Finite Group Databasebeta

← #38745092

Subgroups — #38745092

Order 25216.

1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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
1C23×C4×D197C211yesmaximal, characteristic
2C2×#20263282C212yesmaximal, complemented
3#27160942C211yesmaximal, characteristic, complemented
4#27160938C214yesmaximal, complemented
5#27160934C212yesmaximal
6#27160926C214yesmaximal, complemented
7#381×C197C211yesmaximal, characteristic, complemented
8C24×D197C2211yescharacteristic
9C23×Dic197C2211yescharacteristic
10C22×C4×D197—28no—
11C22×C4×D197C418yescomplemented
12C22×C4×D197C2212yes—
13C22×C4×D197C2212yes—
14#20263282—28no—
15C2×#15691337C2214yescomplemented
16C2×C22⋊Dic197C2212yes—
17C2×#15691335C2218yes—
18C2×C4×Dic197C2214yescomplemented
19#20263233C2214yescomplemented
20C23×C4×C197C2211yescharacteristic
21C2×C22⋊C4×C197C2212yes—
22#95×C197C2214yescomplemented
23C23×D197—28no—
24C23×D197—24no—
25C23×D197C2×C414yes—
26C23×D197C2312yes—
27C22×Dic197C2×C414yes—
28C22×Dic197D418yes—
29C22×Dic197C2314yes—
30C22×Dic197C2311yescharacteristic
31C22×Dic197C2311yescharacteristic
32C2×C4×D197—232no—
33C2×C4×D197—28no—
34C2×C4×D197—28no—
35C2×C4×D197C2×C418yes—
36C2×C4×D197C2×C418yes—
37#15691337—28no—
38C22⋊Dic197—24no—
39#15691335—216no—
40C4×Dic197—28no—
41C24×C197C2311yescharacteristic
42C22×C4×C197—24no—
43C22×C4×C197C2×C414yes—
44C22×C4×C197C2314yes—
45C22×C4×C197C2312yes—
46C22⋊C4×C197—24no—
47C22×D197—232no—
48C22×D197—28no—
49C22×D197—24no—
50C22×D197—24no—
51C22×D197—216no—
52C22×D197C22×C414yes—
53C22×D197#4118yes—
54C2×Dic197—24no—
55C2×Dic197—28no—
56C2×Dic197C22⋊C4116yescomplemented
57C2×Dic197C22×C412yes—
58C2×Dic197C22×C412yes—
59C2×Dic197C2×D414yes—
60C2×Dic197C2×D414yes—
61C4×D197—216no—
62C4×D197—216no—
63C23×C197—24no—
64C23×C197C22×C412yes—
65C23×C197C2×D414yes—
66C23×C197C2411yescharacteristic
67C2×C4×C197—28no—
68C2×C4×C197—24no—
69C2×C4×C197—24no—
70C2×C4×C197—28no—
71C2×C4×C197C22×C414yes—
72C22×C197—24no—
73C22×C197—28no—
74C22×C197C2×C22⋊C414yes—
75C22×C197C23×C411yescharacteristic
76C22×C197C22×D412yes—
77C22×C197C2×#4114yes—
78C2×D197—232no—
79C2×D197—24no—
80C2×D197—24no—
81C2×D197—216no—
82C2×D197#11718yescomplemented
83C4×C197—24no—
84C4×C197—44no—
85Dic197—44no—
86Dic197C2×C22⋊C414yes—
87Dic197C2×C22⋊C414yes—
88C2×C197—24no—
89C2×C197C22×C22⋊C411yescharacteristic
90C2×C197C2×#11712yes—
91C2×C197#52514yes—
92D197—28no—
93C197#228011yescharacteristic, complemented, Sylow
94#2280—1971nomaximal, Sylow
95C24×C4—1971no—
96C2×#117—1972no—
97#381—1971no—
98#381D19711yescharacteristic, complemented
99#380—1974no—
100#379—1972no—
101C4×C22⋊C4—1974no—
102C25—1971no—
103C23×C4—3948no—
104C23×C4—1978no—
105C23×C4—1972no—
106C23×C4—1972no—
107C23×C4—1971no—
108C23×C4C2×D19711yescharacteristic
109#117—3948no—
110C2×C4⋊C4—1974no—
111C2×C22⋊C4—1972no—
112C2×C22⋊C4—1978no—
113C2×C22⋊C4C2×D19712yes—
114C2×C42—1974no—
115#95—1974no—
116#95C2×D19714yescomplemented
117C24—3948no—
118C24—3944no—
119C24—1974no—
120C24—1972no—
121C24C22×D19711yescharacteristic
122C22×C4—24no—
123C22×C4—39432no—
124C22×C4—3948no—
125C22×C4—3948no—
126C22×C4—1974no—
127C22×C4—1978no—
128C22×C4—1978no—
129C22×C4—1974no—
130C22×C4—1978no—
131C22×C4—1971no—
132C22×C4—1971no—
133C22×C4C4×D19714yes—
134C22×C4C22×D19714yes—
135C22×C4C22×D19712yes—
136C4⋊C4—3948no—
137C22⋊C4—24no—
138C22⋊C4—39416no—
139C22⋊C4—3944no—
140C42—3948no—
141C23—24no—
142C23—39432no—
143C23—39416no—
144C23—3948no—
145C23—3944no—
146C23—3944no—
147C23—1974no—
148C23—1978no—
149C23C2×C4×D19712yes—
150C23D4×D19714yes—
151C23C23×D19711yescharacteristic
152C2×C4—28no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—39416no—
157C2×C4—39416no—
158C2×C4—3944no—
159C2×C4—3948no—
160C2×C4—19716no—
161C2×C4—1972no—
162C2×C4—1972no—
163C2×C4—1974no—
164C2×C4—1974no—
165C2×C4C2×C4×D19714yes—
166C22—24no—
167C22—28no—
168C22—39432no—
169C22—3944no—
170C22—3944no—
171C22—39416no—
172C22—1978no—
173C22C22⋊C4×D19714yes—
174C22C22×C4×D19711yescharacteristic
175C22C2×D4×D19712yes—
176C22#41×D19714yes—
177C4—24no—
178C4—44no—
179C4—7884no—
180C4—1974no—
181C4—1974no—
182C2—24no—
183C2—3948no—
184C2C2×C22⋊C4×D19711yescharacteristic
185C2#117×D19712yes—
186C2#2716158714yes—
subgroupG/H
center, FrattiniC23C23×D197
commutatorC22×C197C23×C4
Fitting#381×C197C2
socle, cosocleC23×C197C24
prime radicalC24×D197C22
hypercenter#381D197
hypocenterC197#2280
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#20263282C2semidirect
3. #27160942C2semidirect
4. #27160938C2semidirect
6. #27160926C2semidirect
7. #381×C197C2semidirect
11. C22×C4×D197C4semidirect
15. C2×#15691337C22semidirect
18. C2×C4×Dic197C22semidirect
19. #20263233C22semidirect
22. #95×C197C22semidirect
56. C2×Dic197C22⋊C4semidirect
82. C2×D197#117semidirect
93. C197#2280semidirect
98. #381D197semidirect
116. #95C2×D197semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1972
C2×#202632822
#271609422
#271609382
#271609342
#271609262
#381×C1972
#2280197