Finite Group Databasebeta

← #15756541

Subgroups — #15756541

Order 3328.

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

normal subgroups only

This group has 384 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#13117801C211yesmaximal, characteristic
2#13113180C211yesmaximal, characteristic
3#13112730C212yesmaximal
4#13112701C212yesmaximal
5C4×C13×#101C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C13×#101—21no—
8C4×C13×M16C2212yes—
9#11718891—21no—
10#11718642—21no—
11#11718642—21no—
12C4⋊C4×Dic13—21no—
13#11718598C411yescharacteristic
14#11718598C2211yescharacteristic
15#11718597C411yescharacteristic
16C4×C4⋊Dic13C411yescharacteristic
17#11718593C411yescharacteristic
18#11718593C2211yescharacteristic
19#11718587C2212yes—
20C13×#343—21no—
21#11718120—21no—
22#11718120—21no—
23C22×Q8×C13D411yescharacteristic
24C2×C13×M16—22no—
25C4×Q8×C13—22no—
26C4×Q8×C13—22no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C13×#101—24no—
39C13×#97—22no—
40C4×C8×C13—22no—
41#88071—21no—
42#88071—21no—
43#88071—21no—
44#88071—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071C2×C411yescharacteristic
49#88071C2×C411yescharacteristic
50#88071C2×C411yescharacteristic
51#88071C2×C411yescharacteristic
52C22⋊#1055—22no—
53C4⋊#1055—22no—
54#88043—22no—
55#8775—131nomaximal, Sylow
56C2×Q8×C13—22no—
57C2×Q8×C13—22no—
58C2×Q8×C13—41no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C13×M16—24no—
71C13×M16—42no—
72C2×C8×C13—42no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—22no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13#4112yes—
81C42×C13#4112yes—
82C4⋊Dic13—42no—
83C4⋊Dic13—42no—
84C4×Dic13—42no—
85C4×Dic13—42no—
86C4×Dic13—42no—
87C2×#1055—42no—
88#2356—131no—
89C4×#101D1311yescharacteristic
90#1467—131no—
91#1300—132no—
92#1288—132no—
93C23×C13C2×C22⋊C411yescharacteristic
94Q8×C13—44no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13#10412yes—
109C2×C4×C13#11711yescharacteristic
110C2×C4×C13#11711yescharacteristic
111C2×C4×C13#12312yes—
112C2×C4×C13#12312yes—
113C2×Dic13—22no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C8×C13—44no—
126#1055—82no—
127C2×C4×Q8C2×D1311yescharacteristic
128#432—132no—
129C2×#101—21no—
130C4×M16C2×D1312yes—
131#391—261no—
132#387—261no—
133#387—261no—
134#383—131no—
135#383—131no—
136#382—131no—
137C4×C4⋊C4—131no—
138C4×C4⋊C4—261no—
139#376—131no—
140#376—131no—
141#343—21no—
142#324—261no—
143#324—261no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13#38111yescharacteristic
147C22×C13C2×#10411yescharacteristic
148C22×C13#42111yescharacteristic
149C4×C13—22no—
150C4×C13—22no—
151C4×C13—22no—
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157Dic13—42no—
158Dic13—81no—
159Dic13—81no—
160Dic13—81no—
161C22×Q8C22⋊D1311yescharacteristic
162C2×M16—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C2×C4⋊C4—261no—
166C2×C4⋊C4—261no—
167C2×C4⋊C4D5211yescharacteristic
168C2×C4⋊C4D5211yescharacteristic
169C2×C4⋊C4C22⋊D1311yescharacteristic
170C2×C42—261no—
171C2×C42—261no—
172C2×C42—261no—
173C2×C42C4×D1311yescharacteristic
174C2×C42C4×D1311yescharacteristic
175C2×C42C22×D1311yescharacteristic
176C4⋊C8—262no—
177#101—24no—
178C22⋊C8—262no—
179#97—22no—
180#97—262no—
181C4×C8—22no—
182#95—131no—
183#95—131no—
184#95—131no—
185#95—131no—
186#95—261no—
187#95—261no—
188#95—261no—
189#95—261no—
190#95—261no—
191#95—261no—
192#95—261no—
193C2×C13—21no—
194C2×C13—21no—
195C2×C13#182611yescharacteristic
196C2×C13#182711yescharacteristic
197C2×C13#183011yescharacteristic
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—41no—
201C22×C4—261no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4—261no—
205C22×C4#610311yescharacteristic
206C22×C4#610311yescharacteristic
207C22×C4#610311yescharacteristic
208C22×C4#610311yescharacteristic
209C22×C4C2×C4×D1311yescharacteristic
210C22×C4C2×D5211yescharacteristic
211C22×C4C2×C22⋊D1311yescharacteristic
212M16—24no—
213M16—42no—
214C2×C8—42no—
215C2×C8—522no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—522no—
220C4⋊C4—522no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—522no—
226C42—522no—
227C42—522no—
228C42#612912yes—
229C42#612912yes—
230C13#877511yescharacteristic, complemented, Sylow
231C23C2×#610311yescharacteristic
232Q8—44no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—262no—
247C2×C4—521no—
248C2×C4—521no—
249C2×C4—521no—
250C2×C4—521no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4#8804512yes—
259C2×C4#8813111yescharacteristic
260C2×C4#8813111yescharacteristic
261C2×C4#8814012yes—
262C2×C4#8818912yes—
263C8—44no—
264C8—1042no—
265C22—21no—
266C22—21no—
267C22C2×#8804511yescharacteristic
268C22#1171860411yescharacteristic
269C22#1171866611yescharacteristic
270C4—22no—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—522no—
279C4—1041no—
280C4—1041no—
281C4—1041no—
282C2—21no—
283C2—21no—
284C2#1311493611yescharacteristic
285C2#1311494111yescharacteristic
286C2#1311494811yescharacteristic
subgroupG/H
centerC22#11718604
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×#101C2
socleC22×C13#381
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenterC4×#101D13
hypocenterC13#8775
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
230. C13#8775semidirect

Maximal subgroups

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

subgroupindex
#131178012
#131131802
#131127302
#131127012
C4×C13×#1012
#877513