Finite Group Databasebeta

← #15765947

Subgroups — #15765947

Order 3328.

500 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120075C211yesmaximal, characteristic, complemented
2#13115763C211yesmaximal, characteristic
3#13115762C211yesmaximal, characteristic
4#13115642C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic, complemented
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×#88128C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C13C2211yescharacteristic
11C4×C13×C4⋊C4C2211yescharacteristic
12C2×#88061—21no—
13C2×#88061—21no—
14C2×#88061—22no—
15#11718638—21no—
16#11718634—21no—
17C2×#88049—21no—
18C2×#88049—21no—
19#11718597—21no—
20#11718596C2211yescharacteristic
21C4×C4⋊Dic13C2211yescharacteristic
22#11718589—21no—
23C2×C4⋊#1055C2211yescharacteristic
24#11718321—22no—
25C22×D52—21no—
26C22×D52—21no—
27C22×D52—21no—
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13—21no—
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D412yes—
39C2×#6101—22no—
40C2×C4×Dic13—21no—
41C22×#1055—21no—
42#88128—21no—
43#88128—21no—
44#88128—21no—
45#88128Q812yes—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C4×C8×C13—21no—
49C4×C8×C13—21no—
50C13×#95—21no—
51#88071—22no—
52#88071—22no—
53#88071—22no—
54#88071—21no—
55#88061—42no—
56#88061—42no—
57#88061—44no—
58#88049—42no—
59#88049—42no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62#10351—131nomaximal, Sylow
63C23×D13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—22no—
72C2×D52—22no—
73C2×D52—22no—
74C2×D52—22no—
75C2×D52—42no—
76C2×D52—42no—
77C2×D52—41no—
78C2×D52—41no—
79C2×D52—41no—
80C2×D52—41no—
81C2×D52—41no—
82C2×D52—41no—
83C2×D52—41no—
84C2×D52—41no—
85C2×D52—41no—
86C2×D52—41no—
87C2×D52—41no—
88C2×C8×C13—22no—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C42×C13—41no—
99C42×C13—41no—
100C42×C13C2×Q811yescharacteristic
101C42×C13#4111yescharacteristic
102C42×C13#4111yescharacteristic
103C42×C13#4111yescharacteristic
104C4⋊Dic13—21no—
105C4⋊Dic13—21no—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13—42no—
113#6101—82no—
114C4×Dic13—41no—
115C4×Dic13—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119#2571—131no—
120#1982—131no—
121#1982—131no—
122#1957—131no—
123#1296—131no—
124#1279—131no—
125#1279D1311yescharacteristic, complemented
126C23×C13#12011yescharacteristic
127C22×D13—42no—
128C22×D13—81no—
129C22×D13—81no—
130C22×D13—81no—
131C22×D13—81no—
132C22×D13—81no—
133C22×D13—81no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13C22⋊Q811yescharacteristic
143C2×C4×C13C22⋊Q811yescharacteristic
144C2×C4×C13C22⋊Q811yescharacteristic
145C2×C4×C13#12411yescharacteristic
146C2×C4×C13#12411yescharacteristic
147C2×C4×C13#12411yescharacteristic
148C2×C4×C13#13511yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C2×C4×C13#13511yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—41no—
163C2×Dic13—42no—
164C2×Dic13—41no—
165D52—44no—
166D52—42no—
167D52—42no—
168D52—42no—
169D52—42no—
170D52—82no—
171D52—81no—
172D52—81no—
173D52—81no—
174D52—81no—
175C8×C13—42no—
176C8×C13—81no—
177#1055—81no—
178C2×#127—131no—
179C2×C4⋊C8—131no—
180C2×C4⋊C8C2×D1311yescharacteristic
181C2×#102—262no—
182C2×#102—261no—
183C2×#102—261no—
184C2×#102—261no—
185C2×#102—261no—
186C2×C4×C8C2×D1311yescharacteristic
187#400—262no—
188#389—261no—
189#389—261no—
190#384—131no—
191#382—261no—
192#382—261no—
193C4×C4⋊C4—131no—
194C4×C4⋊C4C2×D1311yescharacteristic
195C22×C13#39311yescharacteristic
196C22×C13#44911yescharacteristic
197C22×C13#44911yescharacteristic
198C22×C13#44911yescharacteristic
199C22×C13#44911yescharacteristic
200C22×C13#45311yescharacteristic
201C22×C13#45411yescharacteristic
202C2×D13—82no—
203C2×D13—82no—
204C2×D13—82no—
205C2×D13—161no—
206C2×D13—161no—
207C2×D13—161no—
208C2×D13—161no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—81no—
212C4×C13—81no—
213C4×C13#47811yescharacteristic
214C4×C13#47811yescharacteristic
215C4×C13#47811yescharacteristic
216C4×C13#47811yescharacteristic
217C4×C13#48811yescharacteristic
218C4×C13#48811yescharacteristic
219C4×C13#49011yescharacteristic
220C4×C13#49011yescharacteristic
221Dic13—82no—
222Dic13—81no—
223Dic13—81no—
224C22×D4—261no—
225C22×D4—261no—
226C22×D4—261no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—261no—
230#127—132no—
231#127—261no—
232#127—261no—
233#127—261no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—132no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—262no—
240C2×C4⋊C4D5211yescharacteristic
241C2×C4⋊C4D5211yescharacteristic
242C2×C42—21no—
243C2×C42—261no—
244C2×C42C22×D1311yescharacteristic
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—261no—
248C4⋊C8—261no—
249#102—522no—
250#102—522no—
251#102—522no—
252#102—522no—
253#102—524no—
254C4×C8—21no—
255C4×C8—21no—
256#95—21no—
257#95—262no—
258#95—262no—
259#95—262no—
260#95—261no—
261C2×C13#162011yescharacteristic
262C2×C13#162411yescharacteristic
263C2×C13#162811yescharacteristic
264C2×C13#162811yescharacteristic
265C2×C13#202511yescharacteristic
266C2×C13#202511yescharacteristic
267C2×C13#202711yescharacteristic
268D13—162no—
269C24—521no—
270C2×D4—262no—
271C2×D4—262no—
272C2×D4—262no—
273C2×D4—522no—
274C2×D4—522no—
275C2×D4—521no—
276C2×D4—521no—
277C2×D4—521no—
278C2×D4—521no—
279C2×D4—521no—
280C2×D4—521no—
281C2×D4—521no—
282C2×D4—521no—
283C2×D4—521no—
284C2×D4—521no—
285C2×D4—521no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—262no—
291C22×C4C2×D5211yescharacteristic
292C22×C4D4×D1311yescharacteristic
293C22×C4D4×D1311yescharacteristic
294C2×C8—22no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—521no—
301C2×C8—521no—
302C2×C8—521no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—261no—
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4—261no—
311C4⋊C4—522no—
312C4⋊C4—521no—
313C4⋊C4—521no—
314C4⋊C4—521no—
315C4⋊C4—521no—
316C4⋊C4—1042no—
317C42—41no—
318C42—41no—
319C42—521no—
320C42—521no—
321C42#612711yescharacteristic
322C42#612711yescharacteristic
323C42#612911yescharacteristic
324C42Q8×D1311yescharacteristic
325C13#1035111yescharacteristic, complemented, Sylow
326C23—522no—
327C23—1041no—
328C23—1041no—
329C23—1041no—
330C23—1041no—
331C23—1041no—
332C23—1041no—
333C23#8813611yescharacteristic
334D4—524no—
335D4—522no—
336D4—522no—
337D4—522no—
338D4—522no—
339D4—1042no—
340D4—1041no—
341D4—1041no—
342D4—1041no—
343D4—1041no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—522no—
361C2×C4#8812911yescharacteristic
362C2×C4#8813911yescharacteristic
363C2×C4#8813911yescharacteristic
364C2×C4#8815011yescharacteristic
365C2×C4#8815011yescharacteristic
366C2×C4#8815111yescharacteristic
367C2×C4#8815811yescharacteristic
368C2×C4#8815811yescharacteristic
369C2×C4#8816211yescharacteristic
370C2×C4#8816211yescharacteristic
371C2×C4#8816511yescharacteristic
372C2×C4#8816811yescharacteristic
373C2×C4#8817011yescharacteristic
374C2×C4#8817311yescharacteristic
375C8—42no—
376C8—81no—
377C8—1041no—
378C22—1042no—
379C22—1042no—
380C22—1042no—
381C22—2081no—
382C22—2081no—
383C22—2081no—
384C22—2081no—
385C22#1171833411yescharacteristic
386C22#1171839511yescharacteristic
387C22#1171839511yescharacteristic
388C22#1171844211yescharacteristic
389C22#1171847211yescharacteristic
390C22#1171848311yescharacteristic
391C22#1171848811yescharacteristic
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—1042no—
397C4—1041no—
398C4—1041no—
399C4#1171835811yescharacteristic
400C4#1171837411yescharacteristic
401C4#1171842511yescharacteristic
402C4#1171846111yescharacteristic
403C4#1171850811yescharacteristic
404C4#1171850811yescharacteristic
405C4#1171853211yescharacteristic
406C4#1171855211yescharacteristic
407C2—2082no—
408C2#1311389711yescharacteristic
409C2#1311392111yescharacteristic
410C2#1311394811yescharacteristic
411C2#1311394911yescharacteristic
412C2#1311598111yescharacteristic
413C2#1311598311yescharacteristic
414C2#1311599111yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13#120
prime radicalC2×#88128C22
hypercenter#1279D13
hypocenterC13#10351
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. #13120075C2semidirect
5. #13112720C2semidirect
6. #13112676C2semidirect
7. C13×#1279C2semidirect
125. #1279D13semidirect
325. C13#10351semidirect

Maximal subgroups

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

subgroupindex
#131200752
#131157632
#131157622
#131156422
#131127202
#131126762
C13×#12792
#1035113