Finite Group Databasebeta

← #15890354

Subgroups — #15890354

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×#11718800C211yesmaximal, characteristic
3C2×#11718800C211yesmaximal, characteristic
4C2×#11718667C211yesmaximal, characteristic
5#13116011C218yesmaximal, complemented
6#13114547C211yesmaximal, characteristic, complemented
7C2×#11718149C211yesmaximal, characteristic, complemented
8C2×C13×#344C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C2×#88180C2211yescharacteristic
15C2×#88180C2211yescharacteristic
16#11719224—22no—
17#11719224—22no—
18#11719222—22no—
19#11719222C2214yescomplemented
20#11719205—22no—
21#11719188—22no—
22#11719175—22no—
23#11718800—22no—
24#11718800—22no—
25#11718800—22no—
26#11718800C2214yes—
27C2×#88065—22no—
28C2×#88065C2214yes—
29#11718667—22no—
30#11718667C2214yes—
31C2×#88046—22no—
32C13×#344C2214yescomplemented
33#11718149C2214yescomplemented
34#11718147C2214yescomplemented
35C23×C4×C13C2311yescharacteristic
36C22×C22⋊D13—21no—
37C2×#6127—21no—
38C2×#6127—21no—
39C2×#6127—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127—21no—
45C2×#6127—21no—
46C2×#6127—21no—
47C2×#6127Q812yescomplemented
48C2×#6127C2312yes—
49C22×D52Q811yescharacteristic, complemented
50C22×C4×D13—21no—
51C22×Dic26Q811yescharacteristic, complemented
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16—21no—
58C2×C13×M16—21no—
59C2×C13×M16—21no—
60C2×C13×M16—21no—
61C2×C13×M16—21no—
62C2×C13×M16C2312yes—
63C2×C13×M16C2312yes—
64C22×C8×C13—21no—
65C22×C8×C13—21no—
66C13×#117—21no—
67C13×#117—21no—
68C13×#117D412yes—
69C13×#117C2312yes—
70C2×C13×C4⋊C4—21no—
71C2×C13×C22⋊C4D412yes—
72C2×C42×C13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76#88180—21no—
77#88180—21no—
78#88180—21no—
79#88180—21no—
80#88180—21no—
81#88180—21no—
82#88180—21no—
83#88180D412yes—
84#88180D412yes—
85#88180D412yes—
86#88180C2312yes—
87#88180C2312yes—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91#88178—28no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13D412yes—
94C2×C4×Dic13C2312yes—
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—
104#88065—28no—
105#88065—28no—
106#88046—28no—
107#23472—131nomaximal, Sylow
108C24×C13C2×D411yescharacteristic
109C23×D13—21no—
110C22×C4×C13—22no—
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×Q811yescharacteristic
117C22×C4×C13C2×Q811yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C22×C4×C13#4111yescharacteristic
120C22×C4×C13#4111yescharacteristic
121C22×C4×C13#4111yescharacteristic
122C22×C4×C13#4111yescharacteristic
123C22×C4×C13#4111yescharacteristic
124C22×C4×C13C2411yescharacteristic
125C2×C22⋊D13—22no—
126C2×C22⋊D13—22no—
127C2×C22⋊D13—41no—
128C2×C22⋊D13—41no—
129C2×C22⋊D13—41no—
130C2×C22⋊D13—41no—
131C22×Dic13—21no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—41no—
135#6127—22no—
136#6127—22no—
137#6127—22no—
138#6127—22no—
139#6127—22no—
140#6127—22no—
141#6127—22no—
142#6127—22no—
143#6127—41no—
144#6127—41no—
145#6127—41no—
146#6127—41no—
147#6127—41no—
148#6127—41no—
149#6127—41no—
150#6127—41no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52C2×Q812yes—
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—41no—
160C2×C4×D13—41no—
161C2×C4×D13—41no—
162C2×C4×D13—41no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26—28no—
169C2×Dic26C2×Q812yes—
170C13×M16—22no—
171C13×M16—22no—
172C13×M16—22no—
173C13×M16—22no—
174C13×M16—41no—
175C13×M16—41no—
176C13×M16—41no—
177C13×M16—41no—
178C2×C8×C13—22no—
179C2×C8×C13—22no—
180C2×C8×C13—41no—
181C2×C8×C13—41no—
182C2×C8×C13—41no—
183C2×C8×C13—41no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4C2×D414yes—
188C42×C13—22no—
189C42×C13—22no—
190C22⋊Dic13—22no—
191C22⋊Dic13—22no—
192C22⋊Dic13—22no—
193C22⋊Dic13—22no—
194C22⋊Dic13—22no—
195C22⋊Dic13—41no—
196C4⋊Dic13—28no—
197C4⋊Dic13—22no—
198C4⋊Dic13—22no—
199C4⋊Dic13—22no—
200C4⋊Dic13—22no—
201C4⋊Dic13—22no—
202C4⋊Dic13—41no—
203#6101—28no—
204#6101—28no—
205C4×Dic13—22no—
206C4×Dic13—22no—
207C4×Dic13—22no—
208C4×Dic13—41no—
209C4×Dic13C2×D414yes—
210C4×Dic13C2×D414yes—
211#3458—131no—
212C2×#421—131no—
213C2×#421—131no—
214C2×#410—131no—
215#2031—138no—
216C2×#344D1311yescharacteristic, complemented
217#1733—131no—
218C2×H(3,ℤ/4)—131no—
219C23×C13—81no—
220C23×C13#12011yescharacteristic
221C23×C13#12011yescharacteristic
222C23×C13C22⋊Q811yescharacteristic
223C23×C13C22⋊Q811yescharacteristic
224C23×C13#12411yescharacteristic
225C23×C13#12411yescharacteristic
226C23×C13C22×D411yescharacteristic
227C22×D13—22no—
228C22×D13—41no—
229C22×D13—41no—
230C22×D13—82no—
231C2×C4×C13—24no—
232C2×C4×C13—82no—
233C2×C4×C13#12011yescharacteristic
234C2×C4×C13#12011yescharacteristic
235C2×C4×C13C22⋊Q811yescharacteristic
236C2×C4×C13C22⋊Q811yescharacteristic
237C2×C4×C13C22⋊Q811yescharacteristic
238C2×C4×C13C22⋊Q811yescharacteristic
239C2×C4×C13C22⋊Q811yescharacteristic
240C2×C4×C13C22⋊Q811yescharacteristic
241C2×C4×C13C22⋊Q811yescharacteristic
242C2×C4×C13C22⋊Q811yescharacteristic
243C2×C4×C13C22⋊Q811yescharacteristic
244C2×C4×C13C22⋊Q811yescharacteristic
245C2×C4×C13#12411yescharacteristic
246C2×C4×C13#12411yescharacteristic
247C2×C4×C13#12411yescharacteristic
248C2×C4×C13#12411yescharacteristic
249C2×C4×C13#12411yescharacteristic
250C2×C4×C13#12411yescharacteristic
251C2×C4×C13#12411yescharacteristic
252C2×C4×C13#12411yescharacteristic
253C2×C4×C13#12411yescharacteristic
254C2×C4×C13#12411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C22×Q811yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C22⋊D13—42no—
262C22⋊D13—42no—
263C22⋊D13—42no—
264C22⋊D13—42no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—22no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—42no—
271C2×Dic13—82no—
272C2×Dic13—82no—
273C2×Dic13—82no—
274D52—22no—
275D52—22no—
276D52—41no—
277D52—41no—
278C4×D13—42no—
279C4×D13—42no—
280C4×D13—42no—
281C4×D13—42no—
282Dic26—22no—
283Dic26—22no—
284Dic26—41no—
285Dic26—41no—
286Dic26—88no—
287C8×C13—42no—
288C8×C13—42no—
289C22×#41—131no—
290C22×M16C2×D1311yescharacteristic
291C22×M16C2×D1311yescharacteristic
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×#117—131no—
302C2×#117C2×D1311yescharacteristic
303#421—134no—
304#421—262no—
305#421—262no—
306#421—262no—
307C2×#104—134no—
308C2×#104—262no—
309#410—134no—
310#410—262no—
311C2×#99—262no—
312#344C2×D1314yescomplemented
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#39311yescharacteristic
323C22×C13#39311yescharacteristic
324C22×C13#39311yescharacteristic
325C22×C13#39311yescharacteristic
326C22×C13C2×#12011yescharacteristic
327C22×C13C2×C22⋊Q811yescharacteristic
328C22×C13C2×#12411yescharacteristic
329C2×D13—42no—
330C2×D13—82no—
331C2×D13—82no—
332C2×D13—82no—
333C4×C13—44no—
334C4×C13#39311yescharacteristic
335C4×C13#39311yescharacteristic
336C4×C13#39311yescharacteristic
337C4×C13#39311yescharacteristic
338C4×C13C2×C22⋊Q811yescharacteristic
339C4×C13C2×C22⋊Q811yescharacteristic
340C4×C13C2×#12411yescharacteristic
341C4×C13C2×#12411yescharacteristic
342Dic13—44no—
343Dic13—44no—
344Dic13—42no—
345Dic13—82no—
346C2×#41—132no—
347C2×#41—132no—
348C2×#41—261no—
349C2×#41—261no—
350C2×#41—261no—
351C2×#41—261no—
352C2×#41—261no—
353C2×#41—261no—
354C2×#41—261no—
355C2×#41—261no—
356C2×#41—261no—
357C2×#41—261no—
358C22×Q8—131no—
359C22×D4—131no—
360C22×D4—261no—
361C23×C4—261no—
362C23×C4C22×D1311yescharacteristic
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16C22×D1312yes—
374C2×M16C22×D1312yes—
375C22×C8—21no—
376C22×C8—21no—
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—132no—
390#117—132no—
391#117—132no—
392#117—132no—
393#117—132no—
394#117—261no—
395#117—261no—
396#117—261no—
397#117—261no—
398#117—261no—
399#117—261no—
400#117—261no—
401#117D5212yes—
402#117C22×D1312yes—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C22⋊C4—261no—
408C2×C22⋊C4—261no—
409C2×C22⋊C4—261no—
410C2×C22⋊C4D5212yes—
411C2×C42—21no—
412C2×C42—132no—
413C2×C42—132no—
414C2×C42—261no—
415#104—268no—
416#104—268no—
417#99—268no—
418C2×C13—21no—
419C2×C13—21no—
420C2×C13—21no—
421C2×C13—21no—
422C2×C13—21no—
423C2×C13—21no—
424C2×C13—21no—
425C2×C13C2×#39311yescharacteristic
426D13—82no—
427C24—261no—
428C24C2×D5211yescharacteristic
429#41—262no—
430#41—262no—
431#41—262no—
432#41—262no—
433#41—262no—
434#41—262no—
435#41—262no—
436#41—262no—
437#41—521no—
438#41—521no—
439#41—521no—
440#41—521no—
441#41—521no—
442#41—521no—
443#41—521no—
444#41—521no—
445C2×Q8—132no—
446C2×Q8—268no—
447C2×Q8—261no—
448C2×Q8—261no—
449C2×Q8—261no—
450C2×Q8—261no—
451C2×Q8—261no—
452C2×D4—132no—
453C2×D4—262no—
454C2×D4—262no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4—261no—
459C2×D4—261no—
460C2×D4—521no—
461C2×D4—521no—
462C2×D4—521no—
463C2×D4—521no—
464C22×C4—22no—
465C22×C4—261no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—521no—
471C22×C4—521no—
472C22×C4—521no—
473C22×C4—521no—
474C22×C4—521no—
475C22×C4C2×D5211yescharacteristic
476C22×C4#612711yescharacteristic
477C22×C4#612711yescharacteristic
478C22×C4#612711yescharacteristic
479C22×C4#612711yescharacteristic
480C22×C4D4×D1311yescharacteristic
481C22×C4D4×D1311yescharacteristic
482C22×C4D4×D1311yescharacteristic
483C22×C4D4×D1311yescharacteristic
484C22×C4#612911yescharacteristic
485C22×C4#612911yescharacteristic
486C22×C4Q8×D1311yescharacteristic
487C22×C4Q8×D1311yescharacteristic
488C22×C4C23×D1311yescharacteristic
489M16—22no—
490M16—22no—
491M16—22no—
492M16—22no—
493M16—41no—
494M16—41no—
495M16—41no—
496M16—41no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—268no—
506C4⋊C4—268no—
507C4⋊C4—268no—
508C4⋊C4—262no—
509C4⋊C4—262no—
510C4⋊C4—262no—
511C4⋊C4—262no—
512C4⋊C4—262no—
513C4⋊C4—521no—
514C22⋊C4—22no—
515C22⋊C4—262no—
516C22⋊C4—262no—
517C22⋊C4—262no—
518C22⋊C4—262no—
519C22⋊C4—262no—
520C22⋊C4—521no—
521C22⋊C4C2×D5214yes—
522C42—22no—
523C42—22no—
524C42—134no—
525C42—134no—
526C42—262no—
527C42—262no—
528C42—262no—
529C42—521no—
530C13#2347211yescharacteristic, complemented, Sylow
531C23—81no—
532C23—262no—
533C23—521no—
534C23—521no—
535C23—1042no—
536C23#8812911yescharacteristic
537C23#8812911yescharacteristic
538C23#8813611yescharacteristic
539C23#8813611yescharacteristic
540C23#8815111yescharacteristic
541C23#8815111yescharacteristic
542C23C22×D5211yescharacteristic
543Q8—262no—
544Q8—262no—
545Q8—521no—
546Q8—521no—
547Q8—1048no—
548D4—262no—
549D4—262no—
550D4—522no—
551D4—522no—
552D4—522no—
553D4—522no—
554D4—521no—
555D4—521no—
556C2×C4—24no—
557C2×C4—82no—
558C2×C4—264no—
559C2×C4—264no—
560C2×C4—262no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—1042no—
569C2×C4—1042no—
570C2×C4—1042no—
571C2×C4#8812911yescharacteristic
572C2×C4#8812911yescharacteristic
573C2×C4#8813611yescharacteristic
574C2×C4#8813611yescharacteristic
575C2×C4#8813911yescharacteristic
576C2×C4#8813911yescharacteristic
577C2×C4#8813911yescharacteristic
578C2×C4#8813911yescharacteristic
579C2×C4#8813911yescharacteristic
580C2×C4#8813911yescharacteristic
581C2×C4#8813911yescharacteristic
582C2×C4#8813911yescharacteristic
583C2×C4#8815011yescharacteristic
584C2×C4#8815011yescharacteristic
585C2×C4#8815011yescharacteristic
586C2×C4#8815011yescharacteristic
587C2×C4#8815011yescharacteristic
588C2×C4#8815011yescharacteristic
589C2×C4#8815011yescharacteristic
590C2×C4#8815011yescharacteristic
591C2×C4#8815111yescharacteristic
592C2×C4#8815111yescharacteristic
593C2×C4C2×#612711yescharacteristic
594C2×C4C2×#612711yescharacteristic
595C2×C4C2×D4×D1311yescharacteristic
596C2×C4C2×D4×D1311yescharacteristic
597C2×C4C2×#612911yescharacteristic
598C2×C4C2×Q8×D1311yescharacteristic
599C8—42no—
600C8—42no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—522no—
609C22—1042no—
610C22—1042no—
611C22—1042no—
612C22#1171833411yescharacteristic
613C22#1171833411yescharacteristic
614C22#1171833411yescharacteristic
615C22#1171833411yescharacteristic
616C22C2×#8812911yescharacteristic
617C22C2×#8813611yescharacteristic
618C22C2×#8815111yescharacteristic
619C4—44no—
620C4—524no—
621C4—524no—
622C4—522no—
623C4—1042no—
624C4#1171833411yescharacteristic
625C4#1171833411yescharacteristic
626C4#1171833411yescharacteristic
627C4#1171833411yescharacteristic
628C4C2×#8813911yescharacteristic
629C4C2×#8813911yescharacteristic
630C4C2×#8815011yescharacteristic
631C4C2×#8815011yescharacteristic
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—1042no—
640C2C2×#1171833411yescharacteristic
subgroupG/H
centerC4C2×#88139
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#344C2
socleC2×C13C2×#393
prime radicalC22×#6127C22
hypercenterC2×#344D13
hypocenterC13#23472
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. #13128241C2semidirect
5. #13116011C2semidirect
6. #13114547C2semidirect
7. C2×#11718149C2semidirect
8. C2×C13×#344C2semidirect
19. #11719222C22semidirect
32. C13×#344C22semidirect
33. #11718149C22semidirect
34. #11718147C22semidirect
47. C2×#6127Q8semidirect
49. C22×D52Q8semidirect
51. C22×Dic26Q8semidirect
216. C2×#344D13semidirect
312. #344C2×D13semidirect
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×#117188002
C2×#117186672
#131160112
#131145472
C2×#117181492
C2×C13×#3442
#2347213