Finite Group Databasebeta

← #15789909

Subgroups — #15789909

Order 3328.

1622 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718892C211yesmaximal, characteristic
2C2×#11718891C211yesmaximal, characteristic, complemented
3C2×#11718327C211yesmaximal, characteristic
4#13113100C211yesmaximal, characteristic, complemented
5#13113097C212yesmaximal, complemented
6#13113082C211yesmaximal, characteristic
7#13113080C212yesmaximal
8#13113071C212yesmaximal, complemented
9#13113061C211yesmaximal, characteristic, complemented
10#13113057C212yesmaximal
11C13×#1446C211yesmaximal, characteristic, complemented
12C23×Q8×C13C2211yescharacteristic
13C23×C4×D13C2211yescharacteristic
14C22×#6103C2211yescharacteristic
15C22×#6103C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2212yes—
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2211yescharacteristic
24C2×C13×#95C2212yes—
25C2×C13×#95C2212yes—
26#11718892C418yescomplemented
27#11718891—24no—
28C2×#88071C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37#11718327—24no—
38C24×D13C2311yescharacteristic
39C22×Q8×C13—22no—
40C22×Q8×C13—22no—
41C22×Q8×C13—42no—
42C22×Q8×C13—42no—
43C22×Q8×C13C2×C414yescomplemented
44C23×C4×C13C2312yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—42no—
57C22×C4×D13—42no—
58C22×C4×D13Q814yescomplemented
59C2×#6103—22no—
60C2×#6103—22no—
61C2×#6103—22no—
62C2×#6103—22no—
63C2×#6103—22no—
64C2×#6103—24no—
65C2×#6103—42no—
66C2×#6103—42no—
67C2×#6103—42no—
68C2×#6103—42no—
69C2×#6103C2×C414yes—
70C2×#6103C2×C418yes—
71C2×C4⋊Dic13—22no—
72C2×C4⋊Dic13—42no—
73C2×#6101—24no—
74C2×#6101—42no—
75C2×#6101—42no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—42no—
78C2×C4×Dic13—42no—
79C2×C4×Dic13D414yes—
80C13×#95—22no—
81C13×#95—22no—
82C13×#95—42no—
83C13×#95—42no—
84#88071—22no—
85#88071—24no—
86#88071—24no—
87#88071—24no—
88#88071—42no—
89#88071—42no—
90#88071—42no—
91#88071C2×C418yescomplemented
92#88071C2×C414yescomplemented
93#14319—131nomaximal, Sylow
94C24×C13C2411yescharacteristic
95C23×D13—21no—
96C23×D13—21no—
97C23×D13—21no—
98C23×D13—21no—
99C23×D13—22no—
100C23×D13—22no—
101C23×D13—22no—
102C23×D13—22no—
103C23×D13C22×C412yes—
104C23×D13C2×Q812yes—
105C23×D13#4112yes—
106C2×Q8×C13—28no—
107C2×Q8×C13—48no—
108C2×Q8×C13—44no—
109C2×Q8×C13—44no—
110C2×Q8×C13—48no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
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×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13C22×C414yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×Q812yes—
138C22×C4×C13#4112yes—
139C22×C4×C13#4112yes—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—21no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—21no—
146C22×Dic13—21no—
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×Dic13—22no—
163C22×Dic13C22×C412yes—
164C22×Dic13C22×C414yes—
165C22×Dic13C2×D412yes—
166C22×Dic13C2×D412yes—
167C22×Dic13C2×Q812yes—
168C22×Dic13#4112yes—
169C2×C4×D13—28no—
170C2×C4×D13—48no—
171C2×C4×D13—44no—
172C2×C4×D13—44no—
173C2×C4×D13—48no—
174#6103—28no—
175#6103—28no—
176#6103—48no—
177#6103—48no—
178C4⋊Dic13—44no—
179#6101—48no—
180C4×Dic13—44no—
181C4×Dic13—44no—
182C2×#393—131no—
183C2×#391—131no—
184C2×C4×C22⋊C4—131no—
185#1446D1311yescharacteristic, complemented
186#1444—131no—
187#1443—132no—
188#1439—132no—
189#1439—131no—
190#1436—132no—
191#1434—131no—
192C22⋊#95—132no—
193C23×C13C23×C411yescharacteristic
194C23×C13C22×D411yescharacteristic
195C23×C13C22×Q811yescharacteristic
196C23×C13C2×#4111yescharacteristic
197C23×C13C2×#4111yescharacteristic
198C23×C13C2×#4111yescharacteristic
199C23×C13C2×#4111yescharacteristic
200C23×C13H(5,𝔽2)12yes—
201C23×C13H(5,𝔽2)12yes—
202C23×C13H(5,𝔽2)12yes—
203C23×C132−1+412yes—
204C22×D13—22no—
205C22×D13—22no—
206C22×D13—24no—
207C22×D13—24no—
208C22×D13—22no—
209C22×D13—22no—
210C22×D13—22no—
211C22×D13—22no—
212C22×D13—24no—
213C22×D13—24no—
214C22×D13—24no—
215C22×D13—24no—
216C22×D13—41no—
217C22×D13—41no—
218C22×D13—41no—
219C22×D13—41no—
220C22×D13—42no—
221C22×D13—42no—
222C22×D13—42no—
223C22×D13—42no—
224C22×D13—42no—
225C22×D13—42no—
226C22×D13C4×Q814yes—
227Q8×C13—416no—
228C2×C4×C13—24no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—24no—
239C2×C4×C13—41no—
240C2×C4×C13—42no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
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×C13C4×D414yes—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—22no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—41no—
270C2×Dic13—41no—
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×Dic13C22⋊Q814yes—
286C4×D13—416no—
287C23×Q8C2×D1311yescharacteristic
288C24×C4—131no—
289C22×C4⋊C4—132no—
290C22×C4⋊C4—131no—
291C22×C22⋊C4—131no—
292C22×C22⋊C4—132no—
293C22×C22⋊C4—131no—
294C22×C22⋊C4—132no—
295C22×C42—131no—
296C22×C42—131no—
297#393—138no—
298#391—264no—
299C4×C22⋊C4—264no—
300C2×#95—131no—
301C2×#95—132no—
302C2×#95—132no—
303C2×#95—132no—
304C2×#95—132no—
305C2×#95—131no—
306C2×#95—132no—
307C2×#95—132no—
308C2×#95—132no—
309C2×#95C2×D1311yescharacteristic
310C2×#95C2×D1311yescharacteristic
311C2×#95C2×D1312yes—
312C2×#95C2×D1312yes—
313C22×C13C2×C4×D411yescharacteristic
314C22×C13C2×C4×Q811yescharacteristic
315C22×C13C4×#4111yescharacteristic
316C22×C13#51812yes—
317C22×C13#52012yes—
318C22×C13C2×C22⋊Q811yescharacteristic
319C22×C13#52511yescharacteristic
320C22×C13#52911yescharacteristic
321C22×C13#53311yescharacteristic
322C22×C13#53411yescharacteristic
323C22×C13#53511yescharacteristic
324C22×C13#53511yescharacteristic
325C22×C13#53611yescharacteristic
326C22×C13#53812yes—
327C22×C13#53812yes—
328C22×C13#53812yes—
329C22×C13#53812yes—
330C22×C13#53912yes—
331C22×C13#54212yes—
332C22×C13#54212yes—
333C22×C13#54212yes—
334C22×C13#54312yes—
335C22×C13#54412yes—
336C2×D13—28no—
337C2×D13—24no—
338C2×D13—42no—
339C2×D13—42no—
340C2×D13—44no—
341C2×D13—42no—
342C2×D13—42no—
343C2×D13—42no—
344C2×D13—42no—
345C2×D13—44no—
346C2×D13—44no—
347C4×C13—24no—
348C4×C13—44no—
349C4×C13—42no—
350C4×C13—42no—
351C4×C13—82no—
352Dic13—24no—
353Dic13—42no—
354Dic13—44no—
355Dic13—42no—
356Dic13—82no—
357C25—131no—
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—42no—
361C22×Q8—42no—
362C22×Q8C4×D1314yescomplemented
363C23×C4—131no—
364C23×C4—132no—
365C23×C4—131no—
366C23×C4—131no—
367C23×C4—134no—
368C23×C4—132no—
369C23×C4—262no—
370C23×C4—262no—
371C23×C4—522no—
372C23×C4—522no—
373C23×C4C22×D1312yes—
374C23×C4C22×D1312yes—
375C23×C4C22×D1311yescharacteristic
376C23×C4C22×D1311yescharacteristic
377C23×C4C22×D1311yescharacteristic
378C2×C4⋊C4—262no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—522no—
381C2×C4⋊C4—522no—
382C2×C4⋊C4—522no—
383C2×C22⋊C4—134no—
384C2×C22⋊C4—138no—
385C2×C22⋊C4—262no—
386C2×C22⋊C4—262no—
387C2×C22⋊C4—262no—
388C2×C22⋊C4—262no—
389C2×C22⋊C4—262no—
390C2×C22⋊C4—264no—
391C2×C22⋊C4—522no—
392C2×C22⋊C4—522no—
393C2×C22⋊C4—522no—
394C2×C22⋊C4—522no—
395C2×C42—134no—
396C2×C42—262no—
397C2×C42—522no—
398C2×C42—522no—
399#95—22no—
400#95—22no—
401#95—42no—
402#95—42no—
403#95—138no—
404#95—134no—
405#95—264no—
406#95—262no—
407#95—264no—
408#95—264no—
409#95—522no—
410#95—522no—
411#95—522no—
412C2×C13C4×C22⋊Q811yescharacteristic
413C2×C13#232111yescharacteristic
414C2×C13#232611yescharacteristic
415C2×C13#232912yes—
416C2×C13#233712yes—
417C2×C13#262611yescharacteristic
418C2×C13#262811yescharacteristic
419C2×C13#263111yescharacteristic
420C2×C13#263811yescharacteristic
421C2×C13#265312yes—
422C2×C13#266512yes—
423D13—44no—
424C24—132no—
425C24—132no—
426C24—132no—
427C24—261no—
428C24—261no—
429C24—262no—
430C24—262no—
431C24—261no—
432C24—262no—
433C24—261no—
434C24—262no—
435C24C23×D1311yescharacteristic
436C2×Q8—28no—
437C2×Q8—48no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—48no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—132no—
465C22×C4—132no—
466C22×C4—132no—
467C22×C4—132no—
468C22×C4—134no—
469C22×C4—132no—
470C22×C4—268no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—261no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—261no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—528no—
495C22×C4—524no—
496C22×C4—524no—
497C22×C4—528no—
498C22×C4C2×C4×D1314yes—
499C22×C4C2×C4×D1312yes—
500C22×C4D4×D1312yes—
501C22×C4#612912yes—
502C22×C4Q8×D1312yes—
503C22×C4#613112yes—
504C4⋊C4—528no—
505C4⋊C4—524no—
506C22⋊C4—268no—
507C22⋊C4—268no—
508C22⋊C4—528no—
509C22⋊C4—528no—
510C42—524no—
511C42—524no—
512C13#1431911yescharacteristic, complemented, Sylow
513C23—134no—
514C23—262no—
515C23—264no—
516C23—262no—
517C23—264no—
518C23—262no—
519C23—264no—
520C23—262no—
521C23—262no—
522C23—264no—
523C23—264no—
524C23—264no—
525C23—262no—
526C23—521no—
527C23—522no—
528C23—521no—
529C23—521no—
530C23—522no—
531C23—522no—
532C23—522no—
533C23—522no—
534C23—521no—
535C23—522no—
536C23C22×C4×D1311yescharacteristic
537C23C2×D4×D1311yescharacteristic
538C23C2×#612911yescharacteristic
539C23#8825112yes—
540C23#8825112yes—
541C23C2×Q8×D1311yescharacteristic
542C23C2×#613111yescharacteristic
543C23#8825412yes—
544C23#41×D1311yescharacteristic
545C23#41×D1311yescharacteristic
546C23#8825612yes—
547Q8—416no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—134no—
577C2×C4—262no—
578C2×C4—264no—
579C2×C4—262no—
580C2×C4—264no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—264no—
587C2×C4—262no—
588C2×C4—262no—
589C2×C4—5216no—
590C2×C4—521no—
591C2×C4—522no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—521no—
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#8813514yes—
607C22—268no—
608C22—264no—
609C22—522no—
610C22—522no—
611C22—522no—
612C22—524no—
613C22—522no—
614C22—522no—
615C22—524no—
616C22—524no—
617C22—522no—
618C22C2×#8813511yescharacteristic
619C22#1171919112yes—
620C22C4×Q8×D1311yescharacteristic
621C22C4×#613111yescharacteristic
622C22#1171927912yes—
623C22#1171929411yescharacteristic
624C22#1171929711yescharacteristic
625C22#1171929812yes—
626C22D13×C22⋊Q811yescharacteristic
627C22#1171933211yescharacteristic
628C22#1171933912yes—
629C22#1171934312yes—
630C22#1171934512yes—
631C22#1171934812yes—
632C22#1171934912yes—
633C22#1171937911yescharacteristic
634C22#1171938312yes—
635C22#1171938312yes—
636C22#1171938511yescharacteristic
637C22#1171942911yescharacteristic
638C22#1171943311yescharacteristic
639C22#1171943412yes—
640C22#1171943812yes—
641C4—24no—
642C4—44no—
643C4—42no—
644C4—42no—
645C4—82no—
646C4—264no—
647C4—522no—
648C4—524no—
649C4—522no—
650C4—1042no—
651C2—524no—
652C2#1311737411yescharacteristic
653C2#1311749111yescharacteristic
654C2#1311755011yescharacteristic
655C2#1311756812yes—
656C2#1311764812yes—
657C2#1312064011yescharacteristic
658C2#1312065911yescharacteristic
659C2#1312069411yescharacteristic
660C2#1312076211yescharacteristic
661C2#1312089612yes—
662C2#1312101112yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1446C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1446D13
hypocenterC13#14319
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
2. C2×#11718891C2semidirect
4. #13113100C2semidirect
5. #13113097C2semidirect
8. #13113071C2semidirect
9. #13113061C2semidirect
11. C13×#1446C2semidirect
26. #11718892C4semidirect
43. C22×Q8×C13C2×C4semidirect
58. C22×C4×D13Q8semidirect
91. #88071C2×C4semidirect
92. #88071C2×C4semidirect
185. #1446D13semidirect
362. C22×Q8C4×D13semidirect
512. C13#14319semidirect

Maximal subgroups

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

subgroupindex
C2×#117188922
C2×#117188912
C2×#117183272
#131131002
#131130972
#131130822
#131130802
#131130712
#131130612
#131130572
C13×#14462
#1431913