Finite Group Databasebeta

← #15834876

Subgroups — #15834876

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125442C211yesmaximal, characteristic
2#13123992C211yesmaximal, characteristic
3#13123937C211yesmaximal, characteristic, complemented
4#13113744C211yesmaximal, characteristic, complemented
5#13113725C211yesmaximal, characteristic, complemented
6#13113713C211yesmaximal, characteristic, complemented
7#13113706C211yesmaximal, characteristic, complemented
8#13113685C211yesmaximal, characteristic, complemented
9#13113671C211yesmaximal, characteristic, complemented
10#13113647C211yesmaximal, characteristic, complemented
11#13113642C211yesmaximal, characteristic, complemented
12#13113242C211yesmaximal, characteristic
13#13113238C211yesmaximal, characteristic, complemented
14#13113133C211yesmaximal, characteristic, complemented
15C13×#1565C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C4×C13×M16C2211yescharacteristic
21#11718798C411yescharacteristic
22#11718798C411yescharacteristic
23#11718795C411yescharacteristic
24#11718795C411yescharacteristic
25#11718772—21no—
26C8×C22⋊D13—21no—
27#11718586C2211yescharacteristic
28#11718586C2211yescharacteristic
29#11718501—21no—
30#11718500—21no—
31#11718499C2211yescharacteristic
32#11718495C2211yescharacteristic
33#11718492C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718492C2211yescharacteristic
36#11718491C2211yescharacteristic
37#11718491C2211yescharacteristic
38#11718491C2211yescharacteristic
39#11718381—21no—
40#11718381—21no—
41#11718376C411yescharacteristic
42#11718375C411yescharacteristic
43#11718364C411yescharacteristic
44#11718363C411yescharacteristic
45C4×Dic52C2211yescharacteristic
46C4×Dic52C2211yescharacteristic
47C4×#6095C2211yescharacteristic
48C4×#6095C2211yescharacteristic
49#11718340—21no—
50C8×Dic26—21no—
51C13×#335C2211yescharacteristic
52C13×#335C2211yescharacteristic
53C13×#334C2211yescharacteristic
54C13×#334C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718076C2211yescharacteristic
60#11718076C2211yescharacteristic
61#11718075C2211yescharacteristic
62#11718075C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×M16C2×C411yescharacteristic
68C2×C13×M16C2×C411yescharacteristic
69C22×C8×C13—21no—
70C2×C42×C13C2311yescharacteristic
71#88184C2×C411yescharacteristic
72#88183—21no—
73C4×C22⋊D13—21no—
74#88180—21no—
75#88178—21no—
76#88178C2×C411yescharacteristic
77#88178C2×C411yescharacteristic
78#88178C2×C411yescharacteristic
79C2×Dic52C2×C411yescharacteristic
80C2×Dic52C2×C411yescharacteristic
81C2×#6095C2×C411yescharacteristic
82C2×#6095C2×C411yescharacteristic
83C2×#6094—21no—
84C2×C8×D13—21no—
85#88130—21no—
86#88129C2×C411yescharacteristic
87C4×D52C2311yescharacteristic
88#88126—21no—
89#88124—21no—
90#88124C2×C411yescharacteristic
91#88123C2×C411yescharacteristic
92#88123C2×C411yescharacteristic
93C4×Dic26—21no—
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C22⋊C8—21no—
103C13×#97C2×C411yescharacteristic
104C13×#97C2×C411yescharacteristic
105C4×C8×C13—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C22⋊#1055—21no—
109C22⋊#1055D411yescharacteristic
110C22⋊#1055D411yescharacteristic
111#88061C2×C411yescharacteristic
112#88061C2×C411yescharacteristic
113#88060—21no—
114#88060—21no—
115#88058C2×C411yescharacteristic
116#88058C2×C411yescharacteristic
117#88057C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88056C2×C411yescharacteristic
124#88056C2×C411yescharacteristic
125#88055—21no—
126#88055—21no—
127#88055—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134C8×Dic13—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C4⋊#1055—21no—
138C4⋊#1055D411yescharacteristic
139C4⋊#1055D411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18083—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—21no—
149C2×D52C22×C411yescharacteristic
150C2×C4×D13—21no—
151C2×Dic26—21no—
152C2×Dic26C22×C411yescharacteristic
153C2×Dic26C22×C411yescharacteristic
154C2×Dic26C22×C411yescharacteristic
155C13×M16—22no—
156C13×M16—41no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—81no—
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C42×C13C22×C411yescharacteristic
167C42×C13C2×D411yescharacteristic
168C42×C13#4111yescharacteristic
169C42×C13C2411yescharacteristic
170C22⋊Dic13—21no—
171C22⋊Dic13—21no—
172C22⋊Dic13—21no—
173#6103—21no—
174#6103—21no—
175#6103—21no—
176#6103—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13C22×C411yescharacteristic
181C4⋊Dic13C22×C411yescharacteristic
182C4⋊Dic13C22×C411yescharacteristic
183C4⋊Dic13C22×C411yescharacteristic
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055C2×D411yescharacteristic
198C2×#1055C2×D411yescharacteristic
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201Dic52—22no—
202Dic52—41no—
203#6095—22no—
204#6095—41no—
205#6094—81no—
206C8×D13—81no—
207#3172—131no—
208#2994—131no—
209#2986—131no—
210#1593—131no—
211#1590—131no—
212#1588—131no—
213#1587—131no—
214#1584—131no—
215#1582—131no—
216SD16⋊C8—131no—
217C8×Q16—131no—
218#1565D1311yescharacteristic, complemented
219#1482—131no—
220#1481—131no—
221#1453—131no—
222C23×C13C4×D411yescharacteristic
223C22×D13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—41no—
229C2×C4×C13C4×D411yescharacteristic
230C2×C4×C13C4×D411yescharacteristic
231C2×C4×C13C4×D411yescharacteristic
232C2×C4×C13C23×C411yescharacteristic
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C22⋊D13—42no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243D52—21no—
244D52—21no—
245C4×D13—41no—
246C4×D13—41no—
247Dic26—21no—
248Dic26—21no—
249Dic26—21no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—42no—
254C8×C13—21no—
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—41no—
258C8×C13—41no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13#13112yes—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—41no—
267#1055—41no—
268#533—131no—
269#529—131no—
270#501—131no—
271#497—131no—
272#491—131no—
273#489—131no—
274#470—131no—
275#470—131no—
276#468—131no—
277#468—131no—
278#446—131no—
279#446—131no—
280#446—131no—
281#446—261no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—131no—
285C8×Q8—261no—
286C4×Q16—131no—
287C4×Q16—131no—
288C4×SD16—131no—
289C4×SD16—131no—
290#436—131no—
291#435—261no—
292C8×D4—131no—
293C8×D4—261no—
294#433—261no—
295#433—261no—
296#433—261no—
297#431—131no—
298#431—131no—
299#431C2×D1311yescharacteristic
300#424—261no—
301C2×C4⋊C8C2×D1311yescharacteristic
302C4×M16C2×D1311yescharacteristic
303#335C2×D1311yescharacteristic
304#335C2×D1311yescharacteristic
305#334C2×D1311yescharacteristic
306#334C2×D1311yescharacteristic
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313D4⋊C8—131no—
314D4⋊C8—131no—
315#322—131no—
316#322—131no—
317#322—131no—
318C82—131no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13C2×C4×D411yescharacteristic
323C2×D13—41no—
324C2×D13—41no—
325C2×D13—41no—
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13C2×#13111yescharacteristic
331C4×C13#56811yescharacteristic
332C4×C13#57711yescharacteristic
333C4×C13#57811yescharacteristic
334Dic13—41no—
335Dic13—41no—
336Dic13—41no—
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341C2×Q16—131no—
342C2×Q16—131no—
343C2×SD16—131no—
344C2×SD16—131no—
345C2×M16—261no—
346C2×M16C4×D1311yescharacteristic
347C2×M16C4×D1311yescharacteristic
348C22×C8—21no—
349C22×C8—261no—
350C4⋊Q8—131no—
351C4⋊Q8—131no—
352#126—261no—
353#125—131no—
354#125—261no—
355#124—131no—
356#123—261no—
357C22⋊Q8—131no—
358C22⋊Q8—131no—
359C22⋊Q8—131no—
360C22⋊Q8—261no—
361#121—131no—
362C4×Q8—131no—
363C4×Q8—131no—
364C4×Q8—131no—
365C4×Q8—261no—
366C4×D4—131no—
367C4×D4—261no—
368#117—261no—
369#117—261no—
370C2×C42C22×D1311yescharacteristic
371#107—131no—
372#107—131no—
373#106—131no—
374#106—131no—
375C4⋊C8—21no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—261no—
379C4⋊C8—261no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8C22×D1311yescharacteristic
386C4⋊C8C22×D1311yescharacteristic
387C4⋊C8C22×D1311yescharacteristic
388C4⋊C8C22×D1311yescharacteristic
389#103—131no—
390#103—131no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#102—131no—
396#102—131no—
397C22⋊C8—21no—
398C22⋊C8—131no—
399C22⋊C8—131no—
400C22⋊C8—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—261no—
404#97—261no—
405#97—261no—
406#97C4×D1311yescharacteristic
407#97C4×D1311yescharacteristic
408C4×C8—21no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C2×C13—41no—
419C2×C13#293511yescharacteristic
420C2×C13#294711yescharacteristic
421C2×C13#295511yescharacteristic
422D13—81no—
423C2×Q8—131no—
424C2×Q8—131no—
425C2×Q8—131no—
426C2×Q8—261no—
427C2×D4—131no—
428C2×D4—261no—
429C22×C4—261no—
430C22×C4C2×C4×D1311yescharacteristic
431C22×C4D4×D1311yescharacteristic
432C22×C4#613111yescharacteristic
433Q16—262no—
434Q16—521no—
435SD16—262no—
436SD16—521no—
437M16—22no—
438M16—41no—
439M16—1041no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—81no—
445C2×C8—131no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—1041no—
452C2×C8C2×C4×D1311yescharacteristic
453C2×C8C2×C4×D1311yescharacteristic
454C2×C8C2×C4×D1311yescharacteristic
455C2×C8C2×C4×D1311yescharacteristic
456C4⋊C4—131no—
457C4⋊C4—131no—
458C4⋊C4—131no—
459C4⋊C4—131no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C22⋊C4—261no—
472C22⋊C4—261no—
473C22⋊C4—261no—
474C22⋊C4—261no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C42—261no—
479C42—261no—
480C42—261no—
481C42C2×C4×D1311yescharacteristic
482C42D4×D1311yescharacteristic
483C42#613111yescharacteristic
484C42C23×D1311yescharacteristic
485C13#1808311yescharacteristic, complemented, Sylow
486C23—261no—
487C23#8814711yescharacteristic
488Q8—261no—
489Q8—261no—
490Q8—261no—
491Q8—261no—
492Q8—261no—
493Q8—261no—
494Q8—522no—
495D4—261no—
496D4—261no—
497D4—522no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—261no—
504C2×C4—261no—
505C2×C4—261no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—521no—
511C2×C4—521no—
512C2×C4#8814711yescharacteristic
513C2×C4#8814711yescharacteristic
514C2×C4#8814711yescharacteristic
515C2×C4C22×C4×D1311yescharacteristic
516C2×C4C2×D4×D1311yescharacteristic
517C2×C4C2×#613111yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—261no—
526C8—261no—
527C8—261no—
528C8—261no—
529C8—521no—
530C8—521no—
531C8#8815512yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—521no—
536C22—521no—
537C22—521no—
538C22C2×#8814711yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—521no—
544C4—521no—
545C4—521no—
546C4—521no—
547C4—521no—
548C4—521no—
549C4—521no—
550C4C2×#8815511yescharacteristic
551C4#1171945011yescharacteristic
552C4#1171948011yescharacteristic
553C4#1171948411yescharacteristic
554C2—41no—
555C2—1041no—
556C2#1312357911yescharacteristic
557C2#1312367711yescharacteristic
558C2#1312373811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1565C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#1565D13
hypocenterC13#18083
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
3. #13123937C2semidirect
4. #13113744C2semidirect
5. #13113725C2semidirect
6. #13113713C2semidirect
7. #13113706C2semidirect
8. #13113685C2semidirect
9. #13113671C2semidirect
10. #13113647C2semidirect
11. #13113642C2semidirect
13. #13113238C2semidirect
14. #13113133C2semidirect
15. C13×#1565C2semidirect
218. #1565D13semidirect
485. C13#18083semidirect

Maximal subgroups

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

subgroupindex
#131254422
#131239922
#131239372
#131137442
#131137252
#131137132
#131137062
#131136852
#131136712
#131136472
#131136422
#131132422
#131132382
#131131332
C13×#15652
#1808313