Finite Group Databasebeta

← #15766798

Subgroups — #15766798

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic
2#13115639C211yesmaximal, characteristic, complemented
3#13115629C211yesmaximal, characteristic
4#13114837C211yesmaximal, characteristic
5C2×#11718071C211yesmaximal, characteristic, complemented
6#13112720C211yesmaximal, characteristic, complemented
7C2×C13×#332C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88075—21no—
13C2×#88075—21no—
14C2×#88061—21no—
15C2×#88060—21no—
16C2×#88060—21no—
17#11718748—22no—
18#11718748—22no—
19C2×#88049—21no—
20C2×#88047—21no—
21#11718596C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4×#1055C2211yescharacteristic
24C13×#332—22no—
25#11718143—21no—
26#11718071—22no—
27C22×Q8×C13—21no—
28C22×D52D411yescharacteristic
29C22×C4×D13—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8D412yes—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C42×C13C2311yescharacteristic
39C2×#6103—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13D411yescharacteristic
44C22×#1055—21no—
45C22×#1055D411yescharacteristic
46C22×#1055D411yescharacteristic
47C4×D52—21no—
48C4×D52—21no—
49C4×D52—21no—
50C4×D52—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8—21no—
55#88075—42no—
56#88075—42no—
57#88061—42no—
58#88060—42no—
59#88060—42no—
60#88049—24no—
61#88047—24no—
62C4⋊#1055—21no—
63C4⋊#1055D412yes—
64C4×#1055—21no—
65C4×#1055—21no—
66#10485—131nomaximal, Sylow
67C23×D13—21no—
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13#4111yescharacteristic
78C22×Dic13—21no—
79C22×Dic13—41no—
80C2×D52—21no—
81C2×D52—21no—
82C2×D52—21no—
83C2×D52—21no—
84C2×D52—21no—
85C2×D52Q1612yes—
86C2×C4×D13—41no—
87C2×C4×D13—41no—
88C2×C4×D13—41no—
89C2×C4×D13—41no—
90C2×C4×D13—41no—
91C2×C4×D13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13#4111yescharacteristic
105C42×C13#4111yescharacteristic
106#6103—41no—
107#6103—41no—
108C4⋊Dic13—21no—
109C4⋊Dic13—21no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113C4⋊Dic13—41no—
114C4⋊Dic13—81no—
115C2×#1055—21no—
116C2×#1055—21no—
117C2×#1055—22no—
118C2×#1055—21no—
119C2×#1055—21no—
120C2×#1055—21no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055D812yes—
124C2×#474—131no—
125#1956—131no—
126#1954—131no—
127#1802—131no—
128C2×#335—131no—
129C2×#332D1311yescharacteristic, complemented
130#1296—131no—
131C23×C13#12111yescharacteristic
132C22×D13—22no—
133C22×D13—41no—
134C22×D13—41no—
135C22×D13—41no—
136C22×D13—41no—
137C22×D13—41no—
138C22×D13—41no—
139Q8×C13—42no—
140Q8×C13—42no—
141Q8×C13—81no—
142Q8×C13—81no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—42no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13#12011yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12311yescharacteristic
152C2×C4×C13#12311yescharacteristic
153C2×C4×C13#12411yescharacteristic
154C2×C4×C13C2×D811yescharacteristic
155C2×C4×C13C2×Q1611yescharacteristic
156C2×C4×C13#13511yescharacteristic
157C2×C4×C13#13511yescharacteristic
158C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C13#13711yescharacteristic
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—81no—
166C2×Dic13—81no—
167C2×Dic13—81no—
168D52—22no—
169D52—22no—
170D52—41no—
171D52—41no—
172C4×D13—81no—
173C4×D13—81no—
174C4×D13—81no—
175C4×D13—81no—
176C8×C13—81no—
177C8×C13—81no—
178#1055—22no—
179#1055—42no—
180#1055—41no—
181C2×C4⋊Q8C2×D1311yescharacteristic
182C2×C4×D4—131no—
183#474—262no—
184#474—262no—
185C2×#107—261no—
186C2×C4⋊C8—131no—
187C2×C4⋊C8C2×D1311yescharacteristic
188C2×C4⋊C8C2×D1311yescharacteristic
189C2×#103—261no—
190C2×#103—261no—
191C2×#102—261no—
192C2×#102—261no—
193C2×C22⋊C8—261no—
194C2×C22⋊C8—261no—
195C2×C4×C8—131no—
196#384—131no—
197#340—261no—
198#335—262no—
199#332—22no—
200C22×C13#39411yescharacteristic
201C22×C13#45911yescharacteristic
202C22×C13#46311yescharacteristic
203C22×C13#46711yescharacteristic
204C22×C13#46811yescharacteristic
205C22×C13#47111yescharacteristic
206C22×C13#47311yescharacteristic
207C2×D13—42no—
208C2×D13—42no—
209C2×D13—42no—
210C2×D13—81no—
211C2×D13—81no—
212C2×D13—81no—
213C2×D13—81no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—82no—
217C4×C13#44911yescharacteristic
218C4×C13#45111yescharacteristic
219C4×C13#45911yescharacteristic
220C4×C13#46311yescharacteristic
221C4×C13#46611yescharacteristic
222C4×C13#46911yescharacteristic
223C4×C13#48411yescharacteristic
224C4×C13#48511yescharacteristic
225Dic13—81no—
226Dic13—161no—
227C22×Q8—21no—
228C22×D4—131no—
229C23×C4—261no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—131no—
233C22×C8—131no—
234C22×C8—261no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8C22⋊D1312yes—
239C4×D4—261no—
240C4×D4—261no—
241C4×D4—261no—
242C4×D4—261no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—131no—
246C2×C4⋊C4—261no—
247C2×C4⋊C4—261no—
248C2×C4⋊C4—261no—
249C2×C22⋊C4—261no—
250C2×C42C22×D1311yescharacteristic
251#107—264no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—132no—
257C4⋊C8—261no—
258#103—522no—
259#103—522no—
260#102—264no—
261#102—522no—
262C22⋊C8—522no—
263C22⋊C8—522no—
264C4×C8—261no—
265C4×C8—261no—
266C2×C13#166911yescharacteristic
267C2×C13#168311yescharacteristic
268C2×C13#168511yescharacteristic
269C2×C13#169911yescharacteristic
270C2×C13#203611yescharacteristic
271C2×C13#205211yescharacteristic
272C2×C13#205411yescharacteristic
273D13—82no—
274C24—261no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×D4—132no—
282C2×D4—261no—
283C2×D4—261no—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C22×C4—41no—
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#612711yescharacteristic
297C22×C4D4×D1311yescharacteristic
298C22×C4D4×D1311yescharacteristic
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—132no—
306C2×C8—261no—
307C2×C8—261no—
308C2×C8—261no—
309C2×C8—261no—
310C2×C8—261no—
311C2×C8—262no—
312C2×C8—521no—
313C2×C8—521no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—261no—
319C4⋊C4—261no—
320C4⋊C4—521no—
321C4⋊C4—521no—
322C4⋊C4—521no—
323C4⋊C4—521no—
324C4⋊C4—1041no—
325C22⋊C4—521no—
326C22⋊C4—521no—
327C42#612711yescharacteristic
328C42D4×D1311yescharacteristic
329C42#612911yescharacteristic
330C42C2×C22⋊D1311yescharacteristic
331C13#1048511yescharacteristic, complemented, Sylow
332C23—262no—
333C23—521no—
334C23—521no—
335C23—521no—
336C23—521no—
337C23—521no—
338C23—521no—
339C23#8813811yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344D4—262no—
345D4—262no—
346D4—521no—
347D4—521no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—1041no—
357C2×C4—1041no—
358C2×C4—1041no—
359C2×C4—1041no—
360C2×C4—1041no—
361C2×C4—1041no—
362C2×C4—1041no—
363C2×C4#8813711yescharacteristic
364C2×C4#8813811yescharacteristic
365C2×C4#8813911yescharacteristic
366C2×C4D8×D1311yescharacteristic
367C2×C4#8816511yescharacteristic
368C2×C4#8816811yescharacteristic
369C2×C4#8816811yescharacteristic
370C2×C4#8817011yescharacteristic
371C2×C4#8817011yescharacteristic
372C2×C4Q16×D1311yescharacteristic
373C2×C4#8817211yescharacteristic
374C2×C4#8818311yescharacteristic
375C2×C4#8819111yescharacteristic
376C2×C4#8819311yescharacteristic
377C8—81no—
378C8—81no—
379C8—262no—
380C8—521no—
381C8—522no—
382C22—522no—
383C22—522no—
384C22—522no—
385C22—1041no—
386C22—1041no—
387C22—1041no—
388C22—1041no—
389C22#1171841511yescharacteristic
390C22#1171841611yescharacteristic
391C22#1171844711yescharacteristic
392C22#1171844811yescharacteristic
393C22#1171847311yescharacteristic
394C22#1171847411yescharacteristic
395C22#1171862011yescharacteristic
396C4—21no—
397C4—21no—
398C4—82no—
399C4—1041no—
400C4—2081no—
401C4#1171843611yescharacteristic
402C4#1171844311yescharacteristic
403C4#1171847011yescharacteristic
404C4#1171847611yescharacteristic
405C4#1171881111yescharacteristic
406C4#1171882611yescharacteristic
407C4#1171883311yescharacteristic
408C4#1171884711yescharacteristic
409C2—1042no—
410C2#1311420011yescharacteristic
411C2#1311428611yescharacteristic
412C2#1311430411yescharacteristic
413C2#1311438211yescharacteristic
414C2#1311603711yescharacteristic
415C2#1311613511yescharacteristic
416C2#1311614511yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenterC2×#332D13
hypocenterC13#10485
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #13115639C2semidirect
5. C2×#11718071C2semidirect
6. #13112720C2semidirect
7. C2×C13×#332C2semidirect
129. C2×#332D13semidirect
331. C13#10485semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
#131156392
#131156292
#131148372
C2×#117180712
#131127202
C2×C13×#3322
#1048513