Finite Group Databasebeta

← #13113519

Subgroups — #13113519

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×#332C211yesmaximal, characteristic, complemented
5#11718139C211yesmaximal, characteristic, complemented
6#11718078C211yesmaximal, characteristic, complemented
7#11718074C211yesmaximal, characteristic, complemented
8C2×Q8×D13—21no—
9C13×C4⋊Q8C2211yescharacteristic
10#88198—21no—
11C2×#6094—21no—
12C4⋊C4×D13—21no—
13C4⋊C4×D13C412yes—
14#88142—21no—
15#88142C412yes—
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×C13—21no—
26Q8×D13—42no—
27Q8×D13—42no—
28C2×C4×D13—22no—
29C2×C4×D13C2×C411yescharacteristic
30C2×C4×D13D411yescharacteristic
31C2×C4×D13D411yescharacteristic
32C2×Dic26—21no—
33C2×Dic26—22no—
34C2×C8×C13—21no—
35C2×C8×C13—21no—
36C13×C4⋊C4—21no—
37C13×C4⋊C4C2×C412yes—
38C42×C13C2311yescharacteristic
39C4⋊Dic13—21no—
40C4⋊Dic13C2×C412yes—
41#6101—22no—
42#6101—22no—
43C4×Dic13C2×C411yescharacteristic
44C4×Dic13D411yescharacteristic
45C4×Dic13D411yescharacteristic
46C2×#1055—21no—
47C2×#1055—21no—
48#6094—42no—
49#1549—131nomaximal, Sylow
50C22×D13C22⋊C411yescharacteristic
51Q8×C13—41no—
52Q8×C13—41no—
53C2×C4×C13—22no—
54C2×C4×C13C22×C411yescharacteristic
55C2×C4×C13C2×D411yescharacteristic
56C2×C4×C13C2×D411yescharacteristic
57C2×Dic13—22no—
58C2×Dic13C22⋊C411yescharacteristic
59C2×Dic13C22⋊C411yescharacteristic
60C2×Dic13C22⋊C411yescharacteristic
61C4×D13—21no—
62C4×D13—21no—
63C4×D13—22no—
64C4×D13—44no—
65C4×D13SD1612yes—
66C4×D13Q1612yes—
67Dic26—44no—
68Dic26—41no—
69Dic26—41no—
70C8×C13—41no—
71C8×C13—41no—
72#1055—41no—
73#1055—41no—
74C2×C4⋊Q8—131no—
75#431—131no—
76#423—131no—
77#332—131no—
78#332—131no—
79#332—131no—
80#332D1311yescharacteristic, complemented
81C22×C13C2×C22⋊C411yescharacteristic
82C2×D13—21no—
83C2×D13—21no—
84C2×D13#10312yes—
85C4×C13—21no—
86C4×C13—42no—
87C4×C13C2×SD1611yescharacteristic
88C4×C13C2×Q1611yescharacteristic
89C4×C13AGL(1,ℤ/8)11yescharacteristic
90C4×C13AGL(1,ℤ/8)11yescharacteristic
91Dic13—21no—
92Dic13—42no—
93Dic13#10112yes—
94Dic13#10312yes—
95C22×Q8—261no—
96C2×M16—261no—
97C4⋊Q8—132no—
98C4⋊Q8—131no—
99C4⋊Q8—261no—
100C4⋊Q8—261no—
101C4⋊Q8C2×D1311yescharacteristic
102C2×C4⋊C4—132no—
103C2×C4⋊C4—261no—
104C2×C42—131no—
105C4⋊C8—131no—
106C4⋊C8—131no—
107C4⋊C8—261no—
108C4⋊C8C2×D1311yescharacteristic
109C4⋊C8C2×D1311yescharacteristic
110C22⋊C8—261no—
111C4×C8—261no—
112C2×C13C2×#10111yescharacteristic
113C2×C13C2×#10311yescharacteristic
114C2×C13#41811yescharacteristic
115D13—22no—
116C2×Q8—21no—
117C2×Q8—262no—
118C2×Q8—261no—
119C2×Q8—522no—
120C2×Q8—522no—
121C22×C4—131no—
122C22×C4—131no—
123C22×C4—131no—
124C22×C4—262no—
125M16—522no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—261no—
129C2×C8—261no—
130C4⋊C4—21no—
131C4⋊C4—132no—
132C4⋊C4—262no—
133C4⋊C4—262no—
134C4⋊C4—261no—
135C4⋊C4C4×D1312yes—
136C42—131no—
137C42—131no—
138C42—131no—
139C42C22×D1311yescharacteristic
140C13#154911yescharacteristic, complemented, Sylow
141C23—131no—
142Q8—41no—
143Q8—41no—
144Q8—524no—
145Q8—521no—
146Q8—521no—
147C2×C4—22no—
148C2×C4—131no—
149C2×C4—131no—
150C2×C4—132no—
151C2×C4—132no—
152C2×C4—131no—
153C2×C4—262no—
154C2×C4—261no—
155C2×C4—261no—
156C2×C4—262no—
157C2×C4—524no—
158C2×C4C2×C4×D1311yescharacteristic
159C2×C4D4×D1311yescharacteristic
160C2×C4D4×D1311yescharacteristic
161C8—41no—
162C8—41no—
163C8—521no—
164C8—521no—
165C22—132no—
166C22—261no—
167C22—261no—
168C22C22⋊C4×D1311yescharacteristic
169C4—21no—
170C4—42no—
171C4—132no—
172C4—132no—
173C4—261no—
174C4—522no—
175C4#8816511yescharacteristic
176C4SD16×D1311yescharacteristic
177C4#8816811yescharacteristic
178C4Q16×D1311yescharacteristic
179C2—262no—
180C2D13×#10111yescharacteristic
181C2#1171843111yescharacteristic
182C2D13×#10311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×#332C2
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C22⋊C4
cosocleC42×C13C23
hypercenter#332D13
hypocenterC13#1549
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. C13×#332C2semidirect
5. #11718139C2semidirect
6. #11718078C2semidirect
7. #11718074C2semidirect
80. #332D13semidirect
140. C13#1549semidirect

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×#3322
#117181392
#117180782
#117180742
#154913