Finite Group Databasebeta

← #13130748

Subgroups — #13130748

Order 1664.

296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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#11719226C211yesmaximal, characteristic
2C2×#88107C212yesmaximal
3#11718238C214yesmaximal, complemented
4C22×D52C2211yescharacteristic
5C2×C22⋊#261C2214yes—
6C13×#117C411yescharacteristic, complemented
7#88180C411yescharacteristic, complemented
8#88147—22no—
9C22⋊C4×D13C412yescomplemented
10C22⋊C4×D13C2212yes—
11C4×D52—22no—
12#88107—22no—
13#88107—22no—
14C23×D13C2×C411yescharacteristic
15C23×D13C2311yescharacteristic
16C22×#261—24no—
17C22×C4×C13C2×C411yescharacteristic
18C2×D52—24no—
19C2×D52D412yes—
20C2×D52D412yes—
21C2×C4×D13—22no—
22C2×C4×D13—22no—
23C22⋊#261—24no—
24C22⋊#261—24no—
25C13×C4⋊C4—21no—
26C13×C22⋊C4C2×C412yes—
27C42×C13—21no—
28C22⋊Dic13C2×C412yes—
29#6103—22no—
30#6103—22no—
31C4⋊Dic13—21no—
32C4×Dic13—21no—
33#1828—131nomaximal, Sylow
34C23×C13C22×C411yescharacteristic
35C22×D13—22no—
36C22×D13—81no—
37C22×D13—81no—
38C22×D13C22⋊C412yes—
39C22×D13C2×D412yes—
40C22×D13#4114yes—
41C2×#261—44no—
42C2×#261—84no—
43C2×C4×C13—22no—
44C2×C4×C13—22no—
45C2×C4×C13C22⋊C411yescharacteristic
46C2×C4×C13C22⋊C411yescharacteristic
47C2×Dic13—22no—
48D52—24no—
49D52—24no—
50C4×D13—82no—
51C4×D13—82no—
52#518—131no—
53C2×#99—132no—
54#342—134no—
55C22×C13—41no—
56C22×C13C2×C22⋊C411yescharacteristic
57C22×C13#11712yes—
58C2×D13—22no—
59C2×D13—42no—
60C2×D13—44no—
61C2×D13—42no—
62C2×D13—82no—
63C2×D13#12314yes—
64#261—84no—
65C4×C13—21no—
66C4×C13—21no—
67C4×C13—42no—
68Dic13—42no—
69C22×D4—131no—
70C4×D4—262no—
71C4×D4—262no—
72#117—131no—
73#117#26111yescharacteristic, complemented
74C2×C22⋊C4—132no—
75C2×C22⋊C4—132no—
76C2×C22⋊C4—134no—
77#99—262no—
78#99—262no—
79C2×C13—21no—
80C2×C13—22no—
81C2×C13#38111yescharacteristic
82D13—24no—
83D13—42no—
84C24—131no—
85C24—131no—
86C2×D4—132no—
87C2×D4—132no—
88C2×D4—264no—
89C22×C4—262no—
90C22×C4—262no—
91C22×C4—264no—
92C22×C4C2×#26111yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—261no—
95C22⋊C4—132no—
96C22⋊C4—262no—
97C22⋊C4—262no—
98C22⋊C4—264no—
99C22⋊C4—264no—
100C22⋊C4C2×#26112yes—
101C42—21no—
102C42—261no—
103C13#182811yescharacteristic, complemented, Sylow
104C23—134no—
105C23—132no—
106C23—132no—
107C23—262no—
108C23—1041no—
109C23—1041no—
110C23C22×#26111yescharacteristic
111D4—264no—
112D4—264no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—262no—
116C2×C4—524no—
117C2×C4—1042no—
118C2×C4—1042no—
119C2×C4—1044no—
120C2×C4C22⋊#26111yescharacteristic
121C2×C4C22⋊#26111yescharacteristic
122C22—41no—
123C22—134no—
124C22—262no—
125C22—522no—
126C22—524no—
127C22—522no—
128C22—1042no—
129C22#8823712yes—
130C22C2×C22⋊#26111yescharacteristic
131C4—21no—
132C4—21no—
133C4—42no—
134C4—522no—
135C4—1044no—
136C2—21no—
137C2—22no—
138C2—264no—
139C2—522no—
140C2#1171913511yescharacteristic
subgroupG/H
centerC2#11719135
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC13×#117C4
socleC2×C13#381
prime radicalC22×D52C22
cosocleC23×D13C23
hypercenter#117#261
hypocenterC13#1828
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #11718238C2semidirect
6. C13×#117C4semidirect
7. #88180C4semidirect
9. C22⋊C4×D13C4semidirect
73. #117#261semidirect
103. C13#1828semidirect

Maximal subgroups

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

subgroupindex
#117192262
C2×#881072
#117182382
#182813