Finite Group Databasebeta

← #15834223

Subgroups — #15834223

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124836C211yesmaximal, characteristic
2#13123902C211yesmaximal, characteristic, complemented
3#13113748C211yesmaximal, characteristic, complemented
4#13113719C211yesmaximal, characteristic, complemented
5#13113700C211yesmaximal, characteristic, complemented
6#13113698C211yesmaximal, characteristic, complemented
7#13113665C211yesmaximal, characteristic, complemented
8#13113663C211yesmaximal, characteristic, complemented
9#13113658C211yesmaximal, characteristic, complemented
10C8×#6104C211yesmaximal, characteristic, complemented
11#13113617C211yesmaximal, characteristic, complemented
12#13113304C211yesmaximal, characteristic, complemented
13#13113227C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#2974C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17#11719182C2211yescharacteristic
18C13×#436C2211yescharacteristic
19C13×#436C2211yescharacteristic
20C13×#435—21no—
21C13×#435—21no—
22C8×D4×C13C2211yescharacteristic
23C8×D4×C13C2211yescharacteristic
24C13×#432C2211yescharacteristic
25C13×#431C2211yescharacteristic
26C13×#407—21no—
27C2×C13×C22⋊C8—21no—
28#11718878C411yescharacteristic
29#11718878C411yescharacteristic
30#11718676C411yescharacteristic
31#11718676C411yescharacteristic
32C4×#6104C2211yescharacteristic
33C4×#6104C2211yescharacteristic
34C4×#6104C2211yescharacteristic
35C4×#6104C2211yescharacteristic
36#11718668C411yescharacteristic
37#11718668C411yescharacteristic
38#11718628C411yescharacteristic
39#11718628C411yescharacteristic
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718499—21no—
44#11718495—21no—
45#11718388—21no—
46#11718388—21no—
47#11718349C2211yescharacteristic, complemented
48#11718349C2211yescharacteristic, complemented
49C8×D52C2211yescharacteristic, complemented
50C8×D52C2211yescharacteristic, complemented
51D4⋊#1055C2211yescharacteristic
52D4⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718075C2211yescharacteristic, complemented
56#11718075C2211yescharacteristic, complemented
57#11718075C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic, complemented
59#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718071C2211yescharacteristic, complemented
62#11718071C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C22×D4×C13C2×C411yescharacteristic
68C23×C4×C13—21no—
69C2×#6127—21no—
70C2×C13×M16—21no—
71C2×C13×M16—21no—
72C22×C8×C13—21no—
73C22×C8×C13—21no—
74C4×D4×C13—21no—
75C4×D4×C13—21no—
76C4×D4×C13C2×C411yescharacteristic
77C4×D4×C13C2×C411yescharacteristic
78C4×D4×C13C2311yescharacteristic
79C4×D4×C13C2311yescharacteristic
80C2×C13×C4⋊C4C2×C411yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C42×C13C2311yescharacteristic
83C2×#6104C2×C411yescharacteristic
84C2×#6104C2×C411yescharacteristic
85C2×#6104C2×C411yescharacteristic
86C2×#6104C2×C411yescharacteristic
87#88184—21no—
88#88184C2×C411yescharacteristic
89#88184C2×C411yescharacteristic
90C2×#6094—21no—
91C2×#6094—21no—
92C2×C8×D13—21no—
93C2×C8×D13—21no—
94#88129—21no—
95#88128C2×C411yescharacteristic
96C4×D52—21no—
97C4×D52C2311yescharacteristic
98C4×D52C2311yescharacteristic
99#88123C2×C411yescharacteristic
100C13×C4⋊C8D411yescharacteristic
101C13×C4⋊C8D411yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C22⋊C8—21no—
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C13×C22⋊C8—21no—
109C13×C22⋊C8D411yescharacteristic
110C13×C22⋊C8D411yescharacteristic
111C13×#97—21no—
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114#88072C2×C411yescharacteristic
115#88072C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117#88072C2×C411yescharacteristic
118C22⋊#1055—21no—
119C22⋊#1055—21no—
120C22⋊#1055C2×C411yescharacteristic
121C22⋊#1055C2×C411yescharacteristic
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88049C2×C411yescharacteristic
127#88049C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88047C2×C411yescharacteristic
131#88047C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18026—131nomaximal, Sylow
145C24×C13—21no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—41no—
149C2×D4×C13C22×C411yescharacteristic
150C2×D4×C13C22×C411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—81no—
157C22×C4×C13—81no—
158C22×C4×C13C22×C411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13#4111yescharacteristic
161C2×C22⋊D13—21no—
162C2×C22⋊D13—21no—
163#6127—81no—
164#6127—81no—
165C2×D52—21no—
166C2×D52—21no—
167C2×D52C22×C411yescharacteristic
168C2×D52C22×C411yescharacteristic
169C2×C4×D13—21no—
170C2×C4×D13—21no—
171C2×Dic26—21no—
172C13×M16—81no—
173C13×M16—81no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—81no—
177C2×C8×C13—81no—
178C2×C8×C13C2×D411yescharacteristic
179C2×C8×C13C2×D411yescharacteristic
180C2×C8×C13C2×D411yescharacteristic
181C2×C8×C13C2×D411yescharacteristic
182C13×C4⋊C4—21no—
183C13×C4⋊C4C22×C411yescharacteristic
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C22⋊C4—21no—
186C13×C22⋊C4—21no—
187C13×C22⋊C4—21no—
188C13×C22⋊C4—21no—
189C42×C13C22×C411yescharacteristic
190C42×C13C2×D411yescharacteristic
191C42×C13#4111yescharacteristic
192C42×C13C2411yescharacteristic
193#6104—22no—
194#6104—22no—
195#6104—41no—
196#6104—41no—
197#6103—21no—
198#6103—21no—
199#6103—21no—
200#6103—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13C22×C411yescharacteristic
203C4⋊Dic13C22×C411yescharacteristic
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210C2×#1055C22×C411yescharacteristic
211C2×#1055C22×C411yescharacteristic
212#6094—81no—
213#6094—81no—
214C8×D13—81no—
215C8×D13—81no—
216#3100—131no—
217#2979—131no—
218#2974D1311yescharacteristic, complemented
219#1594—131no—
220#1589—131no—
221#1586—131no—
222#1586—131no—
223#1581—131no—
224#1581—131no—
225#1580—131no—
226C8×D8—131no—
227#1572—131no—
228#1496—131no—
229#1478—131no—
230#1454—131no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—42no—
234C23×C13—42no—
235C23×C13—81no—
236C23×C13C4×D411yescharacteristic
237C22×D13—21no—
238C22×D13—21no—
239D4×C13—21no—
240D4×C13—21no—
241D4×C13—21no—
242D4×C13—42no—
243D4×C13#13112yes—
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—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—81no—
256C2×C4×C13—81no—
257C2×C4×C13—81no—
258C2×C4×C13C4×D411yescharacteristic
259C2×C4×C13C4×D411yescharacteristic
260C2×C4×C13C4×D411yescharacteristic
261C2×C4×C13C23×C411yescharacteristic
262C2×C4×C13C22×D411yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C22⋊D13—81no—
265C22⋊D13—81no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268D52—21no—
269D52—21no—
270D52—21no—
271D52—21no—
272D52—42no—
273D52—81no—
274C4×D13—41no—
275C4×D13—41no—
276C4×D13—41no—
277C4×D13—41no—
278Dic26—81no—
279C8×C13—21no—
280C8×C13—21no—
281C8×C13—21no—
282C8×C13—21no—
283C8×C13—41no—
284C8×C13—41no—
285#1055—21no—
286#1055—21no—
287#1055—21no—
288#1055—21no—
289#1055—41no—
290#1055—41no—
291#1055—41no—
292#1055—41no—
293#532—131no—
294C2×C4×D4C2×D1311yescharacteristic
295#480—131no—
296#480—131no—
297#474—131no—
298#474—131no—
299#459—131no—
300#459—131no—
301#447—131no—
302#447—131no—
303C4×D8—131no—
304C4×D8—131no—
305C4×D8—131no—
306C4×D8—131no—
307#436—131no—
308#436—131no—
309#436—261no—
310#436C2×D1311yescharacteristic
311#436C2×D1311yescharacteristic
312#435—21no—
313#435—21no—
314C8×D4—131no—
315C8×D4—131no—
316C8×D4—261no—
317C8×D4C2×D1311yescharacteristic
318C8×D4C2×D1311yescharacteristic
319#432C2×D1311yescharacteristic
320#431—131no—
321#431—131no—
322#431—131no—
323#431C2×D1311yescharacteristic
324#408—261no—
325#408—261no—
326#407—21no—
327C2×C22⋊C8—21no—
328#335—131no—
329#335—131no—
330#334—131no—
331#334—131no—
332D4⋊C8—131no—
333D4⋊C8—131no—
334D4⋊C8—131no—
335D4⋊C8—131no—
336D4⋊C8—131no—
337D4⋊C8—131no—
338D4⋊C8—131no—
339D4⋊C8—131no—
340#322—131no—
341#322—131no—
342#322—131no—
343C82—131no—
344C22×C13—21no—
345C22×C13—22no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—84no—
354C22×C13C2×C4×D411yescharacteristic
355C2×D13—41no—
356C2×D13—41no—
357C2×D13—41no—
358C2×D13—41no—
359C2×D13—41no—
360C2×D13—41no—
361C4×C13—21no—
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—41no—
366C4×C13—41no—
367C4×C13C2×#13111yescharacteristic
368C4×C13#56811yescharacteristic
369C4×C13#57611yescharacteristic
370C4×C13#57611yescharacteristic
371Dic13—41no—
372Dic13—41no—
373C2×#41—261no—
374C22×D4C4×D1311yescharacteristic
375C23×C4—21no—
376C2×D8—131no—
377C2×D8—131no—
378C2×D8—131no—
379C2×D8—131no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—261no—
383C2×M16—261no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—261no—
387C22×C8—261no—
388C4⋊Q8—131no—
389#127—131no—
390#124—261no—
391#121—131no—
392#121—131no—
393#121—261no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—131no—
397C4×D4—131no—
398C4×D4—261no—
399C4×D4C4×D1311yescharacteristic
400C4×D4C4×D1311yescharacteristic
401C4×D4C22×D1311yescharacteristic
402C4×D4C22×D1311yescharacteristic
403C2×C4⋊C4C4×D1311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C42C22×D1311yescharacteristic
406#107—131no—
407#107—131no—
408#107—131no—
409#107—131no—
410C4⋊C8—131no—
411C4⋊C8—131no—
412C4⋊C8—131no—
413C4⋊C8—131no—
414C4⋊C8—261no—
415C4⋊C8C22⋊D1311yescharacteristic
416C4⋊C8C22⋊D1311yescharacteristic
417C4⋊C8C22×D1311yescharacteristic
418C4⋊C8C22×D1311yescharacteristic
419#102—131no—
420#102—131no—
421#102—131no—
422#102—131no—
423#102—131no—
424#102—131no—
425#102—131no—
426#102—131no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—131no—
433C22⋊C8—131no—
434C22⋊C8—261no—
435C22⋊C8—261no—
436C22⋊C8—261no—
437C22⋊C8—261no—
438C22⋊C8—261no—
439C22⋊C8—261no—
440C22⋊C8C22⋊D1311yescharacteristic
441C22⋊C8C22⋊D1311yescharacteristic
442#97—21no—
443C4×C8—131no—
444C4×C8—131no—
445C4×C8—131no—
446C4×C8—131no—
447C4×C8—261no—
448C4×C8C22×D1311yescharacteristic
449C4×C8C22×D1311yescharacteristic
450C2×C13—41no—
451C2×C13—42no—
452C2×C13—81no—
453C2×C13#293311yescharacteristic
454C2×C13#294811yescharacteristic
455C2×C13#295511yescharacteristic
456D13—81no—
457D13—81no—
458C24—21no—
459#41—1041no—
460#41—1041no—
461C2×Q8—261no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—41no—
465C2×D4—131no—
466C2×D4—131no—
467C2×D4—261no—
468C2×D4—261no—
469C2×D4—261no—
470C2×D4—261no—
471C2×D4C2×C4×D1311yescharacteristic
472C2×D4C2×C4×D1311yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4C2×C4×D1311yescharacteristic
483C22×C4#612711yescharacteristic
484C22×C4C2×C22⋊D1311yescharacteristic
485D8—262no—
486D8—262no—
487D8—521no—
488D8—521no—
489M16—81no—
490M16—81no—
491M16—1041no—
492M16—1041no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—81no—
496C2×C8—81no—
497C2×C8—131no—
498C2×C8—131no—
499C2×C8—131no—
500C2×C8—131no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—1041no—
506C2×C8—1041no—
507C2×C8C2×C22⋊D1311yescharacteristic
508C2×C8C2×C22⋊D1311yescharacteristic
509C2×C8C2×C22⋊D1311yescharacteristic
510C2×C8C2×C22⋊D1311yescharacteristic
511C4⋊C4—21no—
512C4⋊C4—131no—
513C4⋊C4—131no—
514C4⋊C4—261no—
515C4⋊C4C2×C4×D1311yescharacteristic
516C4⋊C4C2×C4×D1311yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—261no—
522C22⋊C4—261no—
523C22⋊C4—261no—
524C22⋊C4—261no—
525C42C2×C4×D1311yescharacteristic
526C42#612711yescharacteristic
527C42C2×C22⋊D1311yescharacteristic
528C42C23×D1311yescharacteristic
529C13#1802611yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—42no—
533C23—42no—
534C23—81no—
535C23—261no—
536C23—261no—
537C23C4×C22⋊D1311yescharacteristic
538Q8—1041no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—42no—
543D4—261no—
544D4—261no—
545D4—261no—
546D4—261no—
547D4—522no—
548D4—1041no—
549D4—1041no—
550D4—1041no—
551D4#8816112yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—261no—
567C2×C4—261no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4C4×C22⋊D1311yescharacteristic
573C2×C4C4×C22⋊D1311yescharacteristic
574C2×C4C4×C22⋊D1311yescharacteristic
575C2×C4C22×C4×D1311yescharacteristic
576C2×C4C2×#612711yescharacteristic
577C2×C4C22×C22⋊D1311yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—261no—
585C8—261no—
586C8—261no—
587C8—261no—
588C8—521no—
589C8—521no—
590C8—521no—
591C8—521no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—84no—
602C22—521no—
603C22—521no—
604C22—521no—
605C22—521no—
606C22—521no—
607C22—521no—
608C22C2×C4×C22⋊D1311yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—521no—
616C4—521no—
617C4C2×#8816111yescharacteristic
618C4#1171945011yescharacteristic
619C4#1171954011yescharacteristic
620C4#1171954011yescharacteristic
621C2—41no—
622C2—42no—
623C2—81no—
624C2—1041no—
625C2—1041no—
626C2#1312356111yescharacteristic
627C2#1312368611yescharacteristic
628C2#1312373711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2974C2
socleC22×C13C2×C4×D4
prime radical#13124836C2
cosocleC42×C13C24
hypercenter#2974D13
hypocenterC13#18026
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #13123902C2semidirect
3. #13113748C2semidirect
4. #13113719C2semidirect
5. #13113700C2semidirect
6. #13113698C2semidirect
7. #13113665C2semidirect
8. #13113663C2semidirect
9. #13113658C2semidirect
10. C8×#6104C2semidirect
11. #13113617C2semidirect
12. #13113304C2semidirect
13. #13113227C2semidirect
14. #13113136C2semidirect
15. C13×#2974C2semidirect
47. #11718349C22semidirect
48. #11718349C22semidirect
49. C8×D52C22semidirect
50. C8×D52C22semidirect
55. #11718075C22semidirect
56. #11718075C22semidirect
57. #11718075C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
61. #11718071C22semidirect
62. #11718071C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
218. #2974D13semidirect
529. C13#18026semidirect

Maximal subgroups

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

subgroupindex
#131248362
#131239022
#131137482
#131137192
#131137002
#131136982
#131136652
#131136632
#131136582
C8×#61042
#131136172
#131133042
#131132272
#131131362
C13×#29742
#1802613