Finite Group Databasebeta

← #15786603

Subgroups — #15786603

Order 3328.

1386 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×C4⋊C4×Dic13C211yesmaximal, characteristic
2C2×C4×C4⋊Dic13C211yesmaximal, characteristic
3#13113104C212yesmaximal
4#13113093C212yesmaximal
5#13113070C212yesmaximal
6#13113068C212yesmaximal
7#13113066C211yesmaximal, characteristic
8#13113065C211yesmaximal, characteristic
9#13113065C211yesmaximal, characteristic
10#13113065C211yesmaximal, characteristic
11C2×C13×#389C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C42×C13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2212yes—
23C13×#389C418yescomplemented
24C2×C13×#95C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C4⋊C4×Dic13—24no—
37C4×C4⋊Dic13—24no—
38C23×C4×C13C2312yes—
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×Dic13C2312yes—
44C23×Dic13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—42no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4C2×C414yes—
56C2×C13×C4⋊C4C2×C414yes—
57C2×C13×C4⋊C4C2×C418yes—
58C2×C42×C13—22no—
59C2×C42×C13—22no—
60C2×C42×C13C2×C414yes—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13—22no—
63C2×C4⋊Dic13—22no—
64C2×C4⋊Dic13—22no—
65C2×C4⋊Dic13—22no—
66C2×C4⋊Dic13—22no—
67C2×C4⋊Dic13—22no—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13Q814yes—
72C2×C4⋊Dic13Q814yes—
73C2×C4×Dic13—22no—
74C2×C4×Dic13—22no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—24no—
79C2×C4×Dic13—42no—
80C2×C4×Dic13—42no—
81C2×C4×Dic13D414yes—
82C13×#95C2×C418yes—
83#88071—24no—
84#88071—22no—
85#88071—22no—
86#88071—24no—
87#88071—24no—
88#88071—24no—
89#88071—42no—
90#88071—42no—
91#88071—42no—
92#88071—42no—
93#88071—42no—
94#14041—131nomaximal, Sylow
95C24×C13C2411yescharacteristic
96C22×C4×C13—21no—
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—21no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
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—21no—
118C22×C4×C13C22×C414yes—
119C22×C4×C13C22×C414yes—
120C22×C4×C13C22×C412yes—
121C22×C4×C13C22×C412yes—
122C22×C4×C13C22×C412yes—
123C22×C4×C13C2×D412yes—
124C22×C4×C13C2×Q812yes—
125C22×C4×C13C2×Q812yes—
126C22×C4×C13#4112yes—
127C22×C4×C13#4112yes—
128C22×C4×C13#4112yes—
129C22×C4×C13#4112yes—
130C22×C4×C13#4112yes—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—22no—
137C22×Dic13—21no—
138C22×Dic13—22no—
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—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13C2×D412yes—
167C22×Dic13C2×D412yes—
168C22×Dic13C2×Q814yes—
169C22×Dic13C2×Q812yes—
170C22×Dic13C2×Q812yes—
171C22×Dic13#4112yes—
172C22×Dic13#4112yes—
173C13×C4⋊C4—28no—
174C13×C4⋊C4—28no—
175C13×C4⋊C4—48no—
176C42×C13—28no—
177C4⋊Dic13—28no—
178C4⋊Dic13—28no—
179C4⋊Dic13—28no—
180C4⋊Dic13—44no—
181C4×Dic13—28no—
182C4×Dic13—48no—
183C4×Dic13—44no—
184C2×#389D1311yescharacteristic
185C2×C4×C4⋊C4—131no—
186C2×C4×C4⋊C4—131no—
187#1445—132no—
188#1442—132no—
189#1436—132no—
190#1436—132no—
191C4⋊#95—131no—
192C4⋊#95—131no—
193C4⋊#95—131no—
194C4⋊#95—131no—
195C23×C13C23×C411yescharacteristic
196C23×C13C22×D411yescharacteristic
197C23×C13C22×Q811yescharacteristic
198C23×C13C22×Q811yescharacteristic
199C23×C13C2×#4111yescharacteristic
200C23×C13C2×#4111yescharacteristic
201C23×C13C2×#4111yescharacteristic
202C23×C13C2×#4111yescharacteristic
203C23×C13C2×#4111yescharacteristic
204C23×C13C2×#4111yescharacteristic
205C23×C13C2×#4111yescharacteristic
206C23×C13H(5,𝔽2)11yescharacteristic
207C23×C13H(5,𝔽2)11yescharacteristic
208C23×C13H(5,𝔽2)11yescharacteristic
209C23×C132−1+411yescharacteristic
210C2×C4×C13—22no—
211C2×C4×C13—22no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—24no—
217C2×C4×C13—22no—
218C2×C4×C13—24no—
219C2×C4×C13—24no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—24no—
223C2×C4×C13—22no—
224C2×C4×C13—24no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—42no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13#11714yes—
238C2×C4×C13C4×D414yes—
239C2×C4×C13C4×Q814yes—
240C2×C4×C13C4×Q814yes—
241C2×C4×C13C22⋊Q814yes—
242C2×C4×C13#12314yes—
243C2×C4×C13#12514yes—
244C2×C4×C13#12614yes—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—24no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13C22⋊Q814yes—
287C22×C4⋊C4—131no—
288C22×C4⋊C4—131no—
289C22×C4⋊C4—131no—
290C22×C4⋊C4—131no—
291C22×C4⋊C4C2×D1311yescharacteristic
292C22×C4⋊C4C2×D1311yescharacteristic
293C22×C4⋊C4C2×D1312yes—
294C22×C42—131no—
295C22×C42—131no—
296C22×C42—132no—
297C22×C42C2×D1311yescharacteristic
298#389Dic1318yescomplemented
299C4×C4⋊C4—264no—
300C4×C4⋊C4—264no—
301C2×#95—132no—
302C2×#95—132no—
303C2×#95—132no—
304C2×#95—131no—
305C2×#95—132no—
306C2×#95—131no—
307C2×#95—132no—
308C2×#95—132no—
309C2×#95—132no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95C2×D1312yes—
313C22×C13C2×#11711yescharacteristic
314C22×C13C2×C4×D411yescharacteristic
315C22×C13C2×C4×Q811yescharacteristic
316C22×C13C2×C4×Q811yescharacteristic
317C22×C13C4×#4111yescharacteristic
318C22×C13#51811yescharacteristic
319C22×C13#52011yescharacteristic
320C22×C13C2×C22⋊Q811yescharacteristic
321C22×C13C2×C22⋊Q811yescharacteristic
322C22×C13C2×#12311yescharacteristic
323C22×C13#52511yescharacteristic
324C22×C13C2×#12511yescharacteristic
325C22×C13C2×#12611yescharacteristic
326C22×C13#52911yescharacteristic
327C22×C13#53311yescharacteristic
328C22×C13#53511yescharacteristic
329C22×C13#53711yescharacteristic
330C22×C13#54011yescharacteristic
331C22×C13#54211yescharacteristic
332C22×C13#55211yescharacteristic
333C22×C13#55311yescharacteristic
334C22×C13#55311yescharacteristic
335C22×C13#55311yescharacteristic
336C22×C13#55411yescharacteristic
337C22×C13#55411yescharacteristic
338C22×C13#55411yescharacteristic
339C22×C13#55411yescharacteristic
340C22×C13#55511yescharacteristic
341C22×C13#55611yescharacteristic
342C22×C13#55711yescharacteristic
343C22×C13#55711yescharacteristic
344C22×C13Q8211yescharacteristic
345C22×C13#55911yescharacteristic
346C22×C13#55911yescharacteristic
347C22×C13#55911yescharacteristic
348C4×C13—24no—
349C4×C13—42no—
350C4×C13—44no—
351C4×C13—44no—
352C4×C13#38718yes—
353Dic13—24no—
354Dic13—44no—
355Dic13—42no—
356Dic13—42no—
357Dic13—42no—
358Dic13—82no—
359C23×C4—131no—
360C23×C4—131no—
361C23×C4—131no—
362C23×C4—132no—
363C23×C4—131no—
364C23×C4—132no—
365C23×C4C22×D1312yes—
366C23×C4C22×D1311yescharacteristic
367C23×C4C22×D1312yes—
368C23×C4C22×D1311yescharacteristic
369C23×C4C22×D1311yescharacteristic
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—134no—
377C2×C4⋊C4—134no—
378C2×C4⋊C4—262no—
379C2×C4⋊C4—262no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—262no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4—262no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4—262no—
386C2×C4⋊C4—262no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4C2×Dic1314yes—
389C2×C4⋊C4C2×Dic1314yes—
390C2×C4⋊C4C2×Dic1318yes—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—134no—
394C2×C42—262no—
395C2×C42—262no—
396C2×C42—264no—
397C2×C42—262no—
398C2×C42—262no—
399C2×C42—262no—
400C2×C42—522no—
401C2×C42—522no—
402C2×C42C2×Dic1314yes—
403#95—264no—
404#95—264no—
405#95—262no—
406#95—262no—
407#95—264no—
408#95—264no—
409#95—522no—
410#95—522no—
411#95—522no—
412#95—522no—
413#95—522no—
414#95C2×Dic1318yes—
415C2×C13C2×#38711yescharacteristic
416C2×C13C4×C22⋊Q811yescharacteristic
417C2×C13#232411yescharacteristic
418C2×C13#235511yescharacteristic
419C2×C13#235711yescharacteristic
420C2×C13#236911yescharacteristic
421C2×C13#237011yescharacteristic
422C2×C13#248511yescharacteristic
423C2×C13#248711yescharacteristic
424C2×C13#250711yescharacteristic
425C2×C13#250911yescharacteristic
426C2×C13#251111yescharacteristic
427C2×C13#251311yescharacteristic
428C2×C13#258011yescharacteristic
429C2×C13#258211yescharacteristic
430C24C23×D1311yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—132no—
454C22×C4—132no—
455C22×C4—132no—
456C22×C4—132no—
457C22×C4—134no—
458C22×C4—132no—
459C22×C4—132no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—262no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—262no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4#612712yes—
496C22×C4#612712yes—
497C22×C4D4×D1312yes—
498C22×C4#612912yes—
499C22×C4Q8×D1312yes—
500C22×C4Q8×D1312yes—
501C22×C4#613112yes—
502C22×C4#613112yes—
503C22×C4C22×Dic1314yes—
504C22×C4C22×Dic1314yes—
505C22×C4C22×Dic1312yes—
506C22×C4C22×Dic1312yes—
507C22×C4C22×Dic1312yes—
508C4⋊C4—28no—
509C4⋊C4—28no—
510C4⋊C4—48no—
511C4⋊C4—268no—
512C4⋊C4—268no—
513C4⋊C4—268no—
514C4⋊C4—524no—
515C42—28no—
516C42—268no—
517C42—528no—
518C42—524no—
519C13#1404111yescharacteristic, complemented, Sylow
520C23C2×#612711yescharacteristic
521C23C2×#612711yescharacteristic
522C23C2×D4×D1311yescharacteristic
523C23C2×#612911yescharacteristic
524C23#8825111yescharacteristic
525C23#8825111yescharacteristic
526C23C2×Q8×D1311yescharacteristic
527C23C2×Q8×D1311yescharacteristic
528C23C2×#613111yescharacteristic
529C23C2×#613111yescharacteristic
530C23#41×D1311yescharacteristic
531C23#41×D1311yescharacteristic
532C23#8825611yescharacteristic
533C23#8825711yescharacteristic
534C23C23×Dic1311yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—134no—
563C2×C4—262no—
564C2×C4—262no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—262no—
570C2×C4—264no—
571C2×C4—262no—
572C2×C4—264no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—262no—
579C2×C4—264no—
580C2×C4—262no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—522no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—522no—
591C2×C4—522no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—522no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—522no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4—522no—
601C2×C4—522no—
602C2×C4—522no—
603C2×C4—522no—
604C2×C4#8814314yes—
605C2×C4#8814814yes—
606C2×C4#8815014yes—
607C2×C4#8815214yes—
608C2×C4#8818014yes—
609C2×C4D4×Dic1314yes—
610C2×C4Q8×Dic1314yes—
611C2×C4Q8×Dic1314yes—
612C22C2×#8814311yescharacteristic
613C22C2×#8814811yescharacteristic
614C22C2×#8815011yescharacteristic
615C22C2×#8815211yescharacteristic
616C22#1171926311yescharacteristic
617C22#1171926311yescharacteristic
618C22#1171926411yescharacteristic
619C22#1171926411yescharacteristic
620C22#1171927211yescharacteristic
621C22#1171928411yescharacteristic
622C22#1171928911yescharacteristic
623C22#1171929011yescharacteristic
624C22#1171930811yescharacteristic
625C22#1171931211yescharacteristic
626C22#1171931311yescharacteristic
627C22#1171932411yescharacteristic
628C22#1171932711yescharacteristic
629C22#1171932911yescharacteristic
630C22D13×C22⋊Q811yescharacteristic
631C22#1171933211yescharacteristic
632C22#1171939011yescharacteristic
633C22#1171939511yescharacteristic
634C22#1171939911yescharacteristic
635C22#1171940011yescharacteristic
636C22#1171942711yescharacteristic
637C22#1171943511yescharacteristic
638C22#1171943511yescharacteristic
639C22#1171943911yescharacteristic
640C22C2×#8818011yescharacteristic
641C22C2×D4×Dic1311yescharacteristic
642C22#1171950311yescharacteristic
643C22C2×Q8×Dic1311yescharacteristic
644C22C2×Q8×Dic1311yescharacteristic
645C22#41×Dic1311yescharacteristic
646C22#1171953211yescharacteristic
647C4—24no—
648C4—42no—
649C4—44no—
650C4—44no—
651C4—264no—
652C4—522no—
653C4—522no—
654C4—522no—
655C4—524no—
656C4—1042no—
657C4#1171864218yes—
658C2C2×#1171864211yescharacteristic
659C2C22⋊Q8×Dic1311yescharacteristic
660C2#1311753111yescharacteristic
661C2#1311779311yescharacteristic
662C2#1311780911yescharacteristic
663C2#1311792611yescharacteristic
664C2#1311793611yescharacteristic
665C2#1311913611yescharacteristic
666C2#1311915111yescharacteristic
667C2#1311936111yescharacteristic
668C2#1311938311yescharacteristic
669C2#1311941411yescharacteristic
670C2#1311943611yescharacteristic
671C2#1312019611yescharacteristic
672C2#1312020811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#389D13
hypocenterC13#14041
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
23. C13×#389C4semidirect
298. #389Dic13semidirect
519. C13#14041semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic132
C2×C4×C4⋊Dic132
#131131042
#131130932
#131130702
#131130682
#131130662
#131130652
C2×C13×#3892
#1404113