Finite Group Databasebeta

← #15917606

Subgroups — #15917606

Order 3328.

1060 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718741C211yesmaximal, characteristic, complemented
2C2×#11718683C211yesmaximal, characteristic, complemented
3#13120002C211yesmaximal, characteristic
4#13116036C212yesmaximal, complemented
5#13116029C212yesmaximal, complemented
6#13115789C211yesmaximal, characteristic, complemented
7#13115635C211yesmaximal, characteristic
8#13115029C212yesmaximal, complemented
9#13115024C212yesmaximal, complemented
10#13114666C211yesmaximal, characteristic, complemented
11C2×C13×#554C211yesmaximal, characteristic
12C13×#554—24no—
13C13×#554—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125—21no—
16C2×C13×C22⋊Q8—22no—
17C2×C13×C22⋊Q8C2212yes—
18C2×C4×Q8×C13C2211yescharacteristic
19C2×C4×D4×C13—21no—
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4C2212yes—
22C2×#88124C2211yescharacteristic
23C2×#88075C2211yescharacteristic
24C2×#88075C2211yescharacteristic
25C2×#88075C2212yes—
26#11718883—21no—
27#11718873C2212yes—
28#11718873C2212yes—
29C2×C22⋊#1055C2212yes—
30C2×C22⋊#1055C2212yes—
31#11718741—24no—
32#11718683—24no—
33#11718643—21no—
34C2×#88048C2211yescharacteristic
35C2×#88048C2212yes—
36C2×#88047C2211yescharacteristic
37C2×#88047C2212yes—
38#11718606—22no—
39C4×C4⋊Dic13C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×#88043C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×Q8×C13—21no—
46C22×Q8×C13C2311yescharacteristic
47C22×D4×C13D411yescharacteristic
48C23×C4×C13—22no—
49C23×C4×C13C2312yes—
50C13×C4⋊Q8—22no—
51C13×C4⋊Q8D414yes—
52C13×#125—28no—
53C13×C22⋊Q8—216no—
54C13×C22⋊Q8—24no—
55C13×C22⋊Q8—24no—
56C4×Q8×C13—22no—
57C4×Q8×C13D414yes—
58C4×D4×C13—28no—
59C4×D4×C13—22no—
60C4×D4×C13—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—24no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2312yes—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4D412yes—
72C2×C42×C13—21no—
73C2×C42×C13C2311yescharacteristic
74C2×C22⋊Dic13—22no—
75C2×C22⋊Dic13—22no—
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2312yes—
79C2×#6101—21no—
80C2×#6101—21no—
81C2×C4×Dic13—21no—
82C22×#1055C2311yescharacteristic
83C22×#1055C2311yescharacteristic
84C22×#1055C2312yes—
85#88124—22no—
86#88124—22no—
87#88075—22no—
88#88075—22no—
89#88075—24no—
90#88071—21no—
91#88071—22no—
92#88071—22no—
93C22⋊#1055—24no—
94C22⋊#1055—24no—
95#88048—22no—
96#88048—24no—
97#88047—22no—
98#88047—24no—
99C4⋊#1055—22no—
100#88043—22no—
101#25712—131nomaximal, Sylow
102C24×C13C2×D412yes—
103C2×Q8×C13—24no—
104C2×Q8×C13—21no—
105C2×Q8×C13—22no—
106C2×Q8×C13—22no—
107C2×Q8×C13—81no—
108C2×Q8×C13—81no—
109C2×Q8×C13C2×D412yes—
110C2×D4×C13—24no—
111C2×D4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—28no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—82no—
123C22×C4×C13—82no—
124C22×C4×C13C2×D412yes—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2411yescharacteristic
128C22×Dic13—22no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C13×C4⋊C4—28no—
132C13×C4⋊C4—28no—
133C13×C4⋊C4—24no—
134C13×C4⋊C4—24no—
135C13×C4⋊C4—22no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—22no—
138C13×C4⋊C4C2×D412yes—
139C13×C4⋊C4C2×D414yes—
140C13×C22⋊C4—28no—
141C13×C22⋊C4—24no—
142C42×C13—24no—
143C42×C13C2×D412yes—
144C42×C13C2×D412yes—
145C22⋊Dic13—44no—
146C22⋊Dic13—82no—
147C4⋊Dic13—21no—
148C4⋊Dic13—21no—
149C4⋊Dic13—21no—
150C4⋊Dic13—21no—
151C4⋊Dic13—22no—
152C4⋊Dic13—22no—
153#6101—42no—
154#6101—42no—
155C4×Dic13—81no—
156C2×#1055—22no—
157C2×#1055—22no—
158C2×#1055—21no—
159C2×#1055—21no—
160C2×#1055—22no—
161C2×#1055—22no—
162C2×#1055#4114yes—
163C2×#554D1311yescharacteristic
164C2×#501—131no—
165C2×#479—131no—
166#2562—131no—
167#2036—132no—
168#2035—132no—
169#1988—131no—
170#1955—131no—
171#1853—132no—
172#1852—132no—
173#1763—131no—
174C23×C13—22no—
175C23×C13—22no—
176C23×C13—22no—
177C23×C13—22no—
178C23×C13—22no—
179C23×C13—22no—
180C23×C13#13714yes—
181C23×C13C22×D411yescharacteristic
182Q8×C13—22no—
183Q8×C13—22no—
184Q8×C13—42no—
185Q8×C13—84no—
186D4×C13—28no—
187C2×C4×C13—22no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—24no—
194C2×C4×C13—22no—
195C2×C4×C13—22no—
196C2×C4×C13—42no—
197C2×C4×C13—41no—
198C2×C4×C13—42no—
199C2×C4×C13—41no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—88no—
206C2×C4×C13#12012yes—
207C2×C4×C13#12012yes—
208C2×C4×C13C22×D411yescharacteristic
209C2×C4×C13C22×D411yescharacteristic
210C2×C4×C13C2×#4112yes—
211C2×C4×C132−1+412yes—
212C2×Dic13—41no—
213C2×Dic13—41no—
214C2×Dic13—42no—
215C2×Dic13—42no—
216C2×Dic13—42no—
217C2×Dic13—42no—
218C2×Dic13—41no—
219C2×Dic13—41no—
220#1055—24no—
221#1055—41no—
222#1055—41no—
223#554—24no—
224#554—24no—
225C2×C4⋊Q8C2×D1311yescharacteristic
226C2×#125—21no—
227C2×#125—131no—
228C2×C22⋊Q8—22no—
229C2×C22⋊Q8C2×D1312yes—
230C2×C4×Q8C2×D1311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4C2×D1311yescharacteristic
233C22×C4⋊C4C2×D1312yes—
234#501—264no—
235#479—264no—
236C2×#107—131no—
237C2×#107—132no—
238C2×#106—131no—
239C2×#106—132no—
240C2×C4⋊C8—131no—
241C2×#103—131no—
242C2×#103—131no—
243C2×#103—132no—
244C2×C22⋊C8—132no—
245C2×C22⋊C8—132no—
246C2×#97—131no—
247#400—261no—
248#394—261no—
249#388—262no—
250#380—132no—
251#380—132no—
252C4×C4⋊C4—131no—
253#340—132no—
254#340—132no—
255#340—132no—
256C22×C13—24no—
257C22×C13—24no—
258C22×C13—24no—
259C22×C13—42no—
260C22×C13—42no—
261C22×C13—42no—
262C22×C13—42no—
263C22×C13C2×#12011yescharacteristic
264C22×C13#54712yes—
265C22×C13C2×#13712yes—
266C22×C13#57611yescharacteristic
267C22×C13#57711yescharacteristic
268C4×C13—22no—
269C4×C13—22no—
270C4×C13—42no—
271C4×C13—42no—
272C4×C13—42no—
273C4×C13—44no—
274C4×C13#53211yescharacteristic
275C4×C13#53611yescharacteristic
276C4×C13#54812yes—
277Dic13—82no—
278Dic13—81no—
279Dic13—81no—
280C22×Q8—21no—
281C22×Q8C22×D1311yescharacteristic
282C22×D4C22⋊D1311yescharacteristic
283C23×C4—22no—
284C23×C4C22×D1312yes—
285C22×C8—132no—
286C22×C8—131no—
287C22×C8—131no—
288C4⋊Q8—22no—
289C4⋊Q8C22⋊D1314yes—
290#125—28no—
291#125—262no—
292#125—262no—
293C22⋊Q8—216no—
294C22⋊Q8—24no—
295C22⋊Q8—24no—
296C4×Q8—22no—
297C4×Q8C22⋊D1314yes—
298C4×D4—28no—
299C4×D4—22no—
300C4×D4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—131no—
308C2×C4⋊C4—131no—
309C2×C4⋊C4—132no—
310C2×C4⋊C4—261no—
311C2×C4⋊C4—261no—
312C2×C4⋊C4C22⋊D1311yescharacteristic
313C2×C4⋊C4C22×D1311yescharacteristic
314C2×C4⋊C4C22×D1312yes—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—262no—
317C2×C22⋊C4—262no—
318C2×C22⋊C4C22⋊D1312yes—
319C2×C42—21no—
320C2×C42—261no—
321C2×C42C22×D1311yescharacteristic
322#107—262no—
323#107—264no—
324#106—262no—
325#106—264no—
326C4⋊C8—262no—
327#103—264no—
328#103—262no—
329#103—262no—
330C22⋊C8—264no—
331C22⋊C8—264no—
332#97—262no—
333#95—261no—
334#95—262no—
335#95—262no—
336C2×C13—44no—
337C2×C13#243211yescharacteristic
338C2×C13#300411yescharacteristic
339C2×C13#301211yescharacteristic
340C2×C13#334412yes—
341C2×C13#334612yes—
342C24C2×C22⋊D1312yes—
343C2×Q8—24no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—81no—
348C2×Q8—81no—
349C2×Q8C2×C22⋊D1312yes—
350C2×D4—24no—
351C2×D4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—28no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—82no—
363C22×C4—82no—
364C22×C4—262no—
365C22×C4—261no—
366C22×C4—261no—
367C22×C4C2×C22⋊D1312yes—
368C22×C4C2×C22⋊D1311yescharacteristic
369C22×C4C2×C22⋊D1311yescharacteristic
370C22×C4C23×D1311yescharacteristic
371C2×C8—134no—
372C2×C8—262no—
373C2×C8—262no—
374C2×C8—262no—
375C2×C8—262no—
376C2×C8—261no—
377C2×C8—261no—
378C4⋊C4—28no—
379C4⋊C4—28no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—262no—
386C4⋊C4—262no—
387C4⋊C4—261no—
388C4⋊C4—261no—
389C4⋊C4—261no—
390C4⋊C4—261no—
391C4⋊C4—522no—
392C4⋊C4—522no—
393C4⋊C4C2×C22⋊D1312yes—
394C4⋊C4C2×C22⋊D1314yes—
395C22⋊C4—28no—
396C22⋊C4—24no—
397C22⋊C4—524no—
398C22⋊C4—1042no—
399C42—24no—
400C42—1041no—
401C42C2×C22⋊D1312yes—
402C42C2×C22⋊D1312yes—
403C13#2571211yescharacteristic, complemented, Sylow
404C23—22no—
405C23—22no—
406C23—22no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23#8819614yes—
411C23C22×C22⋊D1311yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—42no—
415Q8—84no—
416D4—28no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—88no—
436C2×C4—522no—
437C2×C4—522no—
438C2×C4—522no—
439C2×C4—522no—
440C2×C4—521no—
441C2×C4—521no—
442C2×C4—521no—
443C2×C4—521no—
444C2×C4#8820712yes—
445C2×C4#8820712yes—
446C2×C4#41×D1312yes—
447C2×C4#8825712yes—
448C2×C4C22×C22⋊D1311yescharacteristic
449C2×C4C22×C22⋊D1311yescharacteristic
450C8—264no—
451C8—521no—
452C8—521no—
453C22—24no—
454C22—24no—
455C22—24no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22C2×#8819612yes—
461C22#1171952912yes—
462C22#1171954011yescharacteristic
463C22#1171954111yescharacteristic
464C22C2×#8820711yescharacteristic
465C4—22no—
466C4—22no—
467C4—42no—
468C4—44no—
469C4—42no—
470C4—42no—
471C4—1041no—
472C4—1042no—
473C4—1041no—
474C4#1171953011yescharacteristic
475C4#1171953612yes—
476C4#1171953711yescharacteristic
477C2—44no—
478C2#1311846011yescharacteristic
479C2#1312407011yescharacteristic
480C2#1312414011yescharacteristic
481C2#1312728512yes—
482C2#1312731512yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#554D13
hypocenterC13#25712
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11718741C2semidirect
2. C2×#11718683C2semidirect
4. #13116036C2semidirect
5. #13116029C2semidirect
6. #13115789C2semidirect
8. #13115029C2semidirect
9. #13115024C2semidirect
10. #13114666C2semidirect
403. C13#25712semidirect

Maximal subgroups

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

subgroupindex
C2×#117187412
C2×#117186832
#131200022
#131160362
#131160292
#131157892
#131156352
#131150292
#131150242
#131146662
C2×C13×#5542
#2571213