Finite Group Databasebeta

← #14909546

Subgroups — #14909546

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078199C211yesmaximal, characteristic, complemented
2#13078198C211yesmaximal, characteristic, complemented
3#13070826C211yesmaximal, characteristic, complemented
4#13070809C211yesmaximal, characteristic, complemented
5#13070807C211yesmaximal, characteristic, complemented
6#13070715C211yesmaximal, characteristic, complemented
7#13070713C211yesmaximal, characteristic, complemented
8#13070706C211yesmaximal, characteristic, complemented
9#13070703C211yesmaximal, characteristic, complemented
10#13070559C211yesmaximal, characteristic, complemented
11#13070554C211yesmaximal, characteristic, complemented
12#13070542C211yesmaximal, characteristic, complemented
13#13070541C211yesmaximal, characteristic, complemented
14D11×C22⋊C16C211yesmaximal, characteristic, complemented
15C11×#2237C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19#10623158—21no—
20#10623055—21no—
21C11×#467C2211yescharacteristic
22C11×#427C2211yescharacteristic
23#10622801C2211yescharacteristic
24C2×#66893C2211yescharacteristic, complemented
25C2×#66892C2211yescharacteristic, complemented
26#10622728C2211yescharacteristic
27#10622661—21no—
28#10622615—21no—
29C2×#66864C2211yescharacteristic, complemented
30C2×D176C2211yescharacteristic, complemented
31C2×C16×D11C2211yescharacteristic
32C2×C16×D11C2211yescharacteristic
33#10622500C2211yescharacteristic
34#10622500C2211yescharacteristic
35#10622496C2211yescharacteristic
36#10622496C2211yescharacteristic
37#10622496C2211yescharacteristic
38#10622493C2211yescharacteristic
39#10622477—21no—
40#10622477—21no—
41#10622420—21no—
42#10622417—21no—
43C11×#367C2211yescharacteristic, complemented
44C11×#366C2211yescharacteristic, complemented
45C11×#358C2211yescharacteristic, complemented
46C11×#358C2211yescharacteristic, complemented
47C11×C22⋊C16C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic, complemented
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52#10622141C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×#4343—21no—
60C2×#4339—21no—
61C22×C4×D11D411yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—21no—
65C11×#117—21no—
66#66999—21no—
67C2×#4325—21no—
68#66983—21no—
69C22×C11⋊C8D411yescharacteristic
70#66972—41no—
71#66972—41no—
72C2×Dic44C2311yescharacteristic
73#66957—41no—
74#66957—41no—
75C2×D88C2311yescharacteristic
76C2×D88C2311yescharacteristic
77C2×#4314—21no—
78C2×C8×D11—41no—
79C2×C8×D11—41no—
80C2×C8×D11D411yescharacteristic
81C2×C8×D11D411yescharacteristic
82C2×C8×D11C2311yescharacteristic
83C2×C8×D11C2311yescharacteristic
84#66950—21no—
85#66950—21no—
86#66948—21no—
87#66948—21no—
88#66948—21no—
89#66947—41no—
90#66946—41no—
91#66945—21no—
92#66939—41no—
93#66935—41no—
94#66935—41no—
95(C22⋊D11)⋊C4—41no—
96C4×D44—41no—
97C4×D44—41no—
98C2×C11×C16C2311yescharacteristic
99C2×C11×C16C2311yescharacteristic
100C11×#107C2311yescharacteristic
101C11×#107C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#106—21no—
104C11×#103—21no—
105#66899—21no—
106#66893—41no—
107#66892—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—
120C16×D11—41no—
121C16×D11—41no—
122#33757—111nomaximal, Sylow
123C23×D11D811yescharacteristic
124C2×Q8×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C22×Dic11D811yescharacteristic
129#4343—42no—
130#4343—42no—
131#4339—42no—
132#4339—42no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—41no—
136C2×D44—41no—
137C2×D44—41no—
138C2×D44—41no—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11—41no—
142C2×C4×D11—41no—
143C2×C4×D11D811yescharacteristic
144C2×C4×D11D811yescharacteristic
145C2×C4×D11C2×D411yescharacteristic
146C2×C4×D11C2×D411yescharacteristic
147C2×Dic22—21no—
148C11×Q16—21no—
149C11×Q16—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C2×D411yescharacteristic
153C2×C8×C11C2411yescharacteristic
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—41no—
158C11×C22⋊C4—41no—
159C11×C22⋊C4—41no—
160C42×C11—41no—
161#4325—42no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
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—
170C4⋊Dic11—21no—
171C4⋊Dic11—41no—
172C4⋊Dic11—41no—
173Dic11⋊C4—41no—
174C4×Dic11—41no—
175C2×C11⋊C8—41no—
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178Dic44—21no—
179Dic44—21no—
180D88—21no—
181D88—21no—
182D88—21no—
183D88—21no—
184#4314—42no—
185C8×D11—21no—
186C8×D11—21no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—41no—
190C8×D11—41no—
191C11×C16—21no—
192C11×C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3050—111no—
196#3050—111no—
197#2237—111no—
198#2237D1111yescharacteristic, complemented
199#2234—111no—
200#2234—111no—
201#2217—111no—
202#2217—111no—
203#2216—111no—
204#2215—111no—
205#2189—111no—
206#2189—111no—
207#2186—111no—
208#2186—111no—
209C2×C22⋊C16—111no—
210C23×C11C2×D811yescharacteristic
211C22×D11—22no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11C2×D811yescharacteristic
217C22×D11C2×D811yescharacteristic
218Q8×C11—41no—
219Q8×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11C2×D811yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C22⋊D11—82no—
229C22⋊D11—82no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11C2×D811yescharacteristic
234C2×Dic11C2×D811yescharacteristic
235D44—41no—
236D44—41no—
237D44—41no—
238D44—41no—
239D44—82no—
240D44—82no—
241D44—82no—
242D44—82no—
243C4×D11—21no—
244C4×D11—21no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—41no—
248C4×D11—41no—
249C4×D11—82no—
250C4×D11—82no—
251Dic22—41no—
252Dic22—41no—
253C8×C11—21no—
254C8×C11H(5,𝔽2)11yescharacteristic
255C8×C11H(5,𝔽2)11yescharacteristic
256C11⋊C8—21no—
257C11⋊C8—21no—
258C2×#135—111no—
259C2×#135—111no—
260C23×C8—111no—
261#525—221no—
262#525—221no—
263C2×Q32—111no—
264C2×SD32—111no—
265C2×SD32—111no—
266C2×D16—111no—
267C22×C16—111no—
268C22×C16—111no—
269#467—111no—
270#467—111no—
271#467—111no—
272#467C2×D1111yescharacteristic
273#466—111no—
274#466—111no—
275#466—111no—
276#466—111no—
277#465—221no—
278#465—221no—
279#465—221no—
280#465—221no—
281#427—111no—
282#427C2×D1111yescharacteristic
283#416—221no—
284#416—221no—
285#367—111no—
286#367C2×D1111yescharacteristic, complemented
287#366—111no—
288#366C2×D1111yescharacteristic, complemented
289#358—111no—
290#358—111no—
291#358C2×D1111yescharacteristic, complemented
292#358C2×D1111yescharacteristic, complemented
293#357—111no—
294#357—111no—
295#357—111no—
296#357—111no—
297C22⋊C16—111no—
298C22⋊C16—111no—
299C22⋊C16—111no—
300C22⋊C16C2×D1111yescharacteristic
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11C22×D811yescharacteristic
305C2×D11—21no—
306C2×D11—21no—
307C2×D11—21no—
308C2×D11—21no—
309C2×D11—21no—
310C2×D11—44no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11#50812yes—
318C4×C11—21no—
319C4×C11—81no—
320C4×C11—81no—
321C4×C11—81no—
322C4×C11—81no—
323C4×C11#53411yescharacteristic
324C4×C11#57511yescharacteristic
325Dic11—21no—
326Dic11—21no—
327Dic11—81no—
328Dic11—81no—
329C2×#41—221no—
330C2×#41—221no—
331C23×C4—111no—
332#135—441no—
333#135—441no—
334#135—441no—
335#135—441no—
336C2×Q16—111no—
337C2×Q16C22×D1111yescharacteristic
338C2×SD16—221no—
339C2×SD16—221no—
340C2×D8—111no—
341C2×D8—111no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8—111no—
345C22×C8—111no—
346C22×C8—111no—
347C22×C8—441no—
348C22×C8—441no—
349C22×C8C22×D1111yescharacteristic
350#123—441no—
351#123—441no—
352C22⋊Q8—21no—
353C22⋊Q8—221no—
354C22⋊Q8—221no—
355C22⋊Q8—221no—
356#121—221no—
357#121—221no—
358#121—221no—
359#121—221no—
360#120—441no—
361#120—441no—
362C4×D4—441no—
363C4×D4—441no—
364C4×D4—441no—
365C4×D4—441no—
366#117—21no—
367#117—221no—
368Q32—441no—
369SD32—441no—
370SD32—441no—
371D16—441no—
372C2×C16—111no—
373C2×C16—111no—
374C2×C16—441no—
375C2×C16—441no—
376C2×C16C22×D1111yescharacteristic
377C2×C16C22×D1111yescharacteristic
378#107—111no—
379#107C22×D1111yescharacteristic
380#107C22×D1111yescharacteristic
381#107C22×D1111yescharacteristic
382#106—21no—
383#106—221no—
384#103—21no—
385#103—221no—
386#103—221no—
387#103—221no—
388#102—221no—
389#102—221no—
390#102—221no—
391#102—221no—
392C2×C11—41no—
393C2×C11#318611yescharacteristic
394C2×C11C2×#50811yescharacteristic
395C2×C11#341411yescharacteristic
396D11—22no—
397D11—41no—
398D11—161no—
399D11—161no—
400C24—111no—
401#41—442no—
402#41—442no—
403#41—442no—
404#41—442no—
405C2×Q8—21no—
406C2×Q8—221no—
407C2×D4—221no—
408C2×D4—221no—
409C2×D4—441no—
410C2×D4—441no—
411C2×D4—441no—
412C2×D4—441no—
413C2×D4—441no—
414C2×D4—441no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—441no—
421C22×C4—441no—
422C22×C4—441no—
423C22×C4—441no—
424C22×C4D4×D1111yescharacteristic
425Q16—21no—
426Q16—21no—
427Q16—221no—
428Q16—221no—
429SD16—442no—
430SD16—442no—
431D8—221no—
432D8—221no—
433D8—221no—
434D8—221no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—111no—
438C2×C8—111no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—441no—
444C2×C8—441no—
445C2×C8—441no—
446C2×C8D4×D1111yescharacteristic
447C2×C8C23×D1111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—221no—
453C4⋊C4—441no—
454C4⋊C4—441no—
455C4⋊C4—441no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C22⋊C4—441no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C42—41no—
467C42—441no—
468C16—21no—
469C16—21no—
470C16—221no—
471C16—221no—
472C11#3375711yescharacteristic, complemented, Sylow
473C23—111no—
474C23—111no—
475C23—222no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23D8×D1111yescharacteristic
481Q8—41no—
482Q8—41no—
483Q8—441no—
484Q8—441no—
485D4—441no—
486D4—441no—
487D4—441no—
488D4—441no—
489D4—882no—
490D4—882no—
491D4—882no—
492D4—882no—
493D4—882no—
494D4—882no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—111no—
502C2×C4—111no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—882no—
513C2×C4—882no—
514C2×C4D8×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C8—21no—
517C8—221no—
518C8—221no—
519C8#6704211yescharacteristic
520C8#6704211yescharacteristic
521C22—21no—
522C22—21no—
523C22—21no—
524C22—112no—
525C22—221no—
526C22—221no—
527C22—221no—
528C22—221no—
529C22—221no—
530C22—444no—
531C22—881no—
532C22—881no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22C2×D8×D1111yescharacteristic
538C4—21no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—221no—
544C4—221no—
545C4—881no—
546C4—881no—
547C4#1062318411yescharacteristic
548C4#1062330811yescharacteristic
549C2—41no—
550C2—222no—
551C2—441no—
552C2—1761no—
553C2—1761no—
554C2#1307936611yescharacteristic
555C2D11×#50811yescharacteristic
556C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2237C2
socleC22×C11C22×D8
hypercenter#2237D11
hypocenterC11#33757
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
1. #13078199C2semidirect
2. #13078198C2semidirect
3. #13070826C2semidirect
4. #13070809C2semidirect
5. #13070807C2semidirect
6. #13070715C2semidirect
7. #13070713C2semidirect
8. #13070706C2semidirect
9. #13070703C2semidirect
10. #13070559C2semidirect
11. #13070554C2semidirect
12. #13070542C2semidirect
13. #13070541C2semidirect
14. D11×C22⋊C16C2semidirect
15. C11×#2237C2semidirect
24. C2×#66893C22semidirect
25. C2×#66892C22semidirect
29. C2×#66864C22semidirect
30. C2×D176C22semidirect
43. C11×#367C22semidirect
44. C11×#366C22semidirect
45. C11×#358C22semidirect
46. C11×#358C22semidirect
49. #10622147C22semidirect
52. #10622141C22semidirect
53. #10622130C22semidirect
54. #10622129C22semidirect
55. #10622129C22semidirect
56. #10622129C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
198. #2237D11semidirect
286. #367C2×D11semidirect
288. #366C2×D11semidirect
291. #358C2×D11semidirect
292. #358C2×D11semidirect
472. C11#33757semidirect

Maximal subgroups

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

subgroupindex
#130781992
#130781982
#130708262
#130708092
#130708072
#130707152
#130707132
#130707062
#130707032
#130705592
#130705542
#130705422
#130705412
D11×C22⋊C162
C11×#22372
#3375711