Finite Group Databasebeta

← #15919936

Subgroups — #15919936

Order 3328.

1176 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718728C211yesmaximal, characteristic, complemented
2C2×#11718676C211yesmaximal, characteristic
3#13119835C211yesmaximal, characteristic, complemented
4#13115979C212yesmaximal, complemented
5#13115969C212yesmaximal, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115777C211yesmaximal, characteristic, complemented
8#13115184C212yesmaximal, complemented
9#13115184C212yesmaximal, complemented
10#13114661C211yesmaximal, characteristic, complemented
11C2×C13×#554C211yesmaximal, characteristic, complemented
12C13×#554—24no—
13C13×#554—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125C2211yescharacteristic
16C2×C13×#125C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C22×C13×C4⋊C4—21no—
25C2×#88201—21no—
26C22×#6104C2212yes—
27C2×#88128C2211yescharacteristic
28C2×#88072C2212yes—
29#11718728—24no—
30#11718676—24no—
31#11718652—21no—
32#11718652—21no—
33#11718649—21no—
34C2×#88049C2212yes—
35C2×#88049C2212yes—
36C2×#88049C2212yes—
37#11718600C2212yes—
38#11718600C2212yes—
39C4×C4⋊Dic13C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×#88043C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718116C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13D411yescharacteristic
49C22×D4×C13C2311yescharacteristic
50C23×C4×C13—21no—
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C22×D52—21no—
54C22×D52—21no—
55C22×D52C2312yes—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8—22no—
58C13×#125—22no—
59C13×#125—22no—
60C13×#125—22no—
61C13×#125D414yes—
62C13×C22⋊Q8—28no—
63C13×C22⋊Q8—28no—
64C13×C22⋊Q8—28no—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13—22no—
72C4×D4×C13D414yes—
73C2×C13×C4⋊C4—28no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4D411yescharacteristic
81C2×C13×C4⋊C4D411yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C42×C13C2311yescharacteristic
89C2×C42×C13C2311yescharacteristic
90C2×C42×C13C2311yescharacteristic
91#88201—44no—
92C2×#6104—24no—
93C2×#6104—24no—
94C2×#6104—24no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—22no—
98C2×#6103—22no—
99C2×C4⋊Dic13C2312yes—
100C2×C4×Dic13—21no—
101C22×#1055C2312yes—
102C22×#1055C2312yes—
103#88128—22no—
104#88128—22no—
105#88072—24no—
106#88071—21no—
107#88049—24no—
108#88049—24no—
109#88049—24no—
110C4⋊#1055—22no—
111#88043—22no—
112#25946—131nomaximal, Sylow
113C24×C13—21no—
114C23×D13—22no—
115C2×Q8×C13—24no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—41no—
119C2×Q8×C13—82no—
120C2×D4×C13—21no—
121C2×D4×C13—22no—
122C2×D4×C13C2×D412yes—
123C2×D4×C13#4114yes—
124C22×C4×C13—24no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—24no—
129C22×C4×C13—24no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—82no—
133C22×C4×C13—82no—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—22no—
142C2×D52—22no—
143C2×D52—22no—
144C2×D52—22no—
145C2×D52—22no—
146C2×D52—22no—
147C2×D52—22no—
148C2×D52—42no—
149C2×D52—42no—
150C2×D52—42no—
151C2×D52—42no—
152C2×D52—82no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4C2×D412yes—
165C13×C4⋊C4C2×D412yes—
166C13×C4⋊C4C2×D412yes—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—24no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13C2×D412yes—
175C42×C13C2×D412yes—
176#6104—48no—
177#6103—44no—
178#6103—44no—
179#6103—82no—
180#6103—82no—
181C4⋊Dic13—22no—
182C4⋊Dic13—22no—
183C4×Dic13—42no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055—22no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—22no—
190C2×#554D1311yescharacteristic, complemented
191C2×#490—131no—
192C2×#459—131no—
193#2548—131no—
194#2025—132no—
195#2023—132no—
196#1989—131no—
197#1985—131no—
198#1879—132no—
199#1879—132no—
200#1762—131no—
201C23×C13—22no—
202C23×C13—24no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—42no—
206C23×C13C22×D411yescharacteristic
207C22×D13—42no—
208C22×D13—42no—
209C22×D13—42no—
210C22×D13—42no—
211C22×D13—42no—
212C22×D13—42no—
213C22×D13—42no—
214Q8×C13—44no—
215Q8×C13—84no—
216D4×C13—22no—
217D4×C13—24no—
218D4×C13#12414yescomplemented
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—48no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—84no—
240C2×C4×C13—84no—
241C2×C4×C13#12012yes—
242C2×C4×C13#12012yes—
243C2×C4×C13AGL(1,ℤ/8)12yes—
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4112yes—
247C2×C4×C132−1+412yes—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251D52—42no—
252D52—42no—
253D52—42no—
254D52—42no—
255D52—84no—
256D52—84no—
257#1055—42no—
258#1055—42no—
259C22×D8—132no—
260#554—24no—
261#554—24no—
262C2×C4⋊Q8C2×D1311yescharacteristic
263C2×#127—131no—
264C2×#125C2×D1311yescharacteristic
265C2×#125C2×D1311yescharacteristic
266C2×#124—261no—
267C2×C22⋊Q8—21no—
268C2×C22⋊Q8—21no—
269C2×C22⋊Q8—21no—
270C2×C4×Q8C2×D1311yescharacteristic
271C2×C4×D4C2×D1311yescharacteristic
272C2×C4×D4C2×D1311yescharacteristic
273C2×C4×D4C2×D1311yescharacteristic
274C22×C4⋊C4—21no—
275#490—264no—
276#459—264no—
277C2×C4⋊C8—131no—
278C2×#102—132no—
279C2×#102—132no—
280C2×#102—132no—
281C2×#102—132no—
282C2×#97—131no—
283#394—261no—
284#394—261no—
285#390—132no—
286#390—132no—
287#390—261no—
288C4×C4⋊C4—131no—
289#340—132no—
290#340—132no—
291#340—132no—
292#336—132no—
293#336—132no—
294C22×C13—24no—
295C22×C13—44no—
296C22×C13—44no—
297C22×C13—42no—
298C22×C13—42no—
299C22×C13C2×#12011yescharacteristic
300C22×C13#54812yes—
301C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C13#57511yescharacteristic
303C22×C13#57612yes—
304C2×D13—82no—
305C2×D13—82no—
306C2×D13—82no—
307C2×D13—82no—
308C2×D13—82no—
309C2×D13—82no—
310C2×D13—82no—
311C4×C13—22no—
312C4×C13—22no—
313C4×C13—22no—
314C4×C13—41no—
315C4×C13—42no—
316C4×C13—41no—
317C4×C13—41no—
318C4×C13—42no—
319C4×C13—42no—
320C4×C13C2×#12411yescharacteristic
321C4×C13#53611yescharacteristic
322C4×C13#54812yes—
323Dic13—82no—
324C22×Q8—21no—
325C22×Q8C22⋊D1311yescharacteristic
326C22×D4—132no—
327C22×D4—261no—
328C22×D4—261no—
329C22×D4C22×D1311yescharacteristic
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—21no—
333C2×D8—264no—
334C2×D8—264no—
335C2×D8—264no—
336C22×C8—132no—
337C22×C8—132no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340#127—262no—
341#127—262no—
342#125—22no—
343#125—22no—
344#125—22no—
345#125C22⋊D1314yes—
346#124—524no—
347C22⋊Q8—28no—
348C22⋊Q8—28no—
349C22⋊Q8—28no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4C22⋊D1314yes—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—132no—
365C2×C4⋊C4C22⋊D1311yescharacteristic
366C2×C4⋊C4C22⋊D1311yescharacteristic
367C2×C4⋊C4C22⋊D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—262no—
375C2×C22⋊C4—262no—
376C2×C22⋊C4—262no—
377C2×C22⋊C4—262no—
378C2×C42—261no—
379C2×C42C22×D1311yescharacteristic
380C2×C42C22×D1311yescharacteristic
381C2×C42C22×D1311yescharacteristic
382C4⋊C8—262no—
383#102—264no—
384#102—264no—
385#102—264no—
386#102—264no—
387#97—262no—
388#95—261no—
389C2×C13—44no—
390C2×C13#243611yescharacteristic
391C2×C13#300611yescharacteristic
392C2×C13#300811yescharacteristic
393C2×C13#336612yes—
394C2×C13#337012yes—
395D13—162no—
396C24—21no—
397C24—262no—
398C2×Q8—24no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—41no—
402C2×Q8—82no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—262no—
406C2×D4—262no—
407C2×D4—262no—
408C2×D4—262no—
409C2×D4—262no—
410C2×D4—262no—
411C2×D4—522no—
412C2×D4—522no—
413C2×D4—522no—
414C2×D4—522no—
415C2×D4—1042no—
416C2×D4#613114yes—
417C2×D4C2×C22⋊D1312yes—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—82no—
427C22×C4—82no—
428C22×C4—262no—
429C22×C4C2×C22⋊D1311yescharacteristic
430C22×C4C2×C22⋊D1311yescharacteristic
431C22×C4C2×C22⋊D1311yescharacteristic
432C22×C4C2×C22⋊D1311yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434C22×C4C2×C22⋊D1311yescharacteristic
435C22×C4C23×D1311yescharacteristic
436D8—528no—
437C2×C8—262no—
438C2×C8—262no—
439C2×C8—262no—
440C2×C8—262no—
441C2×C8—262no—
442C2×C8—262no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—262no—
455C4⋊C4—262no—
456C4⋊C4C2×C22⋊D1312yes—
457C4⋊C4C2×C22⋊D1312yes—
458C4⋊C4C2×C22⋊D1312yes—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—524no—
463C22⋊C4—524no—
464C22⋊C4—1042no—
465C22⋊C4—1042no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—522no—
471C42C2×C22⋊D1312yes—
472C42C2×C22⋊D1312yes—
473C13#2594611yescharacteristic, complemented, Sylow
474C23—24no—
475C23—22no—
476C23—41no—
477C23—41no—
478C23—42no—
479C23—522no—
480C23—522no—
481C23—522no—
482C23—522no—
483C23—522no—
484C23—522no—
485C23—522no—
486C23C22×C22⋊D1311yescharacteristic
487Q8—44no—
488Q8—84no—
489D4—22no—
490D4—24no—
491D4—522no—
492D4—522no—
493D4—522no—
494D4—522no—
495D4—1044no—
496D4—1044no—
497D4#8820114yescomplemented
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—48no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—84no—
519C2×C4—84no—
520C2×C4—522no—
521C2×C4—522no—
522C2×C4—522no—
523C2×C4#8820312yes—
524C2×C4#8820712yes—
525C2×C4#8820712yes—
526C2×C4C2×#613112yes—
527C2×C4#8825412yes—
528C2×C4C22×C22⋊D1311yescharacteristic
529C2×C4C22×C22⋊D1311yescharacteristic
530C8—522no—
531C8—522no—
532C22—24no—
533C22—42no—
534C22—44no—
535C22—44no—
536C22—42no—
537C22—1042no—
538C22—1042no—
539C22—1042no—
540C22—1042no—
541C22—1042no—
542C22—1042no—
543C22—1042no—
544C22#1171952212yes—
545C22C2×#8820311yescharacteristic
546C22#1171952711yescharacteristic
547C22#1171954012yes—
548C22C2×#8820711yescharacteristic
549C4—22no—
550C4—22no—
551C4—22no—
552C4—41no—
553C4—41no—
554C4—42no—
555C4—42no—
556C4—41no—
557C4—42no—
558C4—1042no—
559C4C2×#8820111yescharacteristic
560C4#1171952111yescharacteristic
561C4#1171952212yes—
562C2—44no—
563C2—2082no—
564C2#1311849011yescharacteristic
565C2#1312408811yescharacteristic
566C2#1312410411yescharacteristic
567C2#1312754312yes—
568C2#1312758912yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radicalC2×#11718676C2
hypercenterC2×#554D13
hypocenterC13#25946
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11718728C2semidirect
3. #13119835C2semidirect
4. #13115979C2semidirect
5. #13115969C2semidirect
6. #13115794C2semidirect
7. #13115777C2semidirect
8. #13115184C2semidirect
9. #13115184C2semidirect
10. #13114661C2semidirect
11. C2×C13×#554C2semidirect
190. C2×#554D13semidirect
218. D4×C13#124semidirect
473. C13#25946semidirect
497. D4#88201semidirect

Maximal subgroups

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

subgroupindex
C2×#117187282
C2×#117186762
#131198352
#131159792
#131159692
#131157942
#131157772
#131151842
#131146612
C2×C13×#5542
#2594613