Finite Group Databasebeta

← #15890348

Subgroups — #15890348

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
1C2×#11718666C211yesmaximal, characteristic
2C2×#11718666C211yesmaximal, characteristic
3C2×#11718667C211yesmaximal, characteristic
4#13116005C218yesmaximal, complemented
5C2×#11718125C211yesmaximal, characteristic, complemented
6#13114546C211yesmaximal, characteristic, complemented
7C2×#11718123C211yesmaximal, characteristic, complemented
8C13×#3458C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C13×#544—22no—
11C13×#544—22no—
12C13×#544—22no—
13C13×#543—22no—
14C13×#533—22no—
15C13×#533—22no—
16C13×#533C2214yescomplemented
17C2×C13×#117C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×C13×#117C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23#11718667—22no—
24#11718667C2214yes—
25#11718666—22no—
26#11718666—22no—
27#11718666—22no—
28#11718666C2214yes—
29C2×#88046—22no—
30C2×#88045—22no—
31C2×#88045C2214yes—
32#11718125C2214yescomplemented
33#11718123C2214yescomplemented
34#11718115C2214yescomplemented
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
52C13×C4⋊Q8—24no—
53C13×C4⋊Q8—24no—
54C13×C4⋊Q8—24no—
55C13×#125—24no—
56C13×#125—24no—
57C13×#125—24no—
58C13×C22⋊Q8—28no—
59C13×C22⋊Q8—28no—
60C13×C22⋊Q8—28no—
61C4×Q8×C13—28no—
62C13×#117—21no—
63C13×#117—21no—
64C13×#117—21no—
65C13×#117—21no—
66C13×#117—21no—
67C13×#117—21no—
68C13×#117D412yes—
69C13×#117D412yes—
70C13×#117D412yes—
71C13×#117D412yes—
72C13×#117C2312yes—
73C13×#117C2312yes—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4D412yes—
80C2×C42×C13—21no—
81C2×C42×C13D412yes—
82C2×C42×C13C2312yes—
83C2×C22⋊Dic13—21no—
84#88180—21no—
85#88180—21no—
86#88180—21no—
87#88180C2312yes—
88C2×C4⋊Dic13—21no—
89C2×C4×Dic13—21no—
90C2×#6099—21no—
91C2×#6099—21no—
92C2×#6099—21no—
93C2×#6099—21no—
94C2×#6099—21no—
95C2×#6099—21no—
96C2×#6099—21no—
97C2×#6099—21no—
98C2×#6099—21no—
99C2×#6099—21no—
100C2×#6099C2312yes—
101C2×#6099C2312yes—
102C22×#1055—21no—
103C22×#1055—21no—
104#88046—28no—
105#88045—28no—
106#88045—28no—
107#23472—131nomaximal, Sylow
108C24×C13C2×D411yescharacteristic
109C23×D13—21no—
110C2×Q8×C13—28no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×Q811yescharacteristic
120C22×C4×C13C2×Q811yescharacteristic
121C22×C4×C13#4111yescharacteristic
122C22×C4×C13#4111yescharacteristic
123C22×C4×C13#4111yescharacteristic
124C22×C4×C13#4111yescharacteristic
125C22×C4×C13#4111yescharacteristic
126C22×C4×C13#4111yescharacteristic
127C22×C4×C13C2411yescharacteristic
128C2×C22⋊D13—22no—
129C2×C22⋊D13—22no—
130C2×C22⋊D13—41no—
131C2×C22⋊D13—41no—
132C2×C22⋊D13—41no—
133C2×C22⋊D13—41no—
134C22×Dic13—21no—
135C22×Dic13—41no—
136#6127—22no—
137#6127—22no—
138#6127—22no—
139#6127—22no—
140#6127—22no—
141#6127—22no—
142#6127—22no—
143#6127—22no—
144#6127—41no—
145#6127—41no—
146#6127—41no—
147#6127—41no—
148#6127—41no—
149#6127—41no—
150#6127—41no—
151#6127—41no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52C2×Q812yes—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—41no—
161C2×C4×D13—41no—
162C2×C4×D13—41no—
163C2×C4×D13—41no—
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26—21no—
169C2×Dic26C2×Q812yes—
170C13×C4⋊C4—28no—
171C13×C4⋊C4—28no—
172C13×C4⋊C4—28no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—22no—
182C13×C22⋊C4—22no—
183C13×C22⋊C4—22no—
184C13×C22⋊C4C2×D414yes—
185C42×C13—22no—
186C42×C13—22no—
187C42×C13—22no—
188C42×C13—22no—
189C42×C13C2×D414yes—
190C42×C13C2×D414yes—
191C22⋊Dic13—22no—
192C22⋊Dic13—41no—
193C4⋊Dic13—22no—
194C4⋊Dic13—41no—
195C4×Dic13—22no—
196C4×Dic13—41no—
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#3458D1311yescharacteristic, complemented
212C2×#421—131no—
213C2×#421—131no—
214C2×#410—131no—
215#2031—138no—
216C2×#344—131no—
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—
231Q8×C13—88no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—82no—
236C2×C4×C13—82no—
237C2×C4×C13—82no—
238C2×C4×C13#12011yescharacteristic
239C2×C4×C13#12011yescharacteristic
240C2×C4×C13C22⋊Q811yescharacteristic
241C2×C4×C13C22⋊Q811yescharacteristic
242C2×C4×C13C22⋊Q811yescharacteristic
243C2×C4×C13C22⋊Q811yescharacteristic
244C2×C4×C13C22⋊Q811yescharacteristic
245C2×C4×C13C22⋊Q811yescharacteristic
246C2×C4×C13C22⋊Q811yescharacteristic
247C2×C4×C13C22⋊Q811yescharacteristic
248C2×C4×C13C22⋊Q811yescharacteristic
249C2×C4×C13C22⋊Q811yescharacteristic
250C2×C4×C13#12411yescharacteristic
251C2×C4×C13#12411yescharacteristic
252C2×C4×C13#12411yescharacteristic
253C2×C4×C13#12411yescharacteristic
254C2×C4×C13#12411yescharacteristic
255C2×C4×C13#12411yescharacteristic
256C2×C4×C13#12411yescharacteristic
257C2×C4×C13#12411yescharacteristic
258C2×C4×C13#12411yescharacteristic
259C2×C4×C13#12411yescharacteristic
260C2×C4×C13C22×D411yescharacteristic
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13C22×Q811yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C22⋊D13—42no—
267C22⋊D13—42no—
268C22⋊D13—42no—
269C22⋊D13—42no—
270C2×Dic13—22no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—42no—
274C2×Dic13—82no—
275D52—22no—
276D52—22no—
277D52—41no—
278D52—41no—
279C4×D13—42no—
280C4×D13—42no—
281C4×D13—42no—
282C4×D13—42no—
283Dic26—22no—
284Dic26—22no—
285Dic26—41no—
286Dic26—41no—
287#1055—42no—
288#1055—42no—
289C22×#41—131no—
290C22×M16—131no—
291C22×M16—131no—
292#544—22no—
293#544—22no—
294#544—22no—
295#543—22no—
296#533—22no—
297#533—22no—
298#533C2×D1314yescomplemented
299C2×#117—131no—
300C2×#117C2×D1311yescharacteristic
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—134no—
310#410—262no—
311C2×#99—262no—
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#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—44no—
335C4×C13—44no—
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—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—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—24no—
378C4⋊Q8—24no—
379C4⋊Q8—24no—
380#125—24no—
381#125—24no—
382#125—24no—
383C22⋊Q8—28no—
384C22⋊Q8—28no—
385C22⋊Q8—28no—
386C4×Q8—28no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—132no—
394#117—261no—
395#117—261no—
396#117—261no—
397#117C22⋊D1312yes—
398#117C22⋊D1312yes—
399#117C22⋊D1312yes—
400#117C22⋊D1312yes—
401#117C22×D1312yes—
402#117C22×D1312yes—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—261no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—261no—
410C2×C22⋊C4C22⋊D1312yes—
411C2×C42—21no—
412C2×C42—261no—
413C2×C42C22⋊D1312yes—
414C2×C42C22×D1312yes—
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×C22⋊D1311yescharacteristic
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—28no—
446C2×Q8—132no—
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—22no—
466C22×C4—22no—
467C22×C4—261no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—521no—
471C22×C4—521no—
472C22×C4—521no—
473C22×C4—521no—
474C22×C4—521no—
475C22×C4Q8×D1311yescharacteristic
476C22×C4Q8×D1311yescharacteristic
477C22×C4#613111yescharacteristic
478C22×C4#613111yescharacteristic
479C22×C4#613111yescharacteristic
480C22×C4#613111yescharacteristic
481C22×C4#613111yescharacteristic
482C22×C4#613111yescharacteristic
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C2×C22⋊D1311yescharacteristic
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
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—28no—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—262no—
513C4⋊C4—521no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—262no—
520C22⋊C4—521no—
521C22⋊C4C2×C22⋊D1314yes—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—262no—
527C42—521no—
528C42C2×C22⋊D1314yes—
529C42C2×C22⋊D1314yes—
530C13#2347211yescharacteristic, complemented, Sylow
531C23—81no—
532C23—262no—
533C23—521no—
534C23—521no—
535C23—1042no—
536C23#8820011yescharacteristic
537C23#8820011yescharacteristic
538C23#8820111yescharacteristic
539C23#8820111yescharacteristic
540C23#8820711yescharacteristic
541C23#8820711yescharacteristic
542C23C22×C22⋊D1311yescharacteristic
543Q8—88no—
544Q8—262no—
545Q8—262no—
546Q8—521no—
547Q8—521no—
548D4—262no—
549D4—262no—
550D4—522no—
551D4—522no—
552D4—522no—
553D4—522no—
554D4—521no—
555D4—521no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—262no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—1042no—
571C2×C4#8820011yescharacteristic
572C2×C4#8820011yescharacteristic
573C2×C4#8820011yescharacteristic
574C2×C4#8820011yescharacteristic
575C2×C4#8820011yescharacteristic
576C2×C4#8820011yescharacteristic
577C2×C4#8820011yescharacteristic
578C2×C4#8820011yescharacteristic
579C2×C4#8820011yescharacteristic
580C2×C4#8820011yescharacteristic
581C2×C4#8820111yescharacteristic
582C2×C4#8820111yescharacteristic
583C2×C4#8820111yescharacteristic
584C2×C4#8820111yescharacteristic
585C2×C4#8820111yescharacteristic
586C2×C4#8820111yescharacteristic
587C2×C4#8820111yescharacteristic
588C2×C4#8820111yescharacteristic
589C2×C4#8820111yescharacteristic
590C2×C4#8820111yescharacteristic
591C2×C4#8820711yescharacteristic
592C2×C4#8820711yescharacteristic
593C2×C4C2×Q8×D1311yescharacteristic
594C2×C4C2×#613111yescharacteristic
595C2×C4C2×#613111yescharacteristic
596C2×C4C2×#613111yescharacteristic
597C2×C4C22×C22⋊D1311yescharacteristic
598C2×C4C22×C22⋊D1311yescharacteristic
599C8—522no—
600C8—522no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—522no—
609C22—1042no—
610C22—1042no—
611C22—1042no—
612C22#1171889211yescharacteristic
613C22#1171889211yescharacteristic
614C22#1171889211yescharacteristic
615C22#1171889211yescharacteristic
616C22C2×#8820011yescharacteristic
617C22C2×#8820111yescharacteristic
618C22C2×#8820711yescharacteristic
619C4—44no—
620C4—44no—
621C4—44no—
622C4—522no—
623C4—1042no—
624C4#1171889211yescharacteristic
625C4#1171889211yescharacteristic
626C4#1171889211yescharacteristic
627C4#1171889211yescharacteristic
628C4C2×#8820011yescharacteristic
629C4C2×#8820011yescharacteristic
630C4C2×#8820111yescharacteristic
631C4C2×#8820111yescharacteristic
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—1042no—
640C2C2×#1171889211yescharacteristic
subgroupG/H
centerC4C2×#88201
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#3458C2
socleC2×C13C2×#393
prime radicalC22×#6127C22
hypercenter#3458D13
hypocenterC13#23472
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3458

Complements

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

NH ≅ G/Ntype
4. #13116005C2semidirect
5. C2×#11718125C2semidirect
6. #13114546C2semidirect
7. C2×#11718123C2semidirect
8. C13×#3458C2semidirect
16. C13×#533C22semidirect
32. #11718125C22semidirect
33. #11718123C22semidirect
34. #11718115C22semidirect
47. C2×#6127Q8semidirect
49. C22×D52Q8semidirect
51. C22×Dic26Q8semidirect
211. #3458D13semidirect
298. #533C2×D13semidirect
530. C13#23472semidirect

Maximal subgroups

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

subgroupindex
C2×#117186662
C2×#117186672
#131160052
C2×#117181252
#131145462
C2×#117181232
C13×#34582
#2347213