Finite Group Databasebeta

← #15832977

Subgroups — #15832977

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124885C211yesmaximal, characteristic
2#13123981C211yesmaximal, characteristic, complemented
3#13123859C211yesmaximal, characteristic, complemented
4#13113699C211yesmaximal, characteristic, complemented
5#13113692C211yesmaximal, characteristic, complemented
6#13113671C211yesmaximal, characteristic, complemented
7#13113664C211yesmaximal, characteristic, complemented
8#13113659C211yesmaximal, characteristic, complemented
9#13113647C211yesmaximal, characteristic, complemented
10#13113635C211yesmaximal, characteristic, complemented
11#13113630C211yesmaximal, characteristic, complemented
12#13113260C211yesmaximal, characteristic, complemented
13#13113242C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#1574C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#423C2211yescharacteristic
21#11718789—21no—
22#11718788—21no—
23#11718586C2211yescharacteristic
24#11718586C2211yescharacteristic
25#11718508C411yescharacteristic
26#11718508C411yescharacteristic
27#11718505C411yescharacteristic
28#11718505C411yescharacteristic
29#11718501—21no—
30#11718500—21no—
31#11718499C2211yescharacteristic, complemented
32#11718495C2211yescharacteristic
33#11718495C2211yescharacteristic
34#11718495C2211yescharacteristic
35#11718495C2211yescharacteristic
36#11718495C2211yescharacteristic, complemented
37#11718492C2211yescharacteristic, complemented
38#11718491C2211yescharacteristic, complemented
39#11718396C411yescharacteristic
40#11718393C411yescharacteristic
41#11718392C411yescharacteristic
42D13×C22⋊C8—21no—
43D13×C22⋊C8—21no—
44#11718383C411yescharacteristic
45C4×D104C2211yescharacteristic
46C4×D104C2211yescharacteristic
47C4×#6095C2211yescharacteristic
48C4×#6095C2211yescharacteristic
49C8×D52—21no—
50C8×D52—21no—
51C13×#335C2211yescharacteristic, complemented
52C13×#335C2211yescharacteristic, complemented
53C13×#334C2211yescharacteristic, complemented
54C13×#334C2211yescharacteristic, complemented
55#11718076C2211yescharacteristic, complemented
56#11718076C2211yescharacteristic, complemented
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718075C2211yescharacteristic
60#11718075C2211yescharacteristic
61#11718075C2211yescharacteristic, complemented
62#11718075C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×M16—21no—
70C2×C42×C13C2311yescharacteristic
71#88184C2×C411yescharacteristic
72#88183—21no—
73C4×C22⋊D13—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13C2×C411yescharacteristic
76#88178C2×C411yescharacteristic
77C2×D104C2×C411yescharacteristic
78C2×D104C2×C411yescharacteristic
79C2×#6095C2×C411yescharacteristic
80C2×#6095C2×C411yescharacteristic
81C2×#6094—21no—
82C2×C8×D13—21no—
83C2×C8×D13—21no—
84C2×C8×D13—21no—
85C2×C8×D13—21no—
86C2×C8×D13—21no—
87#88130—21no—
88#88129C2×C411yescharacteristic
89C4×D52—21no—
90C4×D52—21no—
91C4×D52C2×C411yescharacteristic
92C4×D52C2×C411yescharacteristic
93C4×D52C2311yescharacteristic
94C4×D52C2311yescharacteristic
95C4×D52C2311yescharacteristic
96#88126—21no—
97#88124C2×C411yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×C4⋊C8—21no—
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⋊C8C2×C411yescharacteristic
108C13×C22⋊C8C2×C411yescharacteristic
109C4×C8×C13—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C22⋊#1055—21no—
113C22⋊#1055D411yescharacteristic
114C22⋊#1055D411yescharacteristic
115#88061C2×C411yescharacteristic
116#88061C2×C411yescharacteristic
117#88061C2×C411yescharacteristic
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88060—21no—
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88058C2×C411yescharacteristic
128#88058C2×C411yescharacteristic
129#88057C2×C411yescharacteristic
130#88057C2×C411yescharacteristic
131#88056C2×C411yescharacteristic
132#88056C2×C411yescharacteristic
133#88055—21no—
134#88054—21no—
135#88054—21no—
136C8×Dic13—21no—
137C4⋊#1055—21no—
138C4⋊#1055D411yescharacteristic
139C4⋊#1055D411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17918—131nomaximal, Sylow
145C23×D13—21no—
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13#4111yescharacteristic
149C2×C22⋊D13—21no—
150C22×Dic13—21no—
151C2×D52—21no—
152C2×D52—22no—
153C2×D52—22no—
154C2×D52C22×C411yescharacteristic
155C2×D52C22×C411yescharacteristic
156C2×D52C22×C411yescharacteristic
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—81no—
163C2×C4×D13—81no—
164C2×Dic26C22×C411yescharacteristic
165C13×M16—81no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C42×C13C22×C411yescharacteristic
175C42×C13C2×D411yescharacteristic
176C42×C13#4111yescharacteristic
177C42×C13C2411yescharacteristic
178C22⋊Dic13—21no—
179#6103—21no—
180#6103—21no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192#6101—21no—
193#6101—21no—
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203D104—22no—
204D104—22no—
205#6095—22no—
206#6095—22no—
207#6094—81no—
208C8×D13—81no—
209C8×D13—81no—
210C8×D13—81no—
211C8×D13—81no—
212C8×D13—81no—
213#3105—131no—
214#2993—131no—
215#2972—131no—
216#1586—131no—
217#1585—131no—
218#1582—131no—
219#1581—131no—
220#1580—131no—
221SD16⋊C8—131no—
222C8×SD16—131no—
223C8×D8—131no—
224#1574D1311yescharacteristic, complemented
225#1486—131no—
226#1482—131no—
227#1454—131no—
228C23×C13C4×D411yescharacteristic
229C22×D13—21no—
230C22×D13—21no—
231C22×D13—24no—
232C22×D13—21no—
233C22×D13—81no—
234C22×D13—81no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—41no—
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C22⋊D13—81no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—81no—
253D52—24no—
254D52—21no—
255D52—21no—
256D52—21no—
257D52—21no—
258D52#13112yes—
259D52#13112yes—
260C4×D13—41no—
261C4×D13—41no—
262C4×D13—41no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—81no—
267C4×D13—81no—
268Dic26—21no—
269Dic26—21no—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—41no—
275C8×C13—41no—
276C8×C13—41no—
277C8×C13—41no—
278#1055—21no—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—41no—
283#1055—41no—
284#529—131no—
285C2×C4×D4—131no—
286#484—131no—
287#481—131no—
288#478—131no—
289#478—131no—
290#463—131no—
291#463—131no—
292#450—131no—
293#447—131no—
294#446—131no—
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×D8—131no—
299C4×D8—131no—
300#436—131no—
301#436—261no—
302#435—261no—
303C8×D4—131no—
304C8×D4—131no—
305C8×D4—131no—
306C8×D4—131no—
307C8×D4—131no—
308C8×D4—261no—
309C8×D4—261no—
310#433—261no—
311#431—131no—
312#431—131no—
313#431C2×D1311yescharacteristic
314#431C2×D1311yescharacteristic
315#424—261no—
316#423C2×D1311yescharacteristic
317C2×C22⋊C8—261no—
318C2×C22⋊C8—261no—
319#335C2×D1311yescharacteristic, complemented
320#335C2×D1311yescharacteristic, complemented
321#334C2×D1311yescharacteristic, complemented
322#334C2×D1311yescharacteristic, complemented
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331#322—131no—
332#322—131no—
333#322—131no—
334C82—131no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13C2×C4×D411yescharacteristic
339C2×D13—22no—
340C2×D13—22no—
341C2×D13—41no—
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—84no—
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13C2×#13111yescharacteristic
354C4×C13C2×#13111yescharacteristic
355C4×C13#57611yescharacteristic
356C4×C13#57711yescharacteristic
357Dic13—41no—
358Dic13—41no—
359Dic13—41no—
360Dic13—41no—
361Dic13—41no—
362C22×D4—131no—
363C23×C4—261no—
364C2×SD16—131no—
365C2×SD16—131no—
366C2×D8—131no—
367C2×D8—131no—
368C2×M16—21no—
369C2×M16—261no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375#126—261no—
376#125—131no—
377#124—131no—
378#123—261no—
379C22⋊Q8—131no—
380#121—131no—
381C4×Q8—131no—
382C4×D4—131no—
383C4×D4—131no—
384C4×D4—131no—
385C4×D4—131no—
386C4×D4—131no—
387C4×D4—261no—
388C4×D4—261no—
389C4×D4—261no—
390#117—261no—
391C2×C4⋊C4—131no—
392C2×C22⋊C4—261no—
393C2×C42C22×D1311yescharacteristic
394#107—131no—
395#107—131no—
396#106—131no—
397#106—131no—
398C4⋊C8—21no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—261no—
402C4⋊C8—261no—
403C4⋊C8—261no—
404C4⋊C8C4×D1311yescharacteristic
405C4⋊C8C4×D1311yescharacteristic
406C4⋊C8C22×D1311yescharacteristic
407C4⋊C8C22×D1311yescharacteristic
408C4⋊C8C22×D1311yescharacteristic
409C4⋊C8C22×D1311yescharacteristic
410#103—131no—
411#103—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418C22⋊C8—21no—
419C22⋊C8—131no—
420C22⋊C8—131no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8C4×D1311yescharacteristic
429C22⋊C8C4×D1311yescharacteristic
430#97—261no—
431C4×C8—21no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—261no—
437C4×C8C22×D1311yescharacteristic
438C4×C8C22×D1311yescharacteristic
439C2×C13—41no—
440C2×C13#292911yescharacteristic
441C2×C13#294611yescharacteristic
442C2×C13#295711yescharacteristic
443D13—42no—
444D13—42no—
445D13—81no—
446C24—261no—
447C2×Q8—131no—
448C2×D4—131no—
449C2×D4—131no—
450C2×D4—131no—
451C2×D4—262no—
452C2×D4—262no—
453C2×D4—261no—
454C2×D4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—1041no—
462C22×C4—1041no—
463C22×C4C2×C4×D1311yescharacteristic
464C22×C4D4×D1311yescharacteristic
465C22×C4#613111yescharacteristic
466SD16—262no—
467SD16—262no—
468D8—262no—
469D8—262no—
470M16—81no—
471M16—1041no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—131no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—1041no—
483C2×C8—1041no—
484C2×C8—1041no—
485C2×C8—1041no—
486C2×C8—1041no—
487C2×C8C2×C4×D1311yescharacteristic
488C2×C8C2×C4×D1311yescharacteristic
489C2×C8C2×C4×D1311yescharacteristic
490C2×C8C2×C4×D1311yescharacteristic
491C4⋊C4—131no—
492C4⋊C4—131no—
493C4⋊C4—131no—
494C4⋊C4—131no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C22⋊C4—261no—
501C22⋊C4—261no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C42—261no—
510C42C2×C4×D1311yescharacteristic
511C42D4×D1311yescharacteristic
512C42#613111yescharacteristic
513C42C23×D1311yescharacteristic
514C13#1791811yescharacteristic, complemented, Sylow
515C23—264no—
516C23—261no—
517C23—261no—
518C23—261no—
519C23—1041no—
520C23—1041no—
521C23#8814711yescharacteristic
522Q8—261no—
523Q8—261no—
524D4—132no—
525D4—132no—
526D4—264no—
527D4—261no—
528D4—261no—
529D4—261no—
530D4—261no—
531D4—1041no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—1041no—
549C2×C4—1041no—
550C2×C4—1041no—
551C2×C4#8814711yescharacteristic
552C2×C4#8814711yescharacteristic
553C2×C4#8814711yescharacteristic
554C2×C4C22×C4×D1311yescharacteristic
555C2×C4C2×D4×D1311yescharacteristic
556C2×C4C2×#613111yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—261no—
566C8—261no—
567C8—261no—
568C8—261no—
569C8—521no—
570C8—521no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—262no—
575C22—262no—
576C22—521no—
577C22—521no—
578C22—521no—
579C22—521no—
580C22—521no—
581C22—521no—
582C22—521no—
583C22—1044no—
584C22C2×#8814711yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—521no—
590C4—521no—
591C4—521no—
592C4—521no—
593C4—521no—
594C4D13×#13111yescharacteristic
595C4D13×#13111yescharacteristic
596C4#1171947911yescharacteristic
597C4#1171948311yescharacteristic
598C2—41no—
599C2—522no—
600C2—522no—
601C2—1041no—
602C2#1312352911yescharacteristic
603C2#1312366611yescharacteristic
604C2#1312375211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1574C2
socleC22×C13C2×C4×D4
prime radical#11718393C4
cosocleC42×C13C24
hypercenter#1574D13
hypocenterC13#17918
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
2. #13123981C2semidirect
3. #13123859C2semidirect
4. #13113699C2semidirect
5. #13113692C2semidirect
6. #13113671C2semidirect
7. #13113664C2semidirect
8. #13113659C2semidirect
9. #13113647C2semidirect
10. #13113635C2semidirect
11. #13113630C2semidirect
12. #13113260C2semidirect
13. #13113242C2semidirect
14. #13113136C2semidirect
15. C13×#1574C2semidirect
31. #11718499C22semidirect
36. #11718495C22semidirect
37. #11718492C22semidirect
38. #11718491C22semidirect
51. C13×#335C22semidirect
52. C13×#335C22semidirect
53. C13×#334C22semidirect
54. C13×#334C22semidirect
55. #11718076C22semidirect
56. #11718076C22semidirect
61. #11718075C22semidirect
62. #11718075C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
224. #1574D13semidirect
319. #335C2×D13semidirect
320. #335C2×D13semidirect
321. #334C2×D13semidirect
322. #334C2×D13semidirect
514. C13#17918semidirect

Maximal subgroups

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

subgroupindex
#131248852
#131239812
#131238592
#131136992
#131136922
#131136712
#131136642
#131136592
#131136472
#131136352
#131136302
#131132602
#131132422
#131131362
C13×#15742
#1791813