Finite Group Databasebeta

← #15890353

Subgroups — #15890353

Order 3328.

1148 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128241C211yesmaximal, characteristic, complemented
2C2×#11718897C211yesmaximal, characteristic
3C2×#11718897C211yesmaximal, characteristic
4#13116010C218yesmaximal, complemented
5C2×#11718125C211yesmaximal, characteristic, complemented
6#13114545C211yesmaximal, characteristic, complemented
7C2×#11718123C211yesmaximal, characteristic, complemented
8C2×C13×#410C211yesmaximal, characteristic
9C22×C13×#41C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C22×#6099C2211yescharacteristic
16#11719224—22no—
17#11719224—22no—
18#11719222—22no—
19#11719222C2214yescomplemented
20#11719205—22no—
21#11719188—22no—
22#11719175—22no—
23C13×#410—22no—
24C13×#410C2214yes—
25C2×C13×#99—22no—
26#11718897—22no—
27#11718897—22no—
28#11718897—22no—
29#11718897C2214yes—
30C2×#88077—22no—
31C2×#88077C2214yes—
32#11718125C2214yescomplemented
33#11718124C2214yescomplemented
34#11718123C2214yescomplemented
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×#41Q812yescomplemented
46C2×C13×#41C2312yes—
47C22×Q8×C13Q811yescharacteristic, complemented
48C22×D4×C13—21no—
49C22×D4×C13Q811yescharacteristic, complemented
50C23×C4×C13—21no—
51C23×C4×C13C2311yescharacteristic
52C13×#117—21no—
53C13×#117—21no—
54C13×#117—21no—
55C13×#117—21no—
56C13×#117—21no—
57C13×#117D412yes—
58C13×#117C2312yes—
59C13×#117C2312yes—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4D412yes—
64C2×C42×C13—21no—
65C2×C42×C13—21no—
66C2×C22⋊Dic13—21no—
67C2×C22⋊Dic13—21no—
68#88180—21no—
69#88180—21no—
70#88180—21no—
71#88180—21no—
72#88180D412yes—
73#88180D412yes—
74#88180D412yes—
75#88180C2312yes—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78#88178—28no—
79C2×C4×Dic13D412yes—
80C2×C4×Dic13C2312yes—
81C2×#6099—21no—
82C2×#6099—21no—
83C2×#6099—21no—
84C2×#6099—21no—
85C2×#6099—21no—
86C2×#6099—21no—
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099—21no—
90C2×#6099—21no—
91C2×#6099C2312yes—
92C2×#6099C2312yes—
93C22×#1055—21no—
94C22×#1055—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#88077—28no—
106#88077—28no—
107#23472—131nomaximal, Sylow
108C24×C13—21no—
109C24×C13C2×D411yescharacteristic
110C13×#41—22no—
111C13×#41—22no—
112C13×#41—22no—
113C13×#41—22no—
114C13×#41—22no—
115C13×#41—22no—
116C13×#41—22no—
117C13×#41—22no—
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×C13C2×Q812yes—
132C2×D4×C13—22no—
133C2×D4×C13—22no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—41no—
140C2×D4×C13—41no—
141C2×D4×C13—41no—
142C2×D4×C13—41no—
143C2×D4×C13C2×Q812yes—
144C22×C4×C13—21no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—41no—
149C22×C4×C13—41no—
150C22×C4×C13—41no—
151C22×C4×C13—41no—
152C22×C4×C13—41no—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×Q811yescharacteristic
159C22×C4×C13C2×Q811yescharacteristic
160C22×C4×C13#4111yescharacteristic
161C22×C4×C13#4111yescharacteristic
162C22×C4×C13#4111yescharacteristic
163C22×C4×C13#4111yescharacteristic
164C22×C4×C13#4111yescharacteristic
165C22×C4×C13#4111yescharacteristic
166C22×C4×C13C2411yescharacteristic
167C22×Dic13—22no—
168C22×Dic13—22no—
169C2×Dic26—28no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—41no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4C2×D414yes—
178C42×C13—22no—
179C42×C13—22no—
180C42×C13—22no—
181C42×C13—41no—
182C22⋊Dic13—22no—
183C22⋊Dic13—22no—
184C22⋊Dic13—22no—
185C22⋊Dic13—22no—
186C4⋊Dic13—28no—
187C4⋊Dic13—22no—
188C4⋊Dic13—22no—
189C4⋊Dic13—22no—
190C4⋊Dic13—22no—
191#6101—28no—
192#6101—28no—
193C4×Dic13—22no—
194C4×Dic13—22no—
195C4×Dic13C2×D414yes—
196C4×Dic13C2×D414yes—
197#6099—22no—
198#6099—22no—
199#6099—22no—
200#6099—22no—
201#6099—41no—
202#6099—41no—
203#6099—41no—
204#6099—41no—
205C2×#1055—22no—
206C2×#1055—22no—
207C2×#1055—41no—
208C2×#1055—41no—
209C2×#1055—41no—
210C2×#1055—41no—
211#3458—131no—
212C2×#421—131no—
213C2×#421—131no—
214C2×#410D1311yescharacteristic
215#2031—138no—
216C2×#344—131no—
217#1733—131no—
218C2×H(3,ℤ/4)—131no—
219C23×C13—22no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—81no—
223C23×C13—82no—
224C23×C13#12011yescharacteristic
225C23×C13#12011yescharacteristic
226C23×C13C22⋊Q811yescharacteristic
227C23×C13C22⋊Q811yescharacteristic
228C23×C13#12411yescharacteristic
229C23×C13#12411yescharacteristic
230C23×C13C22×D411yescharacteristic
231Q8×C13—22no—
232Q8×C13—22no—
233Q8×C13—41no—
234Q8×C13—41no—
235D4×C13—22no—
236D4×C13—22no—
237D4×C13—42no—
238D4×C13—42no—
239D4×C13—42no—
240D4×C13—42no—
241D4×C13—41no—
242D4×C13—41no—
243C2×C4×C13—24no—
244C2×C4×C13—22no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
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×C13C22⋊Q811yescharacteristic
257C2×C4×C13C22⋊Q811yescharacteristic
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×C13#12411yescharacteristic
267C2×C4×C13#12411yescharacteristic
268C2×C4×C13#12411yescharacteristic
269C2×C4×C13#12411yescharacteristic
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×C13C22×D411yescharacteristic
277C2×C4×C13C22×D411yescharacteristic
278C2×C4×C13C22×Q811yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—82no—
285C2×Dic13—82no—
286Dic26—88no—
287#1055—42no—
288#1055—42no—
289C22×#41C2×D1311yescharacteristic
290C22×M16—131no—
291C22×M16—131no—
292#544—262no—
293#544—262no—
294#544—262no—
295#543—262no—
296#533—134no—
297#533—262no—
298#533—262no—
299C2×#117—131no—
300C2×#117—131no—
301C2×#117C2×D1311yescharacteristic
302C2×#117C2×D1311yescharacteristic
303#421—134no—
304#421—262no—
305#421—262no—
306#421—262no—
307C2×#104—134no—
308C2×#104—262no—
309#410—22no—
310#410C2×D1314yes—
311C2×#99—22no—
312#344—134no—
313#339—134no—
314H(3,ℤ/4)—134no—
315C22×C13—41no—
316C22×C13—41no—
317C22×C13—41no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13—42no—
323C22×C13—82no—
324C22×C13—82no—
325C22×C13—82no—
326C22×C13#39311yescharacteristic
327C22×C13#39311yescharacteristic
328C22×C13#39311yescharacteristic
329C22×C13#39311yescharacteristic
330C22×C13C2×#12011yescharacteristic
331C22×C13C2×C22⋊Q811yescharacteristic
332C22×C13C2×#12411yescharacteristic
333C4×C13—44no—
334C4×C13—42no—
335C4×C13—82no—
336C4×C13#39311yescharacteristic
337C4×C13#39311yescharacteristic
338C4×C13#39311yescharacteristic
339C4×C13#39311yescharacteristic
340C4×C13C2×C22⋊Q811yescharacteristic
341C4×C13C2×C22⋊Q811yescharacteristic
342C4×C13C2×#12411yescharacteristic
343C4×C13C2×#12411yescharacteristic
344Dic13—44no—
345Dic13—44no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41Dic2612yescomplemented
357C2×#41C22×D1312yes—
358C22×Q8Dic2611yescharacteristic, complemented
359C22×D4—21no—
360C22×D4Dic2611yescharacteristic, complemented
361C23×C4—21no—
362C23×C4C22×D1311yescharacteristic
363C2×M16—132no—
364C2×M16—132no—
365C2×M16—261no—
366C2×M16—261no—
367C2×M16—261no—
368C2×M16—261no—
369C2×M16—261no—
370C2×M16—261no—
371C2×M16—261no—
372C2×M16—261no—
373C2×M16—261no—
374C2×M16—261no—
375C22×C8—261no—
376C22×C8—261no—
377C4⋊Q8—264no—
378C4⋊Q8—264no—
379C4⋊Q8—264no—
380#125—264no—
381#125—264no—
382#125—264no—
383C22⋊Q8—268no—
384C22⋊Q8—268no—
385C22⋊Q8—268no—
386C4×Q8—268no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—132no—
393#117—132no—
394#117—132no—
395#117—132no—
396#117—261no—
397#117—261no—
398#117—261no—
399#117—261no—
400#117C22⋊D1312yes—
401#117C22×D1312yes—
402#117C22×D1312yes—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—261no—
409C2×C22⋊C4—261no—
410C2×C22⋊C4C22⋊D1312yes—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—132no—
414C2×C42—132no—
415#104—268no—
416#104—268no—
417#99—28no—
418C2×C13—21no—
419C2×C13—21no—
420C2×C13—21no—
421C2×C13—21no—
422C2×C13—21no—
423C2×C13—21no—
424C2×C13—21no—
425C2×C13—82no—
426C2×C13C2×#39311yescharacteristic
427C24—21no—
428C24C2×C22⋊D1311yescharacteristic
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—22no—
436#41—22no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442#41—41no—
443#41—41no—
444#41—41no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—268no—
451C2×Q8C2×Dic2612yes—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C2×Dic2612yes—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4C2×Dic2611yescharacteristic
476C22×C4C2×Dic2611yescharacteristic
477C22×C4#612711yescharacteristic
478C22×C4#612711yescharacteristic
479C22×C4D4×D1311yescharacteristic
480C22×C4D4×D1311yescharacteristic
481C22×C4D4×D1311yescharacteristic
482C22×C4D4×D1311yescharacteristic
483C22×C4#612911yescharacteristic
484C22×C4#612911yescharacteristic
485C22×C4#612911yescharacteristic
486C22×C4#612911yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C23×D1311yescharacteristic
489M16—262no—
490M16—262no—
491M16—262no—
492M16—262no—
493M16—521no—
494M16—521no—
495M16—521no—
496M16—521no—
497C2×C8—262no—
498C2×C8—262no—
499C2×C8—521no—
500C2×C8—521no—
501C2×C8—521no—
502C2×C8—521no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—41no—
507C4⋊C4—268no—
508C4⋊C4—268no—
509C4⋊C4—268no—
510C4⋊C4—262no—
511C4⋊C4—262no—
512C4⋊C4—262no—
513C4⋊C4—262no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—41no—
517C22⋊C4—262no—
518C22⋊C4—262no—
519C22⋊C4—262no—
520C22⋊C4—262no—
521C22⋊C4C2×C22⋊D1314yes—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—41no—
526C42—134no—
527C42—134no—
528C42—262no—
529C42—262no—
530C13#2347211yescharacteristic, complemented, Sylow
531C23—22no—
532C23—41no—
533C23—41no—
534C23—81no—
535C23—82no—
536C23#8817811yescharacteristic
537C23#8817811yescharacteristic
538C23#8819011yescharacteristic
539C23#8819011yescharacteristic
540C23#8819111yescharacteristic
541C23#8819111yescharacteristic
542C23C22×C22⋊D1311yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—41no—
546Q8—41no—
547Q8—1048no—
548D4—22no—
549D4—22no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—41no—
555D4—41no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—264no—
568C2×C4—264no—
569C2×C4—1042no—
570C2×C4—1042no—
571C2×C4#8813211yescharacteristic
572C2×C4#8813211yescharacteristic
573C2×C4#8813211yescharacteristic
574C2×C4#8813211yescharacteristic
575C2×C4#8813211yescharacteristic
576C2×C4#8813211yescharacteristic
577C2×C4#8813211yescharacteristic
578C2×C4#8813211yescharacteristic
579C2×C4#8813911yescharacteristic
580C2×C4#8813911yescharacteristic
581C2×C4#8813911yescharacteristic
582C2×C4#8813911yescharacteristic
583C2×C4#8813911yescharacteristic
584C2×C4#8813911yescharacteristic
585C2×C4#8813911yescharacteristic
586C2×C4#8813911yescharacteristic
587C2×C4#8817811yescharacteristic
588C2×C4#8817811yescharacteristic
589C2×C4#8819011yescharacteristic
590C2×C4#8819011yescharacteristic
591C2×C4#8819111yescharacteristic
592C2×C4#8819111yescharacteristic
593C2×C4C22×Dic2611yescharacteristic
594C2×C4C2×#612711yescharacteristic
595C2×C4C2×D4×D1311yescharacteristic
596C2×C4C2×D4×D1311yescharacteristic
597C2×C4C2×#612911yescharacteristic
598C2×C4C2×#612911yescharacteristic
599C8—522no—
600C8—522no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22#1171860811yescharacteristic
613C22#1171860811yescharacteristic
614C22#1171860811yescharacteristic
615C22#1171860811yescharacteristic
616C22C2×#8817811yescharacteristic
617C22C2×#8819011yescharacteristic
618C22C2×#8819111yescharacteristic
619C4—44no—
620C4—42no—
621C4—82no—
622C4—524no—
623C4—524no—
624C4#1171860811yescharacteristic
625C4#1171860811yescharacteristic
626C4#1171860811yescharacteristic
627C4#1171860811yescharacteristic
628C4C2×#8813211yescharacteristic
629C4C2×#8813211yescharacteristic
630C4C2×#8813911yescharacteristic
631C4C2×#8813911yescharacteristic
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—82no—
640C2C2×#1171860811yescharacteristic
subgroupG/H
centerC4C2×#88139
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#410C2
socleC2×C13C2×#393
prime radicalC22×C13×#41C22
hypercenterC2×#410D13
hypocenterC13#23472
LCSG ▷ C22×C4×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. #13116010C2semidirect
5. C2×#11718125C2semidirect
6. #13114545C2semidirect
7. C2×#11718123C2semidirect
19. #11719222C22semidirect
32. #11718125C22semidirect
33. #11718124C22semidirect
34. #11718123C22semidirect
45. C2×C13×#41Q8semidirect
47. C22×Q8×C13Q8semidirect
49. C22×D4×C13Q8semidirect
356. C2×#41Dic26semidirect
358. C22×Q8Dic26semidirect
360. C22×D4Dic26semidirect
530. C13#23472semidirect

Maximal subgroups

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

subgroupindex
#131282412
C2×#117188972
#131160102
C2×#117181252
#131145452
C2×#117181232
C2×C13×#4102
#2347213