Finite Group Databasebeta

← #15757082

Subgroups — #15757082

Order 3328.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×D52C211yesmaximal, characteristic
2#13115594C211yesmaximal, characteristic, complemented
3#13114996C211yesmaximal, characteristic, complemented
4#13114837C211yesmaximal, characteristic
5C2×#11718051C211yesmaximal, characteristic
6#13112720C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D13—21no—
9C2×C4×D52—21no—
10C2×C4×D52C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14C2×#88061—21no—
15C2×#88058—22no—
16#11718648—21no—
17C2×#88047—21no—
18#11718596C2211yescharacteristic
19#11718596C2211yescharacteristic
20#11718589—21no—
21C2×C4⋊#1055C2211yescharacteristic
22#11718329—22no—
23#11718143—21no—
24#11718121—21no—
25#11718051C414yescomplemented
26C22×D52D411yescharacteristic
27C22×C4×D13—21no—
28C22×C4×D13—22no—
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13—21no—
34C2×C42×C13C2311yescharacteristic
35C2×#6103—21no—
36C2×#6103—22no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13D412yes—
44C2×#6101—22no—
45C22×#1055—21no—
46C4⋊C4×D13—42no—
47C4⋊C4×D13—42no—
48C4×D52—21no—
49C4×D52—21no—
50C4×D52—42no—
51C4×D52—42no—
52C4×D52C2×C412yes—
53C4×D52Q812yes—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C4×C8×C13—21no—
57C4×C8×C13C2×C412yescomplemented
58C13×#95—21no—
59#88071—22no—
60#88061—42no—
61#88058—44no—
62#88047—42no—
63C4⋊#1055—21no—
64C4⋊#1055C2×C412yescomplemented
65#8882—131nomaximal, Sylow
66C23×D13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—22no—
74C22×Dic13—41no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52C4⋊C412yes—
79C2×D52D812yes—
80C2×D52Q1612yes—
81C2×C4×D13—22no—
82C2×C4×D13—22no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×C4×D13—44no—
88C2×C4×D13—44no—
89C2×C4×D13—82no—
90C2×C8×C13—22no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4D812yes—
100C42×C13—41no—
101C42×C13—41no—
102C42×C13C22×C411yescharacteristic
103C42×C13C2×Q811yescharacteristic
104C42×C13#4111yescharacteristic
105C42×C13#4111yescharacteristic
106#6103—22no—
107#6103—22no—
108#6103—44no—
109C4⋊Dic13—21no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113C4⋊Dic13—41no—
114C4⋊Dic13—42no—
115C4⋊Dic13—42no—
116C4⋊Dic13—41no—
117C4⋊Dic13—41no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C4⋊Dic13C4⋊C412yes—
121#6101—44no—
122C2×#1055—22no—
123C2×#1055—41no—
124C2×#1055—41no—
125D4×C4⋊C4—131no—
126#1947—131no—
127#1845—131no—
128#1802—131no—
129C2×D4⋊C8—131no—
130#1296—131no—
131#1279D1311yescharacteristic, complemented
132C23×C13#12011yescharacteristic
133C22×D13—22no—
134C22×D13—22no—
135C22×D13—22no—
136C22×D13—41no—
137C22×D13—41no—
138C22×D13—41no—
139C22×D13—41no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—22no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13C2×C4⋊C411yescharacteristic
149C2×C4×C13C4×D411yescharacteristic
150C2×C4×C13C4×D411yescharacteristic
151C2×C4×C13C22⋊Q811yescharacteristic
152C2×C4×C13C22⋊Q811yescharacteristic
153C2×C4×C13#12311yescharacteristic
154C2×C4×C13C2×D811yescharacteristic
155C2×C4×C13C2×D811yescharacteristic
156C2×C4×C13C2×Q1611yescharacteristic
157C2×C4×C13#13511yescharacteristic
158C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C13#13711yescharacteristic
161C2×C4×C13#13711yescharacteristic
162C2×Dic13—22no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—42no—
166C2×Dic13—42no—
167C2×Dic13—42no—
168C2×Dic13—81no—
169C2×Dic13—81no—
170C2×Dic13—81no—
171D52—22no—
172D52—22no—
173D52—22no—
174D52#10714yescomplemented
175C4×D13—42no—
176C4×D13—42no—
177C4×D13—42no—
178C4×D13—42no—
179C4×D13—88no—
180C8×C13—24no—
181C8×C13—81no—
182#1055—42no—
183C2×C4×D4—131no—
184C2×C4×D4—261no—
185C22×C4⋊C4—261no—
186C2×#107—262no—
187C2×#107—261no—
188C2×C4⋊C8—131no—
189C2×C4⋊C8C2×D1311yescharacteristic
190C2×#102—261no—
191C2×C4×C8C2×D1311yescharacteristic
192#389—261no—
193#385—262no—
194#384—131no—
195#384—131no—
196#380—261no—
197C4×C4⋊C4C2×D1311yescharacteristic
198#340—261no—
199#340—261no—
200D4⋊C8—134no—
201C22×C13#38511yescharacteristic
202C22×C13#44711yescharacteristic
203C22×C13#44711yescharacteristic
204C22×C13#45111yescharacteristic
205C22×C13#45211yescharacteristic
206C22×C13#45311yescharacteristic
207C22×C13#45611yescharacteristic
208C2×D13—24no—
209C2×D13—42no—
210C2×D13—42no—
211C2×D13—42no—
212C2×D13—42no—
213C2×D13—42no—
214C2×D13—42no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—42no—
218C4×C13—81no—
219C4×C13C2×#10711yescharacteristic
220C4×C13#42811yescharacteristic
221C4×C13C4×D811yescharacteristic
222C4×C13#44011yescharacteristic
223C4×C13#47411yescharacteristic
224C4×C13#47811yescharacteristic
225C4×C13#48011yescharacteristic
226C4×C13#48411yescharacteristic
227Dic13—42no—
228Dic13—82no—
229Dic13—161no—
230C22×D4—131no—
231C23×C4—262no—
232C23×C4—261no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—261no—
236C4×D4—132no—
237C4×D4—132no—
238C4×D4—261no—
239C4×D4—261no—
240C4×D4—522no—
241C4×D4—522no—
242C2×C4⋊C4—131no—
243C2×C4⋊C4—132no—
244C2×C4⋊C4—262no—
245C2×C4⋊C4—261no—
246C2×C4⋊C4—261no—
247C2×C4⋊C4—261no—
248C2×C4⋊C4—261no—
249C2×C4⋊C4—261no—
250C2×C4⋊C4—522no—
251C2×C4⋊C4—522no—
252C2×C4⋊C4D5211yescharacteristic
253C2×C4⋊C4D5211yescharacteristic
254C2×C22⋊C4—261no—
255C2×C22⋊C4—262no—
256C2×C42—21no—
257C2×C42C22×D1311yescharacteristic
258#107—524no—
259#107—522no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—132no—
263C4⋊C8—261no—
264#102—522no—
265C4×C8—21no—
266C4×C8C4×D1312yescomplemented
267#95—21no—
268#95—262no—
269C2×C13#161911yescharacteristic
270C2×C13#163211yescharacteristic
271C2×C13#164711yescharacteristic
272C2×C13#164911yescharacteristic
273C2×C13#185211yescharacteristic
274C2×C13#185911yescharacteristic
275C2×C13#186211yescharacteristic
276D13—44no—
277C24—261no—
278C2×D4—132no—
279C2×D4—132no—
280C2×D4—132no—
281C2×D4—261no—
282C2×D4—261no—
283C2×D4—261no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—261no—
287C22×C4—262no—
288C22×C4—262no—
289C22×C4—262no—
290C22×C4—524no—
291C22×C4—524no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4—521no—
296C22×C4—521no—
297C22×C4—1042no—
298C22×C4C2×D5211yescharacteristic
299C22×C4D4×D1311yescharacteristic
300C22×C4D4×D1311yescharacteristic
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—262no—
308C2×C8—521no—
309C2×C8—521no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—132no—
314C4⋊C4—261no—
315C4⋊C4—522no—
316C4⋊C4—524no—
317C4⋊C4—522no—
318C4⋊C4—521no—
319C4⋊C4—521no—
320C4⋊C4—521no—
321C4⋊C4—521no—
322C4⋊C4—521no—
323C4⋊C4—521no—
324C4⋊C4—521no—
325C4⋊C4—521no—
326C4⋊C4D10412yes—
327C22⋊C4—262no—
328C22⋊C4—262no—
329C22⋊C4—524no—
330C42—41no—
331C42—41no—
332C42C2×C4×D1311yescharacteristic
333C42#612711yescharacteristic
334C42#612911yescharacteristic
335C42Q8×D1311yescharacteristic
336C13#888211yescharacteristic, complemented, Sylow
337C23—262no—
338C23—262no—
339C23—262no—
340C23—521no—
341C23—521no—
342C23—521no—
343C23—521no—
344C23#8813611yescharacteristic
345D4—134no—
346D4—262no—
347D4—262no—
348D4—262no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—262no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4—522no—
366C2×C4—522no—
367C2×C4—1048no—
368C2×C4—1041no—
369C2×C4—1041no—
370C2×C4—1041no—
371C2×C4C4×D5211yescharacteristic
372C2×C4#8813511yescharacteristic
373C2×C4#8813711yescharacteristic
374C2×C4C4⋊C4×D1311yescharacteristic
375C2×C4#8815011yescharacteristic
376C2×C4#8815111yescharacteristic
377C2×C4C2×D10411yescharacteristic
378C2×C4#8815811yescharacteristic
379C2×C4#8816211yescharacteristic
380C2×C4#8816311yescharacteristic
381C2×C4D8×D1311yescharacteristic
382C2×C4#8816811yescharacteristic
383C2×C4#8816911yescharacteristic
384C2×C4Q16×D1311yescharacteristic
385C8—24no—
386C8—81no—
387C8—522no—
388C22—264no—
389C22—522no—
390C22—522no—
391C22—522no—
392C22—522no—
393C22—522no—
394C22—522no—
395C22#1171832911yescharacteristic
396C22#1171839311yescharacteristic
397C22#1171839411yescharacteristic
398C22#1171843411yescharacteristic
399C22#1171846911yescharacteristic
400C22#1171848311yescharacteristic
401C22#1171848711yescharacteristic
402C4—21no—
403C4—21no—
404C4—42no—
405C4—81no—
406C4—522no—
407C4—1042no—
408C4—2081no—
409C4C4×D10411yescharacteristic
410C4#1171837111yescharacteristic
411C4#1171843511yescharacteristic
412C4#1171847011yescharacteristic
413C4#1171850711yescharacteristic
414C4#1171850811yescharacteristic
415C4#1171852211yescharacteristic
416C4D13×#10711yescharacteristic
417C2—524no—
418C2#1311389211yescharacteristic
419C2#1311397311yescharacteristic
420C2#1311407411yescharacteristic
421C2#1311408711yescharacteristic
422C2#1311502511yescharacteristic
423C2#1311506311yescharacteristic
424C2#1311508611yescharacteristic
subgroupG/H
centerC23#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13#120
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#8882
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #13115594C2semidirect
3. #13114996C2semidirect
6. #13112720C2semidirect
7. C13×#1279C2semidirect
25. #11718051C4semidirect
57. C4×C8×C13C2×C4semidirect
64. C4⋊#1055C2×C4semidirect
131. #1279D13semidirect
174. D52#107semidirect
266. C4×C8C4×D13semidirect
336. C13#8882semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×D522
#131155942
#131149962
#131148372
C2×#117180512
#131127202
C13×#12792
#888213