Finite Group Databasebeta

← C22×#19097733 #34113306

Subgroups — C22×#19097733 #34113306

Order 20096.

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×D628C211yesmaximal, characteristic
2C23×C4×D157C212yesmaximal, complemented
3C2×#19097733C2124yesmaximal, direct product factor
4C22×#14578931C212yesmaximal, complemented
5C22×C4×Dic157C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C157C211yesmaximal, characteristic, complemented
7C24×D157C2212yes—
8C22×D628C4116yescomplemented
9C22×D628C22112yes—
10C23×Dic157C2211yescharacteristic
11C23×Dic157C2211yescharacteristic
12C22×C4×D157—216no—
13C22×C4×D157C22124yescomplemented
14#19097733C22164yesdirect product factor
15C2×#14578931C22124yescomplemented
16C2×C4×Dic157C22112yescomplemented
17C23×C4×C157C2212yes—
18C23×C4×C157C2211yescharacteristic
19C2×C4⋊C4×C157C22112yescomplemented
20C23×D157—28no—
21C23×D157—28no—
22C23×D157C2×C4116yescomplemented
23C23×D157C23112yes—
24C2×D628C2×C4196yescomplemented
25C2×D628C23116yes—
26C22×Dic157—24no—
27C22×Dic157D418yescomplemented
28C22×Dic157C2316yes—
29C22×Dic157C2316yes—
30C2×C4×D157—296no—
31C2×C4×D157C23132yescomplemented
32#14578931C23132yescomplemented
33C4×Dic157C23116yescomplemented
34C24×C157C2311yescharacteristic
35C22×C4×C157—28no—
36C22×C4×C157C2×C418yescomplemented
37C22×C4×C157C23112yes—
38C22×C4×C157C2316yes—
39C4⋊C4×C157C23116yescomplemented
40C22×D157—264no—
41C22×D157—224no—
42C22×D157—224no—
43C22×D157C22×C4148yescomplemented
44C22×D157C2418yes—
45D628C22×C4164yescomplemented
46C2×Dic157—212no—
47C2×Dic157C2×D4124yescomplemented
48C2×Dic157C2414yes—
49C2×Dic157C2414yes—
50C4×D157—264no—
51C23×C157C22×C414yes—
52C23×C157C2×D414yes—
53C23×C157#4114yes—
54C23×C157C2413yes—
55C2×C4×C157—224no—
56C2×C4×C157C22×C4124yescomplemented
57C2×C4×C157C2418yes—
58C2×C4×C157C2414yes—
59C22×C157C4×D4116yescomplemented
60C22×C157C23×C416yes—
61C22×C157C22×D416yes—
62C22×C157C2×#4116yes—
63C22×C157C2511yescharacteristic
64C2×D157—296no—
65C2×D157—28no—
66C2×D157—28no—
67C2×D157C23×C4116yescomplemented
68C4×C157—28no—
69C4×C157C23×C418yescomplemented
70Dic157—24no—
71Dic157C22×D418yescomplemented
72C2×C157C2×C4×D4112yescomplemented
73C2×C157C24×C411yescharacteristic
74C2×C157C23×D411yescharacteristic
75C2×C157C22×#4111yescharacteristic
76D157—216no—
77C157C22×C4×D411yescharacteristic, complemented, Sylow
78C22×C4×D4—1571nomaximal, Sylow
79C23×D4—1571no—
80C24×C4—1572no—
81C2×C4×D4—15724no—
82C22×C4⋊C4D15711yescharacteristic, complemented
83C22×C22⋊C4—1572no—
84C22×C42—1571no—
85C25—1572no—
86C22×D4—15716no—
87C22×D4—15712no—
88C23×C4—31416no—
89C23×C4—1571no—
90C23×C4—15724no—
91C23×C4—1571no—
92C23×C4C2×D15712yes—
93C23×C4C2×D15711yescharacteristic
94C4×D4—15764no—
95C2×C4⋊C4C2×D157112yescomplemented
96C2×C22⋊C4—15724no—
97C2×C42—15712no—
98C24—3148no—
99C24—3148no—
100C24—15716no—
101C24—15712no—
102C24C22×D15711yescharacteristic
103C2×D4—15796no—
104C2×D4—15716no—
105C22×C4—28no—
106C22×C4—31496no—
107C22×C4—3144no—
108C22×C4—1576no—
109C22×C4—15732no—
110C22×C4—1578no—
111C22×C4—1576no—
112C22×C4C4×D15718yescomplemented
113C22×C4C22×D157112yes—
114C22×C4C22×D15716yes—
115C4⋊C4C22×D157116yescomplemented
116C22⋊C4—15732no—
117C42—15716no—
118C23—31464no—
119C23—31424no—
120C23—31424no—
121C23—15748no—
122C23—1578no—
123C23C2×C4×D15714yes—
124C23D4×D15714yes—
125C23#1457895514yes—
126C23C23×D15713yes—
127D4—15764no—
128C2×C4—224no—
129C2×C4—31464no—
130C2×C4—31412no—
131C2×C4—1574no—
132C2×C4—15724no—
133C2×C4—1574no—
134C2×C4C2×C4×D157124yescomplemented
135C2×C4C23×D15718yes—
136C2×C4C23×D15714yes—
137C22—3148no—
138C22—3148no—
139C22—31496no—
140C22—15716no—
141C22#19097733116yesdirect product factor
142C22C22×C4×D15716yes—
143C22C2×D4×D15716yes—
144C22C2×#1457895516yes—
145C22C24×D15711yescharacteristic
146C4—28no—
147C4—3144no—
148C4—1578no—
149C4C22×C4×D15718yescomplemented
150C2—31416no—
151C2C2×#19097733112yesdirect product factor
152C2C23×C4×D15711yescharacteristic
153C2C22×D4×D15711yescharacteristic
154C2C22×#1457895511yescharacteristic
subgroupG/H
centerC24C22×D157
commutatorC2×C157C24×C4
FrattiniC22C24×D157
FittingC22×C4⋊C4×C157C2
socleC24×C157C23
prime radicalC23×D628C2
cosocleC22×C157C25
hypercenterC22×C4⋊C4D157
hypocenterC157C22×C4×D4
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D157C2semidirect
3. C2×#19097733C2direct (N × H)
4. C22×#14578931C2semidirect
5. C22×C4×Dic157C2semidirect
6. C22×C4⋊C4×C157C2semidirect
8. C22×D628C4semidirect
13. C22×C4×D157C22semidirect
14. #19097733C22direct (N × H)
15. C2×#14578931C22semidirect
16. C2×C4×Dic157C22semidirect
19. C2×C4⋊C4×C157C22semidirect
22. C23×D157C2×C4semidirect
24. C2×D628C2×C4semidirect
27. C22×Dic157D4semidirect
31. C2×C4×D157C23semidirect
32. #14578931C23semidirect
33. C4×Dic157C23semidirect
36. C22×C4×C157C2×C4semidirect
39. C4⋊C4×C157C23semidirect
43. C22×D157C22×C4semidirect
45. D628C22×C4semidirect
47. C2×Dic157C2×D4semidirect
56. C2×C4×C157C22×C4semidirect
59. C22×C157C4×D4semidirect
67. C2×D157C23×C4semidirect
69. C4×C157C23×C4semidirect
71. Dic157C22×D4semidirect
72. C2×C157C2×C4×D4semidirect
77. C157C22×C4×D4semidirect
82. C22×C4⋊C4D157semidirect
95. C2×C4⋊C4C2×D157semidirect
112. C22×C4C4×D157semidirect
115. C4⋊C4C22×D157semidirect
134. C2×C4C2×C4×D157semidirect
141. C22#19097733direct (N × H)
149. C4C22×C4×D157semidirect
151. C2C2×#19097733direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D6282
C23×C4×D1572
C2×#190977332
C22×#145789312
C22×C4×Dic1572
C22×C4⋊C4×C1572
C22×C4×D4157