Finite Group Databasebeta

← #15768383

Subgroups — #15768383

Order 3328.

1298 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718897C211yesmaximal, characteristic
2#13123355C211yesmaximal, characteristic
3C2×#11718125C211yesmaximal, characteristic, complemented
4#13114568C211yesmaximal, characteristic, complemented
5C2×#11718115C211yesmaximal, characteristic, complemented
6C2×#11718115C211yesmaximal, characteristic, complemented
7C2×C4×C13×#41C211yesmaximal, characteristic
8C22×C13×#41C2211yescharacteristic
9C4×C13×#41—22no—
10C4×C13×#41—22no—
11C4×C13×#41—22no—
12C4×C13×#41C414yescomplemented
13C2×C4×Q8×C13—21no—
14C2×C4×D4×C13—21no—
15C2×C4×D4×C13—22no—
16C2×C13×#117—21no—
17C2×C13×#117C2211yescharacteristic
18C22×C42×C13—21no—
19C22×C42×C13C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24#11718897—22no—
25#11718897C414yescomplemented
26C2×#88077—22no—
27#11718894—22no—
28#11718893C414yescomplemented
29#11718886—21no—
30#11718876—21no—
31#11718125—22no—
32#11718119—22no—
33#11718115—21no—
34#11718115—21no—
35#11718115—22no—
36C2×C13×#41—21no—
37C2×C13×#41—21no—
38C2×C13×#41—21no—
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—21no—
42C2×C13×#41C2×C412yes—
43C2×C13×#41C2×C412yes—
44C2×C13×#41C2×C412yes—
45C2×C13×#41D412yes—
46C2×C13×#41D412yes—
47C2×C13×#41Q812yes—
48C22×Q8×C13D411yescharacteristic
49C22×D4×C13—21no—
50C22×D4×C13D411yescharacteristic
51C23×C4×C13—21no—
52C23×C4×C13—22no—
53C23×C4×C13—21no—
54C23×C4×C13C2311yescharacteristic
55C4×Q8×C13—24no—
56C4×Q8×C13—24no—
57C4×D4×C13—28no—
58C4×D4×C13—24no—
59C4×D4×C13—24no—
60C4×D4×C13—28no—
61C13×#117—24no—
62C13×#117—21no—
63C13×#117—21no—
64C13×#117—24no—
65C13×#117C2×C412yes—
66C13×#117D412yes—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4D412yes—
71C2×C42×C13—22no—
72C2×C42×C13—24no—
73C2×C42×C13—21no—
74C2×C42×C13—21no—
75C2×C42×C13—21no—
76C2×C42×C13—21no—
77C2×C42×C13—24no—
78C2×C42×C13C2×C412yes—
79C2×C42×C13D411yescharacteristic
80C2×C42×C13D411yescharacteristic
81C2×C42×C13D412yes—
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84#88180—21no—
85#88180—21no—
86#88180—21no—
87#88180—21no—
88#88180—21no—
89#88180—21no—
90#88180—21no—
91#88180C2×C412yescomplemented
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2×C412yescomplemented
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×#6099—21no—
97C2×#6099—21no—
98C2×#6099—21no—
99C2×#6099—21no—
100C2×#6099—21no—
101C2×#6099—21no—
102C2×#6099—21no—
103C2×#6099—21no—
104C2×#6099—21no—
105C2×#6099—21no—
106C2×#6099C2×C412yescomplemented
107C2×#6099C2×C412yescomplemented
108C22×#1055—21no—
109C22×#1055—21no—
110#88077—28no—
111#88075—24no—
112#88072—24no—
113#10772—131nomaximal, Sylow
114C24×C13—21no—
115C24×C13C2×D411yescharacteristic
116C13×#41—22no—
117C13×#41—22no—
118C13×#41—22no—
119C13×#41—22no—
120C13×#41—22no—
121C13×#41—22no—
122C13×#41—22no—
123C13×#41—22no—
124C13×#41—22no—
125C13×#41—22no—
126C13×#41—22no—
127C13×#41—22no—
128C13×#41C4214yes—
129C13×#41C22⋊C414yes—
130C13×#41C4⋊C414yes—
131C13×#41C4⋊C414yes—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13C22⋊C412yes—
136C2×Q8×C13C22⋊C412yes—
137C2×Q8×C13C4⋊C412yes—
138C2×D4×C13—22no—
139C2×D4×C13—22no—
140C2×D4×C13—22no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—22no—
144C2×D4×C13—21no—
145C2×D4×C13—21no—
146C2×D4×C13—21no—
147C2×D4×C13C22⋊C412yes—
148C2×D4×C13C22⋊C412yes—
149C2×D4×C13C4⋊C412yes—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—28no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—21no—
162C22×C4×C13—22no—
163C22×C4×C13—44no—
164C22×C4×C13—48no—
165C22×C4×C13C22×C411yescharacteristic
166C22×C4×C13C22×C411yescharacteristic
167C22×C4×C13C22×C411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×Q811yescharacteristic
175C22×C4×C13#4111yescharacteristic
176C22×C4×C13#4111yescharacteristic
177C22×C4×C13#4111yescharacteristic
178C22×C4×C13#4111yescharacteristic
179C22×Dic13—22no—
180C22×Dic13—41no—
181C13×C4⋊C4—28no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C22⋊C4—28no—
185C13×C22⋊C4—22no—
186C13×C22⋊C4C22⋊C414yes—
187C42×C13—28no—
188C42×C13—22no—
189C42×C13—22no—
190C42×C13—21no—
191C42×C13—22no—
192C42×C13—21no—
193C42×C13—22no—
194C42×C13C22⋊C412yes—
195C42×C13C22⋊C412yes—
196C22⋊Dic13—22no—
197C22⋊Dic13—41no—
198C22⋊Dic13—41no—
199C22⋊Dic13—41no—
200C4⋊Dic13—22no—
201C4⋊Dic13—22no—
202C4⋊Dic13—22no—
203C4⋊Dic13—41no—
204C4×Dic13—22no—
205C4×Dic13—41no—
206C4×Dic13—41no—
207C4×Dic13—41no—
208#6099—22no—
209#6099—22no—
210#6099—22no—
211#6099—22no—
212#6099—41no—
213#6099—41no—
214#6099—41no—
215#6099—41no—
216C2×#1055—22no—
217C2×#1055—22no—
218C2×#1055—41no—
219C2×#1055—41no—
220C2×#1055—41no—
221C2×#1055—41no—
222C2×C4×#41D1311yescharacteristic
223C2×#421—131no—
224#2896—131no—
225C2×#344—131no—
226#1740—131no—
227C2×#339—131no—
228C2×#339—131no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—42no—
233C23×C13—44no—
234C23×C13C2×C22⋊C411yescharacteristic
235C23×C13C4×D411yescharacteristic
236C23×C13C4×D411yescharacteristic
237C23×C13#12011yescharacteristic
238C23×C13#12011yescharacteristic
239C23×C13#12111yescharacteristic
240C23×C13C22⋊Q811yescharacteristic
241Q8×C13—22no—
242Q8×C13—22no—
243Q8×C13—22no—
244Q8×C13#9514yes—
245D4×C13—24no—
246D4×C13—24no—
247D4×C13—24no—
248D4×C13—24no—
249D4×C13—22no—
250D4×C13—22no—
251D4×C13—22no—
252D4×C13#9514yes—
253C2×C4×C13—24no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—24no—
259C2×C4×C13—24no—
260C2×C4×C13—24no—
261C2×C4×C13—24no—
262C2×C4×C13—24no—
263C2×C4×C13—22no—
264C2×C4×C13—44no—
265C2×C4×C13—44no—
266C2×C4×C13—416no—
267C2×C4×C13—44no—
268C2×C4×C13—42no—
269C2×C4×C13C2×C4211yescharacteristic
270C2×C4×C13C2×C22⋊C411yescharacteristic
271C2×C4×C13C2×C22⋊C411yescharacteristic
272C2×C4×C13C2×C22⋊C411yescharacteristic
273C2×C4×C13C2×C22⋊C411yescharacteristic
274C2×C4×C13C2×C4⋊C411yescharacteristic
275C2×C4×C13C2×C4⋊C411yescharacteristic
276C2×C4×C13C2×C4⋊C411yescharacteristic
277C2×C4×C13#11711yescharacteristic
278C2×C4×C13#11711yescharacteristic
279C2×C4×C13C4×D411yescharacteristic
280C2×C4×C13C4×D411yescharacteristic
281C2×C4×C13C4×D411yescharacteristic
282C2×C4×C13C4×D411yescharacteristic
283C2×C4×C13C4×D411yescharacteristic
284C2×C4×C13C4×D411yescharacteristic
285C2×C4×C13#12011yescharacteristic
286C2×C4×C13#12011yescharacteristic
287C2×C4×C13#12111yescharacteristic
288C2×C4×C13#12111yescharacteristic
289C2×C4×C13#12111yescharacteristic
290C2×C4×C13C22⋊Q811yescharacteristic
291C2×C4×C13C22⋊Q811yescharacteristic
292C2×C4×C13C22⋊Q811yescharacteristic
293C2×C4×C13#12311yescharacteristic
294C2×C4×C13#12311yescharacteristic
295C2×C4×C13#12311yescharacteristic
296C2×C4×C13#12311yescharacteristic
297C2×Dic13—42no—
298C2×Dic13—42no—
299C2×Dic13—82no—
300C2×Dic13—82no—
301#1055—42no—
302#1055—42no—
303C22×#41C2×D1311yescharacteristic
304C22×M16—131no—
305C22×M16—131no—
306C4×#41—22no—
307C4×#41—22no—
308C4×#41—22no—
309C4×#41Dic1314yescomplemented
310C2×C4×Q8—21no—
311C2×C4×D4—21no—
312C2×C4×D4—22no—
313C2×#117—21no—
314C2×#117—131no—
315C2×#117—131no—
316C2×#117C2×D1311yescharacteristic
317C22×C42—21no—
318C22×C42C2×D1311yescharacteristic
319#421—134no—
320#421—262no—
321C2×#104—262no—
322#419—261no—
323#418—261no—
324#417—134no—
325#416—262no—
326#344—262no—
327#342—262no—
328#339—261no—
329#339—262no—
330#339—261no—
331C22×C13—22no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—24no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—44no—
340C22×C13—44no—
341C22×C13—44no—
342C22×C13C4×C22⋊C411yescharacteristic
343C22×C13#37911yescharacteristic
344C22×C13#38011yescharacteristic
345C22×C13#38511yescharacteristic
346C22×C13#38511yescharacteristic
347C22×C13#38611yescharacteristic
348C22×C13#38611yescharacteristic
349C4×C13—24no—
350C4×C13—24no—
351C4×C13—44no—
352C4×C13—42no—
353C4×C13C2×#9511yescharacteristic
354C4×C13C4×C22⋊C411yescharacteristic
355C4×C13#38011yescharacteristic
356C4×C13#38111yescharacteristic
357C4×C13#38511yescharacteristic
358C4×C13#38511yescharacteristic
359C4×C13#38611yescharacteristic
360C4×C13#38611yescharacteristic
361Dic13—82no—
362Dic13—82no—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—21no—
367C2×#41—21no—
368C2×#41—21no—
369C2×#41Dic2612yes—
370C2×#41C4×D1312yes—
371C2×#41C4×D1312yes—
372C2×#41D5212yes—
373C2×#41C2×Dic1312yes—
374C2×#41C22⋊D1312yes—
375C22×Q8C22⋊D1311yescharacteristic
376C22×D4—21no—
377C22×D4C22⋊D1311yescharacteristic
378C23×C4—21no—
379C23×C4—22no—
380C23×C4—21no—
381C23×C4C22×D1311yescharacteristic
382C2×M16—132no—
383C2×M16—132no—
384C2×M16—261no—
385C2×M16—261no—
386C2×M16—261no—
387C2×M16—261no—
388C2×M16—261no—
389C2×M16—261no—
390C2×M16—261no—
391C2×M16—261no—
392C2×M16—261no—
393C2×M16—261no—
394C22×C8—261no—
395C22×C8—261no—
396C4×Q8—24no—
397C4×Q8—24no—
398C4×D4—28no—
399C4×D4—24no—
400C4×D4—24no—
401C4×D4—28no—
402#117—24no—
403#117—21no—
404#117—21no—
405#117—24no—
406#117—132no—
407#117—261no—
408#117—261no—
409#117—261no—
410#117—261no—
411#117—261no—
412#117—261no—
413#117—261no—
414#117C2×Dic1312yes—
415#117C22⋊D1312yes—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—132no—
419C2×C4⋊C4—261no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—261no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4C22⋊D1312yes—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—24no—
431C2×C42—261no—
432C2×C42—261no—
433C2×C42C2×Dic1312yes—
434C2×C42C22⋊D1311yescharacteristic
435C2×C42C22⋊D1312yes—
436C2×C42C22⋊D1311yescharacteristic
437#104—268no—
438#103—264no—
439#102—264no—
440C2×C13—21no—
441C2×C13—21no—
442C2×C13—21no—
443C2×C13—21no—
444C2×C13—21no—
445C2×C13—21no—
446C2×C13—44no—
447C2×C13C22⋊#9511yescharacteristic
448C2×C13#190612yes—
449C24—21no—
450C24C2×C22⋊D1311yescharacteristic
451#41—22no—
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—22no—
457#41—22no—
458#41—22no—
459#41—22no—
460#41—22no—
461#41—22no—
462#41—22no—
463#41C4×Dic1314yes—
464#41#610114yes—
465#41C4⋊Dic1314yes—
466#41#610314yes—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8#610112yes—
471C2×Q8#610312yes—
472C2×Q8C22⋊Dic1312yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4#610112yes—
483C2×D4#610312yes—
484C2×D4C22⋊Dic1312yes—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—28no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—44no—
499C22×C4—48no—
500C22×C4—262no—
501C22×C4—521no—
502C22×C4C2×Dic2611yescharacteristic
503C22×C4C2×C4×D1311yescharacteristic
504C22×C4C2×C4×D1311yescharacteristic
505C22×C4C2×D5211yescharacteristic
506C22×C4#612711yescharacteristic
507C22×C4#612711yescharacteristic
508C22×C4#612711yescharacteristic
509C22×C4#612711yescharacteristic
510C22×C4C22×Dic1311yescharacteristic
511C22×C4C2×C22⋊D1311yescharacteristic
512C22×C4C2×C22⋊D1311yescharacteristic
513C22×C4C2×C22⋊D1311yescharacteristic
514C22×C4C2×C22⋊D1311yescharacteristic
515C22×C4C2×C22⋊D1311yescharacteristic
516M16—262no—
517M16—262no—
518M16—262no—
519M16—262no—
520M16—521no—
521M16—521no—
522M16—521no—
523M16—521no—
524C2×C8—262no—
525C2×C8—262no—
526C2×C8—521no—
527C2×C8—521no—
528C2×C8—521no—
529C2×C8—521no—
530C4⋊C4—28no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—262no—
534C4⋊C4—262no—
535C4⋊C4—262no—
536C4⋊C4—521no—
537C22⋊C4—28no—
538C22⋊C4—22no—
539C22⋊C4—262no—
540C22⋊C4—521no—
541C22⋊C4—521no—
542C22⋊C4—521no—
543C22⋊C4C22⋊Dic1314yes—
544C42—28no—
545C42—22no—
546C42—22no—
547C42—21no—
548C42—22no—
549C42—21no—
550C42—22no—
551C42—262no—
552C42—521no—
553C42—521no—
554C42—521no—
555C42C22⋊Dic1312yes—
556C42C22⋊Dic1312yes—
557C13#1077211yescharacteristic, complemented, Sylow
558C23—22no—
559C23—22no—
560C23—22no—
561C23—42no—
562C23—44no—
563C23#8817811yescharacteristic
564C23C4×C22⋊D1311yescharacteristic
565C23C4×C22⋊D1311yescharacteristic
566C23#8818411yescharacteristic
567C23C2×C22⋊Dic1311yescharacteristic
568C23#8820711yescharacteristic
569C23#8820711yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8#8807114yes—
574D4—24no—
575D4—24no—
576D4—24no—
577D4—24no—
578D4—22no—
579D4—22no—
580D4—22no—
581D4#8807114yes—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—416no—
596C2×C4—44no—
597C2×C4—42no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4—1042no—
601C2×C4—1042no—
602C2×C4C2×C4×Dic1311yescharacteristic
603C2×C4C2×#610111yescharacteristic
604C2×C4C2×#610111yescharacteristic
605C2×C4#8817811yescharacteristic
606C2×C4#8817811yescharacteristic
607C2×C4#8817811yescharacteristic
608C2×C4C2×C4⋊Dic1311yescharacteristic
609C2×C4#8818011yescharacteristic
610C2×C4#8818011yescharacteristic
611C2×C4C2×#610311yescharacteristic
612C2×C4C2×#610311yescharacteristic
613C2×C4C4×C22⋊D1311yescharacteristic
614C2×C4C4×C22⋊D1311yescharacteristic
615C2×C4C4×C22⋊D1311yescharacteristic
616C2×C4C4×C22⋊D1311yescharacteristic
617C2×C4C4×C22⋊D1311yescharacteristic
618C2×C4C4×C22⋊D1311yescharacteristic
619C2×C4#8818311yescharacteristic
620C2×C4#8818311yescharacteristic
621C2×C4#8818311yescharacteristic
622C2×C4#8818311yescharacteristic
623C2×C4#8818411yescharacteristic
624C2×C4#8818411yescharacteristic
625C2×C4#8818411yescharacteristic
626C2×C4C2×C22⋊Dic1311yescharacteristic
627C2×C4C2×C22⋊Dic1311yescharacteristic
628C2×C4#8820711yescharacteristic
629C2×C4#8820711yescharacteristic
630C8—522no—
631C8—522no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—24no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—44no—
641C22—44no—
642C22—44no—
643C22C4×C22⋊Dic1311yescharacteristic
644C22#1171887111yescharacteristic
645C22#1171887111yescharacteristic
646C22#1171887311yescharacteristic
647C22#1171887411yescharacteristic
648C22#1171887411yescharacteristic
649C22#1171890811yescharacteristic
650C4—24no—
651C4—24no—
652C4—44no—
653C4—42no—
654C4—1042no—
655C4—1042no—
656C4C2×#8807111yescharacteristic
657C4C4×C22⋊Dic1311yescharacteristic
658C4#1171887111yescharacteristic
659C4#1171887111yescharacteristic
660C4#1171887211yescharacteristic
661C4#1171887311yescharacteristic
662C4#1171887411yescharacteristic
663C4#1171887411yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—44no—
671C2#1311305911yescharacteristic
672C2#1311533712yes—
subgroupG/H
centerC2×C4#88184
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C4×C13×#41C2
socleC22×C13#386
prime radicalC22×C13×#41C22
cosocleC23×C4×C13C23
hypercenterC2×C4×#41D13
hypocenterC13#10772
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
3. C2×#11718125C2semidirect
4. #13114568C2semidirect
5. C2×#11718115C2semidirect
6. C2×#11718115C2semidirect
12. C4×C13×#41C4semidirect
25. #11718897C4semidirect
28. #11718893C4semidirect
91. #88180C2×C4semidirect
93. C2×C4⋊Dic13C2×C4semidirect
106. C2×#6099C2×C4semidirect
107. C2×#6099C2×C4semidirect
309. C4×#41Dic13semidirect
557. C13#10772semidirect

Maximal subgroups

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

subgroupindex
C2×#117188972
#131233552
C2×#117181252
#131145682
C2×#117181152
C2×C4×C13×#412
#1077213