Finite Group Databasebeta

← #15791319

Subgroups — #15791319

Order 3328.

2018 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718881C212yesmaximal
2C2×#11718611C212yesmaximal, complemented
3#13113089C212yesmaximal, complemented
4#13113081C212yesmaximal, complemented
5#13113081C212yesmaximal, complemented
6#13113066C211yesmaximal, characteristic, complemented
7#13113063C211yesmaximal, characteristic, complemented
8#13113058C212yesmaximal, complemented
9C2×C13×#390C211yesmaximal, characteristic
10C23×D4×C13C2211yescharacteristic
11C24×Dic13C2212yes—
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2212yes—
14C22×C13×C22⋊C4C2212yes—
15C22×C42×C13C2211yescharacteristic
16C22×C22⋊Dic13C2212yes—
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C4⋊Dic13C2212yes—
20C22×C4⋊Dic13C2212yes—
21C13×#390C418yescomplemented
22#11718881—28no—
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33#11718611—28no—
34C25×C13C2312yes—
35C22×D4×C13—42no—
36C22×D4×C13—42no—
37C22×D4×C13C2×C414yes—
38C22×D4×C13D414yes—
39C22×D4×C13Q814yes—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×Dic13—24no—
45C23×Dic13—24no—
46C23×Dic13—24no—
47C23×Dic13—42no—
48C23×Dic13—42no—
49C23×Dic13—42no—
50C23×Dic13—42no—
51C23×Dic13C2312yes—
52C23×Dic13C2312yes—
53C23×Dic13C2312yes—
54C23×Dic13C2312yes—
55C2×C13×C4⋊C4—42no—
56C2×C13×C4⋊C4C2×C414yescomplemented
57C2×C13×C22⋊C4—24no—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—42no—
60C2×C13×C22⋊C4—42no—
61C2×C13×C22⋊C4C2×C418yescomplemented
62C2×C13×C22⋊C4C2×C418yescomplemented
63C2×C42×C13—42no—
64C2×C42×C13C2×C414yescomplemented
65C2×C22⋊Dic13—24no—
66C2×C22⋊Dic13—24no—
67C2×C22⋊Dic13—24no—
68C2×C22⋊Dic13—24no—
69C2×C22⋊Dic13—24no—
70C2×C22⋊Dic13—42no—
71C2×C22⋊Dic13—42no—
72C2×C22⋊Dic13—42no—
73C2×C22⋊Dic13—42no—
74C2×C4⋊Dic13—24no—
75C2×C4⋊Dic13—24no—
76C2×C4⋊Dic13—24no—
77C2×C4⋊Dic13—42no—
78C2×C4⋊Dic13—42no—
79C2×C4⋊Dic13—42no—
80#88071—24no—
81#88071—24no—
82#88071—22no—
83#88071—24no—
84#88071—41no—
85#88071—42no—
86#88071—42no—
87#88071—42no—
88#88071—41no—
89#88071D414yescomplemented
90#14438—131nomaximal, Sylow
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13C22×C414yes—
104C24×C13C2×D414yes—
105C24×C13C2×Q814yes—
106C24×C13C2411yescharacteristic
107C2×D4×C13—44no—
108C2×D4×C13—44no—
109C2×D4×C13—48no—
110C2×D4×C13—48no—
111C2×D4×C13C4⋊C4116yescomplemented
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—21no—
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—21no—
126C22×C4×C13C22×C412yes—
127C22×C4×C13C22×C414yes—
128C22×C4×C13C22×C412yes—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C2×D412yes—
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×Q812yes—
133C22×C4×C13#4112yes—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
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—48no—
161C22×Dic13—48no—
162C22×Dic13—48no—
163C22×Dic13—48no—
164C22×Dic13—48no—
165C22×Dic13—48no—
166C22×Dic13—48no—
167C22×Dic13C2×D414yes—
168C22×Dic13#4114yes—
169C13×C4⋊C4—44no—
170C13×C22⋊C4—216no—
171C13×C22⋊C4—48no—
172C42×C13—44no—
173C22⋊Dic13—48no—
174C22⋊Dic13—48no—
175C22⋊Dic13—48no—
176C4⋊Dic13—48no—
177C4⋊Dic13—48no—
178C2×#390D1311yescharacteristic
179C2×#386—132no—
180C2×#385—132no—
181#1441—132no—
182#1439—132no—
183#1439—132no—
184C4⋊#95—131no—
185#1434—131no—
186C22⋊#95—132no—
187C23×C13—24no—
188C23×C13—24no—
189C23×C13—24no—
190C23×C13—24no—
191C23×C13—24no—
192C23×C13—24no—
193C23×C13—24no—
194C23×C13—24no—
195C23×C13—24no—
196C23×C13—24no—
197C23×C13—24no—
198C23×C13—24no—
199C23×C13—24no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—24no—
204C23×C13—24no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13C2×C4⋊C418yes—
222C23×C13C23×C411yescharacteristic
223C23×C13C22×D411yescharacteristic
224C23×C13C22×D411yescharacteristic
225C23×C13C22×Q811yescharacteristic
226C23×C13C2×#4111yescharacteristic
227C23×C13C2×#4112yes—
228C23×C13H(5,𝔽2)12yes—
229C23×C13H(5,𝔽2)12yes—
230C23×C13H(5,𝔽2)12yes—
231C23×C13H(5,𝔽2)11yescharacteristic
232C23×C132−1+411yescharacteristic
233D4×C13—416no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—22no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13C2×C4⋊C414yes—
255C2×C4×C13C4×D414yes—
256C2×Dic13—24no—
257C2×Dic13—24no—
258C2×Dic13—24no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—24no—
262C2×Dic13—432no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C23×D4C2×D1311yescharacteristic
286C24×C4—132no—
287C22×C4⋊C4—132no—
288C22×C4⋊C4—132no—
289C22×C4⋊C4C2×D1311yescharacteristic
290C22×C22⋊C4—132no—
291C22×C22⋊C4—132no—
292C22×C22⋊C4—132no—
293C22×C22⋊C4C2×D1312yes—
294C22×C22⋊C4C2×D1312yes—
295C22×C42C2×D1311yescharacteristic
296#390Dic1318yescomplemented
297#386—268no—
298#385—268no—
299C2×#95—131no—
300C2×#95—132no—
301C2×#95—131no—
302C2×#95—132no—
303C2×#95—132no—
304C2×#95—131no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95—131no—
308C2×#95—132no—
309C22×C13—28no—
310C22×C13—28no—
311C22×C13—28no—
312C22×C13—44no—
313C22×C13—44no—
314C22×C13—44no—
315C22×C13—44no—
316C22×C13—44no—
317C22×C13—44no—
318C22×C13—44no—
319C22×C13—44no—
320C22×C13—44no—
321C22×C13—44no—
322C22×C13—44no—
323C22×C13—44no—
324C22×C13C22×C4⋊C411yescharacteristic
325C22×C13C2×C4×D411yescharacteristic
326C22×C13C4×#4111yescharacteristic
327C22×C13#51811yescharacteristic
328C22×C13#51811yescharacteristic
329C22×C13#51811yescharacteristic
330C22×C13#52011yescharacteristic
331C22×C13#53412yes—
332C22×C13#53512yes—
333C22×C13#53812yes—
334C22×C13#54012yes—
335C22×C13#54212yes—
336C22×C13#54312yes—
337C22×C13D4211yescharacteristic
338C22×C13#54612yes—
339C22×C13#54612yes—
340C22×C13#54711yescharacteristic
341C22×C13D4×Q811yescharacteristic
342C22×C13#55312yes—
343C22×C13#55412yes—
344C22×C13#55411yescharacteristic
345C22×C13#56012yes—
346C22×C13#56212yes—
347C4×C13—24no—
348C4×C13—24no—
349C4×C13—44no—
350C4×C13—42no—
351Dic13—44no—
352Dic13—44no—
353Dic13—82no—
354Dic13—82no—
355C25C22×D1312yes—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4Dic2614yes—
359C22×D4D5214yes—
360C22×D4C2×Dic1314yes—
361C23×C4—132no—
362C23×C4—132no—
363C23×C4—132no—
364C23×C4—132no—
365C23×C4—264no—
366C23×C4—264no—
367C23×C4—264no—
368C23×C4—522no—
369C23×C4—522no—
370C23×C4—522no—
371C23×C4—522no—
372C23×C4C22×D1312yes—
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1311yescharacteristic
376C2×C4⋊C4—42no—
377C2×C4⋊C4—264no—
378C2×C4⋊C4—264no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—522no—
381C2×C4⋊C4—522no—
382C2×C4⋊C4—522no—
383C2×C4⋊C4C2×Dic1314yescomplemented
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—264no—
389C2×C22⋊C4—264no—
390C2×C22⋊C4—264no—
391C2×C22⋊C4—264no—
392C2×C22⋊C4—264no—
393C2×C22⋊C4—522no—
394C2×C22⋊C4—522no—
395C2×C22⋊C4—522no—
396C2×C22⋊C4—522no—
397C2×C22⋊C4C2×Dic1318yescomplemented
398C2×C22⋊C4C2×Dic1318yescomplemented
399C2×C42—42no—
400C2×C42C2×Dic1314yescomplemented
401#95—134no—
402#95—264no—
403#95—264no—
404#95—264no—
405#95—262no—
406#95—522no—
407#95—522no—
408#95—522no—
409#95—521no—
410#95—521no—
411C2×C13—48no—
412C2×C13#231511yescharacteristic
413C2×C13#232811yescharacteristic
414C2×C13#233711yescharacteristic
415C2×C13D4×C4⋊C411yescharacteristic
416C2×C13#234911yescharacteristic
417C2×C13#236411yescharacteristic
418C2×C13#237711yescharacteristic
419C2×C13#267812yes—
420C2×C13#269212yes—
421C2×C13#270112yes—
422C2×C13#278012yes—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24C2×Dic2614yes—
436C24C2×D5214yes—
437C24C22×Dic1314yes—
438C24C23×D1311yescharacteristic
439C2×D4—48no—
440C2×D4—48no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4C4⋊Dic13116yescomplemented
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—134no—
459C22×C4—134no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—528no—
487C22×C4—528no—
488C22×C4—528no—
489C22×C4—528no—
490C22×C4—528no—
491C22×C4—528no—
492C22×C4—528no—
493C22×C4C2×Dic2612yes—
494C22×C4C2×D5212yes—
495C22×C4D4×D1312yes—
496C22×C4#612912yes—
497C22×C4C22×Dic1312yes—
498C22×C4C22×Dic1314yes—
499C22×C4C22×Dic1312yes—
500C22×C4C22×Dic1312yes—
501C4⋊C4—44no—
502C4⋊C4—528no—
503C4⋊C4—528no—
504C22⋊C4—216no—
505C22⋊C4—48no—
506C22⋊C4—528no—
507C22⋊C4—528no—
508C22⋊C4—528no—
509C42—44no—
510C13#1443811yescharacteristic, complemented, Sylow
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23C2×C4⋊Dic1318yes—
546C23C22×Dic2611yescharacteristic
547C23C22×D5211yescharacteristic
548C23C2×D4×D1311yescharacteristic
549C23C2×#612911yescharacteristic
550C23#8825112yes—
551C23#8825112yes—
552C23#8825112yes—
553C23#41×D1312yes—
554C23#8825611yescharacteristic
555C23#8825711yescharacteristic
556C23C23×Dic1311yescharacteristic
557D4—416no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—264no—
579C2×C4—264no—
580C2×C4—264no—
581C2×C4—264no—
582C2×C4—264no—
583C2×C4—264no—
584C2×C4—5232no—
585C2×C4—522no—
586C2×C4—522no—
587C2×C4—522no—
588C2×C4—522no—
589C2×C4—522no—
590C2×C4—522no—
591C2×C4—522no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—522no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4—522no—
601C2×C4—522no—
602C2×C4—522no—
603C2×C4—522no—
604C2×C4—522no—
605C2×C4—522no—
606C2×C4—522no—
607C2×C4C2×C4⋊Dic1314yes—
608C2×C4D4×Dic1314yes—
609C22—28no—
610C22—28no—
611C22—28no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—44no—
622C22—44no—
623C22—44no—
624C22#1171918812yes—
625C22#1171919812yes—
626C22D4×Dic2611yescharacteristic
627C22#1171924412yes—
628C22#1171924811yescharacteristic
629C22D4×D5211yescharacteristic
630C22#1171925912yes—
631C22#1171926011yescharacteristic
632C22#1171930612yes—
633C22#1171931512yes—
634C22#1171932512yes—
635C22#1171932612yes—
636C22#1171937412yes—
637C22#1171938312yes—
638C22#1171942012yes—
639C22#1171942412yes—
640C22C22×C4⋊Dic1311yescharacteristic
641C22C2×D4×Dic1311yescharacteristic
642C22#1171950311yescharacteristic
643C22#1171950311yescharacteristic
644C22#1171950311yescharacteristic
645C22#41×Dic1311yescharacteristic
646C22#1171953211yescharacteristic
647C4—24no—
648C4—24no—
649C4—42no—
650C4—44no—
651C4—524no—
652C4—524no—
653C4—1042no—
654C4—1042no—
655C2—48no—
656C2#1311745011yescharacteristic
657C2#1311756211yescharacteristic
658C2#1311765111yescharacteristic
659C2D4×C4⋊Dic1311yescharacteristic
660C2#1311774611yescharacteristic
661C2#1311788811yescharacteristic
662C2#1311799311yescharacteristic
663C2#1312115612yes—
664C2#1312132912yes—
665C2#1312144712yes—
666C2#1312248512yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#390C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#14438
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#11718611C2semidirect
3. #13113089C2semidirect
4. #13113081C2semidirect
5. #13113081C2semidirect
6. #13113066C2semidirect
7. #13113063C2semidirect
8. #13113058C2semidirect
21. C13×#390C4semidirect
56. C2×C13×C4⋊C4C2×C4semidirect
61. C2×C13×C22⋊C4C2×C4semidirect
62. C2×C13×C22⋊C4C2×C4semidirect
64. C2×C42×C13C2×C4semidirect
89. #88071D4semidirect
111. C2×D4×C13C4⋊C4semidirect
296. #390Dic13semidirect
383. C2×C4⋊C4C2×Dic13semidirect
397. C2×C22⋊C4C2×Dic13semidirect
398. C2×C22⋊C4C2×Dic13semidirect
400. C2×C42C2×Dic13semidirect
443. C2×D4C4⋊Dic13semidirect
510. C13#14438semidirect

Maximal subgroups

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

subgroupindex
C2×#117188812
C2×#117186112
#131130892
#131130812
#131130662
#131130632
#131130582
C2×C13×#3902
#1443813