Finite Group Databasebeta

← #13113572

Subgroups — #13113572

Order 1664.

210 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 67 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#11719433C211yesmaximal, characteristic
2#11718498C211yesmaximal, characteristic
3#11718498C211yesmaximal, characteristic
4C13×#332C211yesmaximal, characteristic, complemented
5#11718139C211yesmaximal, characteristic, complemented
6#11718078C211yesmaximal, characteristic, complemented
7#11718074C211yesmaximal, characteristic, complemented
8C13×C4⋊Q8C2211yescharacteristic
9#88200—21no—
10Q8×Dic13—21no—
11C2×#6094—21no—
12C2×#6094—21no—
13#88151—21no—
14#88146C412yes—
15#88144C412yes—
16#88141—21no—
17C42×D13C2211yescharacteristic
18#88123C2211yescharacteristic
19C13×C4⋊C8C2211yescharacteristic
20C13×C4⋊C8C2211yescharacteristic
21#88054—21no—
22#88054—21no—
23C4⋊#1055C2211yescharacteristic
24C4⋊#1055C2211yescharacteristic
25C2×Q8×C13—21no—
26C2×C4×D13C2×C411yescharacteristic
27C2×C4×D13D411yescharacteristic
28C2×C4×D13D411yescharacteristic
29C2×Dic26—21no—
30C2×C8×C13—21no—
31C2×C8×C13—21no—
32C13×C4⋊C4—21no—
33C13×C4⋊C4C2×C412yes—
34C42×C13C2311yescharacteristic
35#6103—22no—
36C4⋊Dic13—21no—
37C4⋊Dic13—22no—
38C4⋊Dic13C2×C412yes—
39#6101—22no—
40C4×Dic13—22no—
41C4×Dic13C2×C411yescharacteristic
42C4×Dic13D411yescharacteristic
43C4×Dic13D411yescharacteristic
44C2×#1055—21no—
45C2×#1055—21no—
46#6094—42no—
47#6094—42no—
48#1561—131nomaximal, Sylow
49C22×D13C22⋊C411yescharacteristic
50Q8×C13—41no—
51Q8×C13—41no—
52C2×C4×C13—22no—
53C2×C4×C13C22×C411yescharacteristic
54C2×C4×C13C2×D411yescharacteristic
55C2×C4×C13C2×D411yescharacteristic
56C2×Dic13—22no—
57C2×Dic13C22⋊C411yescharacteristic
58C2×Dic13C22⋊C411yescharacteristic
59C2×Dic13C22⋊C411yescharacteristic
60C4×D13—21no—
61C4×D13—21no—
62C4×D13—21no—
63C4×D13—21no—
64C4×D13—22no—
65Dic26—41no—
66Dic26—41no—
67C8×C13—41no—
68C8×C13—41no—
69#1055—41no—
70#1055—41no—
71#533—131no—
72#423—131no—
73#423—131no—
74#332—131no—
75#332—131no—
76#332—131no—
77#332D1311yescharacteristic, complemented
78C22×C13C2×C22⋊C411yescharacteristic
79C2×D13—21no—
80C2×D13—21no—
81C2×D13—21no—
82C4×C13—21no—
83C4×C13—42no—
84C4×C13AGL(1,ℤ/8)11yescharacteristic
85C4×C13AGL(1,ℤ/8)11yescharacteristic
86C4×C13#13711yescharacteristic
87C4×C13#13711yescharacteristic
88Dic13—21no—
89Dic13—21no—
90Dic13—42no—
91Dic13#10112yes—
92C2×M16—261no—
93C2×M16—261no—
94C4⋊Q8—131no—
95C4⋊Q8C2×D1311yescharacteristic
96#125—132no—
97C22⋊Q8—261no—
98C22⋊Q8—261no—
99C4×Q8—261no—
100C4×Q8—261no—
101#117—132no—
102C2×C42—131no—
103C4⋊C8—131no—
104C4⋊C8—131no—
105C4⋊C8—261no—
106C4⋊C8—261no—
107C4⋊C8C2×D1311yescharacteristic
108C4⋊C8C2×D1311yescharacteristic
109C2×C13C2×#10111yescharacteristic
110C2×C13#41711yescharacteristic
111C2×C13#41711yescharacteristic
112D13—41no—
113C2×Q8—21no—
114C2×Q8—261no—
115C22×C4—131no—
116C22×C4—131no—
117C22×C4—131no—
118M16—522no—
119M16—522no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—261no—
123C2×C8—261no—
124C4⋊C4—21no—
125C4⋊C4—132no—
126C4⋊C4—262no—
127C4⋊C4—262no—
128C4⋊C4—261no—
129C4⋊C4C4×D1312yes—
130C22⋊C4—262no—
131C42—131no—
132C42—131no—
133C42—131no—
134C42—262no—
135C42C22×D1311yescharacteristic
136C13#156111yescharacteristic, complemented, Sylow
137C23—131no—
138Q8—41no—
139Q8—41no—
140Q8—521no—
141Q8—521no—
142C2×C4—22no—
143C2×C4—131no—
144C2×C4—131no—
145C2×C4—131no—
146C2×C4—262no—
147C2×C4—261no—
148C2×C4—261no—
149C2×C4—261no—
150C2×C4—261no—
151C2×C4—262no—
152C2×C4C2×C4×D1311yescharacteristic
153C2×C4D4×D1311yescharacteristic
154C2×C4D4×D1311yescharacteristic
155C8—41no—
156C8—41no—
157C8—521no—
158C8—521no—
159C22—261no—
160C22—261no—
161C22—261no—
162C22C22⋊C4×D1311yescharacteristic
163C4—21no—
164C4—42no—
165C4—132no—
166C4—261no—
167C4—261no—
168C4—522no—
169C4#8816511yescharacteristic
170C4#8816811yescharacteristic
171C4#8816911yescharacteristic
172C4#8817211yescharacteristic
173C2—521no—
174C2D13×#10111yescharacteristic
175C2#1171843211yescharacteristic
176C2#1171846411yescharacteristic
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#1561
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
77. #332D13semidirect
136. C13#1561semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117184982
C13×#3322
#117181392
#117180782
#117180742
#156113