Finite Group Databasebeta

← #15774440

Subgroups — #15774440

Order 3328.

268 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 69 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#13125496C211yesmaximal, characteristic
2#13116651C211yesmaximal, characteristic
3#13116600C211yesmaximal, characteristic
4#13112897C211yesmaximal, characteristic, complemented
5#13112874C211yesmaximal, characteristic, complemented
6#13112874C211yesmaximal, characteristic, complemented
7C13×#1366C211yesmaximal, characteristic, complemented
8#11719402C412yes—
9C13×#499C2211yescharacteristic
10#11718730C412yes—
11D13×M32—21no—
12#11718548—21no—
13#11718534—21no—
14#11718529—21no—
15#11718514—21no—
16#11718360C2211yescharacteristic
17#11718350C2211yescharacteristic
18C13×#364C2211yescharacteristic
19C13×#364C2211yescharacteristic
20#11718106—21no—
21#11718104—21no—
22#11718103—21no—
23#11718055C2211yescharacteristic
24#11718055C2211yescharacteristic
25C13×#125C2×C412yes—
26C2×Dic52—21no—
27C2×Dic52—21no—
28C2×#6094D411yescharacteristic
29C2×C8×D13D411yescharacteristic
30#88152—42no—
31#88151—22no—
32#88144—42no—
33#88141—22no—
34#88126C2×C411yescharacteristic
35#88123C2×C412yes—
36C13×M32—21no—
37C13×M32—21no—
38C13×#107—21no—
39C13×#106—21no—
40C4×C8×C13C2311yescharacteristic
41#88055D411yescharacteristic
42C8×Dic13D411yescharacteristic
43#88052—21no—
44#88052—21no—
45#88050—22no—
46#88050—22no—
47#88043C2×C411yescharacteristic
48#88038—41no—
49C16×D13—41no—
50#11990—131nomaximal, Sylow
51C2×C4×D13C22⋊C411yescharacteristic
52C2×Dic26—22no—
53C2×C8×C13C2×D411yescharacteristic
54C2×C8×C13C2×D411yescharacteristic
55C13×C4⋊C4—22no—
56C13×C4⋊C4—42no—
57C42×C13C22×C411yescharacteristic
58#6103—21no—
59#6103—42no—
60C4⋊Dic13—42no—
61C4⋊Dic13—42no—
62#6101—21no—
63#6101—42no—
64C4×Dic13—42no—
65C4×Dic13C22⋊C411yescharacteristic
66C2×#1055C22⋊C411yescharacteristic
67C2×#1055C22⋊C411yescharacteristic
68Dic52—41no—
69Dic52—41no—
70Dic52—41no—
71Dic52—41no—
72#6094—21no—
73#6094—21no—
74C8×D13—21no—
75C8×D13—21no—
76C13×C16—41no—
77C13×C16—41no—
78#6090—41no—
79#6090—41no—
80#3177—131no—
81#2166—131no—
82#2153—131no—
83#1366—131no—
84#1366D1311yescharacteristic, complemented
85#1358—131no—
86#1358—131no—
87C22×D13#10011yescharacteristic
88C2×C4×C13—21no—
89C2×C4×C13—42no—
90C2×C4×C13C2×C22⋊C411yescharacteristic
91C2×Dic13—21no—
92C2×Dic13—42no—
93C2×Dic13#10011yescharacteristic
94C4×D13—21no—
95C4×D13—21no—
96Dic26—42no—
97Dic26—42no—
98C8×C13#13511yescharacteristic
99C8×C13#13511yescharacteristic
100C8×C13AGL(1,ℤ/8)11yescharacteristic
101C8×C13#13711yescharacteristic
102#1055—21no—
103#1055—21no—
104#541—132no—
105C2×M32—261no—
106#499C2×D1311yescharacteristic
107#494—131no—
108#491—132no—
109#470—261no—
110#467—261no—
111#441—261no—
112C4×Q16—261no—
113#405—131no—
114#364—131no—
115#364—131no—
116#364—261no—
117#364C2×D1311yescharacteristic
118#364C2×D1311yescharacteristic
119#349—261no—
120#347—261no—
121C22×C13C2×#10011yescharacteristic
122C2×D13—21no—
123C2×D13—41no—
124C4×C13—41no—
125C4×C13—82no—
126C4×C13#41611yescharacteristic
127C4×C13#41711yescharacteristic
128Dic13—21no—
129Dic13—41no—
130Dic13—82no—
131C2×Q16—261no—
132C2×Q16—261no—
133C2×M16—131no—
134C22×C8—131no—
135C4⋊Q8—132no—
136#126—522no—
137#125—522no—
138#125C4×D1312yes—
139C22⋊Q8—262no—
140C4×Q8—262no—
141#117—131no—
142M32—21no—
143M32—21no—
144M32—261no—
145M32—261no—
146M32—521no—
147C2×C16—521no—
148#107—21no—
149#106—21no—
150#103—262no—
151#103—262no—
152#97—131no—
153#97—131no—
154C4×C8—131no—
155C4×C8C22×D1311yescharacteristic
156C2×C13—21no—
157C2×C13#155111yescharacteristic
158D13—41no—
159C2×Q8—262no—
160C22×C4—131no—
161Q16—521no—
162Q16—521no—
163Q16—521no—
164Q16—521no—
165M16—261no—
166M16—261no—
167C2×C8—131no—
168C2×C8—131no—
169C2×C8—261no—
170C2×C8—261no—
171C2×C8D4×D1311yescharacteristic
172C2×C8D4×D1311yescharacteristic
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—261no—
176C4⋊C4—522no—
177C4⋊C4—522no—
178C4⋊C4—522no—
179C22⋊C4—261no—
180C22⋊C4—522no—
181C42—131no—
182C42—522no—
183C42C2×C4×D1311yescharacteristic
184C16—41no—
185C16—41no—
186C16—521no—
187C16—521no—
188C13#1199011yescharacteristic, complemented, Sylow
189C23—131no—
190Q8—522no—
191Q8—522no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—131no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—522no—
199C2×C4C22⋊C4×D1311yescharacteristic
200C8—261no—
201C8—261no—
202C8#8816811yescharacteristic
203C8#8817011yescharacteristic
204C8#8817211yescharacteristic
205C8#8817311yescharacteristic
206C22—261no—
207C22—521no—
208C22D13×#10011yescharacteristic
209C4—41no—
210C4—82no—
211C4—261no—
212C4—521no—
213C4—1042no—
214C4#1171846411yescharacteristic
215C4#1171846511yescharacteristic
216C2—21no—
217C2—521no—
218C2#1311353011yescharacteristic
subgroupG/H
centerC2#13113530
commutatorC42×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#1366C2
socleC2×C13#1551
prime radicalC22×D13#100
cosocleC4×C8×C13C23
hypercenter#1366D13
hypocenterC13#11990
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
4. #13112897C2semidirect
5. #13112874C2semidirect
6. #13112874C2semidirect
7. C13×#1366C2semidirect
84. #1366D13semidirect
188. C13#11990semidirect

Maximal subgroups

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

subgroupindex
#131254962
#131166512
#131166002
#131128972
#131128742
C13×#13662
#1199013