Finite Group Databasebeta

← #13116504

Subgroups — #13116504

Order 1664.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#11719379C211yesmaximal, characteristic
2D13×#99C212yesmaximal, complemented
3C13×#354C211yesmaximal, characteristic, complemented
4#11718133C211yesmaximal, characteristic, complemented
5#11718066C212yesmaximal, complemented
6C2×#6131C411yescharacteristic, complemented
7C2×D4×D13C2211yescharacteristic
8C13×#124C2211yescharacteristic
9#88201C411yescharacteristic, complemented
10#88194C2211yescharacteristic
11#88138—22no—
12#88136—22no—
13C22⋊C4×D13—22no—
14#88128C411yescharacteristic, complemented
15#88126C411yescharacteristic, complemented
16C13×#99C2212yes—
17#88074C2212yes—
18#88046—22no—
19C23×D13D412yes—
20C2×Q8×C13C2×C411yescharacteristic, complemented
21C2×D4×C13C2311yescharacteristic
22C2×C22⋊D13—22no—
23C2×C22⋊D13D412yes—
24#6131—42no—
25D4×D13—42no—
26C2×D52—21no—
27C2×D52—22no—
28C2×D52C2×C411yescharacteristic
29C2×D52C2×C411yescharacteristic, complemented
30C2×C4×D13—21no—
31C2×C4×D13—42no—
32C2×C4×D13C2×C411yescharacteristic
33C13×C22⋊C4—22no—
34C13×C22⋊C4—22no—
35C42×C13C2×C411yescharacteristic, complemented
36C22⋊Dic13—22no—
37#6103—21no—
38#6103—22no—
39#6103—42no—
40#6101—21no—
41C4×Dic13C2×C411yescharacteristic, complemented
42#2127—131nomaximal, Sylow
43C23×C13C2×D412yes—
44C22×D13—22no—
45C22×D13—22no—
46C22×D13—21no—
47C22×D13—82no—
48C22×D13C22⋊C412yes—
49C22×D13C22⋊C411yescharacteristic
50Q8×C13—41no—
51D4×C13—41no—
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13—42no—
55C2×C4×C13C22×C411yescharacteristic
56C22⋊D13—42no—
57C22⋊D13—82no—
58C2×Dic13—21no—
59C2×Dic13—42no—
60C2×Dic13C22⋊C411yescharacteristic
61D52—41no—
62D52—41no—
63D52—42no—
64D52—82no—
65C4×D13—22no—
66C4×D13—42no—
67C4×D13—84no—
68#535—131no—
69C2×#99—132no—
70#354—131no—
71#354D1311yescharacteristic, complemented
72#353—132no—
73C22×C13—22no—
74C22×C13—42no—
75C22×C13C2×C22⋊C411yescharacteristic
76C2×D13—22no—
77C2×D13—41no—
78C2×D13—44no—
79C2×D13—42no—
80C2×D13—42no—
81C2×D13—41no—
82C2×D13—82no—
83C2×D13#9912yes—
84C4×C13—21no—
85C4×C13—41no—
86C4×C13—41no—
87C4×C13—82no—
88Dic13—21no—
89Dic13—41no—
90Dic13—82no—
91C2×#41—131no—
92C22×D4—131no—
93#127—131no—
94#127—131no—
95#124—131no—
96#124C2×D1311yescharacteristic
97#121—262no—
98#120—262no—
99#117—131no—
100C2×C22⋊C4—262no—
101#99—132no—
102#99—262no—
103#99C2×D1312yes—
104C2×C13—21no—
105C2×C13—42no—
106C2×C13C2×#9911yescharacteristic
107D13—22no—
108D13—42no—
109D13—81no—
110C24—132no—
111#41—522no—
112C2×Q8C4×D1311yescharacteristic, complemented
113C2×D4—132no—
114C2×D4—131no—
115C2×D4—131no—
116C2×D4—261no—
117C2×D4—262no—
118C2×D4—262no—
119C2×D4—522no—
120C2×D4C22×D1311yescharacteristic
121C22×C4—131no—
122C22×C4—261no—
123C22×C4—522no—
124C4⋊C4—261no—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C22⋊C4—261no—
128C22⋊C4—262no—
129C22⋊C4—262no—
130C22⋊C4—522no—
131C42—131no—
132C42C4×D1311yescharacteristic, complemented
133C13#212711yescharacteristic, complemented, Sylow
134C23—131no—
135C23—132no—
136C23—262no—
137C23—262no—
138C23—261no—
139C23—1042no—
140C23D4×D1312yes—
141Q8—41no—
142D4—41no—
143D4—521no—
144D4—521no—
145D4—522no—
146D4—522no—
147D4—1042no—
148D4—1042no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—131no—
153C2×C4—262no—
154C2×C4—261no—
155C2×C4—522no—
156C2×C4—522no—
157C2×C4—1044no—
158C2×C4C2×C4×D1311yescharacteristic
159C22—22no—
160C22—42no—
161C22—132no—
162C22—262no—
163C22—521no—
164C22—522no—
165C22—522no—
166C22—524no—
167C22—521no—
168C22—1042no—
169C22C22⋊C4×D1311yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—261no—
175C4—521no—
176C4—1042no—
177C2—21no—
178C2—42no—
179C2—262no—
180C2—522no—
181C2—1041no—
182C2D13×#9911yescharacteristic
subgroupG/H
centerC2D13×#99
commutatorC2×C4×C13C22×C4
FrattiniC2×D4C22×D13
FittingC13×#354C2
socleC2×C13C2×#99
prime radical#11719379C2
cosocleC2×D4×C13C23
hypercenter#354D13
hypocenterC13#2127
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. D13×#99C2semidirect
3. C13×#354C2semidirect
4. #11718133C2semidirect
5. #11718066C2semidirect
6. C2×#6131C4semidirect
9. #88201C4semidirect
14. #88128C4semidirect
15. #88126C4semidirect
20. C2×Q8×C13C2×C4semidirect
29. C2×D52C2×C4semidirect
35. C42×C13C2×C4semidirect
41. C4×Dic13C2×C4semidirect
71. #354D13semidirect
112. C2×Q8C4×D13semidirect
132. C42C4×D13semidirect
133. C13#2127semidirect

Maximal subgroups

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

subgroupindex
#117193792
D13×#992
C13×#3542
#117181332
#117180662
#212713