Finite Group Databasebeta

← #15768394

Subgroups — #15768394

Order 3328.

1230 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88161C211yesmaximal, characteristic
2C2×#11718794C211yesmaximal, characteristic
3C2×#11718627C211yesmaximal, characteristic
4C2×#11718146C211yesmaximal, characteristic, complemented
5C2×#11718150C211yesmaximal, characteristic, complemented
6C2×#11718121C211yesmaximal, characteristic, complemented
7C2×C13×#343C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic13C2211yescharacteristic
13C22×#6099C2211yescharacteristic
14C23×#1055C2211yescharacteristic
15C2×#88161—22no—
16C2×#88161—22no—
17C2×#88161—22no—
18C2×#88161—22no—
19C2×#88161—22no—
20C2×#88161C414yescomplemented
21C22×#6094—21no—
22C22×C8×D13—21no—
23#11718794—22no—
24#11718794C414yescomplemented
25C2×#88061—21no—
26C2×#88056—21no—
27C2×#88050—21no—
28#11718627—22no—
29#11718627C414yescomplemented
30C2×#88049—21no—
31C13×#343—22no—
32#11718150—22no—
33#11718146—22no—
34#11718121—21no—
35#11718121—21no—
36C23×C4×C13—21no—
37C23×C4×C13C2311yescharacteristic
38C22×C22⋊D13—21no—
39C23×Dic13—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127—21no—
45C2×#6127—21no—
46C2×#6127C2×C412yes—
47C2×#6127C2×C412yes—
48C2×#6127C2×C412yes—
49C2×#6127D412yes—
50C2×#6127D412yes—
51C2×#6127Q812yes—
52C22×D52D411yescharacteristic
53C22×C4×D13—21no—
54C22×Dic26D411yescharacteristic
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16—21no—
58C2×C13×M16—21no—
59C2×C13×M16—21no—
60C2×C13×M16—21no—
61C2×C13×M16—21no—
62C2×C13×M16—21no—
63C2×C13×M16C2×C412yes—
64C2×C13×M16C2×C412yes—
65C2×C13×M16D412yes—
66C2×C13×M16D412yes—
67C22×C8×C13—21no—
68C22×C8×C13—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4C2×C412yes—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13C2×C412yes—
81C2×#6099—21no—
82C2×#6099—21no—
83C2×#6099—21no—
84C2×#6099—21no—
85C2×#6099—21no—
86C2×#6099C2×C412yes—
87C22×#1055—21no—
88C22×#1055—21no—
89C22×#1055—21no—
90C22×#1055—21no—
91C22×#1055—21no—
92C22×#1055C2×C412yes—
93C22×#1055D412yes—
94C22×#1055D411yescharacteristic
95C22×#1055D411yescharacteristic
96#88161—28no—
97#88161—28no—
98#88161—28no—
99#88161—28no—
100C2×#6094—24no—
101C2×#6094—24no—
102C2×#6094—24no—
103C2×C8×D13—24no—
104C2×C8×D13—24no—
105C2×C8×D13—24no—
106#88061—24no—
107#88056—24no—
108#88050—24no—
109#88049—24no—
110#10774—131nomaximal, Sylow
111C24×C13#4111yescharacteristic
112C23×D13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—41no—
115C22×C4×C13—41no—
116C22×C4×C13—81no—
117C22×C4×C13—81no—
118C22×C4×C13C22×C411yescharacteristic
119C22×C4×C13C22×C411yescharacteristic
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×Q811yescharacteristic
129C22×C4×C13#4111yescharacteristic
130C22×C4×C13#4111yescharacteristic
131C22×C4×C13#4111yescharacteristic
132C2×C22⋊D13—22no—
133C2×C22⋊D13—22no—
134C2×C22⋊D13—22no—
135C2×C22⋊D13—22no—
136C2×C22⋊D13—22no—
137C2×C22⋊D13—22no—
138C22×Dic13—21no—
139C22×Dic13—22no—
140C22×Dic13—41no—
141C22×Dic13—41no—
142C22×Dic13—81no—
143C22×Dic13—81no—
144#6127—22no—
145#6127—22no—
146#6127—22no—
147#6127—22no—
148#6127—22no—
149#6127—22no—
150#6127—22no—
151#6127—22no—
152#6127—22no—
153#6127—22no—
154#6127—22no—
155#6127—22no—
156#6127C4214yes—
157#6127C22⋊C414yes—
158#6127C4⋊C414yes—
159#6127C4⋊C414yes—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52C22⋊C412yes—
164C2×D52C22⋊C412yes—
165C2×D52C4⋊C412yes—
166C2×C4×D13—22no—
167C2×C4×D13—22no—
168C2×C4×D13—22no—
169C2×C4×D13—22no—
170C2×C4×D13—22no—
171C2×C4×D13—22no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26C22⋊C412yes—
176C2×Dic26C22⋊C412yes—
177C2×Dic26C4⋊C412yes—
178C13×M16—22no—
179C13×M16—22no—
180C13×M16—22no—
181C13×M16—22no—
182C13×M16—22no—
183C13×M16—41no—
184C13×M16—41no—
185C13×M16C22⋊C414yes—
186C2×C8×C13—22no—
187C2×C8×C13—22no—
188C2×C8×C13—22no—
189C2×C8×C13—22no—
190C2×C8×C13—41no—
191C2×C8×C13—41no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—41no—
195C13×C4⋊C4—41no—
196C4⋊Dic13—22no—
197C4⋊Dic13—22no—
198C4⋊Dic13—41no—
199C4⋊Dic13—41no—
200#6099—22no—
201#6099—22no—
202#6099—41no—
203#6099—41no—
204C2×#1055—22no—
205C2×#1055—22no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—22no—
211C2×#1055—22no—
212C2×#1055—22no—
213C2×#1055—41no—
214C2×#1055—41no—
215C2×#1055C22⋊C412yes—
216C2×#1055C22⋊C412yes—
217#6094—216no—
218C8×D13—216no—
219C22×#131—131no—
220C2×#417—131no—
221C2×#417—131no—
222C2×#343—131no—
223C2×#343D1311yescharacteristic, complemented
224C2×#341—131no—
225C2×#340—131no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13#11711yescharacteristic
231C23×C13C4×D411yescharacteristic
232C23×C13C4×D411yescharacteristic
233C23×C13#12111yescharacteristic
234C23×C13C22⋊Q811yescharacteristic
235C23×C13#12311yescharacteristic
236C23×C13#12311yescharacteristic
237C22×D13—22no—
238C22×D13—22no—
239C22×D13—22no—
240C22×D13—41no—
241C22×D13—41no—
242C22×D13—41no—
243C22×D13—41no—
244C2×C4×C13—42no—
245C2×C4×C13—82no—
246C2×C4×C13—81no—
247C2×C4×C13—81no—
248C2×C4×C13—82no—
249C2×C4×C13C2×C4211yescharacteristic
250C2×C4×C13C2×C22⋊C411yescharacteristic
251C2×C4×C13C2×C22⋊C411yescharacteristic
252C2×C4×C13C2×C22⋊C411yescharacteristic
253C2×C4×C13C2×C22⋊C411yescharacteristic
254C2×C4×C13C2×C22⋊C411yescharacteristic
255C2×C4×C13C2×C4⋊C411yescharacteristic
256C2×C4×C13C2×C4⋊C411yescharacteristic
257C2×C4×C13C2×C4⋊C411yescharacteristic
258C2×C4×C13#11711yescharacteristic
259C2×C4×C13C4×D411yescharacteristic
260C2×C4×C13C4×D411yescharacteristic
261C2×C4×C13C4×D411yescharacteristic
262C2×C4×C13C4×D411yescharacteristic
263C2×C4×C13C4×D411yescharacteristic
264C2×C4×C13C4×D411yescharacteristic
265C2×C4×C13#12011yescharacteristic
266C2×C4×C13#12011yescharacteristic
267C2×C4×C13#12011yescharacteristic
268C2×C4×C13#12011yescharacteristic
269C2×C4×C13#12111yescharacteristic
270C2×C4×C13#12111yescharacteristic
271C2×C4×C13#12111yescharacteristic
272C2×C4×C13C22⋊Q811yescharacteristic
273C2×C4×C13C22⋊Q811yescharacteristic
274C2×C4×C13C22⋊Q811yescharacteristic
275C2×C4×C13#12311yescharacteristic
276C2×C4×C13#12311yescharacteristic
277C22⋊D13—24no—
278C22⋊D13—24no—
279C22⋊D13—24no—
280C22⋊D13—24no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—22no—
284C2×Dic13—42no—
285C2×Dic13—82no—
286C2×Dic13—81no—
287C2×Dic13—81no—
288C2×Dic13—82no—
289D52—22no—
290D52—22no—
291D52—22no—
292D52#9514yes—
293C4×D13—24no—
294C4×D13—24no—
295C4×D13—24no—
296C4×D13—24no—
297Dic26—22no—
298Dic26—22no—
299Dic26—22no—
300Dic26#9514yes—
301C8×C13—24no—
302C8×C13—42no—
303#1055—22no—
304#1055—22no—
305#1055—42no—
306C22×#41—131no—
307C2×#131—134no—
308C2×#131—262no—
309C2×#131—262no—
310C2×#131—262no—
311C2×#131—262no—
312C2×#131—262no—
313C22×M16—131no—
314C22×M16—261no—
315C22×M16C2×D1311yescharacteristic
316C22×M16C2×D1311yescharacteristic
317C23×C8—131no—
318C23×C8—261no—
319C22×C4⋊C4—131no—
320C22×C4⋊C4C2×D1311yescharacteristic
321#417—134no—
322#417—134no—
323#417—262no—
324#417—262no—
325C2×#103—261no—
326C2×#103—261no—
327C2×#102—261no—
328C2×#102—261no—
329#343—22no—
330#343—262no—
331#341—262no—
332#340—261no—
333#340—261no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—21no—
341C22×C13—21no—
342C22×C13—21no—
343C22×C13—21no—
344C22×C13—21no—
345C22×C13—21no—
346C22×C13C4×C22⋊C411yescharacteristic
347C22×C13#38011yescharacteristic
348C22×C13#38111yescharacteristic
349C22×C13#38511yescharacteristic
350C22×C13#38511yescharacteristic
351C22×C13#38611yescharacteristic
352C22×C13#38611yescharacteristic
353C22×C13#47111yescharacteristic
354C22×C13#47111yescharacteristic
355C22×C13#47211yescharacteristic
356C22×C13#47311yescharacteristic
357C2×D13—24no—
358C2×D13—42no—
359C2×D13—42no—
360C2×D13—42no—
361C2×D13—42no—
362C2×D13—42no—
363C2×D13—42no—
364C4×C13—82no—
365C4×C13C2×#9511yescharacteristic
366C4×C13C4×C22⋊C411yescharacteristic
367C4×C13#37911yescharacteristic
368C4×C13#38011yescharacteristic
369C4×C13#38511yescharacteristic
370C4×C13#38511yescharacteristic
371C4×C13#38611yescharacteristic
372C4×C13#38611yescharacteristic
373Dic13—24no—
374Dic13—82no—
375C2×#41—132no—
376C2×#41—132no—
377C2×#41—132no—
378C2×#41—132no—
379C2×#41—132no—
380C2×#41—132no—
381C2×#41—261no—
382C2×#41—261no—
383C2×#41—261no—
384C2×#41—261no—
385C2×#41—261no—
386C2×#41—261no—
387C22×Q8—131no—
388C22×D4—131no—
389C22×D4—261no—
390C23×C4—21no—
391C23×C4—261no—
392C23×C4—261no—
393C23×C4C22×D1311yescharacteristic
394#131—268no—
395#131—268no—
396#131—268no—
397#131—268no—
398C2×M16—21no—
399C2×M16—21no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—21no—
404C2×M16—21no—
405C2×M16—21no—
406C2×M16—132no—
407C2×M16—264no—
408C2×M16—264no—
409C2×M16—264no—
410C2×M16—261no—
411C2×M16—261no—
412C2×M16—261no—
413C2×M16—261no—
414C2×M16—261no—
415C2×M16C4×D1312yes—
416C2×M16C4×D1312yes—
417C2×M16D5212yes—
418C2×M16C22⋊D1312yes—
419C22×C8—21no—
420C22×C8—21no—
421C22×C8—132no—
422C22×C8—131no—
423C22×C8—131no—
424C22×C8—132no—
425C22×C8—264no—
426C22×C8—264no—
427C22×C8—264no—
428C22×C8—261no—
429C22×C8—261no—
430C22×C8—261no—
431C22×C8—261no—
432C22×C8—261no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—132no—
439C2×C4⋊C4—261no—
440C2×C4⋊C4—261no—
441C2×C4⋊C4—261no—
442C2×C4⋊C4—261no—
443C2×C4⋊C4—261no—
444C2×C4⋊C4C4×D1312yes—
445#103—264no—
446#103—264no—
447#102—264no—
448#102—264no—
449C2×C13—21no—
450C2×C13—21no—
451C2×C13—21no—
452C2×C13—21no—
453C2×C13C22⋊#9511yescharacteristic
454C2×C13#181511yescharacteristic
455C2×C13#181611yescharacteristic
456C2×C13#190711yescharacteristic
457C2×C13#190711yescharacteristic
458C2×C13#190811yescharacteristic
459C2×C13#190811yescharacteristic
460D13—44no—
461C24—261no—
462C24#612711yescharacteristic
463#41—134no—
464#41—134no—
465#41—134no—
466#41—134no—
467#41—262no—
468#41—262no—
469#41—262no—
470#41—262no—
471#41—262no—
472#41—262no—
473#41—262no—
474#41—262no—
475#41—262no—
476#41—262no—
477#41—262no—
478#41—262no—
479C2×Q8—132no—
480C2×Q8—132no—
481C2×Q8—132no—
482C2×Q8—261no—
483C2×Q8—261no—
484C2×Q8—261no—
485C2×D4—132no—
486C2×D4—132no—
487C2×D4—132no—
488C2×D4—262no—
489C2×D4—262no—
490C2×D4—262no—
491C2×D4—262no—
492C2×D4—262no—
493C2×D4—262no—
494C2×D4—261no—
495C2×D4—261no—
496C2×D4—261no—
497C22×C4—22no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—261no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—262no—
509C22×C4—262no—
510C22×C4—521no—
511C22×C4—521no—
512C22×C4—1041no—
513C22×C4—1041no—
514C22×C4C2×C4×D1311yescharacteristic
515C22×C4C2×C4×D1311yescharacteristic
516C22×C4C2×C4×D1311yescharacteristic
517C22×C4C2×D5211yescharacteristic
518C22×C4#612711yescharacteristic
519C22×C4D4×D1311yescharacteristic
520C22×C4D4×D1311yescharacteristic
521C22×C4D4×D1311yescharacteristic
522C22×C4D4×D1311yescharacteristic
523C22×C4D4×D1311yescharacteristic
524C22×C4#612911yescharacteristic
525C22×C4Q8×D1311yescharacteristic
526C22×C4#613111yescharacteristic
527C22×C4C2×C22⋊D1311yescharacteristic
528M16—22no—
529M16—22no—
530M16—22no—
531M16—22no—
532M16—22no—
533M16—41no—
534M16—41no—
535M16—2616no—
536M16—262no—
537M16—262no—
538M16—521no—
539M16—521no—
540M16#610314yes—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—132no—
548C2×C8—132no—
549C2×C8—2616no—
550C2×C8—262no—
551C2×C8—261no—
552C2×C8—261no—
553C2×C8—262no—
554C2×C8—262no—
555C2×C8—261no—
556C2×C8—261no—
557C2×C8—262no—
558C2×C8—262no—
559C2×C8—521no—
560C2×C8—521no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—262no—
566C4⋊C4—262no—
567C4⋊C4—521no—
568C4⋊C4—521no—
569C13#1077411yescharacteristic, complemented, Sylow
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—262no—
575C23—262no—
576C23—262no—
577C23—521no—
578C23—521no—
579C23—521no—
580C23—521no—
581C23#8812611yescharacteristic
582C23C4×D5211yescharacteristic
583C23#8813711yescharacteristic
584C23#8813811yescharacteristic
585C23#8814811yescharacteristic
586C23#8815011yescharacteristic
587C23C4×C22⋊D1311yescharacteristic
588Q8—134no—
589Q8—262no—
590Q8—262no—
591Q8—262no—
592D4—134no—
593D4—264no—
594D4—264no—
595D4—264no—
596D4—264no—
597D4—262no—
598D4—262no—
599D4—262no—
600C2×C4—42no—
601C2×C4—82no—
602C2×C4—81no—
603C2×C4—81no—
604C2×C4—82no—
605C2×C4—262no—
606C2×C4—262no—
607C2×C4—262no—
608C2×C4—264no—
609C2×C4—264no—
610C2×C4—264no—
611C2×C4—264no—
612C2×C4—522no—
613C2×C4—1042no—
614C2×C4—1041no—
615C2×C4—1041no—
616C2×C4—1042no—
617C2×C4C42×D1311yescharacteristic
618C2×C4C4×D5211yescharacteristic
619C2×C4C22⋊C4×D1311yescharacteristic
620C2×C4C22⋊C4×D1311yescharacteristic
621C2×C4C22⋊C4×D1311yescharacteristic
622C2×C4C22⋊C4×D1311yescharacteristic
623C2×C4#8813511yescharacteristic
624C2×C4#8813511yescharacteristic
625C2×C4#8813611yescharacteristic
626C2×C4#8813611yescharacteristic
627C2×C4#8813711yescharacteristic
628C2×C4#8813811yescharacteristic
629C2×C4C4⋊C4×D1311yescharacteristic
630C2×C4C4⋊C4×D1311yescharacteristic
631C2×C4C4⋊C4×D1311yescharacteristic
632C2×C4#8814611yescharacteristic
633C2×C4#8814711yescharacteristic
634C2×C4#8814711yescharacteristic
635C2×C4#8814811yescharacteristic
636C2×C4#8814911yescharacteristic
637C2×C4#8815011yescharacteristic
638C2×C4#8815111yescharacteristic
639C2×C4C2×#610311yescharacteristic
640C2×C4C4×C22⋊D1311yescharacteristic
641C2×C4#8819111yescharacteristic
642C2×C4#8819111yescharacteristic
643C2×C4#8819211yescharacteristic
644C2×C4#8820011yescharacteristic
645C8—24no—
646C8—42no—
647C8—262no—
648C8—262no—
649C8—522no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—264no—
663C22—522no—
664C22—522no—
665C22—522no—
666C22—522no—
667C22—522no—
668C22—522no—
669C22#1171832511yescharacteristic
670C22#1171832611yescharacteristic
671C22#1171832811yescharacteristic
672C22#1171832911yescharacteristic
673C22#1171840911yescharacteristic
674C22#1171841011yescharacteristic
675C22#1171841511yescharacteristic
676C22#1171841611yescharacteristic
677C22C4×#610311yescharacteristic
678C22#1171861711yescharacteristic
679C22#1171865011yescharacteristic
680C4—82no—
681C4—264no—
682C4—1042no—
683C4D13×#9511yescharacteristic
684C4#1171832611yescharacteristic
685C4#1171832711yescharacteristic
686C4#1171832911yescharacteristic
687C4#1171861611yescharacteristic
688C4#1171861711yescharacteristic
689C4#1171864811yescharacteristic
690C4#1171865011yescharacteristic
691C2—21no—
692C2—21no—
693C2—21no—
694C2—21no—
695C2—524no—
696C2#1311305711yescharacteristic
697C2#1311489411yescharacteristic
698C2#1311489911yescharacteristic
699C2#1311534111yescharacteristic
700C2#1311534511yescharacteristic
701C2#1311534811yescharacteristic
702C2#1311535211yescharacteristic
subgroupG/H
centerC23#88138
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#343C2
socleC23×C13#121
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×#343D13
hypocenterC13#10774
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. C2×#11718146C2semidirect
5. C2×#11718150C2semidirect
6. C2×#11718121C2semidirect
7. C2×C13×#343C2semidirect
20. C2×#88161C4semidirect
24. #11718794C4semidirect
29. #11718627C4semidirect
223. C2×#343D13semidirect
569. C13#10774semidirect

Maximal subgroups

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

subgroupindex
C22×#881612
C2×#117187942
C2×#117186272
C2×#117181462
C2×#117181502
C2×#117181212
C2×C13×#3432
#1077413