Finite Group Databasebeta

← #15833439

Subgroups — #15833439

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125392C211yesmaximal, characteristic
2#13123767C211yesmaximal, characteristic, complemented
3#13123545C211yesmaximal, characteristic
4#13113728C211yesmaximal, characteristic, complemented
5#13113726C211yesmaximal, characteristic, complemented
6#13113724C211yesmaximal, characteristic, complemented
7#13113639C211yesmaximal, characteristic, complemented
8SD16×#1055C211yesmaximal, characteristic, complemented
9#13113635C211yesmaximal, characteristic, complemented
10#13113633C211yesmaximal, characteristic, complemented
11#13113590C211yesmaximal, characteristic, complemented
12#13113289C211yesmaximal, characteristic, complemented
13#13113285C211yesmaximal, characteristic
14C82×D13C211yesmaximal, characteristic, complemented
15C13×#1590C211yesmaximal, characteristic, complemented
16C2×#88161—21no—
17#11719283C2211yescharacteristic
18#11719253C2211yescharacteristic
19C13×#446C2211yescharacteristic
20C4×C13×SD16C2211yescharacteristic
21C13×#436C2211yescharacteristic
22#11718836C411yescharacteristic
23#11718832C411yescharacteristic
24#11718789—21no—
25C4×#6106C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718525C411yescharacteristic
30#11718516C411yescharacteristic
31#11718500—21no—
32#11718498C2211yescharacteristic
33#11718498C2211yescharacteristic
34#11718495C2211yescharacteristic
35#11718491—21no—
36#11718491C2211yescharacteristic
37#11718468C411yescharacteristic
38#11718453C411yescharacteristic
39#11718439C411yescharacteristic
40#11718421C411yescharacteristic
41#11718388—21no—
42#11718386—21no—
43#11718369—21no—
44#11718362—21no—
45C4×#6095C2211yescharacteristic
46#11718349C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49C4×C8×D13C2211yescharacteristic
50#11718340C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C82×C13C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718048C2211yescharacteristic
64C8×#1055C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6127—21no—
68C2×C13×SD16C2×C411yescharacteristic
69C2×C13×M16—21no—
70C4×Q8×C13C2311yescharacteristic
71C4×D4×C13C2311yescharacteristic
72#88200C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6106C2×C411yescharacteristic
75#88194C2×C411yescharacteristic
76#88192C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C22×#1055—21no—
80#88161—44no—
81C2×#6095C2×C411yescharacteristic
82C2×#6094—21no—
83C2×#6094—21no—
84C2×#6094—21no—
85C2×C8×D13—21no—
86C2×C8×D13—21no—
87C2×C8×D13C2×C411yescharacteristic
88C2×C8×D13C2×C411yescharacteristic
89C2×C8×D13D411yescharacteristic
90C2×C8×D13D411yescharacteristic
91#88151C2×C411yescharacteristic
92#88150—21no—
93#88149C2×C411yescharacteristic
94#88143—21no—
95#88142C2×C411yescharacteristic
96#88142C2×C411yescharacteristic
97#88139—21no—
98#88138—21no—
99C4×D52C2311yescharacteristic
100#88126—21no—
101C42×D13C2311yescharacteristic
102C4×Dic26—21no—
103C4×Dic26C2311yescharacteristic
104C13×#106C2×C411yescharacteristic
105C13×C4⋊C8—21no—
106C13×C4⋊C8C2311yescharacteristic
107C13×C4⋊C8C2311yescharacteristic
108C13×#103C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×C22⋊C8—21no—
111C13×#97—21no—
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115#88075C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117C22⋊#1055—21no—
118#88061C2×C411yescharacteristic
119#88060—21no—
120#88060—21no—
121#88057C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88055—21no—
124#88054—21no—
125#88054—21no—
126#88054—21no—
127#88054—21no—
128C8×Dic13—21no—
129C8×Dic13—21no—
130C8×Dic13C2×C411yescharacteristic
131C8×Dic13C2×C411yescharacteristic
132C8×Dic13D411yescharacteristic
133C8×Dic13D411yescharacteristic
134#88050C2×C411yescharacteristic
135#88049C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88048C2×C411yescharacteristic
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4×#1055—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#17957—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C2×C22⋊D13—21no—
150C2×C22⋊D13—21no—
151C2×C22⋊D13—21no—
152#6127—42no—
153#6127—42no—
154C2×D52—21no—
155C2×D52C22×C411yescharacteristic
156C2×C4×D13—21no—
157C2×C4×D13C22×C411yescharacteristic
158C2×C4×D13C2×D411yescharacteristic
159C2×C4×D13#4111yescharacteristic
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26C22×C411yescharacteristic
163C13×SD16—22no—
164C13×M16—42no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C13×C4⋊C4—21no—
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C22⋊C4—21no—
176C42×C13—21no—
177C42×C13C2411yescharacteristic
178C22⋊Dic13—21no—
179#6106—22no—
180#6105—22no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194C4×Dic13—21no—
195C4×Dic13C22×C411yescharacteristic
196C4×Dic13C2×D411yescharacteristic
197C4×Dic13#4111yescharacteristic
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—42no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206#6095—22no—
207#6094—42no—
208#6094—42no—
209#6094—42no—
210C8×D13—24no—
211C8×D13—22no—
212C8×D13—22no—
213C8×D13—22no—
214C8×D13—42no—
215C8×D13SD1614yescomplemented
216#3167—131no—
217#2960—131no—
218#2931—131no—
219#1590—131no—
220#1590—131no—
221#1590—131no—
222#1590D1311yescharacteristic, complemented
223C8×SD16—131no—
224C8×SD16—131no—
225C8×SD16—131no—
226C8×SD16—131no—
227#1566—131no—
228#1493—131no—
229#1492—131no—
230C2×C82—131no—
231C23×C13—21no—
232C22×D13—21no—
233C22×D13C4×D411yescharacteristic
234Q8×C13—21no—
235Q8×C13—21no—
236D4×C13—21no—
237D4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C22⋊D13—42no—
247C22⋊D13—42no—
248C22⋊D13—42no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13C4×D411yescharacteristic
253C2×Dic13C4×D411yescharacteristic
254C2×Dic13C4×D411yescharacteristic
255D52—21no—
256D52—21no—
257D52—42no—
258C4×D13—21no—
259C4×D13—21no—
260C4×D13—22no—
261C4×D13—41no—
262C4×D13—41no—
263C4×D13C2×SD1612yes—
264C4×D13#13512yes—
265Dic26—21no—
266Dic26—21no—
267Dic26—42no—
268Dic26—42no—
269C8×C13—22no—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—41no—
273C8×C13—41no—
274C8×C13#13112yescomplemented
275C8×C13C2×SD1612yes—
276#1055—22no—
277#1055—21no—
278#1055—21no—
279#1055—41no—
280#1055—41no—
281#1055#13112yescomplemented
282#1055C2×SD1612yes—
283C2×#131—261no—
284#533—131no—
285#532—131no—
286#498—131no—
287#492—131no—
288#487—131no—
289#486—131no—
290#465—131no—
291#465—131no—
292#465—131no—
293#465—131no—
294#446—131no—
295#446—261no—
296#446C2×D1311yescharacteristic
297C8×Q8—131no—
298C8×Q8—131no—
299C8×Q8—261no—
300C4×SD16—131no—
301C4×SD16—131no—
302C4×SD16—131no—
303C4×SD16C2×D1311yescharacteristic
304#436—131no—
305#436—261no—
306#436C2×D1311yescharacteristic
307C8×D4—131no—
308C8×D4—131no—
309C8×D4—261no—
310#424—261no—
311#423—131no—
312#423—131no—
313#408—261no—
314#405—261no—
315C2×C4×C8—131no—
316C2×C4×C8—131no—
317C2×C4×C8—131no—
318#334—131no—
319#334—131no—
320#334—131no—
321#334C2×D1311yescharacteristic
322Q8⋊C8—131no—
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325Q8⋊C8C2×D1311yescharacteristic
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8C2×D1311yescharacteristic
330C82—131no—
331C82—131no—
332C82—131no—
333C82C2×D1311yescharacteristic
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13C2×C4×D411yescharacteristic
338C2×D13—21no—
339C2×D13—21no—
340C2×D13—41no—
341C2×D13—41no—
342C2×D13—41no—
343C2×D13C4×SD1612yes—
344C4×C13—21no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13C2×#13111yescharacteristic
349C4×C13C2×#13111yescharacteristic
350C4×C13C22×SD1611yescharacteristic
351C4×C13C2×#13511yescharacteristic
352Dic13—21no—
353Dic13—41no—
354Dic13—41no—
355Dic13—41no—
356Dic13C4×SD1612yes—
357Dic13#44312yes—
358C2×#41—261no—
359C2×SD16—131no—
360C2×SD16—131no—
361C2×SD16—131no—
362C2×SD16C4×D1311yescharacteristic
363#131—524no—
364C2×M16—21no—
365C2×M16—261no—
366C2×M16—261no—
367C2×M16—261no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—131no—
371C22×C8—131no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375C4⋊Q8—131no—
376C4⋊Q8—131no—
377C4⋊Q8—131no—
378#127—131no—
379#125—261no—
380#124—261no—
381C22⋊Q8—131no—
382C22⋊Q8—131no—
383C22⋊Q8—261no—
384#121—131no—
385#121—131no—
386#121—261no—
387C4×Q8—131no—
388C4×Q8—261no—
389C4×Q8C22×D1311yescharacteristic
390C4×D4—131no—
391C4×D4—261no—
392C4×D4C22×D1311yescharacteristic
393#117—261no—
394C2×C42—131no—
395#106—131no—
396#106—131no—
397#106—131no—
398#106C4×D1311yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—261no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8C22×D1311yescharacteristic
408C4⋊C8C22×D1311yescharacteristic
409#103—131no—
410#103—131no—
411#103—131no—
412#103C4×D1311yescharacteristic
413#102—131no—
414#102—131no—
415#102—131no—
416#102C4×D1311yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—261no—
419C22⋊C8—261no—
420C22⋊C8—261no—
421#97—21no—
422#97—261no—
423C4×C8—131no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—131no—
427C4×C8—131no—
428C4×C8—131no—
429C4×C8—131no—
430C4×C8—261no—
431C4×C8—261no—
432C4×C8—261no—
433C4×C8C22×D1311yescharacteristic
434C4×C8C22×D1311yescharacteristic
435C4×C8C22×D1311yescharacteristic
436C2×C13—81no—
437C2×C13#293111yescharacteristic
438C2×C13C2×C4×SD1611yescharacteristic
439C2×C13C2×#44311yescharacteristic
440D13—22no—
441D13—81no—
442#41—522no—
443#41—522no—
444C2×Q8—131no—
445C2×Q8—261no—
446C2×Q8—261no—
447C2×Q8C2×C4×D1311yescharacteristic
448C2×D4—131no—
449C2×D4—261no—
450C2×D4—261no—
451C2×D4—261no—
452C2×D4—261no—
453C2×D4C2×C4×D1311yescharacteristic
454C22×C4—21no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—261no—
459SD16—22no—
460SD16—262no—
461SD16—262no—
462SD16—262no—
463M16—42no—
464M16—522no—
465M16—522no—
466M16—522no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—131no—
471C2×C8—131no—
472C2×C8—134no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—262no—
476C2×C8—262no—
477C2×C8—264no—
478C2×C8—261no—
479C2×C8—262no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—522no—
483C2×C8—522no—
484C2×C8C2×C4×D1311yescharacteristic
485C2×C8C2×C4×D1311yescharacteristic
486C2×C8D4×D1311yescharacteristic
487C2×C8D4×D1311yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—131no—
490C4⋊C4—131no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4C2×C4×D1311yescharacteristic
499C4⋊C4C2×C4×D1311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—261no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C42—21no—
507C42—131no—
508C42—131no—
509C42—131no—
510C42—261no—
511C42C23×D1311yescharacteristic
512C13#1795711yescharacteristic, complemented, Sylow
513C23—21no—
514C23—131no—
515C23—261no—
516Q8—21no—
517Q8—21no—
518Q8—261no—
519Q8—261no—
520Q8—522no—
521Q8—522no—
522D4—21no—
523D4—21no—
524D4—261no—
525D4—261no—
526D4—522no—
527D4—522no—
528D4—522no—
529D4—522no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—131no—
536C2×C4—131no—
537C2×C4—132no—
538C2×C4—132no—
539C2×C4—131no—
540C2×C4—262no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4C22×C4×D1311yescharacteristic
549C2×C4C2×D4×D1311yescharacteristic
550C2×C4#41×D1311yescharacteristic
551C8—22no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—132no—
557C8—132no—
558C8—262no—
559C8—261no—
560C8—261no—
561C8—521no—
562C8—521no—
563C8#8816112yescomplemented
564C8SD16×D1312yes—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—132no—
569C22—261no—
570C22—261no—
571C22—521no—
572C22—521no—
573C22—521no—
574C22C4×D4×D1311yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—132no—
580C4—132no—
581C4—261no—
582C4—521no—
583C4—521no—
584C4—521no—
585C4C2×#8816111yescharacteristic
586C4D13×#13111yescharacteristic
587C4C2×SD16×D1311yescharacteristic
588C4D13×#13511yescharacteristic
589C2—81no—
590C2—262no—
591C2—1041no—
592C2#1312354511yescharacteristic
593C2C4×SD16×D1311yescharacteristic
594C2D13×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1590C2
socleC22×C13C2×C4×D4
prime radical#11719253C22
cosocleC42×C13C24
hypercenter#1590D13
hypocenterC13#17957
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #13123767C2semidirect
4. #13113728C2semidirect
5. #13113726C2semidirect
6. #13113724C2semidirect
7. #13113639C2semidirect
8. SD16×#1055C2semidirect
9. #13113635C2semidirect
10. #13113633C2semidirect
11. #13113590C2semidirect
12. #13113289C2semidirect
14. C82×D13C2semidirect
15. C13×#1590C2semidirect
215. C8×D13SD16semidirect
222. #1590D13semidirect
274. C8×C13#131semidirect
281. #1055#131semidirect
512. C13#17957semidirect
563. C8#88161semidirect

Maximal subgroups

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

subgroupindex
#131253922
#131237672
#131235452
#131137282
#131137262
#131137242
#131136392
SD16×#10552
#131136352
#131136332
#131135902
#131132892
#131132852
C82×D132
C13×#15902
#1795713