Finite Group Databasebeta

← #13113515

Subgroups — #13113515

Order 1664.

240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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
1D13×C4⋊Q8C211yesmaximal, characteristic
2#11718498C211yesmaximal, characteristic
3#11718494C211yesmaximal, characteristic
4C13×#333C211yesmaximal, characteristic, complemented
5#11718138C211yesmaximal, characteristic, complemented
6#11718073C211yesmaximal, characteristic, complemented
7#11718073C211yesmaximal, characteristic, complemented
8C2×Q8×D13C412yes—
9C13×C4⋊Q8C2211yescharacteristic
10#88198C412yes—
11C2×#6094—21no—
12C4⋊C4×D13—21no—
13C4⋊C4×D13—21no—
14#88142—21no—
15#88142—21no—
16C42×D13C2211yescharacteristic
17#88123C2211yescharacteristic
18C13×C4⋊C8C2211yescharacteristic
19C13×C4⋊C8C2211yescharacteristic
20#88060—21no—
21#88054—21no—
22C8×Dic13—21no—
23C4⋊#1055C2211yescharacteristic
24C4⋊#1055C2211yescharacteristic
25C2×Q8×C13C2×C412yes—
26Q8×D13—44no—
27C2×C4×D13—22no—
28C2×C4×D13C2×C411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×C4×D13D411yescharacteristic
31C2×Dic26—22no—
32C2×Dic26C2×C412yes—
33C2×C8×C13—21no—
34C2×C8×C13—21no—
35C13×C4⋊C4—21no—
36C13×C4⋊C4—21no—
37C42×C13C2311yescharacteristic
38C4⋊Dic13—21no—
39C4⋊Dic13—21no—
40#6101—22no—
41#6101—22no—
42C4×Dic13C2×C411yescharacteristic
43C4×Dic13D411yescharacteristic
44C4×Dic13D411yescharacteristic
45C2×#1055—21no—
46C2×#1055—21no—
47#6094—42no—
48#1548—131nomaximal, Sylow
49C22×D13C22⋊C411yescharacteristic
50Q8×C13—42no—
51C2×C4×C13—22no—
52C2×C4×C13C22×C411yescharacteristic
53C2×C4×C13C2×D411yescharacteristic
54C2×C4×C13C2×D411yescharacteristic
55C2×Dic13—22no—
56C2×Dic13C22⋊C411yescharacteristic
57C2×Dic13C22⋊C411yescharacteristic
58C2×Dic13C22⋊C411yescharacteristic
59C4×D13—21no—
60C4×D13—21no—
61C4×D13—22no—
62C4×D13—44no—
63C4×D13SD1612yes—
64C4×D13Q1612yes—
65Dic26—44no—
66Dic26—42no—
67C8×C13—41no—
68C8×C13—41no—
69#1055—41no—
70#1055—41no—
71C2×C4⋊Q8—131no—
72#431—131no—
73#423—131no—
74#333—131no—
75#333—131no—
76#333—131no—
77#333D1311yescharacteristic, complemented
78C22×C13C2×C22⋊C411yescharacteristic
79C2×D13—21no—
80C2×D13—21no—
81C2×D13#10312yes—
82C4×C13—21no—
83C4×C13—42no—
84C4×C13C2×SD1611yescharacteristic
85C4×C13C2×Q1611yescharacteristic
86C4×C13#13711yescharacteristic
87C4×C13#13711yescharacteristic
88Dic13—21no—
89Dic13—42no—
90Dic13#10012yes—
91Dic13#10312yes—
92C22×Q8—132no—
93C2×M16—261no—
94C4⋊Q8—132no—
95C4⋊Q8—131no—
96C4⋊Q8—261no—
97C4⋊Q8—261no—
98C4⋊Q8C2×D1311yescharacteristic
99C2×C4⋊C4—261no—
100C2×C4⋊C4—261no—
101C2×C42—131no—
102C4⋊C8—131no—
103C4⋊C8—131no—
104C4⋊C8—261no—
105C4⋊C8C2×D1311yescharacteristic
106C4⋊C8C2×D1311yescharacteristic
107C22⋊C8—261no—
108C4×C8—261no—
109C2×C13C2×#10011yescharacteristic
110C2×C13C2×#10311yescharacteristic
111C2×C13#41911yescharacteristic
112D13—22no—
113C2×Q8—132no—
114C2×Q8—262no—
115C2×Q8—524no—
116C2×Q8C4×D1312yes—
117C22×C4—131no—
118C22×C4—131no—
119C22×C4—131no—
120C22×C4—262no—
121M16—522no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—261no—
125C2×C8—261no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—262no—
129C4⋊C4—262no—
130C4⋊C4—261no—
131C4⋊C4—261no—
132C42—131no—
133C42—131no—
134C42—131no—
135C42C22×D1311yescharacteristic
136C13#154811yescharacteristic, complemented, Sylow
137C23—131no—
138Q8—42no—
139Q8—522no—
140Q8—524no—
141C2×C4—22no—
142C2×C4—131no—
143C2×C4—131no—
144C2×C4—132no—
145C2×C4—132no—
146C2×C4—131no—
147C2×C4—262no—
148C2×C4—261no—
149C2×C4—261no—
150C2×C4—262no—
151C2×C4—524no—
152C2×C4C2×C4×D1311yescharacteristic
153C2×C4D4×D1311yescharacteristic
154C2×C4D4×D1311yescharacteristic
155C8—41no—
156C8—41no—
157C8—521no—
158C8—521no—
159C22—132no—
160C22—261no—
161C22—261no—
162C22C22⋊C4×D1311yescharacteristic
163C4—21no—
164C4—42no—
165C4—132no—
166C4—132no—
167C4—261no—
168C4—522no—
169C4SD16×D1311yescharacteristic
170C4#8816911yescharacteristic
171C4Q16×D1311yescharacteristic
172C4#8817211yescharacteristic
173C2—262no—
174C2D13×#10011yescharacteristic
175C2D13×#10311yescharacteristic
176C2#1171846311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×#333C2
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C22⋊C4
cosocleC42×C13C23
hypercenter#333D13
hypocenterC13#1548
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. C13×#333C2semidirect
5. #11718138C2semidirect
6. #11718073C2semidirect
7. #11718073C2semidirect
77. #333D13semidirect
136. C13#1548semidirect

Maximal subgroups

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

subgroupindex
D13×C4⋊Q82
#117184982
#117184942
C13×#3332
#117181382
#117180732
#154813