Finite Group Databasebeta

← #15832947

Subgroups — #15832947

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124920C211yesmaximal, characteristic
2#13123810C211yesmaximal, characteristic
3C8×Q8×D13C211yesmaximal, characteristic, complemented
4#13113684C211yesmaximal, characteristic, complemented
5#13113681C211yesmaximal, characteristic, complemented
6#13113679C211yesmaximal, characteristic, complemented
7#13113655C211yesmaximal, characteristic, complemented
8#13113652C211yesmaximal, characteristic, complemented
9#13113651C211yesmaximal, characteristic, complemented
10#13113647C211yesmaximal, characteristic, complemented
11#13113620C211yesmaximal, characteristic, complemented
12#13113281C211yesmaximal, characteristic, complemented
13#13113248C211yesmaximal, characteristic
14#13113122C211yesmaximal, characteristic, complemented
15C13×#1584C211yesmaximal, characteristic, complemented
16#11719285C2211yescharacteristic
17C4×Q8×D13C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718847C411yescharacteristic
22#11718846C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6106C2211yescharacteristic
25Q8×#1055C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718543C411yescharacteristic
28#11718538C411yescharacteristic
29#11718501—21no—
30#11718496C2211yescharacteristic
31#11718495—21no—
32#11718495C2211yescharacteristic
33D13×C4⋊C8—21no—
34D13×C4⋊C8C2211yescharacteristic
35#11718491—21no—
36#11718491C2211yescharacteristic
37#11718467C411yescharacteristic
38#11718466C411yescharacteristic
39#11718460C411yescharacteristic
40#11718459C411yescharacteristic
41#11718369—21no—
42#11718367—21no—
43C4×#6095C2211yescharacteristic
44#11718349C2211yescharacteristic
45C4×#6094C2211yescharacteristic
46#11718346C2211yescharacteristic
47C4×C8×D13—21no—
48C4×C8×D13C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65#11718047C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71#88201C2×C411yescharacteristic
72#88200C2×C411yescharacteristic
73Q8×Dic13C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76C2×#6095C2×C411yescharacteristic
77C2×#6094—21no—
78C2×#6094—21no—
79C2×C8×D13—21no—
80C2×C8×D13—21no—
81C2×C8×D13D411yescharacteristic
82C2×C8×D13D411yescharacteristic
83#88152—21no—
84#88149C2×C411yescharacteristic
85#88148—21no—
86C4⋊C4×D13—21no—
87C4⋊C4×D13C2×C411yescharacteristic
88#88144C2×C411yescharacteristic
89#88141—21no—
90#88141C2×C411yescharacteristic
91C4×D52—21no—
92C4×D52C2311yescharacteristic
93#88126—21no—
94C42×D13—21no—
95C42×D13C2311yescharacteristic
96C4×Dic26—21no—
97C4×Dic26C2311yescharacteristic
98C13×#107C2×C411yescharacteristic
99C13×C4⋊C8—21no—
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#97—21no—
106C4×C8×C13—21no—
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#88075C2×C411yescharacteristic
111#88075C2×C411yescharacteristic
112#88061C2×C411yescharacteristic
113#88060—21no—
114#88060—21no—
115#88060—21no—
116#88060C2×C411yescharacteristic
117#88060C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88055—21no—
121#88055—21no—
122#88054—21no—
123#88054—21no—
124#88054—21no—
125#88054C2×C411yescharacteristic
126#88054C2×C411yescharacteristic
127C8×Dic13—21no—
128C8×Dic13—21no—
129C8×Dic13D411yescharacteristic
130C8×Dic13D411yescharacteristic
131#88050C2×C411yescharacteristic
132#88049C2×C411yescharacteristic
133#88048C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4×#1055—21no—
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17915—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147Q8×D13—22no—
148Q8×D13—22no—
149C2×D52—21no—
150C2×D52C22×C411yescharacteristic
151C2×C4×D13—21no—
152C2×C4×D13—21no—
153C2×C4×D13—21no—
154C2×C4×D13C22×C411yescharacteristic
155C2×C4×D13C2×D411yescharacteristic
156C2×C4×D13#4111yescharacteristic
157C2×Dic26—21no—
158C2×Dic26C22×C411yescharacteristic
159C13×Q16—22no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C42×C13—21no—
172C42×C13—21no—
173C42×C13C2411yescharacteristic
174#6107—22no—
175#6106—22no—
176#6103—21no—
177#6103—21no—
178#6103—21no—
179#6103—21no—
180#6103—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13C22×C411yescharacteristic
184C4⋊Dic13C22×C411yescharacteristic
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13C22×C411yescharacteristic
194C4×Dic13C2×D411yescharacteristic
195C4×Dic13#4111yescharacteristic
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203#6095—22no—
204#6094—42no—
205#6094—42no—
206C8×D13—22no—
207C8×D13—41no—
208C8×D13—42no—
209C8×D13—42no—
210#3108—131no—
211#2966—131no—
212C2×C8×Q8—131no—
213#1584—131no—
214#1584D1311yescharacteristic, complemented
215#1583—131no—
216#1583—131no—
217#1579—131no—
218#1579—131no—
219SD16⋊C8—131no—
220SD16⋊C8—131no—
221#1573—131no—
222#1491—131no—
223#1483—131no—
224#1451—131no—
225C22×D13—21no—
226C22×D13C4×D411yescharacteristic
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13#13112yes—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13C4×D411yescharacteristic
242C2×Dic13C4×D411yescharacteristic
243C2×Dic13C4×D411yescharacteristic
244D52—21no—
245D52—21no—
246D52—42no—
247C4×D13—24no—
248C4×D13—22no—
249C4×D13—21no—
250C4×D13—21no—
251C4×D13—21no—
252C4×D13—21no—
253C4×D13—42no—
254C4×D13—41no—
255C4×D13—41no—
256Dic26—24no—
257Dic26—21no—
258Dic26#13112yes—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13#13712yes—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—41no—
271#1055—41no—
272#1055—41no—
273#529—131no—
274C2×C4×Q8—131no—
275#483—131no—
276#480—131no—
277#479—131no—
278#479—131no—
279#464—131no—
280#464—131no—
281#451—131no—
282#448—131no—
283#446C2×D1311yescharacteristic
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—261no—
289C8×Q8—261no—
290C8×Q8C2×D1311yescharacteristic
291C4×Q16—131no—
292C4×Q16C2×D1311yescharacteristic
293C4×SD16—131no—
294C4×SD16—131no—
295#436—131no—
296#435—261no—
297C8×D4—131no—
298C8×D4—261no—
299#433—261no—
300#432—131no—
301#431—131no—
302C2×C4⋊C8—131no—
303C2×C4⋊C8—261no—
304#405—261no—
305C4×M16—131no—
306C2×C4×C8—131no—
307C2×C4×C8—261no—
308#335—131no—
309#335C2×D1311yescharacteristic
310#334—131no—
311#334—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8C2×D1311yescharacteristic
317Q8⋊C8C2×D1311yescharacteristic
318D4⋊C8—131no—
319D4⋊C8—131no—
320#322—131no—
321#322—131no—
322#322—131no—
323#322C2×D1311yescharacteristic
324C22×C13C2×C4×D411yescharacteristic
325C2×D13—21no—
326C2×D13—21no—
327C2×D13—41no—
328C2×D13—41no—
329C2×D13—41no—
330C2×D13#44412yes—
331C4×C13—22no—
332C4×C13—21no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13C2×#13111yescharacteristic
337C4×C13C2×#13111yescharacteristic
338C4×C13C2×#13711yescharacteristic
339C4×C13#57511yescharacteristic
340Dic13—21no—
341Dic13—22no—
342Dic13—21no—
343Dic13—21no—
344Dic13—41no—
345Dic13—41no—
346C22×Q8—131no—
347C2×Q16—131no—
348C2×Q16C4×D1311yescharacteristic
349C2×SD16—131no—
350C2×SD16—131no—
351C2×M16—261no—
352C2×M16—261no—
353C22×C8—131no—
354C22×C8—131no—
355C22×C8—261no—
356C22×C8—261no—
357#126—261no—
358#125—131no—
359#124—131no—
360#123—261no—
361C22⋊Q8—131no—
362#121—131no—
363C4×Q8—131no—
364C4×Q8—131no—
365C4×Q8—131no—
366C4×Q8—261no—
367C4×Q8—261no—
368C4×Q8C22×D1311yescharacteristic
369C4×Q8C22×D1311yescharacteristic
370C4×D4—131no—
371C4×D4—261no—
372#117—261no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—261no—
375C2×C42—131no—
376C2×C42—261no—
377#107—131no—
378#107C4×D1311yescharacteristic
379#106—131no—
380#106—131no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—131no—
384C4⋊C8—131no—
385C4⋊C8—131no—
386C4⋊C8—131no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8C22×D1311yescharacteristic
393C4⋊C8C22×D1311yescharacteristic
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#103C4×D1311yescharacteristic
399#103C4×D1311yescharacteristic
400#102—131no—
401#102—131no—
402C22⋊C8—131no—
403C22⋊C8—131no—
404C22⋊C8—261no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—21no—
408#97—261no—
409#97—261no—
410C4×C8—21no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C4×C8C22×D1311yescharacteristic
423C2×C13#292911yescharacteristic
424C2×C13C4×#13711yescharacteristic
425C2×C13C2×#44411yescharacteristic
426D13—22no—
427D13—81no—
428C2×Q8—131no—
429C2×Q8—261no—
430C2×Q8—262no—
431C2×Q8—262no—
432C2×Q8C2×C4×D1311yescharacteristic
433C2×Q8C2×C4×D1311yescharacteristic
434C2×D4—131no—
435C2×D4—261no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442Q16—22no—
443Q16—262no—
444SD16—262no—
445SD16—262no—
446M16—522no—
447M16—522no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—262no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—521no—
460C2×C8—522no—
461C2×C8—522no—
462C2×C8C2×C4×D1311yescharacteristic
463C2×C8C2×C4×D1311yescharacteristic
464C2×C8D4×D1311yescharacteristic
465C2×C8D4×D1311yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—131no—
469C4⋊C4—131no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4C2×C4×D1311yescharacteristic
478C4⋊C4C2×C4×D1311yescharacteristic
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C22⋊C4—261no—
483C22⋊C4—261no—
484C42—21no—
485C42—21no—
486C42—131no—
487C42—131no—
488C42—131no—
489C42—261no—
490C42—261no—
491C42—261no—
492C42C23×D1311yescharacteristic
493C13#1791511yescharacteristic, complemented, Sylow
494C23—131no—
495C23—261no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—132no—
500Q8—264no—
501Q8—261no—
502Q8#8816112yes—
503D4—261no—
504D4—261no—
505D4—522no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—131no—
511C2×C4—131no—
512C2×C4—131no—
513C2×C4—262no—
514C2×C4—264no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—522no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4C22×C4×D1311yescharacteristic
526C2×C4C2×D4×D1311yescharacteristic
527C2×C4#41×D1311yescharacteristic
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—261no—
535C8—261no—
536C8—261no—
537C8—261no—
538C8—521no—
539C8—521no—
540C8—521no—
541C8#8817212yes—
542C22—132no—
543C22—261no—
544C22—261no—
545C22—521no—
546C22—521no—
547C22—521no—
548C22C4×D4×D1311yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—261no—
555C4—261no—
556C4—261no—
557C4—262no—
558C4—521no—
559C4—521no—
560C4C2×#8816111yescharacteristic
561C4D13×#13111yescharacteristic
562C4C2×#8817211yescharacteristic
563C4#1171947311yescharacteristic
564C2—262no—
565C2—1041no—
566C2#1312352711yescharacteristic
567C2C4×#8817211yescharacteristic
568C2D13×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1584C2
socleC22×C13C2×C4×D4
prime radical#88149C2×C4
cosocleC42×C13C24
hypercenter#1584D13
hypocenterC13#17915
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
3. C8×Q8×D13C2semidirect
4. #13113684C2semidirect
5. #13113681C2semidirect
6. #13113679C2semidirect
7. #13113655C2semidirect
8. #13113652C2semidirect
9. #13113651C2semidirect
10. #13113647C2semidirect
11. #13113620C2semidirect
12. #13113281C2semidirect
14. #13113122C2semidirect
15. C13×#1584C2semidirect
214. #1584D13semidirect
493. C13#17915semidirect

Maximal subgroups

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

subgroupindex
#131249202
#131238102
C8×Q8×D132
#131136842
#131136812
#131136792
#131136552
#131136522
#131136512
#131136472
#131136202
#131132812
#131132482
#131131222
C13×#15842
#1791513