Finite Group Databasebeta

← #34094658

Subgroups — #34094658

Order 20032.

330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 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×#19097560C211yesmaximal, characteristic, complemented
2C23×Dic313C211yesmaximal, characteristic, complemented
3#23756481C211yesmaximal, characteristic, complemented
4#23756478C211yesmaximal, characteristic, complemented
5#23756474C212yesmaximal, complemented
6#23756469C212yesmaximal, complemented
7#23756466C211yesmaximal, characteristic, complemented
8D4×Dic313C212yesmaximal, complemented
9#23756457C212yesmaximal, complemented
10#23756453C211yesmaximal, characteristic, complemented
11#120×C313C211yesmaximal, characteristic, complemented
12#19097560—24no—
13C2×Dic626C2211yescharacteristic, complemented
14C2×C22⋊D313C2212yes—
15C2×C22⋊D313C2211yescharacteristic
16C2×C22⋊D313C2211yescharacteristic, complemented
17C22×Dic313—24no—
18C22×Dic313C2212yes—
19C22×Dic313C2212yes—
20C22×Dic313C2211yescharacteristic
21C22×Dic313C2211yescharacteristic
22C22×Dic313C2211yescharacteristic, complemented
23C2×C4×D313C2211yescharacteristic, complemented
24C4⋊Dic313C2212yescomplemented
25#19097540C2212yescomplemented
26#19097540C2212yescomplemented
27C22⋊Dic313C2211yescharacteristic
28C22⋊Dic313C2212yes—
29C22⋊Dic313C2212yescomplemented
30#19097538C2212yescomplemented
31C4×Dic313C2212yescomplemented
32C24×C313C2211yescharacteristic
33C2×D4×C313C2212yes—
34C2×D4×C313C2211yescharacteristic
35C22⋊C4×C313C2211yescharacteristic
36C22⋊C4×C313C2212yes—
37C22×D313C2311yescharacteristic
38Dic626—22no—
39C22⋊D313—22no—
40C22⋊D313—24no—
41C22⋊D313—22no—
42C2×Dic313—22no—
43C2×Dic313—24no—
44C2×Dic313—24no—
45C2×Dic313—22no—
46C2×Dic313D414yescomplemented
47C2×Dic313C2312yes—
48C2×Dic313C2312yes—
49C2×Dic313C2311yescharacteristic
50C2×Dic313C2311yescharacteristic
51C2×Dic313C2311yescharacteristic
52C4×D313—22no—
53C23×C313—22no—
54C23×C313—24no—
55C23×C313C2311yescharacteristic
56C23×C313C2311yescharacteristic
57C23×C313C2312yes—
58D4×C313—22no—
59D4×C313—24no—
60C2×C4×C313C2312yes—
61C2×C4×C313C2311yescharacteristic
62C22×C313—28no—
63C22×C313—22no—
64C22×C313—22no—
65C22×C313—22no—
66C22×C313—21no—
67C22×C313—22no—
68C22×C313C2×D412yes—
69C22×C313#4114yescomplemented
70C22×C313C2411yescharacteristic
71C2×D313—21no—
72C2×D313—22no—
73C4×C313—21no—
74C4×C313—22no—
75Dic313—22no—
76Dic313—21no—
77Dic313—22no—
78Dic313C2×D412yes—
79Dic313C2×D412yes—
80C2×C313—22no—
81C2×C313—24no—
82C2×C313—41no—
83C2×C313C22×D411yescharacteristic
84C2×C313C2×#4112yes—
85D313—41no—
86C313#52511yescharacteristic, complemented, Sylow
87#525—3131nomaximal, Sylow
88C2×#41—3131no—
89C23×C4—3131no—
90#123—3131no—
91#123—3131no—
92C22⋊Q8—3132no—
93#121—3132no—
94#120—3131no—
95#120D31311yescharacteristic, complemented
96C4×D4—3132no—
97C4×D4—3132no—
98#117—3131no—
99C24C2×D31311yescharacteristic
100#41—6264no—
101C2×Q8—3131no—
102C2×D4—3132no—
103C2×D4—3131no—
104C2×D4—3131no—
105C2×D4C2×D31312yes—
106C2×D4C2×D31311yescharacteristic
107C22×C4—3131no—
108C22×C4—3132no—
109C22×C4—3131no—
110C22×C4—3132no—
111C22×C4—3131no—
112C22×C4—3131no—
113C22×C4—6264no—
114C4⋊C4—3132no—
115C4⋊C4—3132no—
116C4⋊C4—3132no—
117C22⋊C4—3131no—
118C22⋊C4—3132no—
119C22⋊C4—3132no—
120C22⋊C4—3132no—
121C22⋊C4C2×D31311yescharacteristic
122C22⋊C4C2×D31312yes—
123C42—3132no—
124C23—22no—
125C23—24no—
126C23—3131no—
127C23C22×D31311yescharacteristic
128C23C22×D31311yescharacteristic
129C23C22×D31312yes—
130Q8—6262no—
131D4—22no—
132D4—24no—
133D4—6262no—
134D4—6262no—
135D4—6264no—
136C2×C4—3134no—
137C2×C4—3131no—
138C2×C4—3131no—
139C2×C4—3132no—
140C2×C4—3132no—
141C2×C4—3131no—
142C2×C4—6262no—
143C2×C4—6264no—
144C2×C4—6264no—
145C2×C4—6262no—
146C2×C4—6262no—
147C2×C4C22×D31312yes—
148C2×C4C22×D31311yescharacteristic
149C22—28no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—22no—
155C22—6261no—
156C22—6262no—
157C22D4×D31312yes—
158C22#1909756014yescomplemented
159C22C23×D31311yescharacteristic
160C4—21no—
161C4—22no—
162C4—3132no—
163C4—3132no—
164C4—6262no—
165C4—6261no—
166C4—6262no—
167C2—22no—
168C2—24no—
169C2—41no—
170C2—12521no—
171C2C2×D4×D31311yescharacteristic
172C2C2×#1909756012yes—
subgroupG/H
center, FrattiniC22C23×D313
commutator, socle, cosocleC22×C313C24
Fitting#120×C313C2
hypercenter#120D313
hypocenterC313#525
LCSG ▷ C22×C313 ▷ C313
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#19097560C2semidirect
2. C23×Dic313C2semidirect
3. #23756481C2semidirect
4. #23756478C2semidirect
5. #23756474C2semidirect
6. #23756469C2semidirect
7. #23756466C2semidirect
8. D4×Dic313C2semidirect
9. #23756457C2semidirect
10. #23756453C2semidirect
11. #120×C313C2semidirect
13. C2×Dic626C22semidirect
16. C2×C22⋊D313C22semidirect
22. C22×Dic313C22semidirect
23. C2×C4×D313C22semidirect
24. C4⋊Dic313C22semidirect
25. #19097540C22semidirect
26. #19097540C22semidirect
29. C22⋊Dic313C22semidirect
30. #19097538C22semidirect
31. C4×Dic313C22semidirect
46. C2×Dic313D4semidirect
69. C22×C313#41semidirect
86. C313#525semidirect
95. #120D313semidirect
158. C22#19097560semidirect

Maximal subgroups

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

subgroupindex
C2×#190975602
C23×Dic3132
#237564812
#237564782
#237564742
#237564692
#237564662
D4×Dic3132
#237564572
#237564532
#120×C3132
#525313