Finite Group Databasebeta

← #15786634

Subgroups — #15786634

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718871C211yesmaximal, characteristic
2C2×#11718871C211yesmaximal, characteristic
3C2×#11718871C211yesmaximal, characteristic
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic
5#13113091C212yesmaximal, complemented
6#13113087C212yesmaximal, complemented
7#13113071C212yesmaximal, complemented
8#13113064C212yesmaximal, complemented
9#13113059C211yesmaximal, characteristic
10#13113059C211yesmaximal, characteristic
11C22×C13×#95C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C22×C22⋊Dic13C2211yescharacteristic
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2211yescharacteristic
18C22×C22⋊Dic13C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×#6101C2212yes—
21C22×#6101C2211yescharacteristic
22C22×#6101C2212yes—
23C22×C4×Dic13C2212yes—
24C2×C13×#95—24no—
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27#11718871—24no—
28#11718871—24no—
29#11718871C418yescomplemented
30C4×C22⋊Dic13—24no—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C25×C13C2311yescharacteristic
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—24no—
47C23×C4×C13—24no—
48C23×C4×C13—22no—
49C23×C4×C13—22no—
50C23×C4×C13—42no—
51C23×C4×C13—42no—
52C23×C4×C13—42no—
53C23×C4×C13—42no—
54C23×C4×C13C2×C414yes—
55C23×C4×C13D414yes—
56C23×C4×C13C2312yes—
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2312yes—
59C23×C4×C13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2312yes—
65C23×Dic13C2312yes—
66C2×C22⋊Dic13—22no—
67C2×C22⋊Dic13—22no—
68C2×C22⋊Dic13—22no—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—22no—
73C2×C22⋊Dic13C2×C414yes—
74C2×C22⋊Dic13C2×C414yes—
75C2×C22⋊Dic13D414yes—
76C2×C22⋊Dic13Q814yes—
77C2×C22⋊Dic13Q814yes—
78C2×#6101—22no—
79C2×#6101—22no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101—24no—
83C2×#6101—42no—
84C2×#6101—42no—
85C2×#6101—42no—
86C2×#6101—42no—
87C2×#6101C2×C418yescomplemented
88C2×C4×Dic13—24no—
89C2×C4×Dic13—24no—
90C2×C4×Dic13—42no—
91C13×#95—24no—
92C13×#95—24no—
93#88071—22no—
94#88071—22no—
95#88071—24no—
96#88071—24no—
97#88071—24no—
98#88071—42no—
99#88071—42no—
100#88071—42no—
101#88071C2×C418yescomplemented
102#14044—131nomaximal, Sylow
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—22no—
106C24×C13—22no—
107C24×C13C22×C412yes—
108C24×C13C2×D412yes—
109C24×C13C2×D412yes—
110C24×C13C2×Q812yes—
111C24×C13C2×Q812yes—
112C24×C13#4112yes—
113C24×C13#4112yes—
114C24×C13C2411yescharacteristic
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—28no—
119C22×C4×C13—28no—
120C22×C4×C13—28no—
121C22×C4×C13—21no—
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—21no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—28no—
138C22×C4×C13—48no—
139C22×C4×C13—44no—
140C22×C4×C13—48no—
141C22×C4×C13—48no—
142C22×C4×C13—48no—
143C22×C4×C13—48no—
144C22×C4×C13—44no—
145C22×C4×C13—44no—
146C22×C4×C13—44no—
147C22×C4×C13—48no—
148C22×C4×C13—44no—
149C22×C4×C13C22×C414yes—
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13#4114yes—
153C22×C4×C13#4114yes—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13C22×C412yes—
183C22×Dic13C22×C412yes—
184C22×Dic13C22×C414yes—
185C22×Dic13C2×D414yes—
186C22×Dic13C2×Q814yes—
187C22×Dic13C2×Q814yes—
188C22⋊Dic13—28no—
189C22⋊Dic13—28no—
190C22⋊Dic13—44no—
191C22⋊Dic13C4⋊C4116yescomplemented
192#6101—48no—
193#6101—48no—
194#6101—44no—
195#6101—44no—
196C4×Dic13—48no—
197C2×#385—131no—
198C2×#385—131no—
199C2×#385—131no—
200C2×C4×C22⋊C4—131no—
201C22×#95D1311yescharacteristic
202#1442—132no—
203#1441—132no—
204#1436—132no—
205C4⋊#95—132no—
206C22⋊#95—131no—
207C22⋊#95—131no—
208C23×C13—24no—
209C23×C13—24no—
210C23×C13—22no—
211C23×C13—22no—
212C23×C13—24no—
213C23×C13—22no—
214C23×C13—22no—
215C23×C13—24no—
216C23×C13—24no—
217C23×C13—24no—
218C23×C13—24no—
219C23×C13—24no—
220C23×C13—24no—
221C23×C13—24no—
222C23×C13—24no—
223C23×C13—24no—
224C23×C13C2×C4⋊C414yes—
225C23×C13C4×D414yes—
226C23×C13C4×Q814yes—
227C23×C13#12114yes—
228C23×C13C22⋊Q814yes—
229C23×C13#12514yes—
230C23×C13C4⋊Q814yes—
231C23×C13C23×C411yescharacteristic
232C23×C13C22×D411yescharacteristic
233C23×C13C22×D411yescharacteristic
234C23×C13C22×Q811yescharacteristic
235C23×C13C22×Q811yescharacteristic
236C23×C13C2×#4111yescharacteristic
237C23×C13C2×#4111yescharacteristic
238C23×C13C2×#4112yes—
239C23×C13C2×#4112yes—
240C23×C13H(5,𝔽2)12yes—
241C23×C13H(5,𝔽2)12yes—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—24no—
252C2×C4×C13—22no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—416no—
256C2×C4×C13—416no—
257C2×C4×C13—416no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C2×C4×C13#12314yes—
269C2×Dic13—24no—
270C2×Dic13—24no—
271C2×Dic13—24no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—24no—
278C2×Dic13—24no—
279C2×Dic13—24no—
280C2×Dic13—24no—
281C2×Dic13—24no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13—42no—
301C2×Dic13—42no—
302C2×Dic13C2×C4⋊C418yes—
303C24×C4C2×D1311yescharacteristic
304C24×C4C2×D1311yescharacteristic
305C24×C4C2×D1311yescharacteristic
306C22×C4⋊C4—132no—
307C22×C4⋊C4—131no—
308C22×C4⋊C4—132no—
309C22×C4⋊C4—131no—
310C22×C22⋊C4—131no—
311C22×C22⋊C4—131no—
312C22×C22⋊C4—131no—
313C22×C22⋊C4—131no—
314C22×C42—132no—
315#385—138no—
316#385—264no—
317#385—264no—
318C4×C22⋊C4—264no—
319C2×#95—24no—
320C2×#95—132no—
321C2×#95—132no—
322C2×#95—131no—
323C2×#95—132no—
324C2×#95—132no—
325C2×#95—131no—
326C2×#95—132no—
327C2×#95—132no—
328C2×#95—132no—
329C2×#95C2×D1312yes—
330C2×#95C2×D1312yes—
331C22×C13—24no—
332C22×C13—24no—
333C22×C13—28no—
334C22×C13—28no—
335C22×C13—24no—
336C22×C13—24no—
337C22×C13—28no—
338C22×C13—24no—
339C22×C13—28no—
340C22×C13—24no—
341C22×C13#38918yes—
342C22×C13C22×C4⋊C411yescharacteristic
343C22×C13C2×C4×D411yescharacteristic
344C22×C13C2×C4×Q811yescharacteristic
345C22×C13C4×#4112yes—
346C22×C13#51812yes—
347C22×C13C2×#12111yescharacteristic
348C22×C13C2×C22⋊Q811yescharacteristic
349C22×C13C2×#12311yescharacteristic
350C22×C13#52511yescharacteristic
351C22×C13C2×#12511yescharacteristic
352C22×C13#52912yes—
353C22×C13C2×C4⋊Q811yescharacteristic
354C22×C13#53411yescharacteristic
355C22×C13#53511yescharacteristic
356C22×C13#53812yes—
357C22×C13#54612yes—
358C22×C13#54612yes—
359C22×C13#55112yes—
360C22×C13#55112yes—
361C22×C13#55412yes—
362C22×C13#55412yes—
363C22×C13#55412yes—
364C22×C13#55412yes—
365C4×C13—24no—
366C4×C13—44no—
367C4×C13—44no—
368C4×C13—42no—
369Dic13—28no—
370Dic13—42no—
371Dic13—44no—
372Dic13—42no—
373Dic13—81no—
374Dic13—81no—
375C25C22×D1311yescharacteristic
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—132no—
390C23×C4—131no—
391C23×C4—131no—
392C23×C4—132no—
393C23×C4—131no—
394C23×C4—131no—
395C23×C4C4×D1314yes—
396C23×C4C22⋊D1314yes—
397C23×C4C22×D1312yes—
398C23×C4C22×D1312yes—
399C23×C4C22×D1311yescharacteristic
400C23×C4C22×D1311yescharacteristic
401C2×C4⋊C4—138no—
402C2×C4⋊C4—264no—
403C2×C4⋊C4—264no—
404C2×C4⋊C4—264no—
405C2×C4⋊C4—262no—
406C2×C4⋊C4—262no—
407C2×C4⋊C4—522no—
408C2×C4⋊C4—522no—
409C2×C4⋊C4—522no—
410C2×C4⋊C4—522no—
411C2×C22⋊C4—134no—
412C2×C22⋊C4—134no—
413C2×C22⋊C4—134no—
414C2×C22⋊C4—134no—
415C2×C22⋊C4—134no—
416C2×C22⋊C4—262no—
417C2×C22⋊C4—262no—
418C2×C22⋊C4—262no—
419C2×C22⋊C4—262no—
420C2×C22⋊C4—262no—
421C2×C22⋊C4—262no—
422C2×C22⋊C4—262no—
423C2×C42—264no—
424C2×C42—264no—
425C2×C42—522no—
426#95—24no—
427#95—24no—
428#95—138no—
429#95—264no—
430#95—264no—
431#95—264no—
432#95—262no—
433#95—262no—
434#95—522no—
435#95—522no—
436#95—522no—
437C2×C13—28no—
438C2×C13C2×#38911yescharacteristic
439C2×C13C4×#12311yescharacteristic
440C2×C13#232111yescharacteristic
441C2×C13#234912yes—
442C2×C13#236812yes—
443C2×C13#241111yescharacteristic
444C2×C13#241211yescharacteristic
445C2×C13#245012yes—
446C2×C13#250211yescharacteristic
447C2×C13#250512yes—
448C2×C13#258311yescharacteristic
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24C2×C4×D1312yes—
454C24#612712yes—
455C24D4×D1312yes—
456C24#612912yes—
457C24Q8×D1312yes—
458C24Q8×D1312yes—
459C24C2×C22⋊D1312yes—
460C24C23×D1311yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—28no—
484C22×C4—48no—
485C22×C4—44no—
486C22×C4—48no—
487C22×C4—48no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—134no—
496C22×C4—134no—
497C22×C4—134no—
498C22×C4—132no—
499C22×C4—132no—
500C22×C4—134no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—262no—
509C22×C4—261no—
510C22×C4—261no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—262no—
517C22×C4—261no—
518C22×C4—261no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4—261no—
524C22×C4—261no—
525C22×C4—262no—
526C22×C4—262no—
527C22×C4—261no—
528C22×C4—261no—
529C22×C4C2×C4×D1314yes—
530C22×C4#612714yes—
531C22×C4#612714yes—
532C22×C4C2×C22⋊D1312yes—
533C22×C4C2×C22⋊D1312yes—
534C4⋊C4—528no—
535C4⋊C4—528no—
536C4⋊C4—524no—
537C4⋊C4—524no—
538C22⋊C4—1316no—
539C22⋊C4—268no—
540C22⋊C4—268no—
541C22⋊C4—524no—
542C42—528no—
543C13#1404411yescharacteristic, complemented, Sylow
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23#8814114yes—
561C23#8814314yes—
562C23C4⋊C4×D1314yes—
563C23#8815014yes—
564C23C4×C22⋊D1314yes—
565C23#8819314yes—
566C23#8819814yes—
567C23C22×C4×D1311yescharacteristic
568C23C2×#612712yes—
569C23C2×#612712yes—
570C23C2×#612711yescharacteristic
571C23C2×D4×D1311yescharacteristic
572C23C2×#612911yescharacteristic
573C23#8825112yes—
574C23#8825112yes—
575C23C2×Q8×D1311yescharacteristic
576C23C2×Q8×D1311yescharacteristic
577C23C22×C22⋊D1311yescharacteristic
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—416no—
592C2×C4—416no—
593C2×C4—416no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—138no—
605C2×C4—264no—
606C2×C4—264no—
607C2×C4—264no—
608C2×C4—264no—
609C2×C4—264no—
610C2×C4—264no—
611C2×C4—264no—
612C2×C4—264no—
613C2×C4—264no—
614C2×C4—264no—
615C2×C4—264no—
616C2×C4—262no—
617C2×C4—262no—
618C2×C4—522no—
619C2×C4—522no—
620C2×C4—522no—
621C2×C4—522no—
622C2×C4—522no—
623C2×C4—522no—
624C2×C4—521no—
625C2×C4—521no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—522no—
629C2×C4—522no—
630C2×C4—522no—
631C2×C4—522no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—521no—
635C2×C4—521no—
636C2×C4—521no—
637C2×C4—521no—
638C2×C4#8818314yes—
639C22—24no—
640C22—24no—
641C22—28no—
642C22—24no—
643C22—24no—
644C22—28no—
645C22—24no—
646C22—28no—
647C22—24no—
648C22—28no—
649C22#1171863318yes—
650C22C4×#612712yes—
651C22#1171918412yes—
652C22#1171919112yes—
653C22#1171919512yes—
654C22#1171919512yes—
655C22#1171919912yes—
656C22#1171920012yes—
657C22#1171920012yes—
658C22C2×#8814111yescharacteristic
659C22C2×#8814311yescharacteristic
660C22C2×C4⋊C4×D1311yescharacteristic
661C22C2×#8815011yescharacteristic
662C22#1171921612yes—
663C22#1171921612yes—
664C22#1171921612yes—
665C22#1171921612yes—
666C22C2×C4×C22⋊D1311yescharacteristic
667C22C2×#8818311yescharacteristic
668C22#1171949611yescharacteristic
669C22C2×#8819311yescharacteristic
670C22#1171950911yescharacteristic
671C22#1171951011yescharacteristic
672C22C2×#8819811yescharacteristic
673C4—24no—
674C4—44no—
675C4—42no—
676C4—44no—
677C4—268no—
678C4—522no—
679C4—522no—
680C4—524no—
681C4—1041no—
682C4—1041no—
683C2—28no—
684C2C2×#1171863311yescharacteristic
685C2C4×#8818311yescharacteristic
686C2#1311749411yescharacteristic
687C2#1311774312yes—
688C2#1311791612yes—
689C2#1311822111yescharacteristic
690C2#1311823211yescharacteristic
691C2#1311866012yes—
692C2#1311931011yescharacteristic
693C2#1311933712yes—
694C2#1312021611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C13×#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×#95D13
hypocenterC13#14044
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
5. #13113091C2semidirect
6. #13113087C2semidirect
7. #13113071C2semidirect
8. #13113064C2semidirect
29. #11718871C4semidirect
87. C2×#6101C2×C4semidirect
101. #88071C2×C4semidirect
191. C22⋊Dic13C4⋊C4semidirect
543. C13#14044semidirect

Maximal subgroups

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

subgroupindex
C2×#117188712
C2×C4×C22⋊Dic132
#131130912
#131130872
#131130712
#131130642
#131130592
C22×C13×#952
#1404413