Finite Group Databasebeta

← #15890361

Subgroups — #15890361

Order 3328.

1164 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128241C211yesmaximal, characteristic, complemented
2C2×#11718901C211yesmaximal, characteristic
3C2×#11718901C211yesmaximal, characteristic
4#13116013C218yesmaximal, complemented
5#13114569C211yesmaximal, characteristic, complemented
6#13114568C211yesmaximal, characteristic, complemented
7#13114568C211yesmaximal, characteristic, complemented
8C2×C13×#410C211yesmaximal, characteristic
9C22×C13×#41C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C2×#88180C2211yescharacteristic
15C2×#88180C2211yescharacteristic
16#11719224—22no—
17#11719224—22no—
18#11719222—22no—
19#11719222—22no—
20#11719205—22no—
21#11719188C2214yes—
22#11719175—22no—
23C13×#410—22no—
24C13×#410—22no—
25C2×C13×#99C2214yes—
26#11718901—22no—
27#11718901—22no—
28#11718901—22no—
29#11718901—22no—
30C2×#88074C2214yes—
31C2×#88074C2214yes—
32#11718119C2214yes—
33#11718119C2214yes—
34#11718118C2214yes—
35C2×C13×#41—21no—
36C2×C13×#41—21no—
37C2×C13×#41—21no—
38C2×C13×#41—21no—
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—21no—
42C2×C13×#41—21no—
43C2×C13×#41—21no—
44C2×C13×#41—21no—
45C2×C13×#41—21no—
46C2×C13×#41—21no—
47C22×Q8×C13Q811yescharacteristic, complemented
48C22×D4×C13Q811yescharacteristic, complemented
49C22×D4×C13C2312yes—
50C23×C4×C13Q812yescomplemented
51C23×C4×C13C2311yescharacteristic
52C13×#117—21no—
53C13×#117—21no—
54C13×#117—21no—
55C13×#117—21no—
56C13×#117—21no—
57C13×#117—21no—
58C13×#117D412yes—
59C13×#117D412yes—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C22⋊C4C2312yes—
63C2×C13×C22⋊C4C2312yes—
64C2×C42×C13—21no—
65C2×C42×C13—21no—
66C2×C22⋊Dic13C2312yes—
67C2×C22⋊Dic13C2312yes—
68C2×C22⋊Dic13C2312yes—
69C2×C22⋊Dic13C2312yes—
70#88180—21no—
71#88180—21no—
72#88180—21no—
73#88180—21no—
74#88180—21no—
75#88180—21no—
76#88180—21no—
77#88180—21no—
78#88180—21no—
79#88180—21no—
80#88180—21no—
81#88180—21no—
82#88180D412yes—
83#88180D412yes—
84#88180D412yes—
85#88180D412yes—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90#88178—28no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95#88144—24no—
96#88144—24no—
97#88142—24no—
98#88142—24no—
99#88132—28no—
100#88132—28no—
101#88124—24no—
102#88123—24no—
103C4×Dic26—28no—
104C13×#99—28no—
105#88074—28no—
106#88074—28no—
107#23474—131nomaximal, Sylow
108C24×C13C2×Q812yes—
109C24×C13C2411yescharacteristic
110C13×#41—41no—
111C13×#41—41no—
112C13×#41—41no—
113C13×#41—41no—
114C13×#41—41no—
115C13×#41—41no—
116C13×#41—41no—
117C13×#41—41no—
118C13×#41—41no—
119C13×#41—41no—
120C13×#41—41no—
121C13×#41—41no—
122C13×#41—41no—
123C13×#41—41no—
124C13×#41—41no—
125C13×#41—41no—
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×D4×C13—22no—
133C2×D4×C13—22no—
134C2×D4×C13—22no—
135C2×D4×C13—22no—
136C2×D4×C13—22no—
137C2×D4×C13—22no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13—21no—
142C2×D4×C13—21no—
143C2×D4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×Q812yes—
159C22×C4×C13C2×Q811yescharacteristic
160C22×C4×C13C2×Q811yescharacteristic
161C22×C4×C13#4111yescharacteristic
162C22×C4×C13#4111yescharacteristic
163C22×C4×C13#4111yescharacteristic
164C22×C4×C13#4111yescharacteristic
165C22×C4×C13#4111yescharacteristic
166C22×C4×C13#4111yescharacteristic
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C2×Dic26—28no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—41no—
175C13×C4⋊C4—41no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—22no—
179C13×C22⋊C4C2×D414yes—
180C42×C13—22no—
181C42×C13—22no—
182C42×C13—41no—
183C42×C13—41no—
184C22⋊Dic13—22no—
185C22⋊Dic13—22no—
186C22⋊Dic13—22no—
187C22⋊Dic13—22no—
188C22⋊Dic13—22no—
189C22⋊Dic13—22no—
190C22⋊Dic13C2×D414yes—
191C22⋊Dic13C2×D414yes—
192C4⋊Dic13—28no—
193C4⋊Dic13—22no—
194C4⋊Dic13—22no—
195C4⋊Dic13—22no—
196C4⋊Dic13—22no—
197C4⋊Dic13—41no—
198C4⋊Dic13—41no—
199C4⋊Dic13—41no—
200C4⋊Dic13—41no—
201#6101—28no—
202#6101—28no—
203C4×Dic13—22no—
204C4×Dic13—22no—
205C4×Dic13—22no—
206C4×Dic13—22no—
207C4×Dic13—41no—
208C4×Dic13—41no—
209C4×Dic13—41no—
210C4×Dic13—41no—
211#3458—131no—
212C2×#410—131no—
213C2×#410—131no—
214C2×#410D1311yescharacteristic
215#2032—138no—
216#1740—131no—
217#1740—131no—
218#1740—131no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—81no—
223C23×C13—82no—
224C23×C13C22×D411yescharacteristic
225C23×C13C22×D411yescharacteristic
226C23×C13C22×D411yescharacteristic
227C23×C13C22×Q811yescharacteristic
228C23×C13C2×#4111yescharacteristic
229C23×C13C2×#4111yescharacteristic
230C23×C13C2×#4111yescharacteristic
231Q8×C13—41no—
232Q8×C13—41no—
233Q8×C13—41no—
234Q8×C13—41no—
235D4×C13—42no—
236D4×C13—42no—
237D4×C13—42no—
238D4×C13—42no—
239D4×C13—41no—
240D4×C13—41no—
241D4×C13—41no—
242D4×C13—41no—
243C2×C4×C13—24no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—82no—
253C2×C4×C13—82no—
254C2×C4×C13#12011yescharacteristic
255C2×C4×C13#12011yescharacteristic
256C2×C4×C13#12011yescharacteristic
257C2×C4×C13#12011yescharacteristic
258C2×C4×C13C22⋊Q811yescharacteristic
259C2×C4×C13C22⋊Q811yescharacteristic
260C2×C4×C13C22⋊Q811yescharacteristic
261C2×C4×C13C22⋊Q811yescharacteristic
262C2×C4×C13C22⋊Q811yescharacteristic
263C2×C4×C13C22⋊Q811yescharacteristic
264C2×C4×C13C22⋊Q811yescharacteristic
265C2×C4×C13C22⋊Q811yescharacteristic
266C2×C4×C13C22⋊Q811yescharacteristic
267C2×C4×C13C22⋊Q811yescharacteristic
268C2×C4×C13C22⋊Q811yescharacteristic
269C2×C4×C13C22⋊Q811yescharacteristic
270C2×C4×C13#12411yescharacteristic
271C2×C4×C13#12411yescharacteristic
272C2×C4×C13#12411yescharacteristic
273C2×C4×C13#12411yescharacteristic
274C2×C4×C13#12411yescharacteristic
275C2×C4×C13#12411yescharacteristic
276C2×C4×C13#12411yescharacteristic
277C2×C4×C13#12411yescharacteristic
278C2×C4×C13#12411yescharacteristic
279C2×C4×C13#12411yescharacteristic
280C2×C4×C13#12411yescharacteristic
281C2×C4×C13#12411yescharacteristic
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—82no—
287C2×Dic13—82no—
288C2×Dic13—82no—
289C2×Dic13—82no—
290Dic26—88no—
291C22×#41C2×D1311yescharacteristic
292#544—262no—
293#544—262no—
294#544—262no—
295#543—134no—
296#533—262no—
297#533—262no—
298#533—262no—
299C2×#117—131no—
300C2×#117—131no—
301C2×#117—131no—
302C2×#117—131no—
303C2×#117C2×D1311yescharacteristic
304C2×#117C2×D1311yescharacteristic
305#410—22no—
306#410—22no—
307#410—262no—
308#410—262no—
309#410—262no—
310#410—262no—
311C2×#99—134no—
312C2×#99—134no—
313C2×#99C2×D1314yes—
314#342—134no—
315#342—134no—
316#342—134no—
317C22×C13—41no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—42no—
325C22×C13—82no—
326C22×C13—82no—
327C22×C13—82no—
328C22×C13C2×#12011yescharacteristic
329C22×C13C2×C22⋊Q811yescharacteristic
330C22×C13C2×C22⋊Q811yescharacteristic
331C22×C13C2×C22⋊Q811yescharacteristic
332C22×C13C2×#12411yescharacteristic
333C22×C13C2×#12411yescharacteristic
334C22×C13C2×#12411yescharacteristic
335C4×C13—44no—
336C4×C13—42no—
337C4×C13—82no—
338C4×C13#39311yescharacteristic
339C4×C13#39311yescharacteristic
340C4×C13#39311yescharacteristic
341C4×C13#39311yescharacteristic
342C4×C13#39311yescharacteristic
343C4×C13#39311yescharacteristic
344C4×C13#39311yescharacteristic
345C4×C13#39311yescharacteristic
346Dic13—44no—
347Dic13—44no—
348Dic13—82no—
349Dic13—82no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—21no—
362C22×Q8Dic2611yescharacteristic, complemented
363C22×D4Dic2611yescharacteristic, complemented
364C22×D4C22×D1312yes—
365C23×C4Dic2612yescomplemented
366C23×C4C22×D1311yescharacteristic
367C4⋊Q8—264no—
368C4⋊Q8—264no—
369C4⋊Q8—264no—
370#125—264no—
371#125—264no—
372#125—264no—
373C22⋊Q8—268no—
374C22⋊Q8—268no—
375C22⋊Q8—268no—
376C4×Q8—268no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—132no—
384#117—132no—
385#117—132no—
386#117—132no—
387#117—261no—
388#117—261no—
389#117—261no—
390#117—261no—
391#117—261no—
392#117—261no—
393#117—261no—
394#117—261no—
395#117—261no—
396#117—261no—
397#117—261no—
398#117—261no—
399#117C22⋊D1312yes—
400#117C22⋊D1312yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C22⋊C4—132no—
408C2×C22⋊C4—132no—
409C2×C22⋊C4—132no—
410C2×C22⋊C4—132no—
411C2×C22⋊C4C22×D1312yes—
412C2×C22⋊C4C22×D1312yes—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—261no—
416C2×C42—261no—
417C2×C42—261no—
418C2×C42—261no—
419#99—28no—
420#99—268no—
421#99—268no—
422C2×C13—21no—
423C2×C13—21no—
424C2×C13—21no—
425C2×C13—21no—
426C2×C13—21no—
427C2×C13—21no—
428C2×C13—21no—
429C2×C13—82no—
430C2×C13C2×#39311yescharacteristic
431C24C2×Dic2612yes—
432C24C23×D1311yescharacteristic
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442#41—41no—
443#41—41no—
444#41—41no—
445#41—41no—
446#41—41no—
447#41—41no—
448#41—41no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—268no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4C2×Dic2612yes—
481C22×C4C2×Dic2611yescharacteristic
482C22×C4C2×Dic2611yescharacteristic
483C22×C4#612711yescharacteristic
484C22×C4#612711yescharacteristic
485C22×C4D4×D1311yescharacteristic
486C22×C4D4×D1311yescharacteristic
487C22×C4D4×D1311yescharacteristic
488C22×C4D4×D1311yescharacteristic
489C22×C4#612911yescharacteristic
490C22×C4#612911yescharacteristic
491C22×C4#612911yescharacteristic
492C22×C4#612911yescharacteristic
493C22×C4C2×C22⋊D1311yescharacteristic
494C22×C4C2×C22⋊D1311yescharacteristic
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—268no—
500C4⋊C4—268no—
501C4⋊C4—268no—
502C4⋊C4—262no—
503C4⋊C4—262no—
504C4⋊C4—262no—
505C4⋊C4—262no—
506C4⋊C4—521no—
507C4⋊C4—521no—
508C4⋊C4—521no—
509C4⋊C4—521no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—134no—
514C22⋊C4—134no—
515C22⋊C4—262no—
516C22⋊C4—262no—
517C22⋊C4—262no—
518C22⋊C4—262no—
519C22⋊C4—262no—
520C22⋊C4—262no—
521C22⋊C4C2×C22⋊D1314yes—
522C42—22no—
523C42—22no—
524C42—41no—
525C42—41no—
526C42—262no—
527C42—262no—
528C42—262no—
529C42—262no—
530C42—521no—
531C42—521no—
532C42—521no—
533C42—521no—
534C13#2347411yescharacteristic, complemented, Sylow
535C23—22no—
536C23—22no—
537C23—22no—
538C23—81no—
539C23—82no—
540C23C22×Dic2611yescharacteristic
541C23C2×#612711yescharacteristic
542C23C2×D4×D1311yescharacteristic
543C23C2×D4×D1311yescharacteristic
544C23C2×#612911yescharacteristic
545C23C2×#612911yescharacteristic
546C23C22×C22⋊D1311yescharacteristic
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—41no—
551Q8—1048no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—41no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—522no—
574C2×C4—522no—
575C2×C4—1042no—
576C2×C4—1042no—
577C2×C4—1042no—
578C2×C4—1042no—
579C2×C4#8813211yescharacteristic
580C2×C4#8813211yescharacteristic
581C2×C4#8813211yescharacteristic
582C2×C4#8813211yescharacteristic
583C2×C4#8813211yescharacteristic
584C2×C4#8813211yescharacteristic
585C2×C4#8813211yescharacteristic
586C2×C4#8813211yescharacteristic
587C2×C4#8813911yescharacteristic
588C2×C4#8813911yescharacteristic
589C2×C4#8813911yescharacteristic
590C2×C4#8813911yescharacteristic
591C2×C4#8813911yescharacteristic
592C2×C4#8813911yescharacteristic
593C2×C4#8813911yescharacteristic
594C2×C4#8813911yescharacteristic
595C2×C4#8817811yescharacteristic
596C2×C4#8817811yescharacteristic
597C2×C4#8817811yescharacteristic
598C2×C4#8817811yescharacteristic
599C2×C4#8819011yescharacteristic
600C2×C4#8819011yescharacteristic
601C2×C4#8819011yescharacteristic
602C2×C4#8819011yescharacteristic
603C2×C4#8819111yescharacteristic
604C2×C4#8819111yescharacteristic
605C2×C4#8819111yescharacteristic
606C2×C4#8819111yescharacteristic
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—42no—
615C22—82no—
616C22—82no—
617C22—82no—
618C22C2×#8813211yescharacteristic
619C22C2×#8813211yescharacteristic
620C22C2×#8813911yescharacteristic
621C22C2×#8813911yescharacteristic
622C22C2×#8817811yescharacteristic
623C22C2×#8819011yescharacteristic
624C22C2×#8819111yescharacteristic
625C4—44no—
626C4—42no—
627C4—82no—
628C4—524no—
629C4—524no—
630C4—1042no—
631C4—1042no—
632C4#1171860811yescharacteristic
633C4#1171860811yescharacteristic
634C4#1171860811yescharacteristic
635C4#1171860811yescharacteristic
636C4#1171860811yescharacteristic
637C4#1171860811yescharacteristic
638C4#1171860811yescharacteristic
639C4#1171860811yescharacteristic
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—21no—
646C2—21no—
647C2—82no—
648C2C2×#1171860811yescharacteristic
subgroupG/H
centerC4#11718608
commutator, cosocleC24×C13C24
FrattiniC24C23×D13
FittingC2×C13×#410C2
socleC2×C13C2×#393
prime radicalC22×C13×#41C22
hypercenterC2×#410D13
hypocenterC13#23474
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
1. #13128241C2semidirect
4. #13116013C2semidirect
5. #13114569C2semidirect
6. #13114568C2semidirect
7. #13114568C2semidirect
47. C22×Q8×C13Q8semidirect
48. C22×D4×C13Q8semidirect
50. C23×C4×C13Q8semidirect
362. C22×Q8Dic26semidirect
363. C22×D4Dic26semidirect
365. C23×C4Dic26semidirect
534. C13#23474semidirect

Maximal subgroups

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

subgroupindex
#131282412
C2×#117189012
#131160132
#131145692
#131145682
C2×C13×#4102
#2347413