Finite Group Databasebeta

← #15834365

Subgroups — #15834365

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123855C211yesmaximal, characteristic, complemented
2#13123849C211yesmaximal, characteristic, complemented
3C4×#88173C211yesmaximal, characteristic
4#13113726C211yesmaximal, characteristic, complemented
5#13113723C211yesmaximal, characteristic, complemented
6#13113687C211yesmaximal, characteristic, complemented
7#13113667C211yesmaximal, characteristic, complemented
8#13113664C211yesmaximal, characteristic, complemented
9C8×#6106C211yesmaximal, characteristic, complemented
10#13113633C211yesmaximal, characteristic, complemented
11#13113598C211yesmaximal, characteristic, complemented
12#13113269C211yesmaximal, characteristic, complemented
13#13113269C211yesmaximal, characteristic, complemented
14#13113115C211yesmaximal, characteristic, complemented
15C13×#1584C211yesmaximal, characteristic, complemented
16C2×#88173C411yescharacteristic
17C4×#6131C2211yescharacteristic
18C4×#6131C2211yescharacteristic
19C13×#446C2211yescharacteristic
20C8×Q8×C13C2211yescharacteristic
21C4×C13×Q16C2211yescharacteristic
22Q16×Dic13C411yescharacteristic
23C4×#6106C2211yescharacteristic
24C4×#6106C2211yescharacteristic
25#11718685C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718541C411yescharacteristic
28#11718533C411yescharacteristic
29#11718499—21no—
30#11718499C2211yescharacteristic
31#11718497—21no—
32#11718496—21no—
33#11718496—21no—
34#11718496C2211yescharacteristic
35#11718496C2211yescharacteristic
36#11718495C2211yescharacteristic
37#11718465C411yescharacteristic
38#11718465C411yescharacteristic
39#11718449C411yescharacteristic
40#11718449C411yescharacteristic
41#11718367—21no—
42D13×#97—21no—
43C4×D104C2211yescharacteristic
44#11718349—21no—
45#11718349C2211yescharacteristic
46C4×#6094—21no—
47C4×#6094C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic
63#11718050C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6131C2×C411yescharacteristic
68C2×#6131C2×C411yescharacteristic
69C2×C13×Q16C2×C411yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71C4×Q8×C13C2311yescharacteristic
72Q8×Dic13C2×C411yescharacteristic
73Q8×Dic13C2×C411yescharacteristic
74C2×#6106C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76#88173—24no—
77C2×D104C2×C411yescharacteristic
78C2×#6094—21no—
79C2×#6094—21no—
80C2×#6094D411yescharacteristic
81C2×#6094D411yescharacteristic
82C2×C8×D13—21no—
83C2×C8×D13—21no—
84C2×C8×D13C2×C411yescharacteristic
85C2×C8×D13C2×C411yescharacteristic
86#88147—21no—
87#88147—21no—
88#88147C2×C411yescharacteristic
89#88147C2×C411yescharacteristic
90#88146—21no—
91#88146—21no—
92#88146C2×C411yescharacteristic
93#88146C2×C411yescharacteristic
94C4×D52—21no—
95C4×D52—21no—
96C4×D52C2311yescharacteristic
97C4×D52C2311yescharacteristic
98C42×D13—21no—
99C42×D13—21no—
100C42×D13C2311yescharacteristic
101C13×#107C2×C411yescharacteristic
102C13×C4⋊C8—21no—
103C13×C4⋊C8—21no—
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#103C2×C411yescharacteristic
108C13×#97—21no—
109C4×C8×C13—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#88075C2×C411yescharacteristic
114#88075C2×C411yescharacteristic
115#88061C2×C411yescharacteristic
116#88061C2×C411yescharacteristic
117#88060—21no—
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88060—21no—
122#88060—21no—
123#88060—21no—
124#88058C2×C411yescharacteristic
125#88055—21no—
126#88055—21no—
127#88055D411yescharacteristic
128#88055D411yescharacteristic
129#88054—21no—
130C8×Dic13C2×C411yescharacteristic
131C8×Dic13C2×C411yescharacteristic
132#88049C2×C411yescharacteristic
133#88049C2×C411yescharacteristic
134#88048C2×C411yescharacteristic
135#88048C2×C411yescharacteristic
136C4⋊#1055—21no—
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140#88043—21no—
141C4×#1055—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18037—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148#6131—22no—
149#6131—22no—
150#6131—41no—
151#6131—41no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52C22×C411yescharacteristic
155C2×D52C22×C411yescharacteristic
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13C22×C411yescharacteristic
163C2×C4×D13C2×D411yescharacteristic
164C2×C4×D13#4111yescharacteristic
165C13×Q16—22no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C4⋊C4C22×C411yescharacteristic
177C42×C13—21no—
178C42×C13—21no—
179C42×C13C2411yescharacteristic
180#6106—22no—
181#6106M1614yescomplemented
182#6103—21no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13C22×C411yescharacteristic
197C4×Dic13C2×D411yescharacteristic
198C4×Dic13#4111yescharacteristic
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206D104—22no—
207#6094—22no—
208#6094—22no—
209#6094—42no—
210#6094—42no—
211C8×D13—22no—
212C8×D13—41no—
213C8×D13—42no—
214C8×D13—42no—
215#2971—131no—
216#2970—131no—
217C4×#135—131no—
218#1590—131no—
219#1590—131no—
220#1584—131no—
221#1584D1311yescharacteristic, complemented
222#1581—131no—
223#1581—131no—
224C8×SD16—131no—
225C8×SD16—131no—
226#1568—131no—
227#1488—131no—
228#1488—131no—
229C8×M16—131no—
230C22×D13—21no—
231C22×D13—21no—
232C22×D13C4×D411yescharacteristic
233Q8×C13—21no—
234Q8×C13—21no—
235Q8×C13—21no—
236Q8×C13C2×M1612yes—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13C23×C411yescharacteristic
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13C4×D411yescharacteristic
247C2×Dic13C4×D411yescharacteristic
248C2×Dic13C4×D411yescharacteristic
249D52—21no—
250D52—21no—
251D52—21no—
252D52—42no—
253D52—42no—
254D52C2×M1612yes—
255C4×D13—21no—
256C4×D13—21no—
257C4×D13—21no—
258C4×D13—21no—
259C4×D13—41no—
260C4×D13—42no—
261C4×D13—42no—
262C4×D13—41no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—81no—
267C4×D13—81no—
268C8×C13—21no—
269C8×C13—21no—
270C8×C13—21no—
271C8×C13—41no—
272C8×C13—41no—
273C8×C13—41no—
274C8×C13#13512yescomplemented
275#1055—21no—
276#1055—21no—
277#1055—41no—
278#1055—41no—
279#1055—41no—
280#1055C2×M1612yes—
281#1055#13512yescomplemented
282C2×#135—131no—
283C4×#41—131no—
284C4×#41—131no—
285#446—131no—
286#446C2×D1311yescharacteristic
287C8×Q8—131no—
288C8×Q8C2×D1311yescharacteristic
289C4×Q16—131no—
290C4×Q16C2×D1311yescharacteristic
291C4×SD16—131no—
292C4×SD16—131no—
293C4×SD16—131no—
294C4×SD16—131no—
295C4×D8—131no—
296C4×D8—131no—
297#436—131no—
298#436—131no—
299#436—261no—
300#436—261no—
301#435—261no—
302#435—261no—
303C8×D4—131no—
304C8×D4—131no—
305#432—131no—
306#432—131no—
307#432—261no—
308#432—261no—
309#431—131no—
310#427—131no—
311#416—131no—
312#416—131no—
313C4×M16—131no—
314C4×M16—261no—
315C2×#97—261no—
316C2×C4×C8—131no—
317#335—131no—
318#335C2×D1311yescharacteristic
319#334—131no—
320#334—131no—
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323Q8⋊C8C2×D1311yescharacteristic
324Q8⋊C8C2×D1311yescharacteristic
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329#322—131no—
330#322C2×D1311yescharacteristic
331C82—131no—
332C82—131no—
333C22×C13C2×C4×D411yescharacteristic
334C2×D13—21no—
335C2×D13—22no—
336C2×D13—21no—
337C2×D13—21no—
338C2×D13—41no—
339C2×D13—41no—
340C2×D13—41no—
341C2×D13—41no—
342C2×D13—41no—
343C4×C13—22no—
344C4×C13—21no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13C22×M1611yescharacteristic
349C4×C13#56811yescharacteristic
350C4×C13C2×#13511yescharacteristic
351C4×C13C2×#13511yescharacteristic
352Dic13—21no—
353Dic13—21no—
354Dic13—21no—
355Dic13—41no—
356Dic13—41no—
357C2×#41—131no—
358C2×#41—131no—
359#135—264no—
360C2×Q16C4×D1311yescharacteristic
361C2×SD16—131no—
362C2×SD16—131no—
363C2×D8—131no—
364C2×M16—131no—
365C2×M16—131no—
366C2×M16—261no—
367C2×M16—261no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—261no—
371C22×C8—261no—
372C4×Q8—131no—
373C4×Q8—131no—
374C4×Q8C22×D1311yescharacteristic
375C4×Q8C22×D1311yescharacteristic
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—131no—
379C4×D4—131no—
380C4×D4—261no—
381C4×D4—261no—
382C4×D4—261no—
383C4×D4—261no—
384#117—131no—
385#117—131no—
386#117—261no—
387#117—261no—
388C2×C42—131no—
389C2×C42—261no—
390C2×C42—261no—
391#107—131no—
392#107C4×D1311yescharacteristic
393#106—131no—
394#106—131no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—131no—
398C4⋊C8—131no—
399C4⋊C8—261no—
400C4⋊C8—261no—
401C4⋊C8—261no—
402C4⋊C8C22×D1311yescharacteristic
403C4⋊C8C22×D1311yescharacteristic
404#103—131no—
405#103—131no—
406#103C4×D1311yescharacteristic
407#103C4×D1311yescharacteristic
408#102—131no—
409#102—131no—
410#102—131no—
411#102—131no—
412C22⋊C8—261no—
413C22⋊C8—261no—
414C22⋊C8—261no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8—261no—
419#97—21no—
420#97—131no—
421#97—131no—
422#97—261no—
423#97—261no—
424#97—261no—
425C4×C8—21no—
426C4×C8—131no—
427C4×C8—131no—
428C4×C8—131no—
429C4×C8—131no—
430C4×C8—131no—
431C4×C8—261no—
432C4×C8C22×D1311yescharacteristic
433C4×C8C22×D1311yescharacteristic
434C4×C8C22×D1311yescharacteristic
435C2×C13D4×M1611yescharacteristic
436C2×C13C4×#13511yescharacteristic
437C2×C13#295711yescharacteristic
438D13—41no—
439D13—42no—
440D13—81no—
441#41—262no—
442#41—262no—
443#41—521no—
444#41—521no—
445C2×Q8C2×C4×D1311yescharacteristic
446C2×Q8C2×C4×D1311yescharacteristic
447C2×D4—131no—
448C2×D4—131no—
449C2×D4—261no—
450C2×D4—261no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460Q16—22no—
461SD16—134no—
462SD16—262no—
463D8—262no—
464M16—262no—
465M16—262no—
466M16—522no—
467M16—522no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—131no—
472C2×C8—131no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—262no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—521no—
480C2×C8—522no—
481C2×C8—522no—
482C2×C8C2×C4×D1311yescharacteristic
483C2×C8C2×C4×D1311yescharacteristic
484C2×C8D4×D1311yescharacteristic
485C2×C8D4×D1311yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—131no—
489C4⋊C4—131no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4C2×C4×D1311yescharacteristic
493C4⋊C4C2×C4×D1311yescharacteristic
494C22⋊C4—261no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C22⋊C4—261no—
498C22⋊C4—261no—
499C22⋊C4—261no—
500C42—21no—
501C42—21no—
502C42—131no—
503C42—131no—
504C42—131no—
505C42—261no—
506C42—261no—
507C42—261no—
508C42—261no—
509C42C23×D1311yescharacteristic
510C13#1803711yescharacteristic, complemented, Sylow
511C23—131no—
512C23—261no—
513C23—261no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8M16×D1312yes—
518D4—132no—
519D4—261no—
520D4—261no—
521D4—261no—
522D4—522no—
523D4—522no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—131no—
529C2×C4—131no—
530C2×C4—131no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—521no—
538C2×C4—522no—
539C2×C4—522no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—1041no—
545C2×C4—1041no—
546C2×C4C22×C4×D1311yescharacteristic
547C2×C4C2×D4×D1311yescharacteristic
548C2×C4#41×D1311yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—132no—
556C8—132no—
557C8—261no—
558C8—261no—
559C8—521no—
560C8—521no—
561C8—521no—
562C8#8817312yescomplemented
563C22—261no—
564C22—261no—
565C22—261no—
566C22—262no—
567C22—521no—
568C22—521no—
569C22—521no—
570C22—521no—
571C22—521no—
572C22C4×D4×D1311yescharacteristic
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—261no—
579C4—261no—
580C4—261no—
581C4—521no—
582C4—521no—
583C4C2×M16×D1311yescharacteristic
584C4#1171945511yescharacteristic
585C4C2×#8817311yescharacteristic
586C4D13×#13511yescharacteristic
587C2—521no—
588C2—522no—
589C2—1041no—
590C2#1312356911yescharacteristic
591C2C4×#8817311yescharacteristic
592C2#1312375011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1584C2
socleC22×C13C2×C4×D4
prime radicalC2×#88173C4
cosocleC42×C13C24
hypercenter#1584D13
hypocenterC13#18037
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
1. #13123855C2semidirect
2. #13123849C2semidirect
4. #13113726C2semidirect
5. #13113723C2semidirect
6. #13113687C2semidirect
7. #13113667C2semidirect
8. #13113664C2semidirect
9. C8×#6106C2semidirect
10. #13113633C2semidirect
11. #13113598C2semidirect
12. #13113269C2semidirect
13. #13113269C2semidirect
14. #13113115C2semidirect
15. C13×#1584C2semidirect
181. #6106M16semidirect
221. #1584D13semidirect
274. C8×C13#135semidirect
281. #1055#135semidirect
510. C13#18037semidirect
562. C8#88173semidirect

Maximal subgroups

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

subgroupindex
#131238552
#131238492
C4×#881732
#131137262
#131137232
#131136872
#131136672
#131136642
C8×#61062
#131136332
#131135982
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