Finite Group Databasebeta

← #15881262

Subgroups — #15881262

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718478C211yesmaximal, characteristic
2C2×#11718687C211yesmaximal, characteristic
3C2×#11718449C211yesmaximal, characteristic
4#13117757C211yesmaximal, characteristic, complemented
5#13117736C211yesmaximal, characteristic
6#13115573C211yesmaximal, characteristic, complemented
7#13115568C211yesmaximal, characteristic, complemented
8#13115102C211yesmaximal, characteristic, complemented
9#13115098C211yesmaximal, characteristic
10#13115088C211yesmaximal, characteristic, complemented
11#13115084C211yesmaximal, characteristic
12#13115002C211yesmaximal, characteristic, complemented
13#13114847C211yesmaximal, characteristic
14#13114713C211yesmaximal, characteristic, complemented
15C13×#1803C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19C22×#6106C2211yescharacteristic
20C2×#88147C2211yescharacteristic
21C2×#88147C2211yescharacteristic
22C2×C4⋊C4×D13—21no—
23C2×C4×D52C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#103C2211yescharacteristic
26C2×C13×#103C2211yescharacteristic
27C13×#384C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88061C2211yescharacteristic
30C2×#88061C2211yescharacteristic
31C2×#88055C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33#11718687C418yescomplemented
34#11718650—21no—
35#11718650—21no—
36#11718648—21no—
37#11718646—21no—
38#11718646—21no—
39#11718646C2211yescharacteristic
40#11718646C2211yescharacteristic
41#11718634C2211yescharacteristic
42#11718634C2211yescharacteristic
43C2×#88049C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48C2×#88047C2211yescharacteristic
49#11718597—21no—
50#11718597C2211yescharacteristic
51C4×C4⋊Dic13—21no—
52C4×C4⋊Dic13C2211yescharacteristic
53C2×#88043C2211yescharacteristic
54#11718478—24no—
55#11718449—24no—
56C13×#340C2211yescharacteristic
57C13×#340C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718142C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C22×C4×D13—21no—
66C22×C4×D13—21no—
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C4×Q8×C13—22no—
70C4×Q8×C13C2×C414yescomplemented
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C42×C13—21no—
78C2×C42×C13C2311yescharacteristic
79Q8×Dic13—22no—
80Q8×Dic13—22no—
81Q8×Dic13—41no—
82Q8×Dic13—41no—
83C2×#6106C2×C414yes—
84C2×#6106D414yes—
85C2×#6106Q814yes—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13D411yescharacteristic
94C2×C4⋊Dic13D411yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×#6101—21no—
99C2×#6101—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13C2311yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106#88147—22no—
107#88147—22no—
108#88147—41no—
109#88147—41no—
110C4⋊C4×D13—44no—
111C4×D52—22no—
112C4×D52C2×C414yes—
113C13×C4⋊C8—22no—
114C13×#103—22no—
115C13×#103—22no—
116#88075C2×C414yescomplemented
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071D411yescharacteristic
124#88071D411yescharacteristic
125#88061—22no—
126#88061—22no—
127#88055—22no—
128C8×Dic13—22no—
129#88049C2×C414yes—
130#88048—22no—
131#88048—41no—
132#88047—22no—
133#88047—41no—
134#88047C2×C414yescomplemented
135#88043C2×C414yescomplemented
136#22677—131nomaximal, Sylow
137C23×D13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13C22×C412yes—
142C2×Q8×C13C2×D412yes—
143C2×Q8×C13C2×Q812yes—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13C2×D411yescharacteristic
157C22×Dic13C2×D411yescharacteristic
158C2×D52—21no—
159C2×D52—21no—
160C2×D52—21no—
161C2×D52C22×C412yes—
162C2×D52C2×D412yes—
163C2×D52C2×Q812yes—
164C2×C4×D13—24no—
165C2×C4×D13—42no—
166C2×C4×D13—42no—
167C2×C4×D13—42no—
168C2×C4×D13—42no—
169C2×C4×D13—42no—
170C2×C4×D13—42no—
171C2×C4×D13—81no—
172C2×C4×D13—81no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C13×C4⋊C4—24no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—42no—
186C13×C4⋊C4—81no—
187C13×C4⋊C4C22×C412yes—
188C42×C13—24no—
189C42×C13C22×C412yes—
190C42×C13#4112yes—
191#6106C4⋊C4116yescomplemented
192#6103—24no—
193#6103—42no—
194#6103—42no—
195C4⋊Dic13—21no—
196C4⋊Dic13—22no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—41no—
202C4⋊Dic13—42no—
203C4⋊Dic13—42no—
204C4⋊Dic13—42no—
205C4⋊Dic13—42no—
206C4⋊Dic13C22×C412yes—
207#6101—42no—
208#6101—42no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213C4×Dic13—42no—
214C4×Dic13—42no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055C22×C412yes—
218C2×#1055C22×C412yes—
219C2×#1055C2×D412yes—
220C2×#1055C2×Q812yes—
221C2×#440—131no—
222C2×#440—131no—
223C2×C4×SD16—131no—
224#2351—131no—
225D4×C4⋊C4—131no—
226#1943—131no—
227#1942—131no—
228#1865—131no—
229#1864—131no—
230#1863—131no—
231#1862—131no—
232#1847—131no—
233#1804—131no—
234#1803D1311yescharacteristic, complemented
235#1771—131no—
236C23×C13C22×D411yescharacteristic
237C22×D13—22no—
238C22×D13—22no—
239C22×D13—22no—
240C22×D13—41no—
241C22×D13—41no—
242C22×D13—41no—
243C22×D13—41no—
244Q8×C13—22no—
245Q8×C13—22no—
246Q8×C13—22no—
247Q8×C13C2×C4⋊C414yescomplemented
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—22no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13C4×D412yes—
265C2×C4×C13C4×D412yes—
266C2×C4×C13C23×C411yescharacteristic
267C2×C4×C13C22×D411yescharacteristic
268C2×C4×C13C22×Q811yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13H(5,𝔽2)11yescharacteristic
271C2×C4×C132−1+411yescharacteristic
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—22no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13AGL(1,ℤ/8)12yes—
293D52—22no—
294D52—22no—
295D52—22no—
296D52C2×C4⋊C414yes—
297C4×D13—48no—
298C4×D13—84no—
299C4×D13—84no—
300C8×C13—41no—
301C8×C13—41no—
302#1055—22no—
303#1055C2×C4⋊C414yescomplemented
304C22×SD16—131no—
305C2×C4×Q8—131no—
306C2×C4×Q8—131no—
307C2×C4×Q8C2×D1311yescharacteristic
308C2×C4×D4—131no—
309C2×C4×D4—131no—
310C2×C4×D4—131no—
311C22×C4⋊C4—261no—
312#440—138no—
313#440—264no—
314C4×SD16—264no—
315C2×#107—131no—
316C2×#107—131no—
317C2×#107—131no—
318C2×#106—131no—
319C2×#106—131no—
320C2×C4⋊C8C2×D1311yescharacteristic
321C2×#103—131no—
322C2×#103C2×D1311yescharacteristic
323C2×#103C2×D1311yescharacteristic
324C2×#102—131no—
325C2×#102—131no—
326C2×#102—131no—
327C2×#97—131no—
328C2×#97—131no—
329C2×C4×C8—131no—
330#389—131no—
331#389—131no—
332#389—131no—
333#389—131no—
334#389—261no—
335#389—261no—
336#385—261no—
337#385—261no—
338#384C2×D1311yescharacteristic
339#382—131no—
340#382—261no—
341#380—261no—
342C4×C4⋊C4—131no—
343C4×C4⋊C4—261no—
344#340—131no—
345#340—131no—
346#340C2×D1311yescharacteristic
347#340C2×D1311yescharacteristic
348#336—131no—
349#336—131no—
350C22×C13C2×C4×D411yescharacteristic
351C22×C13D4211yescharacteristic
352C22×C13D4×Q811yescharacteristic
353C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C13#57511yescharacteristic
355C22×C13#57711yescharacteristic
356C22×C13#57811yescharacteristic
357C2×D13—24no—
358C2×D13—42no—
359C2×D13—42no—
360C2×D13—42no—
361C2×D13—42no—
362C2×D13—42no—
363C2×D13—42no—
364C4×C13—24no—
365C4×C13—22no—
366C4×C13—22no—
367C4×C13—42no—
368C4×C13—81no—
369C4×C13—81no—
370C4×C13C22×C4⋊C411yescharacteristic
371C4×C13#52011yescharacteristic
372C4×C13#54711yescharacteristic
373C4×C13#55411yescharacteristic
374Dic13—22no—
375Dic13—42no—
376Dic13—41no—
377Dic13—41no—
378Dic13—41no—
379Dic13—81no—
380Dic13—81no—
381C22×Q8C22×D1311yescharacteristic
382C22×D4—131no—
383C23×C4—261no—
384C23×C4—261no—
385C23×C4—261no—
386C2×SD16—134no—
387C2×SD16—134no—
388C2×SD16—134no—
389C22×C8—131no—
390C22×C8—131no—
391C22×C8C22×D1311yescharacteristic
392C22×C8C22×D1311yescharacteristic
393C4×Q8—22no—
394C4×Q8—262no—
395C4×Q8—262no—
396C4×Q8—521no—
397C4×Q8—521no—
398C4×Q8C4×D1314yescomplemented
399C4×D4—134no—
400C4×D4—262no—
401C4×D4—262no—
402C4×D4—262no—
403C4×D4—521no—
404C4×D4—521no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4—261no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—524no—
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C4⋊C4C22×D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C22⋊C4—261no—
424C2×C22⋊C4—261no—
425C2×C22⋊C4—261no—
426C2×C42—21no—
427C2×C42—131no—
428C2×C42—131no—
429C2×C42—261no—
430C2×C42—261no—
431C2×C42C22×D1311yescharacteristic
432#107—134no—
433#107—262no—
434#107—521no—
435#106—262no—
436#106—521no—
437C4⋊C8—22no—
438#103—22no—
439#103—22no—
440#103—134no—
441#102—134no—
442#102—262no—
443#102—262no—
444#97—134no—
445#97—262no—
446C4×C8—262no—
447#95—131no—
448#95—131no—
449#95—261no—
450#95—261no—
451#95—261no—
452#95—261no—
453#95—261no—
454#95—261no—
455C2×C13D4×C4⋊C411yescharacteristic
456C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
457C2×C13#294711yescharacteristic
458C2×C13#326511yescharacteristic
459C2×C13#326911yescharacteristic
460C2×C13#338611yescharacteristic
461C2×C13#338811yescharacteristic
462D13—44no—
463C24—261no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8C2×C4×D1312yes—
468C2×Q8D4×D1312yes—
469C2×Q8Q8×D1312yes—
470C2×D4—132no—
471C2×D4—132no—
472C2×D4—132no—
473C2×D4—261no—
474C2×D4—261no—
475C2×D4—261no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—131no—
481C22×C4—131no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—261no—
485C22×C4—264no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—522no—
489C22×C4—522no—
490C22×C4—522no—
491C22×C4—522no—
492C22×C4—522no—
493C22×C4—522no—
494C22×C4—1041no—
495C22×C4—1041no—
496C22×C4D4×D1311yescharacteristic
497C22×C4D4×D1311yescharacteristic
498C22×C4C23×D1311yescharacteristic
499SD16—1316no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—132no—
507C2×C8—132no—
508C2×C8—132no—
509C2×C8—132no—
510C2×C8—261no—
511C2×C8—261no—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—81no—
520C4⋊C4—132no—
521C4⋊C4—262no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—521no—
528C4⋊C4—522no—
529C4⋊C4—522no—
530C4⋊C4—522no—
531C4⋊C4—522no—
532C4⋊C4—522no—
533C4⋊C4—522no—
534C4⋊C4C2×C4×D1312yes—
535C22⋊C4—264no—
536C22⋊C4—522no—
537C22⋊C4—522no—
538C42—24no—
539C42—261no—
540C42—261no—
541C42—261no—
542C42—261no—
543C42—522no—
544C42—522no—
545C42C2×C4×D1312yes—
546C42#612912yes—
547C13#2267711yescharacteristic, complemented, Sylow
548C23—262no—
549C23—262no—
550C23—262no—
551C23—521no—
552C23—521no—
553C23—521no—
554C23—521no—
555C23C2×D4×D1311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—22no—
559Q8C4⋊C4×D1314yescomplemented
560D4—134no—
561D4—262no—
562D4—262no—
563D4—262no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—132no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—262no—
584C2×C4—261no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—261no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—528no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—1044no—
603C2×C4—1044no—
604C2×C4#8813512yes—
605C2×C4#8813512yes—
606C2×C4C22×C4×D1311yescharacteristic
607C2×C4C2×D4×D1311yescharacteristic
608C2×C4C2×#612911yescharacteristic
609C2×C4C2×Q8×D1311yescharacteristic
610C2×C4#8825611yescharacteristic
611C2×C4#8825711yescharacteristic
612C8—41no—
613C8—41no—
614C8—134no—
615C8—262no—
616C22—264no—
617C22—522no—
618C22—522no—
619C22—522no—
620C22—522no—
621C22—522no—
622C22—522no—
623C22C2×#8813511yescharacteristic
624C22#1171931411yescharacteristic
625C22#1171933711yescharacteristic
626C22#1171946711yescharacteristic
627C22#1171947111yescharacteristic
628C22D13×AGL(1,ℤ/8)11yescharacteristic
629C22#1171948211yescharacteristic
630C4—24no—
631C4—22no—
632C4—22no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—262no—
637C4—522no—
638C4—521no—
639C4—521no—
640C4—521no—
641C4—1041no—
642C4—1041no—
643C4C2×C4⋊C4×D1311yescharacteristic
644C4#1171922811yescharacteristic
645C4#1171931611yescharacteristic
646C4#1171934011yescharacteristic
647C2—524no—
648C2#1311773211yescharacteristic
649C2#1312364911yescharacteristic
650C2#1312367311yescharacteristic
651C2#1312632611yescharacteristic
652C2#1312638611yescharacteristic
653C2#1312776011yescharacteristic
654C2#1312778811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1803C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1803D13
hypocenterC13#22677
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
4. #13117757C2semidirect
6. #13115573C2semidirect
7. #13115568C2semidirect
8. #13115102C2semidirect
10. #13115088C2semidirect
12. #13115002C2semidirect
14. #13114713C2semidirect
15. C13×#1803C2semidirect
33. #11718687C4semidirect
70. C4×Q8×C13C2×C4semidirect
116. #88075C2×C4semidirect
134. #88047C2×C4semidirect
135. #88043C2×C4semidirect
191. #6106C4⋊C4semidirect
234. #1803D13semidirect
247. Q8×C13C2×C4⋊C4semidirect
303. #1055C2×C4⋊C4semidirect
398. C4×Q8C4×D13semidirect
547. C13#22677semidirect
559. Q8C4⋊C4×D13semidirect

Maximal subgroups

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

subgroupindex
C2×#117184782
C2×#117186872
C2×#117184492
#131177572
#131177362
#131155732
#131155682
#131151022
#131150982
#131150882
#131150842
#131150022
#131148472
#131147132
C13×#18032
#2267713