Finite Group Databasebeta

← #15931454

Subgroups — #15931454

Order 3328.

812 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119363C211yesmaximal, characteristic, complemented
2#13116239C211yesmaximal, characteristic, complemented
3#13116210C211yesmaximal, characteristic, complemented
4#13116067C211yesmaximal, characteristic
5#13116067C211yesmaximal, characteristic
6#13115522C211yesmaximal, characteristic, complemented
7#13115460C211yesmaximal, characteristic, complemented
8#13115421C211yesmaximal, characteristic, complemented
9#13115421C211yesmaximal, characteristic, complemented
10#13115395C211yesmaximal, characteristic, complemented
11#13115097C211yesmaximal, characteristic, complemented
12#13115097C211yesmaximal, characteristic, complemented
13#13114836C211yesmaximal, characteristic, complemented
14C4×#88072C211yesmaximal, characteristic, complemented
15C13×#2366C211yesmaximal, characteristic
16C2×C13×#127C2211yescharacteristic
17C2×C4×D4×C13—21no—
18C2×C4×D4×C13C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C13×#390—21no—
21C13×#390C2211yescharacteristic
22C13×#390C2211yescharacteristic
23C13×#386—21no—
24C13×#386—21no—
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718645—21no—
36#11718642—21no—
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39#11718596C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718318—21no—
48#11718308—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13—21no—
60C22×D4×C13—21no—
61C22×D4×C13C2311yescharacteristic
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C13×#127—22no—
66C13×#127—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—41no—
70C4×D4×C13—41no—
71C4×D4×C13—44no—
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×C4×Dic13—21no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C13×#95—21no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104#88072—22no—
105#88072—22no—
106#88072—22no—
107#88072—22no—
108#88072—22no—
109#88072—22no—
110#88072—41no—
111#88072—41no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88048—22no—
118#88048—22no—
119C4⋊#1055—41no—
120C4×#1055—41no—
121#26754—131nomaximal, Sylow
122C24×C13—21no—
123C24×C13—21no—
124C2×D4×C13—24no—
125C2×D4×C13—24no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—42no—
137C2×D4×C13—42no—
138C2×D4×C13—81no—
139C2×D4×C13—81no—
140C2×D4×C13#4112yes—
141C2×D4×C13#4112yes—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—81no—
149C22×C4×C13—81no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2411yescharacteristic
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4SD1614yes—
166C13×C4⋊C4#4112yes—
167C13×C22⋊C4—42no—
168C13×C22⋊C4—42no—
169C13×C22⋊C4—42no—
170C13×C22⋊C4—42no—
171C13×C22⋊C4—81no—
172C13×C22⋊C4—81no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—42no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—81no—
188C4⋊Dic13—81no—
189C4⋊Dic13#4112yes—
190#6101—42no—
191#6101—81no—
192#6101—81no—
193#6101—81no—
194C4×Dic13—81no—
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×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207#2507—131no—
208#2366D1311yescharacteristic
209#2071—131no—
210#2065—131no—
211#2041—131no—
212#2041—131no—
213#1934—131no—
214#1926—131no—
215#1920—131no—
216#1920—131no—
217#1916—131no—
218#1864—131no—
219#1864—131no—
220#1802—131no—
221C4×#102—131no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13C22×D411yescharacteristic
237D4×C13—22no—
238D4×C13—22no—
239D4×C13—22no—
240D4×C13—22no—
241D4×C13—48no—
242D4×C13—41no—
243D4×C13—41no—
244D4×C13—41no—
245D4×C13—41no—
246D4×C13—84no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—84no—
269C2×C4×C13—84no—
270C2×C4×C13C2×SD1612yes—
271C2×C4×C13C2×SD1612yes—
272C2×C4×C13C2×SD1612yes—
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13H(5,𝔽2)11yescharacteristic
278C2×C4×C132−1+411yescharacteristic
279C2×Dic13—22no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291#1055—41no—
292#1055—41no—
293#1055—41no—
294#1055—41no—
295C2×#127C2×D1311yescharacteristic
296C2×C4×D4—21no—
297C2×C4×D4C2×D1311yescharacteristic
298C2×C4×D4C2×D1311yescharacteristic
299C2×#106—131no—
300C2×#106—131no—
301C2×C4⋊C8—131no—
302C2×#102—131no—
303C2×#102—131no—
304C2×#102—131no—
305C2×#102—131no—
306C2×#102—131no—
307C2×#102—131no—
308C2×#102—131no—
309C2×#102—131no—
310C2×C4×C8—131no—
311#398—261no—
312#398—261no—
313#390—21no—
314#390C2×D1311yescharacteristic
315#390C2×D1311yescharacteristic
316#389—131no—
317#389—131no—
318#389—131no—
319#389—131no—
320#389—261no—
321#387—261no—
322#386—21no—
323#386—21no—
324#384—131no—
325C4×C4⋊C4—131no—
326C4×C4⋊C4C2×D1311yescharacteristic
327C4×C4⋊C4C2×D1311yescharacteristic
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#336—131no—
335#336—131no—
336#336—131no—
337#336—131no—
338C22×C13—42no—
339C22×C13—42no—
340C22×C13—42no—
341C22×C13—42no—
342C22×C13—42no—
343C22×C13—42no—
344C22×C13—81no—
345C22×C13—81no—
346C22×C13—81no—
347C22×C13—81no—
348C22×C13—81no—
349C22×C13—81no—
350C22×C13—81no—
351C22×C13—81no—
352C22×C13#52511yescharacteristic
353C22×C13#54611yescharacteristic
354C22×C13#54811yescharacteristic
355C22×C13C22×SD1611yescharacteristic
356C22×C13#57511yescharacteristic
357C22×C13#57611yescharacteristic
358C22×C13#57611yescharacteristic
359C4×C13—22no—
360C4×C13—22no—
361C4×C13—22no—
362C4×C13—41no—
363C4×C13—42no—
364C4×C13—41no—
365C4×C13—41no—
366C4×C13—81no—
367C4×C13#52911yescharacteristic
368C4×C13#53911yescharacteristic
369C4×C13#55211yescharacteristic
370C4×C13#55311yescharacteristic
371Dic13—42no—
372Dic13—81no—
373Dic13—81no—
374Dic13—81no—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4C22×D1311yescharacteristic
378C22×D4C22×D1311yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C22×C8—131no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8—131no—
385#127—22no—
386#127—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—41no—
390C4×D4—41no—
391C4×D4—44no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4C22⋊D1311yescharacteristic
403C2×C4⋊C4C22⋊D1311yescharacteristic
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C42—21no—
413C2×C42—261no—
414C2×C42C22×D1311yescharacteristic
415C2×C42C22×D1311yescharacteristic
416C2×C42C22×D1311yescharacteristic
417#106—262no—
418#106—262no—
419C4⋊C8—521no—
420#102—262no—
421#102—262no—
422#102—262no—
423#102—262no—
424#102—262no—
425#102—262no—
426#102—521no—
427#102—521no—
428C4×C8—521no—
429#95—21no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95—261no—
435#95C22⋊D1311yescharacteristic
436#95C22⋊D1311yescharacteristic
437C2×C13—82no—
438C2×C13—82no—
439C2×C13#246011yescharacteristic
440C2×C13#310111yescharacteristic
441C2×C13#312211yescharacteristic
442C2×C13#329511yescharacteristic
443C2×C13#330911yescharacteristic
444C2×C13#336211yescharacteristic
445C2×C13#337011yescharacteristic
446C24—21no—
447C24—21no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4#612712yes—
465C2×D4#612712yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C2×C22⋊D1311yescharacteristic
481C22×C4C2×C22⋊D1311yescharacteristic
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C23×D1311yescharacteristic
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—132no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—522no—
510C4⋊C4—1041no—
511C4⋊C4—1041no—
512C4⋊C4—1041no—
513C4⋊C4—1041no—
514C4⋊C4—1041no—
515C4⋊C4#610514yes—
516C4⋊C4#612912yes—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—42no—
530C42—1041no—
531C13#2675411yescharacteristic, complemented, Sylow
532C23—22no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C22×C22⋊D1311yescharacteristic
547D4—22no—
548D4—22no—
549D4—22no—
550D4—22no—
551D4—48no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—84no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—84no—
579C2×C4—84no—
580C2×C4—262no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4C2×#610512yes—
593C2×C4C2×#610512yes—
594C2×C4C2×#610512yes—
595C2×C4C2×#612711yescharacteristic
596C2×C4C2×#612711yescharacteristic
597C2×C4C2×#612911yescharacteristic
598C2×C4#8825111yescharacteristic
599C2×C4#41×D1311yescharacteristic
600C2×C4#8825711yescharacteristic
601C8—521no—
602C8—521no—
603C8—521no—
604C8—521no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22#1171949611yescharacteristic
620C22C22×#610511yescharacteristic
621C22#1171951111yescharacteristic
622C22#1171952711yescharacteristic
623C22#1171953611yescharacteristic
624C22#1171954011yescharacteristic
625C22#1171954011yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—522no—
635C4—1041no—
636C4—1041no—
637C4—1041no—
638C4#1171924311yescharacteristic
639C4#1171924511yescharacteristic
640C4#1171924611yescharacteristic
641C4#1171926911yescharacteristic
642C2—82no—
643C2—82no—
644C2#1311878211yescharacteristic
645C2#1312484411yescharacteristic
646C2#1312507911yescharacteristic
647C2#1312666011yescharacteristic
648C2#1312684211yescharacteristic
649C2#1312750311yescharacteristic
650C2#1312758311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2366C2
socleC23×C13C22×D4
prime radicalC2×C13×#127C22
hypercenter#2366D13
hypocenterC13#26754
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. #13119363C2semidirect
2. #13116239C2semidirect
3. #13116210C2semidirect
6. #13115522C2semidirect
7. #13115460C2semidirect
8. #13115421C2semidirect
9. #13115421C2semidirect
10. #13115395C2semidirect
11. #13115097C2semidirect
12. #13115097C2semidirect
13. #13114836C2semidirect
14. C4×#88072C2semidirect
531. C13#26754semidirect

Maximal subgroups

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

subgroupindex
#131193632
#131162392
#131162102
#131160672
#131155222
#131154602
#131154212
#131153952
#131150972
#131148362
C4×#880722
C13×#23662
#2675413