Finite Group Databasebeta

← #15786745

Subgroups — #15786745

Order 3328.

1566 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88144C211yesmaximal, characteristic
2C2×#11718634C211yesmaximal, characteristic
3C2×C4×C4⋊Dic13C211yesmaximal, characteristic
4#13113102C212yesmaximal
5#13113088C212yesmaximal
6#13113070C212yesmaximal
7#13113065C211yesmaximal, characteristic
8#13113065C211yesmaximal, characteristic
9#13113064C212yesmaximal
10C4×#88071C211yesmaximal, characteristic
11C13×C4⋊#95C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×C4⋊Dic13C2212yes—
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×#6101C2212yes—
19C22×#6101C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C2×#88144—24no—
24C2×#88144—24no—
25C2×#88144C418yescomplemented
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718634—24no—
39C4×C4⋊Dic13—24no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4C2×C414yes—
57C2×C42×C13—22no—
58C2×C42×C13—22no—
59C2×C42×C13Q814yes—
60C2×C4⋊Dic13—22no—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13—24no—
63C2×C4⋊Dic13—24no—
64C2×C4⋊Dic13C2×C418yes—
65C2×C4⋊Dic13C2×C414yes—
66C2×C4⋊Dic13D414yes—
67C2×C4⋊Dic13D414yes—
68C2×C4⋊Dic13Q814yes—
69C2×#6101—24no—
70C2×#6101—24no—
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101—42no—
74C2×#6101C2×C418yes—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13—22no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—42no—
83C2×C4×Dic13C2×C414yes—
84#88144—232no—
85C13×#95—24no—
86C13×#95—42no—
87#88071—22no—
88#88071—22no—
89#88071—24no—
90#88071—24no—
91#88071—22no—
92#88071—24no—
93#88071—22no—
94#88071—42no—
95#88071—42no—
96#88071—42no—
97#14054—131nomaximal, Sylow
98C24×C13C2411yescharacteristic
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
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×C13C22×C414yes—
123C22×C4×C13C22×C412yes—
124C22×C4×C13C2×D412yes—
125C22×C4×C13C2×D412yes—
126C22×C4×C13C2×Q812yes—
127C22×C4×C13C2×Q812yes—
128C22×C4×C13C2×Q812yes—
129C22×C4×C13C2×Q812yes—
130C22×C4×C13#4112yes—
131C22×C4×C13#4112yes—
132C22×C4×C13#4112yes—
133C22×C4×C13#4112yes—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—21no—
139C22×Dic13—22no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13C22×C412yes—
169C22×Dic13C22×C412yes—
170C22×Dic13C22×C414yes—
171C22×Dic13C2×D414yes—
172C22×Dic13C2×D414yes—
173C22×Dic13C2×Q814yes—
174C22×Dic13#4112yes—
175C22×Dic13#4112yes—
176C13×C4⋊C4—28no—
177C13×C4⋊C4—44no—
178C42×C13—28no—
179C4⋊Dic13—28no—
180C4⋊Dic13—216no—
181C4⋊Dic13C22⋊C4116yes—
182#6101—216no—
183#6101—48no—
184C4×Dic13—28no—
185C4×Dic13—48no—
186C4×Dic13—44no—
187C22×#125—131no—
188C2×#389—131no—
189C2×C4×C4⋊C4—131no—
190#1445—132no—
191#1441—132no—
192#1436—132no—
193C4⋊#95—132no—
194C4⋊#95—131no—
195C4⋊#95—131no—
196C4⋊#95D1311yescharacteristic
197C4×#95—131no—
198C23×C13C23×C411yescharacteristic
199C23×C13C22×D411yescharacteristic
200C23×C13C22×D411yescharacteristic
201C23×C13C22×Q811yescharacteristic
202C23×C13C22×Q811yescharacteristic
203C23×C13C2×#4111yescharacteristic
204C23×C13C2×#4111yescharacteristic
205C23×C13C2×#4111yescharacteristic
206C23×C13C2×#4111yescharacteristic
207C23×C13C2×#4111yescharacteristic
208C23×C13C2×#4111yescharacteristic
209C23×C13H(5,𝔽2)11yescharacteristic
210C23×C13H(5,𝔽2)11yescharacteristic
211C23×C132−1+411yescharacteristic
212C23×C132−1+411yescharacteristic
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—24no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—41no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—42no—
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×C13C2×C22⋊C414yes—
241C2×C4×C13C4×Q814yes—
242C2×C4×C13C4×Q814yes—
243C2×C4×C13C22⋊Q814yes—
244C2×C4×C13C22⋊Q814yes—
245C2×C4×C13#12414yes—
246C2×C4×C13#12514yescomplemented
247C2×C4×C13C4⋊Q814yes—
248C2×Dic13—24no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—24no—
252C2×Dic13—24no—
253C2×Dic13—24no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—42no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—42no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13C2×C22⋊C418yes—
290C2×#125—138no—
291C2×#125—264no—
292C2×#125—264no—
293C22×C4⋊C4—131no—
294C22×C4⋊C4—132no—
295C22×C4⋊C4—132no—
296C22×C4⋊C4—131no—
297C22×C4⋊C4—132no—
298C22×C4⋊C4C2×D1311yescharacteristic
299C22×C4⋊C4C2×D1311yescharacteristic
300C22×C42—131no—
301C22×C42—131no—
302C22×C42—132no—
303C22×C42C2×D1311yescharacteristic
304#389—264no—
305C4×C4⋊C4—264no—
306C2×#95—131no—
307C2×#95—131no—
308C2×#95—131no—
309C2×#95—131no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95—132no—
315C2×#95—132no—
316C2×#95C2×D1312yes—
317C2×#95C2×D1312yes—
318C22×C13C22×C22⋊C411yescharacteristic
319C22×C13C2×C4×Q811yescharacteristic
320C22×C13C2×C4×Q811yescharacteristic
321C22×C13C4×#4111yescharacteristic
322C22×C13C4×#4111yescharacteristic
323C22×C13#52011yescharacteristic
324C22×C13#52011yescharacteristic
325C22×C13C2×C22⋊Q811yescharacteristic
326C22×C13C2×C22⋊Q811yescharacteristic
327C22×C13C2×#12411yescharacteristic
328C22×C13C2×#12511yescharacteristic
329C22×C13#52911yescharacteristic
330C22×C13#52911yescharacteristic
331C22×C13C2×C4⋊Q811yescharacteristic
332C22×C13#53311yescharacteristic
333C22×C13#54011yescharacteristic
334C22×C13#54111yescharacteristic
335C22×C13#54411yescharacteristic
336C22×C13#54411yescharacteristic
337C22×C13#54611yescharacteristic
338C22×C13#54611yescharacteristic
339C22×C13#54711yescharacteristic
340C22×C13#54711yescharacteristic
341C22×C13#54811yescharacteristic
342C22×C13#54811yescharacteristic
343C22×C13#55011yescharacteristic
344C22×C13#55011yescharacteristic
345C22×C13#55211yescharacteristic
346C22×C13#55211yescharacteristic
347C22×C13#55311yescharacteristic
348C22×C13#55311yescharacteristic
349C22×C13#55411yescharacteristic
350C22×C13#55411yescharacteristic
351C22×C13#55711yescharacteristic
352C22×C13#55711yescharacteristic
353C4×C13—24no—
354C4×C13—44no—
355C4×C13—42no—
356C4×C13—82no—
357C4×C13#39118yes—
358Dic13—28no—
359Dic13—42no—
360Dic13—42no—
361Dic13—44no—
362Dic13—42no—
363Dic13—42no—
364C23×C4—132no—
365C23×C4—131no—
366C23×C4—131no—
367C23×C4—131no—
368C23×C4—132no—
369C23×C4—131no—
370C23×C4C22×D1312yes—
371C23×C4C22×D1311yescharacteristic
372C23×C4C22×D1312yes—
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1311yescharacteristic
375#125—2632no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—134no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—134no—
384C2×C4⋊C4—138no—
385C2×C4⋊C4—138no—
386C2×C4⋊C4—134no—
387C2×C4⋊C4—264no—
388C2×C4⋊C4—264no—
389C2×C4⋊C4—264no—
390C2×C4⋊C4—264no—
391C2×C4⋊C4—262no—
392C2×C4⋊C4—262no—
393C2×C4⋊C4—264no—
394C2×C4⋊C4—264no—
395C2×C4⋊C4—522no—
396C2×C4⋊C4C4×D1314yes—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—134no—
400C2×C42—262no—
401C2×C42—262no—
402C2×C42—264no—
403C2×C42—262no—
404C2×C42—262no—
405C2×C42—262no—
406C2×C42—264no—
407C2×C42—522no—
408C2×C42Dic2614yes—
409#95—24no—
410#95—42no—
411#95—262no—
412#95—264no—
413#95—262no—
414#95—264no—
415#95—264no—
416#95—262no—
417#95—262no—
418#95—522no—
419#95—522no—
420#95—522no—
421C2×C13C2×#39111yescharacteristic
422C2×C13C4×#12511yescharacteristic
423C2×C13#233011yescharacteristic
424C2×C13#233911yescharacteristic
425C2×C13#234111yescharacteristic
426C2×C13#237011yescharacteristic
427C2×C13#237011yescharacteristic
428C2×C13#244111yescharacteristic
429C2×C13#244211yescharacteristic
430C2×C13#245311yescharacteristic
431C2×C13#245411yescharacteristic
432C2×C13#248911yescharacteristic
433C2×C13#249011yescharacteristic
434C2×C13#255011yescharacteristic
435C2×C13#255211yescharacteristic
436C24C23×D1311yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—134no—
461C22×C4—134no—
462C22×C4—134no—
463C22×C4—132no—
464C22×C4—132no—
465C22×C4—134no—
466C22×C4—132no—
467C22×C4—132no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—262no—
475C22×C4—261no—
476C22×C4—262no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—262no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—262no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—262no—
497C22×C4—261no—
498C22×C4—262no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4—261no—
502C22×C4C2×Dic2612yes—
503C22×C4C2×Dic2612yes—
504C22×C4C2×Dic2612yes—
505C22×C4C2×C4×D1314yes—
506C22×C4C2×C4×D1312yes—
507C22×C4#612712yes—
508C22×C4D4×D1312yes—
509C22×C4D4×D1312yes—
510C22×C4#612912yes—
511C22×C4#612912yes—
512C22×C4Q8×D1312yes—
513C22×C4#613112yes—
514C4⋊C4—28no—
515C4⋊C4—44no—
516C4⋊C4—1316no—
517C4⋊C4—2616no—
518C4⋊C4—2616no—
519C4⋊C4—268no—
520C4⋊C4—528no—
521C42—28no—
522C42—268no—
523C42—528no—
524C42—524no—
525C13#1405411yescharacteristic, complemented, Sylow
526C23C22×Dic2611yescharacteristic
527C23C22×C4×D1311yescharacteristic
528C23C2×#612711yescharacteristic
529C23C2×D4×D1311yescharacteristic
530C23C2×D4×D1311yescharacteristic
531C23C2×#612911yescharacteristic
532C23C2×#612911yescharacteristic
533C23#8825111yescharacteristic
534C23C2×Q8×D1311yescharacteristic
535C23C2×#613111yescharacteristic
536C23#8825411yescharacteristic
537C23#41×D1311yescharacteristic
538C23#41×D1311yescharacteristic
539C23#8825611yescharacteristic
540C23#8825711yescharacteristic
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—138no—
569C2×C4—264no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—264no—
575C2×C4—264no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—264no—
579C2×C4—262no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—262no—
584C2×C4—262no—
585C2×C4—262no—
586C2×C4—262no—
587C2×C4—262no—
588C2×C4—262no—
589C2×C4—264no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—522no—
601C2×C4—521no—
602C2×C4—522no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4C4×Dic2614yes—
611C2×C4#8813214yes—
612C2×C4C22⋊C4×D1314yes—
613C2×C4#8813914yes—
614C2×C4#8814114yes—
615C2×C4#8814214yes—
616C2×C4#8814414yescomplemented
617C2×C4#8815014yes—
618C22C2×C4×Dic2611yescharacteristic
619C22C2×#8813211yescharacteristic
620C22C2×C22⋊C4×D1311yescharacteristic
621C22C2×#8813911yescharacteristic
622C22C2×#8814111yescharacteristic
623C22C2×#8814211yescharacteristic
624C22C2×#8814411yescharacteristic
625C22#1171920511yescharacteristic
626C22C2×#8815011yescharacteristic
627C22#1171922211yescharacteristic
628C22#1171922411yescharacteristic
629C22C4×#612911yescharacteristic
630C22#1171925111yescharacteristic
631C22#1171926211yescharacteristic
632C22#1171926711yescharacteristic
633C22C4×#613111yescharacteristic
634C22#1171927911yescharacteristic
635C22#1171928511yescharacteristic
636C22#1171928811yescharacteristic
637C22#1171930311yescharacteristic
638C22#1171930411yescharacteristic
639C22#1171931911yescharacteristic
640C22#1171932311yescharacteristic
641C22#1171933511yescharacteristic
642C22#1171933611yescharacteristic
643C22#1171934411yescharacteristic
644C22#1171934711yescharacteristic
645C22#1171938111yescharacteristic
646C22#1171938211yescharacteristic
647C22#1171939011yescharacteristic
648C22#1171939511yescharacteristic
649C22#1171942311yescharacteristic
650C22#1171942611yescharacteristic
651C22#1171943111yescharacteristic
652C22#1171943511yescharacteristic
653C4—24no—
654C4—42no—
655C4—44no—
656C4—82no—
657C4—268no—
658C4—522no—
659C4—522no—
660C4—522no—
661C4—522no—
662C4—524no—
663C4#1171830718yes—
664C2C2×#1171830711yescharacteristic
665C2C4×#8814411yescharacteristic
666C2#1311757311yescharacteristic
667C2#1311766511yescharacteristic
668C2#1311767511yescharacteristic
669C2#1311793111yescharacteristic
670C2#1311793711yescharacteristic
671C2#1311855011yescharacteristic
672C2#1311856111yescharacteristic
673C2#1311869811yescharacteristic
674C2#1311870911yescharacteristic
675C2#1311917811yescharacteristic
676C2#1311918911yescharacteristic
677C2#1311985811yescharacteristic
678C2#1311987211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, prime radical, cosocleC24×C13C24
hypercenterC4⋊#95D13
hypocenterC13#14054
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
25. C2×#88144C4semidirect
246. C2×C4×C13#125semidirect
525. C13#14054semidirect
616. C2×C4#88144semidirect

Maximal subgroups

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

subgroupindex
C22×#881442
C2×#117186342
C2×C4×C4⋊Dic132
#131131022
#131130882
#131130702
#131130652
#131130642
C4×#880712
C13×C4⋊#952
#1405413