Finite Group Databasebeta

← #15785013

Subgroups — #15785013

Order 3328.

1746 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718601C212yesmaximal
2C2×#11718328C211yesmaximal, characteristic
3C2×C4×#6103C211yesmaximal, characteristic
4#13113099C212yesmaximal, complemented
5#13113078C212yesmaximal
6#13113069C212yesmaximal, complemented
7#13113064C211yesmaximal, characteristic, complemented
8#13113063C211yesmaximal, characteristic, complemented
9#13113061C211yesmaximal, characteristic, complemented
10#13113057C211yesmaximal, characteristic
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C42×C13C2212yes—
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2212yes—
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6101C2212yes—
21C22×#6101C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C4×C13×C4⋊C4—24no—
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36#11718601—28no—
37C4×#6103C418yescomplemented
38#11718328—24no—
39C24×D13C2311yescharacteristic
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C22×C4×D13—22no—
51C22×C4×D13—22no—
52C22×C4×D13—24no—
53C22×C4×D13—42no—
54C22×C4×D13C2×C414yes—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4—24no—
58C2×C42×C13—22no—
59C2×C42×C13—22no—
60C2×C42×C13—24no—
61C2×C42×C13—24no—
62C2×C42×C13—42no—
63C2×C42×C13C2×C414yes—
64C2×#6103—24no—
65C2×#6103—24no—
66C2×#6103—24no—
67C2×#6103—24no—
68C2×#6103—24no—
69C2×#6103—42no—
70C2×#6103—42no—
71C2×#6103C2×C414yes—
72C2×#6103C2×C414yes—
73C2×#6103D414yes—
74C2×#6103Q814yes—
75C2×#6101—24no—
76C2×#6101—24no—
77C2×#6101—24no—
78C2×#6101—24no—
79C2×#6101—42no—
80C2×#6101—42no—
81C2×C4×Dic13—42no—
82C2×C4×Dic13C2×C414yes—
83C13×#95—22no—
84C13×#95D414yes—
85#88071—22no—
86#88071—24no—
87#88071—24no—
88#88071—22no—
89#88071—24no—
90#88071—24no—
91#88071—42no—
92#88071—42no—
93#88071C2×C414yes—
94#88071C2×C414yes—
95#13891—131nomaximal, Sylow
96C24×C13C2411yescharacteristic
97C23×D13—21no—
98C23×D13—22no—
99C23×D13—22no—
100C23×D13—21no—
101C23×D13—22no—
102C23×D13—21no—
103C23×D13—22no—
104C23×D13—21no—
105C23×D13C22×C412yes—
106C23×D13C2×D412yes—
107C23×D13C2×Q812yes—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C2×D412yes—
133C22×C4×C13C2×D414yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×Q812yes—
136C22×C4×C13#4114yes—
137C22×C4×C13#4114yes—
138C22×C4×C13#4112yes—
139C22×Dic13—21no—
140C22×Dic13—22no—
141C22×Dic13—21no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—21no—
146C22×Dic13—22no—
147C22×Dic13—21no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13C22×C412yes—
163C22×Dic13C22×C412yes—
164C22×Dic13C22×C412yes—
165C22×Dic13C2×D412yes—
166C22×Dic13C2×Q812yes—
167C22×Dic13#4114yes—
168C2×C4×D13—28no—
169C2×C4×D13—28no—
170C2×C4×D13—44no—
171C2×C4×D13—48no—
172C2×C4×D13—48no—
173C13×C4⋊C4—216no—
174C42×C13—28no—
175C42×C13—48no—
176#6103—28no—
177#6103—48no—
178#6103—48no—
179#6103C4⋊C4116yescomplemented
180#6101—48no—
181#6101—48no—
182C4×Dic13—44no—
183C2×#388—132no—
184C2×#380—131no—
185C2×C4×C4⋊C4D1311yescharacteristic, complemented
186C2×C4×C22⋊C4—131no—
187#1444—132no—
188#1439—132no—
189#1436—132no—
190C4⋊#95—131no—
191#1434—131no—
192#1434—131no—
193C22⋊#95—131no—
194C23×C13C23×C411yescharacteristic
195C23×C13C22×D411yescharacteristic
196C23×C13C22×D411yescharacteristic
197C23×C13C22×Q811yescharacteristic
198C23×C13C2×#4112yes—
199C23×C13C2×#4112yes—
200C23×C13C2×#4111yescharacteristic
201C23×C13C2×#4112yes—
202C23×C13H(5,𝔽2)12yes—
203C23×C13H(5,𝔽2)11yescharacteristic
204C23×C132−1+411yescharacteristic
205C22×D13—22no—
206C22×D13—22no—
207C22×D13—22no—
208C22×D13—22no—
209C22×D13—22no—
210C22×D13—22no—
211C22×D13—24no—
212C22×D13—24no—
213C22×D13—22no—
214C22×D13—24no—
215C22×D13—22no—
216C22×D13—22no—
217C22×D13—22no—
218C22×D13—24no—
219C22×D13—42no—
220C22×D13—42no—
221C22×D13—42no—
222C22×D13—42no—
223C22×D13—42no—
224C22×D13—42no—
225C22×D13—42no—
226C22×D13—42no—
227C22×D13C2×C4⋊C414yes—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13C2×C4⋊C414yes—
257C2×C4×C13#11714yes—
258C2×C4×C13C4×D414yes—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13C2×C4⋊C414yes—
287C2×Dic13#11714yes—
288C4×D13—416no—
289C24×C4—131no—
290C22×C4⋊C4—132no—
291C22×C4⋊C4—132no—
292C22×C4⋊C4C2×D1312yes—
293C22×C22⋊C4—131no—
294C22×C22⋊C4—131no—
295C22×C22⋊C4—132no—
296C22×C22⋊C4—132no—
297C22×C42—131no—
298C22×C42C2×D1312yes—
299C22×C42C2×D1311yescharacteristic
300#388—268no—
301#380—264no—
302C4×C4⋊C4—24no—
303C4×C22⋊C4—138no—
304C2×#95—131no—
305C2×#95—131no—
306C2×#95—131no—
307C2×#95—132no—
308C2×#95—131no—
309C2×#95—132no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95C2×D1311yescharacteristic
315C2×#95C2×D1311yescharacteristic
316C22×C13C22×C4⋊C411yescharacteristic
317C22×C13C2×#11711yescharacteristic
318C22×C13C2×#11711yescharacteristic
319C22×C13C2×C4×D411yescharacteristic
320C22×C13C4×#4111yescharacteristic
321C22×C13#51811yescharacteristic
322C22×C13#52011yescharacteristic
323C22×C13#52512yes—
324C22×C13#52912yes—
325C22×C13#53212yes—
326C22×C13#53312yes—
327C22×C13#54012yes—
328C22×C13#54212yes—
329C22×C13D4211yescharacteristic
330C22×C13#54612yes—
331C22×C13#54612yes—
332C22×C13#54711yescharacteristic
333C22×C13D4×Q811yescharacteristic
334C22×C13#55112yes—
335C22×C13#55312yes—
336C22×C13#55411yescharacteristic
337C22×C13#55412yes—
338C22×C13#55612yes—
339C2×D13—24no—
340C2×D13—24no—
341C2×D13—24no—
342C2×D13—42no—
343C2×D13—42no—
344C2×D13—42no—
345C2×D13—44no—
346C2×D13—44no—
347C2×D13—44no—
348C2×D13—44no—
349C2×D13—42no—
350C4×C13—24no—
351C4×C13—24no—
352C4×C13—24no—
353C4×C13—44no—
354C4×C13—44no—
355Dic13—24no—
356Dic13—24no—
357Dic13—42no—
358Dic13—82no—
359Dic13—82no—
360C25—131no—
361C23×C4—131no—
362C23×C4—131no—
363C23×C4—131no—
364C23×C4—134no—
365C23×C4—132no—
366C23×C4—132no—
367C23×C4—264no—
368C23×C4—262no—
369C23×C4—262no—
370C23×C4—522no—
371C23×C4C22×D1312yes—
372C23×C4C22×D1312yes—
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1311yescharacteristic
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—264no—
381C2×C4⋊C4—264no—
382C2×C4⋊C4—264no—
383C2×C4⋊C4—522no—
384C2×C4⋊C4—522no—
385C2×C22⋊C4—134no—
386C2×C22⋊C4—134no—
387C2×C22⋊C4—134no—
388C2×C22⋊C4—134no—
389C2×C22⋊C4—264no—
390C2×C22⋊C4—264no—
391C2×C22⋊C4—264no—
392C2×C22⋊C4—264no—
393C2×C22⋊C4—264no—
394C2×C22⋊C4—522no—
395C2×C22⋊C4—522no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—42no—
401C2×C42—134no—
402C2×C42—522no—
403C2×C42C4×D1314yes—
404#95—22no—
405#95—134no—
406#95—134no—
407#95—264no—
408#95—264no—
409#95—264no—
410#95—262no—
411#95—264no—
412#95—262no—
413#95—522no—
414#95—522no—
415#95C22⋊D1314yes—
416C2×C13#228511yescharacteristic
417C2×C13#229011yescharacteristic
418C2×C13#231911yescharacteristic
419C2×C13#234211yescharacteristic
420C2×C13#234711yescharacteristic
421C2×C13D4×C4⋊C411yescharacteristic
422C2×C13#234911yescharacteristic
423C2×C13#246412yes—
424C2×C13#246512yes—
425C2×C13#252112yes—
426C2×C13#252212yes—
427D13—44no—
428C24—132no—
429C24—132no—
430C24—132no—
431C24—262no—
432C24—262no—
433C24—261no—
434C24—261no—
435C24—261no—
436C24—262no—
437C24—262no—
438C24—261no—
439C24C23×D1311yescharacteristic
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—132no—
462C22×C4—132no—
463C22×C4—132no—
464C22×C4—132no—
465C22×C4—134no—
466C22×C4—132no—
467C22×C4—268no—
468C22×C4—262no—
469C22×C4—261no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—261no—
473C22×C4—262no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—262no—
477C22×C4—268no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—524no—
493C22×C4—528no—
494C22×C4—528no—
495C22×C4C2×C4×D1312yes—
496C22×C4C2×C4×D1312yes—
497C22×C4C2×C4×D1312yes—
498C22×C4#612714yes—
499C22×C4#612714yes—
500C22×C4#612712yes—
501C22×C4D4×D1312yes—
502C22×C4Q8×D1312yes—
503C22×C4C2×C22⋊D1314yes—
504C22×C4C2×C22⋊D1312yes—
505C4⋊C4—216no—
506C4⋊C4—528no—
507C4⋊C4—528no—
508C22⋊C4—1316no—
509C22⋊C4—268no—
510C22⋊C4—528no—
511C22⋊C4—528no—
512C42—28no—
513C42—48no—
514C42—524no—
515C13#1389111yescharacteristic, complemented, Sylow
516C23—134no—
517C23—262no—
518C23—262no—
519C23—262no—
520C23—262no—
521C23—262no—
522C23—262no—
523C23—262no—
524C23—262no—
525C23—262no—
526C23—264no—
527C23—264no—
528C23—262no—
529C23—264no—
530C23—264no—
531C23—522no—
532C23—522no—
533C23—522no—
534C23—522no—
535C23—522no—
536C23—522no—
537C23—522no—
538C23—522no—
539C23C22×C4×D1311yescharacteristic
540C23C2×#612712yes—
541C23C2×#612712yes—
542C23C2×#612711yescharacteristic
543C23C2×D4×D1311yescharacteristic
544C23#8825111yescharacteristic
545C23C2×Q8×D1311yescharacteristic
546C23#8825411yescharacteristic
547C23#41×D1312yes—
548C23#8825612yes—
549C23C22×C22⋊D1311yescharacteristic
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—134no—
579C2×C4—134no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—264no—
584C2×C4—262no—
585C2×C4—264no—
586C2×C4—264no—
587C2×C4—264no—
588C2×C4—262no—
589C2×C4—262no—
590C2×C4—262no—
591C2×C4—5216no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—522no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4—522no—
601C2×C4—522no—
602C2×C4—522no—
603C2×C4—522no—
604C2×C4—522no—
605C2×C4—522no—
606C2×C4—522no—
607C2×C4—522no—
608C2×C4#8812614yes—
609C2×C4C4⋊C4×D1314yes—
610C2×C4C4×C22⋊D1314yes—
611C22—264no—
612C22—264no—
613C22—264no—
614C22—522no—
615C22—522no—
616C22—524no—
617C22—524no—
618C22—522no—
619C22—524no—
620C22—524no—
621C22—522no—
622C22C2×#8812611yescharacteristic
623C22C4×#612711yescharacteristic
624C22#1171918412yes—
625C22C2×C4⋊C4×D1311yescharacteristic
626C22#1171920911yescharacteristic
627C22#1171921211yescharacteristic
628C22#1171921611yescharacteristic
629C22D13×#11711yescharacteristic
630C22#1171922611yescharacteristic
631C22#1171923212yes—
632C22#1171924512yes—
633C22#1171925312yes—
634C22#1171925512yes—
635C22#1171926712yes—
636C22#1171927312yes—
637C22#1171928312yes—
638C22#1171928412yes—
639C22#1171928712yes—
640C22C2×C4×C22⋊D1311yescharacteristic
641C22#1171949612yes—
642C22D4×C22⋊D1311yescharacteristic
643C22Q8×C22⋊D1311yescharacteristic
644C22#1171953412yes—
645C4—24no—
646C4—24no—
647C4—24no—
648C4—44no—
649C4—44no—
650C4—264no—
651C4—264no—
652C4—522no—
653C4—1042no—
654C4—1042no—
655C2—524no—
656C2#1311724011yescharacteristic
657C2#1311727911yescharacteristic
658C2#1311747411yescharacteristic
659C2#1311768611yescharacteristic
660C2#1311773011yescharacteristic
661C2C4⋊C4×C22⋊D1311yescharacteristic
662C2#1311774711yescharacteristic
663C2#1311883612yes—
664C2#1311885112yes—
665C2#1311953312yes—
666C2#1311954812yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#13891
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #13113099C2semidirect
6. #13113069C2semidirect
7. #13113064C2semidirect
8. #13113063C2semidirect
9. #13113061C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
37. C4×#6103C4semidirect
179. #6103C4⋊C4semidirect
185. C2×C4×C4⋊C4D13semidirect
515. C13#13891semidirect

Maximal subgroups

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

subgroupindex
C2×#117186012
C2×#117183282
C2×C4×#61032
#131130992
#131130782
#131130692
#131130642
#131130632
#131130612
#131130572
C2×C4×C13×C4⋊C42
#1389113