Finite Group Databasebeta

← C22×C4⋊C4×D197 #38755871

Subgroups — C22×C4⋊C4×D197 #38755871

Order 25216.

2488 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.

normal subgroups only

This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1157 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×D197C212yesmaximal
2C23×C4×D197C211yesmaximal, characteristic
3C22×C4⋊Dic197C211yesmaximal, characteristic, complemented
4C22×#15691337C212yesmaximal, complemented
5C2×C4⋊C4×D197C2124yesmaximal, direct product factor
6C22×C4⋊C4×C197C211yesmaximal, characteristic, complemented
7C24×D197C2211yescharacteristic
8C23×Dic197C2212yes—
9C23×Dic197C2211yescharacteristic
10C22×C4×D197—216no—
11C22×C4×D197C4116yescomplemented
12C22×C4×D197C22124yes—
13C22×C4×D197C22112yes—
14C2×C4⋊Dic197C22112yescomplemented
15C2×#15691337C22124yescomplemented
16C4⋊C4×D197C22164yesdirect product factor
17C23×C4×C197C2212yes—
18C23×C4×C197C2211yescharacteristic
19C2×C4⋊C4×C197C22112yescomplemented
20C23×D197C2×C418yes—
21C23×D197D418yes—
22C23×D197Q818yes—
23C23×D197C2316yes—
24C22×Dic197—28no—
25C22×Dic197C2×C418yescomplemented
26C22×Dic197C23112yes—
27C22×Dic197C2316yes—
28C2×C4×D197—296no—
29C2×C4×D197C2×C4196yescomplemented
30C2×C4×D197C23132yes—
31C2×C4×D197C23116yes—
32C4⋊Dic197C23116yescomplemented
33#15691337C23132yescomplemented
34C24×C197C2311yescharacteristic
35C22×C4×C197—28no—
36C22×C4×C197C2×C418yescomplemented
37C22×C4×C197C23112yes—
38C22×C4×C197C2316yes—
39C4⋊C4×C197C23116yescomplemented
40C22×D197C4⋊C4164yesdirect product factor
41C22×D197C22×C4124yes—
42C22×D197C2×D4124yes—
43C22×D197C2×Q8124yes—
44C22×D197C2414yes—
45C2×Dic197—224no—
46C2×Dic197C22×C4124yescomplemented
47C2×Dic197C2418yes—
48C2×Dic197C2414yes—
49C4×D197—264no—
50C4×D197C22×C4164yescomplemented
51C23×C197C22×C414yes—
52C23×C197C2×D414yes—
53C23×C197C2×Q814yes—
54C23×C197C2413yes—
55C2×C4×C197—224no—
56C2×C4×C197C22×C4124yescomplemented
57C2×C4×C197C2418yes—
58C2×C4×C197C2414yes—
59C22×C197C2×C4⋊C4116yescomplemented
60C22×C197C23×C416yes—
61C22×C197C22×D416yes—
62C22×C197C22×Q816yes—
63C22×C197C2511yescharacteristic
64C2×D197C2×C4⋊C4196yesdirect product factor
65C2×D197C23×C418yes—
66C2×D197C22×D418yes—
67C2×D197C22×Q818yes—
68C4×C197—28no—
69C4×C197C23×C418yescomplemented
70Dic197—28no—
71Dic197C23×C418yescomplemented
72C2×C197C22×C4⋊C4112yescomplemented
73C2×C197C24×C411yescharacteristic
74C2×C197C23×D411yescharacteristic
75C2×C197C23×Q811yescharacteristic
76D197C22×C4⋊C4116yesdirect product factor
77C197C23×C4⋊C411yescharacteristic, complemented, Sylow
78C23×C4⋊C4—1971nomaximal, Sylow
79C24×C4—1972no—
80C24×C4—1971no—
81C22×C4⋊C4—1972no—
82C22×C4⋊C4—1971no—
83C22×C4⋊C4—19724no—
84C22×C4⋊C4D19711yescharacteristic, direct product factor
85C25—1971no—
86C23×C4—39416no—
87C23×C4—1972no—
88C23×C4—19724no—
89C23×C4—1971no—
90C23×C4—19716no—
91C23×C4—19712no—
92C23×C4C2×D19712yes—
93C23×C4C2×D19711yescharacteristic
94C2×C4⋊C4—19724no—
95C2×C4⋊C4—19712no—
96C2×C4⋊C4—19764no—
97C2×C4⋊C4C2×D197112yesdirect product factor
98C24—1978no—
99C24—1978no—
100C24—1978no—
101C24—1976no—
102C24C22×D19711yescharacteristic
103C22×C4—28no—
104C22×C4—39496no—
105C22×C4—3948no—
106C22×C4—19712no—
107C22×C4—19732no—
108C22×C4—1978no—
109C22×C4—1976no—
110C22×C4—19796no—
111C22×C4—19716no—
112C22×C4C4×D19718yescomplemented
113C22×C4C22×D197112yes—
114C22×C4C22×D19716yes—
115C4⋊C4—19732no—
116C4⋊C4—19716no—
117C4⋊C4C22×D197116yesdirect product factor
118C23—19764no—
119C23—19724no—
120C23—19724no—
121C23—19724no—
122C23—1974no—
123C23C2×C4×D19714yes—
124C23D4×D19714yes—
125C23Q8×D19714yes—
126C23C23×D19713yes—
127C2×C4—224no—
128C2×C4—39464no—
129C2×C4—39424no—
130C2×C4—1978no—
131C2×C4—19724no—
132C2×C4—1974no—
133C2×C4—19764no—
134C2×C4C2×C4×D197124yescomplemented
135C2×C4C23×D19718yes—
136C2×C4C23×D19714yes—
137C22—1978no—
138C22—1978no—
139C22—1978no—
140C22—19796no—
141C22C4⋊C4×D197116yesdirect product factor
142C22C22×C4×D19716yes—
143C22C2×D4×D19716yes—
144C22C2×Q8×D19716yes—
145C22C24×D19711yescharacteristic
146C4—28no—
147C4—3948no—
148C4—1978no—
149C4C22×C4×D19718yescomplemented
150C2—19716no—
151C2C2×C4⋊C4×D197112yesdirect product factor
152C2C23×C4×D19711yescharacteristic
153C2C22×D4×D19711yescharacteristic
154C2C22×Q8×D19711yescharacteristic
subgroupG/H
centerC24C22×D197
commutatorC2×C197C24×C4
FrattiniC22C24×D197
FittingC22×C4⋊C4×C197C2
socleC24×C197C23
prime radicalC24×D197C22
cosocleC22×C197C25
hypercenterC22×C4⋊C4D197
hypocenterC197C23×C4⋊C4
LCSG ▷ C2×C197 ▷ C197
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic197C2semidirect
4. C22×#15691337C2semidirect
5. C2×C4⋊C4×D197C2direct (N × H)
6. C22×C4⋊C4×C197C2semidirect
11. C22×C4×D197C4semidirect
14. C2×C4⋊Dic197C22semidirect
15. C2×#15691337C22semidirect
16. C4⋊C4×D197C22direct (N × H)
19. C2×C4⋊C4×C197C22semidirect
25. C22×Dic197C2×C4semidirect
29. C2×C4×D197C2×C4semidirect
32. C4⋊Dic197C23semidirect
33. #15691337C23semidirect
36. C22×C4×C197C2×C4semidirect
39. C4⋊C4×C197C23semidirect
40. C22×D197C4⋊C4direct (N × H)
46. C2×Dic197C22×C4semidirect
50. C4×D197C22×C4semidirect
56. C2×C4×C197C22×C4semidirect
59. C22×C197C2×C4⋊C4semidirect
64. C2×D197C2×C4⋊C4direct (N × H)
69. C4×C197C23×C4semidirect
71. Dic197C23×C4semidirect
72. C2×C197C22×C4⋊C4semidirect
76. D197C22×C4⋊C4direct (N × H)
77. C197C23×C4⋊C4semidirect
84. C22×C4⋊C4D197direct (N × H)
97. C2×C4⋊C4C2×D197direct (N × H)
112. C22×C4C4×D197semidirect
117. C4⋊C4C22×D197direct (N × H)
134. C2×C4C2×C4×D197semidirect
141. C22C4⋊C4×D197direct (N × H)
149. C4C22×C4×D197semidirect
151. C2C2×C4⋊C4×D197direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×D1972
C22×C4⋊Dic1972
C22×#156913372
C2×C4⋊C4×D1972
C22×C4⋊C4×C1972
C23×C4⋊C4197