Finite Group Databasebeta

← #15766310

Subgroups — #15766310

Order 3328.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120010C211yesmaximal, characteristic
2#13115592C211yesmaximal, characteristic, complemented
3#13114833C211yesmaximal, characteristic
4C2×#11718138C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1956C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C2×C13×#103—22no—
11C2×C4×C8×C13C2211yescharacteristic
12C13×#384C2211yescharacteristic
13#11718892—22no—
14#11718649—21no—
15#11718648—21no—
16#11718648—21no—
17#11718638—21no—
18C2×#88049—21no—
19C2×#88047—21no—
20C4×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23#11718138—22no—
24#11718121—21no—
25#11718121—21no—
26#11718051—22no—
27C22×Q8×C13D412yes—
28C22×D52D411yescharacteristic
29C22×C4×D13—21no—
30C22×C8×C13—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C42×C13C2311yescharacteristic
41C2×#6103—21no—
42C2×#6103—22no—
43C2×#6103—22no—
44C2×C4⋊Dic13D411yescharacteristic
45C2×C4⋊Dic13D411yescharacteristic
46C2×C4⋊Dic13D411yescharacteristic
47C2×C4×Dic13—21no—
48C22×#1055—21no—
49C22×#1055—21no—
50C4×D52—21no—
51C4×D52—21no—
52C4×D52—21no—
53C4×D52—21no—
54C13×#103—44no—
55C4×C8×C13—21no—
56C4×C8×C13—21no—
57#88071—22no—
58#88071—22no—
59#88071—21no—
60#88049—42no—
61#88047—42no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055D412yes—
66#10413—131nomaximal, Sylow
67C23×D13—21no—
68C2×Q8×C13—22no—
69C2×Q8×C13—22no—
70C2×Q8×C13—42no—
71C2×Q8×C13—42no—
72C22×C4×C13—22no—
73C22×C4×C13—41no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
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—22no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C13×C4⋊C4—42no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C42×C13C2×D411yescharacteristic
105C42×C13#4111yescharacteristic
106C42×C13#4111yescharacteristic
107C42×C13#4111yescharacteristic
108#6103—41no—
109#6103—41no—
110#6103—82no—
111#6103—82no—
112C4⋊Dic13—21no—
113C4⋊Dic13—21no—
114C4⋊Dic13—21no—
115C4⋊Dic13—21no—
116C4⋊Dic13—21no—
117C4⋊Dic13—21no—
118C4×Dic13—41no—
119C4×Dic13—41no—
120C2×#1055—22no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055—41no—
124C2×#1055—41no—
125C2×#1055—41no—
126#2563—131no—
127#1956D1311yescharacteristic, complemented
128#1947—131no—
129#1802—131no—
130C2×#333—131no—
131C2×D4⋊C8—131no—
132#1279—131no—
133C23×C13#12011yescharacteristic
134C22×D13—22no—
135C22×D13—41no—
136C22×D13—41no—
137C22×D13—41no—
138C22×D13—41no—
139C22×D13—41no—
140C22×D13—41no—
141Q8×C13—44no—
142Q8×C13—82no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13#12311yescharacteristic
155C2×C4×C13#12311yescharacteristic
156C2×C4×C13#12411yescharacteristic
157C2×C4×C13C2×Q1611yescharacteristic
158C2×C4×C13#13511yescharacteristic
159C2×C4×C13#13511yescharacteristic
160C2×C4×C13#13511yescharacteristic
161C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C13#13711yescharacteristic
164C2×C4×C13#13711yescharacteristic
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171C2×Dic13—41no—
172C2×Dic13—41no—
173C2×Dic13—41no—
174D52—22no—
175D52—22no—
176D52—41no—
177D52—41no—
178C4×D13—81no—
179C4×D13—81no—
180C4×D13—81no—
181C4×D13—81no—
182C8×C13—42no—
183#1055—42no—
184#1055—81no—
185C2×C4⋊Q8C2×D1311yescharacteristic
186C2×C4×D4—131no—
187C2×#107—261no—
188C2×C4⋊C8—131no—
189C2×C4⋊C8—131no—
190C2×#103—22no—
191C2×#102—261no—
192C2×C4×C8C2×D1311yescharacteristic
193#393—262no—
194#390—261no—
195#384C2×D1311yescharacteristic
196#382—261no—
197#380—261no—
198#380—261no—
199C4×C4⋊C4—131no—
200#340—261no—
201#340—261no—
202#333—262no—
203D4⋊C8—262no—
204C22×C13#39411yescharacteristic
205C22×C13#44911yescharacteristic
206C22×C13#44911yescharacteristic
207C22×C13#45111yescharacteristic
208C22×C13#45211yescharacteristic
209C22×C13#45311yescharacteristic
210C22×C13#45511yescharacteristic
211C2×D13—42no—
212C2×D13—42no—
213C2×D13—42no—
214C2×D13—81no—
215C2×D13—81no—
216C2×D13—81no—
217C2×D13—81no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—82no—
221C4×C13—161no—
222C4×C13#46311yescharacteristic
223C4×C13#46411yescharacteristic
224C4×C13#46711yescharacteristic
225C4×C13#46811yescharacteristic
226C4×C13#48411yescharacteristic
227C4×C13#48511yescharacteristic
228C4×C13#48811yescharacteristic
229C4×C13#48911yescharacteristic
230Dic13—81no—
231Dic13—81no—
232Dic13—81no—
233C22×Q8C22⋊D1312yes—
234C22×D4—131no—
235C23×C4—261no—
236C22×C8—21no—
237C22×C8—261no—
238C22×C8—261no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4×D4—261no—
244C4×D4—261no—
245C4×D4—261no—
246C4×D4—261no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—131no—
253C2×C4⋊C4—131no—
254C2×C4⋊C4—131no—
255C2×C22⋊C4—261no—
256C2×C22⋊C4—262no—
257C2×C22⋊C4—262no—
258C2×C42—261no—
259C2×C42C22×D1311yescharacteristic
260#107—522no—
261C4⋊C8—132no—
262C4⋊C8—261no—
263C4⋊C8—261no—
264C4⋊C8—261no—
265#103—44no—
266#102—522no—
267C4×C8—21no—
268C4×C8—21no—
269#95—262no—
270#95—262no—
271#95—261no—
272C2×C13#162411yescharacteristic
273C2×C13#163211yescharacteristic
274C2×C13#164411yescharacteristic
275C2×C13#164611yescharacteristic
276C2×C13#203611yescharacteristic
277C2×C13#203711yescharacteristic
278C2×C13#204211yescharacteristic
279D13—82no—
280C24—261no—
281C2×Q8—22no—
282C2×Q8—22no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×D4—132no—
286C2×D4—261no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—261no—
290C2×D4—261no—
291C22×C4—22no—
292C22×C4—41no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4—521no—
297C22×C4—521no—
298C22×C4—521no—
299C22×C4—521no—
300C22×C4—521no—
301C22×C4—521no—
302C22×C4D4×D1311yescharacteristic
303C22×C4D4×D1311yescharacteristic
304C22×C4C2×C22⋊D1311yescharacteristic
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—262no—
309C2×C8—521no—
310C2×C8—521no—
311C2×C8—521no—
312C2×C8—521no—
313C2×C8—521no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—261no—
324C4⋊C4—261no—
325C4⋊C4—261no—
326C4⋊C4—261no—
327C4⋊C4—261no—
328C4⋊C4—261no—
329C22⋊C4—521no—
330C22⋊C4—521no—
331C22⋊C4—1042no—
332C22⋊C4—1042no—
333C42—521no—
334C42—521no—
335C42#612711yescharacteristic
336C42#612711yescharacteristic
337C42D4×D1311yescharacteristic
338C42#612911yescharacteristic
339C13#1041311yescharacteristic, complemented, Sylow
340C23—262no—
341C23—521no—
342C23—521no—
343C23—521no—
344C23—521no—
345C23—521no—
346C23—521no—
347C23#8819111yescharacteristic
348Q8—44no—
349Q8—82no—
350D4—262no—
351D4—262no—
352D4—521no—
353D4—521no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—521no—
368C2×C4—521no—
369C2×C4—521no—
370C2×C4—521no—
371C2×C4—1041no—
372C2×C4—1041no—
373C2×C4—1041no—
374C2×C4—1041no—
375C2×C4#8813711yescharacteristic
376C2×C4#8813811yescharacteristic
377C2×C4#8813811yescharacteristic
378C2×C4#8813911yescharacteristic
379C2×C4#8816811yescharacteristic
380C2×C4#8816811yescharacteristic
381C2×C4#8817011yescharacteristic
382C2×C4#8817011yescharacteristic
383C2×C4Q16×D1311yescharacteristic
384C2×C4#8817211yescharacteristic
385C2×C4#8817211yescharacteristic
386C2×C4#8817311yescharacteristic
387C2×C4#8818311yescharacteristic
388C2×C4#8819311yescharacteristic
389C8—42no—
390C8—522no—
391C8—1041no—
392C22—522no—
393C22—522no—
394C22—522no—
395C22—1041no—
396C22—1041no—
397C22—1041no—
398C22—1041no—
399C22#1171862011yescharacteristic
400C22#1171872211yescharacteristic
401C22#1171873811yescharacteristic
402C22#1171883311yescharacteristic
403C22#1171883311yescharacteristic
404C22#1171884711yescharacteristic
405C22#1171884811yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—161no—
410C4—1041no—
411C4—1041no—
412C4—1041no—
413C4#1171845611yescharacteristic
414C4#1171845911yescharacteristic
415C4#1171846111yescharacteristic
416C4#1171847011yescharacteristic
417C4#1171847311yescharacteristic
418C4#1171847411yescharacteristic
419C4#1171847611yescharacteristic
420C4#1171848011yescharacteristic
421C2—1042no—
422C2#1311391711yescharacteristic
423C2#1311396711yescharacteristic
424C2#1311404711yescharacteristic
425C2#1311406111yescharacteristic
426C2#1311603711yescharacteristic
427C2#1311604611yescharacteristic
428C2#1311607311yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1956C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenter#1956D13
hypocenterC13#10413
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
2. #13115592C2semidirect
4. C2×#11718138C2semidirect
6. #13112676C2semidirect
7. C13×#1956C2semidirect
127. #1956D13semidirect
339. C13#10413semidirect

Maximal subgroups

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

subgroupindex
#131200102
#131155922
#131148332
C2×#117181382
C2×#117180512
#131126762
C13×#19562
#1041313