Finite Group Databasebeta

← #15912386

Subgroups — #15912386

Order 3328.

760 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718743C211yesmaximal, characteristic
2C2×#11718683C211yesmaximal, characteristic
3#13117930C211yesmaximal, characteristic
4#13116231C211yesmaximal, characteristic
5#13116217C211yesmaximal, characteristic
6#13116079C211yesmaximal, characteristic
7#13116079C211yesmaximal, characteristic
8#13115760C211yesmaximal, characteristic
9#13115760C211yesmaximal, characteristic
10#13115760C211yesmaximal, characteristic
11#13115560C211yesmaximal, characteristic
12#13115474C211yesmaximal, characteristic
13#13115467C211yesmaximal, characteristic
14#13114666C211yesmaximal, characteristic
15C13×#2546C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C4⋊Q8C2211yescharacteristic
18C2×C13×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C13C2211yescharacteristic
20C2×#88124C2211yescharacteristic
21C13×#398—21no—
22C13×#398—21no—
23C13×#391C2211yescharacteristic
24C13×#391C2211yescharacteristic
25C13×#389—21no—
26C13×#389—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88075C2211yescharacteristic
40#11718743—24no—
41#11718683—24no—
42#11718639—21no—
43#11718633—21no—
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49#11718589C2211yescharacteristic
50#11718589C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53C2×C4⋊#1055C2211yescharacteristic
54C2×#88043C2211yescharacteristic
55#11718313—21no—
56#11718310—21no—
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×Q8×C13C2311yescharacteristic
64C13×C4⋊Q8—22no—
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8—41no—
69C13×C4⋊Q8—41no—
70C4×Q8×C13—22no—
71C4×Q8×C13—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4D411yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101#88124—22no—
102#88124D414yes—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109#88075—22no—
110#88075—22no—
111#88075—22no—
112#88075—22no—
113#88075—22no—
114#88075—22no—
115#88075—22no—
116#88075—22no—
117#88075—22no—
118#88075—22no—
119#88075—41no—
120#88075—41no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88048—22no—
127#88047—22no—
128C4⋊#1055—22no—
129C4⋊#1055—41no—
130C4⋊#1055—41no—
131#88043—22no—
132#25290—131nomaximal, Sylow
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—21no—
143C2×Q8×C13—21no—
144C2×Q8×C13—21no—
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13#4112yes—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2411yescharacteristic
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4—42no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—42no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—42no—
182C42×C13C2×D412yes—
183C42×C13#4112yes—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13C2×D412yes—
190C4⋊Dic13C2×D412yes—
191C4⋊Dic13#4112yes—
192#6101—24no—
193#6101—24no—
194#6101—42no—
195#6101—81no—
196C4×Dic13—42no—
197C4×Dic13—81no—
198C4×Dic13—81no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#491—131no—
212C2×#479—131no—
213#2546D1311yescharacteristic
214#2370—131no—
215#2068—131no—
216#2066—131no—
217#2043—131no—
218#2043—131no—
219#1981—131no—
220#1981—131no—
221#1981—131no—
222#1940—131no—
223#1928—131no—
224#1927—131no—
225#1763—131no—
226C23×C13C22×D411yescharacteristic
227Q8×C13—22no—
228Q8×C13—22no—
229Q8×C13—41no—
230Q8×C13—41no—
231Q8×C13—41no—
232Q8×C13—41no—
233Q8×C13—41no—
234Q8×C13—41no—
235Q8×C13—41no—
236Q8×C13—41no—
237Q8×C13—41no—
238Q8×C13—41no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
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—21no—
248C2×C4×C13—21no—
249C2×C4×C13—22no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
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—41no—
264C2×C4×C13—41no—
265C2×C4×C13#12112yes—
266C2×C4×C13#12112yes—
267C2×C4×C13#13712yes—
268C2×C4×C13#13712yes—
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13H(5,𝔽2)11yescharacteristic
274C2×C4×C132−1+411yescharacteristic
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—22no—
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—
287#1055—41no—
288#1055—41no—
289#1055—41no—
290#1055—41no—
291C2×C4⋊Q8C2×D1311yescharacteristic
292C2×C4⋊Q8C2×D1311yescharacteristic
293C2×C4⋊Q8C2×D1311yescharacteristic
294C2×#125—131no—
295C2×C4×Q8C2×D1311yescharacteristic
296#491—264no—
297#479—264no—
298C2×#107—131no—
299C2×#106—131no—
300C2×C4⋊C8—131no—
301C2×C4⋊C8—131no—
302C2×C4⋊C8—131no—
303C2×#103—131no—
304C2×#103—131no—
305C2×#103—131no—
306C2×#103—131no—
307C2×#103—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103—131no—
311C2×#103—131no—
312C2×#103—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#97—131no—
316#398—21no—
317#398—21no—
318#391C2×D1311yescharacteristic
319#391C2×D1311yescharacteristic
320#389—21no—
321#389—21no—
322#389—131no—
323#389—131no—
324#389—261no—
325#387—261no—
326#387—261no—
327C4×C4⋊C4—131no—
328C4×C4⋊C4—131no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4—261no—
331C4×C4⋊C4C2×D1311yescharacteristic
332#340—131no—
333#340—131no—
334#336—131no—
335#336—131no—
336C22×C13C2×#12111yescharacteristic
337C22×C13#54611yescharacteristic
338C22×C13#54811yescharacteristic
339C22×C13C2×#13711yescharacteristic
340C22×C13C2×#13711yescharacteristic
341C22×C13#57711yescharacteristic
342C22×C13#57811yescharacteristic
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—42no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—81no—
351C4×C13—81no—
352C4×C13—81no—
353C4×C13#52911yescharacteristic
354C4×C13#54211yescharacteristic
355C4×C13#54811yescharacteristic
356C4×C13#55011yescharacteristic
357Dic13—42no—
358Dic13—42no—
359Dic13—42no—
360Dic13—81no—
361C22×Q8C22×D1311yescharacteristic
362C22×Q8C22×D1311yescharacteristic
363C22×Q8C22×D1311yescharacteristic
364C22×C8—131no—
365C22×C8—131no—
366C22×C8—131no—
367C22×C8—131no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372C4⋊Q8—41no—
373C4⋊Q8—41no—
374#125—134no—
375#125—262no—
376C4×Q8—22no—
377C4×Q8—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4C22⋊D1311yescharacteristic
394C2×C4⋊C4C22⋊D1311yescharacteristic
395C2×C4⋊C4C22×D1311yescharacteristic
396C2×C42—21no—
397C2×C42—261no—
398C2×C42—261no—
399C2×C42—261no—
400C2×C42C22×D1311yescharacteristic
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403#107—262no—
404#106—262no—
405C4⋊C8—262no—
406C4⋊C8—521no—
407C4⋊C8—521no—
408#103—262no—
409#103—262no—
410#103—262no—
411#103—262no—
412#103—262no—
413#103—262no—
414#103—262no—
415#103—262no—
416#103—262no—
417#103—262no—
418#103—521no—
419#103—521no—
420#97—262no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95—261no—
430#95C22⋊D1311yescharacteristic
431#95C22⋊D1311yescharacteristic
432C2×C13#242611yescharacteristic
433C2×C13#303911yescharacteristic
434C2×C13#304611yescharacteristic
435C2×C13#331211yescharacteristic
436C2×C13#332011yescharacteristic
437C2×C13#337211yescharacteristic
438C2×C13#337411yescharacteristic
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8#612912yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4C2×C22⋊D1311yescharacteristic
466C22×C4C2×C22⋊D1311yescharacteristic
467C22×C4C2×C22⋊D1311yescharacteristic
468C22×C4C2×C22⋊D1311yescharacteristic
469C22×C4C2×C22⋊D1311yescharacteristic
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C23×D1311yescharacteristic
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—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—132no—
496C4⋊C4—132no—
497C4⋊C4—132no—
498C4⋊C4—264no—
499C4⋊C4—264no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—522no—
506C4⋊C4—1041no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—522no—
513C42—1041no—
514C42—1041no—
515C42D4×D1312yes—
516C42#612912yes—
517C13#2529011yescharacteristic, complemented, Sylow
518C23C22×C22⋊D1311yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531C2×C4—21no—
532C2×C4—21no—
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—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
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—262no—
558C2×C4—262no—
559C2×C4—262no—
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#8819212yes—
570C2×C4#8819212yes—
571C2×C4#8819612yes—
572C2×C4#8819612yes—
573C2×C4C2×D4×D1311yescharacteristic
574C2×C4C2×#612911yescharacteristic
575C2×C4C2×#612911yescharacteristic
576C2×C4#8825111yescharacteristic
577C2×C4#41×D1311yescharacteristic
578C2×C4#8825711yescharacteristic
579C8—521no—
580C8—521no—
581C8—521no—
582C8—521no—
583C22C2×#8819211yescharacteristic
584C22#1171951111yescharacteristic
585C22C2×#8819611yescharacteristic
586C22C2×#8819611yescharacteristic
587C22#1171953611yescharacteristic
588C22#1171954211yescharacteristic
589C22#1171954311yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—42no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—522no—
601C4—522no—
602C4—522no—
603C4—1041no—
604C4#1171930311yescharacteristic
605C4#1171930411yescharacteristic
606C4#1171930511yescharacteristic
607C4#1171930811yescharacteristic
608C2#1311839811yescharacteristic
609C2#1312431911yescharacteristic
610C2#1312438211yescharacteristic
611C2#1312688711yescharacteristic
612C2#1312700711yescharacteristic
613C2#1312761311yescharacteristic
614C2#1312763511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2546C2
socle, prime radicalC23×C13C22×D4
hypercenter#2546D13
hypocenterC13#25290
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2546

Complements

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

NH ≅ G/Ntype
517. C13#25290semidirect

Maximal subgroups

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

subgroupindex
C2×#117187432
C2×#117186832
#131179302
#131162312
#131162172
#131160792
#131157602
#131155602
#131154742
#131154672
#131146662
C13×#25462
#2529013