Finite Group Databasebeta

← #15833563

Subgroups — #15833563

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125440C211yesmaximal, characteristic
2#13123988C211yesmaximal, characteristic
3#13123932C211yesmaximal, characteristic, complemented
4#13113740C211yesmaximal, characteristic, complemented
5#13113731C211yesmaximal, characteristic, complemented
6#13113726C211yesmaximal, characteristic, complemented
7#13113652C211yesmaximal, characteristic, complemented
8#13113651C211yesmaximal, characteristic, complemented
9Q16×#1055C211yesmaximal, characteristic, complemented
10#13113635C211yesmaximal, characteristic, complemented
11#13113600C211yesmaximal, characteristic, complemented
12#13113295C211yesmaximal, characteristic
13#13113289C211yesmaximal, characteristic, complemented
14#13113115C211yesmaximal, characteristic, complemented
15C13×#1593C211yesmaximal, characteristic, complemented
16#11719285C2211yescharacteristic
17#11719283C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C13×#446C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718851C411yescharacteristic
22#11718850C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6106C2211yescharacteristic
25Q8×#1055C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718547C411yescharacteristic
28#11718537C411yescharacteristic
29#11718501—21no—
30#11718500—21no—
31#11718499—21no—
32#11718498C2211yescharacteristic
33#11718496C2211yescharacteristic
34#11718495C2211yescharacteristic
35#11718492—21no—
36#11718491C2211yescharacteristic
37#11718477C411yescharacteristic
38#11718473C411yescharacteristic
39#11718458C411yescharacteristic
40#11718456C411yescharacteristic
41#11718370—21no—
42#11718370—21no—
43#11718367—21no—
44#11718362—21no—
45C4×#6095C2211yescharacteristic
46#11718349C2211yescharacteristic
47C4×#6094C2211yescharacteristic
48#11718346C2211yescharacteristic
49C4×C8×D13C2211yescharacteristic
50#11718340C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718050C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×Q16C2×C411yescharacteristic
68C4×Q8×C13C2311yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70#88201C2×C411yescharacteristic
71#88200C2×C411yescharacteristic
72#88200C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76C2×#6095C2×C411yescharacteristic
77C2×#6094—21no—
78C2×#6094—21no—
79C2×#6094C2×C411yescharacteristic
80C2×#6094C2×C411yescharacteristic
81C2×C8×D13—21no—
82C2×C8×D13—21no—
83#88152—21no—
84#88151C2×C411yescharacteristic
85#88150—21no—
86#88149C2×C411yescharacteristic
87#88148—21no—
88#88144C2×C411yescharacteristic
89#88143—21no—
90#88142C2×C411yescharacteristic
91C4×D52—21no—
92C4×D52C2311yescharacteristic
93#88126—21no—
94#88126—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—
106C13×#97—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#88060D411yescharacteristic
117#88060D411yescharacteristic
118#88057C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88055—21no—
121#88055—21no—
122#88055C2×C411yescharacteristic
123#88055C2×C411yescharacteristic
124#88054—21no—
125#88054—21no—
126#88054—21no—
127#88054D411yescharacteristic
128#88054D411yescharacteristic
129C8×Dic13—21no—
130C8×Dic13—21no—
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#17969—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147C2×D52—21no—
148C2×D52C22×C411yescharacteristic
149C2×C4×D13—21no—
150C2×C4×D13C22×C411yescharacteristic
151C2×C4×D13C2×D411yescharacteristic
152C2×C4×D13#4111yescharacteristic
153C2×Dic26—21no—
154C2×Dic26C22×C411yescharacteristic
155C13×Q16—22no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13C22×C411yescharacteristic
160C2×C8×C13C22×C411yescharacteristic
161C2×C8×C13C2×D411yescharacteristic
162C2×C8×C13C2×D411yescharacteristic
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4C22×C411yescharacteristic
166C13×C4⋊C4C22×C411yescharacteristic
167C42×C13—21no—
168C42×C13—21no—
169C42×C13C2411yescharacteristic
170#6107—22no—
171#6106—22no—
172#6103—21no—
173#6103—21no—
174#6103—21no—
175#6103—21no—
176#6103—21no—
177#6103—21no—
178#6103—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13C22×C411yescharacteristic
182C4⋊Dic13C22×C411yescharacteristic
183#6101—21no—
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13C22×C411yescharacteristic
192C4×Dic13C2×D411yescharacteristic
193C4×Dic13#4111yescharacteristic
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055C22×C411yescharacteristic
198C2×#1055C22×C411yescharacteristic
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201#6095—22no—
202#6094—22no—
203#6094—22no—
204#6094—81no—
205#6094—81no—
206C8×D13—42no—
207C8×D13—81no—
208#3172—131no—
209#2993—131no—
210#2985—131no—
211#1593D1311yescharacteristic, complemented
212#1592—131no—
213#1591—131no—
214#1590—131no—
215#1579—131no—
216SD16⋊C8—131no—
217C8×Q16—131no—
218C8×SD16—131no—
219#1569—131no—
220#1494—131no—
221#1493—131no—
222C8×M16—131no—
223C22×D13—21no—
224C22×D13C4×D411yescharacteristic
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13C4×D411yescharacteristic
240C2×Dic13C4×D411yescharacteristic
241C2×Dic13C4×D411yescharacteristic
242D52—21no—
243D52—21no—
244D52—81no—
245C4×D13—21no—
246C4×D13—21no—
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—41no—
250C4×D13—41no—
251C4×D13—41no—
252Dic26—21no—
253Dic26—21no—
254Dic26—81no—
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—41no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13#13112yes—
262#1055—22no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—41no—
267#1055—41no—
268#1055#13112yes—
269#533—131no—
270#529—131no—
271#501—131no—
272#497—131no—
273#491—131no—
274#489—131no—
275#470—131no—
276#470—131no—
277#468—131no—
278#468—131no—
279#446—131no—
280#446—261no—
281#446—261no—
282#446C2×D1311yescharacteristic
283#446C2×D1311yescharacteristic
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C4×Q16—131no—
288C4×Q16C2×D1311yescharacteristic
289C4×SD16—131no—
290C4×SD16—131no—
291#436—131no—
292#436—261no—
293#435—261no—
294C8×D4—131no—
295#433—261no—
296#433—261no—
297#433—261no—
298#432—131no—
299#431—131no—
300#424—261no—
301#423—131no—
302C4×M16—131no—
303C2×C4×C8—131no—
304#335—131no—
305#335—131no—
306#334—131no—
307#334C2×D1311yescharacteristic
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8C2×D1311yescharacteristic
313Q8⋊C8C2×D1311yescharacteristic
314D4⋊C8—131no—
315D4⋊C8—131no—
316#322—131no—
317#322C2×D1311yescharacteristic
318C82—131no—
319C82—131no—
320C22×C13C2×C4×D411yescharacteristic
321C2×D13—21no—
322C2×D13—21no—
323C2×D13—21no—
324C2×D13—41no—
325C2×D13—41no—
326C2×D13—41no—
327C4×C13—21no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13C2×#13111yescharacteristic
333C4×C13C2×#13111yescharacteristic
334C4×C13#57711yescharacteristic
335C4×C13#57811yescharacteristic
336Dic13—21no—
337Dic13—21no—
338Dic13—21no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342C2×Q16—131no—
343C2×Q16C4×D1311yescharacteristic
344C2×SD16—131no—
345C2×SD16—131no—
346C2×M16—131no—
347C2×M16—131no—
348C2×M16—261no—
349C2×M16—261no—
350C22×C8—261no—
351C22×C8—261no—
352C4⋊Q8—131no—
353C4⋊Q8—131no—
354#126—261no—
355#125—131no—
356#125—261no—
357#124—131no—
358#123—261no—
359C22⋊Q8—131no—
360C22⋊Q8—131no—
361C22⋊Q8—131no—
362C22⋊Q8—261no—
363#121—131no—
364C4×Q8—131no—
365C4×Q8—261no—
366C4×Q8C22×D1311yescharacteristic
367C4×Q8C22×D1311yescharacteristic
368C4×D4—131no—
369C4×D4—261no—
370#117—261no—
371#117—261no—
372C2×C42—131no—
373#107—131no—
374#107C4×D1311yescharacteristic
375#106—131no—
376#106—131no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8C22×D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
390#103—131no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103C4×D1311yescharacteristic
395#103C4×D1311yescharacteristic
396#102—131no—
397#102—131no—
398C22⋊C8—131no—
399C22⋊C8—131no—
400C22⋊C8—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—21no—
404#97—21no—
405#97—131no—
406#97—131no—
407#97—261no—
408#97—261no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—261no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C2×C13#293111yescharacteristic
420C2×C13#294711yescharacteristic
421C2×C13#295611yescharacteristic
422D13—41no—
423D13—81no—
424C2×Q8—131no—
425C2×Q8—261no—
426C2×Q8C2×C4×D1311yescharacteristic
427C2×Q8C2×C4×D1311yescharacteristic
428C2×D4—131no—
429C2×D4—261no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—261no—
434Q16—22no—
435Q16—262no—
436SD16—262no—
437SD16—262no—
438M16—262no—
439M16—262no—
440M16—1041no—
441M16—1041no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—131no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—522no—
453C2×C8—1041no—
454C2×C8C2×C4×D1311yescharacteristic
455C2×C8C2×C4×D1311yescharacteristic
456C2×C8D4×D1311yescharacteristic
457C2×C8D4×D1311yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—131no—
461C4⋊C4—131no—
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—
471C4⋊C4C2×C4×D1311yescharacteristic
472C4⋊C4C2×C4×D1311yescharacteristic
473C22⋊C4—261no—
474C22⋊C4—261no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C42—21no—
481C42—21no—
482C42—131no—
483C42—131no—
484C42—131no—
485C42—261no—
486C42C23×D1311yescharacteristic
487C13#1796911yescharacteristic, complemented, Sylow
488C23—131no—
489C23—261no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—261no—
495Q8—261no—
496Q8—1041no—
497D4—261no—
498D4—261no—
499D4—1041no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—131no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—521no—
515C2×C4—521no—
516C2×C4—521no—
517C2×C4C22×C4×D1311yescharacteristic
518C2×C4C2×D4×D1311yescharacteristic
519C2×C4#41×D1311yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—132no—
527C8—262no—
528C8—261no—
529C8—261no—
530C8—261no—
531C8—521no—
532C8—521no—
533C8#8816112yes—
534C22—261no—
535C22—261no—
536C22—261no—
537C22—521no—
538C22—521no—
539C22—521no—
540C22C4×D4×D1311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—261no—
547C4—261no—
548C4—261no—
549C4—521no—
550C4—521no—
551C4—521no—
552C4C2×#8816111yescharacteristic
553C4D13×#13111yescharacteristic
554C4#1171948311yescharacteristic
555C4#1171948411yescharacteristic
556C2—521no—
557C2—1041no—
558C2#1312354511yescharacteristic
559C2#1312367811yescharacteristic
560C2#1312374411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1593C2
socleC22×C13C2×C4×D4
prime radical#88149C2×C4
cosocleC42×C13C24
hypercenter#1593D13
hypocenterC13#17969
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1593

Complements

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

NH ≅ G/Ntype
3. #13123932C2semidirect
4. #13113740C2semidirect
5. #13113731C2semidirect
6. #13113726C2semidirect
7. #13113652C2semidirect
8. #13113651C2semidirect
9. Q16×#1055C2semidirect
10. #13113635C2semidirect
11. #13113600C2semidirect
13. #13113289C2semidirect
14. #13113115C2semidirect
15. C13×#1593C2semidirect
211. #1593D13semidirect
487. C13#17969semidirect

Maximal subgroups

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

subgroupindex
#131254402
#131239882
#131239322
#131137402
#131137312
#131137262
#131136522
#131136512
Q16×#10552
#131136352
#131136002
#131132952
#131132892
#131131152
C13×#15932
#1796913