22no—
159M16—832no—
160M16—1662no—
161M16C22×D8312yes—
162C2×C8—22no—
163C2×C8—1662no—
164C2×C8C22×D8311yescharacteristic
165C2×C8C22×D8311yescharacteristic
166C42C22×D8311yescharacteristic
167C23—3324no—
168C23—1664no—
169Q8—832no—
170Q8C2×D33212yes—
171D4—22no—
172D4—3324no—
173D4—3324no—
174D4—832no—
175D4—6644no—
176D4—1662no—
177D4—1664no—
178D4—1664no—
179D4C2×D33212yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—3324no—
183C2×C4—1662no—
184C2×C4C23×D8311yescharacteristic
185C8—22no—
186C8—1662no—
187C8D4×D8311yescharacteristic
188C8D4×D8311yescharacteristic
189C8C2×D33211yescharacteristic
190C8C2×D33211yescharacteristic
191C22—22no—
192C22—13284no—
193C22—3324no—
194C22—6644no—
195C22—1662no—
196C22#1458183811yescharacteristic
197C4—22no—
198C4—22no—
199C4—1662no—
200C4C2×D4×D8311yescharacteristic
201C4C22×D33211yescharacteristic
202C2—21no—
203C2—42no—
204C2—3322no—
205C2—6644no—
206C2D4×D33211yescharacteristic
subgroupG/H
centerC2D4×D332
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#443×C83C2
socleC2×C83D42
hypercenter#443D83
hypocenterC83#3292
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #19128506C2semidirect
2. #19128503C2semidirect
3. #19128078C2semidirect
4. #19127972C2semidirect
5. #19127971C2semidirect
6. #19127870C2semidirect
7. #19127819C2semidirect
8. #443×C83C2semidirect
9. #14581838C22semidirect
11. #14581820C22semidirect
13. #14581817C22semidirect
18. C2×D664C22semidirect
19. C2×D664C22semidirect
21. #14581798C22semidirect
22. #14581789C22semidirect
23. #14581728C22semidirect
24. #14581720C22semidirect
25. #14581708C22semidirect
27. #131×C83C22semidirect
28. #108×C83C22semidirect
29. #104×C83C22semidirect
30. C4×C8×C83C22semidirect
39. Dic332D4semidirect
41. #13050579D4semidirect
48. D664D4semidirect
54. Q16×C83D4semidirect
55. SD16×C83D4semidirect
56. D8×C83D4semidirect
104. C83#3292semidirect
112. #443D83semidirect
127. #131C2×D83semidirect
130. #108C2×D83semidirect
132. #104C2×D83semidirect
134. C4×C8C2×D83semidirect
145. Q16D332semidirect
149. SD16D332semidirect
157. D8D332semidirect

Maximal subgroups

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

subgroupindex
#191285062
#191285032
#191280782
#191279722
#191279712
#191278702
#191278192
#443×C832
#329283