Finite Group Databasebeta

← #15890454

Subgroups — #15890454

Order 3328.

1482 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718625C211yesmaximal, characteristic, complemented
2C2×#11718893C211yesmaximal, characteristic, complemented
3C2×#11718894C211yesmaximal, characteristic, complemented
4C2×#11718895C211yesmaximal, characteristic, complemented
5#13117428C211yesmaximal, characteristic, complemented
6#13116036C212yesmaximal, complemented
7#13116029C212yesmaximal, complemented
8#13116022C212yesmaximal, complemented
9#13116015C212yesmaximal, complemented
10C2×#11718121C211yesmaximal, characteristic, complemented
11C2×C13×#537C211yesmaximal, characteristic
12C22×C13×#41C2211yescharacteristic
13C22×C13×#41C2211yescharacteristic
14C13×#537—24no—
15C13×#537—24no—
16C2×C13×C22⋊Q8—21no—
17C2×C13×C22⋊Q8C2212yes—
18C2×C13×#121—21no—
19C2×C13×#121—22no—
20C2×C13×#121C2212yes—
21C22×C13×C4⋊C4C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C23×#1055C2211yescharacteristic
26#11718895—24no—
27#11718894—24no—
28#11718893—24no—
29#11718891—21no—
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2212yes—
33#11718882—21no—
34#11718881—22no—
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2212yes—
38#11718873C2212yes—
39#11718873C2212yes—
40C2×C22⋊#1055C2212yes—
41C2×C22⋊#1055C2212yes—
42#11718625—24no—
43C2×#88048C2212yes—
44C2×#88047C2212yes—
45#11718121C2212yes—
46#11718121C2212yes—
47C2×C13×#41—22no—
48C2×C13×#41—22no—
49C2×C13×#41—22no—
50C2×C13×#41—22no—
51C2×C13×#41—22no—
52C2×C13×#41—22no—
53C2×C13×#41—22no—
54C2×C13×#41—22no—
55C2×C13×#41—22no—
56C2×C13×#41—22no—
57C2×C13×#41—22no—
58C2×C13×#41D414yes—
59C22×Q8×C13D411yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D4×C13—21no—
62C22×D4×C13—22no—
63C22×D4×C13D412yes—
64C22×D4×C13D411yescharacteristic
65C22×D4×C13C2311yescharacteristic
66C23×C4×C13—21no—
67C23×C4×C13—21no—
68C23×C4×C13C2312yes—
69C23×C4×C13C2311yescharacteristic
70C23×Dic13—21no—
71C13×C22⋊Q8—28no—
72C13×C22⋊Q8—24no—
73C13×C22⋊Q8—24no—
74C13×#121—216no—
75C13×#121—28no—
76C13×#121—24no—
77C13×#121—24no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4D414yes—
82C2×C13×C4⋊C4C2312yes—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—22no—
88#88180—22no—
89#88180—22no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2312yes—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4×Dic13—21no—
97C2×#6099—22no—
98C2×#6099—22no—
99C2×#6099D414yescomplemented
100C22×#1055—22no—
101C22×#1055—22no—
102C22×#1055—22no—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2312yes—
106#88075—22no—
107#88075—22no—
108#88075—24no—
109#88072—22no—
110#88072—22no—
111#88072—24no—
112#88071—22no—
113#88071—22no—
114C22⋊#1055—24no—
115C22⋊#1055—24no—
116#88048—24no—
117#88047—24no—
118#23485—131nomaximal, Sylow
119C24×C13—21no—
120C24×C13C2×D412yes—
121C24×C13C2×D411yescharacteristic
122C13×#41—28no—
123C13×#41—28no—
124C13×#41—44no—
125C13×#41—44no—
126C13×#41—44no—
127C13×#41—44no—
128C13×#41—44no—
129C13×#41—44no—
130C2×Q8×C13—22no—
131C2×Q8×C13—22no—
132C2×Q8×C13—22no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13C2×D412yes—
139C2×D4×C13—24no—
140C2×D4×C13—24no—
141C2×D4×C13—24no—
142C2×D4×C13—24no—
143C2×D4×C13—28no—
144C2×D4×C13—22no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—42no—
153C2×D4×C13—42no—
154C2×D4×C13—82no—
155C2×D4×C13—82no—
156C2×D4×C13C2×D412yes—
157C22×C4×C13—22no—
158C22×C4×C13—21no—
159C22×C4×C13—24no—
160C22×C4×C13—24no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—42no—
168C22×C4×C13—42no—
169C22×C4×C13—81no—
170C22×C4×C13—81no—
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D412yes—
176C22×C4×C13#4112yes—
177C22×C4×C13#4112yes—
178C22×C4×C13#4112yes—
179C22×C4×C13C2411yescharacteristic
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—42no—
184C22×Dic13—81no—
185C22×Dic13—81no—
186C13×C4⋊C4—28no—
187C13×C4⋊C4—24no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4C2×D414yes—
190C13×C22⋊C4—28no—
191C13×C22⋊C4—28no—
192C22⋊Dic13—42no—
193C22⋊Dic13—82no—
194C22⋊Dic13—82no—
195C4⋊Dic13—22no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—22no—
201C4⋊Dic13—42no—
202C4×Dic13—42no—
203#6099—28no—
204C2×#1055—22no—
205C2×#1055—22no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—44no—
213C2×#1055C2×D414yes—
214C2×#537D1311yescharacteristic
215C2×#428—131no—
216C2×#417—131no—
217C2×#416—131no—
218C2×#408—131no—
219#2311—131no—
220#2036—132no—
221#2035—132no—
222#2034—132no—
223#2033—132no—
224C2×#340—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13#12012yes—
244C23×C13#12112yes—
245C23×C13#12312yes—
246C23×C13C22×D411yescharacteristic
247Q8×C13—22no—
248Q8×C13—22no—
249Q8×C13—41no—
250Q8×C13—41no—
251Q8×C13—44no—
252D4×C13—22no—
253D4×C13—22no—
254D4×C13—48no—
255D4×C13—48no—
256D4×C13—41no—
257D4×C13—41no—
258D4×C13—44no—
259D4×C13—88no—
260C2×C4×C13—24no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—42no—
268C2×C4×C13—42no—
269C2×C4×C13—42no—
270C2×C4×C13—42no—
271C2×C4×C13—42no—
272C2×C4×C13—42no—
273C2×C4×C13—48no—
274C2×C4×C13—84no—
275C2×C4×C13#12012yes—
276C2×C4×C13#12114yes—
277C2×C4×C13#12114yes—
278C2×C4×C13#12112yes—
279C2×C4×C13#12314yes—
280C2×C4×C13#12312yes—
281C2×C4×C13#12414yes—
282C2×C4×C13C22×D411yescharacteristic
283C2×C4×C13C22×D411yescharacteristic
284C2×C4×C13C22×D411yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13C2×#4111yescharacteristic
287C2×C4×C13C2×#4111yescharacteristic
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—42no—
291C2×Dic13—41no—
292C2×Dic13—42no—
293C2×Dic13—41no—
294C2×Dic13—42no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—84no—
298#1055—24no—
299#1055—41no—
300#1055—41no—
301C22×#41C2×D1311yescharacteristic
302C22×#41C2×D1311yescharacteristic
303C22×M16—131no—
304C23×C8—131no—
305#537—24no—
306#537—24no—
307C2×C22⋊Q8—21no—
308C2×C22⋊Q8C2×D1312yes—
309C2×#121—21no—
310C2×#121—22no—
311C2×#121C2×D1312yes—
312C2×#117—131no—
313C22×C4⋊C4—131no—
314C22×C4⋊C4C2×D1311yescharacteristic
315#428—264no—
316C2×#107—132no—
317C2×#106—132no—
318#417—264no—
319#416—264no—
320C2×#103—131no—
321C2×#103—131no—
322C2×#103—132no—
323C2×#102—131no—
324C2×#102—131no—
325C2×#102—132no—
326#408—264no—
327C2×C22⋊C8—132no—
328C2×C22⋊C8—132no—
329#391—261no—
330#390—261no—
331#386—262no—
332#380—132no—
333#380—132no—
334#340—132no—
335#340—132no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—42no—
343C22×C13—42no—
344C22×C13—42no—
345C22×C13—42no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13—42no—
350C22×C13—42no—
351C22×C13—42no—
352C22×C13—81no—
353C22×C13—81no—
354C22×C13—81no—
355C22×C13—81no—
356C22×C13#39414yes—
357C22×C13C2×#12011yescharacteristic
358C22×C13C2×#12111yescharacteristic
359C22×C13C2×#12311yescharacteristic
360C22×C13#57611yescharacteristic
361C22×C13#57711yescharacteristic
362C22×C13#57711yescharacteristic
363C22×C13#57811yescharacteristic
364C4×C13—42no—
365C4×C13—42no—
366C4×C13—44no—
367C4×C13#39414yes—
368C4×C13C2×#12111yescharacteristic
369C4×C13C2×#12111yescharacteristic
370C4×C13C2×#12311yescharacteristic
371C4×C13C2×#12411yescharacteristic
372Dic13—81no—
373Dic13—81no—
374Dic13—82no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—22no—
378C2×#41—22no—
379C2×#41—22no—
380C2×#41—22no—
381C2×#41—22no—
382C2×#41—22no—
383C2×#41—22no—
384C2×#41—22no—
385C2×#41—22no—
386C2×#41C22⋊D1314yes—
387C22×Q8C22⋊D1311yescharacteristic
388C22×Q8C22×D1311yescharacteristic
389C22×D4—21no—
390C22×D4—22no—
391C22×D4C22⋊D1312yes—
392C22×D4C22⋊D1311yescharacteristic
393C22×D4C22×D1311yescharacteristic
394C23×C4—21no—
395C23×C4—21no—
396C23×C4—261no—
397C23×C4C22×D1312yes—
398C23×C4C22×D1311yescharacteristic
399C2×M16—134no—
400C2×M16—262no—
401C2×M16—262no—
402C22×C8—132no—
403C22×C8—131no—
404C22×C8—131no—
405C22×C8—262no—
406C22×C8—262no—
407C22×C8—262no—
408C22⋊Q8—28no—
409C22⋊Q8—24no—
410C22⋊Q8—24no—
411#121—216no—
412#121—28no—
413#121—24no—
414#121—24no—
415#117—262no—
416#117—262no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—132no—
421C2×C4⋊C4—131no—
422C2×C4⋊C4—131no—
423C2×C4⋊C4—262no—
424C2×C4⋊C4—262no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4C22⋊D1314yes—
427C2×C4⋊C4C22×D1312yes—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—261no—
431C2×C22⋊C4—262no—
432C2×C22⋊C4—262no—
433C2×C42—261no—
434#107—264no—
435#106—264no—
436#103—264no—
437#103—262no—
438#103—262no—
439#102—264no—
440#102—262no—
441#102—262no—
442C22⋊C8—264no—
443C22⋊C8—264no—
444#95—262no—
445#95—262no—
446C2×C13—24no—
447C2×C13—82no—
448C2×C13—82no—
449C2×C13C2×#39411yescharacteristic
450C2×C13#301211yescharacteristic
451C2×C13#301311yescharacteristic
452C2×C13#306211yescharacteristic
453C2×C13#306311yescharacteristic
454C2×C13#309811yescharacteristic
455C2×C13#309911yescharacteristic
456C24—21no—
457C24C2×C22⋊D1312yes—
458C24C2×C22⋊D1311yescharacteristic
459#41—28no—
460#41—28no—
461#41—44no—
462#41—44no—
463#41—44no—
464#41—44no—
465#41—44no—
466#41—44no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8C2×C22⋊D1312yes—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—28no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—82no—
492C2×D4—82no—
493C2×D4C2×C22⋊D1312yes—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—261no—
509C22×C4—261no—
510C22×C4—262no—
511C22×C4—522no—
512C22×C4—1041no—
513C22×C4—1041no—
514C22×C4D4×D1312yes—
515C22×C4#612912yes—
516C22×C4#612912yes—
517C22×C4#612912yes—
518C22×C4C2×C22⋊D1312yes—
519C22×C4C2×C22⋊D1311yescharacteristic
520C22×C4C2×C22⋊D1312yes—
521C22×C4C2×C22⋊D1312yes—
522C22×C4C23×D1311yescharacteristic
523M16—268no—
524C2×C8—134no—
525C2×C8—262no—
526C2×C8—262no—
527C2×C8—261no—
528C2×C8—261no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—524no—
534C4⋊C4—28no—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—262no—
538C4⋊C4—262no—
539C4⋊C4—261no—
540C4⋊C4—261no—
541C4⋊C4—261no—
542C4⋊C4—261no—
543C4⋊C4—522no—
544C4⋊C4C2×C22⋊D1314yes—
545C22⋊C4—28no—
546C22⋊C4—28no—
547C22⋊C4—522no—
548C22⋊C4—1042no—
549C22⋊C4—1042no—
550C42—522no—
551C13#2348511yescharacteristic, complemented, Sylow
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23#8818912yes—
571C23#8819312yes—
572C23#8820712yes—
573C23C22×C22⋊D1311yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—41no—
577Q8—41no—
578Q8—44no—
579D4—22no—
580D4—22no—
581D4—48no—
582D4—48no—
583D4—41no—
584D4—41no—
585D4—44no—
586D4—88no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—48no—
601C2×C4—84no—
602C2×C4—522no—
603C2×C4—521no—
604C2×C4—522no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—522no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—1044no—
612C2×C4#8818914yes—
613C2×C4#8818912yes—
614C2×C4#8819014yes—
615C2×C4#8819214yes—
616C2×C4#8819314yes—
617C2×C4#8819312yes—
618C2×C4#8820712yes—
619C2×C4C2×D4×D1311yescharacteristic
620C2×C4C2×#612911yescharacteristic
621C2×C4C2×#612911yescharacteristic
622C2×C4C2×#612911yescharacteristic
623C2×C4C22×C22⋊D1311yescharacteristic
624C2×C4C22×C22⋊D1311yescharacteristic
625C8—264no—
626C8—521no—
627C8—521no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22#1171888314yes—
649C22C2×#8818911yescharacteristic
650C22C2×#8819311yescharacteristic
651C22#1171954011yescharacteristic
652C22#1171954111yescharacteristic
653C22#1171954211yescharacteristic
654C22#1171954311yescharacteristic
655C22C2×#8820711yescharacteristic
656C4—44no—
657C4—42no—
658C4—42no—
659C4—1041no—
660C4—1041no—
661C4—1042no—
662C4#1171888314yes—
663C4C2×#8818911yescharacteristic
664C4C2×#8819011yescharacteristic
665C4C2×#8819211yescharacteristic
666C4C2×#8819311yescharacteristic
667C2—24no—
668C2—82no—
669C2—82no—
670C2C2×#1171888311yescharacteristic
671C2#1312414011yescharacteristic
672C2#1312415111yescharacteristic
673C2#1312451811yescharacteristic
674C2#1312452911yescharacteristic
675C2#1312481011yescharacteristic
676C2#1312482111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#537C2
socleC23×C13C22×D4
hypercenterC2×#537D13
hypocenterC13#23485
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#11718625C2semidirect
2. C2×#11718893C2semidirect
3. C2×#11718894C2semidirect
4. C2×#11718895C2semidirect
5. #13117428C2semidirect
6. #13116036C2semidirect
7. #13116029C2semidirect
8. #13116022C2semidirect
9. #13116015C2semidirect
10. C2×#11718121C2semidirect
99. C2×#6099D4semidirect
551. C13#23485semidirect

Maximal subgroups

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

subgroupindex
C2×#117186252
C2×#117188932
C2×#117188942
C2×#117188952
#131174282
#131160362
#131160292
#131160222
#131160152
C2×#117181212
C2×C13×#5372
#2348513