Finite Group Databasebeta

← #15834147

Subgroups — #15834147

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124885C211yesmaximal, characteristic
2#13123992C211yesmaximal, characteristic, complemented
3#13123873C211yesmaximal, characteristic, complemented
4#13113749C211yesmaximal, characteristic, complemented
5#13113737C211yesmaximal, characteristic, complemented
6#13113678C211yesmaximal, characteristic, complemented
7#13113671C211yesmaximal, characteristic, complemented
8#13113664C211yesmaximal, characteristic, complemented
9#13113664C211yesmaximal, characteristic, complemented
10#13113659C211yesmaximal, characteristic, complemented
11#13113647C211yesmaximal, characteristic, complemented
12#13113294C211yesmaximal, characteristic, complemented
13C2×#11718075C211yesmaximal, characteristic, complemented
14#13113129C211yesmaximal, characteristic, complemented
15C13×#1573C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21#11718772—21no—
22C8×C22⋊D13—21no—
23#11718586C2211yescharacteristic
24C2×C4×#1055C2211yescharacteristic
25#11718508C411yescharacteristic
26#11718508C411yescharacteristic
27#11718505C411yescharacteristic
28#11718505C411yescharacteristic
29#11718501—21no—
30#11718500—21no—
31#11718499C2211yescharacteristic
32#11718499C2211yescharacteristic
33#11718499C2211yescharacteristic, complemented
34#11718495C2211yescharacteristic
35#11718495C2211yescharacteristic
36#11718495C2211yescharacteristic, complemented
37#11718492C2211yescharacteristic, complemented
38#11718491C2211yescharacteristic, complemented
39#11718396C411yescharacteristic
40#11718393C411yescharacteristic
41#11718392C411yescharacteristic
42#11718387—21no—
43D13×C22⋊C8—21no—
44#11718383C411yescharacteristic
45#11718367—21no—
46#11718367—21no—
47C4×D104C2211yescharacteristic
48C4×D104C2211yescharacteristic
49C4×#6095C2211yescharacteristic
50C4×#6095C2211yescharacteristic
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#11718047C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C22×C8×C13—21no—
70C2×C42×C13C2311yescharacteristic
71#88184C2×C411yescharacteristic
72#88183—21no—
73C4×C22⋊D13—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13C2×C411yescharacteristic
76#88178C2×C411yescharacteristic
77C22×#1055—21no—
78C2×D104C2×C411yescharacteristic
79C2×D104C2×C411yescharacteristic
80C2×#6095C2×C411yescharacteristic
81C2×#6095C2×C411yescharacteristic
82C2×#6094—21no—
83C2×#6094—21no—
84C2×#6094—21no—
85C2×C8×D13—21no—
86C2×C8×D13—21no—
87C2×C8×D13—21no—
88#88130—21no—
89#88129C2×C411yescharacteristic
90C4×D52—21no—
91C4×D52—21no—
92C4×D52C2×C411yescharacteristic
93C4×D52C2×C411yescharacteristic
94C4×D52C2311yescharacteristic
95C4×D52C2311yescharacteristic
96C4×D52C2311yescharacteristic
97#88126—21no—
98#88124C2×C411yescharacteristic
99C4×Dic26C2311yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2×C411yescharacteristic
102C13×C4⋊C8C2×C411yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×C4⋊C8C2311yescharacteristic
107C13×C22⋊C8—21no—
108C13×C22⋊C8C2×C411yescharacteristic
109C13×C22⋊C8C2×C411yescharacteristic
110C13×#97—21no—
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
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⋊#1055D411yescharacteristic
138C4⋊#1055D411yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18020—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—22no—
152C2×D52—21no—
153C2×D52—41no—
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
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—81no—
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×#1055—42no—
200C2×#1055C2×D411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204D104—22no—
205D104—41no—
206#6095—22no—
207#6095—41no—
208#6094—81no—
209#6094—81no—
210#6094—81no—
211C8×D13—81no—
212C8×D13—81no—
213C8×D13—81no—
214#3105—131no—
215#2994—131no—
216#2974—131no—
217#1594—131no—
218#1592—131no—
219#1583—131no—
220#1582—131no—
221#1581—131no—
222#1581—131no—
223#1580—131no—
224SD16⋊C8—131no—
225#1573D1311yescharacteristic, complemented
226#1494—131no—
227C2×D4⋊C8—131no—
228#1452—131no—
229C23×C13C4×D411yescharacteristic
230C22×D13—21no—
231C22×D13—21no—
232C22×D13—21no—
233C22×D13—42no—
234C22×D13—42no—
235C22×D13—81no—
236C2×C4×C13—22no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C22⋊D13—42no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—81no—
254D52—21no—
255D52—21no—
256D52—21no—
257D52—21no—
258D52—21no—
259D52—42no—
260D52#13112yes—
261C4×D13—41no—
262C4×D13—41no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—81no—
268C4×D13—81no—
269Dic26—21no—
270Dic26—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—41no—
276C8×C13—41no—
277C8×C13—41no—
278C8×C13—41no—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—21no—
283#1055—41no—
284#1055—41no—
285#529—131no—
286C2×C4×D4—131no—
287#484—131no—
288#481—131no—
289#478—131no—
290#478—131no—
291#463—131no—
292#463—131no—
293#450—131no—
294#447—131no—
295#446—131no—
296C8×Q8—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299C4×D8—131no—
300C4×D8—131no—
301#436—131no—
302#436—131no—
303#436—131no—
304#435—261no—
305#435—261no—
306#435—261no—
307C8×D4—131no—
308C8×D4—131no—
309C8×D4—131no—
310C8×D4—261no—
311#433—261no—
312#432C2×D1311yescharacteristic
313#431—131no—
314#431C2×D1311yescharacteristic
315#424—261no—
316C2×C4⋊C8C2×D1311yescharacteristic
317#407—261no—
318C2×C22⋊C8—261no—
319C2×C4×C8—131no—
320#335C2×D1311yescharacteristic, complemented
321#335C2×D1311yescharacteristic, complemented
322#334C2×D1311yescharacteristic, complemented
323#334C2×D1311yescharacteristic, complemented
324Q8⋊C8—131no—
325Q8⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332#322—131no—
333#322—131no—
334#322—131no—
335#322—131no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13#44412yes—
339C22×C13C2×C4×D411yescharacteristic
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—41no—
349C2×D13—84no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13C2×#13111yescharacteristic
355C4×C13#56811yescharacteristic
356C4×C13#57611yescharacteristic
357C4×C13#57711yescharacteristic
358Dic13—41no—
359Dic13—41no—
360Dic13—41no—
361Dic13—41no—
362Dic13—41no—
363C22×D4—131no—
364C23×C4—261no—
365C2×SD16—131no—
366C2×SD16—131no—
367C2×D8—131no—
368C2×D8—131no—
369C2×M16—261no—
370C2×M16—261no—
371C2×M16—261no—
372C22×C8—21no—
373C22×C8—261no—
374C22×C8—261no—
375C22×C8—261no—
376C22×C8—261no—
377#126—261no—
378#125—131no—
379#124—131no—
380#123—261no—
381C22⋊Q8—131no—
382#121—131no—
383C4×Q8—131no—
384C4×D4—131no—
385C4×D4—131no—
386C4×D4—131no—
387C4×D4—131no—
388C4×D4—131no—
389C4×D4—261no—
390C4×D4—261no—
391C4×D4—261no—
392#117—261no—
393C2×C4⋊C4—131no—
394C2×C22⋊C4—261no—
395C2×C42C22×D1311yescharacteristic
396#107—131no—
397#107—131no—
398#106—131no—
399#106—131no—
400C4⋊C8—21no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8C4×D1311yescharacteristic
406C4⋊C8C4×D1311yescharacteristic
407C4⋊C8C22×D1311yescharacteristic
408C4⋊C8C22×D1311yescharacteristic
409C4⋊C8C22×D1311yescharacteristic
410C4⋊C8C22×D1311yescharacteristic
411#103—131no—
412#103—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418#102—131no—
419C22⋊C8—21no—
420C22⋊C8—131no—
421C22⋊C8—131no—
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—21no—
431#97—261no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—261no—
437C4×C8—261no—
438C4×C8C22×D1311yescharacteristic
439C4×C8C22×D1311yescharacteristic
440C2×C13—22no—
441C2×C13#293311yescharacteristic
442C2×C13#294611yescharacteristic
443C2×C13C2×#44411yescharacteristic
444D13—42no—
445D13—81no—
446D13—81no—
447C24—261no—
448C2×Q8—131no—
449C2×D4—131no—
450C2×D4—131no—
451C2×D4—131no—
452C2×D4—262no—
453C2×D4—261no—
454C2×D4—261no—
455C2×D4—521no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—1041no—
463C22×C4—1041no—
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4D4×D1311yescharacteristic
466C22×C4#613111yescharacteristic
467SD16—262no—
468SD16—521no—
469D8—262no—
470D8—521no—
471M16—1041no—
472M16—1041no—
473M16—1041no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—81no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—131no—
482C2×C8—131no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—522no—
486C2×C8—1041no—
487C2×C8—1041no—
488C2×C8—1041no—
489C2×C8C2×C4×D1311yescharacteristic
490C2×C8C2×C4×D1311yescharacteristic
491C2×C8C2×C4×D1311yescharacteristic
492C2×C8C2×C4×D1311yescharacteristic
493C4⋊C4—131no—
494C4⋊C4—131no—
495C4⋊C4—131no—
496C4⋊C4—131no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C22⋊C4—261no—
510C22⋊C4—261no—
511C42—261no—
512C42C2×C4×D1311yescharacteristic
513C42D4×D1311yescharacteristic
514C42#613111yescharacteristic
515C42C23×D1311yescharacteristic
516C13#1802011yescharacteristic, complemented, Sylow
517C23—261no—
518C23—261no—
519C23—261no—
520C23—522no—
521C23—522no—
522C23—1041no—
523C23#8814711yescharacteristic
524Q8—261no—
525Q8—261no—
526D4—132no—
527D4—261no—
528D4—261no—
529D4—261no—
530D4—261no—
531D4—261no—
532D4—522no—
533D4—522no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—1041no—
551C2×C4—1041no—
552C2×C4—1041no—
553C2×C4#8814711yescharacteristic
554C2×C4#8814711yescharacteristic
555C2×C4#8814711yescharacteristic
556C2×C4C22×C4×D1311yescharacteristic
557C2×C4C2×D4×D1311yescharacteristic
558C2×C4C2×#613111yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—261no—
568C8—261no—
569C8—261no—
570C8—261no—
571C8—521no—
572C8—521no—
573C22—21no—
574C22—21no—
575C22—262no—
576C22—521no—
577C22—521no—
578C22—521no—
579C22—521no—
580C22—521no—
581C22—521no—
582C22—521no—
583C22—521no—
584C22—1044no—
585C22#1171855512yes—
586C22C2×#8814711yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—521no—
592C4—521no—
593C4—521no—
594C4—521no—
595C4—521no—
596C4D13×#13111yescharacteristic
597C4#1171945511yescharacteristic
598C4#1171947911yescharacteristic
599C4#1171948311yescharacteristic
600C2—22no—
601C2—522no—
602C2—1041no—
603C2—1041no—
604C2#1312356011yescharacteristic
605C2#1312366611yescharacteristic
606C2C2×#1171855511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1573C2
socleC22×C13C2×C4×D4
prime radical#11718393C4
cosocleC42×C13C24
hypercenter#1573D13
hypocenterC13#18020
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #13123992C2semidirect
3. #13123873C2semidirect
4. #13113749C2semidirect
5. #13113737C2semidirect
6. #13113678C2semidirect
7. #13113671C2semidirect
8. #13113664C2semidirect
9. #13113664C2semidirect
10. #13113659C2semidirect
11. #13113647C2semidirect
12. #13113294C2semidirect
13. C2×#11718075C2semidirect
14. #13113129C2semidirect
15. C13×#1573C2semidirect
33. #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. #11718047C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
225. #1573D13semidirect
320. #335C2×D13semidirect
321. #335C2×D13semidirect
322. #334C2×D13semidirect
323. #334C2×D13semidirect
516. C13#18020semidirect

Maximal subgroups

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

subgroupindex
#131248852
#131239922
#131238732
#131137492
#131137372
#131136782
#131136712
#131136642
#131136592
#131136472
#131132942
C2×#117180752
#131131292
C13×#15732
#1802013