Finite Group Databasebeta

← #14725732

Subgroups — #14725732

Order 2816.

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#13079216C211yesmaximal, characteristic
2#13077778C211yesmaximal, characteristic
3#13067523C211yesmaximal, characteristic, complemented
4#13067506C211yesmaximal, characteristic, complemented
5#13067494C211yesmaximal, characteristic, complemented
6#13067485C211yesmaximal, characteristic, complemented
7#13067466C211yesmaximal, characteristic, complemented
8#13067450C211yesmaximal, characteristic, complemented
9#13067426C211yesmaximal, characteristic, complemented
10C8×#4326C211yesmaximal, characteristic, complemented
11#13067369C211yesmaximal, characteristic, complemented
12#13067022C211yesmaximal, characteristic
13#13067019C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#2986C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#446—21no—
19C11×#446C2211yescharacteristic
20C11×#446C2211yescharacteristic
21C8×Q8×C11—21no—
22C8×Q8×C11C2211yescharacteristic
23C8×Q8×C11C2211yescharacteristic
24C11×#433—21no—
25C11×#433—21no—
26C11×#431C2211yescharacteristic
27C11×#431C2211yescharacteristic
28#10622702C411yescharacteristic
29#10622699C411yescharacteristic
30#10622695C411yescharacteristic
31#10622693C411yescharacteristic
32#10622665C411yescharacteristic
33#10622665C411yescharacteristic
34#10622662C411yescharacteristic
35#10622662C411yescharacteristic
36C4×#4326C2211yescharacteristic
37C4×#4326C2211yescharacteristic
38C4×#4325C2211yescharacteristic
39C4×#4325C2211yescharacteristic
40#10622538C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622453—21no—
44#10622452—21no—
45#10622343—21no—
46(C22⋊D11)⋊C8—21no—
47#10622301C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53Q8⋊(C11⋊C8)C2211yescharacteristic
54Q8⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C11×C4⋊Q8C2×C411yescharacteristic
68C11×C4⋊Q8C2×C411yescharacteristic
69C11×#125—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8C2×C411yescharacteristic
72C11×C22⋊Q8C2×C411yescharacteristic
73C4×Q8×C11—21no—
74C4×Q8×C11C2311yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C11×#117—21no—
77C2×C42×C11C2311yescharacteristic
78C2×#4326C2×C411yescharacteristic
79C2×#4326C2×C411yescharacteristic
80C2×#4325C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82#66983C2×C411yescharacteristic
83#66982—21no—
84C4×C22⋊D11—21no—
85#66977C2×C411yescharacteristic
86C2×#4318C2×C411yescharacteristic
87C2×#4318C2×C411yescharacteristic
88C22×C11⋊C8—21no—
89C2×#4313—21no—
90C2×C8×D11—21no—
91#66929—21no—
92#66928C2×C411yescharacteristic
93C4×D44C2311yescharacteristic
94#66925—21no—
95#66923C2×C411yescharacteristic
96C4×Dic22C2311yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8D411yescharacteristic
102C11×C4⋊C8D411yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8D411yescharacteristic
107C11×C22⋊C8D411yescharacteristic
108C11×#97—21no—
109C11×#97—21no—
110C4×C8×C11—21no—
111C4×C8×C11—21no—
112C4×C8×C11—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899C2×C411yescharacteristic
116#66899C2×C411yescharacteristic
117#66899C2×C411yescharacteristic
118#66899C2×C411yescharacteristic
119C22⋊(C11⋊C8)—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66879—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867C2×C411yescharacteristic
139#66867C2×C411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18083—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C2×C22⋊D11—21no—
152C2×D44C22×C411yescharacteristic
153C2×C4×D11—21no—
154C2×Dic22C22×C411yescharacteristic
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11C2×D411yescharacteristic
158C2×C8×C11C2×D411yescharacteristic
159C2×C8×C11C2×D411yescharacteristic
160C2×C8×C11C2×D411yescharacteristic
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C411yescharacteristic
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11C22×C411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11#4111yescharacteristic
177C42×C11C2411yescharacteristic
178C22⋊Dic11—21no—
179#4326—22no—
180#4326—41no—
181#4325—22no—
182#4325—41no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194#4318—22no—
195#4318—41no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—81no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205#4313—81no—
206C8×D11—81no—
207#3172—111no—
208#2994—111no—
209#2986D1111yescharacteristic, complemented
210#1593—111no—
211#1590—111no—
212#1588—111no—
213#1587—111no—
214#1584—111no—
215#1582—111no—
216SD16⋊C8—111no—
217C8×Q16—111no—
218#1565—111no—
219#1482—111no—
220#1481—111no—
221#1453—111no—
222C23×C11C4×D411yescharacteristic
223C22×D11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—42no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—42no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248D44—21no—
249D44—21no—
250C4×D11—41no—
251C4×D11—41no—
252Dic22—21no—
253Dic22—21no—
254C8×C11—21no—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—41no—
259C8×C11—41no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8#13112yes—
268#533C2×D1111yescharacteristic
269#529—111no—
270#501—111no—
271#497—111no—
272#491—111no—
273#489—111no—
274#470—111no—
275#470—111no—
276#468—111no—
277#468—111no—
278#446—21no—
279#446—111no—
280#446C2×D1111yescharacteristic
281#446C2×D1111yescharacteristic
282C8×Q8—21no—
283C8×Q8—111no—
284C8×Q8C2×D1111yescharacteristic
285C8×Q8C2×D1111yescharacteristic
286C4×Q16—111no—
287C4×Q16—111no—
288C4×SD16—111no—
289C4×SD16—111no—
290#436—111no—
291#435—221no—
292C8×D4—111no—
293C8×D4—221no—
294#433—21no—
295#433—21no—
296#433—221no—
297#431—111no—
298#431C2×D1111yescharacteristic
299#431C2×D1111yescharacteristic
300#424—221no—
301C2×C4⋊C8—111no—
302C4×M16—111no—
303#335—111no—
304#335—111no—
305#334—111no—
306#334—111no—
307Q8⋊C8—111no—
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313D4⋊C8—111no—
314D4⋊C8—111no—
315#322—111no—
316#322—111no—
317#322—111no—
318C82—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11C2×C4×D411yescharacteristic
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—41no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11C2×#13111yescharacteristic
335C4×C11#56811yescharacteristic
336C4×C11#57711yescharacteristic
337C4×C11#57811yescharacteristic
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341C2×Q16—111no—
342C2×Q16—111no—
343C2×SD16—111no—
344C2×SD16—111no—
345C2×M16—111no—
346C2×M16—111no—
347C2×M16—221no—
348C22×C8—221no—
349C22×C8—221no—
350C4⋊Q8C4×D1111yescharacteristic
351C4⋊Q8C4×D1111yescharacteristic
352#126—221no—
353#125—21no—
354#125—111no—
355#124—111no—
356#123—221no—
357C22⋊Q8—21no—
358C22⋊Q8—111no—
359C22⋊Q8C4×D1111yescharacteristic
360C22⋊Q8C4×D1111yescharacteristic
361#121—111no—
362C4×Q8—21no—
363C4×Q8—111no—
364C4×Q8C22×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—111no—
367C4×D4—221no—
368#117—21no—
369#117—221no—
370C2×C42C22×D1111yescharacteristic
371#107—111no—
372#107—111no—
373#106—111no—
374#106—111no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8C22⋊D1111yescharacteristic
386C4⋊C8C22⋊D1111yescharacteristic
387C4⋊C8C22×D1111yescharacteristic
388C4⋊C8C22×D1111yescharacteristic
389#103—111no—
390#103—111no—
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#102—111no—
396#102—111no—
397C22⋊C8—21no—
398C22⋊C8—221no—
399C22⋊C8—221no—
400C22⋊C8—221no—
401C22⋊C8C22⋊D1111yescharacteristic
402C22⋊C8C22⋊D1111yescharacteristic
403#97—21no—
404#97—21no—
405#97—111no—
406#97—111no—
407#97—221no—
408C4×C8—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11—41no—
419C2×C11#293511yescharacteristic
420C2×C11#294711yescharacteristic
421C2×C11#295511yescharacteristic
422D11—81no—
423C2×Q8—21no—
424C2×Q8—111no—
425C2×Q8C2×C4×D1111yescharacteristic
426C2×Q8C2×C4×D1111yescharacteristic
427C2×D4—111no—
428C2×D4—221no—
429C22×C4—221no—
430C22×C4C2×C4×D1111yescharacteristic
431C22×C4#433911yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433Q16—222no—
434Q16—441no—
435SD16—222no—
436SD16—441no—
437M16—222no—
438M16—441no—
439M16—881no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—111no—
445C2×C8—111no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—881no—
451C2×C8—881no—
452C2×C8C2×C22⋊D1111yescharacteristic
453C2×C8C2×C22⋊D1111yescharacteristic
454C2×C8C2×C22⋊D1111yescharacteristic
455C2×C8C2×C22⋊D1111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—111no—
464C4⋊C4—111no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4C2×C4×D1111yescharacteristic
470C4⋊C4C2×C4×D1111yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—21no—
479C42—21no—
480C42—221no—
481C42C2×C4×D1111yescharacteristic
482C42#433911yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1808311yescharacteristic, complemented, Sylow
486C23—221no—
487C23C4×C22⋊D1111yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—42no—
493Q8—221no—
494Q8—221no—
495D4—221no—
496D4—221no—
497D4—442no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4C4×C22⋊D1111yescharacteristic
513C2×C4C4×C22⋊D1111yescharacteristic
514C2×C4C4×C22⋊D1111yescharacteristic
515C2×C4C22×C4×D1111yescharacteristic
516C2×C4C2×#433911yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—112no—
525C8—221no—
526C8—221no—
527C8—221no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—441no—
536C22—441no—
537C22—441no—
538C22C2×C4×C22⋊D1111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—441no—
548C4—441no—
549C4—441no—
550C4D11×#13111yescharacteristic
551C4#1062328111yescharacteristic
552C4#1062336811yescharacteristic
553C4#1062336911yescharacteristic
554C2—41no—
555C2—881no—
556C2#1307735811yescharacteristic
557C2#1307745911yescharacteristic
558C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2986C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenter#2986D11
hypocenterC11#18083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2986

Complements

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

NH ≅ G/Ntype
3. #13067523C2semidirect
4. #13067506C2semidirect
5. #13067494C2semidirect
6. #13067485C2semidirect
7. #13067466C2semidirect
8. #13067450C2semidirect
9. #13067426C2semidirect
10. C8×#4326C2semidirect
11. #13067369C2semidirect
13. #13067019C2semidirect
14. #13066911C2semidirect
15. C11×#2986C2semidirect
209. #2986D11semidirect
485. C11#18083semidirect

Maximal subgroups

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

subgroupindex
#130792162
#130777782
#130675232
#130675062
#130674942
#130674852
#130674662
#130674502
#130674262
C8×#43262
#130673692
#130670222
#130670192
#130669112
C11×#29862
#1808311