Finite Group Databasebeta

← #38751343

Subgroups — #38751343

Order 25216.

484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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
1C2×C42×D197C211yesmaximal, characteristic
2#27161134C214yesmaximal, complemented
3#27161130C214yesmaximal, complemented
4#27161102C212yesmaximal, complemented
5#27161042C212yesmaximal
6C4×#15691342C211yesmaximal, characteristic, complemented
7C4×M16×C197C211yesmaximal, characteristic, complemented
8C22×C4×D197C412yes—
9C22×C4×D197C2211yescharacteristic
10C2×#15691342C2212yes—
11C2×C4×Dic197C412yes—
12C2×C4×Dic197C2211yescharacteristic
13C42×D197C412yes—
14C42×D197C412yes—
15C42×D197C2212yes—
16C42×D197C2212yes—
17#20263255C2218yescomplemented
18#20263238C2218yes—
19#20263237C2212yescomplemented
20C4×#13096802C2212yescomplemented
21C2×M16×C197C2212yes—
22C2×C42×C197C2211yescharacteristic
23#97×C197C2212yescomplemented
24C4×C8×C197C2212yescomplemented
25C23×D197C2×C411yescharacteristic
26C22×Dic197C2×C411yescharacteristic
27C22×Dic197C2×C412yes—
28C2×C4×D197—28no—
29C2×C4×D197—24no—
30C2×C4×D197C2×C412yes—
31C2×C4×D197C2×C412yes—
32C2×C4×D197C2×C412yes—
33C2×C4×D197C2×C412yes—
34C2×C4×D197C2×C412yes—
35C2×C4×D197C2312yes—
36#15691342—24no—
37C2×#13096802C2314yes—
38C4×Dic197C2×C411yescharacteristic
39C4×Dic197C2×C411yescharacteristic
40C4×Dic197C2×C412yes—
41C4×Dic197C2×C412yes—
42C4×Dic197C2×C412yes—
43C4×Dic197C2×C412yes—
44C4×Dic197C2312yes—
45C22×C4×C197C2×C412yes—
46C22×C4×C197C2311yescharacteristic
47M16×C197—24no—
48C2×C8×C197C2314yes—
49C42×C197C2×C412yes—
50C42×C197C2311yescharacteristic
51C42×C197C2311yescharacteristic
52C22×D197—22no—
53C22×D197—24no—
54C22×D197C22×C412yes—
55C2×Dic197—22no—
56C2×Dic197—24no—
57C2×Dic197C22×C412yes—
58C2×Dic197C22×C412yes—
59C2×Dic197C22×C412yes—
60C4×D197—24no—
61C4×D197—24no—
62C4×D197—24no—
63C4×D197—24no—
64C4×D197—24no—
65C4×D197M1618yescomplemented
66#13096802—24no—
67C23×C197C22×C411yescharacteristic
68C2×C4×C197—24no—
69C2×C4×C197C22×C412yes—
70C2×C4×C197C22×C411yescharacteristic
71C2×C4×C197C22×C412yes—
72C2×C4×C197#4114yes—
73C2×C4×C197C2411yescharacteristic
74C8×C197—24no—
75C22×C197—22no—
76C22×C197#11712yes—
77C22×C197C23×C411yescharacteristic
78C2×D197—28no—
79C2×D197—22no—
80C2×D197—22no—
81C2×D197C2×M1614yes—
82C4×C197—22no—
83C4×C197#11712yes—
84C4×C197C2×M1614yes—
85C4×C197C2×#4112yes—
86Dic197—22no—
87Dic197—22no—
88Dic197C2×M1614yes—
89C2×C197—22no—
90C2×C197C2×#11711yescharacteristic
91C2×C197C22×M1612yes—
92D197—24no—
93C197#292011yescharacteristic, complemented, Sylow
94#2920—1971nomaximal, Sylow
95C22×C42—1971no—
96#432—1974no—
97#431—1974no—
98#423—1972no—
99#407—1972no—
100C4×M16—1971no—
101C4×M16D19711yescharacteristic, complemented
102C23×C4—1972no—
103C23×C4—1971no—
104C2×M16—1972no—
105C2×M16C2×D19712yes—
106C2×C42—1972no—
107C2×C42—1971no—
108C2×C42—1972no—
109C2×C42—1972no—
110C2×C42—1972no—
111C2×C42—1972no—
112C2×C42C2×D19711yescharacteristic
113C4⋊C8—1978no—
114C22⋊C8—1978no—
115#97—1972no—
116#97C2×D19712yescomplemented
117C4×C8—1972no—
118C4×C8C2×D19712yescomplemented
119C24—1971no—
120C22×C4—3948no—
121C22×C4—3944no—
122C22×C4—1971no—
123C22×C4—1972no—
124C22×C4—1972no—
125C22×C4—1972no—
126C22×C4—1972no—
127C22×C4—1972no—
128C22×C4—1972no—
129C22×C4—1972no—
130C22×C4C4×D19712yes—
131C22×C4C22×D19711yescharacteristic
132M16—24no—
133M16—3944no—
134C2×C8—1974no—
135C2×C8C22×D19714yes—
136C42—1972no—
137C42—1971no—
138C42—1972no—
139C42—1972no—
140C42—1972no—
141C42—1971no—
142C42—1972no—
143C42C4×D19712yes—
144C42C22×D19711yescharacteristic
145C42C22×D19711yescharacteristic
146C23—3944no—
147C23—3942no—
148C23—1972no—
149C23C2×C4×D19711yescharacteristic
150C2×C4—24no—
151C2×C4—3944no—
152C2×C4—3944no—
153C2×C4—3942no—
154C2×C4—3944no—
155C2×C4—3944no—
156C2×C4—3944no—
157C2×C4—3944no—
158C2×C4—1972no—
159C2×C4—1972no—
160C2×C4—1972no—
161C2×C4—1978no—
162C2×C4C2×C4×D19712yes—
163C2×C4C2×C4×D19711yescharacteristic
164C2×C4C2×C4×D19712yes—
165C2×C4#1569135814yes—
166C2×C4C23×D19711yescharacteristic
167C8—24no—
168C8—3944no—
169C22—22no—
170C22—3948no—
171C22—3942no—
172C22—3942no—
173C22—1974no—
174C22#2026328312yes—
175C22C22×C4×D19711yescharacteristic
176C4—22no—
177C4—3942no—
178C4—3942no—
179C4—1974no—
180C4#2026328312yes—
181C4M16×D19714yes—
182C4C2×#1569135812yes—
183C2—22no—
184C2—3944no—
185C2C2×#2026328311yescharacteristic
186C2C2×M16×D19712yes—
subgroupG/H
centerC42C22×D197
commutator, socleC22×C197C23×C4
FrattiniC2×C4C23×D197
FittingC4×M16×C197C2
prime radicalC23×D197C2×C4
cosocleC2×C4×C197C24
hypercenterC4×M16D197
hypocenterC197#2920
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #27161134C2semidirect
3. #27161130C2semidirect
4. #27161102C2semidirect
6. C4×#15691342C2semidirect
7. C4×M16×C197C2semidirect
17. #20263255C22semidirect
19. #20263237C22semidirect
20. C4×#13096802C22semidirect
23. #97×C197C22semidirect
24. C4×C8×C197C22semidirect
65. C4×D197M16semidirect
93. C197#2920semidirect
101. C4×M16D197semidirect
116. #97C2×D197semidirect
118. C4×C8C2×D197semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D1972
#271611342
#271611302
#271611022
#271610422
C4×#156913422
C4×M16×C1972
#2920197