Finite Group Databasebeta

← #15834882

Subgroups — #15834882

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#13123998C211yesmaximal, characteristic
3#13123937C211yesmaximal, characteristic, complemented
4#13113746C211yesmaximal, characteristic, complemented
5#13113728C211yesmaximal, characteristic, complemented
6#13113716C211yesmaximal, characteristic, complemented
7#13113709C211yesmaximal, characteristic, complemented
8#13113688C211yesmaximal, characteristic, complemented
9#13113674C211yesmaximal, characteristic, complemented
10#13113650C211yesmaximal, characteristic, complemented
11C8×Dic52C211yesmaximal, characteristic, complemented
12#13113588C211yesmaximal, characteristic, complemented
13#13113245C211yesmaximal, characteristic
14#13113240C211yesmaximal, characteristic, complemented
15C13×#1453C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C4×C13×M16C2211yescharacteristic
21#11718798C411yescharacteristic
22#11718798C411yescharacteristic
23#11718795C411yescharacteristic
24#11718795C411yescharacteristic
25#11718586C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718501—21no—
28#11718500—21no—
29#11718492—21no—
30#11718491—21no—
31#11718391—21no—
32#11718386—21no—
33#11718381—21no—
34#11718381—21no—
35#11718376C411yescharacteristic
36#11718375C411yescharacteristic
37#11718364C411yescharacteristic
38#11718363C411yescharacteristic
39C4×Dic52C2211yescharacteristic
40C4×Dic52C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44C8×D52C2211yescharacteristic
45#11718340C2211yescharacteristic
46#11718340C2211yescharacteristic
47#11718340C2211yescharacteristic
48C8×Dic26C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#322C2211yescharacteristic
52C13×#322C2211yescharacteristic
53C13×#322C2211yescharacteristic
54C82×C13C2211yescharacteristic
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718050C2211yescharacteristic
58#11718050C2211yescharacteristic
59#11718049C2211yescharacteristic
60#11718049C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718048C2211yescharacteristic
65#11718048C2211yescharacteristic
66#11718048C2211yescharacteristic
67C2×C13×M16C2×C411yescharacteristic
68C2×C13×M16C2×C411yescharacteristic
69C2×C42×C13C2311yescharacteristic
70#88184C2×C411yescharacteristic
71#88183—21no—
72C4×C22⋊D13—21no—
73#88180—21no—
74#88178—21no—
75#88178C2×C411yescharacteristic
76#88178C2×C411yescharacteristic
77#88178C2×C411yescharacteristic
78C22×#1055—21no—
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⋊C8D411yescharacteristic
99C13×C4⋊C8D411yescharacteristic
100C13×C22⋊C8—21no—
101C13×C22⋊C8D411yescharacteristic
102C13×C22⋊C8D411yescharacteristic
103C13×#97C2×C411yescharacteristic
104C13×#97C2×C411yescharacteristic
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C22⋊#1055—21no—
112#88061C2×C411yescharacteristic
113#88061C2×C411yescharacteristic
114#88060—21no—
115#88060—21no—
116#88058C2×C411yescharacteristic
117#88058C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88057C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88056C2×C411yescharacteristic
124#88056C2×C411yescharacteristic
125#88056C2×C411yescharacteristic
126#88055—21no—
127#88055—21no—
128#88055—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134#88054—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C8×Dic13—21no—
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143C4×#1055—21no—
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×C13C22×C411yescharacteristic
160C2×C8×C13C22×C411yescharacteristic
161C2×C8×C13C22×C411yescharacteristic
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C2×D411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C42×C13C22×C411yescharacteristic
168C42×C13C2×D411yescharacteristic
169C42×C13#4111yescharacteristic
170C42×C13C2411yescharacteristic
171C22⋊Dic13—21no—
172C22⋊Dic13—21no—
173C22⋊Dic13—21no—
174#6103—21no—
175#6103—21no—
176#6103—21no—
177#6103—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13C22×C411yescharacteristic
182C4⋊Dic13C22×C411yescharacteristic
183C4⋊Dic13C22×C411yescharacteristic
184C4⋊Dic13C22×C411yescharacteristic
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—81no—
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#1565—131no—
219#1482—131no—
220#1481—131no—
221#1453D1311yescharacteristic, complemented
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—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13#13112yes—
264#1055—41no—
265#1055—41no—
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#431C2×D1311yescharacteristic
299#431C2×D1311yescharacteristic
300#424—261no—
301C2×C4⋊C8—131no—
302C4×M16C2×D1311yescharacteristic
303#335—131no—
304#335—131no—
305#334—131no—
306#334—131no—
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#322C2×D1311yescharacteristic
316#322C2×D1311yescharacteristic
317#322C2×D1311yescharacteristic
318C82C2×D1311yescharacteristic
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—261no—
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—131no—
379C4⋊C8—131no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8D5211yescharacteristic
388C4⋊C8D5211yescharacteristic
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—261no—
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8D5211yescharacteristic
402C22⋊C8D5211yescharacteristic
403#97—261no—
404#97—261no—
405#97—261no—
406#97C4×D1311yescharacteristic
407#97C4×D1311yescharacteristic
408C4×C8—261no—
409C4×C8—261no—
410C4×C8—261no—
411C4×C8—261no—
412C4×C8C22×D1311yescharacteristic
413C4×C8C22×D1311yescharacteristic
414C4×C8C22×D1311yescharacteristic
415C4×C8C22×D1311yescharacteristic
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×C4C2×D5211yescharacteristic
432C22×C4#612711yescharacteristic
433Q16—262no—
434Q16—521no—
435SD16—262no—
436SD16—521no—
437M16—22no—
438M16—41no—
439M16—1041no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—1041no—
447C2×C8—1041no—
448C2×C8C2×C4×D1311yescharacteristic
449C2×C8C2×C4×D1311yescharacteristic
450C2×C8C2×C4×D1311yescharacteristic
451C2×C8C2×C4×D1311yescharacteristic
452C2×C8C2×D5211yescharacteristic
453C2×C8C2×D5211yescharacteristic
454C2×C8C2×D5211yescharacteristic
455C2×C8C2×D5211yescharacteristic
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
482C42C2×D5211yescharacteristic
483C42#612711yescharacteristic
484C42C23×D1311yescharacteristic
485C13#1808311yescharacteristic, complemented, Sylow
486C23—261no—
487C23C4×D5211yescharacteristic
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×C4C4×D5211yescharacteristic
513C2×C4C4×D5211yescharacteristic
514C2×C4C4×D5211yescharacteristic
515C2×C4C22×C4×D1311yescharacteristic
516C2×C4C22×D5211yescharacteristic
517C2×C4C2×#612711yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—521no—
528C8—521no—
529C8—521no—
530C8—521no—
531C8#8816112yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—521no—
536C22—521no—
537C22—521no—
538C22C2×C4×D5211yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—521no—
544C4—521no—
545C4—521no—
546C4—521no—
547C4—521no—
548C4—521no—
549C4—521no—
550C4C2×#8816111yescharacteristic
551C4#1171945011yescharacteristic
552C4#1171945611yescharacteristic
553C4#1171945811yescharacteristic
554C2—41no—
555C2—1041no—
556C2#1312358211yescharacteristic
557C2#1312368111yescharacteristic
558C2#1312374011yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1453C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#1453D13
hypocenterC13#18083
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1453

Complements

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

NH ≅ G/Ntype
3. #13123937C2semidirect
4. #13113746C2semidirect
5. #13113728C2semidirect
6. #13113716C2semidirect
7. #13113709C2semidirect
8. #13113688C2semidirect
9. #13113674C2semidirect
10. #13113650C2semidirect
11. C8×Dic52C2semidirect
12. #13113588C2semidirect
14. #13113240C2semidirect
15. C13×#1453C2semidirect
221. #1453D13semidirect
485. C13#18083semidirect

Maximal subgroups

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

subgroupindex
#131254422
#131239982
#131239372
#131137462
#131137282
#131137162
#131137092
#131136882
#131136742
#131136502
C8×Dic522
#131135882
#131132452
#131132402
C13×#14532
#1808313