Finite Group Databasebeta

← #13130972

Subgroups — #13130972

Order 1664.

320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 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
1#11719430C211yesmaximal, characteristic
2C2×#88118C214yesmaximal, complemented
3#11719057C211yesmaximal, characteristic, complemented
4#11719053C211yesmaximal, characteristic, complemented
5C2×#6131C2212yes—
6C2×C4×#261C2212yes—
7C2×#6118C2212yes—
8C13×C4⋊Q8C411yescharacteristic, complemented
9#88201C412yescomplemented
10#88149—22no—
11#88147—22no—
12#88128C411yescharacteristic, complemented
13C42×D13C2211yescharacteristic
14#88118—28no—
15(C2×#261)⋊C4—22no—
16#88112—22no—
17C22×#261—22no—
18C2×Q8×C13C2×C412yes—
19#6131—24no—
20#6131—24no—
21C2×D52—22no—
22C2×D52—22no—
23C2×D52C2×C412yes—
24C2×C4×D13—22no—
25C2×C4×D13D412yes—
26C2×C4×D13C2311yescharacteristic
27C2×#1057—22no—
28C4×#261—22no—
29C4×#261D414yescomplemented
30#6118—24no—
31C13×C4⋊C4—22no—
32C42×C13C2×C411yescharacteristic
33#6103—24no—
34C4×Dic13C2×C411yescharacteristic
35C4×Dic13D412yes—
36#1963—131nomaximal, Sylow
37C22×D13—22no—
38C22×D13C2×D411yescharacteristic
39C2×#261—24no—
40C2×#261—44no—
41Q8×C13—24no—
42C2×C4×C13—22no—
43C2×C4×C13C22⋊C412yes—
44C2×C4×C13C22×C411yescharacteristic
45C2×Dic13C22⋊C412yes—
46C2×Dic13C2×D411yescharacteristic
47D52—24no—
48D52—44no—
49D52—44no—
50C4×D13—42no—
51C4×D13—42no—
52C4×D13—42no—
53C4×D13C2×D412yes—
54C4×D13#4112yes—
55#1057—42no—
56#532—131no—
57#423—131no—
58C2×#104—134no—
59#376—131no—
60C22×C13C2×C22⋊C411yescharacteristic
61C2×D13—22no—
62C2×D13—42no—
63C2×D13—44no—
64C2×D13#12112yes—
65#261—44no—
66C4×C13—22no—
67C4×C13—42no—
68C4×C13C4×D412yes—
69Dic13—22no—
70Dic13#12411yescharacteristic
71Dic13#12711yescharacteristic
72C2×#41—132no—
73C2×M16—132no—
74C4⋊Q8#26111yescharacteristic, complemented
75#127—131no—
76#124—132no—
77#121—262no—
78C4×D4—262no—
79C2×C42—131no—
80C2×C42—132no—
81C4⋊C8—262no—
82#104—268no—
83#95—262no—
84C2×C13#39011yescharacteristic
85C2×C13#42112yes—
86D13—22no—
87D13—82no—
88#41—264no—
89#41—264no—
90C2×Q8C2×#26112yes—
91C2×D4—132no—
92C2×D4—262no—
93C2×D4—262no—
94C22×C4—131no—
95C22×C4—132no—
96C22×C4—262no—
97C22×C4—262no—
98M16—264no—
99C2×C8—262no—
100C4⋊C4—22no—
101C22⋊C4—264no—
102C42—132no—
103C42—131no—
104C42—134no—
105C42—262no—
106C42C2×#26111yescharacteristic
107C13#196311yescharacteristic, complemented, Sylow
108C23—131no—
109C23—262no—
110Q8—24no—
111D4—264no—
112D4—524no—
113D4—524no—
114C2×C4—22no—
115C2×C4—131no—
116C2×C4—132no—
117C2×C4—132no—
118C2×C4—132no—
119C2×C4—264no—
120C2×C4—522no—
121C2×C4—522no—
122C2×C4—522no—
123C2×C4—524no—
124C2×C4C22⋊#26112yes—
125C2×C4C22×#26111yescharacteristic
126C8—522no—
127C22—132no—
128C22—262no—
129C22—522no—
130C22—524no—
131C22C2×C22⋊#26111yescharacteristic
132C4—22no—
133C4—42no—
134C4—131no—
135C4—131no—
136C4—262no—
137C4—524no—
138C4D4×#26112yes—
139C2—262no—
140C2—1042no—
141C2#1171915111yescharacteristic
142C2#1171915512yes—
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radical#11719430C2
cosocleC2×C4×D13C23
hypercenterC4⋊Q8#261
hypocenterC13#1963
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#88118C2semidirect
3. #11719057C2semidirect
4. #11719053C2semidirect
8. C13×C4⋊Q8C4semidirect
9. #88201C4semidirect
12. #88128C4semidirect
29. C4×#261D4semidirect
74. C4⋊Q8#261semidirect
107. C13#1963semidirect

Maximal subgroups

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

subgroupindex
#117194302
C2×#881182
#117190572
#117190532
#196313