Finite Group Databasebeta

← #15764098

Subgroups — #15764098

Order 3328.

614 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718744C211yesmaximal, characteristic
2#13120010C211yesmaximal, characteristic
3#13115789C211yesmaximal, characteristic, complemented
4C2×#11718138C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C2×C13×#487C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C22×#6106—21no—
11C2×C4×D52C2211yescharacteristic
12C13×#487—22no—
13C13×#487—22no—
14C2×C13×#103—22no—
15C2×C4×C8×C13C2211yescharacteristic
16#11718892—22no—
17C2×#88075—21no—
18#11718744—22no—
19#11718744—22no—
20#11718649—21no—
21#11718648—22no—
22#11718638—21no—
23C4×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26#11718138—22no—
27#11718121—22no—
28#11718051—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D412yes—
31C22×D52D411yescharacteristic
32C22×C4×D13—21no—
33C22×C8×C13—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8D412yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6106—24no—
48C2×#6106—42no—
49C2×#6106—42no—
50C2×#6103—21no—
51C2×#6103—24no—
52C2×C4⋊Dic13D411yescharacteristic
53C2×C4⋊Dic13D412yes—
54C2×C4×Dic13—21no—
55C22×#1055—21no—
56C22×#1055—21no—
57C4×D52—21no—
58C4×D52—21no—
59C4×D52—21no—
60C4×D52—21no—
61C13×#103—28no—
62C4×C8×C13—21no—
63C4×C8×C13D412yes—
64#88075—24no—
65#88071—24no—
66#88071—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055D412yes—
71#10064—131nomaximal, Sylow
72C23×D13—21no—
73C2×Q8×C13—22no—
74C2×Q8×C13—22no—
75C2×Q8×C13—22no—
76C2×Q8×C13—44no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C22×C4×C13—22no—
83C22×C4×C13—41no—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×Dic13—21no—
88C22×Dic13—22no—
89C2×D52—21no—
90C2×D52—21no—
91C2×D52—21no—
92C2×D52—21no—
93C2×D52—21no—
94C2×D52SD1612yes—
95C2×C4×D13—41no—
96C2×C4×D13—41no—
97C2×C4×D13—42no—
98C2×C4×D13—42no—
99C2×C8×C13—22no—
100C2×C8×C13—42no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112C42×C13#4111yescharacteristic
113#6106—48no—
114#6103—41no—
115#6103—41no—
116#6103—84no—
117C4⋊Dic13—21no—
118C4⋊Dic13—21no—
119C4⋊Dic13—22no—
120C4⋊Dic13—22no—
121C4×Dic13—41no—
122C4×Dic13—41no—
123C2×#1055—22no—
124C2×#1055—41no—
125C2×#1055—41no—
126C2×#1055—41no—
127C2×#1055—42no—
128C2×#487D1311yescharacteristic, complemented
129C2×#461—131no—
130#2563—131no—
131#1988—131no—
132C2×#333—131no—
133C2×D4⋊C8—131no—
134#1279—131no—
135C23×C13#12011yescharacteristic
136C22×D13—22no—
137C22×D13—41no—
138C22×D13—41no—
139C22×D13—42no—
140C22×D13—42no—
141Q8×C13—44no—
142Q8×C13—42no—
143Q8×C13—42no—
144Q8×C13—82no—
145Q8×C13—81no—
146Q8×C13—81no—
147C2×C4×C13—22no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—44no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12711yescharacteristic
159C2×C4×C13C2×SD1611yescharacteristic
160C2×C4×C13#13511yescharacteristic
161C2×C4×C13#13512yes—
162C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C13#13711yescharacteristic
164C2×C4×C13#13712yes—
165C2×Dic13—41no—
166C2×Dic13—42no—
167C2×Dic13—42no—
168C2×Dic13—42no—
169C2×Dic13—42no—
170D52—22no—
171D52—22no—
172D52—41no—
173D52—41no—
174C4×D13—82no—
175C4×D13—81no—
176C4×D13—81no—
177C8×C13—42no—
178#1055—42no—
179#1055—81no—
180C22×SD16—261no—
181C2×C4⋊Q8C2×D1311yescharacteristic
182C2×C4⋊Q8C2×D1311yescharacteristic
183C2×C4×D4—131no—
184#487—22no—
185#487—22no—
186#461—262no—
187#461—262no—
188C2×C4⋊C8—131no—
189C2×C4⋊C8—131no—
190C2×#103—22no—
191C2×#103—261no—
192C2×C4×C8C2×D1311yescharacteristic
193#393—262no—
194#390—261no—
195#382—261no—
196#380—262no—
197C4×C4⋊C4—131no—
198#340—262no—
199#333—262no—
200D4⋊C8—262no—
201C22×C13#39211yescharacteristic
202C22×C13#44811yescharacteristic
203C22×C13#44911yescharacteristic
204C22×C13#45212yes—
205C22×C13#45512yes—
206C2×D13—44no—
207C2×D13—42no—
208C2×D13—82no—
209C2×D13—81no—
210C2×D13—81no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—82no—
214C4×C13—82no—
215C4×C13#45011yescharacteristic
216C4×C13#45211yescharacteristic
217C4×C13#46412yes—
218C4×C13#46511yescharacteristic
219C4×C13#46811yescharacteristic
220C4×C13#49511yescharacteristic
221C4×C13#49711yescharacteristic
222Dic13—82no—
223Dic13—81no—
224C22×Q8—21no—
225C22×Q8C22⋊D1312yes—
226C22×D4—131no—
227C23×C4—261no—
228C2×SD16—264no—
229C2×SD16—522no—
230C2×SD16—522no—
231C22×C8—21no—
232C22×C8—261no—
233C22×C8—261no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8C22⋊D1312yes—
242C4×D4—261no—
243C4×D4—261no—
244C4×D4—261no—
245C4×D4—261no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—131no—
251C2×C4⋊C4—132no—
252C2×C22⋊C4—261no—
253C2×C22⋊C4—264no—
254C2×C42—261no—
255C2×C42C22×D1311yescharacteristic
256C4⋊C8—132no—
257C4⋊C8—261no—
258C4⋊C8—261no—
259C4⋊C8—261no—
260#103—28no—
261#103—264no—
262C4×C8—21no—
263C4×C8C22⋊D1312yes—
264#95—264no—
265#95—261no—
266C2×C13#164312yes—
267C2×C13#164612yes—
268C2×C13#200011yescharacteristic
269C2×C13#200411yescharacteristic
270C2×C13#201511yescharacteristic
271D13—82no—
272C24—261no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—44no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—132no—
283C2×D4—261no—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—261no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—261no—
291C22×C4—262no—
292C22×C4—522no—
293C22×C4—522no—
294C22×C4—521no—
295C22×C4—521no—
296C22×C4D4×D1311yescharacteristic
297C22×C4D4×D1311yescharacteristic
298C22×C4C2×C22⋊D1311yescharacteristic
299SD16—528no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—262no—
303C2×C8—521no—
304C2×C8—521no—
305C2×C8—522no—
306C2×C8—521no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—262no—
316C4⋊C4—262no—
317C4⋊C4—261no—
318C4⋊C4—261no—
319C22⋊C4—521no—
320C22⋊C4—521no—
321C22⋊C4—1044no—
322C42—521no—
323C42—521no—
324C42D4×D1311yescharacteristic
325C42#612911yescharacteristic
326C42C2×C22⋊D1311yescharacteristic
327C42C2×C22⋊D1311yescharacteristic
328C13#1006411yescharacteristic, complemented, Sylow
329C23—262no—
330C23—522no—
331C23—521no—
332C23—522no—
333C23—521no—
334C23#8819111yescharacteristic
335Q8—44no—
336Q8—42no—
337Q8—42no—
338Q8—82no—
339Q8—81no—
340Q8—81no—
341D4—262no—
342D4—262no—
343D4—521no—
344D4—521no—
345C2×C4—22no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—522no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4—522no—
355C2×C4—521no—
356C2×C4—1042no—
357C2×C4—1041no—
358C2×C4—1041no—
359C2×C4SD16×D1311yescharacteristic
360C2×C4#8816811yescharacteristic
361C2×C4#8816911yescharacteristic
362C2×C4#8817011yescharacteristic
363C2×C4#8817212yes—
364C2×C4#8817312yes—
365C2×C4#8819111yescharacteristic
366C2×C4#8819211yescharacteristic
367C2×C4#8819311yescharacteristic
368C2×C4#8819311yescharacteristic
369C2×C4#8819411yescharacteristic
370C2×C4#8820711yescharacteristic
371C8—42no—
372C8—522no—
373C8—1041no—
374C22—524no—
375C22—522no—
376C22—1041no—
377C22—1042no—
378C22—1041no—
379C22#1171872212yes—
380C22#1171883111yescharacteristic
381C22#1171883311yescharacteristic
382C22#1171884812yes—
383C22#1171888411yescharacteristic
384C4—21no—
385C4—21no—
386C4—82no—
387C4—82no—
388C4—1041no—
389C4—1042no—
390C4#1171883011yescharacteristic
391C4#1171883211yescharacteristic
392C4#1171883411yescharacteristic
393C4#1171883511yescharacteristic
394C4#1171884612yes—
395C4#1171885111yescharacteristic
396C4#1171885211yescharacteristic
397C2—1042no—
398C2#1311404012yes—
399C2#1311406112yes—
400C2#1311583611yescharacteristic
401C2#1311586511yescharacteristic
402C2#1311592711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#487C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×#487D13
hypocenterC13#10064
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
3. #13115789C2semidirect
4. C2×#11718138C2semidirect
6. #13112676C2semidirect
7. C2×C13×#487C2semidirect
128. C2×#487D13semidirect
328. C13#10064semidirect

Maximal subgroups

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

subgroupindex
C2×#117187442
#131200102
#131157892
C2×#117181382
C2×#117180512
#131126762
C2×C13×#4872
#1006413