Finite Group Databasebeta

← #16804897

Subgroups — #16804897

Order 3328.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131566C211yesmaximal, characteristic
2#13131526C211yesmaximal, characteristic, complemented
3#13130945C211yesmaximal, characteristic, complemented
4#13130932C211yesmaximal, characteristic, complemented
5#13130918C211yesmaximal, characteristic, complemented
6#13130904C211yesmaximal, characteristic, complemented
7#13130904C211yesmaximal, characteristic, complemented
8#13130854C211yesmaximal, characteristic
9#13130805C211yesmaximal, characteristic, complemented
10#13130789C211yesmaximal, characteristic, complemented
11#13130643C211yesmaximal, characteristic, complemented
12#13130615C211yesmaximal, characteristic, complemented
13#13130564C211yesmaximal, characteristic, complemented
14C2×#11718247C211yesmaximal, characteristic, complemented
15#13124744C211yesmaximal, characteristic
16C2×#88238C2211yescharacteristic
17C22×C4×#261C2211yescharacteristic
18C22×#6118C2211yescharacteristic
19#11719311C2211yescharacteristic
20C2×#88146C2211yescharacteristic
21#11719147C2211yescharacteristic
22#11719144—21no—
23D4×#1057—21no—
24C2×#88116C2211yescharacteristic
25C2×#88116C2211yescharacteristic
26#11719128—21no—
27#11719127C2211yescharacteristic
28D13⋊(C22⋊C8)C2211yescharacteristic
29#11719119—21no—
30C2×#88103C2211yescharacteristic
31C2×#88103C2211yescharacteristic
32C2×#88100C2211yescharacteristic
33C2×#88100C2211yescharacteristic
34#11719079C2211yescharacteristic
35#11719079C2211yescharacteristic
36#11719079C2211yescharacteristic
37#11719077—21no—
38#11719077—21no—
39#11719072C2211yescharacteristic
40#11719072C2211yescharacteristic
41#11719072C2211yescharacteristic
42#11719066—21no—
43#11719064—21no—
44C13×#480C411yescharacteristic, complemented
45#11718695C411yescharacteristic, complemented
46#11718632C411yescharacteristic, complemented
47#11718549C411yescharacteristic, complemented
48#11718549C411yescharacteristic, complemented
49#11718541C2211yescharacteristic
50#11718541C2211yescharacteristic
51#11718445C411yescharacteristic, complemented
52#11718445C411yescharacteristic, complemented
53#11718433C2211yescharacteristic
54#11718433C2211yescharacteristic
55D13×C22⋊C8C2211yescharacteristic
56#11718383C411yescharacteristic, complemented
57#11718268C2211yescharacteristic
58#11718268C2211yescharacteristic
59(C2×#261)⋊C8C2211yescharacteristic
60(C2×#261)⋊C8C2211yescharacteristic
61#11718247C2211yescharacteristic
62#11718247C2211yescharacteristic
63#11718247C2211yescharacteristic
64#11718247C2211yescharacteristic
65#11718247C2211yescharacteristic
66#11718247C2211yescharacteristic
67C23×#261—21no—
68C2×#6129C2311yescharacteristic
69C22×C4×D13C2311yescharacteristic
70C2×#6122—21no—
71C22×#1057—21no—
72C22×#1057—21no—
73#88238—22no—
74#88238—41no—
75C2×C4×#261—22no—
76C2×C4×#261—21no—
77C2×C4×#261—41no—
78C2×C4×#261C2311yescharacteristic
79C2×C4×#261C2311yescharacteristic
80C2×#6118—22no—
81C2×#6118—21no—
82C2×#6118—41no—
83C2×#6118C2311yescharacteristic
84C2×#6118C2311yescharacteristic
85C2×#6118C2311yescharacteristic
86C2×#6118C2311yescharacteristic
87C2×D13⋊C8C2311yescharacteristic
88C2×D13⋊C8C2311yescharacteristic
89C13×#121C2×C411yescharacteristic
90C2×C13×C4⋊C4C2×C411yescharacteristic
91#88192C2×C411yescharacteristic
92#88191—21no—
93D4×Dic13—21no—
94C2×#6103—21no—
95C2×C4⋊Dic13C2×C411yescharacteristic
96#88178C2×C411yescharacteristic
97C2×C4×Dic13—21no—
98C2×C8×D13C2311yescharacteristic
99C2×C8×D13C2311yescharacteristic
100#88151C2×C411yescharacteristic
101#88146—21no—
102#88146—21no—
103#88146C2×C411yescharacteristic
104#88146C2×C411yescharacteristic
105#88146C2311yescharacteristic
106#88146C2311yescharacteristic
107#88146C2311yescharacteristic
108#88137—21no—
109#88135—21no—
110C22⋊#1057—21no—
111C22⋊#1057—21no—
112C22⋊#1057—21no—
113C22⋊#1057D411yescharacteristic
114C22⋊#1057D411yescharacteristic
115#88116—22no—
116#88116—41no—
117#88112—21no—
118#88112—21no—
119#88112—21no—
120#88111—21no—
121#88111D411yescharacteristic
122#88111D411yescharacteristic
123#88110—21no—
124#88110—21no—
125#88110—21no—
126C4⋊#1057—21no—
127C4⋊#1057—21no—
128C4⋊#1057—21no—
129C4×#1057—21no—
130C4×#1057—21no—
131C4×#1057—21no—
132#88103—22no—
133#88103—41no—
134#88100—22no—
135#88100—41no—
136C13×#107C2×C411yescharacteristic, complemented
137C13×#107C2×C411yescharacteristic, complemented
138C13×#102C2×C411yescharacteristic, complemented
139C13×#102C2×C411yescharacteristic, complemented
140C13×C22⋊C8C2×C411yescharacteristic
141#88072C2×C411yescharacteristic, complemented
142#88072C2×C411yescharacteristic, complemented
143C22⋊#1055C2×C411yescharacteristic
144#88060C2×C411yescharacteristic
145#88060C2×C411yescharacteristic
146#88058C2×C411yescharacteristic, complemented
147#88058C2×C411yescharacteristic, complemented
148#88056C2×C411yescharacteristic, complemented
149#88056C2×C411yescharacteristic, complemented
150#88050C2×C411yescharacteristic, complemented
151#88050C2×C411yescharacteristic, complemented
152#88048C2×C411yescharacteristic, complemented
153#88048C2×C411yescharacteristic, complemented
154#88048C2×C411yescharacteristic, complemented
155#88048C2×C411yescharacteristic, complemented
156#22950—131nomaximal, Sylow
157C23×D13#4111yescharacteristic
158C22×#261—21no—
159C22×#261—21no—
160C22×#261—42no—
161C22×#261—42no—
162C22×#261—42no—
163C2×D4×C13—21no—
164C2×D4×C13C22×C411yescharacteristic
165C22×C4×C13—21no—
166C22×C4×C13C22×C411yescharacteristic
167C2×C22⋊D13—21no—
168C2×C22⋊D13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13C2×D411yescharacteristic
172#6129—21no—
173#6129—21no—
174#6129—21no—
175#6129—21no—
176C2×C4×D13—21no—
177C2×C4×D13—21no—
178C2×C4×D13—21no—
179C2×C4×D13—21no—
180C2×C4×D13C22×C411yescharacteristic
181C2×C4×D13C2×D411yescharacteristic
182C2×C4×D13#4111yescharacteristic
183C2×C4×D13C2411yescharacteristic
184C2×Dic26C22×C411yescharacteristic
185#6122—42no—
186C2×#1057—21no—
187C2×#1057—21no—
188C2×#1057—21no—
189C2×#1057—21no—
190C2×#1057—42no—
191C2×#1057—42no—
192C2×#1057C2×D411yescharacteristic
193C2×#1057C2×D411yescharacteristic
194C2×#1057C2×D411yescharacteristic
195C2×#1057C2×D411yescharacteristic
196C4×#261—21no—
197C4×#261—21no—
198C4×#261—21no—
199C4×#261—42no—
200C4×#261#4112yes—
201#6118—21no—
202#6118—21no—
203#6118—21no—
204#6118—21no—
205#6118—21no—
206#6118—21no—
207#6118—21no—
208#6118—42no—
209#6118#4112yes—
210D13⋊C8—21no—
211D13⋊C8—21no—
212D13⋊C8—21no—
213D13⋊C8—21no—
214C2×C8×C13C22×C411yescharacteristic
215C2×C8×C13C22×C411yescharacteristic
216C13×C4⋊C4—21no—
217C13×C4⋊C4C22×C411yescharacteristic
218C13×C4⋊C4C22×C411yescharacteristic
219C13×C4⋊C4C22×C411yescharacteristic
220C13×C22⋊C4—21no—
221C22⋊Dic13—21no—
222C22⋊Dic13—21no—
223#6103—21no—
224#6103—21no—
225#6103—21no—
226#6103—21no—
227#6103—21no—
228#6103—21no—
229C4⋊Dic13—21no—
230C4⋊Dic13—21no—
231C4⋊Dic13C22×C411yescharacteristic
232C4⋊Dic13C22×C411yescharacteristic
233C4⋊Dic13C22×C411yescharacteristic
234#6101—21no—
235C4×Dic13—21no—
236C4×Dic13—21no—
237C4×Dic13—21no—
238C4×Dic13—21no—
239C4×Dic13—21no—
240C2×#1055C22×C411yescharacteristic
241C2×#1055C22×C411yescharacteristic
242C8×D13—21no—
243C8×D13—21no—
244C8×D13—21no—
245C8×D13—21no—
246#3091—131no—
247#2933—131no—
248#2924—131no—
249#1946—131no—
250#1938—131no—
251#1929—131no—
252#1922—131no—
253#1922—131no—
254#1896—131no—
255#1866—131no—
256#1855—131no—
257#1773—131no—
258#1765—131no—
259#1749—131no—
260C2×#339—131no—
261C23×C13—21no—
262C23×C13C4×D411yescharacteristic
263C22×D13—22no—
264C22×D13—21no—
265C22×D13—21no—
266C22×D13—41no—
267C22×D13C4×D411yescharacteristic
268C22×D13C2×#4111yescharacteristic
269C2×#261—22no—
270C2×#261—22no—
271C2×#261—41no—
272C2×#261—41no—
273C2×#261—41no—
274C2×#261—48no—
275C2×#261—41no—
276D4×C13—21no—
277D4×C13—21no—
278D4×C13—42no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—42no—
285C2×C4×C13C4×D411yescharacteristic
286C2×C4×C13C23×C411yescharacteristic
287C22⋊D13—41no—
288C22⋊D13—41no—
289C22⋊D13—81no—
290C2×Dic13—21no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13—21no—
294C2×Dic13—21no—
295C2×Dic13—21no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—81no—
299C2×Dic13C4×D411yescharacteristic
300C2×Dic13C22×D411yescharacteristic
301C4×D13—21no—
302C4×D13—21no—
303C4×D13—21no—
304C4×D13—21no—
305C4×D13—21no—
306C4×D13—21no—
307C4×D13C2×#4111yescharacteristic
308C4×D13C2×#4111yescharacteristic
309C4×D13H(5,𝔽2)11yescharacteristic
310C4×D132−1+411yescharacteristic
311Dic26—21no—
312Dic26—21no—
313#1057—21no—
314#1057—21no—
315#1057—22no—
316#1057—21no—
317#1057—21no—
318#1057—41no—
319#1057—41no—
320#1057—41no—
321C8×C13—21no—
322C8×C13—21no—
323#1055—21no—
324#1055—21no—
325C2×#131—131no—
326C22×M16—131no—
327#525—131no—
328C2×#117—131no—
329C22×C42—131no—
330#485—131no—
331#485—131no—
332#484—131no—
333#483—131no—
334#482—131no—
335#482—131no—
336#481—131no—
337#480#26111yescharacteristic, complemented
338#436—261no—
339#435—261no—
340#435—261no—
341C8×D4—261no—
342#433—261no—
343#433—261no—
344#432—261no—
345#431—261no—
346C2×#108—131no—
347C2×#108—131no—
348#427—131no—
349#427—131no—
350#424—131no—
351#424—131no—
352#424—131no—
353C2×#104—131no—
354C2×#104—131no—
355#416—131no—
356#416—131no—
357#408—131no—
358#407—131no—
359C2×C22⋊C8—131no—
360C2×C22⋊C8—131no—
361#405—131no—
362#405—131no—
363#405—131no—
364C2×#97—131no—
365C2×#97—131no—
366#341—131no—
367#341—131no—
368#339—131no—
369#339—131no—
370#339—131no—
371#339—131no—
372#339—131no—
373#339—131no—
374#336—131no—
375#336—131no—
376C22×C13—21no—
377C22×C13—21no—
378C22×C13—41no—
379C22×C13—41no—
380C22×C13—41no—
381C22×C13#44412yes—
382C22×C13C2×C4×D411yescharacteristic
383C2×D13—21no—
384C2×D13—21no—
385C2×D13—21no—
386C2×D13—21no—
387C2×D13—21no—
388C2×D13—42no—
389C2×D13—42no—
390C2×D13#55111yescharacteristic
391C2×D13#55211yescharacteristic
392#261—42no—
393#261—42no—
394C4×C13—21no—
395C4×C13—41no—
396C4×C13—41no—
397C4×C13—41no—
398C4×C13C4×#4111yescharacteristic
399C4×C13#52011yescharacteristic
400Dic13—21no—
401Dic13—41no—
402Dic13—41no—
403Dic13—41no—
404Dic13—41no—
405Dic13#54611yescharacteristic
406Dic13#54711yescharacteristic
407C2×#41—131no—
408C23×C4—131no—
409C23×C4—261no—
410#131—262no—
411#131—521no—
412C2×M16—131no—
413C2×M16—131no—
414C2×M16—131no—
415C2×M16—131no—
416C2×M16—261no—
417C2×M16—261no—
418C2×M16—262no—
419C2×M16—521no—
420C22×C8—131no—
421C22×C8—131no—
422C22×C8—131no—
423C22×C8—131no—
424C22×C8—261no—
425C22×C8—261no—
426#123—261no—
427C22⋊Q8—131no—
428C22⋊Q8—131no—
429#121—131no—
430#121C2×#26111yescharacteristic
431#120—261no—
432C4×D4—261no—
433C4×D4—261no—
434#117—131no—
435#117—131no—
436#117—131no—
437#117—131no—
438#117—131no—
439#117—261no—
440#117—261no—
441C2×C4⋊C4—131no—
442C2×C4⋊C4C2×#26111yescharacteristic
443C2×C22⋊C4—261no—
444C2×C42—131no—
445C2×C42—131no—
446C2×C42—262no—
447C2×C42—261no—
448C2×C42—261no—
449C2×C42—521no—
450#108—262no—
451#108—521no—
452#107—131no—
453#107—131no—
454#107C2×#26111yescharacteristic, complemented
455#107C2×#26111yescharacteristic, complemented
456#106—131no—
457#106—131no—
458#106—131no—
459#106—131no—
460C4⋊C8—261no—
461C4⋊C8—261no—
462C4⋊C8—261no—
463C4⋊C8—261no—
464C4⋊C8—261no—
465C4⋊C8—261no—
466#104—262no—
467#104—521no—
468#103—131no—
469#103—131no—
470#103—131no—
471#103—131no—
472#102—131no—
473#102—131no—
474#102C2×#26111yescharacteristic, complemented
475#102C2×#26111yescharacteristic, complemented
476C22⋊C8—131no—
477C22⋊C8—131no—
478C22⋊C8—131no—
479C22⋊C8—131no—
480C22⋊C8—131no—
481C22⋊C8—131no—
482C22⋊C8—131no—
483C22⋊C8—261no—
484C22⋊C8—261no—
485C22⋊C8—261no—
486C22⋊C8—261no—
487C22⋊C8C2×#26111yescharacteristic
488#97—262no—
489#97—261no—
490#97—261no—
491#97—261no—
492#97—521no—
493C4×C8—261no—
494C4×C8—261no—
495C4×C8—261no—
496C2×C13—22no—
497C2×C13—81no—
498C2×C13#235911yescharacteristic
499C2×C13C2×#44411yescharacteristic
500C2×C13#295611yescharacteristic
501D13—21no—
502D13—21no—
503D13—41no—
504C24—131no—
505#41—261no—
506#41—261no—
507#41—261no—
508#41—261no—
509C2×Q8—131no—
510C2×D4—21no—
511C2×D4—261no—
512C2×D4—261no—
513C2×D4C22×#26111yescharacteristic
514C22×C4—21no—
515C22×C4—131no—
516C22×C4—131no—
517C22×C4—131no—
518C22×C4—131no—
519C22×C4—131no—
520C22×C4—261no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4—261no—
524C22×C4—261no—
525C22×C4—261no—
526C22×C4—261no—
527C22×C4—261no—
528C22×C4—522no—
529C22×C4—522no—
530C22×C4—522no—
531C22×C4C22×#26111yescharacteristic
532M16—132no—
533M16—261no—
534M16—261no—
535M16—261no—
536M16—261no—
537M16—261no—
538M16—261no—
539M16—261no—
540M16—522no—
541M16—522no—
542C2×C8—131no—
543C2×C8—131no—
544C2×C8—131no—
545C2×C8—131no—
546C2×C8—131no—
547C2×C8—131no—
548C2×C8—261no—
549C2×C8—261no—
550C2×C8—261no—
551C2×C8—261no—
552C2×C8—261no—
553C2×C8—261no—
554C2×C8—261no—
555C2×C8—261no—
556C2×C8—261no—
557C2×C8—261no—
558C2×C8—261no—
559C2×C8—261no—
560C2×C8—522no—
561C2×C8—522no—
562C2×C8C22×#26111yescharacteristic
563C2×C8C22×#26111yescharacteristic
564C4⋊C4—21no—
565C4⋊C4—131no—
566C4⋊C4—131no—
567C4⋊C4—131no—
568C4⋊C4—261no—
569C4⋊C4—261no—
570C4⋊C4—261no—
571C4⋊C4C22×#26111yescharacteristic
572C4⋊C4C22×#26111yescharacteristic
573C4⋊C4C22×#26111yescharacteristic
574C22⋊C4—21no—
575C22⋊C4—261no—
576C22⋊C4—261no—
577C22⋊C4—261no—
578C22⋊C4—261no—
579C22⋊C4—261no—
580C22⋊C4—261no—
581C22⋊C4—261no—
582C22⋊C4—261no—
583C42—132no—
584C42—261no—
585C42—261no—
586C42—261no—
587C42—261no—
588C42—261no—
589C42—261no—
590C42—261no—
591C42—261no—
592C42—522no—
593C13#2295011yescharacteristic, complemented, Sylow
594C23—21no—
595C23—131no—
596C23—131no—
597C23—261no—
598C23—261no—
599C23—262no—
600C23—521no—
601C23D4×#26111yescharacteristic
602Q8—261no—
603Q8—261no—
604D4—21no—
605D4—21no—
606D4—42no—
607D4—521no—
608D4—521no—
609D4—1041no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—42no—
616C2×C4—131no—
617C2×C4—131no—
618C2×C4—131no—
619C2×C4—131no—
620C2×C4—131no—
621C2×C4—131no—
622C2×C4—261no—
623C2×C4—261no—
624C2×C4—261no—
625C2×C4—261no—
626C2×C4—261no—
627C2×C4—261no—
628C2×C4—261no—
629C2×C4—261no—
630C2×C4—262no—
631C2×C4—262no—
632C2×C4—261no—
633C2×C4—261no—
634C2×C4—261no—
635C2×C4—261no—
636C2×C4—521no—
637C2×C4—521no—
638C2×C4—521no—
639C2×C4—521no—
640C2×C4—521no—
641C2×C4—521no—
642C2×C4—528no—
643C2×C4—1041no—
644C2×C4D4×#26111yescharacteristic
645C2×C4C23×#26111yescharacteristic
646C8—21no—
647C8—21no—
648C8—261no—
649C8—261no—
650C8—261no—
651C8—261no—
652C8—262no—
653C8—261no—
654C8—261no—
655C8—521no—
656C8—521no—
657C8—521no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—131no—
664C22—131no—
665C22—261no—
666C22—261no—
667C22—261no—
668C22—261no—
669C22—261no—
670C22—522no—
671C22—522no—
672C22#1171910412yes—
673C22C2×D4×#26111yescharacteristic
674C4—21no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—131no—
679C4—131no—
680C4—261no—
681C4—522no—
682C4—522no—
683C4—521no—
684C4—521no—
685C4—521no—
686C4—521no—
687C4#41×#26111yescharacteristic
688C4#1171963111yescharacteristic
689C2—22no—
690C2—81no—
691C2—261no—
692C2—261no—
693C2—521no—
694C2#1313135911yescharacteristic
695C2C2×#1171910411yescharacteristic
696C2#1313161111yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#480C4
socleC22×C13C2×C4×D4
prime radical#11719311C22
cosocleC2×C4×D13C24
hypercenter#480#261
hypocenterC13#22950
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #13131526C2semidirect
3. #13130945C2semidirect
4. #13130932C2semidirect
5. #13130918C2semidirect
6. #13130904C2semidirect
7. #13130904C2semidirect
9. #13130805C2semidirect
10. #13130789C2semidirect
11. #13130643C2semidirect
12. #13130615C2semidirect
13. #13130564C2semidirect
14. C2×#11718247C2semidirect
44. C13×#480C4semidirect
45. #11718695C4semidirect
46. #11718632C4semidirect
47. #11718549C4semidirect
48. #11718549C4semidirect
51. #11718445C4semidirect
52. #11718445C4semidirect
56. #11718383C4semidirect
136. C13×#107C2×C4semidirect
137. C13×#107C2×C4semidirect
138. C13×#102C2×C4semidirect
139. C13×#102C2×C4semidirect
141. #88072C2×C4semidirect
142. #88072C2×C4semidirect
146. #88058C2×C4semidirect
147. #88058C2×C4semidirect
148. #88056C2×C4semidirect
149. #88056C2×C4semidirect
150. #88050C2×C4semidirect
151. #88050C2×C4semidirect
152. #88048C2×C4semidirect
153. #88048C2×C4semidirect
154. #88048C2×C4semidirect
155. #88048C2×C4semidirect
337. #480#261semidirect
454. #107C2×#261semidirect
455. #107C2×#261semidirect
474. #102C2×#261semidirect
475. #102C2×#261semidirect
593. C13#22950semidirect

Maximal subgroups

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

subgroupindex
#131315662
#131315262
#131309452
#131309322
#131309182
#131309042
#131308542
#131308052
#131307892
#131306432
#131306152
#131305642
C2×#117182472
#131247442
#2295013