Finite Group Databasebeta

← #14807524

Subgroups — #14807524

Order 2816.

1294 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079069C211yesmaximal, characteristic, complemented
2#13078992C211yesmaximal, characteristic, complemented
3#13073562C211yesmaximal, characteristic, complemented
4#13069629C214yesmaximal, complemented
5#13069561C211yesmaximal, characteristic, complemented
6#13069536C211yesmaximal, characteristic, complemented
7#13068992C214yesmaximal, complemented
8C4×#66897C211yesmaximal, characteristic, complemented
9C11×#3506C211yesmaximal, characteristic, complemented
10C11×#559—22no—
11C11×#556—21no—
12C11×#555—21no—
13C11×#553—22no—
14C11×#550—21no—
15C11×#547—21no—
16C11×#538—22no—
17C11×#535C2212yes—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#525—22no—
21C11×#520C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23C2×#67002C2214yes—
24C2×#66993C2212yes—
25C2×#66983—22no—
26C2×#66927C2211yescharacteristic
27C2×#66901C2214yes—
28C2×#66897C2212yes—
29#10622701—21no—
30#10622701—21no—
31#10622698—21no—
32#10622686—21no—
33#10622680—22no—
34#10622671—22no—
35#10622614C2214yes—
36#10622601C2212yes—
37#10622573—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622170C2214yes—
42#10622168C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41C2312yes—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11D412yes—
47C22×C22⋊D11—24no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44C2312yes—
51C11×C4⋊Q8D411yescharacteristic, complemented
52C11×C4⋊Q8D411yescharacteristic, complemented
53C11×C4⋊Q8D411yescharacteristic, complemented
54C11×#127—22no—
55C11×#127D411yescharacteristic, complemented
56C11×#126—24no—
57C11×#125D412yescomplemented
58C11×#124—24no—
59C11×#124—22no—
60C11×#124D412yescomplemented
61C11×#123—24no—
62C11×#123—24no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×#121—22no—
67C11×#121—24no—
68C11×#121—21no—
69C11×#121—21no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#120—24no—
73C4×Q8×C11—22no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×D4×C11—24no—
77C4×D4×C11—22no—
78C4×D4×C11—24no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117C2312yes—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4D412yes—
91C2×C42×C11C2311yescharacteristic
92#67002—28no—
93#67002—44no—
94C2×#4325—24no—
95#66993—44no—
96C2×#4323—24no—
97#66983—48no—
98C2×(C2×D11)⋊C4—24no—
99C2×C4⋊Dic11—21no—
100C2×C4×Dic11C2312yes—
101C2×#4318C2312yes—
102C2×#4318C2312yes—
103#66927—21no—
104#66927—21no—
105#66927—21no—
106#66927—21no—
107#66901—44no—
108#66897—24no—
109C11⋊#95—21no—
110#66873—24no—
111#66873—24no—
112#66867—21no—
113#66867—21no—
114C4×C11⋊C8—21no—
115C4×C11⋊C8—21no—
116#25622—111nomaximal, Sylow
117C24×C11C2×D412yes—
118C23×D11—22no—
119C11×#41—24no—
120C11×#41—24no—
121C11×#41—84no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11C2×D412yes—
125C2×D4×C11—22no—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—44no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—48no—
145C2×C22⋊D11—48no—
146C2×C22⋊D11—84no—
147C22×Dic11—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—24no—
151C2×D44—24no—
152C2×D44—44no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44—41no—
157C2×D44—82no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C42×C11—24no—
178C42×C11—22no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183#4325—48no—
184#4323—48no—
185(C2×D11)⋊C4—48no—
186C4⋊Dic11—24no—
187C4×Dic11—24no—
188#4318—22no—
189#4318—22no—
190#4318—22no—
191#4318#4114yescomplemented
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194#3506D1111yescharacteristic, complemented
195#3151—111no—
196#3138—111no—
197#2541—111no—
198#2002—114no—
199#1986—111no—
200#1980—111no—
201#1883—114no—
202C4×#100—111no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11C22×D411yescharacteristic
210C22×D11—44no—
211C22×D11—44no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215Q8×C11—24no—
216Q8×C11—42no—
217Q8×C11—81no—
218D4×C11—24no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—81no—
225D4×C11—84no—
226D4×C11—84no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—41no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11—42no—
236C2×C4×C11—82no—
237C2×C4×C11—84no—
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4112yes—
245C2×C4×C11H(5,𝔽2)12yes—
246C22⋊D11—816no—
247C2×Dic11—24no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250D44—44no—
251D44—44no—
252D44—82no—
253D44—82no—
254D44—82no—
255D44—82no—
256C11⋊C8—24no—
257C11⋊C8—42no—
258C2×AGL(1,ℤ/8)—114no—
259#559—22no—
260#556—21no—
261#555—21no—
262#553—22no—
263#550—21no—
264#547—21no—
265#538—22no—
266#535C2×D1112yes—
267#533C2×D1111yescharacteristic
268#532C2×D1111yescharacteristic
269C2×#127—112no—
270C2×#127—111no—
271#525—22no—
272C2×#121—222no—
273#520C2×D1112yes—
274C2×C4×D4C2×D1111yescharacteristic
275#496—222no—
276#493—221no—
277#492—221no—
278#490—222no—
279#486—221no—
280#486—221no—
281C2×#104—114no—
282#418—114no—
283C2×#100—112no—
284C4×M16—111no—
285C4×M16—111no—
286#392—222no—
287#390—112no—
288C4×C4⋊C4—111no—
289#343—112no—
290#339—114no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—44no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—82no—
301C22×C11C2×#12011yescharacteristic
302C22×C11#53211yescharacteristic
303C22×C11#53511yescharacteristic
304C2×D11—84no—
305C2×D11—84no—
306C2×D11—82no—
307C2×D11—82no—
308C2×D11—82no—
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11#45312yes—
317C4×C11#54612yes—
318C4×C11#55012yes—
319Dic11—44no—
320C2×#41—22no—
321C2×#41C22×D1112yes—
322C22×D4—112no—
323C22×D4—224no—
324C22×D4—221no—
325C22×D4—221no—
326C22×D4C22×D1111yescharacteristic
327C23×C4C22⋊D1112yes—
328AGL(1,ℤ/8)—228no—
329AGL(1,ℤ/8)—444no—
330C2×SD16—224no—
331C2×D8—224no—
332C2×M16—112no—
333C2×M16—112no—
334C4⋊Q8C22⋊D1111yescharacteristic, complemented
335C4⋊Q8C22⋊D1111yescharacteristic, complemented
336C4⋊Q8C22⋊D1111yescharacteristic, complemented
337#127—22no—
338#127—221no—
339#127—221no—
340#127—221no—
341#127—221no—
342#127—444no—
343#127C22⋊D1111yescharacteristic, complemented
344#126—24no—
345#125C22⋊D1112yescomplemented
346#124—24no—
347#124—22no—
348#124C22⋊D1112yescomplemented
349#123—24no—
350#123—24no—
351C22⋊Q8—22no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354#121—22no—
355#121—24no—
356#121—21no—
357#121—21no—
358#121—22no—
359#121—22no—
360#121—448no—
361#120—24no—
362C4×Q8—22no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×D4—24no—
366C4×D4—22no—
367C4×D4—24no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374#117—22no—
375#117—22no—
376#117C22×D1112yes—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—224no—
381C2×C22⋊C4C22⋊D1112yes—
382C2×C42—112no—
383C2×C42C22×D1111yescharacteristic
384#104—444no—
385#102—224no—
386#102—224no—
387#100—224no—
388#97—221no—
389#97—221no—
390C4×C8—221no—
391C4×C8—221no—
392#95—221no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—82no—
396C2×C11—82no—
397C2×C11#243111yescharacteristic
398C2×C11C2×#45311yescharacteristic
399C2×C11#302111yescharacteristic
400D11—162no—
401C24—222no—
402C24C2×C22⋊D1112yes—
403#41—24no—
404#41—24no—
405#41—84no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C2×C22⋊D1112yes—
409C2×D4—22no—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—224no—
419C2×D4—224no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4—444no—
423C2×D4—448no—
424C2×D4—448no—
425C2×D4—441no—
426C2×D4—441no—
427C2×D4—441no—
428C2×D4—441no—
429C2×D4—882no—
430C2×D4—884no—
431C2×D4C2×C22⋊D1112yes—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—222no—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1112yes—
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C23×D1111yescharacteristic
442SD16—448no—
443D8—448no—
444M16—114no—
445M16—222no—
446M16—222no—
447M16—222no—
448C2×C8—222no—
449C2×C8—222no—
450C4⋊C4—24no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—224no—
460C4⋊C4C2×C22⋊D1112yes—
461C4⋊C4C2×C22⋊D1112yes—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—448no—
471C42—24no—
472C42—22no—
473C42—224no—
474C42C2×C22⋊D1111yescharacteristic
475C42C2×C22⋊D1111yescharacteristic
476C42C2×C22⋊D1111yescharacteristic
477C42C2×C22⋊D1111yescharacteristic
478C11#2562211yescharacteristic, complemented, Sylow
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—42no—
484C23—42no—
485C23—444no—
486C23—444no—
487C23—442no—
488C23—442no—
489C23—442no—
490C23C22×C22⋊D1111yescharacteristic
491Q8—24no—
492Q8—42no—
493Q8—81no—
494D4—24no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—42no—
500D4—81no—
501D4—84no—
502D4—84no—
503D4—444no—
504D4—444no—
505D4—882no—
506D4—882no—
507D4—882no—
508D4—8816no—
509D4—882no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—82no—
520C2×C4—84no—
521C2×C4—224no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4#6700611yescharacteristic
525C2×C4#6700611yescharacteristic
526C2×C4#6700611yescharacteristic
527C2×C4#6700611yescharacteristic
528C2×C4#41×D1112yes—
529C2×C4#6704212yes—
530C2×C4C22×C22⋊D1111yescharacteristic
531C2×C4C22×C22⋊D1111yescharacteristic
532C8—224no—
533C8—442no—
534C22—21no—
535C22—21no—
536C22—44no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—82no—
544C22—884no—
545C22—884no—
546C22—882no—
547C22—882no—
548C22—882no—
549C22#1062336111yescharacteristic
550C22#1062336311yescharacteristic
551C22C2×#6700611yescharacteristic
552C4—21no—
553C4—21no—
554C4—21no—
555C4—42no—
556C4—42no—
557C4—42no—
558C4—42no—
559C4—444no—
560C4#1062285412yes—
561C4#1062336012yes—
562C4#1062336512yes—
563C2—21no—
564C2—21no—
565C2—82no—
566C2—82no—
567C2—1762no—
568C2#1307223111yescharacteristic
569C2C2×#1062285411yescharacteristic
570C2#1307798811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3506C2
socleC22×C11C2×#120
hypercenter#3506D11
hypocenterC11#25622
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13079069C2semidirect
2. #13078992C2semidirect
3. #13073562C2semidirect
4. #13069629C2semidirect
5. #13069561C2semidirect
6. #13069536C2semidirect
7. #13068992C2semidirect
8. C4×#66897C2semidirect
9. C11×#3506C2semidirect
51. C11×C4⋊Q8D4semidirect
52. C11×C4⋊Q8D4semidirect
53. C11×C4⋊Q8D4semidirect
55. C11×#127D4semidirect
57. C11×#125D4semidirect
60. C11×#124D4semidirect
191. #4318#41semidirect
194. #3506D11semidirect
334. C4⋊Q8C22⋊D11semidirect
335. C4⋊Q8C22⋊D11semidirect
336. C4⋊Q8C22⋊D11semidirect
343. #127C22⋊D11semidirect
345. #125C22⋊D11semidirect
348. #124C22⋊D11semidirect
478. C11#25622semidirect

Maximal subgroups

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

subgroupindex
#130790692
#130789922
#130735622
#130696292
#130695612
#130695362
#130689922
C4×#668972
C11×#35062
#2562211