Finite Group Databasebeta

← #14910863

Subgroups — #14910863

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081008C211yesmaximal, characteristic, complemented
2#13080300C211yesmaximal, characteristic
3#13070817C211yesmaximal, characteristic, complemented
4#13070795C211yesmaximal, characteristic, complemented
5#13070750C211yesmaximal, characteristic, complemented
6#13070728C211yesmaximal, characteristic, complemented
7#13070706C211yesmaximal, characteristic, complemented
8#13070675C211yesmaximal, characteristic, complemented
9#13070559C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11#13070482C211yesmaximal, characteristic, complemented
12#13070443C211yesmaximal, characteristic, complemented
13#13070327C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2243C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18#10623261—21no—
19#10623207—21no—
20C11×#500C2211yescharacteristic, complemented
21C11×#495C2211yescharacteristic
22#10622801C2211yescharacteristic
23C2×#66893C2211yescharacteristic, complemented
24#10622785—21no—
25#10622782—21no—
26#10622770C2211yescharacteristic
27C2×#66891C2211yescharacteristic
28#10622704—21no—
29#10622670—21no—
30C2×#66864C2211yescharacteristic
31C2×#66862C2211yescharacteristic, complemented
32C2×C16×D11C2211yescharacteristic
33#10622500C2211yescharacteristic
34#10622500C2211yescharacteristic, complemented
35#10622497—21no—
36#10622497—21no—
37D11×#107C2211yescharacteristic
38D11×#107C2211yescharacteristic, complemented
39C4×Dic44C2211yescharacteristic, complemented
40C4×D88C2211yescharacteristic
41C8×D44C2211yescharacteristic
42C11×#358C2211yescharacteristic, complemented
43C11×#358C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46C11×#346C2211yescharacteristic, complemented
47#10622202C2211yescharacteristic, complemented
48#10622200C2211yescharacteristic
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic, complemented
52#10622142C2211yescharacteristic, complemented
53#10622141C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622127C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58C4⋊(C11⋊C16)C2211yescharacteristic, complemented
59C2×#4343—21no—
60C2×D4×D11—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8C2311yescharacteristic
64C11×C4⋊Q8—21no—
65C11×#124—21no—
66#66999—21no—
67#66999—41no—
68#66999—41no—
69C2×#4325—21no—
70#66991—21no—
71C2×#4323—21no—
72#66972—22no—
73#66972—41no—
74D8×D11—22no—
75D8×D11—41no—
76C2×Dic44C2311yescharacteristic
77C2×D88C2311yescharacteristic
78C2×C8×D11C2311yescharacteristic
79C2×C8×D11C2311yescharacteristic
80#66950—21no—
81#66950—21no—
82#66946—41no—
83C4⋊C4×D11—21no—
84C4⋊C4×D11—21no—
85#66943—41no—
86#66937—41no—
87#66936—41no—
88#66935—41no—
89C22⋊C4×D11—41no—
90C4×D44—21no—
91C4×D44D411yescharacteristic
92C4×Dic22—21no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107—21no—
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C4×C8×C11C2311yescharacteristic
99#66899—21no—
100#66896—21no—
101#66893—41no—
102#66891—41no—
103#66885—21no—
104(C2×D11)⋊C8D411yescharacteristic
105(C2×D11)⋊C8D411yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111#66874—21no—
112#66874—21no—
113#66871—21no—
114#66871—21no—
115C4⋊(C11⋊C8)D411yescharacteristic
116#66864—22no—
117#66862—41no—
118C16×D11—41no—
119#33881—111nomaximal, Sylow
120C23×D11—41no—
121C2×Q8×C11—21no—
122C2×Q8×C11—41no—
123C2×D4×C11—21no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126#4343—42no—
127#4343—81no—
128D4×D11—42no—
129D4×D11—81no—
130C2×D44—21no—
131C2×D44—41no—
132C2×D44D811yescharacteristic
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11C2×D411yescharacteristic
138C2×C4×D11C2×D411yescharacteristic
139C2×Dic22—21no—
140C11×Q16—21no—
141C11×Q16—21no—
142C11×SD16—81no—
143C11×D8—21no—
144C11×D8—21no—
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C42×C11C2×D411yescharacteristic
153C22⋊Dic11—41no—
154#4325—42no—
155#4323—42no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4D811yescharacteristic
161(C2×D11)⋊C4D811yescharacteristic
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166C4⋊Dic11D811yescharacteristic
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171C4×Dic11—41no—
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174Dic44—21no—
175Dic44—21no—
176D88—21no—
177D88#4112yes—
178C8×D11—21no—
179C8×D11—21no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3338—111no—
187#3280—111no—
188#2243D1111yescharacteristic, complemented
189#2236—111no—
190#2232—111no—
191#2224—111no—
192#2220—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2187—111no—
197#2175—111no—
198#2168—111no—
199#2139—111no—
200C2×#357—111no—
201C23×C11—41no—
202C22×D11—41no—
203C22×D11—82no—
204C22×D11—82no—
205C22×D11—161no—
206C22×D11C2×D811yescharacteristic
207C22×D11C2×D811yescharacteristic
208Q8×C11—41no—
209Q8×C11—41no—
210Q8×C11—161no—
211D4×C11—41no—
212D4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C2×D811yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C22⋊D11—82no—
220C22⋊D11—161no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226D44—22no—
227D44—22no—
228D44—41no—
229D44—82no—
230C4×D11—21no—
231C4×D11—21no—
232C4×D11—21no—
233C4×D11—21no—
234C4×D11—82no—
235C4×D11—161no—
236C4×D11—161no—
237C4×D11—161no—
238Dic22—41no—
239Dic22—41no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C11⋊C8—21no—
244C11⋊C8—21no—
245C2×#135—111no—
246C22×D8—111no—
247#554—221no—
248#546—221no—
249C2×Q32—111no—
250C2×SD32—111no—
251C2×SD32—111no—
252C2×M32—111no—
253C22×C16—111no—
254#500C2×D1111yescharacteristic, complemented
255#495C2×D1111yescharacteristic
256#484—221no—
257#484—221no—
258#477—221no—
259#467—111no—
260#467—111no—
261#467—111no—
262#466—111no—
263#463—221no—
264#450—221no—
265#449—221no—
266C4×Q16—111no—
267C4×D8—111no—
268C8×D4—111no—
269C2×#107—111no—
270C2×#107—111no—
271#366—111no—
272#366—111no—
273#366—111no—
274C4⋊C16—111no—
275#358—111no—
276#358—111no—
277#358C2×D1111yescharacteristic, complemented
278#358C2×D1111yescharacteristic, complemented
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357C2×D1111yescharacteristic
284#357C2×D1111yescharacteristic
285C22⋊C16—111no—
286C22⋊C16—111no—
287#346C2×D1111yescharacteristic, complemented
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11C22×D811yescharacteristic
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—21no—
296C2×D11—21no—
297C2×D11—42no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—164no—
301C2×D11#51012yes—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11—81no—
307C4×C11#54611yescharacteristic
308C4×C11#57711yescharacteristic
309Dic11—21no—
310Dic11—21no—
311Dic11—81no—
312Dic11—81no—
313Dic11—81no—
314C2×#41—221no—
315C22×D4—221no—
316#135—222no—
317#135—441no—
318C2×Q16—111no—
319C2×Q16C22×D1111yescharacteristic
320C2×SD16—21no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8—221no—
324C2×D8—222no—
325C2×D8—441no—
326C2×D8C22×D1111yescharacteristic
327C22×C8—111no—
328C22×C8—111no—
329C4⋊Q8—21no—
330#125—441no—
331#124—21no—
332#123—441no—
333C22⋊Q8—221no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336C22⋊Q8—441no—
337C22⋊Q8—441no—
338#121—221no—
339#121—441no—
340#120—441no—
341C4×Q8—221no—
342C4×D4—111no—
343C4×D4—221no—
344C4×D4—441no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C22⋊C4—441no—
348Q32—441no—
349SD32—222no—
350SD32—441no—
351M32—441no—
352C2×C16—111no—
353C2×C16—111no—
354C2×C16—441no—
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357#107—21no—
358#107—111no—
359#107—111no—
360#107—221no—
361#107—221no—
362#107C22×D1111yescharacteristic
363#107C22×D1111yescharacteristic
364C4⋊C8—111no—
365#103—221no—
366#103—221no—
367#103—221no—
368#103—221no—
369#102—221no—
370#102—221no—
371C22⋊C8—111no—
372C22⋊C8—111no—
373C4×C8C22×D1111yescharacteristic
374C2×C11—161no—
375C2×C11#329411yescharacteristic
376C2×C11C2×#51011yescharacteristic
377C2×C11#341511yescharacteristic
378D11—22no—
379D11—41no—
380D11—82no—
381C24—441no—
382#41—442no—
383#41—881no—
384C2×Q8—21no—
385C2×Q8—41no—
386C2×Q8—221no—
387C2×D4—21no—
388C2×D4—111no—
389C2×D4—221no—
390C2×D4—441no—
391C2×D4—441no—
392C2×D4—442no—
393C2×D4—441no—
394C2×D4—881no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4—441no—
401Q16—21no—
402Q16—21no—
403Q16—221no—
404Q16—221no—
405SD16—81no—
406SD16—442no—
407D8—21no—
408D8—21no—
409D8—112no—
410D8—221no—
411D8—442no—
412C2×C8—111no—
413C2×C8—111no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8—221no—
417C2×C8—221no—
418C2×C8D4×D1111yescharacteristic
419C2×C8C23×D1111yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—111no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—111no—
435C22⋊C4—111no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C42—441no—
442C42D4×D1111yescharacteristic
443C16—21no—
444C16—21no—
445C16—221no—
446C16—221no—
447C11#3388111yescharacteristic, complemented, Sylow
448C23—41no—
449C23—111no—
450C23—111no—
451C23—441no—
452C23—882no—
453C23—882no—
454C23—1761no—
455Q8—41no—
456Q8—41no—
457Q8—161no—
458Q8—441no—
459Q8—441no—
460D4—41no—
461D4—41no—
462D4—222no—
463D4—222no—
464D4—441no—
465D4—882no—
466D4—882no—
467D4—1761no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—111no—
472C2×C4—111no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—882no—
481C2×C4—1761no—
482C2×C4—1761no—
483C2×C4—1761no—
484C2×C4D8×D1111yescharacteristic
485C2×C4D8×D1111yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C8—21no—
488C8—221no—
489C8—221no—
490C8#41×D1111yescharacteristic
491C8#6704211yescharacteristic
492C22—81no—
493C22—81no—
494C22—81no—
495C22—112no—
496C22—221no—
497C22—221no—
498C22—221no—
499C22—221no—
500C22—221no—
501C22—442no—
502C22—881no—
503C22—881no—
504C22—1764no—
505C22C2×D8×D1111yescharacteristic
506C4—21no—
507C4—21no—
508C4—81no—
509C4—81no—
510C4—81no—
511C4—221no—
512C4—221no—
513C4—881no—
514C4—881no—
515C4—881no—
516C4#1062320711yescharacteristic
517C4#1062329311yescharacteristic
518C2—161no—
519C2—222no—
520C2—441no—
521C2—882no—
522C2#1308042811yescharacteristic
523C2D11×#51011yescharacteristic
524C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2243C2
socleC22×C11C22×D8
prime radical#13080300C2
hypercenter#2243D11
hypocenterC11#33881
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
1. #13081008C2semidirect
3. #13070817C2semidirect
4. #13070795C2semidirect
5. #13070750C2semidirect
6. #13070728C2semidirect
7. #13070706C2semidirect
8. #13070675C2semidirect
9. #13070559C2semidirect
10. #13070546C2semidirect
11. #13070482C2semidirect
12. #13070443C2semidirect
13. #13070327C2semidirect
14. D11×#357C2semidirect
15. C11×#2243C2semidirect
20. C11×#500C22semidirect
23. C2×#66893C22semidirect
31. C2×#66862C22semidirect
34. #10622500C22semidirect
38. D11×#107C22semidirect
39. C4×Dic44C22semidirect
42. C11×#358C22semidirect
43. C11×#358C22semidirect
46. C11×#346C22semidirect
47. #10622202C22semidirect
51. (C2×D11)⋊C16C22semidirect
52. #10622142C22semidirect
53. #10622141C22semidirect
56. #10622127C22semidirect
57. #10622127C22semidirect
58. C4⋊(C11⋊C16)C22semidirect
188. #2243D11semidirect
254. #500C2×D11semidirect
277. #358C2×D11semidirect
278. #358C2×D11semidirect
287. #346C2×D11semidirect
447. C11#33881semidirect

Maximal subgroups

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

subgroupindex
#130810082
#130803002
#130708172
#130707952
#130707502
#130707282
#130707062
#130706752
#130705592
#130705462
#130704822
#130704432
#130703272
D11×#3572
C11×#22432
#3388111