Finite Group Databasebeta

← #16778628

Subgroups — #16778628

Order 3328.

468 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 94 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#13130727C211yesmaximal, characteristic
2C4×C22⋊#1057C211yesmaximal, characteristic
3#13129655C212yesmaximal, complemented
4#13129654C212yesmaximal, complemented
5#13123144C211yesmaximal, characteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×#88144C411yescharacteristic
8C2×C22⋊#1057—21no—
9C2×C22⋊#1057—21no—
10C2×C4×#1057—21no—
11C13×#380C411yescharacteristic
12#11718873C411yescharacteristic
13#11718646C2211yescharacteristic
14#11718638C411yescharacteristic
15#11718634C2211yescharacteristic
16#11718611—21no—
17#11718607—21no—
18#11718316—21no—
19#11718315—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×#1057—22no—
27C22×#1057—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4—21no—
31C2×C22⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13—42no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13C2311yescharacteristic
43#88144—42no—
44C22⋊#1057—24no—
45C22⋊#1057—42no—
46C4×#1057—42no—
47C13×#95—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#7671—131nomaximal, Sylow
54C24×C13C22⋊C411yescharacteristic
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—41no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—41no—
69C22×Dic13—41no—
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C2×#1057—24no—
75C2×#1057—42no—
76C2×#1057—42no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—42no—
83C22⋊Dic13—42no—
84C4⋊Dic13—22no—
85C4⋊Dic13—42no—
86C4⋊Dic13—42no—
87C4⋊Dic13—41no—
88#6101—42no—
89#6101—42no—
90C4×Dic13—22no—
91C4×Dic13—22no—
92C4×Dic13—41no—
93C4×Dic13—41no—
94#2851—131no—
95#1817—131no—
96C4×C22⋊C8—131no—
97#1271—132no—
98#1271—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13#10412yes—
106C23×C13C2×C22⋊C411yescharacteristic
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—44no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13#10112yes—
119C2×C4×C13#13112yes—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—44no—
130C2×Dic13—44no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13#9912yes—
138C2×Dic13#13512yes—
139C2×Dic13#13512yes—
140#1057—44no—
141#1057—82no—
142C2×#125—131no—
143C22×C42—131no—
144C2×C22⋊C8—261no—
145C2×C22⋊C8—261no—
146C2×C4×C8—261no—
147#389—131no—
148#389—131no—
149#387—261no—
150#387—261no—
151#385—261no—
152#385—261no—
153#382—131no—
154#380—131no—
155#380#26111yescharacteristic
156#336—132no—
157#336—132no—
158#336—261no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13#40811yescharacteristic
167C22×C13C2×#9911yescharacteristic
168C22×C13C2×#10111yescharacteristic
169C22×C13#41611yescharacteristic
170C22×C13#41611yescharacteristic
171C22×C13C2×#10411yescharacteristic
172C22×C13#42111yescharacteristic
173C4×C13—22no—
174C4×C13—22no—
175C4×C13—81no—
176C4×C13—81no—
177Dic13—22no—
178Dic13—22no—
179Dic13—22no—
180Dic13—41no—
181Dic13—81no—
182Dic13—81no—
183C23×C4—131no—
184C23×C4—131no—
185C23×C4C2×#26111yescharacteristic
186C22×C8—262no—
187C22×C8—262no—
188#125—522no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—131no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4C2×#26111yescharacteristic
196C2×C4⋊C4C2×#26111yescharacteristic
197C2×C22⋊C4—21no—
198C2×C22⋊C4—261no—
199C2×C42—131no—
200C2×C42—131no—
201C2×C42—131no—
202C2×C42—131no—
203C2×C42—522no—
204C22⋊C8—264no—
205C22⋊C8—522no—
206C4×C8—522no—
207#95—21no—
208#95—261no—
209#95—261no—
210#95—261no—
211#95—261no—
212#95—261no—
213C2×C13—42no—
214C2×C13#147211yescharacteristic
215C2×C13#148211yescharacteristic
216C2×C13#149411yescharacteristic
217C2×C13#150111yescharacteristic
218C2×C13#151611yescharacteristic
219C2×C13#152811yescharacteristic
220C2×C13#154411yescharacteristic
221C24C22⋊#26111yescharacteristic
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—262no—
232C22×C4—262no—
233C22×C4—262no—
234C22×C4—262no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—521no—
238C22×C4—521no—
239C22×C4C22⋊#26111yescharacteristic
240C22×C4C22×#26111yescharacteristic
241C2×C8—264no—
242C2×C8—522no—
243C2×C8—522no—
244C2×C8—522no—
245C2×C8—522no—
246C2×C8—522no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—262no—
250C4⋊C4—521no—
251C4⋊C4—522no—
252C4⋊C4—522no—
253C4⋊C4—522no—
254C4⋊C4—522no—
255C22⋊C4—42no—
256C22⋊C4—522no—
257C42—262no—
258C42—262no—
259C42—521no—
260C42—521no—
261C13#767111yescharacteristic, complemented, Sylow
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#8811612yes—
269C23C2×C22⋊#26111yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—44no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—132no—
282C2×C4—132no—
283C2×C4—132no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—524no—
294C2×C4—524no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4#8811312yes—
302C2×C4#8823812yes—
303C8—524no—
304C8—1042no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22C2×#8811311yescharacteristic
313C22C2×#8811611yescharacteristic
314C22D13⋊#9911yescharacteristic
315C22#1171914611yescharacteristic
316C22#1171915511yescharacteristic
317C22#1171916511yescharacteristic
318C22#1171916511yescharacteristic
319C4—22no—
320C4—22no—
321C4—81no—
322C4—81no—
323C4—262no—
324C4—262no—
325C4—262no—
326C4—521no—
327C4—1041no—
328C4—1041no—
329C2—42no—
330C2#1313011511yescharacteristic
331C2#1313014911yescharacteristic
332C2#1313018711yescharacteristic
333C2#1313021211yescharacteristic
334C2#1313026311yescharacteristic
335C2#1313029811yescharacteristic
336C2#1313034111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#380C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#380#261
hypocenterC13#7671
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #13129655C2semidirect
4. #13129654C2semidirect
261. C13#7671semidirect

Maximal subgroups

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

subgroupindex
#131307272
C4×C22⋊#10572
#131296552
#131296542
#131231442
#767113