Finite Group Databasebeta

← #14725730

Subgroups — #14725730

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#13079222C211yesmaximal, characteristic
2#13077772C211yesmaximal, characteristic
3#13077717C211yesmaximal, characteristic, complemented
4#13067524C211yesmaximal, characteristic, complemented
5#13067505C211yesmaximal, characteristic, complemented
6#13067493C211yesmaximal, characteristic, complemented
7#13067486C211yesmaximal, characteristic, complemented
8#13067465C211yesmaximal, characteristic, complemented
9#13067451C211yesmaximal, characteristic, complemented
10#13067427C211yesmaximal, characteristic, complemented
11#13067422C211yesmaximal, characteristic, complemented
12#13067022C211yesmaximal, characteristic
13#13067018C211yesmaximal, characteristic, complemented
14#13066913C211yesmaximal, characteristic, complemented
15C11×#1565C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21#10622750C411yescharacteristic
22#10622750C411yescharacteristic
23#10622747C411yescharacteristic
24#10622747C411yescharacteristic
25#10622724—21no—
26C8×C22⋊D11—21no—
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
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
45C4×Dic44C2211yescharacteristic
46C4×Dic44C2211yescharacteristic
47C4×#4314C2211yescharacteristic
48C4×#4314C2211yescharacteristic
49#10622292—21no—
50C8×Dic22—21no—
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#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×M16C2×C411yescharacteristic
68C2×C11×M16C2×C411yescharacteristic
69C22×C8×C11—21no—
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
79C2×Dic44C2×C411yescharacteristic
80C2×Dic44C2×C411yescharacteristic
81C2×#4314C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83C2×#4313—21no—
84C2×C8×D11—21no—
85#66929—21no—
86#66928C2×C411yescharacteristic
87C4×D44C2311yescharacteristic
88#66925—21no—
89#66923—21no—
90#66923C2×C411yescharacteristic
91#66922C2×C411yescharacteristic
92#66922C2×C411yescharacteristic
93C4×Dic22—21no—
94C4×Dic22C2311yescharacteristic
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C22⋊C8—21no—
103C11×#97C2×C411yescharacteristic
104C11×#97C2×C411yescharacteristic
105C4×C8×C11—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C22⋊(C11⋊C8)—21no—
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)—21no—
138C4⋊(C11⋊C8)D411yescharacteristic
139C4⋊(C11⋊C8)D411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18083—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—41no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—81no—
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⋊C8C2×D411yescharacteristic
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201Dic44—22no—
202Dic44—41no—
203#4314—22no—
204#4314—41no—
205#4313—81no—
206C8×D11—81no—
207#3172—111no—
208#2994—111no—
209#2986—111no—
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#1565D1111yescharacteristic, complemented
219#1482—111no—
220#1481—111no—
221#1453—111no—
222C23×C11C4×D411yescharacteristic
223C22×D11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11C4×D411yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C22⋊D11—42no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243D44—21no—
244D44—21no—
245C4×D11—41no—
246C4×D11—41no—
247Dic22—21no—
248Dic22—21no—
249Dic22—21no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—42no—
254C8×C11—21no—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11—41no—
258C8×C11—41no—
259C8×C11—41no—
260C8×C11—41no—
261C8×C11#13112yes—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533—111no—
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—111no—
279#446—111no—
280#446—111no—
281#446—221no—
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—111no—
285C8×Q8—221no—
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—221no—
295#433—221no—
296#433—221no—
297#431—111no—
298#431—111no—
299#431C2×D1111yescharacteristic
300#424—221no—
301C2×C4⋊C8C2×D1111yescharacteristic
302C4×M16C2×D1111yescharacteristic
303#335C2×D1111yescharacteristic
304#335C2×D1111yescharacteristic
305#334C2×D1111yescharacteristic
306#334C2×D1111yescharacteristic
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×C11C2×#13111yescharacteristic
331C4×C11#56811yescharacteristic
332C4×C11#57711yescharacteristic
333C4×C11#57811yescharacteristic
334Dic11—41no—
335Dic11—41no—
336Dic11—41no—
337Dic11—41no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341C2×Q16—111no—
342C2×Q16—111no—
343C2×SD16—111no—
344C2×SD16—111no—
345C2×M16—221no—
346C2×M16C4×D1111yescharacteristic
347C2×M16C4×D1111yescharacteristic
348C22×C8—21no—
349C22×C8—221no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352#126—221no—
353#125—111no—
354#125—221no—
355#124—111no—
356#123—221no—
357C22⋊Q8—111no—
358C22⋊Q8—111no—
359C22⋊Q8—111no—
360C22⋊Q8—221no—
361#121—111no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—221no—
366C4×D4—111no—
367C4×D4—221no—
368#117—221no—
369#117—221no—
370C2×C42C22×D1111yescharacteristic
371#107—111no—
372#107—111no—
373#106—111no—
374#106—111no—
375C4⋊C8—21no—
376C4⋊C8—111no—
377C4⋊C8—111no—
378C4⋊C8—221no—
379C4⋊C8—221no—
380C4⋊C8—221no—
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—111no—
399C22⋊C8—111no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—221no—
404#97—221no—
405#97—221no—
406#97C4×D1111yescharacteristic
407#97C4×D1111yescharacteristic
408C4×C8—21no—
409C4×C8—111no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—221no—
414C4×C8—221no—
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—111no—
424C2×Q8—111no—
425C2×Q8—111no—
426C2×Q8—221no—
427C2×D4—111no—
428C2×D4—221no—
429C22×C4—221no—
430C22×C4C2×C4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4#434311yescharacteristic
433Q16—222no—
434Q16—441no—
435SD16—222no—
436SD16—441no—
437M16—22no—
438M16—41no—
439M16—881no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—81no—
445C2×C8—111no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—881no—
452C2×C8C2×C4×D1111yescharacteristic
453C2×C8C2×C4×D1111yescharacteristic
454C2×C8C2×C4×D1111yescharacteristic
455C2×C8C2×C4×D1111yescharacteristic
456C4⋊C4—111no—
457C4⋊C4—111no—
458C4⋊C4—111no—
459C4⋊C4—111no—
460C4⋊C4—221no—
461C4⋊C4—221no—
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—
471C22⋊C4—221no—
472C22⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—221no—
479C42—221no—
480C42—221no—
481C42C2×C4×D1111yescharacteristic
482C42D4×D1111yescharacteristic
483C42#434311yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1808311yescharacteristic, complemented, Sylow
486C23—221no—
487C23#6694611yescharacteristic
488Q8—221no—
489Q8—221no—
490Q8—221no—
491Q8—221no—
492Q8—221no—
493Q8—221no—
494Q8—442no—
495D4—221no—
496D4—221no—
497D4—442no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4#6694611yescharacteristic
513C2×C4#6694611yescharacteristic
514C2×C4#6694611yescharacteristic
515C2×C4C22×C4×D1111yescharacteristic
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4C2×#434311yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—221no—
526C8—221no—
527C8—221no—
528C8—221no—
529C8—441no—
530C8—441no—
531C8#6695412yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—441no—
536C22—441no—
537C22—441no—
538C22C2×#6694611yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—441no—
544C4—441no—
545C4—441no—
546C4—441no—
547C4—441no—
548C4—441no—
549C4—441no—
550C4C2×#6695411yescharacteristic
551C4#1062327611yescharacteristic
552C4#1062330611yescharacteristic
553C4#1062331011yescharacteristic
554C2—41no—
555C2—881no—
556C2#1307735911yescharacteristic
557C2#1307745711yescharacteristic
558C2#1307751811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1565C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenter#1565D11
hypocenterC11#18083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
3. #13077717C2semidirect
4. #13067524C2semidirect
5. #13067505C2semidirect
6. #13067493C2semidirect
7. #13067486C2semidirect
8. #13067465C2semidirect
9. #13067451C2semidirect
10. #13067427C2semidirect
11. #13067422C2semidirect
13. #13067018C2semidirect
14. #13066913C2semidirect
15. C11×#1565C2semidirect
218. #1565D11semidirect
485. C11#18083semidirect

Maximal subgroups

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

subgroupindex
#130792222
#130777722
#130777172
#130675242
#130675052
#130674932
#130674862
#130674652
#130674512
#130674272
#130674222
#130670222
#130670182
#130669132
C11×#15652
#1808311