Finite Group Databasebeta

← #15767929

Subgroups — #15767929

Order 3328.

354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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#13115669C211yesmaximal, characteristic
2#13114989C211yesmaximal, characteristic, complemented
3#13113607C211yesmaximal, characteristic, complemented
4#13113606C211yesmaximal, characteristic, complemented
5#13113235C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic, complemented
7C13×#1480C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×#88077—22no—
12C2×#88054—22no—
13#11718593C2211yescharacteristic
14#11718586C2211yescharacteristic
15#11718585C2211yescharacteristic
16C2×C4⋊#1055C2211yescharacteristic
17C13×D4⋊C8—22no—
18D4⋊#1055—22no—
19#11718072—22no—
20#11718049—22no—
21C2×C13×#41—21no—
22C22×C8×C13—21no—
23C13×C4⋊Q8Q811yescharacteristic
24C13×#127Q811yescharacteristic
25C13×#124—21no—
26C13×#121—21no—
27C13×#121—21no—
28C4×D4×C13—21no—
29C4×D4×C13—21no—
30C2×C42×C13C2311yescharacteristic
31C2×C4×Dic13D412yes—
32C2×#6099—21no—
33C22×#1055—21no—
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C4⋊C8—21no—
37C13×C22⋊C8—21no—
38C4×C8×C13D412yes—
39#88077—44no—
40#88071—21no—
41#88071—21no—
42C22⋊#1055—21no—
43#88054—44no—
44C4⋊#1055—21no—
45C4⋊#1055—21no—
46C4⋊#1055—21no—
47C4⋊#1055—21no—
48C4⋊#1055—21no—
49C4×#1055D412yes—
50#10666—131nomaximal, Sylow
51C13×#41—42no—
52C13×#41—42no—
53C2×Q8×C13—21no—
54C2×D4×C13—21no—
55C2×D4×C13—21no—
56C2×D4×C13—21no—
57C2×D4×C13—41no—
58C22×C4×C13—41no—
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13#4111yescharacteristic
61C22×C4×C13#4111yescharacteristic
62C22×Dic13—22no—
63C2×C8×C13—22no—
64C2×C8×C13—41no—
65C2×C8×C13—42no—
66C13×C4⋊C4—21no—
67C13×C4⋊C4—21no—
68C13×C22⋊C4—41no—
69C13×C22⋊C4—41no—
70C42×C13C2×D411yescharacteristic
71C42×C13C2×D411yescharacteristic
72C42×C13C2×Q811yescharacteristic
73C42×C13#4111yescharacteristic
74C4×Dic13—22no—
75C4×Dic13SD1614yes—
76#6099—42no—
77C2×#1055—22no—
78C2×#1055—41no—
79C2×#1055—41no—
80C2×#1055—42no—
81#1963—131no—
82#1843—131no—
83#1570—131no—
84#1570—131no—
85#1480—131no—
86#1480D1311yescharacteristic
87#1274—131no—
88C23×C13—41no—
89C23×C13#12311yescharacteristic
90Q8×C13—42no—
91D4×C13—42no—
92D4×C13—42no—
93D4×C13—42no—
94D4×C13—82no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—81no—
99C2×C4×C13—81no—
100C2×C4×C13C22⋊Q811yescharacteristic
101C2×C4×C13C22⋊Q811yescharacteristic
102C2×C4×C13C22⋊Q811yescharacteristic
103C2×C4×C13#12311yescharacteristic
104C2×C4×C13#12311yescharacteristic
105C2×C4×C13#12711yescharacteristic
106C2×C4×C13C2×SD1612yes—
107C2×C4×C13AGL(1,ℤ/8)12yes—
108C2×Dic13—24no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C8×C13—42no—
112C8×C13—81no—
113#1055—42no—
114#1055—81no—
115#1055—81no—
116#532C2×D1311yescharacteristic
117#431—131no—
118#431C2×D1311yescharacteristic
119#423—131no—
120C2×C4⋊C8—131no—
121C2×C4⋊C8—262no—
122C2×C4⋊C8C2×D1311yescharacteristic
123C2×#104—262no—
124#376—131no—
125#334—262no—
126#334—262no—
127D4⋊C8—22no—
128D4⋊C8—262no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13—81no—
132C22×C13—81no—
133C22×C13—81no—
134C22×C13#39911yescharacteristic
135C22×C13#48112yes—
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—81no—
141C4×C13#47612yes—
142C4×C13#49211yescharacteristic
143C4×C13#49611yescharacteristic
144Dic13—44no—
145C2×#41—21no—
146C2×M16—261no—
147C22×C8—21no—
148C22×C8—261no—
149C4⋊Q8Dic2611yescharacteristic
150#127Dic2611yescharacteristic
151#124—21no—
152#121—21no—
153#121—21no—
154C4×D4—21no—
155C4×D4—21no—
156C2×C42—132no—
157C2×C42C22×D1311yescharacteristic
158C4⋊C8—21no—
159C4⋊C8—21no—
160C4⋊C8—21no—
161C4⋊C8—261no—
162C4⋊C8—261no—
163C4⋊C8—261no—
164C4⋊C8—261no—
165C4⋊C8—261no—
166C4⋊C8—524no—
167#104—524no—
168C22⋊C8—21no—
169C22⋊C8—261no—
170C4×C8—132no—
171C4×C8C22⋊D1312yes—
172#95—261no—
173#95—261no—
174C2×C13—22no—
175C2×C13—161no—
176C2×C13#209411yescharacteristic
177C2×C13#209811yescharacteristic
178C2×C13#209811yescharacteristic
179#41—42no—
180#41—42no—
181C2×Q8—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—41no—
186C22×C4—41no—
187C22×C4—262no—
188C22×C4#612711yescharacteristic
189C22×C4D4×D1311yescharacteristic
190C22×C4#612911yescharacteristic
191M16—522no—
192C2×C8—22no—
193C2×C8—42no—
194C2×C8—41no—
195C2×C8—262no—
196C2×C8—522no—
197C2×C8—521no—
198C2×C8—521no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C22⋊C4—41no—
202C22⋊C4—41no—
203C42—134no—
204C42—262no—
205C42C2×Dic2611yescharacteristic
206C42D4×D1311yescharacteristic
207C42#612911yescharacteristic
208C42C2×C22⋊D1311yescharacteristic
209C13#1066611yescharacteristic, complemented, Sylow
210C23—41no—
211C23#8813711yescharacteristic
212Q8—42no—
213D4—42no—
214D4—42no—
215D4—42no—
216D4—82no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4—264no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4#8813211yescharacteristic
226C2×C4#8813211yescharacteristic
227C2×C4#8813711yescharacteristic
228C2×C4#8816512yes—
229C2×C4SD16×D1312yes—
230C2×C4#8817811yescharacteristic
231C2×C4#8818911yescharacteristic
232C2×C4#8819411yescharacteristic
233C8—42no—
234C8—81no—
235C8—522no—
236C8—1041no—
237C8—1041no—
238C22—21no—
239C22—21no—
240C22—81no—
241C22—81no—
242C22—81no—
243C22#1171843812yes—
244C22#1171861011yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—21no—
249C4—81no—
250C4—524no—
251C4#1171842212yes—
252C4#1171881511yescharacteristic
253C4#1171883611yescharacteristic
254C2—22no—
255C2—161no—
256C2#1311636711yescharacteristic
257C2#1311638911yescharacteristic
258C2#1311639111yescharacteristic
subgroupG/H
centerC2×C4#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1480C2
socleC22×C13#399
prime radicalC13×#532C22
hypercenter#1480D13
hypocenterC13#10666
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #13114989C2semidirect
3. #13113607C2semidirect
4. #13113606C2semidirect
6. #13112664C2semidirect
209. C13#10666semidirect

Maximal subgroups

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

subgroupindex
#131156692
#131149892
#131136072
#131136062
#131132352
#131126642
C13×#14802
#1066613