Finite Group Databasebeta

← #14909608

Subgroups — #14909608

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078288C211yesmaximal, characteristic, complemented
2#13078259C211yesmaximal, characteristic, complemented
3#13070827C211yesmaximal, characteristic, complemented
4#13070809C211yesmaximal, characteristic, complemented
5#13070796C211yesmaximal, characteristic, complemented
6#13070728C211yesmaximal, characteristic, complemented
7#13070720C211yesmaximal, characteristic, complemented
8#13070713C211yesmaximal, characteristic, complemented
9#13070701C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11#13070541C211yesmaximal, characteristic, complemented
12#13070537C211yesmaximal, characteristic, complemented
13#13070529C211yesmaximal, characteristic, complemented
14#13070228C211yesmaximal, characteristic, complemented
15C11×#2233C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17C2×#66957C2211yescharacteristic, complemented
18C2×#66954C2211yescharacteristic
19#10623138—21no—
20#10623041—21no—
21C11×#466C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic, complemented
23#10622770C2211yescharacteristic
24C2×#66891C2211yescharacteristic
25C2×#66890C2211yescharacteristic
26#10622728C2211yescharacteristic
27#10622652—21no—
28#10622579—21no—
29C2×#66864C2211yescharacteristic
30C2×D176C2211yescharacteristic
31C2×#66862C2211yescharacteristic, complemented
32C2×C16×D11C2211yescharacteristic, complemented
33#10622500C2211yescharacteristic
34#10622500C2211yescharacteristic, complemented
35#10622499—21no—
36#10622499—21no—
37#10622496C2211yescharacteristic
38#10622496C2211yescharacteristic
39#10622496C2211yescharacteristic, complemented
40#10622493C2211yescharacteristic
41#10622395—21no—
42#10622383—21no—
43C11×#367C2211yescharacteristic, complemented
44C11×#367C2211yescharacteristic, complemented
45C11×#357C2211yescharacteristic
46C11×#357C2211yescharacteristic
47C11×C22⋊C16C2211yescharacteristic, complemented
48C22⋊(C11⋊C16)C2211yescharacteristic, complemented
49#10622147C2211yescharacteristic, complemented
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52#10622141C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×#4339—21no—
61C2×#4339D411yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#121—21no—
65C2×C11×C4⋊C4—21no—
66#66993—41no—
67#66991—21no—
68#66990—41no—
69C2×#4323—21no—
70#66983—21no—
71#66983—41no—
72#66983—41no—
73C2×#4318D411yescharacteristic
74D8×D11—41no—
75D8×D11—41no—
76C2×Dic44C2311yescharacteristic
77#66957—41no—
78#66957—41no—
79C2×D88C2311yescharacteristic
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82#66954—41no—
83#66954—41no—
84C2×#4313D411yescharacteristic
85C2×#4313D411yescharacteristic
86C2×C8×D11C2311yescharacteristic
87C2×C8×D11C2311yescharacteristic
88#66950—21no—
89#66950—21no—
90#66950—41no—
91#66948—21no—
92#66948—21no—
93#66948—21no—
94#66948—41no—
95#66945—21no—
96#66938—41no—
97#66935—41no—
98C2×C11×C16C2311yescharacteristic
99C2×C11×C16C2311yescharacteristic
100C11×#107—21no—
101C11×#107C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#107C2311yescharacteristic
104C11×#102—21no—
105#66896—21no—
106#66891—41no—
107#66890—41no—
108#66885—21no—
109#66882C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112#66874—21no—
113#66874—21no—
114#66873—21no—
115#66873—21no—
116#66873—21no—
117#66872—21no—
118#66864—41no—
119D176—41no—
120#66862—41no—
121C16×D11—41no—
122#33764—111nomaximal, Sylow
123C23×D11—41no—
124C2×D4×C11—21no—
125C2×D4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11—41no—
132C2×C22⋊D11D811yescharacteristic
133C2×C22⋊D11D811yescharacteristic
134D4×D11—42no—
135D4×D11—42no—
136#4339—41no—
137#4339—41no—
138#4339—42no—
139#4339—42no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—41no—
143C2×D44—41no—
144C2×D44—41no—
145C2×D44D811yescharacteristic
146C2×C4×D11—41no—
147C2×C4×D11C2×D411yescharacteristic
148C2×C4×D11C2×D411yescharacteristic
149C2×Dic22—21no—
150C2×Dic22D811yescharacteristic
151C11×D8—21no—
152C11×D8—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11C2411yescharacteristic
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—41no—
161C11×C22⋊C4—41no—
162C22⋊Dic11—41no—
163#4323—42no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170(C2×D11)⋊C4—41no—
171C4⋊Dic11—21no—
172C4⋊Dic11—41no—
173C4⋊Dic11—41no—
174C4×Dic11—41no—
175#4318—41no—
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178Dic44—21no—
179Dic44—21no—
180D88—21no—
181D88—21no—
182D88—21no—
183D88—21no—
184#4314—42no—
185#4313—41no—
186#4313—41no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—21no—
190C8×D11—21no—
191C11×C16—21no—
192C11×C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3061—111no—
196#3058—111no—
197#2237—111no—
198#2234—111no—
199#2233D1111yescharacteristic, complemented
200#2232—111no—
201#2220—111no—
202#2218—111no—
203#2217—111no—
204#2215—111no—
205#2187—111no—
206#2186—111no—
207#2186—111no—
208#2184—111no—
209#2113—111no—
210C23×C11—41no—
211C23×C11C2×D811yescharacteristic
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—82no—
215C22×D11—161no—
216C22×D11—161no—
217C22×D11C2×D811yescharacteristic
218C22×D11C2×D811yescharacteristic
219D4×C11—41no—
220D4×C11—41no—
221D4×C11—161no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—161no—
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C22⋊D11—41no—
231C22⋊D11—41no—
232C22⋊D11—82no—
233C22⋊D11—82no—
234C22⋊D11—161no—
235C22⋊D11—161no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11C2×D811yescharacteristic
239C2×Dic11C2×D811yescharacteristic
240D44—41no—
241D44—41no—
242D44—41no—
243D44—41no—
244D44—41no—
245D44—161no—
246D44—161no—
247D44—161no—
248C4×D11—21no—
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—82no—
253Dic22—41no—
254Dic22—41no—
255Dic22—41no—
256C8×C11—21no—
257C8×C11H(5,𝔽2)11yescharacteristic
258C8×C11H(5,𝔽2)11yescharacteristic
259C11⋊C8—21no—
260C11⋊C8—21no—
261C2×#135—111no—
262C22×D8—111no—
263C2×#131—111no—
264#537—221no—
265#535—221no—
266C2×SD32—111no—
267C2×SD32—111no—
268C2×D16—111no—
269C2×D16—111no—
270C2×M32—111no—
271C22×C16—111no—
272#469—221no—
273#469—221no—
274#468—221no—
275#468—221no—
276#467—111no—
277#467—111no—
278#466—111no—
279#466—111no—
280#466—111no—
281#466—111no—
282#466—111no—
283#466C2×D1111yescharacteristic
284#427—111no—
285C2×#107C2×D1111yescharacteristic, complemented
286#418—221no—
287#417—221no—
288#367C2×D1111yescharacteristic, complemented
289#367C2×D1111yescharacteristic, complemented
290#366—111no—
291#366—111no—
292#358—111no—
293#358—111no—
294#357—111no—
295#357—111no—
296#357—111no—
297#357—111no—
298#357C2×D1111yescharacteristic
299#357C2×D1111yescharacteristic
300C22⋊C16—111no—
301C22⋊C16—111no—
302C22⋊C16—111no—
303C22⋊C16C2×D1111yescharacteristic, complemented
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11C22×D811yescharacteristic
311C2×D11—21no—
312C2×D11—21no—
313C2×D11—21no—
314C2×D11—21no—
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—81no—
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C2×D11—164no—
324C4×C11—21no—
325C4×C11—81no—
326C4×C11—81no—
327C4×C11—81no—
328C4×C11#53411yescharacteristic
329C4×C11#57511yescharacteristic
330Dic11—21no—
331Dic11—21no—
332Dic11—81no—
333Dic11—81no—
334C2×#41—111no—
335C2×#41—221no—
336C22×D4—221no—
337#135—441no—
338#135—441no—
339C2×Q16—111no—
340C2×SD16—221no—
341C2×D8—111no—
342C2×D8—111no—
343C2×D8—221no—
344C2×D8—441no—
345C2×D8—441no—
346C2×D8C22×D1111yescharacteristic
347#131—441no—
348#131—441no—
349C2×M16—111no—
350C2×M16—111no—
351C2×M16—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8C22×D1111yescharacteristic
355#127—441no—
356#124—441no—
357C22⋊Q8—221no—
358C22⋊Q8—221no—
359C22⋊Q8—441no—
360#121—21no—
361#121—221no—
362#121—221no—
363#121—221no—
364#121—221no—
365#121—221no—
366#121—441no—
367#121—441no—
368#121—441no—
369#120—441no—
370#120—441no—
371#117—221no—
372C2×C4⋊C4—21no—
373SD32—441no—
374SD32—441no—
375D16—441no—
376D16—441no—
377M32—441no—
378C2×C16—111no—
379C2×C16—111no—
380C2×C16—441no—
381C2×C16C22×D1111yescharacteristic
382C2×C16C22×D1111yescharacteristic
383#107—21no—
384#107—111no—
385#107C22×D1111yescharacteristic
386#107C22×D1111yescharacteristic
387#107C22×D1111yescharacteristic
388#106—221no—
389#103—221no—
390#103—221no—
391#102—21no—
392#102—221no—
393#102—221no—
394#102—221no—
395#102—221no—
396#102—221no—
397C2×C11—41no—
398C2×C11—161no—
399C2×C11#318611yescharacteristic
400C2×C11#341511yescharacteristic
401C2×C11#341611yescharacteristic
402D11—41no—
403D11—41no—
404D11—161no—
405D11—161no—
406C24—441no—
407#41—441no—
408#41—441no—
409#41—442no—
410#41—442no—
411C2×Q8—111no—
412C2×Q8—221no—
413C2×D4—21no—
414C2×D4—41no—
415C2×D4—111no—
416C2×D4—111no—
417C2×D4—111no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—441no—
421C2×D4—441no—
422C2×D4—441no—
423C2×D4—441no—
424C2×D4—442no—
425C2×D4—442no—
426C2×D4—441no—
427C2×D4—441no—
428C2×D4—441no—
429C22×C4—41no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—441no—
433C22×C4D4×D1111yescharacteristic
434Q16—221no—
435Q16—221no—
436SD16—442no—
437D8—21no—
438D8—21no—
439D8—221no—
440D8—221no—
441D8—221no—
442D8—221no—
443D8—442no—
444M16—441no—
445M16—441no—
446M16—441no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8D4×D1111yescharacteristic
456C2×C8C23×D1111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—221no—
462C4⋊C4—441no—
463C4⋊C4—441no—
464C22⋊C4—41no—
465C22⋊C4—441no—
466C22⋊C4—441no—
467C22⋊C4—441no—
468C22⋊C4—441no—
469C22⋊C4—441no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C42—441no—
474C16—21no—
475C16—21no—
476C16—221no—
477C16—221no—
478C11#3376411yescharacteristic, complemented, Sylow
479C23—41no—
480C23—111no—
481C23—111no—
482C23—441no—
483C23—441no—
484C23—882no—
485C23—1761no—
486C23—1761no—
487C23D8×D1111yescharacteristic
488Q8—441no—
489Q8—441no—
490Q8—441no—
491D4—41no—
492D4—41no—
493D4—161no—
494D4—441no—
495D4—441no—
496D4—441no—
497D4—441no—
498D4—441no—
499D4—441no—
500D4—441no—
501D4—882no—
502D4—882no—
503D4—1761no—
504D4—1761no—
505D4—1761no—
506D4—1761no—
507D4—1761no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—111no—
514C2×C4—111no—
515C2×C4—161no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—882no—
523C2×C4D8×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C8—21no—
526C8—221no—
527C8—221no—
528C8#6704211yescharacteristic
529C8#6704211yescharacteristic
530C22—21no—
531C22—21no—
532C22—21no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—221no—
537C22—221no—
538C22—221no—
539C22—221no—
540C22—221no—
541C22—221no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22—881no—
548C22—1764no—
549C22C2×D8×D1111yescharacteristic
550C4—21no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4—221no—
555C4—221no—
556C4—881no—
557C4—881no—
558C4#1062318411yescharacteristic
559C4#1062330811yescharacteristic
560C2—41no—
561C2—161no—
562C2—441no—
563C2—441no—
564C2—1761no—
565C2—1761no—
566C2#1307936611yescharacteristic
567C2#1308175611yescharacteristic
568C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2233C2
socleC22×C11C22×D8
hypercenter#2233D11
hypocenterC11#33764
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
1. #13078288C2semidirect
2. #13078259C2semidirect
3. #13070827C2semidirect
4. #13070809C2semidirect
5. #13070796C2semidirect
6. #13070728C2semidirect
7. #13070720C2semidirect
8. #13070713C2semidirect
9. #13070701C2semidirect
10. #13070546C2semidirect
11. #13070541C2semidirect
12. #13070537C2semidirect
13. #13070529C2semidirect
14. #13070228C2semidirect
15. C11×#2233C2semidirect
17. C2×#66957C22semidirect
22. C2×C11×#107C22semidirect
31. C2×#66862C22semidirect
32. C2×C16×D11C22semidirect
34. #10622500C22semidirect
39. #10622496C22semidirect
43. C11×#367C22semidirect
44. C11×#367C22semidirect
47. C11×C22⋊C16C22semidirect
48. C22⋊(C11⋊C16)C22semidirect
49. #10622147C22semidirect
52. #10622141C22semidirect
53. #10622130C22semidirect
56. #10622129C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
199. #2233D11semidirect
285. C2×#107C2×D11semidirect
288. #367C2×D11semidirect
289. #367C2×D11semidirect
303. C22⋊C16C2×D11semidirect
478. C11#33764semidirect

Maximal subgroups

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

subgroupindex
#130782882
#130782592
#130708272
#130708092
#130707962
#130707282
#130707202
#130707132
#130707012
#130705462
#130705412
#130705372
#130705292
#130702282
C11×#22332
#3376411