Finite Group Databasebeta

← #15917650

Subgroups — #15917650

Order 3328.

1058 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718726C211yesmaximal, characteristic, complemented
2C2×#11718682C211yesmaximal, characteristic, complemented
3#13119828C211yesmaximal, characteristic
4#13116036C212yesmaximal, complemented
5#13116029C212yesmaximal, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115635C211yesmaximal, characteristic
8#13115035C212yesmaximal, complemented
9#13115024C212yesmaximal, complemented
10#13114666C211yesmaximal, characteristic, complemented
11C2×C13×#552C211yesmaximal, characteristic
12C13×#552—24no—
13C13×#552—24no—
14C2×C13×#126—21no—
15C2×C13×#125—21no—
16C2×C13×#125C2211yescharacteristic
17C2×C13×#123—21no—
18C2×C13×C22⋊Q8C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×C13×#117—21no—
23C2×C13×#117C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C2×#88190—21no—
26C2×#88123C2211yescharacteristic
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29#11718873C2212yes—
30#11718873C2212yes—
31C2×C22⋊#1055C2212yes—
32C2×C22⋊#1055C2212yes—
33#11718726—24no—
34#11718682—24no—
35#11718635—21no—
36C2×#88048C2212yes—
37C2×#88047C2212yes—
38C2×#88047C2212yes—
39#11718614—21no—
40#11718614—21no—
41C4×C4⋊Dic13C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×#88043C2211yescharacteristic
44#11718121C2212yes—
45#11718121C2212yes—
46#11718121C2212yes—
47C22×Q8×C13C2311yescharacteristic
48C22×D4×C13D411yescharacteristic
49C23×C4×C13—21no—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C22×Dic26—21no—
53C13×#126—28no—
54C13×#125—28no—
55C13×#125—22no—
56C13×#125D414yes—
57C13×#123—28no—
58C13×C22⋊Q8—22no—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—22no—
62C4×Q8×C13—22no—
63C4×Q8×C13D414yes—
64C4×D4×C13—22no—
65C4×D4×C13—22no—
66C13×#117—28no—
67C13×#117—22no—
68C13×#117—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13—21no—
87C2×C42×C13—21no—
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91#88190—44no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2312yes—
94C2×C4⋊Dic13C2312yes—
95C2×C4×Dic13—21no—
96C22×#1055C2312yes—
97C22×#1055C2312yes—
98#88123—22no—
99#88123—22no—
100#88075—24no—
101#88075—24no—
102#88071—21no—
103#88071—22no—
104#88071—22no—
105C22⋊#1055—24no—
106C22⋊#1055—24no—
107#88048—24no—
108#88047—24no—
109#88047—24no—
110C4⋊#1055—22no—
111#88043—22no—
112#25716—131nomaximal, Sylow
113C24×C13C2×D411yescharacteristic
114C24×C13C2×D411yescharacteristic
115C2×Q8×C13—21no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13C2×D412yes—
119C2×D4×C13—22no—
120C2×D4×C13—22no—
121C2×D4×C13—41no—
122C22×C4×C13—24no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—42no—
136C22×C4×C13—42no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2411yescharacteristic
142C22×Dic13—22no—
143C22×Dic13—22no—
144C2×Dic26—42no—
145C2×Dic26—42no—
146C2×Dic26—42no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—24no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4C2×D412yes—
158C13×C4⋊C4C2×D412yes—
159C13×C4⋊C4C2×D412yes—
160C13×C22⋊C4—24no—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—22no—
165C42×C13—24no—
166C42×C13—24no—
167C42×C13C2×D412yes—
168C42×C13C2×D412yes—
169C22⋊Dic13—44no—
170C22⋊Dic13—44no—
171C4⋊Dic13—22no—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—22no—
175C4⋊Dic13—42no—
176C4×Dic13—42no—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055#4114yes—
183C2×#552D1311yescharacteristic
184C2×#501—131no—
185C2×#477—131no—
186#2547—131no—
187#2036—132no—
188#2035—132no—
189#1989—131no—
190#1955—131no—
191#1854—132no—
192#1852—132no—
193#1763—131no—
194C23×C13—21no—
195C23×C13—22no—
196C23×C13—21no—
197C23×C13—22no—
198C23×C13—21no—
199C23×C13—22no—
200C23×C13—21no—
201C23×C13—21no—
202C23×C13—22no—
203C23×C13AGL(1,ℤ/8)12yes—
204C23×C13C22×D411yescharacteristic
205Q8×C13—22no—
206Q8×C13—22no—
207Q8×C13—42no—
208D4×C13—44no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—22no—
212C2×C4×C13—21no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—21no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—48no—
221C2×C4×C13—42no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—42no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13#12012yes—
234C2×C4×C13#12012yes—
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C13C2×#4112yes—
238C2×C4×C132−1+412yes—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245Dic26—84no—
246#1055—24no—
247#1055—42no—
248#552—24no—
249#552—24no—
250C2×C4⋊Q8—131no—
251C2×#126—21no—
252C2×#125—21no—
253C2×#125C2×D1311yescharacteristic
254C2×#124—261no—
255C2×#123—21no—
256C2×C22⋊Q8C2×D1311yescharacteristic
257C2×C22⋊Q8C2×D1311yescharacteristic
258C2×C4×Q8C2×D1311yescharacteristic
259C2×C4×D4C2×D1311yescharacteristic
260C2×#117—21no—
261C2×#117C2×D1311yescharacteristic
262C22×C4⋊C4C2×D1311yescharacteristic
263#501—264no—
264#477—264no—
265C2×#107—132no—
266C2×#107—132no—
267C2×#106—132no—
268C2×C4⋊C8—131no—
269C2×#103—132no—
270C2×#103—132no—
271C2×C22⋊C8—132no—
272C2×C22⋊C8—132no—
273C2×#97—131no—
274#397—261no—
275#397—261no—
276#391—261no—
277#380—132no—
278#380—132no—
279C4×C4⋊C4—131no—
280#340—132no—
281#340—132no—
282#340—132no—
283C22×C13—24no—
284C22×C13—22no—
285C22×C13—42no—
286C22×C13—41no—
287C22×C13—41no—
288C22×C13—42no—
289C22×C13—42no—
290C22×C13—41no—
291C22×C13—41no—
292C22×C13—41no—
293C22×C13C2×#12011yescharacteristic
294C22×C13#54712yes—
295C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C13#57511yescharacteristic
297C22×C13#57812yes—
298C4×C13—22no—
299C4×C13—22no—
300C4×C13—41no—
301C4×C13—41no—
302C4×C13—42no—
303C4×C13—42no—
304C4×C13—42no—
305C4×C13—42no—
306C4×C13#53211yescharacteristic
307C4×C13#53611yescharacteristic
308C4×C13#54812yes—
309Dic13—82no—
310Dic13—82no—
311C22×Q8—261no—
312C22×Q8C22×D1311yescharacteristic
313C22×D4C22⋊D1311yescharacteristic
314C23×C4—21no—
315C23×C4C22×D1311yescharacteristic
316C23×C4C22×D1311yescharacteristic
317C22×C8—132no—
318C22×C8—132no—
319C4⋊Q8—262no—
320C4⋊Q8—262no—
321#126—28no—
322#125—28no—
323#125—22no—
324#125C22⋊D1314yes—
325#124—524no—
326#123—28no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C4×Q8—22no—
332C4×Q8C22⋊D1314yes—
333C4×D4—22no—
334C4×D4—22no—
335#117—28no—
336#117—22no—
337#117—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—132no—
347C2×C4⋊C4—132no—
348C2×C4⋊C4—261no—
349C2×C4⋊C4C22⋊D1311yescharacteristic
350C2×C4⋊C4C22×D1311yescharacteristic
351C2×C4⋊C4C22×D1311yescharacteristic
352C2×C4⋊C4C22×D1311yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—262no—
357C2×C22⋊C4—262no—
358C2×C22⋊C4C22⋊D1311yescharacteristic
359C2×C22⋊C4C22⋊D1311yescharacteristic
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—261no—
363C2×C42C22×D1311yescharacteristic
364#107—264no—
365#107—264no—
366#106—264no—
367C4⋊C8—262no—
368#103—264no—
369#103—264no—
370C22⋊C8—264no—
371C22⋊C8—264no—
372#97—262no—
373#95—261no—
374#95—262no—
375#95—262no—
376C2×C13—42no—
377C2×C13—81no—
378C2×C13#243211yescharacteristic
379C2×C13#300611yescharacteristic
380C2×C13#301111yescharacteristic
381C2×C13#334312yes—
382C2×C13#334912yes—
383C24C2×C22⋊D1311yescharacteristic
384C24C2×C22⋊D1311yescharacteristic
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—522no—
389C2×Q8—522no—
390C2×Q8—522no—
391C2×Q8C2×C22⋊D1312yes—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—41no—
395C22×C4—24no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—262no—
411C22×C4—262no—
412C22×C4C2×C22⋊D1311yescharacteristic
413C22×C4C2×C22⋊D1311yescharacteristic
414C22×C4C2×C22⋊D1311yescharacteristic
415C22×C4C2×C22⋊D1311yescharacteristic
416C22×C4C23×D1311yescharacteristic
417C2×C8—134no—
418C2×C8—262no—
419C2×C8—262no—
420C2×C8—262no—
421C2×C8—262no—
422C2×C8—262no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—262no—
434C4⋊C4—262no—
435C4⋊C4—262no—
436C4⋊C4—262no—
437C4⋊C4—522no—
438C4⋊C4C2×C22⋊D1312yes—
439C4⋊C4C2×C22⋊D1312yes—
440C4⋊C4C2×C22⋊D1312yes—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—524no—
447C22⋊C4—524no—
448C42—24no—
449C42—24no—
450C42—522no—
451C42C2×C22⋊D1312yes—
452C42C2×C22⋊D1312yes—
453C13#2571611yescharacteristic, complemented, Sylow
454C23—21no—
455C23—22no—
456C23—22no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23#8820312yes—
464C23C22×C22⋊D1311yescharacteristic
465Q8—22no—
466Q8—22no—
467Q8—42no—
468Q8—1044no—
469D4—44no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—48no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—522no—
495C2×C4—522no—
496C2×C4—522no—
497C2×C4—522no—
498C2×C4—522no—
499C2×C4—522no—
500C2×C4#8820712yes—
501C2×C4#8820712yes—
502C2×C4#41×D1312yes—
503C2×C4#8825712yes—
504C2×C4C22×C22⋊D1311yescharacteristic
505C2×C4C22×C22⋊D1311yescharacteristic
506C8—264no—
507C8—522no—
508C22—24no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—41no—
513C22—41no—
514C22—42no—
515C22—42no—
516C22—41no—
517C22—41no—
518C22C2×#8820311yescharacteristic
519C22#1171952711yescharacteristic
520C22#1171952912yes—
521C22#1171954312yes—
522C22C2×#8820711yescharacteristic
523C4—22no—
524C4—22no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—41no—
529C4—41no—
530C4—42no—
531C4—1042no—
532C4—1042no—
533C4#1171953011yescharacteristic
534C4#1171953612yes—
535C4#1171953711yescharacteristic
536C2—42no—
537C2—81no—
538C2#1311846011yescharacteristic
539C2#1312408811yescharacteristic
540C2#1312413111yescharacteristic
541C2#1312727612yes—
542C2#1312736612yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#552D13
hypocenterC13#25716
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#11718726C2semidirect
2. C2×#11718682C2semidirect
4. #13116036C2semidirect
5. #13116029C2semidirect
6. #13115794C2semidirect
8. #13115035C2semidirect
9. #13115024C2semidirect
10. #13114666C2semidirect
453. C13#25716semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
C2×#117186822
#131198282
#131160362
#131160292
#131157942
#131156352
#131150352
#131150242
#131146662
C2×C13×#5522
#2571613