Finite Group Databasebeta

← #15834153

Subgroups — #15834153

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#13123998C211yesmaximal, characteristic, complemented
3#13123870C211yesmaximal, characteristic, complemented
4#13113751C211yesmaximal, characteristic, complemented
5#13113740C211yesmaximal, characteristic, complemented
6#13113681C211yesmaximal, characteristic, complemented
7#13113674C211yesmaximal, characteristic, complemented
8#13113667C211yesmaximal, characteristic, complemented
9#13113667C211yesmaximal, characteristic, complemented
10#13113661C211yesmaximal, characteristic, complemented
11#13113650C211yesmaximal, characteristic, complemented
12#13113621C211yesmaximal, characteristic, complemented
13#13113297C211yesmaximal, characteristic, complemented
14C2×#11718051C211yesmaximal, characteristic, complemented
15C13×#1452C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C2×C4×C8×C13C2211yescharacteristic
21#11718587C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23#11718508C411yescharacteristic
24#11718508C411yescharacteristic
25#11718505C411yescharacteristic
26#11718505C411yescharacteristic
27#11718501—21no—
28#11718500—21no—
29#11718497—21no—
30#11718497—21no—
31#11718396C411yescharacteristic
32#11718393C411yescharacteristic
33#11718392C411yescharacteristic
34#11718391—21no—
35#11718387—21no—
36#11718386—21no—
37D13×C22⋊C8—21no—
38#11718383C411yescharacteristic
39C4×D104C2211yescharacteristic
40C4×D104C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45#11718349C2211yescharacteristic, complemented
46C8×D52C2211yescharacteristic
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic, complemented
49#11718340C2211yescharacteristic, complemented
50C8×Dic26C2211yescharacteristic, complemented
51C13×#322C2211yescharacteristic, complemented
52C13×#322C2211yescharacteristic, complemented
53C13×#322C2211yescharacteristic, complemented
54C13×#322C2211yescharacteristic, complemented
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718051C2211yescharacteristic
58#11718051C2211yescharacteristic
59#11718051C2211yescharacteristic, complemented
60#11718051C2211yescharacteristic, complemented
61#11718050C2211yescharacteristic, complemented
62#11718050C2211yescharacteristic, complemented
63#11718049C2211yescharacteristic, complemented
64#11718049C2211yescharacteristic, complemented
65#11718048C2211yescharacteristic, complemented
66#11718048C2211yescharacteristic, 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⋊C8C2×C411yescharacteristic
101C13×C4⋊C8C2×C411yescharacteristic
102C13×C4⋊C8D411yescharacteristic
103C13×C4⋊C8D411yescharacteristic
104C13×C22⋊C8C2×C411yescharacteristic
105C13×C22⋊C8C2×C411yescharacteristic
106C13×C22⋊C8D411yescharacteristic
107C13×C22⋊C8D411yescharacteristic
108C4×C8×C13—21no—
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C22⋊#1055—21no—
116#88061C2×C411yescharacteristic
117#88061C2×C411yescharacteristic
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88060—21no—
128#88058C2×C411yescharacteristic
129#88058C2×C411yescharacteristic
130#88057C2×C411yescharacteristic
131#88057C2×C411yescharacteristic
132#88056C2×C411yescharacteristic
133#88056C2×C411yescharacteristic
134#88055—21no—
135#88054—21no—
136#88054—21no—
137C8×Dic13—21no—
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143#88043—21no—
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—42no—
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C42×C13C22×C411yescharacteristic
177C42×C13C2×D411yescharacteristic
178C42×C13#4111yescharacteristic
179C42×C13C2411yescharacteristic
180C22⋊Dic13—21no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194#6101—21no—
195#6101—21no—
196#6101—21no—
197#6101—21no—
198C4×Dic13—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—81no—
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#1573—131no—
226#1494—131no—
227C2×D4⋊C8—131no—
228#1452D1311yescharacteristic, complemented
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—21no—
276C8×C13—21no—
277C8×C13—21no—
278C8×C13—21no—
279C8×C13—41no—
280C8×C13—41no—
281#1055—41no—
282#1055—41no—
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#432—131no—
313#431C2×D1311yescharacteristic
314#431C2×D1311yescharacteristic
315#424—261no—
316C2×C4⋊C8—131no—
317#407—261no—
318C2×C22⋊C8—261no—
319C2×C4×C8C2×D1311yescharacteristic
320#335—131no—
321#335—131no—
322#334—131no—
323#334—131no—
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#322C2×D1311yescharacteristic, complemented
333#322C2×D1311yescharacteristic, complemented
334#322C2×D1311yescharacteristic, complemented
335#322C2×D1311yescharacteristic, complemented
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—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8C4×D1311yescharacteristic
408C4⋊C8C4×D1311yescharacteristic
409C4⋊C8D5211yescharacteristic
410C4⋊C8D5211yescharacteristic
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—261no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8C4×D1311yescharacteristic
427C22⋊C8C4×D1311yescharacteristic
428C22⋊C8D5211yescharacteristic
429C22⋊C8D5211yescharacteristic
430#97—261no—
431#97—261no—
432C4×C8—21no—
433C4×C8—261no—
434C4×C8C22×D1311yescharacteristic
435C4×C8C22×D1311yescharacteristic
436C4×C8C22×D1311yescharacteristic
437C4×C8C22×D1311yescharacteristic
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×C4C2×D5211yescharacteristic
466C22×C4#612711yescharacteristic
467SD16—262no—
468SD16—521no—
469D8—262no—
470D8—521no—
471M16—1041no—
472M16—1041no—
473M16—1041no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—42no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—1041no—
482C2×C8—1041no—
483C2×C8—1041no—
484C2×C8—1041no—
485C2×C8C2×C4×D1311yescharacteristic
486C2×C8C2×C4×D1311yescharacteristic
487C2×C8C2×C4×D1311yescharacteristic
488C2×C8C2×C4×D1311yescharacteristic
489C2×C8C2×D5211yescharacteristic
490C2×C8C2×D5211yescharacteristic
491C2×C8C2×D5211yescharacteristic
492C2×C8C2×D5211yescharacteristic
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
513C42C2×D5211yescharacteristic
514C42#612711yescharacteristic
515C42C23×D1311yescharacteristic
516C13#1802011yescharacteristic, complemented, Sylow
517C23—261no—
518C23—261no—
519C23—261no—
520C23—522no—
521C23—522no—
522C23—1041no—
523C23C4×D5211yescharacteristic
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×C4C4×D5211yescharacteristic
554C2×C4C4×D5211yescharacteristic
555C2×C4C4×D5211yescharacteristic
556C2×C4C22×C4×D1311yescharacteristic
557C2×C4C22×D5211yescharacteristic
558C2×C4C2×#612711yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—521no—
570C8—521no—
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#1171837812yes—
586C22C2×C4×D5211yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—521no—
592C4—521no—
593C4—521no—
594C4—521no—
595C4—521no—
596C4D13×#13111yescharacteristic
597C4#1171945511yescharacteristic
598C4#1171945611yescharacteristic
599C4#1171945711yescharacteristic
600C2—22no—
601C2—522no—
602C2—1041no—
603C2—1041no—
604C2#1312356411yescharacteristic
605C2#1312367011yescharacteristic
606C2C2×#1171837811yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1452C2
socleC22×C13C2×C4×D4
prime radical#11718393C4
cosocleC42×C13C24
hypercenter#1452D13
hypocenterC13#18020
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1452

Complements

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

NH ≅ G/Ntype
2. #13123998C2semidirect
3. #13123870C2semidirect
4. #13113751C2semidirect
5. #13113740C2semidirect
6. #13113681C2semidirect
7. #13113674C2semidirect
8. #13113667C2semidirect
9. #13113667C2semidirect
10. #13113661C2semidirect
11. #13113650C2semidirect
12. #13113621C2semidirect
13. #13113297C2semidirect
14. C2×#11718051C2semidirect
15. C13×#1452C2semidirect
45. #11718349C22semidirect
48. C8×D52C22semidirect
49. #11718340C22semidirect
50. C8×Dic26C22semidirect
51. C13×#322C22semidirect
52. C13×#322C22semidirect
53. C13×#322C22semidirect
54. C13×#322C22semidirect
59. #11718051C22semidirect
60. #11718051C22semidirect
61. #11718050C22semidirect
62. #11718050C22semidirect
63. #11718049C22semidirect
64. #11718049C22semidirect
65. #11718048C22semidirect
66. #11718048C22semidirect
228. #1452D13semidirect
332. #322C2×D13semidirect
333. #322C2×D13semidirect
334. #322C2×D13semidirect
335. #322C2×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
#131239982
#131238702
#131137512
#131137402
#131136812
#131136742
#131136672
#131136612
#131136502
#131136212
#131132972
C2×#117180512
C13×#14522
#1802013