Finite Group Databasebeta

← #15755891

Subgroups — #15755891

Order 3328.

456 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114874C211yesmaximal, characteristic, complemented
2#13114861C211yesmaximal, characteristic, complemented
3#13113379C212yesmaximal
4#13112741C212yesmaximal, complemented
5C13×#2929C211yesmaximal, characteristic
6C2×C13×#131C411yescharacteristic, complemented
7C23×C8×C13C2211yescharacteristic
8C13×#525C2211yescharacteristic
9C13×#435—21no—
10C13×#435—21no—
11C8×D4×C13—21no—
12C8×D4×C13—21no—
13C13×#424C411yescharacteristic, complemented
14C13×#408C411yescharacteristic, complemented
15C13×#407C2211yescharacteristic
16C13×#405C411yescharacteristic, complemented
17#11718873C2212yes—
18#11718868C2212yes—
19C2×#88059—21no—
20C2×#88057—21no—
21#11718144—21no—
22#11718143—21no—
23#11718130—22no—
24#11718129—22no—
25C2×C13×#41C2×C411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C13×#131—42no—
28C2×C13×M16—21no—
29C2×C13×M16C2×C411yescharacteristic
30C2×C13×M16C2×C411yescharacteristic
31C22×C8×C13—21no—
32C22×C8×C13—42no—
33C22×C8×C13C2×C411yescharacteristic
34C22×C8×C13C2×C411yescharacteristic
35C22×C8×C13D411yescharacteristic
36C22×C8×C13D411yescharacteristic
37C22×C8×C13D411yescharacteristic
38C22×C8×C13D411yescharacteristic
39C13×#123—21no—
40C13×C22⋊Q8D411yescharacteristic
41C13×C22⋊Q8Q811yescharacteristic
42C13×#121D411yescharacteristic
43C13×#121Q811yescharacteristic
44C13×#120—21no—
45C4×D4×C13—21no—
46C4×D4×C13—21no—
47C13×#117C2×C411yescharacteristic
48C2×C22⋊Dic13—22no—
49C2×C4⋊Dic13—22no—
50C2×#6099—22no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C22⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×C22⋊C8—21no—
57C13×#97—21no—
58C4×C8×C13—21no—
59#88071—22no—
60C22⋊#1055—22no—
61C22⋊#1055—22no—
62#88059—42no—
63#88057—42no—
64#8626—131nomaximal, Sylow
65C24×C13#4111yescharacteristic
66C13×#41—41no—
67C13×#41—41no—
68C2×Q8×C13C4⋊C411yescharacteristic
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—21no—
72C2×D4×C13C4⋊C411yescharacteristic
73C22×C4×C13—21no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×Q811yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×Dic13—42no—
83C13×M16—42no—
84C13×M16—41no—
85C13×M16—41no—
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C2×C8×C13—22no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C2×C8×C13—42no—
95C2×C8×C13C22⋊C411yescharacteristic
96C2×C8×C13C22⋊C411yescharacteristic
97C2×C8×C13C22⋊C411yescharacteristic
98C2×C8×C13C22⋊C411yescharacteristic
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4C4⋊C411yescharacteristic
102C13×C4⋊C4C4⋊C411yescharacteristic
103C13×C22⋊C4—21no—
104C13×C22⋊C4—21no—
105C13×C22⋊C4—21no—
106C13×C22⋊C4—21no—
107C13×C22⋊C4—21no—
108C42×C13—21no—
109C22⋊Dic13—82no—
110C4⋊Dic13—42no—
111C4⋊Dic13—42no—
112#6099—42no—
113#6099—42no—
114C2×#1055—42no—
115#2929D1311yescharacteristic
116#1810—131no—
117#1807—131no—
118#1513—132no—
119#1305—132no—
120C23×C13—22no—
121C23×C13—21no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13#11711yescharacteristic
125C23×C13#12111yescharacteristic
126C23×C13C22⋊Q811yescharacteristic
127Q8×C13—41no—
128D4×C13—41no—
129D4×C13—42no—
130D4×C13—42no—
131D4×C13—42no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13C2×C22⋊C411yescharacteristic
147C2×C4×C13C2×C4⋊C411yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13C22⋊Q811yescharacteristic
150C2×Dic13—82no—
151C2×Dic13—82no—
152C2×Dic13—82no—
153C8×C13—21no—
154C8×C13—21no—
155C8×C13—21no—
156C8×C13—41no—
157C8×C13—41no—
158C8×C13#9912yes—
159#1055—82no—
160C2×#131Dic1311yescharacteristic, complemented
161C23×C8C2×D1311yescharacteristic
162#525C2×D1311yescharacteristic
163#435—21no—
164#435—21no—
165C8×D4—21no—
166C8×D4—21no—
167C2×#108—261no—
168C2×#106—261no—
169#424Dic1311yescharacteristic, complemented
170#408Dic1311yescharacteristic, complemented
171#407—132no—
172#407C2×D1311yescharacteristic
173#405Dic1311yescharacteristic, complemented
174#380—132no—
175#341—261no—
176#340—261no—
177#328—262no—
178#327—262no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—44no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13#38011yescharacteristic
192C22×C13#47112yes—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13C2×#9911yescharacteristic
200C4×C13#41011yescharacteristic
201Dic13—162no—
202C2×#41C2×Dic1311yescharacteristic
203C23×C4C22×D1311yescharacteristic
204#131—42no—
205C2×M16—21no—
206C2×M16—262no—
207C2×M16C2×Dic1311yescharacteristic
208C2×M16C2×Dic1311yescharacteristic
209C22×C8—21no—
210C22×C8—42no—
211C22×C8C2×Dic1311yescharacteristic
212C22×C8C2×Dic1311yescharacteristic
213C22×C8C22⋊D1311yescharacteristic
214C22×C8C22⋊D1311yescharacteristic
215C22×C8C22⋊D1311yescharacteristic
216C22×C8C22⋊D1311yescharacteristic
217#123—21no—
218C22⋊Q8Dic2611yescharacteristic
219C22⋊Q8D5211yescharacteristic
220#121Dic2611yescharacteristic
221#121D5211yescharacteristic
222#120—21no—
223C4×D4—21no—
224C4×D4—21no—
225#117C2×Dic1311yescharacteristic
226C2×C4⋊C4—262no—
227C2×C22⋊C4—262no—
228#108—522no—
229#106—522no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—262no—
237C22⋊C8—262no—
238#97—21no—
239C4×C8—21no—
240#95—262no—
241C2×C13—22no—
242C2×C13—41no—
243C2×C13—41no—
244C2×C13—81no—
245C2×C13#179911yescharacteristic
246C2×C13#181411yescharacteristic
247C2×C13#181511yescharacteristic
248C24#612711yescharacteristic
249#41—41no—
250#41—41no—
251C2×Q8C4⋊Dic1311yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4C4⋊Dic1311yescharacteristic
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—522no—
260C22×C4C2×Dic2611yescharacteristic
261C22×C4C2×D5211yescharacteristic
262C22×C4#612711yescharacteristic
263C22×C4C22×Dic1311yescharacteristic
264C22×C4C2×C22⋊D1311yescharacteristic
265C22×C4C2×C22⋊D1311yescharacteristic
266M16—42no—
267M16—41no—
268M16—41no—
269M16—522no—
270M16—522no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—42no—
280C2×C8—522no—
281C2×C8C22⋊Dic1311yescharacteristic
282C2×C8C22⋊Dic1311yescharacteristic
283C2×C8C22⋊Dic1311yescharacteristic
284C2×C8C22⋊Dic1311yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—522no—
288C4⋊C4—522no—
289C4⋊C4C4⋊Dic1311yescharacteristic
290C4⋊C4C4⋊Dic1311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—1042no—
297C42—21no—
298C13#862611yescharacteristic, complemented, Sylow
299C23—22no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23#8817811yescharacteristic
304C23#8818011yescharacteristic
305C23#8818411yescharacteristic
306Q8—41no—
307D4—41no—
308D4—42no—
309D4—42no—
310D4—42no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—1042no—
326C2×C4—1042no—
327C2×C4—1042no—
328C2×C4#8817811yescharacteristic
329C2×C4C2×C4⋊Dic1311yescharacteristic
330C2×C4#8818411yescharacteristic
331C2×C4C2×C22⋊Dic1311yescharacteristic
332C8—21no—
333C8—21no—
334C8—21no—
335C8—41no—
336C8—41no—
337C8—1042no—
338C8#8807412yes—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22#1171880212yes—
352C22#1171887311yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—2082no—
360C4C2×#8807411yescharacteristic
361C4#1171890111yescharacteristic
362C2—22no—
363C2—41no—
364C2—41no—
365C2—81no—
366C2#1311482411yescharacteristic
367C2#1311489011yescharacteristic
368C2#1311489511yescharacteristic
subgroupG/H
centerC22#11718873
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2929C2
socleC22×C13#380
prime radicalC13×#525C22
cosocleC23×C4×C13C23
hypercenter#2929D13
hypocenterC13#8626
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. #13114874C2semidirect
2. #13114861C2semidirect
4. #13112741C2semidirect
6. C2×C13×#131C4semidirect
13. C13×#424C4semidirect
14. C13×#408C4semidirect
16. C13×#405C4semidirect
160. C2×#131Dic13semidirect
169. #424Dic13semidirect
170. #408Dic13semidirect
173. #405Dic13semidirect
298. C13#8626semidirect

Maximal subgroups

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

subgroupindex
#131148742
#131148612
#131133792
#131127412
C13×#29292
#862613