Finite Group Databasebeta

← #14742912

Subgroups — #14742912

Order 2816.

746 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079752C211yesmaximal, characteristic, complemented
2#13079568C211yesmaximal, characteristic, complemented
3#13079554C211yesmaximal, characteristic, complemented
4#13079554C211yesmaximal, characteristic, complemented
5#13079536C211yesmaximal, characteristic
6#13068286C211yesmaximal, characteristic, complemented
7#13068273C211yesmaximal, characteristic, complemented
8#13068258C211yesmaximal, characteristic, complemented
9#13068258C211yesmaximal, characteristic, complemented
10#13068245C211yesmaximal, characteristic, complemented
11#13068241C211yesmaximal, characteristic, complemented
12#13068219C211yesmaximal, characteristic, complemented
13#13068209C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#3231C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18#10623008C2211yescharacteristic
19C2×#66927C2211yescharacteristic
20C11×#500C2211yescharacteristic, complemented
21C11×#498C2211yescharacteristic, complemented
22C11×#487C2211yescharacteristic, complemented
23C11×#487C2211yescharacteristic, complemented
24C11×#485—22no—
25C11×#479—22no—
26C11×#431C2211yescharacteristic
27#10622706C2211yescharacteristic, complemented
28#10622705C2211yescharacteristic, complemented
29#10622701C2211yescharacteristic
30#10622701C2211yescharacteristic
31#10622701C2211yescharacteristic
32#10622701C2211yescharacteristic
33#10622701C2211yescharacteristic, complemented
34#10622701C2211yescharacteristic, complemented
35#10622701C2211yescharacteristic, complemented
36#10622698C2211yescharacteristic
37#10622698C2211yescharacteristic
38#10622698C2211yescharacteristic
39#10622698C2211yescharacteristic
40#10622698C2211yescharacteristic, complemented
41#10622692C2211yescharacteristic, complemented
42#10622691C2211yescharacteristic, complemented
43#10622679—22no—
44#10622660—22no—
45#10622659—22no—
46#10622659—22no—
47#10622641—22no—
48#10622640—22no—
49#10622640—22no—
50#10622616—22no—
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53#10622456—22no—
54#10622345—22no—
55#10622308C2211yescharacteristic
56#10622308C2211yescharacteristic
57#10622307C2211yescharacteristic
58#10622307C2211yescharacteristic
59#10622093C2211yescharacteristic, complemented
60#10622092C2211yescharacteristic, complemented
61#10622092C2211yescharacteristic, complemented
62C8×C11⋊C8C2211yescharacteristic, complemented
63C2×#4339—21no—
64C22×D44—21no—
65C22×D44—21no—
66C22×D44—21no—
67C11×C4⋊Q8C2311yescharacteristic
68C11×C4⋊Q8C2311yescharacteristic
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×#125—21no—
72C11×#125—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C11×#117—21no—
82C11×#117—21no—
83C2×C42×C11C2311yescharacteristic
84C2×#4326—22no—
85C2×#4325—22no—
86C2×#4325—22no—
87C2×#4325—22no—
88C2×#4325—22no—
89C2×#4325—22no—
90#66983—21no—
91#66983—21no—
92C2×D88—22no—
93C2×D88—22no—
94#66928—21no—
95#66927—21no—
96#66927—21no—
97#66927—21no—
98#66927C2311yescharacteristic
99#66927C2311yescharacteristic
100#66927C2311yescharacteristic
101C4×D44—21no—
102C4×D44—21no—
103#66922C2311yescharacteristic
104C11×#107—22no—
105C11×#106—22no—
106C11×C4⋊C8D412yes—
107C11×#103—22no—
108C11×#103—22no—
109C11×C22⋊C8D412yes—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C22⋊(C11⋊C8)D412yes—
113C22⋊(C11⋊C8)D412yes—
114#66885—22no—
115#66885—22no—
116#66874—22no—
117#66873—22no—
118#66873—22no—
119#66873—22no—
120#66873—22no—
121#66873—22no—
122#66873—22no—
123#66873—22no—
124#66872—22no—
125#66871—22no—
126C4⋊(C11⋊C8)D412yes—
127C4⋊(C11⋊C8)D412yes—
128C4×C11⋊C8C2311yescharacteristic
129C4×C11⋊C8C2311yescharacteristic
130C4×C11⋊C8C2311yescharacteristic
131C4×C11⋊C8C2311yescharacteristic
132#19737—111nomaximal, Sylow
133C23×D11—41no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C2×C22⋊D11—41no—
142#4339—82no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—41no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—82no—
156C2×D44—82no—
157C2×D44—82no—
158C2×C4×D11—41no—
159C2×Dic22—21no—
160C2×C8×C11C2×D412yes—
161C2×C8×C11C2×D412yes—
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⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—41no—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C42×C11—41no—
177C42×C11—41no—
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2411yescharacteristic
182#4326—82no—
183#4325—82no—
184#4325—82no—
185#4325—82no—
186#4325—82no—
187#4325—82no—
188(C2×D11)⋊C4—41no—
189(C2×D11)⋊C4—41no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C2×C11⋊C8C2×D412yes—
193C2×C11⋊C8C2×D412yes—
194C2×C11⋊C8C2×D412yes—
195C2×C11⋊C8C2×D412yes—
196D88—82no—
197D88—82no—
198#3231D1111yescharacteristic, complemented
199#3228—111no—
200#3210—111no—
201#3208—111no—
202#3208—111no—
203#3205—111no—
204#1722—111no—
205#1720—111no—
206#1717—111no—
207#1717—111no—
208#1715—111no—
209#1714—111no—
210#1708—111no—
211#1706—111no—
212#1454—111no—
213C23×C11#12711yescharacteristic
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—82no—
218C22×D11—82no—
219C22×D11—82no—
220Q8×C11—42no—
221Q8×C11—42no—
222Q8×C11—42no—
223Q8×C11—42no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11#12711yescharacteristic
232C2×C4×C11#12711yescharacteristic
233C2×C4×C11#12711yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C22⋊D11—82no—
238C2×Dic11—41no—
239D44—42no—
240D44—42no—
241D44—42no—
242D44—42no—
243D44—42no—
244D44—42no—
245D44—42no—
246D44—42no—
247D44—42no—
248D44—82no—
249D44—82no—
250D44—82no—
251C4×D11—82no—
252Dic22—42no—
253C8×C11—22no—
254C8×C11—22no—
255C11⋊C8—22no—
256C11⋊C8—22no—
257C11⋊C8—22no—
258C11⋊C8—22no—
259#533C2×D1111yescharacteristic
260#533C2×D1111yescharacteristic
261#532—111no—
262C2×#127—111no—
263#500—111no—
264#500C2×D1111yescharacteristic, complemented
265#498—111no—
266#498C2×D1111yescharacteristic, complemented
267#494—111no—
268#493—111no—
269#493—111no—
270#492—111no—
271#492—111no—
272#492—111no—
273#492—111no—
274#492—111no—
275#487—111no—
276#487C2×D1111yescharacteristic, complemented
277#487C2×D1111yescharacteristic, complemented
278#486—111no—
279#486—111no—
280#486—111no—
281#486—111no—
282#486—111no—
283#486—111no—
284#486—111no—
285#486—111no—
286#486—111no—
287#485—22no—
288#482—222no—
289#479—22no—
290#478—222no—
291#464—222no—
292#460—222no—
293#460—222no—
294#459—222no—
295#452—222no—
296#450—222no—
297#450—222no—
298#447—222no—
299#431—111no—
300#431—111no—
301#431C2×D1111yescharacteristic
302#322—111no—
303#322—111no—
304#322—111no—
305C82—111no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11C2×#12711yescharacteristic
310C2×D11—81no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—81no—
318C2×D11—81no—
319C2×D11—164no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—81no—
324C4×C11—81no—
325C4×C11—81no—
326C4×C11—81no—
327C4×C11#57612yes—
328C4×C11#57712yes—
329C4×C11#57712yes—
330Dic11—81no—
331C2×#41—221no—
332C22×D4—221no—
333C22×D4—221no—
334C22×D4—221no—
335C2×Q16—222no—
336C2×SD16—222no—
337C2×SD16—222no—
338C2×SD16—222no—
339C2×SD16—222no—
340C2×SD16—222no—
341C2×D8—222no—
342C2×D8—222no—
343C4⋊Q8—111no—
344C4⋊Q8C22×D1111yescharacteristic
345C4⋊Q8C22×D1111yescharacteristic
346C4⋊Q8C22×D1111yescharacteristic
347C4⋊Q8C22×D1111yescharacteristic
348#127—111no—
349#127—111no—
350#127—111no—
351#127—221no—
352#127—221no—
353#127—221no—
354#125—21no—
355#125—21no—
356#124—221no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361#121—221no—
362#121—221no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×D4—221no—
368C4×D4—221no—
369#117—21no—
370#117—21no—
371C2×C42C22×D1111yescharacteristic
372#107—22no—
373#107—222no—
374#106—22no—
375#106—222no—
376C4⋊C8—112no—
377C4⋊C8—112no—
378C4⋊C8C22⋊D1112yes—
379#103—22no—
380#103—22no—
381#103—222no—
382#102—222no—
383#102—222no—
384#102—222no—
385#102—222no—
386#102—222no—
387#102—222no—
388#102—222no—
389#102—222no—
390#102—222no—
391C22⋊C8—112no—
392C22⋊C8—112no—
393C22⋊C8C22⋊D1112yes—
394C4×C8—111no—
395C4×C8—111no—
396C4×C8—111no—
397C4×C8—111no—
398C4×C8C22×D1111yescharacteristic
399C4×C8C22×D1111yescharacteristic
400C2×C11—41no—
401C2×C11#315411yescharacteristic
402C2×C11#315411yescharacteristic
403C2×C11#315511yescharacteristic
404D11—161no—
405D11—161no—
406D11—161no—
407C24—441no—
408#41—882no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—441no—
424C2×D4—441no—
425C2×D4—441no—
426C2×D4—441no—
427C2×D4—882no—
428C2×D4—882no—
429C2×D4—882no—
430C22×C4—441no—
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434Q16—882no—
435SD16—882no—
436SD16—882no—
437SD16—882no—
438SD16—882no—
439SD16—882no—
440D8—882no—
441D8—882no—
442C2×C8—112no—
443C2×C8—112no—
444C2×C8—112no—
445C2×C8—112no—
446C2×C8C2×C22⋊D1112yes—
447C2×C8C2×C22⋊D1112yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C42—41no—
467C42—41no—
468C42D4×D1111yescharacteristic
469C42D4×D1111yescharacteristic
470C42C2×C22⋊D1111yescharacteristic
471C42C23×D1111yescharacteristic
472C11#1973711yescharacteristic, complemented, Sylow
473C23—441no—
474C23—441no—
475C23—441no—
476C23—882no—
477C23—882no—
478C23—882no—
479C23#6699311yescharacteristic
480Q8—42no—
481Q8—42no—
482Q8—42no—
483Q8—42no—
484Q8—442no—
485D4—442no—
486D4—442no—
487D4—442no—
488D4—442no—
489D4—442no—
490D4—442no—
491D4—442no—
492D4—442no—
493D4—442no—
494D4—882no—
495D4—882no—
496D4—882no—
497D4—882no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—441no—
506C2×C4—882no—
507C2×C4#6699311yescharacteristic
508C2×C4#6699311yescharacteristic
509C2×C4#6699311yescharacteristic
510C2×C4C2×D4×D1111yescharacteristic
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4C22×C22⋊D1111yescharacteristic
513C8—22no—
514C8—22no—
515C8—222no—
516C8—222no—
517C8—222no—
518C8—222no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—881no—
523C22—881no—
524C22—881no—
525C22—881no—
526C22—881no—
527C22—881no—
528C22—881no—
529C22—881no—
530C22—881no—
531C22—1764no—
532C22C2×#6699311yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—81no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—881no—
541C4#1062330012yes—
542C4#1062330912yes—
543C4#1062336812yes—
544C2—41no—
545C2—1761no—
546C2—1761no—
547C2—1761no—
548C2#1307909411yescharacteristic
549C2#1307909511yescharacteristic
550C2#1307910311yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3231C2
socleC22×C11C2×#127
prime radical#13079536C2
hypercenter#3231D11
hypocenterC11#19737
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
1. #13079752C2semidirect
2. #13079568C2semidirect
3. #13079554C2semidirect
4. #13079554C2semidirect
6. #13068286C2semidirect
7. #13068273C2semidirect
8. #13068258C2semidirect
9. #13068258C2semidirect
10. #13068245C2semidirect
11. #13068241C2semidirect
12. #13068219C2semidirect
13. #13068209C2semidirect
14. #13066916C2semidirect
15. C11×#3231C2semidirect
20. C11×#500C22semidirect
21. C11×#498C22semidirect
22. C11×#487C22semidirect
23. C11×#487C22semidirect
27. #10622706C22semidirect
28. #10622705C22semidirect
33. #10622701C22semidirect
34. #10622701C22semidirect
35. #10622701C22semidirect
40. #10622698C22semidirect
41. #10622692C22semidirect
42. #10622691C22semidirect
59. #10622093C22semidirect
60. #10622092C22semidirect
61. #10622092C22semidirect
62. C8×C11⋊C8C22semidirect
198. #3231D11semidirect
264. #500C2×D11semidirect
266. #498C2×D11semidirect
276. #487C2×D11semidirect
277. #487C2×D11semidirect
472. C11#19737semidirect

Maximal subgroups

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

subgroupindex
#130797522
#130795682
#130795542
#130795362
#130682862
#130682732
#130682582
#130682452
#130682412
#130682192
#130682092
#130669162
C11×#32312
#1973711