Finite Group Databasebeta

← #15766739

Subgroups — #15766739

Order 3328.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718502C211yesmaximal, characteristic
2#13115797C211yesmaximal, characteristic, complemented
3#13115630C211yesmaximal, characteristic
4#13114837C211yesmaximal, characteristic
5C2×#11718074C211yesmaximal, characteristic, complemented
6#13112720C211yesmaximal, characteristic, complemented
7C2×C13×#335C211yesmaximal, characteristic, complemented
8C22×#6095—21no—
9C2×C4×D52C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C2×#88061—21no—
15C2×#88060—21no—
16C2×#88060—21no—
17C2×#88056—21no—
18#11718596C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20#11718502—22no—
21#11718502—22no—
22C13×#335—22no—
23#11718143—21no—
24#11718143—21no—
25#11718143—21no—
26#11718074—22no—
27C22×D52D411yescharacteristic
28C22×C4×D13—21no—
29C22×Dic26—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×#6103—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42C22×#1055—21no—
43C2×#6095—24no—
44C2×#6095—42no—
45C2×#6095—42no—
46C4×D52—21no—
47C4×D52—21no—
48C4×D52—21no—
49C4×D52—21no—
50#88123—21no—
51#88123—21no—
52#88123—21no—
53#88123D412yes—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8D412yes—
58C4×C8×C13—21no—
59C4×C8×C13—21no—
60#88061—42no—
61#88060—42no—
62#88060—42no—
63#88056—24no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66#10476—131nomaximal, Sylow
67C23×D13—21no—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4111yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52—21no—
79C2×D52D812yes—
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×Dic26—22no—
87C2×Dic26—41no—
88C2×Dic26—41no—
89C2×Dic26—41no—
90C2×Dic26—41no—
91C2×Dic26—41no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13—22no—
95C2×C8×C13—21no—
96C2×C8×C13—21no—
97C2×C8×C13—21no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13SD1612yescomplemented
104C42×C13C2×D411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13#4111yescharacteristic
107C42×C13#4111yescharacteristic
108#6103—41no—
109#6103—41no—
110C4⋊Dic13—21no—
111C4⋊Dic13—22no—
112C4⋊Dic13—22no—
113C4⋊Dic13—21no—
114C4⋊Dic13—41no—
115C4⋊Dic13—41no—
116C4⋊Dic13—41no—
117C4⋊Dic13—41no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C4⋊Dic13—81no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055—41no—
124#6095—48no—
125C2×#461—131no—
126#1990—131no—
127#1954—131no—
128#1802—131no—
129C2×#335D1311yescharacteristic, complemented
130C2×#332—131no—
131#1296—131no—
132C23×C13#12111yescharacteristic
133C22×D13—22no—
134C22×D13—41no—
135C22×D13—41no—
136C22×D13—41no—
137C22×D13—41no—
138C22×D13—41no—
139C22×D13—41no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13#12011yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12311yescharacteristic
146C2×C4×C13#12311yescharacteristic
147C2×C4×C13#12411yescharacteristic
148C2×C4×C13C2×D811yescharacteristic
149C2×C4×C13C2×SD1611yescharacteristic
150C2×C4×C13#13511yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C13#13711yescharacteristic
155C2×C4×C13#13711yescharacteristic
156C2×Dic13—42no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—81no—
161C2×Dic13—81no—
162C2×Dic13—81no—
163C2×Dic13—81no—
164C2×Dic13—81no—
165D52—22no—
166D52—22no—
167D52—41no—
168D52—41no—
169C4×D13—81no—
170C4×D13—81no—
171C4×D13—81no—
172C4×D13—81no—
173Dic26—42no—
174Dic26—42no—
175Dic26—81no—
176Dic26—81no—
177C8×C13—22no—
178C8×C13—42no—
179C8×C13—41no—
180C8×C13—81no—
181#1055—81no—
182C22×SD16—261no—
183C2×C4⋊Q8—131no—
184C2×C4×D4—131no—
185#461—262no—
186#461—262no—
187C2×C4⋊C8—131no—
188C2×C4⋊C8C2×D1311yescharacteristic
189C2×C4⋊C8C2×D1311yescharacteristic
190C2×#103—261no—
191C2×#102—261no—
192C2×C22⋊C8—261no—
193C2×C22⋊C8—261no—
194C2×C4×C8C2×D1311yescharacteristic
195#384—131no—
196#340—261no—
197#340—261no—
198#340—261no—
199#335—22no—
200#332—262no—
201C22×C13#39411yescharacteristic
202C22×C13#46111yescharacteristic
203C22×C13#46311yescharacteristic
204C22×C13#46611yescharacteristic
205C22×C13#46811yescharacteristic
206C22×C13#47111yescharacteristic
207C22×C13#47311yescharacteristic
208C2×D13—42no—
209C2×D13—42no—
210C2×D13—42no—
211C2×D13—81no—
212C2×D13—81no—
213C2×D13—81no—
214C2×D13—81no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13#44711yescharacteristic
218C4×C13#45211yescharacteristic
219C4×C13#46011yescharacteristic
220C4×C13#46411yescharacteristic
221C4×C13#46511yescharacteristic
222C4×C13#46811yescharacteristic
223C4×C13#48011yescharacteristic
224C4×C13#48211yescharacteristic
225Dic13—81no—
226Dic13—82no—
227Dic13—161no—
228C22×Q8—261no—
229C22×D4—131no—
230C23×C4—261no—
231C2×SD16—264no—
232C2×SD16—522no—
233C2×SD16—522no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—261no—
237C22×C8D5211yescharacteristic
238C22×C8D5211yescharacteristic
239C4⋊Q8—132no—
240C4⋊Q8—261no—
241C4⋊Q8—261no—
242C4⋊Q8—261no—
243C4×D4—261no—
244C4×D4—261no—
245C4×D4—261no—
246C4×D4—261no—
247C2×C4⋊C4—131no—
248C2×C4⋊C4—261no—
249C2×C4⋊C4—261no—
250C2×C4⋊C4—261no—
251C2×C4⋊C4—261no—
252C2×C4⋊C4—261no—
253C2×C22⋊C4—261no—
254C2×C42C22×D1311yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—261no—
259C4⋊C8—261no—
260C4⋊C8C22⋊D1312yes—
261#103—264no—
262#102—522no—
263C22⋊C8—522no—
264C22⋊C8—522no—
265C4×C8—21no—
266C4×C8—21no—
267C2×C13#167311yescharacteristic
268C2×C13#168111yescharacteristic
269C2×C13#169111yescharacteristic
270C2×C13#169911yescharacteristic
271C2×C13#203311yescharacteristic
272C2×C13#205211yescharacteristic
273C2×C13#205511yescharacteristic
274D13—82no—
275C24—261no—
276C2×Q8—262no—
277C2×Q8—521no—
278C2×Q8—521no—
279C2×Q8—521no—
280C2×Q8—521no—
281C2×Q8—521no—
282C2×D4—132no—
283C2×D4—261no—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—261no—
288C22×C4—261no—
289C22×C4—521no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4—521no—
296C22×C4—521no—
297C22×C4C2×D5211yescharacteristic
298C22×C4D4×D1311yescharacteristic
299C22×C4#613111yescharacteristic
300SD16—528no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—521no—
313C2×C8—521no—
314C2×C8—521no—
315C2×C8#609512yescomplemented
316C4⋊C4—261no—
317C4⋊C4—262no—
318C4⋊C4—262no—
319C4⋊C4—261no—
320C4⋊C4—521no—
321C4⋊C4—521no—
322C4⋊C4—521no—
323C4⋊C4—521no—
324C4⋊C4—521no—
325C4⋊C4—521no—
326C4⋊C4—1041no—
327C22⋊C4—521no—
328C22⋊C4—521no—
329C42#612711yescharacteristic
330C42D4×D1311yescharacteristic
331C42#613111yescharacteristic
332C42C2×C22⋊D1311yescharacteristic
333C13#1047611yescharacteristic, complemented, Sylow
334C23—262no—
335C23—521no—
336C23—521no—
337C23—521no—
338C23—521no—
339C23—521no—
340C23—521no—
341C23#8814911yescharacteristic
342Q8—522no—
343Q8—522no—
344Q8—1041no—
345Q8—1041no—
346D4—262no—
347D4—262no—
348D4—521no—
349D4—521no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—522no—
356C2×C4—1041no—
357C2×C4—1041no—
358C2×C4—1041no—
359C2×C4—1041no—
360C2×C4—1041no—
361C2×C4—1041no—
362C2×C4—1041no—
363C2×C4—1041no—
364C2×C4—1041no—
365C2×C4#8814811yescharacteristic
366C2×C4#8814811yescharacteristic
367C2×C4#8814911yescharacteristic
368C2×C4C2×#609511yescharacteristic
369C2×C4#8815811yescharacteristic
370C2×C4#8816211yescharacteristic
371C2×C4#8816311yescharacteristic
372C2×C4D8×D1311yescharacteristic
373C2×C4#8816511yescharacteristic
374C2×C4#8817211yescharacteristic
375C2×C4#8817311yescharacteristic
376C2×C4#8818411yescharacteristic
377C2×C4#8819111yescharacteristic
378C2×C4#8820111yescharacteristic
379C8—22no—
380C8—41no—
381C8—42no—
382C8—81no—
383C8—1041no—
384C22—522no—
385C22—522no—
386C22—522no—
387C22—1041no—
388C22—1041no—
389C22—1041no—
390C22—1041no—
391C22#1171850211yescharacteristic
392C22#1171850511yescharacteristic
393C22#1171854411yescharacteristic
394C22#1171854711yescharacteristic
395C22#1171855711yescharacteristic
396C22#1171855911yescharacteristic
397C22#1171865211yescharacteristic
398C4—21no—
399C4—21no—
400C4—1042no—
401C4—1041no—
402C4—2081no—
403C4#1171850611yescharacteristic
404C4#1171850911yescharacteristic
405C4#1171854311yescharacteristic
406C4#1171854611yescharacteristic
407C4#1171877511yescharacteristic
408C4#1171879511yescharacteristic
409C4#1171881711yescharacteristic
410C4#1171884811yescharacteristic
411C2—1042no—
412C2#1311422611yescharacteristic
413C2#1311427411yescharacteristic
414C2#1311433611yescharacteristic
415C2#1311438411yescharacteristic
416C2#1311602011yescharacteristic
417C2#1311613711yescharacteristic
418C2#1311615411yescharacteristic
subgroupG/H
centerC23#88149
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#335C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenterC2×#335D13
hypocenterC13#10476
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #13115797C2semidirect
5. C2×#11718074C2semidirect
6. #13112720C2semidirect
7. C2×C13×#335C2semidirect
103. C2×C8×C13SD16semidirect
129. C2×#335D13semidirect
315. C2×C8#6095semidirect
333. C13#10476semidirect

Maximal subgroups

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

subgroupindex
C2×#117185022
#131157972
#131156302
#131148372
C2×#117180742
#131127202
C2×C13×#3352
#1047613