Finite Group Databasebeta

← #14909657

Subgroups — #14909657

Order 2816.

576 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078286C211yesmaximal, characteristic, complemented
2#13070813C211yesmaximal, characteristic, complemented
3#13070811C211yesmaximal, characteristic, complemented
4#13070801C211yesmaximal, characteristic, complemented
5#13070799C211yesmaximal, characteristic, complemented
6#13070722C211yesmaximal, characteristic, complemented
7#13070717C211yesmaximal, characteristic, complemented
8#13070714C211yesmaximal, characteristic, complemented
9#13070710C211yesmaximal, characteristic, complemented
10#13070556C211yesmaximal, characteristic, complemented
11#13070554C211yesmaximal, characteristic, complemented
12#13070539C211yesmaximal, characteristic, complemented
13#13070537C211yesmaximal, characteristic, complemented
14#13070230C211yesmaximal, characteristic, complemented
15C11×#3061C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C11×#537—21no—
19#10623364—21no—
20C2×#66957C2211yescharacteristic
21C11×#468—21no—
22C11×#468—21no—
23C11×#467C2211yescharacteristic
24C11×#467C2211yescharacteristic
25C11×#466C2211yescharacteristic
26C11×#466C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C11×#417—21no—
29C2×#66893C2211yescharacteristic
30C2×#66892C2211yescharacteristic
31C2×#66891C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622747—21no—
34#10622747—21no—
35#10622746—21no—
36#10622729C2211yescharacteristic
37#10622729C2211yescharacteristic
38#10622728C2211yescharacteristic
39#10622728C2211yescharacteristic
40C2×#66882C2211yescharacteristic
41C2×#66876C2211yescharacteristic
42C22×C11⋊C16C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49C22⋊(C11⋊C16)C2211yescharacteristic
50C22⋊(C11⋊C16)C2211yescharacteristic
51#10622130C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C2×C11×#41—21no—
60C2×C11×#41D411yescharacteristic
61C2×#4339—21no—
62C11×#135—41no—
63C11×#135—41no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×SD16—21no—
66C2×C11×D8C2311yescharacteristic
67C11×#131—41no—
68C11×#131—41no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—41no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—41no—
81C11×#121—41no—
82C11×#121—41no—
83C2×C11×C4⋊C4—21no—
84#66999—41no—
85#66992—41no—
86#66992—41no—
87#66991—41no—
88#66983—21no—
89#66983—21no—
90C2×C4⋊Dic11—21no—
91#66977—21no—
92#66977—21no—
93C2×Dic44C2311yescharacteristic
94#66957—41no—
95#66957—41no—
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C11×#107—21no—
99C11×#107C2311yescharacteristic
100C11×#107C2311yescharacteristic
101C11×#103—21no—
102C11×#103—21no—
103C11×#102—21no—
104C11×#102—21no—
105#66893—41no—
106#66892—41no—
107#66891—41no—
108#66890—41no—
109#66885—21no—
110#66885—21no—
111#66882—21no—
112#66882C2311yescharacteristic
113#66882C2311yescharacteristic
114#66880—21no—
115#66880—21no—
116#66876—41no—
117C2×C11⋊C16—41no—
118C2×C11⋊C16C2311yescharacteristic
119C2×C11⋊C16C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#33770—111nomaximal, Sylow
123C11×#41—41no—
124C11×#41—41no—
125C11×#41—42no—
126C11×#41—42no—
127C2×Q8×C11—21no—
128C2×Q8×C11D811yescharacteristic
129C2×D4×C11—21no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11D811yescharacteristic
134C2×D4×C11D811yescharacteristic
135C2×D4×C11D811yescharacteristic
136C22×C4×C11—41no—
137C22×C4×C11—41no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11—41no—
144C22×Dic11—41no—
145#4339—42no—
146#4339—42no—
147C2×D44—21no—
148C2×C4×D11—41no—
149C2×Dic22—21no—
150C11×Q16—21no—
151C11×Q16—21no—
152C11×SD16—42no—
153C11×D8—21no—
154C11×D8—21no—
155C11×M16—41no—
156C11×M16—41no—
157C11×M16—41no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C22⋊C4—41no—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—41no—
184Dic11⋊C4—41no—
185Dic11⋊C4—41no—
186Dic44—21no—
187Dic44—21no—
188D88—21no—
189D88—21no—
190#4314—42no—
191C11⋊C16—21no—
192C11⋊C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3061—111no—
196#3061D1111yescharacteristic, complemented
197#2235—111no—
198#2235—111no—
199#2233—111no—
200#2233—111no—
201#2219—111no—
202#2218—111no—
203#2217—111no—
204#2217—111no—
205#2189—111no—
206#2189—111no—
207#2186—111no—
208#2186—111no—
209#2113—111no—
210C23×C11—41no—
211C23×C11C2×D811yescharacteristic
212C23×C11C2×D811yescharacteristic
213C23×C11C2×D811yescharacteristic
214C22×D11—41no—
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—41no—
218D4×C11—41no—
219D4×C11—41no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—82no—
224D4×C11—161no—
225D4×C11—161no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—82no—
236C2×C4×C11—161no—
237C2×C4×C11C2×D811yescharacteristic
238C2×C4×C11C2×D811yescharacteristic
239C2×C4×C11C2×D811yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C22⋊D11—82no—
242C22⋊D11—161no—
243C22⋊D11—161no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—161no—
248D44—41no—
249D44—41no—
250C4×D11—82no—
251Dic22—41no—
252Dic22—41no—
253C8×C11—21no—
254C8×C11—21no—
255C8×C11—21no—
256C8×C11H(5,𝔽2)11yescharacteristic
257C8×C11H(5,𝔽2)11yescharacteristic
258C2×#135—111no—
259C2×#135C2×D1111yescharacteristic
260C2×#131C2×D1111yescharacteristic
261#537—21no—
262#537—221no—
263C2×Q32—111no—
264C2×SD32—111no—
265C2×SD32—111no—
266C2×D16—111no—
267C2×M32—111no—
268C22×C16—111no—
269#468—21no—
270#468—21no—
271#468—221no—
272#468—221no—
273#467—111no—
274#467—111no—
275#467C2×D1111yescharacteristic
276#467C2×D1111yescharacteristic
277#466—111no—
278#466—111no—
279#466C2×D1111yescharacteristic
280#466C2×D1111yescharacteristic
281C2×#107—111no—
282C2×#107C2×D1111yescharacteristic
283#417—21no—
284#417—221no—
285#367—111no—
286#367—111no—
287#367—111no—
288#367—111no—
289#358—111no—
290#358—111no—
291#358—111no—
292#358—111no—
293#357—111no—
294#357—111no—
295#357—111no—
296#357—111no—
297C22⋊C16—111no—
298C22⋊C16—111no—
299C22⋊C16—111no—
300C22⋊C16—111no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11C22×D811yescharacteristic
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—21no—
320C4×C11—81no—
321C4×C11—81no—
322C4×C11—81no—
323C4×C11#53411yescharacteristic
324C4×C11#57511yescharacteristic
325Dic11—81no—
326Dic11—81no—
327Dic11—81no—
328C2×#41—21no—
329C2×#41—221no—
330C2×#41C22⋊D1111yescharacteristic
331#135—41no—
332#135—41no—
333#135—441no—
334#135—441no—
335C2×Q16—111no—
336C2×Q16C22×D1111yescharacteristic
337C2×SD16—21no—
338C2×SD16—221no—
339C2×D8—111no—
340C2×D8C22×D1111yescharacteristic
341#131—41no—
342#131—41no—
343C2×M16C22⋊D1111yescharacteristic
344C2×M16C22⋊D1111yescharacteristic
345C2×M16C22⋊D1111yescharacteristic
346C22×C8C22×D1111yescharacteristic
347C22×C8C22×D1111yescharacteristic
348C22×C8C22×D1111yescharacteristic
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8—41no—
352C22⋊Q8—221no—
353C22⋊Q8—221no—
354C22⋊Q8—441no—
355#121—21no—
356#121—21no—
357#121—41no—
358#121—41no—
359#121—41no—
360#121—221no—
361#121—221no—
362#121—441no—
363#121—441no—
364#121—441no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—221no—
367Q32—441no—
368SD32—441no—
369SD32—441no—
370D16—441no—
371M32—441no—
372C2×C16—111no—
373C2×C16—111no—
374C2×C16—111no—
375C2×C16—111no—
376C2×C16—441no—
377#107—21no—
378#107—111no—
379#107—111no—
380#107—221no—
381#107C22×D1111yescharacteristic
382#107C22×D1111yescharacteristic
383#103—21no—
384#103—21no—
385#103—221no—
386#103—221no—
387#102—21no—
388#102—21no—
389#102—221no—
390#102—221no—
391C2×C11—41no—
392C2×C11—41no—
393C2×C11—41no—
394C2×C11—161no—
395C2×C11#318611yescharacteristic
396C2×C11#341611yescharacteristic
397C2×C11#341611yescharacteristic
398D11—161no—
399#41—41no—
400#41—41no—
401#41—42no—
402#41—42no—
403#41—442no—
404#41—442no—
405C2×Q8—21no—
406C2×Q8—221no—
407C2×Q8#432311yescharacteristic
408C2×D4—21no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—221no—
413C2×D4—441no—
414C2×D4—441no—
415C2×D4—441no—
416C2×D4#432311yescharacteristic
417C2×D4#432311yescharacteristic
418C2×D4#432311yescharacteristic
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—441no—
422C22×C4—441no—
423C22×C4C2×C22⋊D1111yescharacteristic
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C2×C22⋊D1111yescharacteristic
426Q16—21no—
427Q16—21no—
428Q16—221no—
429Q16—221no—
430SD16—42no—
431SD16—442no—
432D8—21no—
433D8—21no—
434D8—221no—
435D8—221no—
436M16—41no—
437M16—41no—
438M16—41no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8C2×C22⋊D1111yescharacteristic
446C2×C8C2×C22⋊D1111yescharacteristic
447C2×C8C2×C22⋊D1111yescharacteristic
448C2×C8C23×D1111yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—441no—
457C4⋊C4—441no—
458C4⋊C4—441no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—441no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C22⋊C4—441no—
467C16—221no—
468C16—221no—
469C16—221no—
470C16—221no—
471C11#3377011yescharacteristic, complemented, Sylow
472C23—41no—
473C23—441no—
474C23C2×#432311yescharacteristic
475C23C2×#432311yescharacteristic
476C23C2×#432311yescharacteristic
477Q8—41no—
478Q8—41no—
479Q8—41no—
480Q8—441no—
481Q8—441no—
482D4—41no—
483D4—41no—
484D4—41no—
485D4—41no—
486D4—41no—
487D4—82no—
488D4—161no—
489D4—161no—
490D4—441no—
491D4—441no—
492D4—882no—
493D4—1761no—
494D4—1761no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—82no—
505C2×C4—161no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—882no—
510C2×C4—1761no—
511C2×C4C2×#432311yescharacteristic
512C2×C4C2×#432311yescharacteristic
513C2×C4C2×#432311yescharacteristic
514C2×C4C22×C22⋊D1111yescharacteristic
515C8—21no—
516C8—21no—
517C8—21no—
518C8#6703711yescharacteristic
519C8#6703711yescharacteristic
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22—881no—
533C22—881no—
534C22—881no—
535C22C22×#432311yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—881no—
543C4—881no—
544C4—881no—
545C4#1062333511yescharacteristic
546C4#1062335311yescharacteristic
547C2—41no—
548C2—41no—
549C2—41no—
550C2—161no—
551C2—1761no—
552C2#1307936411yescharacteristic
553C2#1308176011yescharacteristic
554C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3061C2
socleC22×C11C22×D8
hypercenter#3061D11
hypocenterC11#33770
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3061

Complements

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

NH ≅ G/Ntype
1. #13078286C2semidirect
2. #13070813C2semidirect
3. #13070811C2semidirect
4. #13070801C2semidirect
5. #13070799C2semidirect
6. #13070722C2semidirect
7. #13070717C2semidirect
8. #13070714C2semidirect
9. #13070710C2semidirect
10. #13070556C2semidirect
11. #13070554C2semidirect
12. #13070539C2semidirect
13. #13070537C2semidirect
14. #13070230C2semidirect
15. C11×#3061C2semidirect
196. #3061D11semidirect
471. C11#33770semidirect

Maximal subgroups

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

subgroupindex
#130782862
#130708132
#130708112
#130708012
#130707992
#130707222
#130707172
#130707142
#130707102
#130705562
#130705542
#130705392
#130705372
#130702302
C11×#30612
#3377011