Finite Group Databasebeta

← #15775364

Subgroups — #15775364

Order 3328.

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

normal subgroups only

This group has 390 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#13126181C211yesmaximal, characteristic, complemented
2#13116765C212yesmaximal
3#13112847C212yesmaximal, complemented
4#13112776C211yesmaximal, characteristic, complemented
5C13×#2054C211yesmaximal, characteristic
6C22×C13×D8C2211yescharacteristic
7#11719175—21no—
8C2×C13×C4⋊C8C2211yescharacteristic
9C2×C13×#102—21no—
10C13×#390—21no—
11C2×#88067—22no—
12#11718777—21no—
13#11718777C2212yes—
14#11718511—22no—
15#11718510—22no—
16C13×#340C2211yescharacteristic
17#11718154—22no—
18C22⋊#6090C2212yes—
19C22×D4×C13—21no—
20C2×C13×D8—22no—
21C2×C13×D8—42no—
22C22×C8×C13D411yescharacteristic
23C22×C8×C13C2311yescharacteristic
24C2×C13×C4⋊C4—21no—
25C2×C13×C22⋊C4—41no—
26C2×C13×C22⋊C4—41no—
27C2×C42×C13D411yescharacteristic
28#88180—41no—
29#88178—22no—
30#88178—41no—
31C2×Dic52—21no—
32C2×Dic52D412yes—
33#88124—41no—
34#88123—21no—
35#88123—21no—
36C4×Dic26—22no—
37C4×Dic26—41no—
38C13×C4⋊C8—22no—
39C13×#102—42no—
40#88067—44no—
41#88058—21no—
42#88058D412yes—
43#88056—22no—
44#88056—22no—
45C2×#6090—22no—
46#12159—131nomaximal, Sylow
47C24×C13—41no—
48C2×D4×C13—22no—
49C2×D4×C13—41no—
50C2×D4×C13—41no—
51C2×D4×C13—41no—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13D811yescharacteristic
56C22×C4×C13D811yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C2×Dic26—22no—
59C2×Dic26—41no—
60C13×D8—24no—
61C13×D8—42no—
62C2×C8×C13—21no—
63C2×C8×C13—41no—
64C2×C8×C13—41no—
65C2×C8×C13C2×D412yes—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C22⋊C4—82no—
69C13×C22⋊C4—82no—
70C42×C13—21no—
71C42×C13—21no—
72C22⋊Dic13—42no—
73C4⋊Dic13—22no—
74C4⋊Dic13—41no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77#6101—42no—
78#6101—42no—
79C4×Dic13—42no—
80Dic52—42no—
81Dic52—81no—
82#6090—42no—
83#3249—131no—
84#2187—132no—
85#2054D1311yescharacteristic
86#1348—132no—
87#1322—131no—
88C23×C13—42no—
89C23×C13—81no—
90C23×C13—81no—
91C23×C13—81no—
92C23×C13—81no—
93C23×C13—81no—
94C23×C13—81no—
95C23×C13C2×D811yescharacteristic
96D4×C13—42no—
97D4×C13—42no—
98D4×C13—81no—
99D4×C13—81no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—41no—
106C2×C4×C13—81no—
107C2×C4×C13—81no—
108C2×C4×C13—81no—
109C2×C4×C13SD3212yescomplemented
110C2×C4×C13#12011yescharacteristic
111C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
112C2×Dic13—42no—
113C2×Dic13—42no—
114Dic26—42no—
115Dic26—42no—
116Dic26—82no—
117C8×C13—22no—
118C8×C13—41no—
119C22×D8C2×D1311yescharacteristic
120#533—261no—
121C2×SD32—262no—
122#477—262no—
123#467—132no—
124#467—261no—
125#462—262no—
126C2×C4⋊C8C2×D1311yescharacteristic
127C2×#102—21no—
128#390—21no—
129#357—262no—
130C22⋊C16—132no—
131#340C2×D1311yescharacteristic
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—82no—
135C22×C13—82no—
136C22×C13—82no—
137C22×C13—161no—
138C22×C13—161no—
139C22×C13—161no—
140C22×C13—161no—
141C22×C13#44711yescharacteristic
142C22×C13C2×SD3211yescharacteristic
143C22×C13#51011yescharacteristic
144C4×C13—21no—
145C4×C13—22no—
146C4×C13—41no—
147C4×C13—161no—
148C4×C13#45411yescharacteristic
149C4×C13B(4,𝔽2)11yescharacteristic
150Dic13—82no—
151Dic13—82no—
152C22×D4—21no—
153C2×Q16—132no—
154C2×Q16—261no—
155C2×D8—22no—
156C2×D8—42no—
157C22×C8C22⋊D1311yescharacteristic
158C22×C8C22×D1311yescharacteristic
159C4⋊Q8—261no—
160C4⋊Q8—261no—
161#125—521no—
162C22⋊Q8—262no—
163C22⋊Q8—521no—
164C4×Q8—262no—
165C4×Q8—521no—
166#117—521no—
167C2×C4⋊C4—21no—
168C2×C22⋊C4—41no—
169C2×C22⋊C4—41no—
170C2×C42C22⋊D1311yescharacteristic
171SD32—524no—
172C2×C16—262no—
173#107—132no—
174#107—261no—
175C4⋊C8—22no—
176#103—262no—
177#103—262no—
178#102—42no—
179C2×C13—21no—
180C2×C13—21no—
181C2×C13—162no—
182C2×C13#159811yescharacteristic
183C2×C13#218511yescharacteristic
184C2×C13#219011yescharacteristic
185C24—41no—
186C2×Q8—262no—
187C2×Q8—521no—
188C2×D4—22no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—41no—
194C22×C4—41no—
195C22×C4#610411yescharacteristic
196C22×C4#610411yescharacteristic
197C22×C4C2×C22⋊D1311yescharacteristic
198Q16—522no—
199Q16—1041no—
200D8—24no—
201D8—42no—
202C2×C8—21no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8D4×D1312yes—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—262no—
209C4⋊C4—521no—
210C4⋊C4—521no—
211C4⋊C4—522no—
212C4⋊C4—521no—
213C4⋊C4—522no—
214C22⋊C4—82no—
215C22⋊C4—82no—
216C22⋊C4—522no—
217C42—21no—
218C42—21no—
219C42—522no—
220C16—522no—
221C13#1215911yescharacteristic, complemented, Sylow
222C23—42no—
223C23—81no—
224C23—81no—
225C23—81no—
226C23—81no—
227C23—81no—
228C23—81no—
229C23C2×#610411yescharacteristic
230Q8—522no—
231Q8—522no—
232Q8—1042no—
233D4—42no—
234D4—42no—
235D4—81no—
236D4—81no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—522no—
247C2×C4—522no—
248C2×C4#8806712yescomplemented
249C2×C4#8819111yescharacteristic
250C2×C4#8820311yescharacteristic
251C8—22no—
252C8—41no—
253C22—21no—
254C22—21no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—161no—
259C22—161no—
260C22—161no—
261C22—161no—
262C22#1171869711yescharacteristic
263C22C2×#8806711yescharacteristic
264C22#1171885611yescharacteristic
265C4—22no—
266C4—21no—
267C4—41no—
268C4—161no—
269C4—1042no—
270C4—1042no—
271C4#1171869311yescharacteristic
272C4#1171872311yescharacteristic
273C2—21no—
274C2—21no—
275C2—162no—
276C2#1311377011yescharacteristic
277C2#1311675211yescharacteristic
278C2#1311678111yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#2054C2
socleC22×C13#447
prime radicalC22×C13×D8C22
hypercenter#2054D13
hypocenterC13#12159
LCSG ▷ C22×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2054

Complements

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

NH ≅ G/Ntype
1. #13126181C2semidirect
3. #13112847C2semidirect
4. #13112776C2semidirect
109. C2×C4×C13SD32semidirect
221. C13#12159semidirect
248. C2×C4#88067semidirect

Maximal subgroups

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

subgroupindex
#131261812
#131167652
#131128472
#131127762
C13×#20542
#1215913