Finite Group Databasebeta

← #15904197

Subgroups — #15904197

Order 3328.

784 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718683C211yesmaximal, characteristic, complemented
2C2×#11718587C211yesmaximal, characteristic
3#13123146C211yesmaximal, characteristic
4#13116273C211yesmaximal, characteristic
5#13116267C211yesmaximal, characteristic
6#13116036C211yesmaximal, characteristic
7#13116029C211yesmaximal, characteristic
8#13115793C211yesmaximal, characteristic, complemented
9#13115604C211yesmaximal, characteristic, complemented
10#13115576C211yesmaximal, characteristic, complemented
11#13115571C211yesmaximal, characteristic, complemented
12#13115529C211yesmaximal, characteristic, complemented
13#13115529C211yesmaximal, characteristic, complemented
14#13114851C211yesmaximal, characteristic, complemented
15C4×C13×C22⋊Q8C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C2×#88124C2211yescharacteristic
20C13×#391C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#387—21no—
23C13×#385—21no—
24C13×#380C2211yescharacteristic
25C4×C13×C4⋊C4—21no—
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C22⋊C4—21no—
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32#11718873C2211yescharacteristic
33#11718873C2211yescharacteristic
34#11718871—21no—
35#11718871—21no—
36C2×C22⋊#1055C2211yescharacteristic
37C2×C22⋊#1055C2211yescharacteristic
38#11718683—24no—
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718597C2211yescharacteristic
44#11718594—21no—
45#11718594—21no—
46#11718589C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718587—24no—
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C23×C4×C13D411yescharacteristic
63C23×C4×C13D411yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C4×Q8×C13—22no—
68C4×Q8×C13—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13D411yescharacteristic
82C2×C42×C13D411yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88124—22no—
100#88124—22no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106#88075—22no—
107#88075—22no—
108#88075—22no—
109#88075—22no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116C22⋊#1055—22no—
117C22⋊#1055—22no—
118#88048—22no—
119#88048—22no—
120#88047—22no—
121#88047—22no—
122C4⋊#1055—22no—
123C4⋊#1055D414yes—
124#88043—22no—
125#88043—22no—
126#24707—131nomaximal, Sylow
127C24×C13C2×D411yescharacteristic
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13#4112yes—
134C22×C4×C13—22no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
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—21no—
147C22×C4×C13—41no—
148C22×C4×C13—41no—
149C22×C4×C13—41no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2411yescharacteristic
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4—42no—
168C13×C4⋊C4#4112yes—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—42no—
171C42×C13—22no—
172C42×C13—22no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—42no—
176C42×C13—42no—
177C42×C13C2×D412yes—
178C42×C13#4112yes—
179C22⋊Dic13—42no—
180C22⋊Dic13—42no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189#6101—42no—
190#6101—42no—
191#6101—42no—
192#6101—42no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055C2×D412yes—
204C2×#1055C2×D412yes—
205C2×#479—131no—
206C2×#432—131no—
207#2851—131no—
208C4×C22⋊Q8D1311yescharacteristic
209#2077—131no—
210#2076—131no—
211#2036—131no—
212#2035—131no—
213#1989—131no—
214#1949—131no—
215#1944—131no—
216#1943—131no—
217#1935—131no—
218#1935—131no—
219#1805—131no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13#13712yes—
227C23×C13C22×D411yescharacteristic
228Q8×C13—22no—
229Q8×C13—22no—
230Q8×C13—41no—
231Q8×C13—41no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—44no—
248C2×C4×C13—44no—
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—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13#12112yes—
264C2×C4×C13#12112yes—
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C132−1+411yescharacteristic
270C2×C4×C132−1+411yescharacteristic
271C2×Dic13—41no—
272C2×Dic13—41no—
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—41no—
282C2×Dic13—41no—
283#1055—22no—
284#1055—22no—
285#1055—41no—
286#1055—41no—
287C2×#125—131no—
288C2×C22⋊Q8C2×D1311yescharacteristic
289C2×C4×Q8C2×D1311yescharacteristic
290C22×C42C2×D1311yescharacteristic
291#479—264no—
292#432—264no—
293C2×#107—131no—
294C2×#107—131no—
295C2×#106—131no—
296C2×#106—131no—
297C2×C4⋊C8—131no—
298C2×C4⋊C8—131no—
299C2×#103—131no—
300C2×#103—131no—
301C2×#103—131no—
302C2×#103—131no—
303C2×C22⋊C8—131no—
304C2×C22⋊C8—131no—
305C2×#97—131no—
306C2×#97—131no—
307#391C2×D1311yescharacteristic
308#389—131no—
309#389—131no—
310#389C2×D1311yescharacteristic
311#387—21no—
312#387—261no—
313#387—261no—
314#385—21no—
315#385—261no—
316#385—261no—
317#382—131no—
318#380—131no—
319#380—131no—
320#380C2×D1311yescharacteristic
321C4×C4⋊C4—21no—
322C4×C4⋊C4C2×D1311yescharacteristic
323C4×C22⋊C4—21no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13C2×#12111yescharacteristic
340C22×C13#52511yescharacteristic
341C22×C13#53611yescharacteristic
342C22×C13C2×#13711yescharacteristic
343C22×C13#57511yescharacteristic
344C22×C13#57511yescharacteristic
345C22×C13#57511yescharacteristic
346C4×C13—22no—
347C4×C13—22no—
348C4×C13—42no—
349C4×C13—41no—
350C4×C13—42no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13—81no—
354C4×C13—81no—
355C4×C13#54711yescharacteristic
356C4×C13#54811yescharacteristic
357C4×C13#55211yescharacteristic
358C4×C13#55611yescharacteristic
359Dic13—81no—
360Dic13—81no—
361Dic13—81no—
362Dic13—81no—
363C22×Q8C22×D1311yescharacteristic
364C23×C4C22⋊D1311yescharacteristic
365C23×C4C22⋊D1311yescharacteristic
366C23×C4C22×D1311yescharacteristic
367C22×C8—131no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—131no—
371#125—262no—
372#125—262no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C4×Q8—22no—
376C4×Q8—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C4⋊C4C22×D1311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4—261no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42C22⋊D1311yescharacteristic
400C2×C42C22⋊D1311yescharacteristic
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403#107—262no—
404#107—262no—
405#106—262no—
406#106—262no—
407C4⋊C8—134no—
408C4⋊C8—262no—
409#103—262no—
410#103—262no—
411#103—262no—
412#103—262no—
413C22⋊C8—262no—
414C22⋊C8—262no—
415#97—262no—
416#97—262no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428C2×C13—42no—
429C2×C13#241511yescharacteristic
430C2×C13#305411yescharacteristic
431C2×C13#305611yescharacteristic
432C2×C13#311111yescharacteristic
433C2×C13#311711yescharacteristic
434C2×C13#323611yescharacteristic
435C2×C13#324011yescharacteristic
436C24C2×C22⋊D1311yescharacteristic
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8#612712yes—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C2×C22⋊D1311yescharacteristic
465C22×C4C2×C22⋊D1311yescharacteristic
466C22×C4C2×C22⋊D1311yescharacteristic
467C22×C4C2×C22⋊D1311yescharacteristic
468C22×C4C23×D1311yescharacteristic
469C2×C8—132no—
470C2×C8—132no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C4⋊C4—24no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—522no—
498C4⋊C4—522no—
499C4⋊C4—522no—
500C4⋊C4—522no—
501C4⋊C4#612712yes—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—522no—
505C22⋊C4—522no—
506C42—22no—
507C42—22no—
508C42—21no—
509C42—21no—
510C42—42no—
511C42—42no—
512C42D4×D1312yes—
513C42#612912yes—
514C13#2470711yescharacteristic, complemented, Sylow
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23#8819612yes—
522C23C22×C22⋊D1311yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—41no—
545C2×C4—41no—
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—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4#8819312yes—
571C2×C4#8819312yes—
572C2×C4C2×#612711yescharacteristic
573C2×C4C2×#612711yescharacteristic
574C2×C4C2×D4×D1311yescharacteristic
575C2×C4C2×#612911yescharacteristic
576C2×C4#8825711yescharacteristic
577C2×C4#8825711yescharacteristic
578C8—262no—
579C8—262no—
580C8—521no—
581C8—521no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22#1171949611yescharacteristic
590C22C2×#8819311yescharacteristic
591C22C2×#8819611yescharacteristic
592C22#1171952711yescharacteristic
593C22#1171952711yescharacteristic
594C22#1171952711yescharacteristic
595C22#1171953011yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—42no—
600C4—42no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—1041no—
606C4—1041no—
607C4—1041no—
608C4—1041no—
609C4#1171924611yescharacteristic
610C4#1171924711yescharacteristic
611C4#1171925611yescharacteristic
612C4#1171925711yescharacteristic
613C2—42no—
614C2#1311826511yescharacteristic
615C2#1312444211yescharacteristic
616C2#1312446211yescharacteristic
617C2#1312494511yescharacteristic
618C2#1312500711yescharacteristic
619C2#1312603811yescharacteristic
620C2#1312607211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC4×C13×C22⋊Q8C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC4×C22⋊Q8D13
hypocenterC13#24707
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11718683C2semidirect
8. #13115793C2semidirect
9. #13115604C2semidirect
10. #13115576C2semidirect
11. #13115571C2semidirect
12. #13115529C2semidirect
13. #13115529C2semidirect
14. #13114851C2semidirect
514. C13#24707semidirect

Maximal subgroups

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

subgroupindex
C2×#117186832
C2×#117185872
#131231462
#131162732
#131162672
#131160362
#131160292
#131157932
#131156042
#131155762
#131155712
#131155292
#131148512
C4×C13×C22⋊Q82
#2470713