Finite Group Databasebeta

← #15834792

Subgroups — #15834792

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125442C211yesmaximal, characteristic
2#13123840C211yesmaximal, characteristic
3#13123783C211yesmaximal, characteristic, complemented
4#13113740C211yesmaximal, characteristic, complemented
5#13113734C211yesmaximal, characteristic, complemented
6#13113716C211yesmaximal, characteristic, complemented
7#13113709C211yesmaximal, characteristic, complemented
8#13113688C211yesmaximal, characteristic, complemented
9#13113674C211yesmaximal, characteristic, complemented
10#13113656C211yesmaximal, characteristic, complemented
11C8×#6095C211yesmaximal, characteristic, complemented
12#13113588C211yesmaximal, characteristic, complemented
13#13113258C211yesmaximal, characteristic, complemented
14#13113250C211yesmaximal, characteristic
15C13×#1455C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17#11719175C2211yescharacteristic
18C4×C13×M16C2211yescharacteristic
19C4×C13×M16C2211yescharacteristic
20C4×C13×M16C2211yescharacteristic
21#11718798C411yescharacteristic
22#11718798C411yescharacteristic
23#11718795C411yescharacteristic
24#11718795C411yescharacteristic
25#11718789—21no—
26#11718788—21no—
27#11718783—21no—
28#11718780—21no—
29#11718586C2211yescharacteristic
30C2×C4⋊#1055C2211yescharacteristic
31#11718376C411yescharacteristic
32#11718375C411yescharacteristic
33#11718370—21no—
34#11718369—21no—
35#11718364C411yescharacteristic
36#11718363C411yescharacteristic
37#11718362—21no—
38#11718362—21no—
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×M16—21no—
68C2×C13×M16C2×C411yescharacteristic
69C2×C13×M16C2×C411yescharacteristic
70C2×C13×M16D411yescharacteristic
71C2×C13×M16D411yescharacteristic
72C2×C42×C13C2311yescharacteristic
73#88184C2×C411yescharacteristic
74#88183—21no—
75C4×C22⋊D13—21no—
76#88180—21no—
77#88178—21no—
78#88178C2×C411yescharacteristic
79#88178C2×C411yescharacteristic
80#88178C2×C411yescharacteristic
81C22×#1055—21no—
82C2×Dic52C2×C411yescharacteristic
83C2×Dic52C2×C411yescharacteristic
84C2×#6095C2×C411yescharacteristic
85C2×#6095C2×C411yescharacteristic
86C2×#6094—21no—
87C2×C8×D13—21no—
88#88130—21no—
89#88129C2×C411yescharacteristic
90C4×D52C2311yescharacteristic
91#88126—21no—
92#88124—21no—
93#88124C2×C411yescharacteristic
94#88123C2×C411yescharacteristic
95#88123C2×C411yescharacteristic
96C4×Dic26—21no—
97C4×Dic26C2311yescharacteristic
98C4×Dic26C2311yescharacteristic
99C4×Dic26C2311yescharacteristic
100C13×#97—21no—
101C13×#97C2×C411yescharacteristic
102C13×#97C2×C411yescharacteristic
103C13×#97D411yescharacteristic
104C13×#97D411yescharacteristic
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#18077—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—22no—
157C13×M16—41no—
158C13×M16—41no—
159C13×M16—42no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
170C42×C13C22×C411yescharacteristic
171C42×C13C2×D411yescharacteristic
172C42×C13#4111yescharacteristic
173C42×C13C2411yescharacteristic
174C22⋊Dic13—21no—
175C22⋊Dic13—21no—
176C22⋊Dic13—21no—
177#6103—21no—
178#6103—21no—
179#6103—21no—
180#6103—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13C22×C411yescharacteristic
185C4⋊Dic13C22×C411yescharacteristic
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—42no—
204Dic52—22no—
205Dic52—41no—
206#6095—22no—
207#6095—41no—
208#6094—42no—
209C8×D13—42no—
210#3172—131no—
211#2969—131no—
212#2962—131no—
213#1592—131no—
214#1591—131no—
215#1588—131no—
216#1587—131no—
217#1584—131no—
218#1582—131no—
219#1579—131no—
220C8×SD16—131no—
221#1565—131no—
222#1485—131no—
223#1483—131no—
224#1455D1311yescharacteristic, complemented
225C23×C13C4×D411yescharacteristic
226C22×D13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—41no—
232C2×C4×C13C4×D411yescharacteristic
233C2×C4×C13C4×D411yescharacteristic
234C2×C4×C13C4×D411yescharacteristic
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C22⋊D13—81no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246D52—21no—
247D52—21no—
248C4×D13—41no—
249C4×D13—41no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—21no—
256Dic26—81no—
257C8×C13—22no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—21no—
264C8×C13—41no—
265C8×C13#13112yes—
266C8×C13#13712yes—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271#533—131no—
272#529—131no—
273#501—131no—
274#497—131no—
275#491—131no—
276#489—131no—
277#470—131no—
278#470—131no—
279#468—131no—
280#468—131no—
281#446—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C4×Q16—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293#436—131no—
294#436—261no—
295#435—261no—
296C8×D4—131no—
297#433—261no—
298#431—131no—
299#424—261no—
300C2×C4⋊C8—131no—
301#405—261no—
302#405—261no—
303C4×M16C2×D1311yescharacteristic
304C4×M16C2×D1311yescharacteristic
305C4×M16C2×D1311yescharacteristic
306#335—131no—
307#335—131no—
308#334—131no—
309#334—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316D4⋊C8—131no—
317D4⋊C8—131no—
318#322C2×D1311yescharacteristic
319#322C2×D1311yescharacteristic
320#322C2×D1311yescharacteristic
321C82C2×D1311yescharacteristic
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13C2×C4×D411yescharacteristic
326C2×D13—41no—
327C2×D13—41no—
328C2×D13—41no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13C2×#13111yescharacteristic
334C4×C13#56811yescharacteristic
335C4×C13C2×#13711yescharacteristic
336C4×C13#57511yescharacteristic
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344C2×Q16—131no—
345C2×Q16—131no—
346C2×SD16—131no—
347C2×SD16—131no—
348C2×M16—21no—
349C2×M16—261no—
350C2×M16C4×D1311yescharacteristic
351C2×M16C4×D1311yescharacteristic
352C2×M16D5211yescharacteristic
353C2×M16D5211yescharacteristic
354C22×C8—261no—
355C22×C8—261no—
356C4⋊Q8—131no—
357C4⋊Q8—131no—
358#126—261no—
359#125—131no—
360#125—261no—
361#124—131no—
362#123—261no—
363C22⋊Q8—131no—
364C22⋊Q8—131no—
365C22⋊Q8—131no—
366C22⋊Q8—261no—
367#121—131no—
368C4×Q8—131no—
369C4×Q8—131no—
370C4×Q8—131no—
371C4×Q8—261no—
372C4×D4—131no—
373C4×D4—261no—
374#117—261no—
375#117—261no—
376C2×C42C22×D1311yescharacteristic
377#107—131no—
378#107—131no—
379#106—131no—
380#106—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—131no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#102—131no—
399#102—131no—
400C22⋊C8—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—21no—
404#97—261no—
405#97—261no—
406#97—261no—
407#97C4×D1311yescharacteristic
408#97C4×D1311yescharacteristic
409#97D5211yescharacteristic
410#97D5211yescharacteristic
411C4×C8—261no—
412C4×C8—261no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8C22×D1311yescharacteristic
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13—41no—
422C2×C13#293511yescharacteristic
423C2×C13C4×#13711yescharacteristic
424C2×C13#295611yescharacteristic
425D13—81no—
426C2×Q8—131no—
427C2×Q8—131no—
428C2×Q8—131no—
429C2×Q8—261no—
430C2×D4—131no—
431C2×D4—261no—
432C22×C4—261no—
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4C2×D5211yescharacteristic
435C22×C4#612711yescharacteristic
436Q16—262no—
437Q16—521no—
438SD16—262no—
439SD16—521no—
440M16—22no—
441M16—22no—
442M16—41no—
443M16—41no—
444M16—42no—
445M16—522no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—522no—
453C2×C8—522no—
454C2×C8C2×C4×D1311yescharacteristic
455C2×C8C2×C4×D1311yescharacteristic
456C2×C8C2×C4×D1311yescharacteristic
457C2×C8C2×C4×D1311yescharacteristic
458C2×C8C2×D5211yescharacteristic
459C2×C8C2×D5211yescharacteristic
460C2×C8C2×D5211yescharacteristic
461C2×C8C2×D5211yescharacteristic
462C4⋊C4—131no—
463C4⋊C4—131no—
464C4⋊C4—131no—
465C4⋊C4—131no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C22⋊C4—261no—
483C22⋊C4—261no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42C2×D5211yescharacteristic
489C42#612711yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1807711yescharacteristic, complemented, Sylow
492C23—261no—
493C23C4×D5211yescharacteristic
494Q8—261no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—261no—
499Q8—261no—
500Q8—1041no—
501D4—261no—
502D4—261no—
503D4—1041no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—521no—
517C2×C4—521no—
518C2×C4C4×D5211yescharacteristic
519C2×C4C4×D5211yescharacteristic
520C2×C4C4×D5211yescharacteristic
521C2×C4C22×C4×D1311yescharacteristic
522C2×C4C22×D5211yescharacteristic
523C2×C4C2×#612711yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—521no—
533C8—521no—
534C8—521no—
535C8—521no—
536C8#8816112yes—
537C8#8816312yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—521no—
542C22—521no—
543C22—521no—
544C22C2×C4×D5211yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—521no—
550C4—521no—
551C4—521no—
552C4—521no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4C2×#8816111yescharacteristic
557C4#1171945011yescharacteristic
558C4C2×#8816311yescharacteristic
559C4#1171945311yescharacteristic
560C2—41no—
561C2—1041no—
562C2#1312358211yescharacteristic
563C2C4×#8816311yescharacteristic
564C2#1312374711yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1455C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#1455D13
hypocenterC13#18077
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1455

Complements

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

NH ≅ G/Ntype
3. #13123783C2semidirect
4. #13113740C2semidirect
5. #13113734C2semidirect
6. #13113716C2semidirect
7. #13113709C2semidirect
8. #13113688C2semidirect
9. #13113674C2semidirect
10. #13113656C2semidirect
11. C8×#6095C2semidirect
12. #13113588C2semidirect
13. #13113258C2semidirect
15. C13×#1455C2semidirect
224. #1455D13semidirect
491. C13#18077semidirect

Maximal subgroups

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

subgroupindex
#131254422
#131238402
#131237832
#131137402
#131137342
#131137162
#131137092
#131136882
#131136742
#131136562
C8×#60952
#131135882
#131132582
#131132502
C13×#14552
#1807713