Finite Group Databasebeta

← #15891787

Subgroups — #15891787

Order 3328.

1166 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718782C211yesmaximal, characteristic, complemented
2#13117219C211yesmaximal, characteristic
3C2×#11718873C211yesmaximal, characteristic
4#13116269C212yesmaximal, complemented
5#13116269C212yesmaximal, complemented
6#13116264C212yesmaximal, complemented
7#13116259C212yesmaximal, complemented
8#13114556C211yesmaximal, characteristic, complemented
9#13114556C211yesmaximal, characteristic, complemented
10#13114556C211yesmaximal, characteristic, complemented
11C2×C13×#407C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×M16C2211yescharacteristic
14C22×C13×M16C2211yescharacteristic
15C22×C22⋊Dic13—21no—
16C2×#88180C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C13×#407—24no—
21C2×C13×C22⋊C8C2212yes—
22C2×C13×C22⋊C8C2212yes—
23#11718908—21no—
24#11718873—21no—
25#11718873—21no—
26#11718873C2212yes—
27#11718873C2212yes—
28#11718873C2211yescharacteristic
29#11718873C2211yescharacteristic
30#11718873C2211yescharacteristic
31#11718873C2211yescharacteristic
32#11718872—21no—
33C4×C22⋊Dic13—21no—
34C4×C22⋊Dic13—21no—
35C2×#88071—21no—
36#11718782—24no—
37C2×#88058C2212yescomplemented
38C2×#88057C2212yescomplemented
39#11718143C2212yescomplemented
40#11718143C2212yescomplemented
41#11718143C2212yescomplemented
42#11718143C2212yescomplemented
43#11718143C2212yescomplemented
44#11718143C2212yescomplemented
45C25×C13D411yescharacteristic
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13—22no—
50C23×C4×C13—22no—
51C23×C4×C13—22no—
52C23×C4×C13D411yescharacteristic
53C23×C4×C13D411yescharacteristic
54C23×C4×C13D411yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×Dic13—21no—
59C23×Dic13—21no—
60C2×C13×M16—22no—
61C2×C13×M16—22no—
62C2×C13×M16—22no—
63C2×C13×M16—22no—
64C2×C13×M16—22no—
65C2×C13×M16D414yes—
66C22×C8×C13C2312yes—
67C22×C8×C13C2312yes—
68C2×C22⋊Dic13—21no—
69C2×C22⋊Dic13—21no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—44no—
77#88180—22no—
78#88180—22no—
79#88180—22no—
80#88180—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13C2312yes—
88C2×C4⋊Dic13C2312yes—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C13×C22⋊C8—24no—
96C13×C22⋊C8—24no—
97#88071—22no—
98#88071—22no—
99#88071—21no—
100#88071—21no—
101#88071—21no—
102#88071—21no—
103#88058—24no—
104#88057—24no—
105#23642—131nomaximal, Sylow
106C24×C13—22no—
107C24×C13—22no—
108C24×C13—22no—
109C24×C13—22no—
110C24×C13—22no—
111C24×C13—41no—
112C24×C13—41no—
113C24×C13C2×D411yescharacteristic
114C24×C13C2×D411yescharacteristic
115C24×C13C2×D411yescharacteristic
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—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—44no—
138C22×C4×C13—44no—
139C22×C4×C13—44no—
140C22×C4×C13—44no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D412yes—
145C22×C4×C13#4112yes—
146C22×C4×C13#4112yes—
147C22×C4×C13#4112yes—
148C22×C4×C13#4112yes—
149C22×C4×C13#4112yes—
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—42no—
158C22×Dic13—42no—
159C22×Dic13—42no—
160C22×Dic13—42no—
161C22×Dic13—42no—
162C22×Dic13—42no—
163C13×M16—28no—
164C13×M16—44no—
165C2×C8×C13—22no—
166C2×C8×C13—22no—
167C2×C8×C13—22no—
168C2×C8×C13—22no—
169C2×C8×C13—22no—
170C2×C8×C13C2×D414yes—
171C22⋊Dic13—42no—
172C22⋊Dic13—42no—
173C22⋊Dic13—44no—
174C22⋊Dic13—42no—
175C22⋊Dic13—42no—
176C22⋊Dic13—42no—
177C22⋊Dic13—44no—
178C22⋊Dic13—42no—
179C4⋊Dic13—22no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—22no—
183C4⋊Dic13—22no—
184C4⋊Dic13—22no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—42no—
192C4⋊Dic13—42no—
193C4×Dic13—42no—
194C4×Dic13—42no—
195C2×#428—131no—
196C2×#407D1311yescharacteristic
197#2280—131no—
198C2×#380—131no—
199#2077—132no—
200#2077—132no—
201#2076—132no—
202#2075—132no—
203#1736—131no—
204#1736—131no—
205#1736—131no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—28no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—44no—
224C23×C13—44no—
225C23×C13—44no—
226C23×C13—44no—
227C23×C13—44no—
228C23×C13—44no—
229C23×C13#12112yes—
230C23×C13#12312yes—
231C23×C13#12312yes—
232C23×C13AGL(1,ℤ/8)12yes—
233C23×C13#13712yes—
234C23×C13C22×D411yescharacteristic
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—44no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—44no—
251C2×C4×C13—44no—
252C2×C4×C13#12112yes—
253C2×C4×C13#12314yes—
254C2×C4×C13#12312yes—
255C2×C4×C13#12312yes—
256C2×C4×C13#12414yes—
257C2×C4×C13#12614yes—
258C2×C4×C13#12614yes—
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—42no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—84no—
284C2×Dic13—84no—
285C8×C13—24no—
286C8×C13—42no—
287C24×C4C2×D1311yescharacteristic
288C22×M16C2×D1311yescharacteristic
289C22×M16C2×D1311yescharacteristic
290C2×#117—131no—
291C2×#117—131no—
292C22×C4⋊C4—131no—
293C22×C4⋊C4—131no—
294C22×C22⋊C4—261no—
295#428—264no—
296C2×#107—132no—
297C2×#106—132no—
298#407—24no—
299C2×C22⋊C8C2×D1312yes—
300C2×C22⋊C8C2×D1312yes—
301#381—261no—
302#380—131no—
303#380—132no—
304#380—131no—
305#380—132no—
306#380—131no—
307#380—131no—
308#380—261no—
309#380—261no—
310#379—261no—
311C4×C22⋊C4—261no—
312C4×C22⋊C4—261no—
313C2×#95—261no—
314#340—132no—
315#340—132no—
316#340—132no—
317#340—132no—
318#340—132no—
319#340—132no—
320C22×C13—22no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13—22no—
327C22×C13—22no—
328C22×C13—22no—
329C22×C13—22no—
330C22×C13—22no—
331C22×C13—22no—
332C22×C13—416no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13#39714yes—
342C22×C13C2×#12111yescharacteristic
343C22×C13C2×#12311yescharacteristic
344C22×C13C2×#12311yescharacteristic
345C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C13C2×#13711yescharacteristic
347C22×C13#57511yescharacteristic
348C22×C13#57511yescharacteristic
349C4×C13—41no—
350C4×C13—41no—
351C4×C13#39714yes—
352C4×C13C2×#12311yescharacteristic
353C4×C13C2×#12411yescharacteristic
354C4×C13C2×#12611yescharacteristic
355C4×C13C2×#12611yescharacteristic
356Dic13—81no—
357Dic13—81no—
358Dic13—82no—
359Dic13—81no—
360Dic13—82no—
361Dic13—81no—
362C25D5211yescharacteristic
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—261no—
370C23×C4—261no—
371C23×C4D5211yescharacteristic
372C23×C4D5211yescharacteristic
373C23×C4D5211yescharacteristic
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1311yescharacteristic
376C23×C4C22×D1311yescharacteristic
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16C22⋊D1314yes—
383C22×C8C22×D1312yes—
384C22×C8C22×D1312yes—
385#117—262no—
386#117—262no—
387#117—262no—
388#117—262no—
389C2×C4⋊C4—132no—
390C2×C4⋊C4—132no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—262no—
396C2×C4⋊C4—262no—
397C2×C4⋊C4—262no—
398C2×C4⋊C4—262no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C22⋊C4—262no—
402C2×C22⋊C4—262no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4—261no—
405C2×C22⋊C4—261no—
406C2×C22⋊C4—261no—
407C2×C22⋊C4—261no—
408C2×C22⋊C4—261no—
409C2×C22⋊C4—524no—
410C2×C42—261no—
411C2×C42—261no—
412#107—264no—
413#106—264no—
414C22⋊C8—24no—
415C22⋊C8—24no—
416#95—262no—
417#95—262no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95—261no—
422C2×C13—24no—
423C2×C13—42no—
424C2×C13—42no—
425C2×C13C2×#39711yescharacteristic
426C2×C13#305511yescharacteristic
427C2×C13#305611yescharacteristic
428C2×C13#309211yescharacteristic
429C2×C13#309311yescharacteristic
430C2×C13#309411yescharacteristic
431C2×C13#309511yescharacteristic
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—41no—
438C24—41no—
439C24C2×D5211yescharacteristic
440C24C2×D5211yescharacteristic
441C24C2×D5211yescharacteristic
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—522no—
474C22×C4—522no—
475C22×C4—522no—
476C22×C4—522no—
477C22×C4—522no—
478C22×C4—522no—
479C22×C4C2×D5211yescharacteristic
480C22×C4C2×D5211yescharacteristic
481C22×C4C2×D5211yescharacteristic
482C22×C4#612712yes—
483C22×C4#612912yes—
484C22×C4#612912yes—
485C22×C4#612912yes—
486C22×C4#612912yes—
487C22×C4C2×C22⋊D1312yes—
488C22×C4C23×D1311yescharacteristic
489M16—28no—
490M16—44no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8C2×C22⋊D1314yes—
497C4⋊C4—262no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—262no—
501C4⋊C4—262no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—262no—
508C4⋊C4—261no—
509C4⋊C4—522no—
510C4⋊C4—522no—
511C22⋊C4—524no—
512C22⋊C4—522no—
513C22⋊C4—522no—
514C22⋊C4—522no—
515C22⋊C4—524no—
516C22⋊C4—522no—
517C22⋊C4—522no—
518C22⋊C4—522no—
519C42—522no—
520C42—522no—
521C13#2364211yescharacteristic, complemented, Sylow
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—28no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23#8814012yes—
546C23#8814012yes—
547C23#8816212yes—
548C23#8816312yes—
549C23#8818412yes—
550C23C22×D5211yescharacteristic
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—522no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—522no—
586C2×C4—1044no—
587C2×C4—1044no—
588C2×C4#8813314yes—
589C2×C4#8813314yes—
590C2×C4#8814012yes—
591C2×C4#8814012yes—
592C2×C4#8818412yes—
593C2×C4#8818914yes—
594C2×C4#8819014yes—
595C2×C4C2×#612711yescharacteristic
596C2×C4C2×#612911yescharacteristic
597C2×C4C2×#612911yescharacteristic
598C2×C4C2×#612911yescharacteristic
599C2×C4C2×#612911yescharacteristic
600C2×C4C22×C22⋊D1311yescharacteristic
601C8—24no—
602C8—42no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—416no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22#1171861414yes—
625C22C2×#8814011yescharacteristic
626C22C2×#8814011yescharacteristic
627C22C2×#8816211yescharacteristic
628C22C2×#8816311yescharacteristic
629C22#1171945311yescharacteristic
630C22#1171945311yescharacteristic
631C22C2×#8818411yescharacteristic
632C4—41no—
633C4—41no—
634C4—1041no—
635C4—1042no—
636C4—1041no—
637C4—1041no—
638C4—1041no—
639C4—1042no—
640C4#1171861414yes—
641C4C2×#8813311yescharacteristic
642C4C2×#8813311yescharacteristic
643C4C2×#8818911yescharacteristic
644C4C2×#8819011yescharacteristic
645C2—24no—
646C2—42no—
647C2—42no—
648C2C2×#1171861411yescharacteristic
649C2#1312445511yescharacteristic
650C2#1312446611yescharacteristic
651C2#1312476111yescharacteristic
652C2#1312476911yescharacteristic
653C2#1312477711yescharacteristic
654C2#1312478511yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#407C2
socleC23×C13C22×D4
prime radicalC25×C13D4
hypercenterC2×#407D13
hypocenterC13#23642
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#11718782C2semidirect
4. #13116269C2semidirect
5. #13116269C2semidirect
6. #13116264C2semidirect
7. #13116259C2semidirect
8. #13114556C2semidirect
9. #13114556C2semidirect
10. #13114556C2semidirect
37. C2×#88058C22semidirect
38. C2×#88057C22semidirect
39. #11718143C22semidirect
40. #11718143C22semidirect
41. #11718143C22semidirect
42. #11718143C22semidirect
43. #11718143C22semidirect
44. #11718143C22semidirect
521. C13#23642semidirect

Maximal subgroups

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

subgroupindex
C2×#117187822
#131172192
C2×#117188732
#131162692
#131162642
#131162592
#131145562
C2×C13×#4072
#2364213