Finite Group Databasebeta

← #15833564

Subgroups — #15833564

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#13125436C211yesmaximal, characteristic
2#13123987C211yesmaximal, characteristic
3#13113743C211yesmaximal, characteristic, complemented
4#13113736C211yesmaximal, characteristic, complemented
5#13113731C211yesmaximal, characteristic, complemented
6#13113726C211yesmaximal, characteristic, complemented
7#13113653C211yesmaximal, characteristic, complemented
8#13113646C211yesmaximal, characteristic, complemented
9C8×#6107C211yesmaximal, characteristic, complemented
10C8×#6106C211yesmaximal, characteristic, complemented
11#13113604C211yesmaximal, characteristic, complemented
12#13113294C211yesmaximal, characteristic
13#13113291C211yesmaximal, characteristic, complemented
14#13113117C211yesmaximal, characteristic, complemented
15C13×#2985C211yesmaximal, characteristic, complemented
16C13×#533C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#446—21no—
19C13×#446—21no—
20C13×#446C2211yescharacteristic
21C13×#446C2211yescharacteristic
22C8×Q8×C13C2211yescharacteristic
23C8×Q8×C13C2211yescharacteristic
24C13×#433—21no—
25C13×#433—21no—
26C13×#432C2211yescharacteristic
27C13×#431C2211yescharacteristic
28#11718750C411yescharacteristic
29#11718747C411yescharacteristic
30#11718743C411yescharacteristic
31#11718741C411yescharacteristic
32#11718713C411yescharacteristic
33#11718713C411yescharacteristic
34#11718710C411yescharacteristic
35#11718710C411yescharacteristic
36C4×#6107C2211yescharacteristic
37C4×#6107C2211yescharacteristic
38C4×#6106C2211yescharacteristic
39C4×#6106C2211yescharacteristic
40#11718585C2211yescharacteristic
41C4×#6099C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718501—21no—
44#11718500—21no—
45#11718390—21no—
46#11718389—21no—
47#11718349C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718340C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53Q8⋊#1055C2211yescharacteristic
54Q8⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C13×C4⋊Q8C2×C411yescharacteristic
68C13×C4⋊Q8C2×C411yescharacteristic
69C13×#125—21no—
70C13×C22⋊Q8—21no—
71C13×C22⋊Q8C2×C411yescharacteristic
72C13×C22⋊Q8C2×C411yescharacteristic
73C4×Q8×C13—21no—
74C4×Q8×C13C2311yescharacteristic
75C4×Q8×C13C2311yescharacteristic
76C13×#117—21no—
77C2×C42×C13C2311yescharacteristic
78C2×#6107C2×C411yescharacteristic
79C2×#6107C2×C411yescharacteristic
80C2×#6106C2×C411yescharacteristic
81C2×#6106C2×C411yescharacteristic
82#88184C2×C411yescharacteristic
83#88183—21no—
84C4×C22⋊D13—21no—
85#88178C2×C411yescharacteristic
86C2×#6099—21no—
87C2×#6099C2×C411yescharacteristic
88C2×#6099C2×C411yescharacteristic
89C22×#1055—21no—
90C2×#6094—21no—
91C2×C8×D13—21no—
92#88130—21no—
93#88129C2×C411yescharacteristic
94C4×D52C2311yescharacteristic
95#88126—21no—
96#88124C2×C411yescharacteristic
97C4×Dic26C2311yescharacteristic
98C13×C4⋊C8—21no—
99C13×C4⋊C8—21no—
100C13×C4⋊C8—21no—
101C13×C4⋊C8—21no—
102C13×C4⋊C8D411yescharacteristic
103C13×C4⋊C8D411yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×C22⋊C8—21no—
107C13×C22⋊C8D411yescharacteristic
108C13×C22⋊C8D411yescharacteristic
109C13×#97—21no—
110C13×#97—21no—
111C13×#97—21no—
112C4×C8×C13—21no—
113C4×C8×C13—21no—
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116#88075C2×C411yescharacteristic
117#88075C2×C411yescharacteristic
118#88075C2×C411yescharacteristic
119#88075C2×C411yescharacteristic
120#88060—21no—
121#88060—21no—
122#88055—21no—
123#88054—21no—
124#88054—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055C2311yescharacteristic
136C4⋊#1055C2311yescharacteristic
137#88043C2×C411yescharacteristic
138#88043C2×C411yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17969—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148C22×C4×C13C22×C411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13#4111yescharacteristic
151C2×C22⋊D13—21no—
152C2×D52C22×C411yescharacteristic
153C2×C4×D13—21no—
154C2×Dic26C22×C411yescharacteristic
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13C2×D411yescharacteristic
158C2×C8×C13C2×D411yescharacteristic
159C2×C8×C13C2×D411yescharacteristic
160C2×C8×C13C2×D411yescharacteristic
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4C22×C411yescharacteristic
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C22⋊C4—21no—
171C13×C22⋊C4—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13C22×C411yescharacteristic
175C42×C13C2×D411yescharacteristic
176C42×C13#4111yescharacteristic
177C42×C13C2411yescharacteristic
178C22⋊Dic13—21no—
179#6107—22no—
180#6107—22no—
181#6106—22no—
182#6106—22no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187C4⋊Dic13C22×C411yescharacteristic
188C4⋊Dic13C22×C411yescharacteristic
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193C4×Dic13—21no—
194#6099—22no—
195#6099—22no—
196#6099—81no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—42no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206#6094—81no—
207C8×D13—81no—
208#3172—131no—
209#2993—131no—
210#2985D1311yescharacteristic, complemented
211#1593—131no—
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—
223C23×C13C4×D411yescharacteristic
224C22×D13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—81no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—41no—
239C2×C4×C13C4×D411yescharacteristic
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C23×C411yescharacteristic
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C22⋊D13—81no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249D52—21no—
250D52—21no—
251C4×D13—41no—
252C4×D13—41no—
253Dic26—21no—
254Dic26—21no—
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—41no—
260C8×C13—41no—
261#1055—22no—
262#1055—21no—
263#1055—21no—
264#1055—41no—
265#1055—41no—
266#1055—41no—
267#1055#13112yes—
268#1055#13112yes—
269#533C2×D1311yescharacteristic
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—21no—
280#446—21no—
281#446—131no—
282#446C2×D1311yescharacteristic
283#446C2×D1311yescharacteristic
284C8×Q8—131no—
285C8×Q8C2×D1311yescharacteristic
286C8×Q8C2×D1311yescharacteristic
287C4×Q16—131no—
288C4×Q16—131no—
289C4×SD16—131no—
290C4×SD16—131no—
291#436—131no—
292#436—261no—
293#435—261no—
294C8×D4—131no—
295#433—21no—
296#433—21no—
297#433—261no—
298#432C2×D1311yescharacteristic
299#431C2×D1311yescharacteristic
300#424—261no—
301#423—131no—
302C4×M16—131no—
303C2×C4×C8—131no—
304#335—131no—
305#335—131no—
306#334—131no—
307#334—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314D4⋊C8—131no—
315D4⋊C8—131no—
316#322—131no—
317#322—131no—
318C82—131no—
319C82—131no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13C2×C4×D411yescharacteristic
324C2×D13—41no—
325C2×D13—41no—
326C2×D13—41no—
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13C2×#13111yescharacteristic
336C4×C13C2×#13111yescharacteristic
337C4×C13#57711yescharacteristic
338C4×C13#57811yescharacteristic
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342C2×Q16—131no—
343C2×Q16—131no—
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⋊Q8C4×D1311yescharacteristic
353C4⋊Q8C4×D1311yescharacteristic
354#126—261no—
355#125—21no—
356#125—131no—
357#124—131no—
358#123—261no—
359C22⋊Q8—21no—
360C22⋊Q8—131no—
361C22⋊Q8C4×D1311yescharacteristic
362C22⋊Q8C4×D1311yescharacteristic
363#121—131no—
364C4×Q8—21no—
365C4×Q8—131no—
366C4×Q8C22×D1311yescharacteristic
367C4×Q8C22×D1311yescharacteristic
368C4×D4—131no—
369C4×D4—261no—
370#117—21no—
371#117—261no—
372C2×C42C22×D1311yescharacteristic
373#107—131no—
374#107—131no—
375#106—131no—
376#106—131no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8C22⋊D1311yescharacteristic
387C4⋊C8C22⋊D1311yescharacteristic
388C4⋊C8C22×D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
390#103—131no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#102—131no—
397#102—131no—
398C22⋊C8—21no—
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8C22⋊D1311yescharacteristic
402C22⋊C8C22⋊D1311yescharacteristic
403#97—21no—
404#97—21no—
405#97—21no—
406#97—131no—
407#97—131no—
408#97—261no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C2×C13—41no—
420C2×C13#293111yescharacteristic
421C2×C13#294711yescharacteristic
422C2×C13#295611yescharacteristic
423D13—81no—
424C2×Q8—21no—
425C2×Q8—131no—
426C2×Q8C2×C4×D1311yescharacteristic
427C2×Q8C2×C4×D1311yescharacteristic
428C2×D4—131no—
429C2×D4—261no—
430C22×C4—261no—
431C22×C4C2×C4×D1311yescharacteristic
432C22×C4#612711yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434Q16—262no—
435Q16—262no—
436SD16—262no—
437SD16—262no—
438M16—262no—
439M16—262no—
440M16—1041no—
441M16—1041no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—131no—
445C2×C8—131no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—522no—
453C2×C8—1041no—
454C2×C8C2×C22⋊D1311yescharacteristic
455C2×C8C2×C22⋊D1311yescharacteristic
456C2×C8C2×C22⋊D1311yescharacteristic
457C2×C8C2×C22⋊D1311yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—131no—
466C4⋊C4—131no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4C2×C4×D1311yescharacteristic
472C4⋊C4C2×C4×D1311yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C42—21no—
481C42—21no—
482C42—261no—
483C42C2×C4×D1311yescharacteristic
484C42#612711yescharacteristic
485C42C2×C22⋊D1311yescharacteristic
486C42C23×D1311yescharacteristic
487C13#1796911yescharacteristic, complemented, Sylow
488C23—261no—
489C23C4×C22⋊D1311yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—261no—
496Q8—261no—
497D4—261no—
498D4—261no—
499D4—1041no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
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—521no—
513C2×C4—521no—
514C2×C4C4×C22⋊D1311yescharacteristic
515C2×C4C4×C22⋊D1311yescharacteristic
516C2×C4C4×C22⋊D1311yescharacteristic
517C2×C4C22×C4×D1311yescharacteristic
518C2×C4C2×#612711yescharacteristic
519C2×C4C22×C22⋊D1311yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—132no—
527C8—132no—
528C8—262no—
529C8—261no—
530C8—261no—
531C8—521no—
532C8—521no—
533C8—521no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—521no—
538C22—521no—
539C22—521no—
540C22C2×C4×C22⋊D1311yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—521no—
550C4—521no—
551C4—521no—
552C4D13×#13111yescharacteristic
553C4D13×#13111yescharacteristic
554C4#1171954211yescharacteristic
555C4#1171954311yescharacteristic
556C2—41no—
557C2—1041no—
558C2#1312354611yescharacteristic
559C2#1312367911yescharacteristic
560C2#1312374311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2985C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#2985D13
hypocenterC13#17969
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2985

Complements

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

NH ≅ G/Ntype
3. #13113743C2semidirect
4. #13113736C2semidirect
5. #13113731C2semidirect
6. #13113726C2semidirect
7. #13113653C2semidirect
8. #13113646C2semidirect
9. C8×#6107C2semidirect
10. C8×#6106C2semidirect
11. #13113604C2semidirect
13. #13113291C2semidirect
14. #13113117C2semidirect
15. C13×#2985C2semidirect
210. #2985D13semidirect
487. C13#17969semidirect

Maximal subgroups

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

subgroupindex
#131254362
#131239872
#131137432
#131137362
#131137312
#131137262
#131136532
#131136462
C8×#61072
C8×#61062
#131136042
#131132942
#131132912
#131131172
C13×#29852
#1796913