Finite Group Databasebeta

← #38753085

Subgroups — #38753085

Order 25216.

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#27161635C211yesmaximal, characteristic, complemented
2#127×D197C211yesmaximal, characteristic
3#27161445C211yesmaximal, characteristic, complemented
4#27161444C211yesmaximal, characteristic, complemented
5#27161443C211yesmaximal, characteristic, complemented
6#27161424C214yesmaximal, complemented
7#27161082C214yesmaximal, complemented
8#27161031C211yesmaximal, characteristic, complemented
9#490×C197C211yesmaximal, characteristic, complemented
10C2×D4×D197—22no—
11C2×D4×D197C2212yes—
12C2×#15691341C2212yes—
13#20263325C2212yescomplemented
14#20263323C2211yescharacteristic
15#20263322—22no—
16#20263322C2212yes—
17#20263318C2211yescharacteristic, complemented
18#20263304—22no—
19#20263291—22no—
20#20263284C2212yes—
21C42×D197C2211yescharacteristic
22#20263248C2214yescomplemented
23#20263247C2214yescomplemented
24#20263246C2214yescomplemented
25#20263237C2211yescharacteristic, complemented
26C8×Dic197C2212yescomplemented
27#127×C197C2211yescharacteristic
28#125×C197C2211yescharacteristic, complemented
29#102×C197C2214yescomplemented
30#97×C197C2211yescharacteristic, complemented
31C23×D197—22no—
32C2×Dic394—22no—
33C2×D788—22no—
34C2×D788C2312yes—
35C2×C22⋊D197—22no—
36C2×C22⋊D197—24no—
37D4×D197—28no—
38D4×D197—48no—
39C2×C4×D197D412yes—
40C2×C4×D197C2311yescharacteristic
41#15691341—24no—
42C2×#13096802C2312yes—
43C4⋊Dic197C2312yes—
44#15691337—22no—
45#15691337—22no—
46#15691335—22no—
47C4×Dic197—22no—
48C4×Dic197D412yes—
49C4×Dic197C2311yescharacteristic
50C2×D4×C197—22no—
51C2×D4×C197C2312yes—
52C2×C8×C197C2312yes—
53C4⋊C4×C197—22no—
54C4⋊C4×C197C2312yes—
55C42×C197C2311yescharacteristic
56C22×D197—22no—
57C22×D197—48no—
58C22×D197—44no—
59C22×D197C2×D411yescharacteristic
60Dic394—44no—
61D788—24no—
62D788—44no—
63C22⋊D197—44no—
64C22⋊D197—48no—
65C2×Dic197—22no—
66C2×Dic197C2×D411yescharacteristic
67C2×Dic197C2×D412yes—
68C4×D197—24no—
69C4×D197#4114yes—
70#13096802—22no—
71C23×C197—22no—
72D4×C197—24no—
73D4×C197—44no—
74C2×C4×C197—22no—
75C2×C4×C197C2×D412yes—
76C2×C4×C197C2411yescharacteristic
77C8×C197—22no—
78C22×C197—42no—
79C22×C197—44no—
80C22×C197C22×D411yescharacteristic
81C2×D197—22no—
82C2×D197—42no—
83C2×D197—44no—
84C2×D197—88no—
85C2×D197#12412yes—
86C4×C197—22no—
87C4×C197—42no—
88C4×C197C2×#4112yes—
89Dic197—42no—
90Dic197#12412yes—
91Dic197AGL(1,ℤ/8)14yes—
92C2×C197—82no—
93C2×C197C2×#12411yescharacteristic
94C2×C197C2×AGL(1,ℤ/8)12yes—
95D197—22no—
96D197—82no—
97C197#313811yescharacteristic, complemented, Sylow
98#3138—1971nomaximal, Sylow
99#533—1971no—
100C2×#127—1971no—
101#490—1971no—
102#490—1971no—
103#490—1971no—
104#490D19711yescharacteristic, complemented
105#486—1974no—
106#418—1974no—
107C4×M16—1971no—
108C22×D4—3942no—
109C22×D4—1972no—
110C2×M16—1972no—
111C4⋊Q8—1972no—
112#127—3942no—
113#127—1972no—
114#127—1971no—
115#127C2×D19711yescharacteristic
116#125—1971no—
117#125C2×D19711yescharacteristic, complemented
118C22⋊Q8—3942no—
119C4×Q8—3942no—
120#117—1972no—
121C2×C42—1971no—
122#102—1974no—
123#102—1974no—
124#102—1974no—
125#102C2×D19714yescomplemented
126#97—1971no—
127#97C2×D19711yescharacteristic, complemented
128C4×C8—1972no—
129C24—3942no—
130C2×Q8—3942no—
131C2×D4—22no—
132C2×D4—7888no—
133C2×D4—3948no—
134C2×D4—3942no—
135C2×D4—3944no—
136C2×D4—3942no—
137C2×D4—1972no—
138C2×D4C22×D19712yes—
139C22×C4—1972no—
140C22×C4—1971no—
141M16—3944no—
142C2×C8—1972no—
143C2×C8C22×D19712yes—
144C4⋊C4—22no—
145C4⋊C4—3942no—
146C4⋊C4—3942no—
147C4⋊C4—1972no—
148C4⋊C4C22×D19712yes—
149C22⋊C4—3942no—
150C42—3942no—
151C42—1972no—
152C42—1971no—
153C42C22×D19711yescharacteristic
154C23—22no—
155C23—7888no—
156C23—7884no—
157C23—3942no—
158C23—1971no—
159Q8—7884no—
160D4—24no—
161D4—44no—
162D4—7884no—
163D4—7888no—
164D4—7884no—
165D4—3944no—
166C2×C4—22no—
167C2×C4—3944no—
168C2×C4—3942no—
169C2×C4—1971no—
170C2×C4—1972no—
171C2×C4—1974no—
172C2×C4D4×D19712yes—
173C2×C4C23×D19711yescharacteristic
174C8—22no—
175C8—3942no—
176C22—44no—
177C22—42no—
178C22—7884no—
179C22—7882no—
180C22—15768no—
181C22—3942no—
182C22—1972no—
183C22C2×D4×D19711yescharacteristic
184C4—22no—
185C4—42no—
186C4—7882no—
187C4—1974no—
188C4—1972no—
189C4#41×D19712yes—
190C2—82no—
191C2—15762no—
192C2—3942no—
193C2#124×D19711yescharacteristic
194C2AGL(1,ℤ/8)×D19712yes—
subgroupG/H
centerC22C2×D4×D197
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
Fitting#490×C197C2
socleC22×C197C22×D4
prime radical#127×D197C2
hypercenter#490D197
hypocenterC197#3138
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #27161635C2semidirect
3. #27161445C2semidirect
4. #27161444C2semidirect
5. #27161443C2semidirect
6. #27161424C2semidirect
7. #27161082C2semidirect
8. #27161031C2semidirect
9. #490×C197C2semidirect
13. #20263325C22semidirect
17. #20263318C22semidirect
22. #20263248C22semidirect
23. #20263247C22semidirect
24. #20263246C22semidirect
25. #20263237C22semidirect
26. C8×Dic197C22semidirect
28. #125×C197C22semidirect
29. #102×C197C22semidirect
30. #97×C197C22semidirect
97. C197#3138semidirect
104. #490D197semidirect
117. #125C2×D197semidirect
125. #102C2×D197semidirect
127. #97C2×D197semidirect

Maximal subgroups

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

subgroupindex
#271616352
#127×D1972
#271614452
#271614442
#271614432
#271614242
#271610822
#271610312
#490×C1972
#3138197