Finite Group Databasebeta

← #14910811

Subgroups — #14910811

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080986C211yesmaximal, characteristic, complemented
2#13080291C211yesmaximal, characteristic
3#13070857C211yesmaximal, characteristic, complemented
4#13070806C211yesmaximal, characteristic, complemented
5#13070795C211yesmaximal, characteristic, complemented
6#13070774C211yesmaximal, characteristic, complemented
7#13070726C211yesmaximal, characteristic, complemented
8#13070709C211yesmaximal, characteristic, complemented
9#13070543C211yesmaximal, characteristic, complemented
10#13070543C211yesmaximal, characteristic, complemented
11#13070478C211yesmaximal, characteristic, complemented
12#13070440C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2207C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18#10623248—21no—
19#10623112—21no—
20C2×C11×SD32C2211yescharacteristic, complemented
21C2×C11×SD32C2211yescharacteristic, complemented
22C11×#493C2211yescharacteristic
23C4×C11×Q16C2211yescharacteristic, complemented
24#10622801C2211yescharacteristic, complemented
25#10622801C2211yescharacteristic, complemented
26C2×#66892C2211yescharacteristic
27#10622770C2211yescharacteristic
28#10622770C2211yescharacteristic
29#10622769—21no—
30#10622769—21no—
31#10622685—21no—
32#10622635—21no—
33C2×#66862C2211yescharacteristic, complemented
34C2×C16×D11C2211yescharacteristic, complemented
35#10622493C2211yescharacteristic, complemented
36D11×#107C2211yescharacteristic, complemented
37#10622428—21no—
38#10622418—21no—
39C4×D88C2211yescharacteristic
40C8×D44C2211yescharacteristic
41#10622296C2211yescharacteristic, complemented
42C11×C4⋊C16C2211yescharacteristic, complemented
43C11×#357C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic, complemented
47#10622200C2211yescharacteristic, complemented
48#10622200C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic, complemented
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53(C2×D11)⋊C16C2211yescharacteristic, complemented
54#10622143C2211yescharacteristic, complemented
55#10622142C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic
57#10622127C2211yescharacteristic, complemented
58#10622099C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×D4×D11—21no—
61C2×D4×D11—41no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8—21no—
64C2×C11×D8C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C11×#127—21no—
67C4×Q8×C11—21no—
68#66999—21no—
69#66999—21no—
70#66991—21no—
71#66991—21no—
72#66991—41no—
73#66990—41no—
74#66990—41no—
75C2×#4323—21no—
76C2×#4323—21no—
77D8×D11—22no—
78D8×D11—22no—
79D8×D11—41no—
80D8×D11—41no—
81C2×D88C2311yescharacteristic
82C2×C8×D11C2311yescharacteristic
83C2×C8×D11C2311yescharacteristic
84#66947—41no—
85#66945—21no—
86C4⋊C4×D11—21no—
87#66942—41no—
88#66929—41no—
89C4×D44—21no—
90C4×D44D411yescharacteristic
91#66925—41no—
92#66923—21no—
93C11×SD32—41no—
94C11×SD32—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99C4×C8×C11C2311yescharacteristic
100#66899—21no—
101#66899—21no—
102#66896—21no—
103#66896—21no—
104#66892—22no—
105#66885—21no—
106(C2×D11)⋊C8D411yescharacteristic
107(C2×D11)⋊C8D411yescharacteristic
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66881—21no—
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66872—21no—
115#66871—21no—
116C4⋊(C11⋊C8)D411yescharacteristic
117#66862—41no—
118C16×D11—41no—
119#33877—111nomaximal, Sylow
120C23×D11—41no—
121C23×D11—41no—
122C2×Q8×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131D4×D11—42no—
132D4×D11—42no—
133D4×D11—81no—
134D4×D11—81no—
135D4×D11—84no—
136C2×D44—21no—
137C2×D44D811yescharacteristic
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11C2×D411yescharacteristic
141C2×C4×D11C2×D411yescharacteristic
142C11×Q16—21no—
143C11×Q16—21no—
144C11×D8—21no—
145C11×D8—21no—
146C11×D8—21no—
147C11×D8—21no—
148C11×D8—81no—
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2411yescharacteristic
151C11×C4⋊C4—21no—
152C11×C4⋊C4—41no—
153C42×C11—41no—
154C42×C11C2×D411yescharacteristic
155C22⋊Dic11—41no—
156C22⋊Dic11—41no—
157#4323—42no—
158#4323—42no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4D811yescharacteristic
164(C2×D11)⋊C4D811yescharacteristic
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11D811yescharacteristic
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4—41no—
174C4×Dic11—41no—
175C2×C11⋊C8C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177D88—21no—
178D88#4112yes—
179C8×D11—21no—
180C8×D11—21no—
181C8×D11—21no—
182C8×D11—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3336—111no—
188D4×D8—111no—
189#2244—111no—
190#2234—111no—
191#2232—111no—
192#2228—111no—
193#2220—111no—
194#2217—111no—
195#2207D1111yescharacteristic, complemented
196#2187—111no—
197#2187—111no—
198#2175—111no—
199#2168—111no—
200#2140—111no—
201C2×#357—111no—
202C23×C11—41no—
203C23×C11—41no—
204C22×D11—41no—
205C22×D11—82no—
206C22×D11—82no—
207C22×D11—82no—
208C22×D11—82no—
209C22×D11—161no—
210C22×D11—161no—
211C22×D11C2×D811yescharacteristic
212C22×D11C2×D811yescharacteristic
213Q8×C11—41no—
214Q8×C11—41no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219D4×C11—82no—
220D4×C11—161no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11C2×D811yescharacteristic
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C22⋊D11—82no—
227C22⋊D11—82no—
228C22⋊D11—82no—
229C22⋊D11—82no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11C2×D811yescharacteristic
234C2×Dic11C2×D811yescharacteristic
235D44—22no—
236D44—22no—
237D44—41no—
238C4×D11—21no—
239C4×D11—21no—
240C4×D11—21no—
241C4×D11—21no—
242C4×D11—82no—
243C4×D11—82no—
244C8×C11—21no—
245C8×C11C2×#4111yescharacteristic
246C8×C11H(5,𝔽2)11yescharacteristic
247C11⋊C8—21no—
248C11⋊C8—21no—
249C22×D8—111no—
250C22×D8—111no—
251#552—221no—
252D42—221no—
253C2×SD32—111no—
254C2×SD32C2×D1111yescharacteristic, complemented
255C2×SD32C2×D1111yescharacteristic, complemented
256C2×M32—111no—
257C22×C16—111no—
258#499—111no—
259#493C2×D1111yescharacteristic
260#485—221no—
261#483—221no—
262#479—221no—
263#467—111no—
264#467—111no—
265#466—111no—
266#466—111no—
267#459—221no—
268#447—221no—
269#447—221no—
270C4×Q16C2×D1111yescharacteristic, complemented
271C4×D8—111no—
272C8×D4—111no—
273#427—111no—
274C2×#107—111no—
275#367—111no—
276#366—111no—
277#366—111no—
278C4⋊C16C2×D1111yescharacteristic, complemented
279#358—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286#357—111no—
287#357C2×D1111yescharacteristic, complemented
288#357C2×D1111yescharacteristic, complemented
289C22⋊C16—111no—
290C22⋊C16—111no—
291#346—111no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11C22×D811yescharacteristic
299C2×D11—21no—
300C2×D11—21no—
301C2×D11—21no—
302C2×D11—21no—
303C2×D11—21no—
304C2×D11—42no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—164no—
308C2×D11—164no—
309C2×D11#50912yes—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—81no—
313C4×C11—81no—
314C4×C11#54611yescharacteristic
315C4×C11#57711yescharacteristic
316Dic11—21no—
317Dic11—21no—
318Dic11—81no—
319Dic11—81no—
320Dic11—81no—
321C22×D4—221no—
322C22×D4—221no—
323C22×D4—441no—
324C2×Q16C22×D1111yescharacteristic
325C2×D8—21no—
326C2×D8—111no—
327C2×D8—221no—
328C2×D8—221no—
329C2×D8—222no—
330C2×D8—222no—
331C2×D8—441no—
332C2×D8—441no—
333C2×D8C22×D1111yescharacteristic
334C2×D8C22×D1111yescharacteristic
335C22×C8—111no—
336C22×C8—111no—
337#127—21no—
338#126—441no—
339#125—221no—
340#125—441no—
341#123—441no—
342C22⋊Q8—221no—
343C22⋊Q8—221no—
344#121—221no—
345#121—221no—
346#121—441no—
347#120—441no—
348#120—441no—
349C4×Q8—21no—
350C4×D4—111no—
351C4×D4—221no—
352#117—221no—
353#117—441no—
354C2×C4⋊C4—221no—
355SD32—41no—
356SD32—41no—
357SD32—222no—
358M32—441no—
359C2×C16—111no—
360C2×C16—111no—
361C2×C16—441no—
362C2×C16C22×D1111yescharacteristic
363C2×C16C22×D1111yescharacteristic
364#107—111no—
365#107—111no—
366#107—111no—
367#107—221no—
368#107C22×D1111yescharacteristic
369#106—221no—
370#106—221no—
371C4⋊C8—111no—
372#103—21no—
373#103—221no—
374#103—221no—
375#102—221no—
376#102—221no—
377#102—221no—
378C22⋊C8—111no—
379C22⋊C8—111no—
380C4×C8C22×D1111yescharacteristic
381C2×C11—161no—
382C2×C11—161no—
383C2×C11#329411yescharacteristic
384C2×C11C2×#50911yescharacteristic
385C2×C11#341611yescharacteristic
386D11—22no—
387D11—41no—
388D11—82no—
389C24—441no—
390C24—441no—
391C2×Q8—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—111no—
397C2×D4—221no—
398C2×D4—441no—
399C2×D4—441no—
400C2×D4—442no—
401C2×D4—442no—
402C2×D4—441no—
403C2×D4—441no—
404C2×D4—881no—
405C2×D4—881no—
406C2×D4—884no—
407C22×C4—111no—
408C22×C4—111no—
409C22×C4—441no—
410C22×C4—441no—
411Q16—21no—
412Q16—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416D8—21no—
417D8—81no—
418D8—112no—
419D8—221no—
420D8—442no—
421D8—442no—
422C2×C8—111no—
423C2×C8—111no—
424C2×C8—221no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—221no—
428C2×C8D4×D1111yescharacteristic
429C2×C8C23×D1111yescharacteristic
430C4⋊C4—21no—
431C4⋊C4—41no—
432C4⋊C4—111no—
433C4⋊C4—221no—
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4—441no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4—441no—
440C4⋊C4—441no—
441C22⋊C4—111no—
442C22⋊C4—111no—
443C22⋊C4—441no—
444C22⋊C4—441no—
445C22⋊C4—441no—
446C22⋊C4—441no—
447C22⋊C4—441no—
448C22⋊C4—441no—
449C42—41no—
450C42—441no—
451C42D4×D1111yescharacteristic
452C16—21no—
453C16—21no—
454C16—221no—
455C16—221no—
456C11#3387711yescharacteristic, complemented, Sylow
457C23—41no—
458C23—41no—
459C23—111no—
460C23—111no—
461C23—441no—
462C23—882no—
463C23—882no—
464C23—882no—
465C23—882no—
466C23—1761no—
467C23—1761no—
468Q8—41no—
469Q8—41no—
470D4—41no—
471D4—41no—
472D4—41no—
473D4—41no—
474D4—82no—
475D4—161no—
476D4—222no—
477D4—222no—
478D4—441no—
479D4—882no—
480D4—882no—
481D4—882no—
482D4—882no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—111no—
486C2×C4—111no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—882no—
495C2×C4—882no—
496C2×C4D8×D1111yescharacteristic
497C2×C4D8×D1111yescharacteristic
498C2×C4C2×D4×D1111yescharacteristic
499C8—21no—
500C8—221no—
501C8—221no—
502C8#6703711yescharacteristic
503C8#41×D1111yescharacteristic
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—112no—
511C22—221no—
512C22—221no—
513C22—221no—
514C22—221no—
515C22—221no—
516C22—442no—
517C22—881no—
518C22—881no—
519C22—1764no—
520C22—1764no—
521C22C2×D8×D1111yescharacteristic
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—221no—
527C4—221no—
528C4—881no—
529C4—881no—
530C4—881no—
531C4#1062314311yescharacteristic
532C4#1062330611yescharacteristic
533C2—161no—
534C2—161no—
535C2—222no—
536C2—441no—
537C2—882no—
538C2#1308043211yescharacteristic
539C2D11×#50911yescharacteristic
540C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2207C2
socleC22×C11C22×D8
prime radical#13080291C2
hypercenter#2207D11
hypocenterC11#33877
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #13080986C2semidirect
3. #13070857C2semidirect
4. #13070806C2semidirect
5. #13070795C2semidirect
6. #13070774C2semidirect
7. #13070726C2semidirect
8. #13070709C2semidirect
9. #13070543C2semidirect
10. #13070543C2semidirect
11. #13070478C2semidirect
12. #13070440C2semidirect
13. #13070330C2semidirect
14. D11×#357C2semidirect
15. C11×#2207C2semidirect
20. C2×C11×SD32C22semidirect
21. C2×C11×SD32C22semidirect
23. C4×C11×Q16C22semidirect
24. #10622801C22semidirect
25. #10622801C22semidirect
33. C2×#66862C22semidirect
34. C2×C16×D11C22semidirect
35. #10622493C22semidirect
36. D11×#107C22semidirect
41. #10622296C22semidirect
42. C11×C4⋊C16C22semidirect
43. C11×#357C22semidirect
44. C11×#357C22semidirect
45. #10622202C22semidirect
46. #10622200C22semidirect
47. #10622200C22semidirect
48. #10622200C22semidirect
49. #10622200C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. (C2×D11)⋊C16C22semidirect
54. #10622143C22semidirect
55. #10622142C22semidirect
57. #10622127C22semidirect
58. #10622099C22semidirect
195. #2207D11semidirect
254. C2×SD32C2×D11semidirect
255. C2×SD32C2×D11semidirect
270. C4×Q16C2×D11semidirect
278. C4⋊C16C2×D11semidirect
287. #357C2×D11semidirect
288. #357C2×D11semidirect
456. C11#33877semidirect

Maximal subgroups

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

subgroupindex
#130809862
#130802912
#130708572
#130708062
#130707952
#130707742
#130707262
#130707092
#130705432
#130704782
#130704402
#130703302
D11×#3572
C11×#22072
#3387711