Finite Group Databasebeta

← #15778947

Subgroups — #15778947

Order 3328.

420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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#13123551C211yesmaximal, characteristic
2#13116499C212yesmaximal
3#13114880C212yesmaximal, complemented
4#13112957C211yesmaximal, characteristic, complemented
5C13×#1391C211yesmaximal, characteristic, complemented
6#11719537C2211yescharacteristic
7C2×#88202C2211yescharacteristic
8C2×#88161C411yescharacteristic, complemented
9C13×#410C2212yes—
10C13×#408C2211yescharacteristic
11#11718901C2212yes—
12#11718779C411yescharacteristic, complemented
13#11718771C411yescharacteristic, complemented
14C2×#88055C411yescharacteristic, complemented
15#11718659—22no—
16#11718391—22no—
17#11718389—22no—
18#11718123—22no—
19#11718066—22no—
20#11718065—22no—
21C2×C13×#41C2311yescharacteristic
22C2×#6127C2×C411yescharacteristic
23C2×C13×M16C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C13×#117—22no—
26#88202—42no—
27#88201Q811yescharacteristic
28#88198Q811yescharacteristic
29#88194D411yescharacteristic
30#88193—22no—
31#88190D411yescharacteristic
32C4×C22⋊D13—22no—
33#88180—22no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×#6099C2×C411yescharacteristic
36C2×#6099D412yes—
37C22×#1055C2×C411yescharacteristic
38C22×#1055D412yes—
39#88161—42no—
40C2×#6094—21no—
41C2×C8×D13—21no—
42C13×#99—22no—
43C13×#99—22no—
44C13×C22⋊C8—22no—
45#88074—22no—
46#88074—22no—
47#88060—22no—
48#88055—21no—
49#88055—21no—
50#88054—22no—
51#88048—42no—
52#88047—42no—
53#12808—131nomaximal, Sylow
54C13×#41—41no—
55C13×#41—41no—
56C2×Q8×C13C2×Q811yescharacteristic
57C2×D4×C13C2×D411yescharacteristic
58C2×D4×C13#4112yes—
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D412yes—
61C2×C22⋊D13—21no—
62C2×C22⋊D13—22no—
63C22×Dic13—21no—
64#6127—41no—
65#6127—41no—
66C2×D52C4⋊C411yescharacteristic
67C2×C4×D13—21no—
68C2×Dic26C4⋊C411yescharacteristic
69C13×M16—41no—
70C2×C8×C13—21no—
71C2×C8×C13—21no—
72C2×C8×C13—41no—
73C13×C4⋊C4—42no—
74C13×C22⋊C4—42no—
75C42×C13—42no—
76C22⋊Dic13—22no—
77C22⋊Dic13—42no—
78#6103—22no—
79C4⋊Dic13—42no—
80#6101—22no—
81C4×Dic13—21no—
82C4×Dic13—42no—
83C4×Dic13C4⋊C411yescharacteristic
84C4×Dic13C4⋊C411yescharacteristic
85#6099—41no—
86#6099—42no—
87C2×#1055—22no—
88C2×#1055—22no—
89C2×#1055—22no—
90C2×#1055C22⋊C411yescharacteristic
91C2×#1055C22⋊C412yes—
92C2×#1055C22⋊C411yescharacteristic
93#6094—42no—
94C8×D13—42no—
95#2932—131no—
96#2126—132no—
97#1812—132no—
98#1391—131no—
99#1391D1311yescharacteristic, complemented
100C23×C13#11711yescharacteristic
101C23×C13#12112yes—
102C22×D13—21no—
103Q8×C13—41no—
104D4×C13—41no—
105D4×C13—42no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—21no—
110C2×C4×C13—82no—
111C2×C4×C13C2×C22⋊C411yescharacteristic
112C2×C4×C13C2×C4⋊C411yescharacteristic
113C2×C4×C13C22⋊Q812yes—
114C22⋊D13—42no—
115C22⋊D13—82no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—81no—
120C2×Dic13—82no—
121D52—41no—
122C4×D13—41no—
123C4×D13—41no—
124Dic26—41no—
125C8×C13—41no—
126C8×C13—41no—
127#1055—21no—
128#1055—22no—
129#1055#9912yes—
130C2×#131—131no—
131C2×#131—131no—
132#532—131no—
133#435—262no—
134#435—262no—
135#427—262no—
136#423—131no—
137#410—132no—
138#410C2×D1312yes—
139#408—131no—
140#408C2×D1311yescharacteristic
141C2×#97—131no—
142#354—262no—
143#353—262no—
144H(3,ℤ/4)—262no—
145C22×C13—22no—
146C22×C13—21no—
147C22×C13—41no—
148C22×C13—42no—
149C22×C13#38011yescharacteristic
150C2×D13—42no—
151C2×D13—41no—
152C4×C13—21no—
153C4×C13—22no—
154C4×C13—162no—
155C4×C13C2×#9911yescharacteristic
156C4×C13#41011yescharacteristic
157Dic13—41no—
158Dic13—41no—
159Dic13—41no—
160Dic13—162no—
161C2×#41—131no—
162C2×#41C22×D1311yescharacteristic
163#131—522no—
164#131—522no—
165C2×M16—131no—
166C2×M16—132no—
167C2×M16—261no—
168C2×M16C4×D1311yescharacteristic
169C22×C8—131no—
170C22×C8—132no—
171C22×C8—261no—
172C22×C8C4×D1311yescharacteristic
173C4⋊Q8—131no—
174#127—131no—
175#124—131no—
176#124—131no—
177#121—262no—
178C4×D4—262no—
179#117—22no—
180#117—262no—
181C2×C42—131no—
182#107—522no—
183#106—522no—
184C4⋊C8—262no—
185#99—22no—
186#99—22no—
187#99—262no—
188#99—262no—
189C22⋊C8—22no—
190C22⋊C8—262no—
191#97—261no—
192#97—261no—
193C2×C13—21no—
194C2×C13—42no—
195C2×C13—41no—
196C2×C13#179911yescharacteristic
197D13—81no—
198#41—41no—
199#41—41no—
200#41—521no—
201#41—521no—
202C2×Q8—131no—
203C2×Q8Q8×D1311yescharacteristic
204C2×D4—131no—
205C2×D4—261no—
206C2×D4—262no—
207C2×D4#612712yes—
208C2×D4D4×D1311yescharacteristic
209C22×C4—261no—
210C22×C4—261no—
211C22×C4C2×C4×D1311yescharacteristic
212C22×C4D4×D1312yes—
213M16—41no—
214M16—522no—
215M16—522no—
216M16—521no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—41no—
220C2×C8—131no—
221C2×C8—131no—
222C2×C8—132no—
223C2×C8—262no—
224C2×C8—262no—
225C2×C8—262no—
226C2×C8—522no—
227C4⋊C4—42no—
228C4⋊C4—262no—
229C4⋊C4—522no—
230C22⋊C4—42no—
231C22⋊C4—262no—
232C22⋊C4—262no—
233C22⋊C4—522no—
234C42—42no—
235C42—131no—
236C42—131no—
237C42—261no—
238C42—522no—
239C13#1280811yescharacteristic, complemented, Sylow
240C23—261no—
241C23#8812611yescharacteristic
242C23#8813812yes—
243Q8—41no—
244Q8—521no—
245D4—42no—
246D4—41no—
247D4—521no—
248D4—522no—
249D4—1042no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—82no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4—1041no—
261C2×C4—1042no—
262C2×C4C22⋊C4×D1311yescharacteristic
263C2×C4C4⋊C4×D1311yescharacteristic
264C2×C4#8815012yes—
265C8—41no—
266C8—41no—
267C8—132no—
268C8—261no—
269C8—262no—
270C22—22no—
271C22—21no—
272C22—41no—
273C22—42no—
274C22—522no—
275C22—521no—
276C22#1171832811yescharacteristic
277C4—21no—
278C4—22no—
279C4—162no—
280C4—521no—
281C4—521no—
282C4—521no—
283C4—2082no—
284C4#1171840111yescharacteristic
285C4D13×#9911yescharacteristic
286C2—21no—
287C2—42no—
288C2—41no—
289C2—1041no—
290C2#1311482311yescharacteristic
subgroupG/H
centerC4#11718401
commutatorC22×C4×C13C22×C4
FrattiniC2×#41C22×D13
FittingC13×#1391C2
socleC2×C13#1799
prime radical#11719537C22
cosocleC2×C13×#41C23
hypercenter#1391D13
hypocenterC13#12808
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1391

Complements

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

NH ≅ G/Ntype
3. #13114880C2semidirect
4. #13112957C2semidirect
5. C13×#1391C2semidirect
8. C2×#88161C4semidirect
12. #11718779C4semidirect
13. #11718771C4semidirect
14. C2×#88055C4semidirect
99. #1391D13semidirect
239. C13#12808semidirect

Maximal subgroups

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

subgroupindex
#131235512
#131164992
#131148802
#131129572
C13×#13912
#1280813