Finite Group Databasebeta

← #15834869

Subgroups — #15834869

Order 3328.

612 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125425C211yesmaximal, characteristic
2#13123992C211yesmaximal, characteristic, complemented
3#13123903C211yesmaximal, characteristic, complemented
4#13113735C211yesmaximal, characteristic, complemented
5#13113718C211yesmaximal, characteristic, complemented
6#13113717C211yesmaximal, characteristic, complemented
7#13113697C211yesmaximal, characteristic, complemented
8#13113669C211yesmaximal, characteristic, complemented
9#13113668C211yesmaximal, characteristic, complemented
10#13113657C211yesmaximal, characteristic, complemented
11#13113639C211yesmaximal, characteristic, complemented
12#13113586C211yesmaximal, characteristic, complemented
13#13113245C211yesmaximal, characteristic, complemented
14#13113131C211yesmaximal, characteristic, complemented
15C13×#1480C211yesmaximal, characteristic, complemented
16C13×#532C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20#11718895—21no—
21#11718895—21no—
22#11718772—21no—
23C8×C22⋊D13—21no—
24#11718750C411yescharacteristic
25#11718741C411yescharacteristic
26#11718735C411yescharacteristic
27#11718732C411yescharacteristic
28#11718703C411yescharacteristic
29#11718703C411yescharacteristic
30#11718700C411yescharacteristic
31#11718700C411yescharacteristic
32C4×#6105C2211yescharacteristic
33C4×#6105C2211yescharacteristic
34C4×#6104C2211yescharacteristic
35C4×#6104C2211yescharacteristic
36#11718673—21no—
37#11718673C2211yescharacteristic
38#11718673C2211yescharacteristic
39D4×#1055—21no—
40D4×#1055C2211yescharacteristic
41D4×#1055C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718586C2211yescharacteristic
44C4×#6099C2211yescharacteristic
45#11718501—21no—
46#11718500—21no—
47#11718499C2211yescharacteristic
48#11718495C2211yescharacteristic
49#11718492C2211yescharacteristic
50#11718491C2211yescharacteristic
51C13×D4⋊C8C2211yescharacteristic
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41—21no—
68C22×C8×C13—21no—
69C13×C4⋊Q8C2×C411yescharacteristic
70C13×#127C2×C411yescharacteristic
71C13×#124—21no—
72C13×#121—21no—
73C13×#121C2×C411yescharacteristic
74C13×#121C2×C411yescharacteristic
75C4×D4×C13—21no—
76C4×D4×C13C2311yescharacteristic
77C4×D4×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×#6105C2×C411yescharacteristic
80C2×#6105C2×C411yescharacteristic
81C2×#6104C2×C411yescharacteristic
82C2×#6104C2×C411yescharacteristic
83#88184C2×C411yescharacteristic
84#88183—21no—
85C4×C22⋊D13—21no—
86#88178C2×C411yescharacteristic
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099C2×C411yescharacteristic
90C2×#6099C2×C411yescharacteristic
91C22×#1055—21no—
92C22×#1055—21no—
93C2×#6094—21no—
94C2×C8×D13—21no—
95#88130—21no—
96#88129C2×C411yescharacteristic
97C4×D52C2311yescharacteristic
98#88126—21no—
99#88124C2×C411yescharacteristic
100C4×Dic26C2311yescharacteristic
101C13×C4⋊C8—21no—
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C22⋊C8—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108#88072C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110#88072C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112C22⋊#1055—21no—
113C22⋊#1055—21no—
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117C22⋊#1055D411yescharacteristic
118C22⋊#1055D411yescharacteristic
119#88060—21no—
120#88060—21no—
121#88055—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—21no—
125#88050C2×C411yescharacteristic
126#88050C2×C411yescharacteristic
127#88049C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88048C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88047C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133C4⋊#1055D411yescharacteristic
134C4⋊#1055D411yescharacteristic
135C4⋊#1055C2311yescharacteristic
136C4⋊#1055C2311yescharacteristic
137#88043C2×C411yescharacteristic
138#88043C2×C411yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18082—131nomaximal, Sylow
145C13×#41—81no—
146C13×#41—81no—
147C2×Q8×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13C22×C411yescharacteristic
153C2×D4×C13C22×C411yescharacteristic
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13#4111yescharacteristic
159C2×C22⋊D13—21no—
160C2×D52C22×C411yescharacteristic
161C2×C4×D13—21no—
162C2×Dic26C22×C411yescharacteristic
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—81no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C22⋊C4—21no—
172C13×C22⋊C4—21no—
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C42×C13C22×C411yescharacteristic
176C42×C13C2×D411yescharacteristic
177C42×C13#4111yescharacteristic
178C42×C13C2411yescharacteristic
179C22⋊Dic13—21no—
180#6105—22no—
181#6105—41no—
182#6104—22no—
183#6104—41no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194C4×Dic13—21no—
195#6099—22no—
196#6099—41no—
197#6099—81no—
198#6099—81no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—81no—
202C2×#1055—81no—
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210C2×#1055C2×D411yescharacteristic
211#6094—81no—
212C8×D13—81no—
213#3171—131no—
214#2994—131no—
215#2979—131no—
216#1592—131no—
217#1589—131no—
218#1588—131no—
219#1586—131no—
220#1582—131no—
221#1581—131no—
222#1580—131no—
223C8×SD16—131no—
224#1565—131no—
225#1482—131no—
226#1480D1311yescharacteristic, complemented
227#1453—131no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13C4×D411yescharacteristic
231C22×D13—21no—
232Q8×C13—81no—
233D4×C13—21no—
234D4×C13—21no—
235D4×C13—21no—
236D4×C13—21no—
237D4×C13—42no—
238D4×C13—81no—
239D4×C13—81no—
240D4×C13—81no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13C4×D411yescharacteristic
254C2×C4×C13C4×D411yescharacteristic
255C2×C4×C13C23×C411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C22⋊D13—42no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262D52—21no—
263D52—21no—
264C4×D13—41no—
265C4×D13—41no—
266Dic26—21no—
267Dic26—21no—
268C8×C13—41no—
269C8×C13—41no—
270C8×C13—41no—
271C8×C13—41no—
272#1055—21no—
273#1055—21no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—41no—
280#1055—41no—
281#1055#13112yes—
282#532C2×D1311yescharacteristic
283#529—131no—
284#501—131no—
285#496—131no—
286#490—131no—
287#489—131no—
288#469—131no—
289#469—131no—
290#468—131no—
291#468—131no—
292#446—131no—
293C8×Q8—131no—
294C4×SD16—131no—
295C4×SD16—131no—
296C4×D8—131no—
297C4×D8—131no—
298#436—131no—
299#436—131no—
300#436—131no—
301#436—261no—
302#435—261no—
303C8×D4—131no—
304C8×D4—131no—
305C8×D4—131no—
306C8×D4—261no—
307C8×D4—261no—
308#433—261no—
309#431—131no—
310#431—131no—
311#431C2×D1311yescharacteristic
312#424—261no—
313C2×C4⋊C8C2×D1311yescharacteristic
314#408—261no—
315#408—261no—
316C4×M16—131no—
317#335—131no—
318#335—131no—
319#334—131no—
320#334—131no—
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323D4⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8C2×D1311yescharacteristic
326D4⋊C8C2×D1311yescharacteristic
327D4⋊C8C2×D1311yescharacteristic
328D4⋊C8C2×D1311yescharacteristic
329#322—131no—
330#322—131no—
331#322—131no—
332C82—131no—
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13C2×C4×D411yescharacteristic
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C4×C13—21no—
347C4×C13—21no—
348C4×C13—21no—
349C4×C13—21no—
350C4×C13—41no—
351C4×C13—41no—
352C4×C13C2×#13111yescharacteristic
353C4×C13#56811yescharacteristic
354C4×C13#57611yescharacteristic
355C4×C13#57711yescharacteristic
356Dic13—41no—
357Dic13—41no—
358Dic13—41no—
359C2×#41—21no—
360C2×SD16—131no—
361C2×SD16—131no—
362C2×D8—131no—
363C2×D8—131no—
364C2×M16—131no—
365C2×M16—131no—
366C2×M16—261no—
367C2×M16—261no—
368C2×M16—261no—
369C22×C8—21no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C4⋊Q8C4×D1311yescharacteristic
374#127C4×D1311yescharacteristic
375#126—261no—
376#125—131no—
377#124—21no—
378#124—131no—
379#123—261no—
380C22⋊Q8—131no—
381#121—21no—
382#121—131no—
383#121C4×D1311yescharacteristic
384#121C4×D1311yescharacteristic
385C4×Q8—131no—
386C4×D4—21no—
387C4×D4—131no—
388C4×D4—261no—
389C4×D4C22×D1311yescharacteristic
390C4×D4C22×D1311yescharacteristic
391#117—261no—
392C2×C42C22×D1311yescharacteristic
393#107—131no—
394#107—131no—
395#106—131no—
396#106—131no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8C22×D1311yescharacteristic
406C4⋊C8C22×D1311yescharacteristic
407#103—131no—
408#103—131no—
409#102—131no—
410#102—131no—
411#102—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415C22⋊C8—21no—
416C22⋊C8—131no—
417C22⋊C8—131no—
418C22⋊C8—261no—
419C22⋊C8—261no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425#97—131no—
426#97—131no—
427#97—261no—
428C4×C8—131no—
429C4×C8—131no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—261no—
433C4×C8—261no—
434C4×C8C22×D1311yescharacteristic
435C4×C8C22×D1311yescharacteristic
436C2×C13—41no—
437C2×C13—81no—
438C2×C13—81no—
439C2×C13#293511yescharacteristic
440C2×C13#294611yescharacteristic
441C2×C13#295511yescharacteristic
442D13—81no—
443#41—81no—
444#41—81no—
445C2×Q8—21no—
446C2×Q8—131no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—131no—
452C2×D4—261no—
453C2×D4C2×C4×D1311yescharacteristic
454C2×D4C2×C4×D1311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—261no—
458C22×C4C2×C4×D1311yescharacteristic
459C22×C4D4×D1311yescharacteristic
460C22×C4#612911yescharacteristic
461SD16—262no—
462SD16—521no—
463D8—262no—
464D8—521no—
465M16—262no—
466M16—521no—
467M16—1041no—
468M16—1041no—
469M16—1041no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—131no—
476C2×C8—131no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—131no—
482C2×C8—131no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—1041no—
486C2×C8—1041no—
487C2×C8—1041no—
488C4⋊C4—21no—
489C4⋊C4—131no—
490C4⋊C4—131no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4C2×C4×D1311yescharacteristic
496C4⋊C4C2×C4×D1311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—261no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C42—261no—
507C42C2×C4×D1311yescharacteristic
508C42D4×D1311yescharacteristic
509C42#612911yescharacteristic
510C42C23×D1311yescharacteristic
511C13#1808211yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—261no—
515C23#8813511yescharacteristic
516Q8—81no—
517Q8—261no—
518Q8—261no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—42no—
524D4—81no—
525D4—81no—
526D4—81no—
527D4—261no—
528D4—261no—
529D4—522no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4#8813511yescharacteristic
547C2×C4#8813511yescharacteristic
548C2×C4#8813511yescharacteristic
549C2×C4C22×C4×D1311yescharacteristic
550C2×C4C2×D4×D1311yescharacteristic
551C2×C4C2×#612911yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—132no—
557C8—261no—
558C8—261no—
559C8—261no—
560C8—261no—
561C8—261no—
562C8—261no—
563C8—261no—
564C8—521no—
565C8—521no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—521no—
576C22—521no—
577C22—521no—
578C22C2×#8813511yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—521no—
586C4—521no—
587C4—521no—
588C4D13×#13111yescharacteristic
589C4#1171945511yescharacteristic
590C4#1171946211yescharacteristic
591C4#1171946711yescharacteristic
592C2—41no—
593C2—81no—
594C2—81no—
595C2—1041no—
596C2#1312357611yescharacteristic
597C2#1312366211yescharacteristic
598C2#1312373511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1480C2
socleC22×C13C2×C4×D4
prime radical#13125425C2
cosocleC42×C13C24
hypercenter#1480D13
hypocenterC13#18082
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #13123992C2semidirect
3. #13123903C2semidirect
4. #13113735C2semidirect
5. #13113718C2semidirect
6. #13113717C2semidirect
7. #13113697C2semidirect
8. #13113669C2semidirect
9. #13113668C2semidirect
10. #13113657C2semidirect
11. #13113639C2semidirect
12. #13113586C2semidirect
13. #13113245C2semidirect
14. #13113131C2semidirect
15. C13×#1480C2semidirect
226. #1480D13semidirect
511. C13#18082semidirect

Maximal subgroups

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

subgroupindex
#131254252
#131239922
#131239032
#131137352
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