Finite Group Databasebeta

← #15786606

Subgroups — #15786606

Order 3328.

1442 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718634C211yesmaximal, characteristic
2C2×#11718594C212yesmaximal
3C2×C4×#6101C211yesmaximal, characteristic
4#13113097C212yesmaximal
5#13113087C212yesmaximal
6#13113066C211yesmaximal, characteristic
7#13113065C211yesmaximal, characteristic
8#13113065C211yesmaximal, characteristic
9#13113065C211yesmaximal, characteristic
10#13113063C212yesmaximal
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C42×C13C2212yes—
15C22×C42×C13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×#6101C2211yescharacteristic
19C22×#6101C2212yes—
20C22×#6101C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C4×C13×C4⋊C4—24no—
24C2×C13×#95C2212yes—
25C2×#88071C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36#11718634C418yescomplemented
37#11718594—28no—
38C4×#6101—24no—
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×Dic13C2312yes—
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4C2×C414yes—
55C2×C13×C4⋊C4Q814yes—
56C2×C42×C13—22no—
57C2×C42×C13—22no—
58C2×C42×C13—24no—
59C2×C42×C13—24no—
60C2×C42×C13—24no—
61C2×C42×C13D414yes—
62C2×C4⋊Dic13—22no—
63C2×C4⋊Dic13—22no—
64C2×C4⋊Dic13—22no—
65C2×C4⋊Dic13—22no—
66C2×C4⋊Dic13—22no—
67C2×C4⋊Dic13C2×C414yes—
68C2×#6101—22no—
69C2×#6101—22no—
70C2×#6101—22no—
71C2×#6101—24no—
72C2×#6101—22no—
73C2×#6101—22no—
74C2×#6101—24no—
75C2×#6101C2×C418yes—
76C2×#6101D414yes—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13—22no—
80C2×C4×Dic13—22no—
81C2×C4×Dic13—22no—
82C2×C4×Dic13C2×C414yes—
83C13×#95—24no—
84#88071—22no—
85#88071—22no—
86#88071—24no—
87#88071—24no—
88#88071—24no—
89#88071—24no—
90#88071—24no—
91#88071—42no—
92#88071—42no—
93#88071—42no—
94#88071C2×C418yes—
95#14042—131nomaximal, Sylow
96C24×C13C2411yescharacteristic
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13C22×C414yes—
120C22×C4×C13C22×C412yes—
121C22×C4×C13C2×D412yes—
122C22×C4×C13C2×D412yes—
123C22×C4×C13C2×D412yes—
124C22×C4×C13C2×D412yes—
125C22×C4×C13C2×Q814yes—
126C22×C4×C13C2×Q812yes—
127C22×C4×C13#4112yes—
128C22×C4×C13#4112yes—
129C22×C4×C13#4112yes—
130C22×C4×C13#4112yes—
131C22×C4×C13#4112yes—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—22no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—22no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13C22×C412yes—
168C22×Dic13C22×C414yes—
169C22×Dic13C22×C412yes—
170C22×Dic13C2×D412yes—
171C22×Dic13C2×D412yes—
172C22×Dic13#4112yes—
173C22×Dic13#4112yes—
174C13×C4⋊C4—28no—
175C13×C4⋊C4—28no—
176C42×C13—28no—
177C42×C13—48no—
178C4⋊Dic13—28no—
179C4⋊Dic13—44no—
180#6101—28no—
181#6101—28no—
182#6101—216no—
183C4×Dic13—28no—
184C4×Dic13—44no—
185C2×#389—131no—
186C2×#387—132no—
187C2×C4×C4⋊C4—131no—
188C2×C4×C4⋊C4D1311yescharacteristic
189#1443—132no—
190#1441—132no—
191C4⋊#95—131no—
192C4⋊#95—131no—
193C4⋊#95—131no—
194C4⋊#95—131no—
195#1434—132no—
196C23×C13C23×C411yescharacteristic
197C23×C13C22×D411yescharacteristic
198C23×C13C22×D411yescharacteristic
199C23×C13C22×Q811yescharacteristic
200C23×C13C2×#4111yescharacteristic
201C23×C13C2×#4111yescharacteristic
202C23×C13C2×#4111yescharacteristic
203C23×C13C2×#4111yescharacteristic
204C23×C13C2×#4111yescharacteristic
205C23×C13C2×#4111yescharacteristic
206C23×C13C2×#4111yescharacteristic
207C23×C13H(5,𝔽2)11yescharacteristic
208C23×C132−1+411yescharacteristic
209C23×C132−1+411yescharacteristic
210C23×C132−1+411yescharacteristic
211C2×C4×C13—22no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—24no—
218C2×C4×C13—24no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13#11714yes—
239C2×C4×C13C4×D414yes—
240C2×C4×C13C4×Q814yes—
241C2×C4×C13#12114yes—
242C2×C4×C13C22⋊Q814yes—
243C2×C4×C13#12314yes—
244C2×C4×C13#12514yes—
245C2×C4×C13#12614yes—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—24no—
253C2×Dic13—22no—
254C2×Dic13—24no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—24no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—42no—
277C2×Dic13—41no—
278C2×Dic13—42no—
279C2×Dic13—41no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—42no—
287C2×Dic13C4×D414yes—
288C22×C4⋊C4—132no—
289C22×C4⋊C4—131no—
290C22×C4⋊C4—131no—
291C22×C4⋊C4—131no—
292C22×C4⋊C4—131no—
293C22×C4⋊C4C2×D1311yescharacteristic
294C22×C4⋊C4C2×D1311yescharacteristic
295C22×C42—131no—
296C22×C42—131no—
297C22×C42C2×D1312yes—
298C22×C42C2×D1311yescharacteristic
299#389—138no—
300#387—268no—
301C4×C4⋊C4—24no—
302C4×C4⋊C4—264no—
303C2×#95—132no—
304C2×#95—131no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95—132no—
308C2×#95—132no—
309C2×#95—132no—
310C2×#95—131no—
311C2×#95—132no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95C2×D1312yes—
315C22×C13C2×#11711yescharacteristic
316C22×C13C2×C4×D411yescharacteristic
317C22×C13C2×C4×D411yescharacteristic
318C22×C13C2×C4×Q811yescharacteristic
319C22×C13C4×#4111yescharacteristic
320C22×C13#51911yescharacteristic
321C22×C13#52011yescharacteristic
322C22×C13C2×#12111yescharacteristic
323C22×C13C2×C22⋊Q811yescharacteristic
324C22×C13C2×#12311yescharacteristic
325C22×C13#52511yescharacteristic
326C22×C13C2×#12511yescharacteristic
327C22×C13C2×#12611yescharacteristic
328C22×C13#52911yescharacteristic
329C22×C13#53211yescharacteristic
330C22×C13#53611yescharacteristic
331C22×C13#53711yescharacteristic
332C22×C13#54111yescharacteristic
333C22×C13#54211yescharacteristic
334C22×C13#54711yescharacteristic
335C22×C13#54711yescharacteristic
336C22×C13D4×Q811yescharacteristic
337C22×C13#55011yescharacteristic
338C22×C13#55211yescharacteristic
339C22×C13#55211yescharacteristic
340C22×C13#55211yescharacteristic
341C22×C13#55311yescharacteristic
342C22×C13#55411yescharacteristic
343C22×C13#55511yescharacteristic
344C22×C13#55611yescharacteristic
345C22×C13#55611yescharacteristic
346C22×C13#55611yescharacteristic
347C22×C13#55611yescharacteristic
348C22×C13#55711yescharacteristic
349C22×C13#55711yescharacteristic
350C4×C13—24no—
351C4×C13—42no—
352C4×C13—44no—
353C4×C13—44no—
354C4×C13#38718yescomplemented
355Dic13—24no—
356Dic13—42no—
357Dic13—44no—
358Dic13—42no—
359Dic13—42no—
360Dic13—82no—
361C23×C4—131no—
362C23×C4—132no—
363C23×C4—131no—
364C23×C4—131no—
365C23×C4—131no—
366C23×C4—132no—
367C23×C4C22×D1312yes—
368C23×C4C22×D1312yes—
369C23×C4C22×D1311yescharacteristic
370C23×C4C22×D1311yescharacteristic
371C23×C4C22×D1311yescharacteristic
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—138no—
377C2×C4⋊C4—134no—
378C2×C4⋊C4—134no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—262no—
382C2×C4⋊C4—264no—
383C2×C4⋊C4—262no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4—262no—
386C2×C4⋊C4—262no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4—262no—
389C2×C4⋊C4—262no—
390C2×C4⋊C4—262no—
391C2×C4⋊C4Dic2614yes—
392C2×C4⋊C4C4×D1314yes—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—134no—
399C2×C42—262no—
400C2×C42—262no—
401C2×C42—262no—
402C2×C42—262no—
403C2×C42—262no—
404C2×C42C22⋊D1314yes—
405#95—24no—
406#95—138no—
407#95—264no—
408#95—264no—
409#95—264no—
410#95—264no—
411#95—264no—
412#95—262no—
413#95—262no—
414#95—522no—
415#95—522no—
416#95—522no—
417C2×C13C2×#38711yescharacteristic
418C2×C13C4×#12111yescharacteristic
419C2×C13#232311yescharacteristic
420C2×C13#235411yescharacteristic
421C2×C13#235611yescharacteristic
422C2×C13#236511yescharacteristic
423C2×C13#237011yescharacteristic
424C2×C13#248511yescharacteristic
425C2×C13#248611yescharacteristic
426C2×C13#250611yescharacteristic
427C2×C13#250811yescharacteristic
428C2×C13#251211yescharacteristic
429C2×C13#251411yescharacteristic
430C2×C13#253811yescharacteristic
431C2×C13#258111yescharacteristic
432C24C23×D1311yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—132no—
456C22×C4—132no—
457C22×C4—132no—
458C22×C4—132no—
459C22×C4—134no—
460C22×C4—132no—
461C22×C4—132no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—262no—
479C22×C4—261no—
480C22×C4—262no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—262no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4C2×Dic2614yes—
498C22×C4C2×Dic2612yes—
499C22×C4C2×C4×D1314yes—
500C22×C4C2×C4×D1312yes—
501C22×C4#612712yes—
502C22×C4#612712yes—
503C22×C4#612712yes—
504C22×C4#612712yes—
505C22×C4D4×D1312yes—
506C22×C4#612912yes—
507C22×C4C2×C22⋊D1312yes—
508C22×C4C2×C22⋊D1312yes—
509C22×C4C2×C22⋊D1312yes—
510C4⋊C4—28no—
511C4⋊C4—28no—
512C4⋊C4—2616no—
513C4⋊C4—268no—
514C4⋊C4—268no—
515C4⋊C4—268no—
516C4⋊C4—524no—
517C42—28no—
518C42—48no—
519C42—268no—
520C42—524no—
521C13#1404211yescharacteristic, complemented, Sylow
522C23C22×Dic2611yescharacteristic
523C23C22×C4×D1311yescharacteristic
524C23C2×#612711yescharacteristic
525C23C2×#612711yescharacteristic
526C23C2×#612711yescharacteristic
527C23C2×#612711yescharacteristic
528C23C2×D4×D1311yescharacteristic
529C23C2×#612911yescharacteristic
530C23#8825411yescharacteristic
531C23#8825411yescharacteristic
532C23#41×D1311yescharacteristic
533C23#41×D1311yescharacteristic
534C23#8825611yescharacteristic
535C23#8825711yescharacteristic
536C23C22×C22⋊D1311yescharacteristic
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—134no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—264no—
572C2×C4—262no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—262no—
577C2×C4—264no—
578C2×C4—262no—
579C2×C4—262no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—264no—
583C2×C4—522no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—522no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—522no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—522no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—522no—
600C2×C4—522no—
601C2×C4—522no—
602C2×C4—522no—
603C2×C4—522no—
604C2×C4—522no—
605C2×C4—522no—
606C2×C4C4×Dic2614yes—
607C2×C4#8812414yes—
608C2×C4#8812614yes—
609C2×C4#8813014yes—
610C2×C4#8817814yes—
611C2×C4C4×C22⋊D1314yes—
612C2×C4#8818314yes—
613C2×C4#8819214yes—
614C22C2×C4×Dic2611yescharacteristic
615C22C2×#8812411yescharacteristic
616C22C2×#8812611yescharacteristic
617C22C2×#8813011yescharacteristic
618C22#1171921211yescharacteristic
619C22#1171921211yescharacteristic
620C22#1171921811yescharacteristic
621C22#1171921811yescharacteristic
622C22#1171923411yescharacteristic
623C22#1171923511yescharacteristic
624C22#1171923711yescharacteristic
625C22#1171923811yescharacteristic
626C22C4×#612911yescharacteristic
627C22D4×Dic2611yescharacteristic
628C22#1171924711yescharacteristic
629C22#1171924811yescharacteristic
630C22C4×D4×D1311yescharacteristic
631C22#1171925311yescharacteristic
632C22#1171925811yescharacteristic
633C22#1171926211yescharacteristic
634C22#1171927311yescharacteristic
635C22#1171927311yescharacteristic
636C22#1171927411yescharacteristic
637C22#1171927411yescharacteristic
638C22#1171927711yescharacteristic
639C22#1171927911yescharacteristic
640C22#1171928711yescharacteristic
641C22#1171928811yescharacteristic
642C22C2×#8817811yescharacteristic
643C22C2×C4×C22⋊D1311yescharacteristic
644C22C2×#8818311yescharacteristic
645C22C2×#8819211yescharacteristic
646C22#1171952111yescharacteristic
647C22#1171953311yescharacteristic
648C22#1171953811yescharacteristic
649C4—24no—
650C4—44no—
651C4—42no—
652C4—44no—
653C4—264no—
654C4—522no—
655C4—524no—
656C4—522no—
657C4—522no—
658C4—1042no—
659C4#1171859418yescomplemented
660C2C2×#1171859411yescharacteristic
661C2C4×#8819211yescharacteristic
662C2#1311751211yescharacteristic
663C2#1311778111yescharacteristic
664C2#1311779711yescharacteristic
665C2#1311789511yescharacteristic
666C2#1311793411yescharacteristic
667C2#1311912711yescharacteristic
668C2#1311913811yescharacteristic
669C2#1311934611yescharacteristic
670C2#1311936811yescharacteristic
671C2#1311941611yescharacteristic
672C2#1311943811yescharacteristic
673C2#1311975811yescharacteristic
674C2#1312019811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#14042
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
36. #11718634C4semidirect
354. C4×C13#387semidirect
521. C13#14042semidirect
659. C4#11718594semidirect

Maximal subgroups

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

subgroupindex
C2×#117186342
C2×#117185942
C2×C4×#61012
#131130972
#131130872
#131130662
#131130652
#131130632
C2×C4×C13×C4⋊C42
#1404213