Finite Group Databasebeta

← #15784339

Subgroups — #15784339

Order 3328.

2182 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
1C22×#88126C211yesmaximal, characteristic
2C2×#11718328C211yesmaximal, characteristic
3C2×#11718310C212yesmaximal, complemented
4C2×#11718327C211yesmaximal, characteristic
5#13113072C212yesmaximal
6#13113072C212yesmaximal
7#13113064C212yesmaximal, complemented
8#13113061C211yesmaximal, characteristic, complemented
9C4×#88071C211yesmaximal, characteristic, complemented
10#95×Dic13C211yesmaximal, characteristic, complemented
11C13×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C22×#6103C2211yescharacteristic
15C22×#6103C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2212yes—
18C22×#6101C2212yes—
19C22×#6101C2211yescharacteristic
20C22×#6101C2211yescharacteristic
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2212yes—
25C2×#88126—28no—
26C2×#88126C418yescomplemented
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37#11718328C418yescomplemented
38#11718327C418yescomplemented
39#11718310—28no—
40C24×D13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C22×C4×D13—24no—
52C22×C4×D13—24no—
53C22×C4×D13C2×C414yes—
54C22×C4×D13C2×C414yes—
55C22×C4×D13C2×C414yes—
56C2×C42×C13—24no—
57C2×C42×C13C2×C414yes—
58C2×#6103—24no—
59C2×#6103—24no—
60C2×#6103—24no—
61C2×#6103—24no—
62C2×#6103—42no—
63C2×#6103—42no—
64C2×#6103C2×C414yes—
65C2×#6103C2×C414yes—
66C2×#6103C2×C418yes—
67C2×#6103C2×C418yes—
68C2×#6101—24no—
69C2×#6101—24no—
70C2×#6101—24no—
71C2×#6101C2×C414yes—
72C2×#6101C2×C418yes—
73C2×#6101C2×C414yes—
74C2×#6101D418yes—
75C2×C4×Dic13—24no—
76C2×C4×Dic13—24no—
77C2×C4×Dic13—24no—
78C2×C4×Dic13—24no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—42no—
83C2×C4×Dic13—42no—
84C2×C4×Dic13C2×C414yes—
85C2×C4×Dic13C2×C418yes—
86#88126—232no—
87C13×#95—24no—
88C13×#95—42no—
89C13×#95C2×C414yes—
90C13×#95C2×C414yes—
91#88071—24no—
92#88071—24no—
93#88071—24no—
94#88071—42no—
95#88071C2×C414yes—
96#88071C2×C414yes—
97#13801—131nomaximal, Sylow
98C24×C13C2411yescharacteristic
99C23×D13—22no—
100C23×D13—22no—
101C23×D13—22no—
102C23×D13—22no—
103C23×D13—21no—
104C23×D13—21no—
105C23×D13—21no—
106C23×D13—21no—
107C23×D13C22×C412yes—
108C23×D13C22×C412yes—
109C23×D13C22×C412yes—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
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×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13C22×C414yes—
132C22×C4×C13C22×C414yes—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C22×C412yes—
137C22×C4×C13C22×C412yes—
138C22×C4×C13C2×D414yes—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—21no—
144C22×Dic13—21no—
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×Dic13—22no—
155C22×Dic13—21no—
156C22×Dic13C22×C414yes—
157C22×Dic13C22×C412yes—
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C414yes—
160C22×Dic13C22×C412yes—
161C22×Dic13C22×C412yes—
162C22×Dic13C22×C412yes—
163C22×Dic13C2×D414yes—
164C22×Dic13C2×D414yes—
165C22×Dic13#4114yes—
166C22×Dic13#4114yes—
167C22×Dic13#4114yes—
168C2×C4×D13—28no—
169C2×C4×D13—28no—
170C2×C4×D13—216no—
171C2×C4×D13—216no—
172C2×C4×D13C42116yescomplemented
173C42×C13—28no—
174#6103—28no—
175#6103—28no—
176#6103—216no—
177#6103—48no—
178#6101—28no—
179#6101—216no—
180#6101C22⋊C4116yescomplemented
181C4×Dic13—28no—
182C4×Dic13—216no—
183C4×Dic13—48no—
184C4×Dic13—48no—
185C22×#117—131no—
186C2×#380—131no—
187C2×C4×C4⋊C4—132no—
188C2×C4×C22⋊C4—131no—
189#1437—132no—
190#1437—132no—
191C4⋊#95—132no—
192#1434—131no—
193#1434D1311yescharacteristic, complemented
194C4×#95—131no—
195C4×#95—131no—
196C23×C13C23×C411yescharacteristic
197C23×C13C23×C411yescharacteristic
198C23×C13C23×C411yescharacteristic
199C23×C13C22×D412yes—
200C23×C13C2×#4112yes—
201C23×C13C2×#4112yes—
202C23×C13C2×#4112yes—
203C23×C13H(5,𝔽2)11yescharacteristic
204C23×C13H(5,𝔽2)11yescharacteristic
205C23×C132−1+411yescharacteristic
206C23×C132−1+411yescharacteristic
207C22×D13—22no—
208C22×D13—24no—
209C22×D13—22no—
210C22×D13—24no—
211C22×D13—24no—
212C22×D13—22no—
213C22×D13—22no—
214C22×D13—24no—
215C22×D13—22no—
216C22×D13—22no—
217C22×D13—22no—
218C22×D13—22no—
219C22×D13—22no—
220C22×D13—22no—
221C22×D13—42no—
222C22×D13—42no—
223C22×D13—42no—
224C22×D13—42no—
225C22×D13—42no—
226C22×D13—42no—
227C22×D13—42no—
228C22×D13—42no—
229C22×D13C2×C4214yes—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—22no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
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×C4214yes—
258C2×C4×C13C2×C22⋊C414yes—
259C2×Dic13—24no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—22no—
270C2×Dic13—24no—
271C2×Dic13—22no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—22no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13C2×C4214yes—
282C2×Dic13C2×C22⋊C414yes—
283C2×Dic13C2×C22⋊C414yes—
284C2×Dic13#11714yes—
285C2×Dic13#11718yescomplemented
286C2×Dic13C4×D418yes—
287C2×Dic13C4×D418yes—
288C4×D13—232no—
289C24×C4—131no—
290C2×#117—138no—
291C2×#117—268no—
292C22×C4⋊C4—131no—
293C22×C4⋊C4—131no—
294C22×C4⋊C4—132no—
295C22×C22⋊C4—131no—
296C22×C22⋊C4—131no—
297C22×C22⋊C4—132no—
298C22×C22⋊C4—132no—
299C22×C42—131no—
300C22×C42—132no—
301C22×C42—132no—
302C22×C42—132no—
303C22×C42C2×D1311yescharacteristic
304#380—138no—
305C4×C4⋊C4—268no—
306C4×C22⋊C4—138no—
307C2×#95—131no—
308C2×#95—131no—
309C2×#95—132no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95—132no—
313C2×#95C2×D1312yes—
314C2×#95C2×D1312yes—
315C2×#95C2×D1311yescharacteristic
316C2×#95C2×D1311yescharacteristic
317C22×C13C22×C4211yescharacteristic
318C22×C13C22×C22⋊C411yescharacteristic
319C22×C13C2×#11711yescharacteristic
320C22×C13C2×#11712yes—
321C22×C13C2×C4×D412yes—
322C22×C13C2×C4×D412yes—
323C22×C13C4×#4111yescharacteristic
324C22×C13C4×#4111yescharacteristic
325C22×C13C4×#4112yes—
326C22×C13#51811yescharacteristic
327C22×C13#51911yescharacteristic
328C22×C13#52011yescharacteristic
329C22×C13#52011yescharacteristic
330C22×C13#52011yescharacteristic
331C22×C13#52011yescharacteristic
332C22×C13#54612yes—
333C22×C13#54712yes—
334C22×C13#54812yes—
335C22×C13#55012yes—
336C22×C13#55212yes—
337C22×C13#55312yes—
338C22×C13#55512yes—
339C22×C13#55612yes—
340C2×D13—24no—
341C2×D13—24no—
342C2×D13—24no—
343C2×D13—42no—
344C2×D13—42no—
345C2×D13—42no—
346C2×D13—42no—
347C2×D13—44no—
348C2×D13—44no—
349C2×D13—44no—
350C2×D13—44no—
351C4×C13—24no—
352C4×C13—24no—
353C4×C13—42no—
354C4×C13—44no—
355C4×C13—44no—
356Dic13—24no—
357Dic13—28no—
358Dic13—42no—
359Dic13—44no—
360Dic13C4×C22⋊C418yes—
361C25—131no—
362C23×C4—131no—
363C23×C4—131no—
364C23×C4—132no—
365C23×C4—134no—
366C23×C4—134no—
367C23×C4—134no—
368C23×C4—132no—
369C23×C4—131no—
370C23×C4—264no—
371C23×C4—264no—
372C23×C4C22×D1311yescharacteristic
373C23×C4C22×D1312yes—
374C23×C4C22×D1312yes—
375C23×C4C22×D1311yescharacteristic
376C23×C4C22×D1311yescharacteristic
377#117—2632no—
378C2×C4⋊C4—134no—
379C2×C4⋊C4—138no—
380C2×C4⋊C4—134no—
381C2×C4⋊C4—138no—
382C2×C4⋊C4—264no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4—264no—
385C2×C22⋊C4—134no—
386C2×C22⋊C4—134no—
387C2×C22⋊C4—138no—
388C2×C22⋊C4—138no—
389C2×C22⋊C4—264no—
390C2×C22⋊C4—264no—
391C2×C22⋊C4—264no—
392C2×C22⋊C4—264no—
393C2×C22⋊C4—522no—
394C2×C22⋊C4—522no—
395C2×C42—24no—
396C2×C42—134no—
397C2×C42—138no—
398C2×C42—264no—
399C2×C42—264no—
400C2×C42—264no—
401C2×C42—264no—
402C2×C42—264no—
403C2×C42—264no—
404C2×C42—264no—
405C2×C42—522no—
406C2×C42—522no—
407C2×C42C4×D1314yes—
408#95—24no—
409#95—42no—
410#95—134no—
411#95—134no—
412#95—264no—
413#95—264no—
414#95—264no—
415#95—522no—
416#95C4×D1314yes—
417#95C4×D1314yes—
418C2×C13C2×C4×C22⋊C411yescharacteristic
419C2×C13C4×#11711yescharacteristic
420C2×C13#227411yescharacteristic
421C2×C13#233911yescharacteristic
422C2×C13#234111yescharacteristic
423C2×C13#234611yescharacteristic
424C2×C13#234711yescharacteristic
425C2×C13#235212yes—
426C2×C13#235412yes—
427C2×C13#236212yes—
428C2×C13#236312yes—
429D13—44no—
430C24—132no—
431C24—132no—
432C24—132no—
433C24—262no—
434C24—261no—
435C24—261no—
436C24—262no—
437C24—262no—
438C24—262no—
439C24—261no—
440C24—261no—
441C24C23×D1311yescharacteristic
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
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—132no—
464C22×C4—132no—
465C22×C4—132no—
466C22×C4—134no—
467C22×C4—134no—
468C22×C4—134no—
469C22×C4—132no—
470C22×C4—134no—
471C22×C4—134no—
472C22×C4—134no—
473C22×C4—1316no—
474C22×C4—134no—
475C22×C4—132no—
476C22×C4—268no—
477C22×C4—268no—
478C22×C4—2616no—
479C22×C4—2616no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—261no—
485C22×C4—262no—
486C22×C4—261no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—261no—
490C22×C4—262no—
491C22×C4—261no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4C2×C4×D1314yes—
498C22×C4C2×C4×D1314yes—
499C22×C4C2×C4×D1312yes—
500C22×C4C2×C4×D1312yes—
501C22×C4C2×C4×D1312yes—
502C22×C4C2×C4×D1312yes—
503C22×C4C2×C4×D1312yes—
504C22×C4D4×D1314yes—
505C4⋊C4—1316no—
506C4⋊C4—268no—
507C4⋊C4—2616no—
508C22⋊C4—268no—
509C22⋊C4—2616no—
510C22⋊C4—268no—
511C22⋊C4—528no—
512C42—28no—
513C42—268no—
514C42—2616no—
515C42—528no—
516C42—528no—
517C13#1380111yescharacteristic, complemented, Sylow
518C23—134no—
519C23—262no—
520C23—262no—
521C23—264no—
522C23—262no—
523C23—262no—
524C23—262no—
525C23—264no—
526C23—262no—
527C23—264no—
528C23—264no—
529C23—262no—
530C23—262no—
531C23—262no—
532C23—262no—
533C23—522no—
534C23—522no—
535C23—522no—
536C23—522no—
537C23—522no—
538C23—522no—
539C23—522no—
540C23—522no—
541C23C22×C4×D1311yescharacteristic
542C23C22×C4×D1311yescharacteristic
543C23C22×C4×D1311yescharacteristic
544C23C2×D4×D1312yes—
545C23#8825111yescharacteristic
546C23#8825411yescharacteristic
547C23#41×D1312yes—
548C23#41×D1312yes—
549C23#41×D1312yes—
550C23#8825611yescharacteristic
551C23#8825711yescharacteristic
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—42no—
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—42no—
579C2×C4—134no—
580C2×C4—134no—
581C2×C4—134no—
582C2×C4—138no—
583C2×C4—138no—
584C2×C4—134no—
585C2×C4—138no—
586C2×C4—2632no—
587C2×C4—262no—
588C2×C4—262no—
589C2×C4—264no—
590C2×C4—264no—
591C2×C4—264no—
592C2×C4—264no—
593C2×C4—264no—
594C2×C4—264no—
595C2×C4—264no—
596C2×C4—264no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—264no—
600C2×C4—262no—
601C2×C4—264no—
602C2×C4—264no—
603C2×C4—522no—
604C2×C4—522no—
605C2×C4—522no—
606C2×C4—522no—
607C2×C4—522no—
608C2×C4—522no—
609C2×C4C42×D1314yes—
610C2×C4C22⋊C4×D1314yes—
611C22—264no—
612C22—264no—
613C22—264no—
614C22—522no—
615C22—522no—
616C22—524no—
617C22—524no—
618C22—524no—
619C22—524no—
620C22—522no—
621C22—522no—
622C22C2×C42×D1311yescharacteristic
623C22C2×C22⋊C4×D1311yescharacteristic
624C22#1171920911yescharacteristic
625C22D13×#11711yescharacteristic
626C22D13×#11712yes—
627C22#1171922711yescharacteristic
628C22#1171922711yescharacteristic
629C22#1171922712yes—
630C22#1171922811yescharacteristic
631C22C4×D4×D1312yes—
632C22C4×D4×D1312yes—
633C22#1171925011yescharacteristic
634C22#1171925111yescharacteristic
635C22#1171927711yescharacteristic
636C22#1171927911yescharacteristic
637C22#1171930412yes—
638C22#1171933812yes—
639C22#1171935912yes—
640C22#1171936012yes—
641C22#1171937512yes—
642C22#1171939812yes—
643C22#1171940712yes—
644C22#1171941412yes—
645C4—24no—
646C4—24no—
647C4—44no—
648C4—44no—
649C4—42no—
650C4—138no—
651C4—268no—
652C4—264no—
653C4—524no—
654C4—522no—
655C2—524no—
656C2C4×C22⋊C4×D1311yescharacteristic
657C2#1311717511yescharacteristic
658C2#1311719011yescharacteristic
659C2#1311766011yescharacteristic
660C2#1311767311yescharacteristic
661C2#1311771611yescharacteristic
662C2#1311772411yescharacteristic
663C2#1311776012yes—
664C2#1311778212yes—
665C2#1311785812yes—
666C2#1311786912yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC13×#1434C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1434D13
hypocenterC13#13801
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#11718310C2semidirect
7. #13113064C2semidirect
8. #13113061C2semidirect
9. C4×#88071C2semidirect
10. #95×Dic13C2semidirect
11. C13×#1434C2semidirect
26. C2×#88126C4semidirect
37. #11718328C4semidirect
38. #11718327C4semidirect
172. C2×C4×D13C42semidirect
180. #6101C22⋊C4semidirect
193. #1434D13semidirect
285. C2×Dic13#117semidirect
517. C13#13801semidirect

Maximal subgroups

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

subgroupindex
C22×#881262
C2×#117183282
C2×#117183102
C2×#117183272
#131130722
#131130642
#131130612
C4×#880712
#95×Dic132
C13×#14342
#1380113