Finite Group Databasebeta

← #15784254

Subgroups — #15784254

Order 3328.

1710 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718601C212yesmaximal
2C2×C4×#6103C211yesmaximal, characteristic
3#13113072C212yesmaximal
4#13113067C212yesmaximal, complemented
5#13113064C211yesmaximal, characteristic, complemented
6#13113063C212yesmaximal, complemented
7#13113062C211yesmaximal, characteristic, complemented
8#13113057C211yesmaximal, characteristic
9#13113057C211yesmaximal, characteristic
10C4×#88071C211yesmaximal, characteristic, complemented
11C4×C13×#95C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C22×C42×C13C2212yes—
15C22×#6103C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2212yes—
18C22×#6103C2211yescharacteristic
19C22×#6101C2212yes—
20C22×C4×Dic13C2212yes—
21C22×C4×Dic13C2211yescharacteristic
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2211yescharacteristic
24C2×C13×#95C2212yes—
25C2×#88071C2211yescharacteristic
26C2×#88071C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35#11718601C4116yescomplemented
36C4×#6103C418yescomplemented
37C24×D13C2311yescharacteristic
38C23×C4×C13C2312yes—
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×Dic13C2312yes—
44C23×Dic13C2312yes—
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C22×C4×D13—22no—
49C22×C4×D13—22no—
50C22×C4×D13—42no—
51C22×C4×D13—42no—
52C22×C4×D13C2×C414yes—
53C2×C42×C13—42no—
54C2×C42×C13—42no—
55C2×C42×C13—42no—
56C2×C42×C13C2×C414yes—
57C2×C42×C13C2×C418yescomplemented
58C2×#6103—24no—
59C2×#6103—42no—
60C2×#6103—42no—
61C2×#6103—42no—
62C2×#6103—42no—
63C2×#6103C2×C414yes—
64C2×#6103C2×C418yes—
65C2×#6103C2×C418yes—
66C2×#6103C2×C414yes—
67C2×#6103C2×C418yes—
68C2×#6101—42no—
69C2×#6101—42no—
70C2×#6101C2×C418yescomplemented
71C2×C4×Dic13—24no—
72C2×C4×Dic13—42no—
73C2×C4×Dic13—42no—
74C2×C4×Dic13—42no—
75C2×C4×Dic13C2×C414yes—
76C13×#95—22no—
77C13×#95—22no—
78C13×#95—24no—
79#88071—22no—
80#88071—22no—
81#88071—42no—
82#88071—42no—
83#88071—42no—
84#88071—42no—
85#88071C2×C414yes—
86#88071C2×C414yes—
87#88071C2×C418yescomplemented
88#88071C2×C418yescomplemented
89#13788—131nomaximal, Sylow
90C24×C13C2411yescharacteristic
91C23×D13—22no—
92C23×D13—21no—
93C23×D13—21no—
94C23×D13—21no—
95C23×D13—21no—
96C23×D13—22no—
97C23×D13—22no—
98C23×D13—21no—
99C23×D13—21no—
100C23×D13C22×C414yes—
101C23×D13C22×C412yes—
102C22×C4×C13—21no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13C22×C414yes—
123C22×C4×C13C22×C414yes—
124C22×C4×C13C22×C412yes—
125C22×C4×C13C22×C414yes—
126C22×C4×C13C22×C412yes—
127C22×C4×C13C22×C412yes—
128C22×C4×C13#4112yes—
129C22×C4×C13#4112yes—
130C22×C4×C13#4114yes—
131C22×Dic13—22no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—21no—
153C22×Dic13—22no—
154C22×Dic13C22×C412yes—
155C22×Dic13C22×C412yes—
156C22×Dic13C22×C414yes—
157C22×Dic13C22×C414yes—
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C414yes—
160C2×C4×D13—28no—
161C2×C4×D13—44no—
162C2×C4×D13—44no—
163C2×C4×D13—48no—
164C2×C4×D13—48no—
165C42×C13—44no—
166C42×C13—48no—
167#6103—28no—
168#6103—48no—
169#6103—48no—
170#6103C42116yescomplemented
171#6101—48no—
172C4×Dic13—44no—
173C4×Dic13—48no—
174C2×#388—132no—
175C2×C4×C22⋊C4—131no—
176#1437—132no—
177#1436—132no—
178C4⋊#95—131no—
179#1434—132no—
180#1434—131no—
181C22⋊#95—131no—
182C22⋊#95—131no—
183C4×#95—131no—
184C4×#95D1311yescharacteristic, complemented
185C23×C13C23×C411yescharacteristic
186C23×C13C23×C412yes—
187C23×C13C2×#4111yescharacteristic
188C23×C13C2×#4111yescharacteristic
189C23×C13C2×#4112yes—
190C23×C13H(5,𝔽2)12yes—
191C23×C13H(5,𝔽2)12yes—
192C23×C13H(5,𝔽2)11yescharacteristic
193C23×C13H(5,𝔽2)11yescharacteristic
194C23×C132−1+411yescharacteristic
195C23×C132−1+411yescharacteristic
196C22×D13—22no—
197C22×D13—22no—
198C22×D13—24no—
199C22×D13—24no—
200C22×D13—24no—
201C22×D13—24no—
202C22×D13—22no—
203C22×D13—22no—
204C22×D13—22no—
205C22×D13—22no—
206C22×D13—24no—
207C22×D13—24no—
208C22×D13—42no—
209C22×D13—42no—
210C22×D13—42no—
211C22×D13—42no—
212C22×D13—41no—
213C22×D13—42no—
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—42no—
218C22×D13C2×C4214yes—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—24no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13C2×C4214yes—
246C2×C4×C13#11714yes—
247C2×C4×C13#11714yes—
248C2×Dic13—22no—
249C2×Dic13—24no—
250C2×Dic13—22no—
251C2×Dic13—24no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—22no—
257C2×Dic13—24no—
258C2×Dic13—24no—
259C2×Dic13—24no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—24no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13C2×C4214yes—
277C4×D13—416no—
278C24×C4—131no—
279C22×C4⋊C4—132no—
280C22×C22⋊C4—131no—
281C22×C22⋊C4—131no—
282C22×C22⋊C4—132no—
283C22×C22⋊C4—132no—
284C22×C42—131no—
285C22×C42—132no—
286C22×C42C2×D1311yescharacteristic
287C22×C42C2×D1312yes—
288#388—1316no—
289C4×C22⋊C4—138no—
290C2×#95—132no—
291C2×#95—131no—
292C2×#95—132no—
293C2×#95—131no—
294C2×#95—131no—
295C2×#95—131no—
296C2×#95—132no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95C2×D1311yescharacteristic
301C2×#95C2×D1311yescharacteristic
302C2×#95C2×D1312yes—
303C22×C13C22×C4211yescharacteristic
304C22×C13C2×#11711yescharacteristic
305C22×C13C2×#11711yescharacteristic
306C22×C13C4×#4112yes—
307C22×C13C4×#4112yes—
308C22×C13#51811yescharacteristic
309C22×C13#51812yes—
310C22×C13#51811yescharacteristic
311C22×C13#51812yes—
312C22×C13#52011yescharacteristic
313C22×C13#52012yes—
314C22×C13#52011yescharacteristic
315C22×C13#52012yes—
316C22×C13#53812yes—
317C22×C13#53812yes—
318C22×C13#53812yes—
319C22×C13#53912yes—
320C22×C13#54011yescharacteristic
321C22×C13#54012yes—
322C22×C13#54111yescharacteristic
323C22×C13#54211yescharacteristic
324C22×C13#54211yescharacteristic
325C22×C13#54212yes—
326C2×D13—24no—
327C2×D13—24no—
328C2×D13—24no—
329C2×D13—42no—
330C2×D13—42no—
331C2×D13—42no—
332C2×D13—42no—
333C2×D13—44no—
334C2×D13—44no—
335C2×D13—44no—
336C2×D13—44no—
337C4×C13—24no—
338C4×C13—24no—
339C4×C13—24no—
340C4×C13—44no—
341C4×C13—44no—
342Dic13—24no—
343Dic13—42no—
344Dic13—42no—
345Dic13—44no—
346Dic13—44no—
347C25—131no—
348C23×C4—131no—
349C23×C4—132no—
350C23×C4—132no—
351C23×C4—131no—
352C23×C4—131no—
353C23×C4—134no—
354C23×C4—262no—
355C23×C4—262no—
356C23×C4—522no—
357C23×C4—522no—
358C23×C4C22×D1312yes—
359C23×C4C22×D1312yes—
360C23×C4C22×D1311yescharacteristic
361C23×C4C22×D1311yescharacteristic
362C23×C4C22×D1311yescharacteristic
363C2×C4⋊C4—138no—
364C2×C4⋊C4—522no—
365C2×C4⋊C4—522no—
366C2×C22⋊C4—134no—
367C2×C22⋊C4—138no—
368C2×C22⋊C4—134no—
369C2×C22⋊C4—138no—
370C2×C22⋊C4—138no—
371C2×C22⋊C4—264no—
372C2×C22⋊C4—522no—
373C2×C22⋊C4—522no—
374C2×C22⋊C4—522no—
375C2×C22⋊C4—522no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—134no—
380C2×C42—264no—
381C2×C42—522no—
382C2×C42—522no—
383C2×C42—522no—
384C2×C42C4×D1314yes—
385C2×C42C4×D1318yescomplemented
386#95—22no—
387#95—22no—
388#95—24no—
389#95—134no—
390#95—134no—
391#95—138no—
392#95—138no—
393#95—262no—
394#95—262no—
395#95—522no—
396#95—522no—
397#95—522no—
398#95—522no—
399C2×C13C4×#11711yescharacteristic
400C2×C13#227511yescharacteristic
401C2×C13#227511yescharacteristic
402C2×C13#231211yescharacteristic
403C2×C13#231411yescharacteristic
404C2×C13#231811yescharacteristic
405C2×C13#231911yescharacteristic
406C2×C13#233312yes—
407C2×C13#233412yes—
408C2×C13#233512yes—
409C2×C13#233712yes—
410D13—44no—
411C24—134no—
412C24—132no—
413C24—262no—
414C24—261no—
415C24—261no—
416C24—261no—
417C24—262no—
418C24—261no—
419C24—261no—
420C24—262no—
421C24—261no—
422C24C23×D1311yescharacteristic
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—132no—
444C22×C4—134no—
445C22×C4—134no—
446C22×C4—132no—
447C22×C4—132no—
448C22×C4—134no—
449C22×C4—262no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—261no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—268no—
473C22×C4—524no—
474C22×C4—524no—
475C22×C4—528no—
476C22×C4—528no—
477C22×C4C2×C4×D1314yes—
478C22×C4C2×C4×D1314yes—
479C22×C4C2×C4×D1312yes—
480C22×C4C2×C4×D1314yes—
481C22×C4C2×C4×D1312yes—
482C22×C4C2×C4×D1312yes—
483C22×C4#612712yes—
484C22×C4#612712yes—
485C22×C4#612714yes—
486C4⋊C4—528no—
487C22⋊C4—1316no—
488C22⋊C4—268no—
489C22⋊C4—528no—
490C22⋊C4—528no—
491C42—44no—
492C42—48no—
493C42—524no—
494C42—528no—
495C13#1378811yescharacteristic, complemented, Sylow
496C23—134no—
497C23—262no—
498C23—262no—
499C23—264no—
500C23—264no—
501C23—264no—
502C23—262no—
503C23—262no—
504C23—264no—
505C23—264no—
506C23—262no—
507C23—262no—
508C23—264no—
509C23—522no—
510C23—522no—
511C23—522no—
512C23—521no—
513C23—521no—
514C23—522no—
515C23—522no—
516C23—521no—
517C23—522no—
518C23—521no—
519C23C22×C4×D1311yescharacteristic
520C23C22×C4×D1312yes—
521C23C2×#612711yescharacteristic
522C23C2×#612711yescharacteristic
523C23C2×#612712yes—
524C23#8825112yes—
525C23#8825111yescharacteristic
526C23#8825411yescharacteristic
527C23#8825612yes—
528C23#8825611yescharacteristic
529C23#8825711yescharacteristic
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—134no—
557C2×C4—262no—
558C2×C4—264no—
559C2×C4—262no—
560C2×C4—264no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—264no—
564C2×C4—264no—
565C2×C4—264no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—264no—
569C2×C4—262no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—262no—
573C2×C4—5216no—
574C2×C4—522no—
575C2×C4—522no—
576C2×C4—522no—
577C2×C4—522no—
578C2×C4—522no—
579C2×C4—522no—
580C2×C4—522no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4—522no—
586C2×C4C42×D1314yes—
587C2×C4#8812614yes—
588C2×C4#8812614yes—
589C22—264no—
590C22—264no—
591C22—264no—
592C22—522no—
593C22—522no—
594C22—522no—
595C22—524no—
596C22—524no—
597C22—524no—
598C22—524no—
599C22—522no—
600C22C2×C42×D1311yescharacteristic
601C22C2×#8812611yescharacteristic
602C22C2×#8812611yescharacteristic
603C22C4×#612712yes—
604C22C4×#612712yes—
605C22#1171919111yescharacteristic
606C22#1171919112yes—
607C22#1171920911yescharacteristic
608C22#1171920912yes—
609C22#1171922611yescharacteristic
610C22#1171922612yes—
611C22#1171922811yescharacteristic
612C22#1171922812yes—
613C22#1171926512yes—
614C22#1171926512yes—
615C22#1171926512yes—
616C22#1171926611yescharacteristic
617C22#1171926711yescharacteristic
618C22#1171926712yes—
619C22#1171926912yes—
620C22#1171928711yescharacteristic
621C22#1171928712yes—
622C22#1171928811yescharacteristic
623C4—24no—
624C4—24no—
625C4—24no—
626C4—44no—
627C4—44no—
628C4—264no—
629C4—522no—
630C4—524no—
631C4—524no—
632C4—522no—
633C2—524no—
634C2C4×#8812611yescharacteristic
635C2#1311719411yescharacteristic
636C2#1311719811yescharacteristic
637C2#1311743111yescharacteristic
638C2#1311744111yescharacteristic
639C2#1311746311yescharacteristic
640C2#1311747411yescharacteristic
641C2#1311760112yes—
642C2#1311761112yes—
643C2#1311762612yes—
644C2#1311764912yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC4×C13×#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4×#95D13
hypocenterC13#13788
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
4. #13113067C2semidirect
5. #13113064C2semidirect
6. #13113063C2semidirect
7. #13113062C2semidirect
10. C4×#88071C2semidirect
11. C4×C13×#95C2semidirect
35. #11718601C4semidirect
36. C4×#6103C4semidirect
57. C2×C42×C13C2×C4semidirect
70. C2×#6101C2×C4semidirect
87. #88071C2×C4semidirect
88. #88071C2×C4semidirect
170. #6103C42semidirect
184. C4×#95D13semidirect
385. C2×C42C4×D13semidirect
495. C13#13788semidirect

Maximal subgroups

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

subgroupindex
C2×#117186012
C2×C4×#61032
#131130722
#131130672
#131130642
#131130632
#131130622
#131130572
C4×#880712
C4×C13×#952
#1378813