Finite Group Databasebeta

← #15935615

Subgroups — #15935615

Order 3328.

784 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119236C211yesmaximal, characteristic, complemented
2#13116249C211yesmaximal, characteristic, complemented
3#13116224C211yesmaximal, characteristic, complemented
4#13116022C211yesmaximal, characteristic
5#13116015C211yesmaximal, characteristic
6#13115604C211yesmaximal, characteristic, complemented
7#13115566C211yesmaximal, characteristic, complemented
8#13115444C211yesmaximal, characteristic, complemented
9#13115428C211yesmaximal, characteristic, complemented
10#13115411C211yesmaximal, characteristic, complemented
11#13115083C211yesmaximal, characteristic, complemented
12#13115024C211yesmaximal, characteristic, complemented
13#13114926C211yesmaximal, characteristic, complemented
14C4×#88072C211yesmaximal, characteristic, complemented
15C13×#2361C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13—21no—
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C13×#390C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#388—21no—
23C13×#386—21no—
24C13×#385—21no—
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C22⋊C4C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31#11718873C2211yescharacteristic
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718613—21no—
40#11718606—21no—
41#11718597C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47C13⋊#401—21no—
48#11718313—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13—21no—
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C13×#121—22no—
65C13×#121—22no—
66C4×D4×C13—22no—
67C4×D4×C13—41no—
68C4×D4×C13—44no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—21no—
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×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C42×C13—21no—
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×C4×Dic13—21no—
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C13×#95—21no—
99C13×#95—21no—
100C13×#95D411yescharacteristic
101C13×#95D411yescharacteristic
102#88072—22no—
103#88072—22no—
104#88072—22no—
105#88072—41no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113C22⋊#1055—22no—
114C22⋊#1055—41no—
115#88048—22no—
116#88047—22no—
117#88047—22no—
118#88047—41no—
119C4⋊#1055—22no—
120C4×#1055—41no—
121#27033—131nomaximal, Sylow
122C24×C13—21no—
123C24×C13C2×D411yescharacteristic
124C2×D4×C13—24no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—42no—
131C2×D4×C13—42no—
132C2×D4×C13#4112yes—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—81no—
147C22×C4×C13—81no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2411yescharacteristic
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4#4112yes—
165C13×C4⋊C4#4112yes—
166C13×C22⋊C4—24no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—42no—
170C13×C22⋊C4—42no—
171C13×C22⋊C4—81no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—42no—
177C22⋊Dic13—42no—
178C22⋊Dic13—81no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187#6101—42no—
188#6101—81no—
189C4×Dic13—81no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
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#4112yes—
202#2494—131no—
203#2361D1311yescharacteristic
204#2073—131no—
205#2067—131no—
206#2034—131no—
207#2033—131no—
208#1949—131no—
209#1942—131no—
210#1923—131no—
211#1921—131no—
212#1919—131no—
213#1862—131no—
214#1852—131no—
215#1824—131no—
216C4×#102—131no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—22no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13#13512yes—
231C23×C13C22×D411yescharacteristic
232D4×C13—22no—
233D4×C13—22no—
234D4×C13—48no—
235D4×C13—41no—
236D4×C13—41no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—22no—
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—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
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—41no—
264C2×C4×C13—84no—
265C2×C4×C13—84no—
266C2×C4×C13AGL(1,ℤ/8)12yes—
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13H(5,𝔽2)11yescharacteristic
272C2×C4×C132−1+411yescharacteristic
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—
283C2×Dic13—41no—
284C2×Dic13—41no—
285#1055—22no—
286#1055—41no—
287#1055—41no—
288#1055—41no—
289C2×#121C2×D1311yescharacteristic
290C2×C4×D4—21no—
291C2×C4×D4C2×D1311yescharacteristic
292C22×C4⋊C4C2×D1311yescharacteristic
293C2×#107—131no—
294C2×#107—131no—
295C2×#107—131no—
296C2×#106—131no—
297C2×C4⋊C8—131no—
298C2×#102—131no—
299C2×#102—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×C22⋊C8—131no—
303C2×C22⋊C8—131no—
304C2×C4×C8—131no—
305#401—261no—
306#397—261no—
307#390C2×D1311yescharacteristic
308#389—131no—
309#389—131no—
310#389C2×D1311yescharacteristic
311#388—21no—
312#388—261no—
313#387—261no—
314#386—21no—
315#385—21no—
316#382—131no—
317#380—131no—
318#380—131no—
319C4×C4⋊C4—131no—
320C4×C4⋊C4C2×D1311yescharacteristic
321C4×C22⋊C4C2×D1311yescharacteristic
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#336—131no—
331#336—131no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—42no—
340C22×C13—42no—
341C22×C13—42no—
342C22×C13—81no—
343C22×C13—81no—
344C22×C13—81no—
345C22×C13—81no—
346C22×C13#52511yescharacteristic
347C22×C13#54611yescharacteristic
348C22×C13#54711yescharacteristic
349C22×C13C2×#13511yescharacteristic
350C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C13#57611yescharacteristic
352C22×C13#57811yescharacteristic
353C4×C13—22no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—42no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13—42no—
360C4×C13—81no—
361C4×C13#52911yescharacteristic
362C4×C13#53911yescharacteristic
363C4×C13#55311yescharacteristic
364C4×C13#55611yescharacteristic
365Dic13—81no—
366Dic13—81no—
367Dic13—81no—
368Dic13—81no—
369C22×D4—21no—
370C22×D4C22×D1311yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4C22×D1311yescharacteristic
374C22×C8—131no—
375C22×C8—131no—
376C22×C8—131no—
377C22×C8—131no—
378#121—22no—
379#121—22no—
380C4×D4—22no—
381C4×D4—41no—
382C4×D4—44no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4C22×D1311yescharacteristic
394C2×C4⋊C4C22×D1311yescharacteristic
395C2×C4⋊C4C22×D1311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—261no—
401C2×C22⋊C4—261no—
402C2×C22⋊C4C22⋊D1311yescharacteristic
403C2×C22⋊C4C22⋊D1311yescharacteristic
404C2×C42—21no—
405C2×C42—261no—
406C2×C42C22×D1311yescharacteristic
407C2×C42C22×D1311yescharacteristic
408#107—262no—
409#107—262no—
410#107—521no—
411#106—262no—
412C4⋊C8—262no—
413#102—262no—
414#102—262no—
415#102—262no—
416#102—521no—
417C22⋊C8—262no—
418C22⋊C8—521no—
419C4×C8—521no—
420#95—21no—
421#95—21no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95C22⋊D1311yescharacteristic
430#95C22⋊D1311yescharacteristic
431C2×C13—42no—
432C2×C13—82no—
433C2×C13#246611yescharacteristic
434C2×C13#310511yescharacteristic
435C2×C13#312411yescharacteristic
436C2×C13#330011yescharacteristic
437C2×C13#331811yescharacteristic
438C2×C13#333911yescharacteristic
439C2×C13#335311yescharacteristic
440C24—21no—
441C24C2×C22⋊D1311yescharacteristic
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4#612712yes—
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—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—81no—
465C22×C4—81no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C23×D1311yescharacteristic
476C2×C8—132no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—522no—
503C4⋊C4—1041no—
504C4⋊C4#612712yes—
505C4⋊C4#612912yes—
506C22⋊C4—24no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—81no—
512C22⋊C4—522no—
513C22⋊C4—1041no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—42no—
519C42—1041no—
520C13#2703311yescharacteristic, complemented, Sylow
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—22no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23#8820412yes—
535C23C22×C22⋊D1311yescharacteristic
536D4—22no—
537D4—22no—
538D4—48no—
539D4—41no—
540D4—41no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
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—41no—
567C2×C4—41no—
568C2×C4—84no—
569C2×C4—84no—
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—521no—
581C2×C4—521no—
582C2×C4#8818612yes—
583C2×C4C2×#612711yescharacteristic
584C2×C4C2×#612711yescharacteristic
585C2×C4C2×#612911yescharacteristic
586C2×C4#8825111yescharacteristic
587C2×C4#41×D1311yescharacteristic
588C2×C4#8825711yescharacteristic
589C8—262no—
590C8—521no—
591C8—521no—
592C8—521no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#1171949611yescharacteristic
608C22C2×#8818611yescharacteristic
609C22#1171951111yescharacteristic
610C22C2×#8820411yescharacteristic
611C22#1171952911yescharacteristic
612C22#1171954011yescharacteristic
613C22#1171954311yescharacteristic
614C4—22no—
615C4—42no—
616C4—41no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—1041no—
623C4—1041no—
624C4—1041no—
625C4—1041no—
626C4#1171924311yescharacteristic
627C4#1171924711yescharacteristic
628C4#1171926311yescharacteristic
629C4#1171926911yescharacteristic
630C2—42no—
631C2—82no—
632C2#1311886611yescharacteristic
633C2#1312488311yescharacteristic
634C2#1312509811yescharacteristic
635C2#1312672311yescharacteristic
636C2#1312697711yescharacteristic
637C2#1312723211yescharacteristic
638C2#1312742011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2361C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2361D13
hypocenterC13#27033
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. #13119236C2semidirect
2. #13116249C2semidirect
3. #13116224C2semidirect
6. #13115604C2semidirect
7. #13115566C2semidirect
8. #13115444C2semidirect
9. #13115428C2semidirect
10. #13115411C2semidirect
11. #13115083C2semidirect
12. #13115024C2semidirect
13. #13114926C2semidirect
14. C4×#88072C2semidirect
520. C13#27033semidirect

Maximal subgroups

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

subgroupindex
#131192362
#131162492
#131162242
#131160222
#131160152
#131156042
#131155662
#131154442
#131154282
#131154112
#131150832
#131150242
#131149262
C4×#880722
C13×#23612
#2703313