Finite Group Databasebeta

← #15785613

Subgroups — #15785613

Order 3328.

1862 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88180C211yesmaximal, characteristic
2C2×#11718311C211yesmaximal, characteristic, complemented
3C2×#11718309C211yesmaximal, characteristic, complemented
4#13113088C212yesmaximal, complemented
5#13113079C212yesmaximal
6#13113073C212yesmaximal
7#13113070C212yesmaximal, complemented
8#13113060C211yesmaximal, characteristic, complemented
9#13113060C211yesmaximal, characteristic, complemented
10#13113059C211yesmaximal, characteristic
11C13×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C22⋊C4C2212yes—
14C22×C22⋊Dic13C2212yes—
15C22×C22⋊Dic13C2211yescharacteristic
16C22×C22⋊Dic13C2211yescharacteristic
17C2×#88180—24no—
18C2×#88180—24no—
19C2×#88180C418yescomplemented
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6101C2212yes—
23C22×C4×Dic13C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C2×C13×#95C2212yes—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718311—24no—
39#11718309—24no—
40C25×C13C2311yescharacteristic
41C23×C4×C13—24no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—24no—
45C23×C4×C13C2×C414yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2312yes—
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2312yes—
54C23×Dic13C2311yescharacteristic
55C23×Dic13C2311yescharacteristic
56C2×C13×C22⋊C4—24no—
57C2×C13×C22⋊C4—24no—
58C2×C13×C22⋊C4—42no—
59C2×C22⋊Dic13—22no—
60C2×C22⋊Dic13—22no—
61C2×C22⋊Dic13—22no—
62C2×C22⋊Dic13—22no—
63C2×C22⋊Dic13—24no—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—42no—
66C2×C22⋊Dic13C2×C414yes—
67C2×C22⋊Dic13C2×C414yes—
68#88180—232no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—22no—
72C2×C4⋊Dic13—22no—
73C2×C4⋊Dic13C2×C414yes—
74C2×C4⋊Dic13C2×C414yes—
75C2×#6101—24no—
76C2×#6101—42no—
77C2×#6101—42no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13—22no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—24no—
83C2×C4×Dic13C2×C414yes—
84C2×C4×Dic13C2×C414yes—
85C2×C4×Dic13D414yes—
86C2×C4×Dic13D414yes—
87C13×#95—22no—
88C13×#95—22no—
89C13×#95—24no—
90#88071—22no—
91#88071—22no—
92#88071—24no—
93#88071—24no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—42no—
98#88071—42no—
99#13957—131nomaximal, Sylow
100C24×C13—21no—
101C24×C13—21no—
102C24×C13—22no—
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—21no—
106C24×C13—21no—
107C24×C13—21no—
108C24×C13—21no—
109C24×C13C22×C412yes—
110C24×C13#4114yes—
111C24×C13C2411yescharacteristic
112C22×C4×C13—216no—
113C22×C4×C13—216no—
114C22×C4×C13—28no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—28no—
121C22×C4×C13—28no—
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×C13—22no—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C22×C412yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2×D412yes—
139C22×C4×C13#4114yes—
140C22×C4×C13#4114yes—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—22no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13C22×C412yes—
171C22×Dic13C22×C412yes—
172C22×Dic13C22×C412yes—
173C22×Dic13C22×C412yes—
174C22×Dic13C2×D412yes—
175C22×Dic13C2×D412yes—
176C22×Dic13C2×D412yes—
177C22×Dic13C2×D412yes—
178C22×Dic13#4114yes—
179C13×C22⋊C4—48no—
180C22⋊Dic13—28no—
181C22⋊Dic13—28no—
182C22⋊Dic13—48no—
183C4⋊Dic13—28no—
184C4⋊Dic13—28no—
185#6101—48no—
186C4×Dic13—216no—
187C4×Dic13—28no—
188C4×Dic13C22⋊C4116yescomplemented
189C22×#117—131no—
190C2×#382—131no—
191C2×#376—131no—
192#1441—132no—
193#1439—132no—
194#1437—132no—
195#1436—132no—
196#1434—131no—
197#1434—131no—
198C22⋊#95—131no—
199C22⋊#95D1311yescharacteristic
200C23×C13—22no—
201C23×C13—22no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—22no—
205C23×C13—22no—
206C23×C13—24no—
207C23×C13—24no—
208C23×C13—24no—
209C23×C13—24no—
210C23×C13—24no—
211C23×C13—24no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—41no—
215C23×C13—41no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—42no—
222C23×C13#11714yes—
223C23×C13C23×C411yescharacteristic
224C23×C13C22×D411yescharacteristic
225C23×C13C22×D411yescharacteristic
226C23×C13C2×#4112yes—
227C23×C13C2×#4112yes—
228C23×C13C2×#4112yes—
229C23×C13C2×#4112yes—
230C23×C13H(5,𝔽2)11yescharacteristic
231C23×C13H(5,𝔽2)11yescharacteristic
232C23×C132−1+411yescharacteristic
233C23×C132−1+411yescharacteristic
234C2×C4×C13—232no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
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×C13—42no—
257C2×C4×C13C2×C22⋊C414yes—
258C2×C4×C13#11714yes—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—24no—
276C2×Dic13—24no—
277C2×Dic13—24no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—42no—
286C2×Dic13—42no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13C2×C22⋊C414yes—
296C2×Dic13C2×C22⋊C414yes—
297C24×C4C2×D1311yescharacteristic
298C2×#117—138no—
299C2×#117—264no—
300C2×#117—264no—
301C22×C4⋊C4—131no—
302C22×C4⋊C4—131no—
303C22×C4⋊C4—132no—
304C22×C22⋊C4—131no—
305C22×C22⋊C4—131no—
306C22×C22⋊C4—132no—
307C22×C22⋊C4C2×D1312yes—
308C22×C42—131no—
309C22×C42—131no—
310C22×C42—132no—
311#382—264no—
312#376—264no—
313C2×#95—131no—
314C2×#95—131no—
315C2×#95—132no—
316C2×#95—132no—
317C2×#95—132no—
318C2×#95—132no—
319C2×#95—132no—
320C2×#95—132no—
321C2×#95—132no—
322C2×#95C2×D1311yescharacteristic
323C2×#95C2×D1311yescharacteristic
324C2×#95C2×D1312yes—
325C22×C13—24no—
326C22×C13—24no—
327C22×C13—24no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—44no—
332C22×C13—44no—
333C22×C13—44no—
334C22×C13—44no—
335C22×C13—42no—
336C22×C13C22×C22⋊C411yescharacteristic
337C22×C13C2×#11711yescharacteristic
338C22×C13C2×#11711yescharacteristic
339C22×C13C4×#4111yescharacteristic
340C22×C13C4×#4111yescharacteristic
341C22×C13#52011yescharacteristic
342C22×C13#52011yescharacteristic
343C22×C13#52512yes—
344C22×C13#52512yes—
345C22×C13#52512yes—
346C22×C13#53212yes—
347C22×C13#53511yescharacteristic
348C22×C13#53611yescharacteristic
349C22×C13#53711yescharacteristic
350C22×C13#53711yescharacteristic
351C22×C13#55112yes—
352C22×C13#55112yes—
353C22×C13#55212yes—
354C22×C13#55212yes—
355C22×C13#55212yes—
356C22×C13#55212yes—
357C22×C13#55512yes—
358C22×C13#55512yes—
359C4×C13—24no—
360C4×C13—24no—
361C4×C13—44no—
362C4×C13—82no—
363Dic13—24no—
364Dic13—24no—
365Dic13—42no—
366Dic13—44no—
367Dic13—42no—
368Dic13—82no—
369C25C22×D1311yescharacteristic
370C23×C4—24no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—24no—
374C23×C4—131no—
375C23×C4—131no—
376C23×C4—131no—
377C23×C4—131no—
378C23×C4—132no—
379C23×C4—132no—
380C23×C4C4×D1314yes—
381C23×C4C22×D1312yes—
382C23×C4C22×D1312yes—
383C23×C4C22×D1311yescharacteristic
384C23×C4C22×D1311yescharacteristic
385#117—2632no—
386C2×C4⋊C4—134no—
387C2×C4⋊C4—134no—
388C2×C4⋊C4—262no—
389C2×C4⋊C4—262no—
390C2×C4⋊C4—262no—
391C2×C4⋊C4—262no—
392C2×C4⋊C4—264no—
393C2×C4⋊C4—522no—
394C2×C4⋊C4—522no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—134no—
399C2×C22⋊C4—134no—
400C2×C22⋊C4—262no—
401C2×C22⋊C4—262no—
402C2×C22⋊C4—262no—
403C2×C22⋊C4—262no—
404C2×C22⋊C4—264no—
405C2×C22⋊C4—264no—
406C2×C22⋊C4—522no—
407C2×C42—134no—
408C2×C42—134no—
409C2×C42—134no—
410C2×C42—134no—
411C2×C42—264no—
412C2×C42—264no—
413C2×C42—264no—
414C2×C42—262no—
415C2×C42—262no—
416#95—22no—
417#95—22no—
418#95—24no—
419#95—264no—
420#95—264no—
421#95—264no—
422#95—264no—
423#95—262no—
424#95—262no—
425#95—264no—
426#95—522no—
427#95—522no—
428C2×C13—44no—
429C2×C13#228011yescharacteristic
430C2×C13#229711yescharacteristic
431C2×C13#231111yescharacteristic
432C2×C13#234311yescharacteristic
433C2×C13#234311yescharacteristic
434C2×C13#234611yescharacteristic
435C2×C13#234611yescharacteristic
436C2×C13#260912yes—
437C2×C13#260912yes—
438C2×C13#261012yes—
439C2×C13#261112yes—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—21no—
449C24C2×C4×D1312yes—
450C24#612914yes—
451C24C23×D1311yescharacteristic
452C22×C4—216no—
453C22×C4—216no—
454C22×C4—28no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—132no—
476C22×C4—132no—
477C22×C4—132no—
478C22×C4—132no—
479C22×C4—132no—
480C22×C4—132no—
481C22×C4—132no—
482C22×C4—132no—
483C22×C4—134no—
484C22×C4—262no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—262no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—261no—
504C22×C4—262no—
505C22×C4—261no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—262no—
509C22×C4—262no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4C2×C4×D1312yes—
514C22×C4C2×C4×D1312yes—
515C22×C4#612714yes—
516C22×C4D4×D1312yes—
517C22×C4D4×D1312yes—
518C22×C4#612914yes—
519C4⋊C4—268no—
520C4⋊C4—268no—
521C4⋊C4—528no—
522C22⋊C4—48no—
523C22⋊C4—268no—
524C22⋊C4—268no—
525C22⋊C4—528no—
526C42—1316no—
527C42—2616no—
528C42—268no—
529C13#1395711yescharacteristic, complemented, Sylow
530C23—22no—
531C23—22no—
532C23—22no—
533C23—24no—
534C23—22no—
535C23—24no—
536C23—22no—
537C23—22no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—41no—
547C23—41no—
548C23—42no—
549C23—41no—
550C23—41no—
551C23—42no—
552C23#8813114yes—
553C23C22×C4×D1311yescharacteristic
554C23C2×#612712yes—
555C23C2×D4×D1311yescharacteristic
556C23C2×D4×D1311yescharacteristic
557C23C2×#612912yes—
558C23C2×#612912yes—
559C23#8825111yescharacteristic
560C23#8825411yescharacteristic
561C23#41×D1312yes—
562C23#8825611yescharacteristic
563C23#8825711yescharacteristic
564C2×C4—232no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—134no—
588C2×C4—134no—
589C2×C4—262no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—264no—
594C2×C4—264no—
595C2×C4—262no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—264no—
606C2×C4—264no—
607C2×C4—264no—
608C2×C4—522no—
609C2×C4—522no—
610C2×C4—522no—
611C2×C4—522no—
612C2×C4—522no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—522no—
617C2×C4—521no—
618C2×C4—522no—
619C2×C4—522no—
620C2×C4—522no—
621C2×C4—522no—
622C2×C4—522no—
623C2×C4—522no—
624C2×C4—522no—
625C2×C4#8813114yes—
626C2×C4C22⋊C4×D1314yes—
627C22—24no—
628C22—24no—
629C22—24no—
630C22—44no—
631C22—44no—
632C22—44no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—44no—
638C22C4×#612711yescharacteristic
639C22C2×#8813111yescharacteristic
640C22C2×#8813111yescharacteristic
641C22C2×C22⋊C4×D1311yescharacteristic
642C22#1171920012yes—
643C22#1171920911yescharacteristic
644C22#1171921812yes—
645C22#1171922711yescharacteristic
646C22#1171922811yescharacteristic
647C22#1171924612yes—
648C22#1171925212yes—
649C22#1171925312yes—
650C22#1171926812yes—
651C22#1171929112yes—
652C22#1171929112yes—
653C22#1171931211yescharacteristic
654C22#1171931311yescharacteristic
655C22#1171932112yes—
656C22#1171933311yescharacteristic
657C22#1171933411yescharacteristic
658C22#1171934412yes—
659C22#1171935512yes—
660C22#1171936312yes—
661C4—24no—
662C4—24no—
663C4—44no—
664C4—82no—
665C4—264no—
666C4—264no—
667C4—524no—
668C4—522no—
669C4—522no—
670C4—1042no—
671C2—44no—
672C2#1311721411yescharacteristic
673C2#1311732211yescharacteristic
674C2#1311742511yescharacteristic
675C2#1311769211yescharacteristic
676C2#1311769811yescharacteristic
677C2#1311771911yescharacteristic
678C2#1311772311yescharacteristic
679C2#1312051012yes—
680C2#1312051212yes—
681C2#1312051912yes—
682C2#1312053012yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#13957
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718311C2semidirect
3. C2×#11718309C2semidirect
4. #13113088C2semidirect
7. #13113070C2semidirect
8. #13113060C2semidirect
9. #13113060C2semidirect
19. C2×#88180C4semidirect
188. C4×Dic13C22⋊C4semidirect
529. C13#13957semidirect

Maximal subgroups

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

subgroupindex
C22×#881802
C2×#117183112
C2×#117183092
#131130882
#131130792
#131130732
#131130702
#131130602
#131130592
C13×C22⋊#952
#1395713