Finite Group Databasebeta

← #16778726

Subgroups — #16778726

Order 3328.

378 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 90 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#13130752C211yesmaximal, characteristic
2#13130622C211yesmaximal, characteristic
3#13129655C212yesmaximal
4#13129655C212yesmaximal
5#13123221C211yesmaximal, characteristic
6C2×#88112—21no—
7C2×#88110—21no—
8C2×C4⋊#1057—21no—
9C13×#382C411yescharacteristic
10#11718646C411yescharacteristic
11#11718646C411yescharacteristic
12#11718634C2211yescharacteristic
13#11718634C2211yescharacteristic
14#11718597C411yescharacteristic
15C42×Dic13C2211yescharacteristic
16#11718316—21no—
17#11718316—21no—
18#11718315—21no—
19#11718315—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13C2311yescharacteristic
40#88112—42no—
41#88110—42no—
42C4⋊#1057—24no—
43C13×#95—21no—
44C13×#95—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#7697—131nomaximal, Sylow
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×Dic13—21no—
58C22×Dic13—21no—
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C22×Dic13C2×D411yescharacteristic
63C2×#1057—24no—
64C2×#1057—42no—
65C2×#1057—42no—
66C2×#1057—42no—
67C2×#1057—42no—
68C2×#1057—42no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C42×C13—22no—
72C4⋊Dic13—22no—
73C4⋊Dic13—22no—
74C4⋊Dic13—42no—
75C4⋊Dic13—42no—
76#6101—41no—
77#6101—41no—
78#6101—41no—
79#6101—41no—
80C4×Dic13—22no—
81C4×Dic13—22no—
82C4×Dic13—21no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88#2864—131no—
89#1831—131no—
90#1767—131no—
91#1271—132no—
92#1271—132no—
93C23×C13C2×C22⋊C411yescharacteristic
94C2×C4×C13—21no—
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—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13#10112yes—
108C2×C4×C13#13112yes—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13#10412yes—
125C2×Dic13AGL(1,ℤ/8)11yescharacteristic
126C2×Dic13AGL(1,ℤ/8)11yescharacteristic
127C2×Dic13#13711yescharacteristic
128C2×Dic13#13711yescharacteristic
129#1057—44no—
130#1057—82no—
131C2×C4⋊C8—261no—
132C2×C4⋊C8—261no—
133C2×#97—261no—
134#389—131no—
135#389—131no—
136#389—131no—
137#389—131no—
138#387—261no—
139#387—261no—
140#387—261no—
141#387—261no—
142#382—131no—
143#382#26111yescharacteristic
144C43—131no—
145#336—132no—
146#336—132no—
147#336—261no—
148C22×C13#40811yescharacteristic
149C22×C13#41011yescharacteristic
150C22×C13C2×#10111yescharacteristic
151C22×C13#41711yescharacteristic
152C22×C13#41711yescharacteristic
153C22×C13C2×#10411yescharacteristic
154C22×C13#42111yescharacteristic
155C4×C13—22no—
156C4×C13—22no—
157C4×C13—41no—
158C4×C13—81no—
159C4×C13—81no—
160Dic13—22no—
161Dic13—21no—
162Dic13—21no—
163Dic13—21no—
164Dic13—21no—
165Dic13—41no—
166Dic13—81no—
167Dic13—81no—
168C22×C8—262no—
169C22×C8—262no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—131no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4C2×#26111yescharacteristic
177C2×C4⋊C4C2×#26111yescharacteristic
178C2×C42—131no—
179C2×C42—131no—
180C2×C42—131no—
181C2×C42—131no—
182C2×C42—131no—
183C2×C42—131no—
184C2×C42C2×#26111yescharacteristic
185C4⋊C8—264no—
186C4⋊C8—522no—
187#97—522no—
188#95—21no—
189#95—21no—
190#95—261no—
191#95—261no—
192#95—261no—
193#95—261no—
194#95—261no—
195#95—261no—
196C2×C13#147011yescharacteristic
197C2×C13#148311yescharacteristic
198C2×C13#149511yescharacteristic
199C2×C13#150911yescharacteristic
200C2×C13#151211yescharacteristic
201C2×C13#153111yescharacteristic
202C2×C13#156111yescharacteristic
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—131no—
206C22×C4—131no—
207C22×C4—131no—
208C22×C4—131no—
209C22×C4—261no—
210C22×C4—261no—
211C22×C4C22⋊#26111yescharacteristic
212C22×C4C22⋊#26111yescharacteristic
213C22×C4C22×#26111yescharacteristic
214C2×C8—264no—
215C2×C8—522no—
216C2×C8—522no—
217C2×C8—522no—
218C2×C8—522no—
219C2×C8—522no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—262no—
223C4⋊C4—262no—
224C4⋊C4—521no—
225C4⋊C4—521no—
226C4⋊C4—521no—
227C4⋊C4—521no—
228C4⋊C4—522no—
229C4⋊C4—522no—
230C42—22no—
231C42—261no—
232C42—262no—
233C42—261no—
234C42—261no—
235C42—261no—
236C42—262no—
237C42—521no—
238C42—521no—
239C13#769711yescharacteristic, complemented, Sylow
240C23C2×C22⋊#26111yescharacteristic
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—132no—
255C2×C4—131no—
256C2×C4—131no—
257C2×C4—131no—
258C2×C4—131no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4#8811312yes—
275C2×C4#8824012yes—
276C8—524no—
277C8—1042no—
278C22C2×#8811311yescharacteristic
279C22#1171914211yescharacteristic
280C22#1171915911yescharacteristic
281C22D13⋊#10411yescharacteristic
282C22#1171916411yescharacteristic
283C22#1171916411yescharacteristic
284C22#1171916611yescharacteristic
285C4—22no—
286C4—22no—
287C4—41no—
288C4—81no—
289C4—81no—
290C4—261no—
291C4—261no—
292C4—262no—
293C4—261no—
294C4—261no—
295C4—521no—
296C4—1041no—
297C4—1041no—
298C2#1313011011yescharacteristic
299C2#1313015411yescharacteristic
300C2#1313019411yescharacteristic
301C2#1313023711yescharacteristic
302C2#1313024811yescharacteristic
303C2#1313030811yescharacteristic
304C2#1313037511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#382C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#382#261
hypocenterC13#7697
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
239. C13#7697semidirect

Maximal subgroups

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

subgroupindex
#131307522
#131306222
#131296552
#131232212
#769713