Finite Group Databasebeta

← #14725640

Subgroups — #14725640

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079222C211yesmaximal, characteristic
2#13077614C211yesmaximal, characteristic
3#13077559C211yesmaximal, characteristic, complemented
4#13067517C211yesmaximal, characteristic, complemented
5#13067512C211yesmaximal, characteristic, complemented
6#13067493C211yesmaximal, characteristic, complemented
7#13067486C211yesmaximal, characteristic, complemented
8#13067465C211yesmaximal, characteristic, complemented
9#13067451C211yesmaximal, characteristic, complemented
10#13067434C211yesmaximal, characteristic, complemented
11#13067415C211yesmaximal, characteristic, complemented
12#13067036C211yesmaximal, characteristic, complemented
13#13067027C211yesmaximal, characteristic
14#13066919C211yesmaximal, 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#10622715—21no—
26#10622714—21no—
27C4×#4318C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29#10622451C2211yescharacteristic
30#10622447C2211yescharacteristic
31#10622444C2211yescharacteristic
32#10622444C2211yescharacteristic
33#10622444C2211yescharacteristic
34#10622443C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622441—21no—
38#10622441—21no—
39#10622342—21no—
40#10622341—21no—
41#10622328C411yescharacteristic
42#10622327C411yescharacteristic
43#10622316C411yescharacteristic
44#10622315C411yescharacteristic
45C4×Dic44C2211yescharacteristic
46C4×Dic44C2211yescharacteristic
47C4×#4314C2211yescharacteristic
48C4×#4314C2211yescharacteristic
49#10622303—21no—
50#10622302—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×#4318—21no—
80C2×#4318D411yescharacteristic
81C2×#4318D411yescharacteristic
82C2×Dic44C2×C411yescharacteristic
83C2×Dic44C2×C411yescharacteristic
84C2×#4314C2×C411yescharacteristic
85C2×#4314C2×C411yescharacteristic
86C2×#4313—21no—
87C2×C8×D11—21no—
88#66929—21no—
89#66928C2×C411yescharacteristic
90C4×D44C2311yescharacteristic
91#66925—21no—
92#66923—21no—
93#66923C2×C411yescharacteristic
94#66922C2×C411yescharacteristic
95#66922C2×C411yescharacteristic
96C4×Dic22—21no—
97C4×Dic22C2311yescharacteristic
98C4×Dic22C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C22⋊C8—21no—
106C11×#97C2×C411yescharacteristic
107C11×#97C2×C411yescharacteristic
108C4×C8×C11—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
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—
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18077—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—42no—
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—
195#4318—22no—
196#4318—41no—
197#4318—42no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204Dic44—22no—
205Dic44—41no—
206#4314—22no—
207#4314—41no—
208#4313—42no—
209C8×D11—42no—
210#3172—111no—
211#2969—111no—
212#2962—111no—
213#1592—111no—
214#1591—111no—
215#1588—111no—
216#1587—111no—
217#1584—111no—
218#1582—111no—
219#1579—111no—
220C8×SD16—111no—
221#1565D1111yescharacteristic, complemented
222#1485—111no—
223#1483—111no—
224#1455—111no—
225C23×C11C4×D411yescharacteristic
226C22×D11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—41no—
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C22⋊D11—81no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246D44—21no—
247D44—21no—
248C4×D11—41no—
249C4×D11—41no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—81no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11—41no—
264C8×C11#13112yes—
265C11⋊C8—22no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8#13712yes—
271#533—111no—
272#529—111no—
273#501—111no—
274#497—111no—
275#491—111no—
276#489—111no—
277#470—111no—
278#470—111no—
279#468—111no—
280#468—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C4×Q16—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293#436—111no—
294#436—221no—
295#435—221no—
296C8×D4—111no—
297#433—221no—
298#431C2×D1111yescharacteristic
299#424—221no—
300C2×C4⋊C8C2×D1111yescharacteristic
301#405—221no—
302#405—221no—
303C4×M16—111no—
304C4×M16—111no—
305C4×M16C2×D1111yescharacteristic
306#335C2×D1111yescharacteristic
307#335C2×D1111yescharacteristic
308#334C2×D1111yescharacteristic
309#334C2×D1111yescharacteristic
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316D4⋊C8—111no—
317D4⋊C8—111no—
318#322—111no—
319#322—111no—
320#322—111no—
321C82—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11C2×C4×D411yescharacteristic
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11C2×#13111yescharacteristic
334C4×C11#56811yescharacteristic
335C4×C11C2×#13711yescharacteristic
336C4×C11#57511yescharacteristic
337Dic11—41no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C2×M16—111no—
349C2×M16—111no—
350C2×M16—221no—
351C2×M16—221no—
352C2×M16C4×D1111yescharacteristic
353C2×M16C4×D1111yescharacteristic
354C22×C8—21no—
355C22×C8—221no—
356C4⋊Q8—111no—
357C4⋊Q8—111no—
358#126—221no—
359#125—111no—
360#125—221no—
361#124—111no—
362#123—221no—
363C22⋊Q8—111no—
364C22⋊Q8—111no—
365C22⋊Q8—111no—
366C22⋊Q8—221no—
367#121—111no—
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8—221no—
372C4×D4—111no—
373C4×D4—221no—
374#117—221no—
375#117—221no—
376C2×C42C22×D1111yescharacteristic
377#107—111no—
378#107—111no—
379#106—111no—
380#106—111no—
381C4⋊C8—21no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8C22×D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391C4⋊C8C22×D1111yescharacteristic
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#102—111no—
399#102—111no—
400C22⋊C8—21no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—111no—
404#97—111no—
405#97—221no—
406#97—221no—
407#97—221no—
408#97—221no—
409#97C4×D1111yescharacteristic
410#97C4×D1111yescharacteristic
411C4×C8—21no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11—41no—
422C2×C11#293511yescharacteristic
423C2×C11C4×#13711yescharacteristic
424C2×C11#295611yescharacteristic
425D11—81no—
426C2×Q8—111no—
427C2×Q8—111no—
428C2×Q8—111no—
429C2×Q8—221no—
430C2×D4—111no—
431C2×D4—221no—
432C22×C4—221no—
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4D4×D1111yescharacteristic
435C22×C4#434311yescharacteristic
436Q16—222no—
437Q16—441no—
438SD16—222no—
439SD16—441no—
440M16—22no—
441M16—41no—
442M16—222no—
443M16—442no—
444M16—441no—
445M16—442no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—442no—
458C2×C8C2×C4×D1111yescharacteristic
459C2×C8C2×C4×D1111yescharacteristic
460C2×C8C2×C4×D1111yescharacteristic
461C2×C8C2×C4×D1111yescharacteristic
462C4⋊C4—111no—
463C4⋊C4—111no—
464C4⋊C4—111no—
465C4⋊C4—111no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42C2×C4×D1111yescharacteristic
488C42D4×D1111yescharacteristic
489C42#434311yescharacteristic
490C42C23×D1111yescharacteristic
491C11#1807711yescharacteristic, complemented, Sylow
492C23—221no—
493C23#6694611yescharacteristic
494Q8—221no—
495Q8—221no—
496Q8—221no—
497Q8—221no—
498Q8—221no—
499Q8—221no—
500Q8—881no—
501D4—221no—
502D4—221no—
503D4—881no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4#6694611yescharacteristic
519C2×C4#6694611yescharacteristic
520C2×C4#6694611yescharacteristic
521C2×C4C22×C4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×#434311yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—112no—
532C8—222no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—441no—
537C8#6695412yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—441no—
542C22—441no—
543C22—441no—
544C22C2×#6694611yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—441no—
550C4—441no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4—441no—
555C4—441no—
556C4C2×#6695411yescharacteristic
557C4#1062327611yescharacteristic
558C4#1062330411yescharacteristic
559C4D11×#13711yescharacteristic
560C2—41no—
561C2—881no—
562C2#1307735911yescharacteristic
563C2#1307743411yescharacteristic
564C2#1307752511yescharacteristic
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#18077
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. #13077559C2semidirect
4. #13067517C2semidirect
5. #13067512C2semidirect
6. #13067493C2semidirect
7. #13067486C2semidirect
8. #13067465C2semidirect
9. #13067451C2semidirect
10. #13067434C2semidirect
11. #13067415C2semidirect
12. #13067036C2semidirect
14. #13066919C2semidirect
15. C11×#1565C2semidirect
221. #1565D11semidirect
491. C11#18077semidirect

Maximal subgroups

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

subgroupindex
#130792222
#130776142
#130775592
#130675172
#130675122
#130674932
#130674862
#130674652
#130674512
#130674342
#130674152
#130670362
#130670272
#130669192
C11×#15652
#1807711