Finite Group Databasebeta

← #15834221

Subgroups — #15834221

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#13124837C211yesmaximal, characteristic
2#13123902C211yesmaximal, characteristic, complemented
3#13123873C211yesmaximal, characteristic, complemented
4#13113749C211yesmaximal, characteristic, complemented
5#13113720C211yesmaximal, characteristic, complemented
6#13113699C211yesmaximal, characteristic, complemented
7#13113699C211yesmaximal, characteristic, complemented
8#13113664C211yesmaximal, characteristic, complemented
9#13113664C211yesmaximal, characteristic, complemented
10#13113659C211yesmaximal, characteristic, complemented
11#13113630C211yesmaximal, characteristic, complemented
12#13113304C211yesmaximal, characteristic, complemented
13#13113226C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#1572C211yesmaximal, characteristic, complemented
16#11719182C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21#11718586C2211yescharacteristic
22#11718586C2211yescharacteristic
23#11718507C411yescharacteristic
24#11718507C411yescharacteristic
25#11718504C411yescharacteristic
26#11718504C411yescharacteristic
27#11718499C2211yescharacteristic
28#11718499C2211yescharacteristic
29#11718499C2211yescharacteristic, complemented
30#11718499C2211yescharacteristic, complemented
31#11718495C2211yescharacteristic
32#11718495C2211yescharacteristic
33#11718495C2211yescharacteristic, complemented
34#11718495C2211yescharacteristic, complemented
35#11718397C411yescharacteristic
36#11718397C411yescharacteristic
37#11718393C411yescharacteristic
38#11718393C411yescharacteristic
39#11718388—21no—
40#11718388—21no—
41#11718387—21no—
42D13×C22⋊C8—21no—
43#11718367—21no—
44#11718367—21no—
45C4×D104C2211yescharacteristic
46C4×D104C2211yescharacteristic
47C4×D104C2211yescharacteristic
48C4×D104C2211yescharacteristic
49#11718349—21no—
50C8×D52—21no—
51C13×#335C2211yescharacteristic, complemented
52C13×#335C2211yescharacteristic, complemented
53C13×#334C2211yescharacteristic, complemented
54C13×#334C2211yescharacteristic, complemented
55#11718075C2211yescharacteristic
56#11718075C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718075C2211yescharacteristic, complemented
60#11718075C2211yescharacteristic, complemented
61#11718075C2211yescharacteristic, complemented
62#11718075C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C2×#6127—21no—
68C22×D52C2×C411yescharacteristic
69C22×C4×D13—21no—
70C2×C42×C13C2311yescharacteristic
71#88184—21no—
72#88184C2×C411yescharacteristic
73#88184C2×C411yescharacteristic
74C2×#6103—21no—
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×D104C2×C411yescharacteristic
77C2×D104C2×C411yescharacteristic
78C2×D104C2×C411yescharacteristic
79C2×D104C2×C411yescharacteristic
80C2×#6094—21no—
81C2×#6094—21no—
82C2×#6094—21no—
83C2×#6094—21no—
84C2×C8×D13—21no—
85C2×C8×D13—21no—
86C2×C8×D13—21no—
87C2×C8×D13—21no—
88#88129—21no—
89#88128C2×C411yescharacteristic
90C4×D52—21no—
91C4×D52—21no—
92C4×D52—21no—
93C4×D52C2×C411yescharacteristic
94C4×D52C2×C411yescharacteristic
95C4×D52C2311yescharacteristic
96C4×D52C2311yescharacteristic
97C4×D52C2311yescharacteristic
98C4×D52C2311yescharacteristic
99#88123C2×C411yescharacteristic
100C13×C4⋊C8C2×C411yescharacteristic
101C13×C4⋊C8C2×C411yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C13×C22⋊C8C2×C411yescharacteristic
109C13×C22⋊C8C2×C411yescharacteristic
110C13×#97—21no—
111C4×C8×C13—21no—
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C22⋊#1055—21no—
115C22⋊#1055D411yescharacteristic
116C22⋊#1055D411yescharacteristic
117#88061C2×C411yescharacteristic
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88061C2×C411yescharacteristic
123#88061C2×C411yescharacteristic
124#88061C2×C411yescharacteristic
125#88060—21no—
126#88060—21no—
127#88060—21no—
128#88060—21no—
129#88060—21no—
130#88060—21no—
131#88060—21no—
132#88060—21no—
133#88058C2×C411yescharacteristic
134#88058C2×C411yescharacteristic
135#88058C2×C411yescharacteristic
136#88058C2×C411yescharacteristic
137C4⋊#1055—21no—
138C4⋊#1055D411yescharacteristic
139C4⋊#1055D411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18026—131nomaximal, Sylow
145C23×D13—21no—
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13#4111yescharacteristic
149C2×C22⋊D13—21no—
150C2×C22⋊D13—21no—
151C22×Dic13—21no—
152#6127—81no—
153#6127—81no—
154C2×D52—22no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52—21no—
158C2×D52—41no—
159C2×D52C22×C411yescharacteristic
160C2×D52C22×C411yescharacteristic
161C2×D52C22×C411yescharacteristic
162C2×D52C22×C411yescharacteristic
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—21no—
169C2×C4×D13—81no—
170C2×C4×D13—81no—
171C2×Dic26—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13C22×C411yescharacteristic
177C2×C8×C13C22×C411yescharacteristic
178C2×C8×C13C22×C411yescharacteristic
179C2×C8×C13C22×C411yescharacteristic
180C42×C13C22×C411yescharacteristic
181C42×C13C2×D411yescharacteristic
182C42×C13#4111yescharacteristic
183C42×C13C2411yescharacteristic
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13C22×C411yescharacteristic
195C4⋊Dic13C22×C411yescharacteristic
196C4⋊Dic13C22×C411yescharacteristic
197C4⋊Dic13C22×C411yescharacteristic
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055C2×D411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204D104—22no—
205D104—22no—
206D104—41no—
207D104—41no—
208#6094—81no—
209#6094—81no—
210#6094—81no—
211#6094—81no—
212C8×D13—81no—
213C8×D13—81no—
214C8×D13—81no—
215C8×D13—81no—
216#3100—131no—
217#2979—131no—
218#2974—131no—
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#1572D1311yescharacteristic, complemented
228#1496—131no—
229#1478—131no—
230#1454—131no—
231C23×C13C4×D411yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—42no—
237C22×D13—42no—
238C22×D13—81no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—41no—
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C23×C411yescharacteristic
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C22⋊D13—81no—
251C22⋊D13—81no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—81no—
257D52—21no—
258D52—21no—
259D52—21no—
260D52—21no—
261D52—21no—
262D52—21no—
263D52—21no—
264D52—42no—
265D52—42no—
266D52—81no—
267D52#13112yes—
268C4×D13—41no—
269C4×D13—41no—
270C4×D13—41no—
271C4×D13—41no—
272C4×D13—41no—
273C4×D13—41no—
274C4×D13—41no—
275C4×D13—41no—
276C4×D13—81no—
277C4×D13—81no—
278Dic26—81no—
279C8×C13—21no—
280C8×C13—21no—
281C8×C13—21no—
282C8×C13—21no—
283C8×C13—41no—
284C8×C13—41no—
285C8×C13—41no—
286C8×C13—41no—
287#1055—21no—
288#1055—21no—
289#1055—21no—
290#1055—21no—
291#1055—41no—
292#1055—41no—
293#532—131no—
294C2×C4×D4—131no—
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—131no—
310#436—131no—
311#436—261no—
312#435—261no—
313#435—261no—
314C8×D4—131no—
315C8×D4—131no—
316C8×D4—131no—
317C8×D4—131no—
318C8×D4—261no—
319#432C2×D1311yescharacteristic
320#431—131no—
321#431—131no—
322#431C2×D1311yescharacteristic
323#431C2×D1311yescharacteristic
324#408—261no—
325#408—261no—
326#407—261no—
327C2×C22⋊C8—261no—
328#335C2×D1311yescharacteristic, complemented
329#335C2×D1311yescharacteristic, complemented
330#334C2×D1311yescharacteristic, complemented
331#334C2×D1311yescharacteristic, complemented
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—21no—
346C22×C13—21no—
347C22×C13C2×C4×D411yescharacteristic
348C2×D13—22no—
349C2×D13—41no—
350C2×D13—41no—
351C2×D13—41no—
352C2×D13—41no—
353C2×D13—41no—
354C2×D13—41no—
355C2×D13—41no—
356C2×D13—41no—
357C2×D13—41no—
358C2×D13—41no—
359C2×D13—41no—
360C2×D13—84no—
361C4×C13—21no—
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13C2×#13111yescharacteristic
366C4×C13#56811yescharacteristic
367C4×C13#57611yescharacteristic
368C4×C13#57611yescharacteristic
369Dic13—41no—
370Dic13—41no—
371Dic13—41no—
372Dic13—41no—
373C2×#41—261no—
374C22×D4—131no—
375C23×C4—261no—
376C2×D8—131no—
377C2×D8—131no—
378C2×D8—131no—
379C2×D8—131no—
380C2×M16—261no—
381C2×M16—261no—
382C2×M16—261no—
383C2×M16—261no—
384C22×C8—261no—
385C22×C8—261no—
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—131no—
395C4×D4—131no—
396C4×D4—131no—
397C4×D4—131no—
398C4×D4—131no—
399C4×D4—131no—
400C4×D4—261no—
401C4×D4—261no—
402C4×D4—261no—
403C2×C4⋊C4—131no—
404C2×C22⋊C4—261no—
405C2×C42C22×D1311yescharacteristic
406#107—131no—
407#107—131no—
408#107—131no—
409#107—131no—
410C4⋊C8—131no—
411C4⋊C8—131no—
412C4⋊C8—261no—
413C4⋊C8C4×D1311yescharacteristic
414C4⋊C8C4×D1311yescharacteristic
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—131no—
430C22⋊C8—131no—
431C22⋊C8—261no—
432C22⋊C8—261no—
433C22⋊C8—261no—
434C22⋊C8—261no—
435C22⋊C8—261no—
436C22⋊C8—261no—
437C22⋊C8—261no—
438C22⋊C8—261no—
439C22⋊C8—261no—
440C22⋊C8C4×D1311yescharacteristic
441C22⋊C8C4×D1311yescharacteristic
442#97—21no—
443C4×C8—21no—
444C4×C8—131no—
445C4×C8—131no—
446C4×C8—131no—
447C4×C8—131no—
448C4×C8C22×D1311yescharacteristic
449C4×C8C22×D1311yescharacteristic
450C2×C13—41no—
451C2×C13#293311yescharacteristic
452C2×C13#294811yescharacteristic
453C2×C13#295511yescharacteristic
454D13—42no—
455D13—81no—
456D13—81no—
457D13—81no—
458C24—261no—
459#41—1041no—
460#41—1041no—
461C2×Q8—261no—
462C2×D4—131no—
463C2×D4—131no—
464C2×D4—131no—
465C2×D4—131no—
466C2×D4—262no—
467C2×D4—261no—
468C2×D4—261no—
469C2×D4—261no—
470C2×D4—261no—
471C2×D4—261no—
472C2×D4—521no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—1041no—
481C22×C4—1041no—
482C22×C4C2×C4×D1311yescharacteristic
483C22×C4D4×D1311yescharacteristic
484C22×C4#613111yescharacteristic
485D8—262no—
486D8—262no—
487D8—521no—
488D8—521no—
489M16—1041no—
490M16—1041no—
491M16—1041no—
492M16—1041no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—131no—
498C2×C8—131no—
499C2×C8—131no—
500C2×C8—131no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—1041no—
504C2×C8—1041no—
505C2×C8—1041no—
506C2×C8—1041no—
507C2×C8C2×C4×D1311yescharacteristic
508C2×C8C2×C4×D1311yescharacteristic
509C2×C8C2×C4×D1311yescharacteristic
510C2×C8C2×C4×D1311yescharacteristic
511C4⋊C4—131no—
512C4⋊C4—131no—
513C4⋊C4—131no—
514C4⋊C4—131no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C22⋊C4—261no—
518C22⋊C4—261no—
519C22⋊C4—261no—
520C22⋊C4—261no—
521C22⋊C4—261no—
522C22⋊C4—261no—
523C22⋊C4—261no—
524C22⋊C4—261no—
525C42C2×C4×D1311yescharacteristic
526C42D4×D1311yescharacteristic
527C42#613111yescharacteristic
528C42C23×D1311yescharacteristic
529C13#1802611yescharacteristic, complemented, Sylow
530C23—261no—
531C23—261no—
532C23—261no—
533C23—261no—
534C23—522no—
535C23—522no—
536C23—1041no—
537C23#8814711yescharacteristic
538Q8—1041no—
539D4—132no—
540D4—261no—
541D4—261no—
542D4—261no—
543D4—261no—
544D4—261no—
545D4—261no—
546D4—261no—
547D4—522no—
548D4—522no—
549D4—1041no—
550D4—1041no—
551D4—1041no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
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—1041no—
570C2×C4—1041no—
571C2×C4—1041no—
572C2×C4#8814711yescharacteristic
573C2×C4#8814711yescharacteristic
574C2×C4#8814711yescharacteristic
575C2×C4C22×C4×D1311yescharacteristic
576C2×C4C2×D4×D1311yescharacteristic
577C2×C4C2×#613111yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—261no—
587C8—261no—
588C8—261no—
589C8—261no—
590C8—521no—
591C8—521no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—262no—
596C22—521no—
597C22—521no—
598C22—521no—
599C22—521no—
600C22—521no—
601C22—521no—
602C22—521no—
603C22—521no—
604C22—521no—
605C22—521no—
606C22—521no—
607C22—1044no—
608C22C2×#8814711yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—521no—
614C4—521no—
615C4—521no—
616C4—521no—
617C4D13×#13111yescharacteristic
618C4#1171945511yescharacteristic
619C4#1171947411yescharacteristic
620C4#1171947411yescharacteristic
621C2—41no—
622C2—522no—
623C2—1041no—
624C2—1041no—
625C2—1041no—
626C2#1312356011yescharacteristic
627C2#1312368711yescharacteristic
628C2#1312373811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1572C2
socleC22×C13C2×C4×D4
prime radical#13124837C2
cosocleC42×C13C24
hypercenter#1572D13
hypocenterC13#18026
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #13123902C2semidirect
3. #13123873C2semidirect
4. #13113749C2semidirect
5. #13113720C2semidirect
6. #13113699C2semidirect
7. #13113699C2semidirect
8. #13113664C2semidirect
9. #13113664C2semidirect
10. #13113659C2semidirect
11. #13113630C2semidirect
12. #13113304C2semidirect
13. #13113226C2semidirect
14. #13113136C2semidirect
15. C13×#1572C2semidirect
29. #11718499C22semidirect
30. #11718499C22semidirect
33. #11718495C22semidirect
34. #11718495C22semidirect
51. C13×#335C22semidirect
52. C13×#335C22semidirect
53. C13×#334C22semidirect
54. C13×#334C22semidirect
59. #11718075C22semidirect
60. #11718075C22semidirect
61. #11718075C22semidirect
62. #11718075C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
227. #1572D13semidirect
328. #335C2×D13semidirect
329. #335C2×D13semidirect
330. #334C2×D13semidirect
331. #334C2×D13semidirect
529. C13#18026semidirect

Maximal subgroups

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

subgroupindex
#131248372
#131239022
#131238732
#131137492
#131137202
#131136992
#131136642
#131136592
#131136302
#131133042
#131132262
#131131362
C13×#15722
#1802613