Finite Group Databasebeta

← #15925544

Subgroups — #15925544

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718457C211yesmaximal, characteristic, complemented
2C22×#88048C211yesmaximal, characteristic
3#13118554C211yesmaximal, characteristic
4#13117845C211yesmaximal, characteristic
5#13116382C211yesmaximal, characteristic, complemented
6#13116340C211yesmaximal, characteristic, complemented
7#13116213C211yesmaximal, characteristic, complemented
8#13116177C211yesmaximal, characteristic, complemented
9#13115607C211yesmaximal, characteristic, complemented
10#13115424C211yesmaximal, characteristic, complemented
11#13115260C211yesmaximal, characteristic
12#13115102C211yesmaximal, characteristic, complemented
13#13115026C211yesmaximal, characteristic
14#13115013C211yesmaximal, characteristic
15C13×#1872C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88144C2211yescharacteristic
22C2×C13×#103C2211yescharacteristic
23C2×C13×#103C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25#11718891C2211yescharacteristic
26C2×#88075C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28#11718873—21no—
29#11718873C2211yescharacteristic
30#11718871—21no—
31C4×C22⋊Dic13C2211yescharacteristic
32C2×#88058C2211yescharacteristic
33C2×#88058C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35C2×#88054C2211yescharacteristic
36#11718647—21no—
37#11718646—21no—
38#11718646C2211yescharacteristic
39#11718646C2211yescharacteristic
40#11718645—21no—
41#11718642—21no—
42#11718638C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44#11718634C2211yescharacteristic
45C2×#88048—24no—
46C2×#88048C2211yescharacteristic
47C2×#88048C2211yescharacteristic
48C2×#88048C2211yescharacteristic
49C2×#88048C2211yescharacteristic
50#11718611—21no—
51C22⋊C4×Dic13—21no—
52#11718457—24no—
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C23×Dic13—21no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8Q814yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—41no—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C22⋊C4—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13D411yescharacteristic
79C2×C22⋊Dic13D411yescharacteristic
80Q8×Dic13—22no—
81Q8×Dic13—41no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—41no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C22×#1055—22no—
100C22×#1055—22no—
101C22×#1055—22no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88144—22no—
105#88144—41no—
106C13×#103—22no—
107C13×#103—41no—
108C13×C22⋊C8—22no—
109#88075—22no—
110#88075—22no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071D411yescharacteristic
121#88071D411yescharacteristic
122#88058—22no—
123#88058—41no—
124#88054—22no—
125#88054—22no—
126#88048—22no—
127#88048—22no—
128#88048—22no—
129#88048D414yes—
130#26346—131nomaximal, Sylow
131C24×C13C2×D411yescharacteristic
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13C2×Q812yes—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—81no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×Q812yes—
151C22×C4×C13#4112yes—
152C22×C4×C13C2411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—42no—
158C22×Dic13—42no—
159C22×Dic13—81no—
160C22×Dic13C2×D411yescharacteristic
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C13×C4⋊C4—24no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4C2×D412yes—
177C13×C4⋊C4C2×Q812yes—
178C13×C22⋊C4—24no—
179C22⋊Dic13—22no—
180C22⋊Dic13—22no—
181C22⋊Dic13—42no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—42no—
190C4⋊Dic13—42no—
191C4⋊Dic13—42no—
192C4⋊Dic13—81no—
193C4⋊Dic13—81no—
194C4⋊Dic13C2×D412yes—
195#6101—42no—
196#6101—81no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—42no—
202C4×Dic13—81no—
203C2×#1055—28no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055C2×D412yes—
209C2×#1055#4112yes—
210C2×#479—131no—
211C22×#106—131no—
212#2442—131no—
213#2360—131no—
214#2097—131no—
215#2088—131no—
216#2066—131no—
217#2059—131no—
218#1949—131no—
219#1920—131no—
220#1892—131no—
221#1872D1311yescharacteristic
222#1865—131no—
223#1852—131no—
224#1850—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13C22⋊Q812yes—
230C23×C13#13512yes—
231C23×C13#13712yes—
232C23×C13C22×D411yescharacteristic
233Q8×C13—22no—
234Q8×C13—22no—
235Q8×C13—41no—
236Q8×C13—41no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—22no—
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—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—84no—
256C2×C4×C13C22⋊Q812yes—
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C22×Q811yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13H(5,𝔽2)11yescharacteristic
262C2×C4×C132−1+411yescharacteristic
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—22no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—84no—
288C8×C13—41no—
289C8×C13—41no—
290#1055—22no—
291#1055—22no—
292C23×C8—131no—
293C2×#125—131no—
294C2×C22⋊Q8C2×D1311yescharacteristic
295C2×C4×Q8—131no—
296C22×C4⋊C4—131no—
297C22×C4⋊C4C2×D1311yescharacteristic
298#479—264no—
299C2×#107—131no—
300C2×#107—131no—
301C2×#106—131no—
302C2×#106—131no—
303C2×#106—131no—
304C2×#106—131no—
305C2×#106—264no—
306C2×C4⋊C8—131no—
307C2×C4⋊C8—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103C2×D1311yescharacteristic
311C2×#103C2×D1311yescharacteristic
312C2×C22⋊C8C2×D1311yescharacteristic
313#400—261no—
314#398—261no—
315#391—131no—
316#389—131no—
317#389—131no—
318#389—131no—
319#389—261no—
320#387—261no—
321#385—261no—
322#385—261no—
323#382—131no—
324#380—131no—
325#380—261no—
326C4×C4⋊C4—131no—
327C4×C22⋊C4—131no—
328C4×C22⋊C4—261no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340C2×D1311yescharacteristic
334#340C2×D1311yescharacteristic
335#336—131no—
336#336—131no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13#47914yescomplemented
344C22×C13C2×C22⋊Q811yescharacteristic
345C22×C13D4211yescharacteristic
346C22×C13#54711yescharacteristic
347C22×C13C2×#13511yescharacteristic
348C22×C13C2×#13711yescharacteristic
349C22×C13#57711yescharacteristic
350C22×C13#57711yescharacteristic
351C4×C13—22no—
352C4×C13—42no—
353C4×C13—42no—
354C4×C13—42no—
355C4×C13—81no—
356C4×C13#52511yescharacteristic
357C4×C13#53911yescharacteristic
358C4×C13D4×Q811yescharacteristic
359C4×C13#55411yescharacteristic
360Dic13—41no—
361Dic13—41no—
362Dic13—41no—
363Dic13—41no—
364Dic13—42no—
365Dic13—81no—
366Dic13—81no—
367Dic13—81no—
368C22×Q8C22×D1311yescharacteristic
369C23×C4—21no—
370C23×C4—261no—
371C23×C4C22×D1311yescharacteristic
372C22×C8—131no—
373C22×C8—131no—
374C22×C8—262no—
375C22×C8—262no—
376C22×C8—262no—
377C22×C8C22×D1311yescharacteristic
378C22×C8C22×D1311yescharacteristic
379#125—262no—
380#125—521no—
381C22⋊Q8—22no—
382C22⋊Q8Dic2614yes—
383C4×Q8—262no—
384C4×Q8—521no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—262no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—521no—
402C2×C4⋊C4C22×D1311yescharacteristic
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—131no—
407C2×C22⋊C4—131no—
408C2×C22⋊C4—261no—
409C2×C42—131no—
410C2×C42—131no—
411C2×C42—261no—
412C2×C42—261no—
413#107—262no—
414#107—521no—
415#106—134no—
416#106—262no—
417#106—262no—
418#106—262no—
419C4⋊C8—262no—
420C4⋊C8—262no—
421#103—22no—
422#103—41no—
423#103—262no—
424#103—262no—
425C22⋊C8—22no—
426#95—131no—
427#95—131no—
428#95—261no—
429#95—261no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95—261no—
435#95—261no—
436#95—261no—
437C2×C13—24no—
438C2×C13#244911yescharacteristic
439C2×C13C2×#47911yescharacteristic
440C2×C13#308411yescharacteristic
441C2×C13#326611yescharacteristic
442C2×C13#328211yescharacteristic
443C2×C13#333711yescharacteristic
444C2×C13#334411yescharacteristic
445C24D4×D1311yescharacteristic
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×Dic2612yes—
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—42no—
461C22×C4—42no—
462C22×C4—81no—
463C22×C4—131no—
464C22×C4—131no—
465C22×C4—131no—
466C22×C4—131no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—522no—
472C22×C4—522no—
473C22×C4—1041no—
474C22×C4C2×Dic2612yes—
475C22×C4D4×D1311yescharacteristic
476C22×C4#612912yes—
477C22×C4C23×D1311yescharacteristic
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—132no—
485C2×C8—132no—
486C2×C8—268no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C4⋊C4—24no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—132no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—522no—
506C4⋊C4—522no—
507C4⋊C4—522no—
508C4⋊C4—522no—
509C4⋊C4—1041no—
510C4⋊C4—1041no—
511C4⋊C4—1041no—
512C4⋊C4C2×Dic2612yes—
513C4⋊C4D4×D1312yes—
514C22⋊C4—24no—
515C22⋊C4—262no—
516C22⋊C4—262no—
517C22⋊C4—522no—
518C42—261no—
519C42—261no—
520C42—261no—
521C42—261no—
522C42—522no—
523C42—1041no—
524C13#2634611yescharacteristic, complemented, Sylow
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23#8813212yes—
530C23#8816912yes—
531C23#8817312yes—
532C23C2×D4×D1311yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—41no—
536Q8—41no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—84no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—261no—
566C2×C4—262no—
567C2×C4—261no—
568C2×C4—261no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—1044no—
581C2×C4#8813212yes—
582C2×C4C22×Dic2611yescharacteristic
583C2×C4C2×D4×D1311yescharacteristic
584C2×C4C2×#612911yescharacteristic
585C2×C4#8825111yescharacteristic
586C2×C4#41×D1311yescharacteristic
587C2×C4#8825711yescharacteristic
588C8—41no—
589C8—41no—
590C8—262no—
591C8—262no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22#1171845714yescomplemented
599C22C2×#8813211yescharacteristic
600C22#1171929511yescharacteristic
601C22#1171936011yescharacteristic
602C22C2×#8816911yescharacteristic
603C22C2×#8817311yescharacteristic
604C22#1171948011yescharacteristic
605C22#1171948311yescharacteristic
606C4—22no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—81no—
611C4—521no—
612C4—521no—
613C4—521no—
614C4—522no—
615C4—521no—
616C4—1041no—
617C4—1041no—
618C4—1041no—
619C4D4×Dic2611yescharacteristic
620C4#1171924411yescharacteristic
621C4#1171930711yescharacteristic
622C4#1171931111yescharacteristic
623C2—24no—
624C2#1311864911yescharacteristic
625C2C2×#1171845711yescharacteristic
626C2#1312470211yescharacteristic
627C2#1312635011yescharacteristic
628C2#1312653611yescharacteristic
629C2#1312721311yescharacteristic
630C2#1312729511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1872C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1872D13
hypocenterC13#26346
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. C2×#11718457C2semidirect
5. #13116382C2semidirect
6. #13116340C2semidirect
7. #13116213C2semidirect
8. #13116177C2semidirect
9. #13115607C2semidirect
10. #13115424C2semidirect
12. #13115102C2semidirect
343. C22×C13#479semidirect
524. C13#26346semidirect
598. C22#11718457semidirect

Maximal subgroups

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

subgroupindex
C2×#117184572
C22×#880482
#131185542
#131178452
#131163822
#131163402
#131162132
#131161772
#131156072
#131154242
#131152602
#131151022
#131150262
#131150132
C13×#18722
#2634613