Finite Group Databasebeta

← #15784310

Subgroups — #15784310

Order 3328.

1958 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6103C211yesmaximal, characteristic
2C2×#11718327C211yesmaximal, characteristic
3C2×D13×#95C211yesmaximal, characteristic
4#13113063C211yesmaximal, characteristic, complemented
5#13113062C212yesmaximal, complemented
6#13113061C211yesmaximal, characteristic, complemented
7#13113061C211yesmaximal, characteristic, complemented
8#13113060C212yesmaximal, complemented
9#13113057C212yesmaximal
10#13113057C212yesmaximal
11C13×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D13C2212yes—
13C23×C4×D13C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×#6103C2212yes—
16C22×#6103C2211yescharacteristic
17C22×#6103C2211yescharacteristic
18C22×C4×Dic13C2212yes—
19C22×C4×Dic13C2211yescharacteristic
20C2×C13×#95C2212yes—
21C2×C13×#95C2212yes—
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2211yescharacteristic
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C4×#6103C418yescomplemented
36#11718327C418yescomplemented
37D13×#95C418yescomplemented
38C24×D13C2311yescharacteristic
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×Dic13C2312yes—
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C22×C4×D13—24no—
50C22×C4×D13—24no—
51C22×C4×D13—42no—
52C22×C4×D13—42no—
53C22×C4×D13—42no—
54C22×C4×D13—42no—
55C22×C4×D13—42no—
56C22×C4×D13—42no—
57C22×C4×D13C2×C418yes—
58C22×C4×D13C2×C414yes—
59C22×C4×D13C2×C414yes—
60C22×C4×D13C2×C414yes—
61C2×C42×C13—42no—
62C2×C42×C13C2×C414yescomplemented
63C2×#6103—24no—
64C2×#6103—24no—
65C2×#6103—24no—
66C2×#6103—24no—
67C2×#6103C2×C418yes—
68C2×#6103C2×C414yes—
69C2×#6103C2×C414yes—
70C2×C4×Dic13—42no—
71C2×C4×Dic13—42no—
72C2×C4×Dic13—42no—
73C2×C4×Dic13C2×C418yescomplemented
74C2×C4×Dic13C2×C414yescomplemented
75C13×#95—42no—
76C13×#95—42no—
77C13×#95C2×C414yes—
78C13×#95C2×C414yescomplemented
79#88071—42no—
80#88071—42no—
81#88071—42no—
82#88071—42no—
83#88071—42no—
84#88071—42no—
85#88071C2×C414yes—
86#88071C2×C418yes—
87#88071C2×C414yescomplemented
88#88071C2×C414yescomplemented
89#88071C2×C414yescomplemented
90#13796—131nomaximal, Sylow
91C24×C13C2411yescharacteristic
92C23×D13—22no—
93C23×D13—21no—
94C23×D13—22no—
95C23×D13—21no—
96C23×D13—21no—
97C23×D13—21no—
98C23×D13C22×C412yes—
99C23×D13C22×C412yes—
100C23×D13C22×C412yes—
101C23×D13#4114yes—
102C23×D13#4114yes—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—21no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13C22×C414yes—
126C22×C4×C13C22×C412yes—
127C22×C4×C13C22×C412yes—
128C22×C4×C13C22×C414yes—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C412yes—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—21no—
141C22×Dic13—21no—
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—21no—
152C22×Dic13—22no—
153C22×Dic13—21no—
154C22×Dic13C22×C414yes—
155C22×Dic13C22×C414yes—
156C22×Dic13C22×C412yes—
157C22×Dic13C22×C412yes—
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C412yes—
160C22×Dic13C22×C412yes—
161C2×C4×D13—216no—
162C2×C4×D13—48no—
163C2×C4×D13—44no—
164C2×C4×D13—44no—
165C2×C4×D13—48no—
166C2×C4×D13—48no—
167C2×C4×D13—48no—
168C2×C4×D13—48no—
169C2×C4×D13—48no—
170C2×C4×D13—48no—
171C2×C4×D13—48no—
172C2×C4×D13C42116yes—
173C42×C13—44no—
174#6103—216no—
175#6103—28no—
176#6103—28no—
177C4×Dic13—48no—
178C4×Dic13—44no—
179C2×C4×C22⋊C4—131no—
180C2×C4×C22⋊C4—131no—
181C22×#95—131no—
182#1434—131no—
183#1434—132no—
184#1434—131no—
185#1434—131no—
186#1434—132no—
187#1434D1311yescharacteristic, complemented
188C22⋊#95—132no—
189C22⋊#95—132no—
190C23×C13C23×C411yescharacteristic
191C23×C13C23×C411yescharacteristic
192C23×C13C23×C411yescharacteristic
193C23×C13C2×#4112yes—
194C23×C13C2×#4112yes—
195C23×C13H(5,𝔽2)12yes—
196C23×C13H(5,𝔽2)12yes—
197C23×C13H(5,𝔽2)11yescharacteristic
198C23×C13H(5,𝔽2)11yescharacteristic
199C23×C132−1+411yescharacteristic
200C23×C132−1+411yescharacteristic
201C22×D13—22no—
202C22×D13—24no—
203C22×D13—22no—
204C22×D13—22no—
205C22×D13—24no—
206C22×D13—22no—
207C22×D13—22no—
208C22×D13—22no—
209C22×D13—22no—
210C22×D13—22no—
211C22×D13—24no—
212C22×D13—24no—
213C22×D13—24no—
214C22×D13—24no—
215C22×D13—24no—
216C22×D13—24no—
217C22×D13—24no—
218C22×D13—24no—
219C22×D13C2×C4214yes—
220C22×D13#11714yes—
221C22×D13#11718yes—
222C22×D13#11714yes—
223C22×D13#11718yes—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13C2×C4214yes—
253C2×Dic13—24no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—24no—
257C2×Dic13—22no—
258C2×Dic13—24no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—24no—
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×Dic13C2×C4214yes—
282C4×D13—416no—
283C4×D13—432no—
284C24×C4—131no—
285C24×C4—132no—
286C22×C22⋊C4—131no—
287C22×C22⋊C4—131no—
288C22×C22⋊C4—132no—
289C22×C42—132no—
290C22×C42—131no—
291C22×C42C2×D1311yescharacteristic
292C4×C22⋊C4—138no—
293C4×C22⋊C4—138no—
294C2×#95—132no—
295C2×#95—131no—
296C2×#95—131no—
297C2×#95—131no—
298C2×#95—131no—
299C2×#95—138no—
300C2×#95—132no—
301C2×#95—132no—
302C2×#95—132no—
303C2×#95—132no—
304C2×#95—132no—
305C2×#95—132no—
306C2×#95C2×D1312yes—
307C2×#95C2×D1312yes—
308C2×#95C2×D1311yescharacteristic
309C2×#95C2×D1311yescharacteristic
310C22×C13C22×C4211yescharacteristic
311C22×C13C2×#11712yes—
312C22×C13C2×#11711yescharacteristic
313C22×C13C2×#11712yes—
314C22×C13C2×#11711yescharacteristic
315C22×C13#51811yescharacteristic
316C22×C13#51811yescharacteristic
317C22×C13#51811yescharacteristic
318C22×C13#51812yes—
319C22×C13#51812yes—
320C22×C13#51911yescharacteristic
321C22×C13#52011yescharacteristic
322C22×C13#52011yescharacteristic
323C22×C13#52011yescharacteristic
324C22×C13#52011yescharacteristic
325C22×C13#53812yes—
326C22×C13#53812yes—
327C22×C13#53812yes—
328C22×C13#53812yes—
329C22×C13#53912yes—
330C22×C13#53912yes—
331C22×C13#53912yes—
332C22×C13#53912yes—
333C2×D13—28no—
334C2×D13—28no—
335C2×D13—24no—
336C2×D13—28no—
337C2×D13—24no—
338C2×D13—28no—
339C2×D13—24no—
340C2×D13—24no—
341C2×D13—24no—
342C2×D13—24no—
343C2×D13#37618yes—
344C4×C13—24no—
345C4×C13—44no—
346C4×C13—42no—
347C4×C13—44no—
348C4×C13—42no—
349Dic13—24no—
350Dic13—44no—
351Dic13—42no—
352Dic13—44no—
353Dic13—42no—
354C25—131no—
355C23×C4—131no—
356C23×C4—134no—
357C23×C4—134no—
358C23×C4—134no—
359C23×C4—131no—
360C23×C4—132no—
361C23×C4—131no—
362C23×C4—132no—
363C23×C4—138no—
364C23×C4—264no—
365C23×C4—264no—
366C23×C4—522no—
367C23×C4—522no—
368C23×C4—522no—
369C23×C4—522no—
370C23×C4—522no—
371C23×C4—522no—
372C23×C4C22×D1311yescharacteristic
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1312yes—
375C23×C4C22×D1312yes—
376C23×C4C22×D1311yescharacteristic
377C2×C22⋊C4—134no—
378C2×C22⋊C4—134no—
379C2×C22⋊C4—138no—
380C2×C22⋊C4—264no—
381C2×C22⋊C4—264no—
382C2×C22⋊C4—264no—
383C2×C22⋊C4—264no—
384C2×C42—42no—
385C2×C42—138no—
386C2×C42—134no—
387C2×C42—522no—
388C2×C42—522no—
389C2×C42—522no—
390C2×C42C4×D1314yescomplemented
391#95—42no—
392#95—42no—
393#95—138no—
394#95—134no—
395#95—134no—
396#95—134no—
397#95—134no—
398#95—522no—
399#95—522no—
400#95—522no—
401#95—522no—
402#95—522no—
403#95—522no—
404#95C4×D1314yes—
405#95C4×D1314yescomplemented
406C2×C13C2×#37611yescharacteristic
407C2×C13#227311yescharacteristic
408C2×C13#227411yescharacteristic
409C2×C13#231212yes—
410C2×C13#231312yes—
411C2×C13#231811yescharacteristic
412C2×C13#231812yes—
413C2×C13#231811yescharacteristic
414C2×C13#231812yes—
415C2×C13#231811yescharacteristic
416C2×C13#231811yescharacteristic
417D13—28no—
418C24—132no—
419C24—132no—
420C24—132no—
421C24—134no—
422C24—134no—
423C24—262no—
424C24—261no—
425C24—261no—
426C24—262no—
427C24—261no—
428C24—261no—
429C24C23×D1311yescharacteristic
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—132no—
453C22×C4—132no—
454C22×C4—132no—
455C22×C4—1316no—
456C22×C4—134no—
457C22×C4—132no—
458C22×C4—132no—
459C22×C4—134no—
460C22×C4—2616no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—261no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—261no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—261no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—261no—
483C22×C4—524no—
484C22×C4—524no—
485C22×C4—528no—
486C22×C4—528no—
487C22×C4—528no—
488C22×C4—528no—
489C22×C4—528no—
490C22×C4—528no—
491C22×C4—528no—
492C22×C4—528no—
493C22×C4C2×C4×D1314yes—
494C22×C4C2×C4×D1312yes—
495C22×C4C2×C4×D1312yes—
496C22×C4C2×C4×D1314yes—
497C22×C4C2×C4×D1312yes—
498C22×C4C2×C4×D1312yes—
499C22×C4C2×C4×D1312yes—
500C22⋊C4—268no—
501C22⋊C4—2616no—
502C22⋊C4—268no—
503C42—44no—
504C42—524no—
505C42—528no—
506C13#1379611yescharacteristic, complemented, Sylow
507C23—134no—
508C23—134no—
509C23—138no—
510C23—134no—
511C23—138no—
512C23—262no—
513C23—262no—
514C23—262no—
515C23—262no—
516C23—264no—
517C23—262no—
518C23—264no—
519C23—262no—
520C23—262no—
521C23—262no—
522C23—264no—
523C23—264no—
524C23—264no—
525C23—264no—
526C23—264no—
527C23—264no—
528C23—264no—
529C23—264no—
530C23C22×C4×D1311yescharacteristic
531C23C22×C4×D1311yescharacteristic
532C23C22×C4×D1311yescharacteristic
533C23#8825112yes—
534C23#8825111yescharacteristic
535C23#8825411yescharacteristic
536C23#41×D1312yes—
537C23#41×D1312yes—
538C23#8825612yes—
539C23#8825611yescharacteristic
540C23#8825711yescharacteristic
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—42no—
558C2×C4—42no—
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—42no—
569C2×C4—134no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—264no—
577C2×C4—262no—
578C2×C4—264no—
579C2×C4—262no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—264no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—5216no—
587C2×C4—5232no—
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×C4C42×D1314yes—
601C22—138no—
602C22—264no—
603C22—264no—
604C22—264no—
605C22—268no—
606C22—264no—
607C22—268no—
608C22—264no—
609C22—264no—
610C22—268no—
611C22—268no—
612C22C2×C42×D1311yescharacteristic
613C22#1171919111yescharacteristic
614C22#1171920911yescharacteristic
615C22D13×#11711yescharacteristic
616C22D13×#11712yes—
617C22D13×#11711yescharacteristic
618C22D13×#11712yes—
619C22#1171922611yescharacteristic
620C22#1171922811yescharacteristic
621C22#1171925012yes—
622C22#1171925012yes—
623C22#1171925011yescharacteristic
624C22#1171925111yescharacteristic
625C22#1171927711yescharacteristic
626C22#1171927911yescharacteristic
627C22#1171931812yes—
628C22#1171934312yes—
629C22#1171936212yes—
630C22#1171936512yes—
631C22#1171938312yes—
632C22#1171939712yes—
633C22#1171940912yes—
634C22#1171941212yes—
635C4—24no—
636C4—42no—
637C4—44no—
638C4—42no—
639C4—44no—
640C4—264no—
641C4—522no—
642C4—524no—
643C4—522no—
644C4—524no—
645C2—268no—
646C2D13×#37611yescharacteristic
647C2#1311718811yescharacteristic
648C2#1311719011yescharacteristic
649C2#1311743012yes—
650C2#1311743512yes—
651C2#1311746511yescharacteristic
652C2#1311746612yes—
653C2#1311746711yescharacteristic
654C2#1311746812yes—
655C2#1311747111yescharacteristic
656C2#1311747211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC13×#1434C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1434D13
hypocenterC13#13796
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
4. #13113063C2semidirect
5. #13113062C2semidirect
6. #13113061C2semidirect
7. #13113061C2semidirect
8. #13113060C2semidirect
11. C13×#1434C2semidirect
35. C4×#6103C4semidirect
36. #11718327C4semidirect
37. D13×#95C4semidirect
62. C2×C42×C13C2×C4semidirect
73. C2×C4×Dic13C2×C4semidirect
74. C2×C4×Dic13C2×C4semidirect
78. C13×#95C2×C4semidirect
87. #88071C2×C4semidirect
88. #88071C2×C4semidirect
89. #88071C2×C4semidirect
187. #1434D13semidirect
390. C2×C42C4×D13semidirect
405. #95C4×D13semidirect
506. C13#13796semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#61032
C2×#117183272
C2×D13×#952
#131130632
#131130622
#131130612
#131130602
#131130572
C13×#14342
#1379613