Finite Group Databasebeta

← #34094665

Subgroups — #34094665

Order 20032.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19097562C211yesmaximal, characteristic, complemented
2C22×C4×D313C211yesmaximal, characteristic, complemented
3#23756482C212yesmaximal, complemented
4#23756473C211yesmaximal, characteristic, complemented
5#23756472C211yesmaximal, characteristic, complemented
6#23756471C211yesmaximal, characteristic, complemented
7#23756467C212yesmaximal, complemented
8#23756459C212yesmaximal, complemented
9#23756457C212yesmaximal, complemented
10#23756455C211yesmaximal, characteristic, complemented
11C22⋊Q8×C313C211yesmaximal, characteristic, complemented
12C23×D313C2211yescharacteristic
13#19097562—24no—
14C2×D1252C2212yes—
15C2×D1252C2212yes—
16C2×D1252C2211yescharacteristic, complemented
17C2×C22⋊D313C2212yes—
18C22×Dic313C2211yescharacteristic
19C2×C4×D313—24no—
20C2×C4×D313C2211yescharacteristic
21C2×C4×D313C2211yescharacteristic
22C2×C4×D313C2211yescharacteristic
23C2×C4×D313C2211yescharacteristic
24C2×C4×D313C2212yescomplemented
25C4⋊Dic313C2211yescharacteristic, complemented
26#19097540C2212yescomplemented
27#19097538C2212yes—
28#19097538C2212yes—
29#19097538C2212yescomplemented
30#19097538C2212yescomplemented
31C4×Dic313C2212yescomplemented
32C2×Q8×C313C2211yescharacteristic, complemented
33C22×C4×C313C2211yescharacteristic
34C4⋊C4×C313C2211yescharacteristic, complemented
35C4⋊C4×C313C2212yescomplemented
36C22⋊C4×C313C2212yes—
37C22×D313—22no—
38C22×D313—22no—
39C22×D313—22no—
40C22×D313C2312yes—
41C22×D313C2311yescharacteristic
42C22×D313C2311yescharacteristic
43D1252—24no—
44D1252—24no—
45D1252—22no—
46C22⋊D313—24no—
47C2×Dic313—22no—
48C2×Dic313C2312yes—
49C2×Dic313C2311yescharacteristic
50C2×Dic313C2311yescharacteristic
51C4×D313—22no—
52C4×D313—22no—
53C4×D313—22no—
54C4×D313—24no—
55C4×D313D414yescomplemented
56C23×C313C2311yescharacteristic
57Q8×C313—22no—
58C2×C4×C313—22no—
59C2×C4×C313C2312yes—
60C2×C4×C313C2312yes—
61C2×C4×C313C2311yescharacteristic
62C2×C4×C313C2311yescharacteristic
63C22×C313—21no—
64C22×C313—21no—
65C22×C313#4112yescomplemented
66C22×C313C2411yescharacteristic
67C2×D313—28no—
68C2×D313—21no—
69C2×D313—21no—
70C2×D313—21no—
71C2×D313—21no—
72C2×D313—22no—
73C2×D313—22no—
74C2×D313—22no—
75C2×D313C2×D412yes—
76C2×D313#4112yescomplemented
77C4×C313—21no—
78C4×C313—22no—
79C4×C313—22no—
80C4×C313C2×D412yes—
81Dic313—21no—
82Dic313—22no—
83Dic313C2×D412yes—
84C2×C313—22no—
85C2×C313C22×D411yescharacteristic
86C2×C313C2×#4111yescharacteristic
87C2×C313C2×#4111yescharacteristic
88D313—22no—
89D313—22no—
90D313—42no—
91C313#52511yescharacteristic, complemented, Sylow
92#525—3131nomaximal, Sylow
93C2×#41—3131no—
94C23×C4—3131no—
95#123—3132no—
96C22⋊Q8—3131no—
97C22⋊Q8D31311yescharacteristic, complemented
98#121—3131no—
99#121—3131no—
100#120—3132no—
101C4×D4—3132no—
102C4×D4—3132no—
103#117—3131no—
104C24—3131no—
105#41—6264no—
106C2×Q8C2×D31311yescharacteristic, complemented
107C2×D4—3132no—
108C2×D4—3132no—
109C2×D4—3132no—
110C2×D4—3131no—
111C22×C4—3131no—
112C22×C4—3131no—
113C22×C4—3131no—
114C22×C4—3132no—
115C22×C4—3131no—
116C22×C4—3131no—
117C22×C4—6264no—
118C22×C4C2×D31311yescharacteristic
119C4⋊C4—3131no—
120C4⋊C4—3132no—
121C4⋊C4C2×D31311yescharacteristic, complemented
122C4⋊C4C2×D31312yescomplemented
123C22⋊C4—3132no—
124C22⋊C4—3132no—
125C22⋊C4—3132no—
126C22⋊C4—3132no—
127C22⋊C4C2×D31312yes—
128C42—3132no—
129C23—3131no—
130C23—3131no—
131C23—3132no—
132C23—6262no—
133C23—6262no—
134C23—6262no—
135C23C22×D31311yescharacteristic
136Q8—22no—
137D4—6264no—
138D4—6264no—
139D4—6264no—
140D4—6262no—
141C2×C4—22no—
142C2×C4—3131no—
143C2×C4—3134no—
144C2×C4—3132no—
145C2×C4—3131no—
146C2×C4—6262no—
147C2×C4—6264no—
148C2×C4—6262no—
149C2×C4—6262no—
150C2×C4—6262no—
151C2×C4C22×D31312yes—
152C2×C4C22×D31311yescharacteristic
153C2×C4C22×D31312yes—
154C2×C4C22×D31311yescharacteristic
155C22—21no—
156C22—21no—
157C22—3132no—
158C22—3132no—
159C22—6268no—
160C22—6261no—
161C22—6261no—
162C22—6261no—
163C22—6261no—
164C22—6262no—
165C22—6262no—
166C22—6262no—
167C22#1909756212yescomplemented
168C22C23×D31311yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—3132no—
173C4—6261no—
174C4—6262no—
175C4D4×D31312yes—
176C2—22no—
177C2—6262no—
178C2—6262no—
179C2—12522no—
180C2C2×D4×D31311yescharacteristic
181C2#41×D31311yescharacteristic
182C2C2×#1909756211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D313
commutator, socle, cosocleC22×C313C24
FittingC22⋊Q8×C313C2
hypercenterC22⋊Q8D313
hypocenterC313#525
LCSG ▷ C22×C313 ▷ C313
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#19097562C2semidirect
2. C22×C4×D313C2semidirect
3. #23756482C2semidirect
4. #23756473C2semidirect
5. #23756472C2semidirect
6. #23756471C2semidirect
7. #23756467C2semidirect
8. #23756459C2semidirect
9. #23756457C2semidirect
10. #23756455C2semidirect
11. C22⋊Q8×C313C2semidirect
16. C2×D1252C22semidirect
24. C2×C4×D313C22semidirect
25. C4⋊Dic313C22semidirect
26. #19097540C22semidirect
29. #19097538C22semidirect
30. #19097538C22semidirect
31. C4×Dic313C22semidirect
32. C2×Q8×C313C22semidirect
34. C4⋊C4×C313C22semidirect
35. C4⋊C4×C313C22semidirect
55. C4×D313D4semidirect
65. C22×C313#41semidirect
76. C2×D313#41semidirect
91. C313#525semidirect
97. C22⋊Q8D313semidirect
106. C2×Q8C2×D313semidirect
121. C4⋊C4C2×D313semidirect
122. C4⋊C4C2×D313semidirect
167. C22#19097562semidirect

Maximal subgroups

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

subgroupindex
C2×#190975622
C22×C4×D3132
#237564822
#237564732
#237564722
#237564712
#237564672
#237564592
#237564572
#237564552
C22⋊Q8×C3132
#525313