Finite Group Databasebeta

← #15785329

Subgroups — #15785329

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic
2C2×#11718307C212yesmaximal
3C2×#11718637C211yesmaximal, characteristic
4C2×#11718310C211yesmaximal, characteristic
5#13113090C211yesmaximal, characteristic
6#13113089C211yesmaximal, characteristic
7#13113086C211yesmaximal, characteristic
8#13113064C212yesmaximal
9#13113064C212yesmaximal
10#13113064C212yesmaximal
11C13×#1441C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2212yes—
17C22×#6101C2212yes—
18C22×#6101C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×#6101C2212yes—
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C2×#88141—24no—
26C2×#88141—24no—
27C2×#88141C418yescomplemented
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718637—24no—
39#11718310—24no—
40#11718307—28no—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C22×Dic26—22no—
53C22×Dic26—22no—
54C22×Dic26—22no—
55C22×Dic26—22no—
56C22×Dic26C2×C414yes—
57C22×Dic26D414yes—
58C22×Dic26Q814yes—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—42no—
63C2×C13×C4⋊C4C2×C414yes—
64C2×C4⋊Dic13—22no—
65C2×C4⋊Dic13—42no—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×#6101—22no—
69C2×#6101—22no—
70C2×#6101—24no—
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101—24no—
74C2×#6101—24no—
75C2×#6101—24no—
76C2×#6101—24no—
77C2×#6101—24no—
78C2×#6101C2×C414yes—
79C2×#6101C2×C414yes—
80C2×#6101Q818yescomplemented
81C2×C4×Dic13—22no—
82C2×C4×Dic13—22no—
83C2×C4×Dic13—22no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13—24no—
86C2×C4×Dic13—24no—
87C2×C4×Dic13—24no—
88C2×C4×Dic13C2×C414yes—
89C2×C4×Dic13C2×C414yes—
90C2×C4×Dic13C2×C414yes—
91C2×C4×Dic13D414yes—
92C2×C4×Dic13D414yes—
93#88141—232no—
94C13×#95—24no—
95C13×#95—22no—
96C13×#95—42no—
97#88071—24no—
98#88071—22no—
99#88071—24no—
100#88071—24no—
101#88071—42no—
102#88071—42no—
103#88071—42no—
104#13926—131nomaximal, Sylow
105C24×C13C2411yescharacteristic
106C22×C4×C13—21no—
107C22×C4×C13—21no—
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—21no—
115C22×C4×C13—21no—
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—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C2×D412yes—
133C22×C4×C13C2×D412yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×Q814yes—
136C22×C4×C13C2×Q812yes—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
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—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C412yes—
160C22×Dic13C22×C412yes—
161C22×Dic13C22×C412yes—
162C22×Dic13C2×D412yes—
163C22×Dic13C2×D412yes—
164C22×Dic13C2×D412yes—
165C22×Dic13C2×D412yes—
166C22×Dic13C2×D412yes—
167C22×Dic13C2×D412yes—
168C22×Dic13C2×Q814yes—
169C22×Dic13C2×Q812yes—
170C22×Dic13C2×Q812yes—
171C22×Dic13C2×Q814yes—
172C22×Dic13#4112yes—
173C22×Dic13#4112yes—
174C22×Dic13#4114yes—
175C2×Dic26—28no—
176C2×Dic26—28no—
177C2×Dic26—28no—
178C2×Dic26—28no—
179C2×Dic26—28no—
180C2×Dic26—28no—
181C2×Dic26C4⋊C4116yescomplemented
182C13×C4⋊C4—28no—
183C13×C4⋊C4—44no—
184C4⋊Dic13—44no—
185#6101—28no—
186#6101—28no—
187#6101—216no—
188#6101—48no—
189#6101—48no—
190C4×Dic13—28no—
191C4×Dic13—28no—
192C4×Dic13—48no—
193C4×Dic13C22⋊C4116yes—
194C22×C4×Q8—131no—
195C2×#391—132no—
196C2×#384—131no—
197C2×C4×C4⋊C4—131no—
198#1441—131no—
199#1441—131no—
200#1441—131no—
201#1441D1311yescharacteristic
202C4⋊#95—132no—
203C4⋊#95—132no—
204C4⋊#95—132no—
205C23×C13C23×C411yescharacteristic
206C23×C13C22×D411yescharacteristic
207C23×C13C22×D411yescharacteristic
208C23×C13C22×D411yescharacteristic
209C23×C13C22×Q811yescharacteristic
210C23×C13C22×Q812yes—
211C23×C13C2×#4111yescharacteristic
212C23×C13C2×#4111yescharacteristic
213C23×C13C2×#4112yes—
214C23×C13H(5,𝔽2)12yes—
215C23×C132−1+412yes—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—24no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—24no—
226C2×C4×C13—22no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—24no—
231C2×C4×C13—42no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
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×C22⋊C414yes—
246C2×C4×C13C2×C4⋊C414yes—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—24no—
258C2×Dic13—42no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
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×Dic13C2×C22⋊C414yes—
273C2×Dic13C2×C22⋊C414yes—
274C2×Dic13C2×C4⋊C414yes—
275C2×Dic13C2×C4⋊C414yes—
276C2×Dic13#11714yes—
277C2×Dic13C4×Q818yes—
278C2×Dic13#12114yes—
279C2×Dic13#12114yes—
280C2×Dic13C22⋊Q814yes—
281C2×Dic13C22⋊Q814yes—
282C2×Dic13C22⋊Q818yes—
283C2×Dic13#12414yes—
284C2×Dic13C4⋊Q814yes—
285Dic26—232no—
286C23×Q8—131no—
287C2×C4×Q8—138no—
288C2×C4×Q8—264no—
289C2×C4×Q8—264no—
290C22×C4⋊C4—131no—
291C22×C4⋊C4—131no—
292C22×C4⋊C4—132no—
293C22×C4⋊C4—132no—
294C22×C4⋊C4—132no—
295C22×C4⋊C4—131no—
296C22×C4⋊C4C2×D1311yescharacteristic
297C22×C4⋊C4C2×D1311yescharacteristic
298C22×C42—131no—
299C22×C42—131no—
300C22×C42—131no—
301C22×C42—132no—
302#391—268no—
303#384—264no—
304C4×C4⋊C4—264no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95—132no—
308C2×#95—131no—
309C2×#95—132no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95C2×D1312yes—
313C2×#95C2×D1311yescharacteristic
314C2×#95C2×D1312yes—
315C22×C13C22×C22⋊C411yescharacteristic
316C22×C13C22×C4⋊C411yescharacteristic
317C22×C13C2×#11711yescharacteristic
318C22×C13C2×C4×Q812yes—
319C22×C13#52012yes—
320C22×C13C2×#12111yescharacteristic
321C22×C13C2×#12111yescharacteristic
322C22×C13C2×C22⋊Q811yescharacteristic
323C22×C13C2×C22⋊Q811yescharacteristic
324C22×C13C2×C22⋊Q812yes—
325C22×C13C2×#12411yescharacteristic
326C22×C13C2×C4⋊Q811yescharacteristic
327C22×C13#53511yescharacteristic
328C22×C13#53611yescharacteristic
329C22×C13#53712yes—
330C22×C13D4×Q812yes—
331C22×C13#55012yes—
332C22×C13#55412yes—
333C22×C13#55612yes—
334C22×C13#55712yes—
335C22×C13#55712yes—
336C22×C13Q8212yes—
337C22×C13#55912yes—
338C4×C13—24no—
339C4×C13—24no—
340C4×C13—42no—
341C4×C13—44no—
342C4×C13—82no—
343Dic13—24no—
344Dic13—42no—
345Dic13—44no—
346Dic13—82no—
347Dic13#38018yes—
348Dic13#39118yescomplemented
349C22×Q8—134no—
350C22×Q8—134no—
351C22×Q8—134no—
352C22×Q8—262no—
353C22×Q8—262no—
354C22×Q8—262no—
355C22×Q8—262no—
356C23×C4—131no—
357C23×C4—131no—
358C23×C4—131no—
359C23×C4—131no—
360C23×C4—132no—
361C23×C4—132no—
362C23×C4C22×D1312yes—
363C23×C4C22×D1311yescharacteristic
364C23×C4C22×D1312yes—
365C23×C4C22×D1311yescharacteristic
366C23×C4C22×D1311yescharacteristic
367C4×Q8—2632no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—134no—
373C2×C4⋊C4—134no—
374C2×C4⋊C4—138no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—264no—
378C2×C4⋊C4—264no—
379C2×C4⋊C4—262no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—264no—
382C2×C4⋊C4—264no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4—264no—
385C2×C4⋊C4—264no—
386C2×C4⋊C4—264no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4—522no—
389C2×C4⋊C4C4×D1314yes—
390C2×C42—134no—
391C2×C42—134no—
392C2×C42—134no—
393C2×C42—134no—
394C2×C42—134no—
395C2×C42—262no—
396C2×C42—262no—
397C2×C42—262no—
398C2×C42—262no—
399C2×C42—264no—
400C2×C42—264no—
401C2×C42—264no—
402#95—22no—
403#95—24no—
404#95—42no—
405#95—264no—
406#95—264no—
407#95—262no—
408#95—264no—
409#95—522no—
410#95—522no—
411#95—522no—
412C2×C13C2×#38011yescharacteristic
413C2×C13C2×#39111yescharacteristic
414C2×C13#231111yescharacteristic
415C2×C13Q8×C4⋊C412yes—
416C2×C13#235512yes—
417C2×C13#253812yes—
418C2×C13#254611yescharacteristic
419C2×C13#254811yescharacteristic
420C2×C13#256711yescharacteristic
421C2×C13#256811yescharacteristic
422C2×C13#258212yes—
423C24C23×D1311yescharacteristic
424C2×Q8—1316no—
425C2×Q8—268no—
426C2×Q8—268no—
427C2×Q8—268no—
428C2×Q8—268no—
429C2×Q8—268no—
430C2×Q8—268no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—132no—
455C22×C4—132no—
456C22×C4—132no—
457C22×C4—132no—
458C22×C4—132no—
459C22×C4—132no—
460C22×C4—132no—
461C22×C4—134no—
462C22×C4—132no—
463C22×C4—132no—
464C22×C4—134no—
465C22×C4—132no—
466C22×C4—132no—
467C22×C4—132no—
468C22×C4—132no—
469C22×C4—132no—
470C22×C4—134no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4C2×C4×D1312yes—
493C22×C4C2×C4×D1312yes—
494C22×C4C2×C4×D1312yes—
495C22×C4D4×D1312yes—
496C22×C4D4×D1312yes—
497C22×C4D4×D1312yes—
498C22×C4Q8×D1314yes—
499C22×C4Q8×D1312yes—
500C4⋊C4—28no—
501C4⋊C4—44no—
502C4⋊C4—268no—
503C4⋊C4—2616no—
504C4⋊C4—268no—
505C4⋊C4—524no—
506C4⋊C4—528no—
507C4⋊C4—528no—
508C42—1316no—
509C42—268no—
510C42—268no—
511C42—528no—
512C13#1392611yescharacteristic, complemented, Sylow
513C23C22×C4×D1311yescharacteristic
514C23C2×D4×D1311yescharacteristic
515C23C2×D4×D1311yescharacteristic
516C23C2×D4×D1311yescharacteristic
517C23#8825112yes—
518C23C2×Q8×D1311yescharacteristic
519C23C2×Q8×D1312yes—
520C23#41×D1311yescharacteristic
521C23#41×D1311yescharacteristic
522C23#41×D1312yes—
523C23#8825712yes—
524Q8—2632no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—134no—
555C2×C4—134no—
556C2×C4—134no—
557C2×C4—134no—
558C2×C4—134no—
559C2×C4—138no—
560C2×C4—134no—
561C2×C4—134no—
562C2×C4—138no—
563C2×C4—134no—
564C2×C4—134no—
565C2×C4—134no—
566C2×C4—134no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—262no—
573C2×C4—262no—
574C2×C4—264no—
575C2×C4—264no—
576C2×C4—264no—
577C2×C4—264no—
578C2×C4—521no—
579C2×C4—522no—
580C2×C4—522no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—521no—
584C2×C4—522no—
585C2×C4—522no—
586C2×C4—522no—
587C2×C4—522no—
588C2×C4—522no—
589C2×C4—522no—
590C2×C4—522no—
591C2×C4—522no—
592C2×C4C22⋊C4×D1314yes—
593C2×C4C4⋊C4×D1314yes—
594C22C2×C22⋊C4×D1311yescharacteristic
595C22C2×C4⋊C4×D1311yescharacteristic
596C22D13×#11711yescharacteristic
597C22#1171925112yes—
598C22C4×Q8×D1312yes—
599C22#1171929711yescharacteristic
600C22#1171930212yes—
601C22#1171930412yes—
602C22D13×#12111yescharacteristic
603C22D13×#12111yescharacteristic
604C22D13×C22⋊Q812yes—
605C22D13×C22⋊Q811yescharacteristic
606C22D13×C22⋊Q811yescharacteristic
607C22#1171933712yes—
608C22#1171934112yes—
609C22#1171935311yescharacteristic
610C22#1171936912yes—
611C22D13×#12411yescharacteristic
612C22#1171939012yes—
613C22#1171939012yes—
614C22#1171940712yes—
615C22#1171942712yes—
616C22D13×C4⋊Q811yescharacteristic
617C4—24no—
618C4—24no—
619C4—44no—
620C4—42no—
621C4—82no—
622C4—138no—
623C4—138no—
624C4—264no—
625C4—524no—
626C4—522no—
627C4—1042no—
628C2D13×#38011yescharacteristic
629C2D13×#39111yescharacteristic
630C2#1311742311yescharacteristic
631C2#1311775012yes—
632C2#1311779012yes—
633C2#1311975312yes—
634C2#1311982011yescharacteristic
635C2#1311983411yescharacteristic
636C2#1312004011yescharacteristic
637C2#1312004711yescharacteristic
638C2#1312020512yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13#13926
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
27. C2×#88141C4semidirect
80. C2×#6101Q8semidirect
181. C2×Dic26C4⋊C4semidirect
348. Dic13#391semidirect
512. C13#13926semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C2×#117183072
C2×#117186372
C2×#117183102
#131130902
#131130892
#131130862
#131130642
C13×#14412
#1392613