Finite Group Databasebeta

← #14724416

Subgroups — #14724416

Order 2816.

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#13079222C211yesmaximal, characteristic
2#13077761C211yesmaximal, characteristic
3#13077713C211yesmaximal, characteristic, complemented
4#13067524C211yesmaximal, characteristic, complemented
5#13067517C211yesmaximal, characteristic, complemented
6#13067512C211yesmaximal, characteristic, complemented
7#13067505C211yesmaximal, characteristic, complemented
8#13067434C211yesmaximal, characteristic, complemented
9#13067427C211yesmaximal, characteristic, complemented
10#13067422C211yesmaximal, characteristic, complemented
11#13067415C211yesmaximal, characteristic, complemented
12#13067074C211yesmaximal, characteristic
13#13067070C211yesmaximal, characteristic, complemented
14M16×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#1569C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#423C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21#10622750C411yescharacteristic
22#10622750C411yescharacteristic
23#10622747C411yescharacteristic
24#10622747C411yescharacteristic
25#10622741—21no—
26#10622740—21no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622453—21no—
30#10622452—21no—
31#10622451C2211yescharacteristic
32#10622447C2211yescharacteristic
33#10622444C2211yescharacteristic
34#10622444C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622443C2211yescharacteristic
38#10622443C2211yescharacteristic
39#10622333—21no—
40#10622333—21no—
41#10622328C411yescharacteristic
42#10622327C411yescharacteristic
43#10622316C411yescharacteristic
44#10622315C411yescharacteristic
45#10622314—21no—
46#10622314—21no—
47C4×Dic44C2211yescharacteristic
48C4×Dic44C2211yescharacteristic
49C4×#4314C2211yescharacteristic
50C4×#4314C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622122C2211yescharacteristic
60#10622122C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×M16—21no—
68C2×C11×M16C2×C411yescharacteristic
69C2×C11×M16C2×C411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71#66983C2×C411yescharacteristic
72#66982—21no—
73C4×C22⋊D11—21no—
74#66979—21no—
75#66977—21no—
76#66977C2×C411yescharacteristic
77#66977C2×C411yescharacteristic
78#66977C2×C411yescharacteristic
79C22×C11⋊C8—21no—
80C2×Dic44C2×C411yescharacteristic
81C2×Dic44C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83C2×#4314C2×C411yescharacteristic
84C2×#4313—21no—
85C2×C8×D11—21no—
86#66929—21no—
87#66928C2×C411yescharacteristic
88C4×D44C2311yescharacteristic
89#66925—21no—
90#66923—21no—
91#66923C2×C411yescharacteristic
92#66922C2×C411yescharacteristic
93#66922C2×C411yescharacteristic
94C4×Dic22—21no—
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C22⋊C8—21no—
104C11×#97—21no—
105C11×#97C2×C411yescharacteristic
106C11×#97C2×C411yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C22⋊(C11⋊C8)D411yescharacteristic
110C22⋊(C11⋊C8)D411yescharacteristic
111#66885C2×C411yescharacteristic
112#66885C2×C411yescharacteristic
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115#66882C2×C411yescharacteristic
116#66882C2×C411yescharacteristic
117#66881C2×C411yescharacteristic
118#66881C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66879—21no—
126#66879—21no—
127#66879—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134C8×Dic11—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C4⋊(C11⋊C8)D411yescharacteristic
138C4⋊(C11⋊C8)D411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17969—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C2×D44C22×C411yescharacteristic
150C2×C4×D11—21no—
151C2×Dic22—21no—
152C2×Dic22C22×C411yescharacteristic
153C2×Dic22C22×C411yescharacteristic
154C2×Dic22C22×C411yescharacteristic
155C11×M16—22no—
156C11×M16—22no—
157C11×M16—81no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C42×C11C22×C411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11#4111yescharacteristic
169C42×C11C2411yescharacteristic
170C22⋊Dic11—21no—
171C22⋊Dic11—21no—
172C22⋊Dic11—21no—
173(C2×D11)⋊C4—21no—
174(C2×D11)⋊C4—21no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11C22×C411yescharacteristic
181C4⋊Dic11C22×C411yescharacteristic
182C4⋊Dic11C22×C411yescharacteristic
183C4⋊Dic11C22×C411yescharacteristic
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—42no—
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202Dic44—22no—
203Dic44—22no—
204#4314—22no—
205#4314—22no—
206#4313—81no—
207C8×D11—81no—
208#3172—111no—
209#2993—111no—
210#2985—111no—
211#1593—111no—
212#1592—111no—
213#1591—111no—
214#1590—111no—
215#1579—111no—
216SD16⋊C8—111no—
217C8×Q16—111no—
218C8×SD16—111no—
219#1569D1111yescharacteristic, complemented
220#1494—111no—
221#1493—111no—
222C8×M16—111no—
223C23×C11C4×D411yescharacteristic
224C22×D11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—41no—
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C22⋊D11—81no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244D44—21no—
245D44—21no—
246C4×D11—41no—
247C4×D11—41no—
248Dic22—21no—
249Dic22—21no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—81no—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11—41no—
258C8×C11—41no—
259C8×C11—41no—
260C8×C11—41no—
261C8×C11#13112yes—
262C8×C11#13112yes—
263C11⋊C8—22no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—41no—
269#533—111no—
270#529—111no—
271#501—111no—
272#497—111no—
273#491—111no—
274#489—111no—
275#470—111no—
276#470—111no—
277#468—111no—
278#468—111no—
279#446—111no—
280#446—111no—
281#446—111no—
282#446—221no—
283#446—221no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C4×Q16—111no—
288C4×Q16—111no—
289C4×SD16—111no—
290C4×SD16—111no—
291#436—111no—
292#436—221no—
293#435—221no—
294C8×D4—111no—
295#433—221no—
296#433—221no—
297#433—221no—
298#432C2×D1111yescharacteristic
299#431—111no—
300#424—221no—
301#423C2×D1111yescharacteristic
302C4×M16C2×D1111yescharacteristic
303C2×C4×C8—111no—
304#335C2×D1111yescharacteristic
305#335C2×D1111yescharacteristic
306#334C2×D1111yescharacteristic
307#334C2×D1111yescharacteristic
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314D4⋊C8—111no—
315D4⋊C8—111no—
316#322—111no—
317#322—111no—
318C82—111no—
319C82—111no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11C2×C4×D411yescharacteristic
324C2×D11—41no—
325C2×D11—41no—
326C2×D11—41no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11C2×#13111yescharacteristic
332C4×C11C2×#13111yescharacteristic
333C4×C11#57711yescharacteristic
334C4×C11#57811yescharacteristic
335Dic11—41no—
336Dic11—41no—
337Dic11—41no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342C2×Q16—111no—
343C2×Q16—111no—
344C2×SD16—111no—
345C2×SD16—111no—
346C2×M16—21no—
347C2×M16—221no—
348C2×M16C4×D1111yescharacteristic
349C2×M16C4×D1111yescharacteristic
350C22×C8—221no—
351C22×C8—221no—
352C4⋊Q8—111no—
353C4⋊Q8—111no—
354#126—221no—
355#125—111no—
356#125—221no—
357#124—111no—
358#123—221no—
359C22⋊Q8—111no—
360C22⋊Q8—111no—
361C22⋊Q8—111no—
362C22⋊Q8—221no—
363#121—111no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—111no—
367C4×Q8—221no—
368C4×D4—111no—
369C4×D4—221no—
370#117—221no—
371#117—221no—
372C2×C42C22×D1111yescharacteristic
373#107—111no—
374#107—111no—
375#106—111no—
376#106—111no—
377C4⋊C8—21no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—221no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8C22×D1111yescharacteristic
387C4⋊C8C22×D1111yescharacteristic
388C4⋊C8C22×D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390#103—111no—
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#102—111no—
397#102—111no—
398C22⋊C8—21no—
399C22⋊C8—111no—
400C22⋊C8—111no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—21no—
404#97—221no—
405#97—221no—
406#97—221no—
407#97C4×D1111yescharacteristic
408#97C4×D1111yescharacteristic
409C4×C8—111no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C2×C11—41no—
420C2×C11#293111yescharacteristic
421C2×C11#294711yescharacteristic
422C2×C11#295611yescharacteristic
423D11—81no—
424C2×Q8—111no—
425C2×Q8—111no—
426C2×Q8—111no—
427C2×Q8—221no—
428C2×D4—111no—
429C2×D4—221no—
430C22×C4—221no—
431C22×C4C2×C4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433C22×C4#434311yescharacteristic
434Q16—222no—
435Q16—222no—
436SD16—222no—
437SD16—222no—
438M16—22no—
439M16—22no—
440M16—81no—
441M16—881no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—442no—
453C2×C8—881no—
454C2×C8C2×C4×D1111yescharacteristic
455C2×C8C2×C4×D1111yescharacteristic
456C2×C8C2×C4×D1111yescharacteristic
457C2×C8C2×C4×D1111yescharacteristic
458C4⋊C4—111no—
459C4⋊C4—111no—
460C4⋊C4—111no—
461C4⋊C4—111no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42C2×C4×D1111yescharacteristic
484C42D4×D1111yescharacteristic
485C42#434311yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1796911yescharacteristic, complemented, Sylow
488C23—221no—
489C23#6694611yescharacteristic
490Q8—221no—
491Q8—221no—
492Q8—221no—
493Q8—221no—
494Q8—221no—
495Q8—221no—
496Q8—881no—
497D4—221no—
498D4—221no—
499D4—881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4#6694611yescharacteristic
515C2×C4#6694611yescharacteristic
516C2×C4#6694611yescharacteristic
517C2×C4C22×C4×D1111yescharacteristic
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4C2×#434311yescharacteristic
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—222no—
527C8—221no—
528C8—221no—
529C8—221no—
530C8—221no—
531C8—441no—
532C8#6696012yes—
533C8#6696012yes—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—441no—
538C22—441no—
539C22—441no—
540C22C2×#6694611yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—441no—
546C4—441no—
547C4—441no—
548C4—441no—
549C4—441no—
550C4—441no—
551C4—441no—
552C4C2×#6696011yescharacteristic
553C4C2×#6696011yescharacteristic
554C4#1062330611yescharacteristic
555C4#1062331011yescharacteristic
556C2—41no—
557C2—881no—
558C2#1307732711yescharacteristic
559C2#1307745711yescharacteristic
560C2#1307752511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1569C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenter#1569D11
hypocenterC11#17969
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
3. #13077713C2semidirect
4. #13067524C2semidirect
5. #13067517C2semidirect
6. #13067512C2semidirect
7. #13067505C2semidirect
8. #13067434C2semidirect
9. #13067427C2semidirect
10. #13067422C2semidirect
11. #13067415C2semidirect
13. #13067070C2semidirect
14. M16×C11⋊C8C2semidirect
15. C11×#1569C2semidirect
219. #1569D11semidirect
487. C11#17969semidirect

Maximal subgroups

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

subgroupindex
#130792222
#130777612
#130777132
#130675242
#130675172
#130675122
#130675052
#130674342
#130674272
#130674222
#130674152
#130670742
#130670702
M16×C11⋊C82
C11×#15692
#1796911