Finite Group Databasebeta

← #15756459

Subgroups — #15756459

Order 3328.

474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 91 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#13117434C211yesmaximal, characteristic
2#13113163C211yesmaximal, characteristic
3#13112743C212yesmaximal, complemented
4#13112741C212yesmaximal, complemented
5C13×#1462C211yesmaximal, characteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C13×#407C2212yes—
8#11718908C412yes—
9#11718873C2211yescharacteristic
10#11718873C2211yescharacteristic
11C4×C22⋊Dic13C412yes—
12#11718868C2212yes—
13#11718612—22no—
14#11718612—22no—
15C13×#323—22no—
16#11718117—22no—
17C25×C13C2×C411yescharacteristic
18C23×C4×C13C2×C411yescharacteristic
19C23×C4×C13C2311yescharacteristic
20C2×C13×M16—22no—
21C2×C13×C22⋊C4—22no—
22C2×C13×C22⋊C4—22no—
23C2×C13×C22⋊C4D412yes—
24C2×C13×C22⋊C4D412yes—
25C2×C22⋊Dic13—22no—
26C2×C22⋊Dic13—22no—
27C2×C22⋊Dic13C2×C412yes—
28C2×C22⋊Dic13C2×C412yes—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4×Dic13—22no—
32C2×#6099—22no—
33C13×C22⋊C8—22no—
34C13×C22⋊C8—22no—
35#88071—22no—
36#88071—21no—
37#88071—21no—
38C22⋊#1055—22no—
39C22⋊#1055—22no—
40#8759—131nomaximal, Sylow
41C24×C13—21no—
42C24×C13—21no—
43C24×C13—41no—
44C24×C13—41no—
45C24×C13—81no—
46C24×C13—81no—
47C24×C13C22⋊C412yes—
48C24×C13C22×C411yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—81no—
52C22×C4×C13—81no—
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13#4112yes—
57C22×C4×C13#4112yes—
58C22×Dic13—22no—
59C22×Dic13—22no—
60C13×M16—82no—
61C2×C8×C13—42no—
62C13×C22⋊C4—24no—
63C13×C22⋊C4—24no—
64C22⋊Dic13—42no—
65C22⋊Dic13—42no—
66C22⋊Dic13—82no—
67C22⋊Dic13—82no—
68C4⋊Dic13—81no—
69C4⋊Dic13—81no—
70C4×Dic13—82no—
71#6099—82no—
72C2×#1055—42no—
73#2312—131no—
74#1462—131no—
75#1462D1311yescharacteristic
76#1305—132no—
77#1305—132no—
78C23×C13—21no—
79C23×C13—21no—
80C23×C13—22no—
81C23×C13—22no—
82C23×C13—22no—
83C23×C13—41no—
84C23×C13—41no—
85C23×C13—42no—
86C23×C13—42no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13—81no—
90C23×C13—81no—
91C23×C13—81no—
92C23×C13—81no—
93C23×C13—84no—
94C23×C13—84no—
95C23×C13C2×C22⋊C411yescharacteristic
96C23×C13#11711yescharacteristic
97C23×C13#11711yescharacteristic
98C2×C4×C13—22no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—81no—
105C2×C4×C13—81no—
106C2×C4×C13#12312yes—
107C2×C4×C13#12312yes—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C8×C13—82no—
115#1055—82no—
116C22×C22⋊C4C2×D1311yescharacteristic
117#407—132no—
118#407C2×D1312yes—
119#388—262no—
120#388—262no—
121#380—131no—
122#380—131no—
123#379—132no—
124C4×C22⋊C4—132no—
125#323—22no—
126#323—262no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13—82no—
141C22×C13—82no—
142C22×C13—84no—
143C22×C13—84no—
144C22×C13#38111yescharacteristic
145C22×C13#41311yescharacteristic
146C22×C13#41311yescharacteristic
147C4×C13—22no—
148C4×C13—22no—
149C4×C13—42no—
150Dic13—82no—
151Dic13—82no—
152C25C4×D1311yescharacteristic
153C23×C4C4×D1311yescharacteristic
154C23×C4C22×D1311yescharacteristic
155C2×M16—22no—
156C2×M16—262no—
157C2×C4⋊C4—261no—
158C2×C4⋊C4—261no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—132no—
162C2×C22⋊C4—132no—
163C2×C22⋊C4—262no—
164C2×C22⋊C4—262no—
165C2×C22⋊C4D5212yes—
166C2×C22⋊C4C22⋊D1312yes—
167C2×C42—262no—
168C22⋊C8—22no—
169C22⋊C8—22no—
170C22⋊C8—262no—
171C22⋊C8—262no—
172#95—262no—
173#95—261no—
174#95—261no—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13—41no—
178C2×C13—41no—
179C2×C13—82no—
180C2×C13#182211yescharacteristic
181C2×C13#182811yescharacteristic
182C2×C13#182911yescharacteristic
183C24—21no—
184C24—21no—
185C24—41no—
186C24—41no—
187C24—81no—
188C24—81no—
189C24#610312yes—
190C24C2×C4×D1311yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—81no—
194C22×C4—81no—
195C22×C4—262no—
196C22×C4—262no—
197C22×C4#610312yes—
198C22×C4C2×D5211yescharacteristic
199C22×C4#612912yes—
200C22×C4#612912yes—
201C22×C4C2×C22⋊D1311yescharacteristic
202M16—82no—
203M16—1042no—
204C2×C8—42no—
205C2×C8—522no—
206C4⋊C4—1041no—
207C4⋊C4—1041no—
208C22⋊C4—24no—
209C22⋊C4—24no—
210C22⋊C4—522no—
211C22⋊C4—522no—
212C22⋊C4—1042no—
213C22⋊C4—1042no—
214C42—1042no—
215C13#875911yescharacteristic, complemented, Sylow
216C23—21no—
217C23—21no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—41no—
222C23—41no—
223C23—42no—
224C23—42no—
225C23—42no—
226C23—42no—
227C23—81no—
228C23—81no—
229C23—81no—
230C23—81no—
231C23—84no—
232C23—84no—
233C23#8813111yescharacteristic
234C23#8813111yescharacteristic
235C23C2×#610311yescharacteristic
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4—522no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4#8814012yes—
251C2×C4#8818912yes—
252C8—82no—
253C8—1042no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—82no—
268C22—82no—
269C22—84no—
270C22—84no—
271C22#1171860411yescharacteristic
272C22#1171879311yescharacteristic
273C22#1171879311yescharacteristic
274C4—22no—
275C4—22no—
276C4—42no—
277C4—1042no—
278C4—1042no—
279C2—21no—
280C2—21no—
281C2—41no—
282C2—41no—
283C2—82no—
284C2#1311491711yescharacteristic
285C2#1311494211yescharacteristic
286C2#1311494511yescharacteristic
subgroupG/H
centerC22#11718604
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1462C2
socleC22×C13#381
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#1462D13
hypocenterC13#8759
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
3. #13112743C2semidirect
4. #13112741C2semidirect
215. C13#8759semidirect

Maximal subgroups

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

subgroupindex
#131174342
#131131632
#131127432
#131127412
C13×#14622
#875913