Finite Group Databasebeta

← #13116518

Subgroups — #13116518

Order 1664.

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

normal subgroups only

This group has 250 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#11719373C211yesmaximal, characteristic
2#11718412C212yesmaximal, complemented
3C13×#355C211yesmaximal, characteristic, complemented
4#11718134C211yesmaximal, characteristic, complemented
5#11718070C212yesmaximal, complemented
6C2×#6131C2211yescharacteristic
7C2×#6129C411yescharacteristic
8C13×#124C2211yescharacteristic
9#88198C2211yescharacteristic
10#88194C411yescharacteristic
11M16×D13—22no—
12#88138—22no—
13#88135—22no—
14#88129C411yescharacteristic
15C42×D13C411yescharacteristic
16C13×#101C2212yes—
17#88076C2212yes—
18#88063—22no—
19C2×Q8×C13C2311yescharacteristic
20C2×D4×C13C2×C411yescharacteristic
21C2×C22⋊D13—22no—
22C2×C22⋊D13—21no—
23C22×Dic13—21no—
24#6131—41no—
25#6131—41no—
26#6129—41no—
27#6129—41no—
28C2×D52C2×C411yescharacteristic
29C2×D52D412yes—
30C2×C4×D13—21no—
31C2×C4×D13C2×C411yescharacteristic
32C2×C4×D13D412yes—
33C2×Dic26C2×C411yescharacteristic
34C13×M16—22no—
35C13×C22⋊C4—22no—
36C42×C13C2×C411yescharacteristic
37#6103—22no—
38#6101—22no—
39C4×Dic13—21no—
40C4×Dic13C2×C411yescharacteristic
41#6099—22no—
42#6094—42no—
43C8×D13—42no—
44#2132—131nomaximal, Sylow
45C23×C13—21no—
46C22×D13C22⋊C412yes—
47C22×D13C22⋊C411yescharacteristic
48Q8×C13—41no—
49D4×C13—41no—
50C2×C4×C13—21no—
51C2×C4×C13C22×C411yescharacteristic
52C2×C4×C13C2×D412yes—
53C22⋊D13—44no—
54C22⋊D13—42no—
55C2×Dic13—21no—
56C2×Dic13—21no—
57C2×Dic13—41no—
58C2×Dic13—41no—
59C2×Dic13C22⋊C411yescharacteristic
60D52—41no—
61D52—42no—
62C4×D13—22no—
63C4×D13—22no—
64C4×D13—21no—
65C4×D13—21no—
66C4×D13—42no—
67Dic26—41no—
68C8×C13—42no—
69#1055—42no—
70#532—131no—
71#413—132no—
72#356—132no—
73#355—131no—
74#355D1311yescharacteristic, complemented
75C22×C13—42no—
76C22×C13—41no—
77C22×C13C2×C22⋊C411yescharacteristic
78C2×D13—21no—
79C2×D13—22no—
80C2×D13—41no—
81C2×D13—42no—
82C4×C13—22no—
83C4×C13—21no—
84C4×C13—41no—
85Dic13—22no—
86Dic13—41no—
87Dic13#9911yescharacteristic
88Dic13#9911yescharacteristic
89C2×#41—131no—
90C2×#41—131no—
91C2×M16—262no—
92C4⋊Q8—131no—
93#127—131no—
94#124—131no—
95#124C2×D1311yescharacteristic
96#121—262no—
97C4×D4—262no—
98C2×C42—131no—
99#101—132no—
100#101C2×D1312yes—
101#100—262no—
102C2×C13—21no—
103C2×C13—81no—
104C2×C13C2×#9911yescharacteristic
105D13—41no—
106D13—42no—
107#41—521no—
108#41—521no—
109#41—521no—
110#41—521no—
111C2×Q8—131no—
112C2×Q8C22×D1311yescharacteristic
113C2×D4—131no—
114C2×D4—132no—
115C2×D4—262no—
116C2×D4—261no—
117C2×D4C4×D1311yescharacteristic
118C22×C4—131no—
119C22×C4—132no—
120C22×C4—261no—
121C22×C4—261no—
122M16—22no—
123M16—262no—
124M16—522no—
125C2×C8—522no—
126C4⋊C4—262no—
127C22⋊C4—22no—
128C22⋊C4—262no—
129C42—131no—
130C42—261no—
131C42C4×D1311yescharacteristic
132C13#213211yescharacteristic, complemented, Sylow
133C23—21no—
134C23—132no—
135C23—131no—
136Q8—41no—
137Q8—521no—
138D4—41no—
139D4—522no—
140D4—521no—
141D4—524no—
142D4—522no—
143C2×C4—21no—
144C2×C4—131no—
145C2×C4—262no—
146C2×C4—262no—
147C2×C4—261no—
148C2×C4—261no—
149C2×C4—261no—
150C2×C4—261no—
151C2×C4—522no—
152C2×C4—521no—
153C2×C4—521no—
154C2×C4C2×C4×D1311yescharacteristic
155C2×C4D4×D1312yes—
156C8—42no—
157C8—522no—
158C22—42no—
159C22—41no—
160C22—261no—
161C22—262no—
162C22—521no—
163C22—522no—
164C22C22⋊C4×D1311yescharacteristic
165C4—22no—
166C4—21no—
167C4—41no—
168C4—131no—
169C4—131no—
170C4—262no—
171C4—521no—
172C2—21no—
173C2—81no—
174C2—521no—
175C2—522no—
176C2D13×#9911yescharacteristic
subgroupG/H
centerC2D13×#99
commutatorC2×C4×C13C22×C4
FrattiniC2×Q8C22×D13
FittingC13×#355C2
socleC2×C13C2×#99
prime radical#11719373C2
cosocleC2×Q8×C13C23
hypercenter#355D13
hypocenterC13#2132
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #11718412C2semidirect
3. C13×#355C2semidirect
4. #11718134C2semidirect
5. #11718070C2semidirect
74. #355D13semidirect
132. C13#2132semidirect

Maximal subgroups

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

subgroupindex
#117193732
#117184122
C13×#3552
#117181342
#117180702
#213213