Finite Group Databasebeta

← #15785674

Subgroups — #15785674

Order 3328.

2150 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718329C212yesmaximal
2C2×#11718650C212yesmaximal
3C2×#11718328C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic
5C2×D13×#95C211yesmaximal, characteristic
6#13113100C212yesmaximal, complemented
7#13113099C212yesmaximal, complemented
8#13113066C211yesmaximal, characteristic, complemented
9#13113064C211yesmaximal, characteristic, complemented
10#13113064C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D13C2212yes—
13C23×C4×D13C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×C4⋊Dic13C2212yes—
20C22×#6101C2212yes—
21C22×#6101C2212yes—
22C22×#6101C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C2×C13×#95C2212yes—
25C2×C13×#95C2211yescharacteristic
26C2×C13×#95C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35#11718650—28no—
36C4×#6103C418yescomplemented
37#11718329—28no—
38#11718328—24no—
39D13×#95—24no—
40C24×D13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C22×C4×D13—24no—
52C22×C4×D13—24no—
53C22×C4×D13—24no—
54C22×C4×D13—24no—
55C22×C4×D13—24no—
56C22×C4×D13—42no—
57C22×C4×D13—42no—
58C22×C4×D13—42no—
59C22×C4×D13—42no—
60C22×C4×D13C2×C414yes—
61C22×C4×D13D414yes—
62C22×C4×D13Q814yes—
63C2×C13×C4⋊C4—24no—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4—42no—
66C2×C42×C13—42no—
67C2×C42×C13C2×C414yescomplemented
68C2×#6103—24no—
69C2×#6103—24no—
70C2×#6103—24no—
71C2×#6103C2×C414yes—
72C2×#6103C2×C414yes—
73C2×#6103D414yes—
74C2×#6103D414yes—
75C2×#6103Q814yes—
76C2×#6103Q814yes—
77C2×C4⋊Dic13—24no—
78C2×C4⋊Dic13—24no—
79C2×C4⋊Dic13—42no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101—24no—
83C2×#6101—24no—
84C2×#6101—24no—
85C2×#6101—42no—
86C2×#6101—42no—
87C2×#6101—42no—
88C2×#6101—42no—
89C2×C4×Dic13—42no—
90C2×C4×Dic13C2×C414yescomplemented
91C13×#95—22no—
92C13×#95—22no—
93C13×#95—24no—
94#88071—22no—
95#88071—22no—
96#88071—24no—
97#88071—24no—
98#88071—24no—
99#88071—24no—
100#88071C2×C414yescomplemented
101#88071C2×C414yescomplemented
102#13965—131nomaximal, Sylow
103C24×C13C2411yescharacteristic
104C23×D13—22no—
105C23×D13—22no—
106C23×D13—22no—
107C23×D13—22no—
108C23×D13C22×C412yes—
109C23×D13C2×D412yes—
110C23×D13C2×D412yes—
111C23×D13C2×D412yes—
112C23×D13C2×Q812yes—
113C23×D13C2×Q812yes—
114C23×D13C2×Q812yes—
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×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×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C22×C412yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D412yes—
140C22×C4×C13C2×Q812yes—
141C22×C4×C13C2×Q812yes—
142C22×C4×C13C2×Q812yes—
143C22×C4×C13#4114yes—
144C22×Dic13—22no—
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×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13C22×C412yes—
164C22×Dic13C22×C412yes—
165C22×Dic13C22×C412yes—
166C22×Dic13C2×D412yes—
167C22×Dic13C2×D412yes—
168C22×Dic13C2×D412yes—
169C22×Dic13C2×Q812yes—
170C22×Dic13C2×Q812yes—
171C22×Dic13C2×Q812yes—
172C22×Dic13#4114yes—
173C2×C4×D13—216no—
174C2×C4×D13—44no—
175C2×C4×D13—44no—
176C2×C4×D13—48no—
177C2×C4×D13—48no—
178C2×C4×D13—48no—
179C2×C4×D13—48no—
180C2×C4×D13—48no—
181C2×C4×D13—48no—
182C2×C4×D13—48no—
183C2×C4×D13—48no—
184C2×C4×D13C4⋊C4116yescomplemented
185C13×C4⋊C4—48no—
186C42×C13—44no—
187#6103—48no—
188#6103C4⋊C4116yescomplemented
189#6103C4⋊C4116yescomplemented
190C4⋊Dic13—48no—
191#6101—48no—
192#6101—48no—
193#6101—48no—
194C4×Dic13—44no—
195C2×#385—132no—
196C2×#385—132no—
197C2×#380—131no—
198C2×C4×C22⋊C4—131no—
199C22×#95—131no—
200#1444—132no—
201#1444—132no—
202C4⋊#95—131no—
203C4⋊#95—131no—
204C4⋊#95—131no—
205C4⋊#95D1311yescharacteristic, complemented
206C23×C13C23×C411yescharacteristic
207C23×C13C22×D411yescharacteristic
208C23×C13C22×D411yescharacteristic
209C23×C13C22×D411yescharacteristic
210C23×C13C22×Q811yescharacteristic
211C23×C13C22×Q811yescharacteristic
212C23×C13C22×Q811yescharacteristic
213C23×C13C2×#4112yes—
214C23×C13C2×#4112yes—
215C23×C13H(5,𝔽2)12yes—
216C23×C13H(5,𝔽2)12yes—
217C22×D13—22no—
218C22×D13—22no—
219C22×D13—22no—
220C22×D13—22no—
221C22×D13—24no—
222C22×D13—24no—
223C22×D13—24no—
224C22×D13—24no—
225C22×D13—24no—
226C22×D13—24no—
227C22×D13—24no—
228C22×D13—24no—
229C22×D13—24no—
230C22×D13—24no—
231C22×D13—24no—
232C22×D13—24no—
233C22×D13C2×C4⋊C414yes—
234C22×D13C2×C4⋊C414yes—
235C22×D13C2×C4⋊C414yes—
236C22×D13#12714yes—
237C22×D13C4⋊Q814yes—
238C22×D13C4⋊Q814yes—
239C22×D13C4⋊Q814yes—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
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×C13C2×C4⋊C414yes—
267C2×C4×C13C2×C4⋊C414yes—
268C2×C4×C13C2×C4⋊C414yes—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—24no—
276C2×Dic13—24no—
277C2×Dic13—24no—
278C2×Dic13—24no—
279C2×Dic13—24no—
280C2×Dic13—24no—
281C2×Dic13—24no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—42no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13C2×C4⋊C414yes—
296C2×Dic13C2×C4⋊C414yes—
297C2×Dic13C2×C4⋊C414yes—
298C4×D13—416no—
299C4×D13—432no—
300C24×C4—131no—
301C24×C4—132no—
302C22×C4⋊C4—132no—
303C22×C4⋊C4—132no—
304C22×C4⋊C4—132no—
305C22×C4⋊C4—132no—
306C22×C4⋊C4C2×D1312yes—
307C22×C22⋊C4—131no—
308C22×C22⋊C4—131no—
309C22×C22⋊C4—132no—
310C22×C42—131no—
311C22×C42C2×D1311yescharacteristic
312#385—268no—
313#385—268no—
314#380—264no—
315C4×C22⋊C4—138no—
316C2×#95—131no—
317C2×#95—131no—
318C2×#95—131no—
319C2×#95—131no—
320C2×#95—132no—
321C2×#95—132no—
322C2×#95—132no—
323C2×#95—132no—
324C2×#95—264no—
325C2×#95C2×D1311yescharacteristic
326C2×#95C2×D1311yescharacteristic
327C2×#95C2×D1312yes—
328C22×C13C22×C4⋊C411yescharacteristic
329C22×C13C22×C4⋊C411yescharacteristic
330C22×C13C22×C4⋊C411yescharacteristic
331C22×C13C4×#4111yescharacteristic
332C22×C13C4×#4111yescharacteristic
333C22×C13#51811yescharacteristic
334C22×C13#51811yescharacteristic
335C22×C13#52512yes—
336C22×C13C2×#12711yescharacteristic
337C22×C13C2×C4⋊Q811yescharacteristic
338C22×C13C2×C4⋊Q811yescharacteristic
339C22×C13C2×C4⋊Q811yescharacteristic
340C22×C13#53312yes—
341C22×C13#53412yes—
342C22×C13#54312yes—
343C22×C13#54612yes—
344C22×C13#54612yes—
345C22×C13#54612yes—
346C22×C13#54612yes—
347C22×C13#55412yes—
348C22×C13#55412yes—
349C22×C13#55412yes—
350C22×C13#55412yes—
351C2×D13—24no—
352C2×D13—28no—
353C2×D13—24no—
354C2×D13—24no—
355C2×D13—24no—
356C2×D13—24no—
357C2×D13—28no—
358C2×D13—28no—
359C2×D13—28no—
360C2×D13—24no—
361C2×D13#38418yes—
362C4×C13—24no—
363C4×C13—24no—
364C4×C13—24no—
365C4×C13—44no—
366C4×C13—82no—
367Dic13—24no—
368Dic13—24no—
369Dic13—24no—
370Dic13—44no—
371Dic13—82no—
372C25—131no—
373C23×C4—131no—
374C23×C4—131no—
375C23×C4—131no—
376C23×C4—134no—
377C23×C4—134no—
378C23×C4—134no—
379C23×C4—132no—
380C23×C4—132no—
381C23×C4—264no—
382C23×C4—264no—
383C23×C4—264no—
384C23×C4—264no—
385C23×C4—264no—
386C23×C4—522no—
387C23×C4—522no—
388C23×C4—522no—
389C23×C4—522no—
390C23×C4C22×D1312yes—
391C23×C4C22×D1312yes—
392C23×C4C22×D1311yescharacteristic
393C23×C4C22×D1311yescharacteristic
394C23×C4C22×D1311yescharacteristic
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—264no—
399C2×C4⋊C4—264no—
400C2×C4⋊C4—264no—
401C2×C4⋊C4—264no—
402C2×C4⋊C4—264no—
403C2×C4⋊C4—264no—
404C2×C4⋊C4—264no—
405C2×C4⋊C4—522no—
406C2×C4⋊C4—522no—
407C2×C4⋊C4—522no—
408C2×C4⋊C4—522no—
409C2×C4⋊C4—522no—
410C2×C22⋊C4—134no—
411C2×C22⋊C4—134no—
412C2×C22⋊C4—134no—
413C2×C22⋊C4—134no—
414C2×C22⋊C4—134no—
415C2×C22⋊C4—134no—
416C2×C22⋊C4—264no—
417C2×C22⋊C4—264no—
418C2×C22⋊C4—264no—
419C2×C42—42no—
420C2×C42—134no—
421C2×C42—522no—
422C2×C42C4×D1314yescomplemented
423#95—22no—
424#95—22no—
425#95—24no—
426#95—134no—
427#95—134no—
428#95—264no—
429#95—264no—
430#95—264no—
431#95—262no—
432#95—262no—
433#95—264no—
434C2×C13C2×#38411yescharacteristic
435C2×C13#229611yescharacteristic
436C2×C13#231511yescharacteristic
437C2×C13#234911yescharacteristic
438C2×C13#234911yescharacteristic
439C2×C13#234911yescharacteristic
440C2×C13#234911yescharacteristic
441C2×C13#253912yes—
442C2×C13#254912yes—
443C2×C13#254912yes—
444C2×C13#258312yes—
445D13—28no—
446C24—132no—
447C24—132no—
448C24—132no—
449C24—132no—
450C24—132no—
451C24—132no—
452C24—132no—
453C24—262no—
454C24—262no—
455C24—262no—
456C24—262no—
457C24C23×D1311yescharacteristic
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—132no—
478C22×C4—132no—
479C22×C4—132no—
480C22×C4—132no—
481C22×C4—132no—
482C22×C4—132no—
483C22×C4—132no—
484C22×C4—132no—
485C22×C4—132no—
486C22×C4—1316no—
487C22×C4—134no—
488C22×C4—2616no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—524no—
509C22×C4—524no—
510C22×C4—528no—
511C22×C4—528no—
512C22×C4—528no—
513C22×C4—528no—
514C22×C4—528no—
515C22×C4—528no—
516C22×C4—528no—
517C22×C4—528no—
518C22×C4C2×C4×D1312yes—
519C22×C4C2×C4×D1312yes—
520C22×C4C2×C4×D1312yes—
521C22×C4#612714yes—
522C22×C4D4×D1312yes—
523C22×C4D4×D1312yes—
524C22×C4D4×D1312yes—
525C22×C4Q8×D1312yes—
526C22×C4Q8×D1312yes—
527C22×C4Q8×D1312yes—
528C4⋊C4—48no—
529C4⋊C4—528no—
530C4⋊C4—528no—
531C4⋊C4—528no—
532C4⋊C4—528no—
533C22⋊C4—1316no—
534C22⋊C4—1316no—
535C22⋊C4—528no—
536C42—44no—
537C42—524no—
538C13#1396511yescharacteristic, complemented, Sylow
539C23—134no—
540C23—134no—
541C23—134no—
542C23—134no—
543C23—134no—
544C23—134no—
545C23—134no—
546C23—262no—
547C23—262no—
548C23—264no—
549C23—264no—
550C23—262no—
551C23—262no—
552C23—264no—
553C23—264no—
554C23—264no—
555C23—264no—
556C23—264no—
557C23—264no—
558C23—264no—
559C23—264no—
560C23—264no—
561C23—264no—
562C23C22×C4×D1311yescharacteristic
563C23C2×#612712yes—
564C23C2×D4×D1311yescharacteristic
565C23C2×D4×D1311yescharacteristic
566C23C2×D4×D1311yescharacteristic
567C23#8825112yes—
568C23C2×Q8×D1311yescharacteristic
569C23C2×Q8×D1311yescharacteristic
570C23C2×Q8×D1311yescharacteristic
571C23#41×D1312yes—
572C23#8825612yes—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—134no—
600C2×C4—134no—
601C2×C4—134no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—262no—
606C2×C4—262no—
607C2×C4—262no—
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—264no—
617C2×C4—5216no—
618C2×C4—5232no—
619C2×C4—522no—
620C2×C4—522no—
621C2×C4—522no—
622C2×C4—522no—
623C2×C4—522no—
624C2×C4—522no—
625C2×C4—522no—
626C2×C4—522no—
627C2×C4—522no—
628C2×C4—522no—
629C2×C4—522no—
630C2×C4C4⋊C4×D1314yes—
631C2×C4C4⋊C4×D1314yes—
632C2×C4C4⋊C4×D1314yes—
633C22—138no—
634C22—264no—
635C22—268no—
636C22—264no—
637C22—264no—
638C22—264no—
639C22—264no—
640C22—268no—
641C22—268no—
642C22—264no—
643C22—268no—
644C22C4×#612711yescharacteristic
645C22#1171919111yescharacteristic
646C22#1171919512yes—
647C22C2×C4⋊C4×D1311yescharacteristic
648C22C2×C4⋊C4×D1311yescharacteristic
649C22C2×C4⋊C4×D1311yescharacteristic
650C22#1171921612yes—
651C22#1171922611yescharacteristic
652C22#1171922711yescharacteristic
653C22#1171925212yes—
654C22#1171925512yes—
655C22#1171928312yes—
656C22#1171928412yes—
657C22#1171931012yes—
658C22#1171931512yes—
659C22#1171933912yes—
660C22#1171934112yes—
661C22#1171938112yes—
662C22#1171939512yes—
663C22D13×#12711yescharacteristic
664C22D13×C4⋊Q811yescharacteristic
665C22D13×C4⋊Q811yescharacteristic
666C22D13×C4⋊Q811yescharacteristic
667C4—24no—
668C4—24no—
669C4—24no—
670C4—44no—
671C4—82no—
672C4—264no—
673C4—264no—
674C4—264no—
675C4—524no—
676C4—1042no—
677C2—268no—
678C2D13×#38411yescharacteristic
679C2#1311731611yescharacteristic
680C2#1311744911yescharacteristic
681C2#1311774011yescharacteristic
682C2#1311774311yescharacteristic
683C2#1311774411yescharacteristic
684C2#1311774711yescharacteristic
685C2#1311976512yes—
686C2#1311984512yes—
687C2#1311984612yes—
688C2#1312021412yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#13965
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
6. #13113100C2semidirect
7. #13113099C2semidirect
8. #13113066C2semidirect
9. #13113064C2semidirect
10. #13113064C2semidirect
11. C13×C4⋊#95C2semidirect
36. C4×#6103C4semidirect
67. C2×C42×C13C2×C4semidirect
90. C2×C4×Dic13C2×C4semidirect
100. #88071C2×C4semidirect
101. #88071C2×C4semidirect
184. C2×C4×D13C4⋊C4semidirect
188. #6103C4⋊C4semidirect
189. #6103C4⋊C4semidirect
205. C4⋊#95D13semidirect
422. C2×C42C4×D13semidirect
538. C13#13965semidirect

Maximal subgroups

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

subgroupindex
C2×#117183292
C2×#117186502
C2×#117183282
C2×C4×#61032
C2×D13×#952
#131131002
#131130992
#131130662
#131130642
C13×C4⋊#952
#1396513