Finite Group Databasebeta

← C22×#20263288 #38755882

Subgroups — C22×#20263288 #38755882

Order 25216.

2528 conjugacy classes of subgroups; only the 941 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 941 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×D788C211yesmaximal, characteristic
2C23×C4×D197C212yesmaximal, complemented
3C2×#20263288C2124yesmaximal, direct product factor
4C22×#15691335C212yesmaximal, complemented
5C22×C4×Dic197C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C197C211yesmaximal, characteristic, complemented
7C24×D197C2212yes—
8C22×D788C4116yescomplemented
9C22×D788C22112yes—
10C23×Dic197C2211yescharacteristic
11C23×Dic197C2211yescharacteristic
12C22×C4×D197—216no—
13C22×C4×D197C22124yescomplemented
14#20263288C22164yesdirect product factor
15C2×#15691335C22124yescomplemented
16C2×C4×Dic197C22112yescomplemented
17C23×C4×C197C2212yes—
18C23×C4×C197C2211yescharacteristic
19C2×C4⋊C4×C197C22112yescomplemented
20C23×D197—28no—
21C23×D197—28no—
22C23×D197C2×C4116yescomplemented
23C23×D197C23112yes—
24C2×D788C2×C4196yescomplemented
25C2×D788C23116yes—
26C22×Dic197—24no—
27C22×Dic197D418yescomplemented
28C22×Dic197C2316yes—
29C22×Dic197C2316yes—
30C2×C4×D197—296no—
31C2×C4×D197C23132yescomplemented
32#15691335C23132yescomplemented
33C4×Dic197C23116yescomplemented
34C24×C197C2311yescharacteristic
35C22×C4×C197—28no—
36C22×C4×C197C2×C418yescomplemented
37C22×C4×C197C23112yes—
38C22×C4×C197C2316yes—
39C4⋊C4×C197C23116yescomplemented
40C22×D197—264no—
41C22×D197—224no—
42C22×D197—224no—
43C22×D197C22×C4148yescomplemented
44C22×D197C2418yes—
45D788C22×C4164yescomplemented
46C2×Dic197—212no—
47C2×Dic197C2×D4124yescomplemented
48C2×Dic197C2414yes—
49C2×Dic197C2414yes—
50C4×D197—264no—
51C23×C197C22×C414yes—
52C23×C197C2×D414yes—
53C23×C197#4114yes—
54C23×C197C2413yes—
55C2×C4×C197—224no—
56C2×C4×C197C22×C4124yescomplemented
57C2×C4×C197C2418yes—
58C2×C4×C197C2414yes—
59C22×C197C4×D4116yescomplemented
60C22×C197C23×C416yes—
61C22×C197C22×D416yes—
62C22×C197C2×#4116yes—
63C22×C197C2511yescharacteristic
64C2×D197—296no—
65C2×D197—28no—
66C2×D197—28no—
67C2×D197C23×C4116yescomplemented
68C4×C197—28no—
69C4×C197C23×C418yescomplemented
70Dic197—24no—
71Dic197C22×D418yescomplemented
72C2×C197C2×C4×D4112yescomplemented
73C2×C197C24×C411yescharacteristic
74C2×C197C23×D411yescharacteristic
75C2×C197C22×#4111yescharacteristic
76D197—216no—
77C197C22×C4×D411yescharacteristic, complemented, Sylow
78C22×C4×D4—1971nomaximal, Sylow
79C23×D4—1971no—
80C24×C4—1972no—
81C2×C4×D4—19724no—
82C22×C4⋊C4D19711yescharacteristic, complemented
83C22×C22⋊C4—1972no—
84C22×C42—1971no—
85C25—1972no—
86C22×D4—19716no—
87C22×D4—19712no—
88C23×C4—39416no—
89C23×C4—1971no—
90C23×C4—19724no—
91C23×C4—1971no—
92C23×C4C2×D19712yes—
93C23×C4C2×D19711yescharacteristic
94C4×D4—19764no—
95C2×C4⋊C4C2×D197112yescomplemented
96C2×C22⋊C4—19724no—
97C2×C42—19712no—
98C24—3948no—
99C24—3948no—
100C24—19716no—
101C24—19712no—
102C24C22×D19711yescharacteristic
103C2×D4—19796no—
104C2×D4—19716no—
105C22×C4—28no—
106C22×C4—39496no—
107C22×C4—3944no—
108C22×C4—1976no—
109C22×C4—19732no—
110C22×C4—1978no—
111C22×C4—1976no—
112C22×C4C4×D19718yescomplemented
113C22×C4C22×D197112yes—
114C22×C4C22×D19716yes—
115C4⋊C4C22×D197116yescomplemented
116C22⋊C4—19732no—
117C42—19716no—
118C23—39464no—
119C23—39424no—
120C23—39424no—
121C23—19748no—
122C23—1978no—
123C23C2×C4×D19714yes—
124C23D4×D19714yes—
125C23#1569135914yes—
126C23C23×D19713yes—
127D4—19764no—
128C2×C4—224no—
129C2×C4—39464no—
130C2×C4—39412no—
131C2×C4—1974no—
132C2×C4—19724no—
133C2×C4—1974no—
134C2×C4C2×C4×D197124yescomplemented
135C2×C4C23×D19718yes—
136C2×C4C23×D19714yes—
137C22—3948no—
138C22—3948no—
139C22—39496no—
140C22—19716no—
141C22#20263288116yesdirect product factor
142C22C22×C4×D19716yes—
143C22C2×D4×D19716yes—
144C22C2×#1569135916yes—
145C22C24×D19711yescharacteristic
146C4—28no—
147C4—3944no—
148C4—1978no—
149C4C22×C4×D19718yescomplemented
150C2—39416no—
151C2C2×#20263288112yesdirect product factor
152C2C23×C4×D19711yescharacteristic
153C2C22×D4×D19711yescharacteristic
154C2C22×#1569135911yescharacteristic
subgroupG/H
centerC24C22×D197
commutatorC2×C197C24×C4
FrattiniC22C24×D197
FittingC22×C4⋊C4×C197C2
socleC24×C197C23
prime radicalC23×D788C2
cosocleC22×C197C25
hypercenterC22×C4⋊C4D197
hypocenterC197C22×C4×D4
LCSG ▷ C2×C197 ▷ C197
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D197C2semidirect
3. C2×#20263288C2direct (N × H)
4. C22×#15691335C2semidirect
5. C22×C4×Dic197C2semidirect
6. C22×C4⋊C4×C197C2semidirect
8. C22×D788C4semidirect
13. C22×C4×D197C22semidirect
14. #20263288C22direct (N × H)
15. C2×#15691335C22semidirect
16. C2×C4×Dic197C22semidirect
19. C2×C4⋊C4×C197C22semidirect
22. C23×D197C2×C4semidirect
24. C2×D788C2×C4semidirect
27. C22×Dic197D4semidirect
31. C2×C4×D197C23semidirect
32. #15691335C23semidirect
33. C4×Dic197C23semidirect
36. C22×C4×C197C2×C4semidirect
39. C4⋊C4×C197C23semidirect
43. C22×D197C22×C4semidirect
45. D788C22×C4semidirect
47. C2×Dic197C2×D4semidirect
56. C2×C4×C197C22×C4semidirect
59. C22×C197C4×D4semidirect
67. C2×D197C23×C4semidirect
69. C4×C197C23×C4semidirect
71. Dic197C22×D4semidirect
72. C2×C197C2×C4×D4semidirect
77. C197C22×C4×D4semidirect
82. C22×C4⋊C4D197semidirect
95. C2×C4⋊C4C2×D197semidirect
112. C22×C4C4×D197semidirect
115. C4⋊C4C22×D197semidirect
134. C2×C4C2×C4×D197semidirect
141. C22#20263288direct (N × H)
149. C4C22×C4×D197semidirect
151. C2C2×#20263288direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D7882
C23×C4×D1972
C2×#202632882
C22×#156913352
C22×C4×Dic1972
C22×C4⋊C4×C1972
C22×C4×D4197