Finite Group Databasebeta

← #14908703

Subgroups — #14908703

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079199C211yesmaximal, characteristic, complemented
2C4×D8×D11C211yesmaximal, characteristic
3#13070815C211yesmaximal, characteristic, complemented
4#13070812C211yesmaximal, characteristic, complemented
5#13070762C211yesmaximal, characteristic, complemented
6#13070761C211yesmaximal, characteristic, complemented
7#13070660C211yesmaximal, characteristic, complemented
8#13070659C211yesmaximal, characteristic, complemented
9#13070546C211yesmaximal, characteristic
10#13070543C211yesmaximal, characteristic
11C4×#66864C211yesmaximal, characteristic, complemented
12C4×#66892C211yesmaximal, characteristic, complemented
13C4×#66891C211yesmaximal, characteristic, complemented
14#13070413C211yesmaximal, characteristic, complemented
15C4×C11×SD32C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17#10623109—21no—
18C4×D4×D11—21no—
19C2×C11×SD32C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic, complemented
21C4×C11×D8C2211yescharacteristic
22#10622801C2211yescharacteristic
23#10622794C2211yescharacteristic, complemented
24C2×#66892C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27C4×#4326—21no—
28C4×#4323—21no—
29C2×#66864C2211yescharacteristic
30#10622500C2211yescharacteristic
31D11×#107C2211yescharacteristic
32#10622487C2211yescharacteristic, complemented
33#10622485C2211yescharacteristic
34#10622426—21no—
35#10622405—21no—
36D11×#102—21no—
37#10622369—21no—
38C4×Dic44C2211yescharacteristic, complemented
39C4×D88C2211yescharacteristic
40C4×C8×D11C2211yescharacteristic
41C11×#367C2211yescharacteristic, complemented
42C11×#358C2211yescharacteristic, complemented
43C11×#357C2211yescharacteristic
44C4×C11×C16C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic
47#10622147C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622143C2211yescharacteristic, complemented
51#10622141C2211yescharacteristic, complemented
52Dic11⋊C16C2211yescharacteristic, complemented
53Dic11⋊C16C2211yescharacteristic, complemented
54#10622130C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622128C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58C4×C11⋊C16C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C22×C4×D11—41no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C4×Q8×C11—21no—
64C4×D4×C11—21no—
65#66999—21no—
66#66997—21no—
67C2×#4326—21no—
68D4×Dic11—21no—
69C2×#4323—21no—
70C4×C22⋊D11—41no—
71D8×D11—22no—
72D8×D11—22no—
73C2×Dic44C2311yescharacteristic
74C2×D88C2311yescharacteristic
75C2×C8×D11D411yescharacteristic
76C2×C8×D11C2311yescharacteristic
77#66950—21no—
78#66949—41no—
79#66946—21no—
80C4⋊C4×D11—21no—
81#66942—41no—
82#66941—21no—
83(C22⋊D11)⋊C4—41no—
84C22⋊C4×D11—41no—
85C4×D44—21no—
86#66925—41no—
87C42×D11D411yescharacteristic
88C4×Dic22—21no—
89C4×Dic22—41no—
90C11×SD32—22no—
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#103—21no—
96C11×#102—21no—
97C4×C8×C11C2311yescharacteristic
98#66899—21no—
99#66896—21no—
100#66892—22no—
101#66891—22no—
102#66885—21no—
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66880—21no—
106C8×Dic11D411yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66874—21no—
111#66873—21no—
112#66871—21no—
113#66871—21no—
114C4×C11⋊C8D411yescharacteristic
115#66864—22no—
116#33661—111nomaximal, Sylow
117C23×D11—41no—
118C2×Q8×C11—21no—
119C2×D4×C11—21no—
120C22×C4×C11—41no—
121C2×C22⋊D11—41no—
122C22×Dic11—41no—
123D4×D11—24no—
124D4×D11—42no—
125C2×D44—21no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11—84no—
130C2×C4×D11D811yescharacteristic
131C2×C4×D11D811yescharacteristic
132C2×C4×D11C2×D411yescharacteristic
133C2×Dic22—21no—
134C2×Dic22—41no—
135C11×Q16—21no—
136C11×Q16—21no—
137C11×D8—21no—
138C11×D8#4112yes—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C22⋊C4—41no—
145C42×C11—41no—
146C42×C11C2×D411yescharacteristic
147C22⋊Dic11—41no—
148#4326—42no—
149#4323—24no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164C4×Dic11D811yescharacteristic
165C4×Dic11D811yescharacteristic
166C4×Dic11C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169Dic44—21no—
170Dic44—21no—
171D88—21no—
172D88#4112yes—
173C8×D11—21no—
174C8×D11—21no—
175C8×D11—41no—
176C11×C16—21no—
177C11×C16—21no—
178C11⋊C16—21no—
179C11⋊C16—21no—
180#3170—111no—
181C2×C4×D8—111no—
182#2235—111no—
183#2235—111no—
184#2226—111no—
185#2226—111no—
186#2208—111no—
187#2208—111no—
188#2187—111no—
189#2187—111no—
190C4×SD32—111no—
191C4×SD32—111no—
192C4×SD32—111no—
193C4×SD32D1111yescharacteristic, complemented
194#2162—111no—
195C23×C11—41no—
196C22×D11—44no—
197C22×D11—41no—
198C22×D11—82no—
199C22×D11—82no—
200C22×D11C2×D811yescharacteristic
201Q8×C11—41no—
202Q8×C11—41no—
203D4×C11—22no—
204D4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—82no—
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C22⋊D11—44no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—82no—
217C2×Dic11C2×D811yescharacteristic
218C2×Dic11C2×D811yescharacteristic
219C2×Dic11C2×D811yescharacteristic
220D44—22no—
221D44—41no—
222C4×D11—21no—
223C4×D11—21no—
224C4×D11—41no—
225C4×D11—82no—
226C4×D11—82no—
227C4×D11—82no—
228C4×D11SD3214yescomplemented
229Dic22—41no—
230Dic22—41no—
231Dic22—82no—
232C8×C11—21no—
233C8×C11C2×#4111yescharacteristic
234C8×C11C2×#4111yescharacteristic
235C11⋊C8—21no—
236C11⋊C8—21no—
237C22×D8—111no—
238#533—221no—
239C2×C4×D4—221no—
240C2×SD32—111no—
241C2×SD32—111no—
242C2×SD32—111no—
243C2×SD32C2×D1111yescharacteristic
244#500—111no—
245#494—111no—
246#487—221no—
247#467—111no—
248#467—111no—
249#467—221no—
250C4×Q16—111no—
251C4×Q16—221no—
252C4×Q16C2×D1111yescharacteristic, complemented
253C4×D8—111no—
254C4×D8—111no—
255C4×D8—111no—
256C4×D8—221no—
257C4×D8—221no—
258C4×D8C2×D1111yescharacteristic
259C2×#107—111no—
260C2×#102—221no—
261C2×C4×C8—111no—
262#367—111no—
263#367—111no—
264#367—111no—
265#367C2×D1111yescharacteristic, complemented
266C4⋊C16—111no—
267C4⋊C16—111no—
268#358—111no—
269#358—111no—
270#358—111no—
271#358C2×D1111yescharacteristic, complemented
272#357—111no—
273#357—111no—
274#357—111no—
275#357C2×D1111yescharacteristic
276C22⋊C16—111no—
277C22⋊C16—111no—
278C4×C16—111no—
279C4×C16C2×D1111yescharacteristic, complemented
280C22×C11—42no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11C22×D811yescharacteristic
284C2×D11—21no—
285C2×D11—21no—
286C2×D11—42no—
287C2×D11—88no—
288C2×D11—81no—
289C2×D11—81no—
290C2×D11C2×SD3212yes—
291C4×C11—21no—
292C4×C11—81no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11C2×SD3212yes—
296C4×C11#52511yescharacteristic
297C4×C11#57511yescharacteristic
298Dic11—21no—
299Dic11—21no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303Dic11C2×SD3212yes—
304C22×D4—221no—
305C23×C4—441no—
306C2×Q16—111no—
307C2×Q16—221no—
308C2×Q16C22×D1111yescharacteristic
309C2×D8—111no—
310C2×D8—221no—
311C2×D8—222no—
312C2×D8—222no—
313C2×D8C22×D1111yescharacteristic
314C22×C8—111no—
315C22×C8—111no—
316C4⋊Q8—221no—
317C4⋊Q8—221no—
318#125—441no—
319C22⋊Q8—221no—
320C22⋊Q8—221no—
321C22⋊Q8—441no—
322C4×Q8—21no—
323C4×Q8—221no—
324C4×Q8—441no—
325C4×D4—21no—
326C4×D4—221no—
327C4×D4—221no—
328C4×D4—221no—
329C4×D4—441no—
330C4×D4—441no—
331#117—441no—
332C2×C4⋊C4—221no—
333C2×C22⋊C4—441no—
334C2×C42—111no—
335SD32—22no—
336SD32—222no—
337SD32—222no—
338SD32—222no—
339C2×C16—111no—
340C2×C16—111no—
341C2×C16C22×D1111yescharacteristic
342C2×C16C22×D1111yescharacteristic
343#107—111no—
344#107—111no—
345#107—221no—
346#107—221no—
347#107C22×D1111yescharacteristic
348#107C22×D1111yescharacteristic
349#103—21no—
350#103—221no—
351#103—221no—
352#103—221no—
353#102—21no—
354#102—221no—
355#102—221no—
356#102—221no—
357C4×C8—111no—
358C4×C8—111no—
359C4×C8—111no—
360C4×C8C22×D1111yescharacteristic
361C2×C11—82no—
362C2×C11#310011yescharacteristic
363C2×C11C22×SD3211yescharacteristic
364C2×C11#341411yescharacteristic
365D11—22no—
366D11—82no—
367C24—441no—
368C2×Q8—21no—
369C2×Q8—221no—
370C2×Q8—441no—
371C2×D4—21no—
372C2×D4—224no—
373C2×D4—221no—
374C2×D4—441no—
375C2×D4—442no—
376C22×C4—41no—
377C22×C4—111no—
378C22×C4—111no—
379C22×C4—111no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—884no—
385Q16—21no—
386Q16—21no—
387Q16—221no—
388Q16—221no—
389Q16—442no—
390D8—21no—
391D8—112no—
392D8—224no—
393D8—221no—
394D8#433912yes—
395C2×C8—111no—
396C2×C8—111no—
397C2×C8—221no—
398C2×C8—221no—
399C2×C8—441no—
400C2×C8D4×D1111yescharacteristic
401C2×C8C23×D1111yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—441no—
408C4⋊C4—441no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C22⋊C4—41no—
415C22⋊C4—441no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4—441no—
420C42—41no—
421C42—111no—
422C42—111no—
423C42—111no—
424C42—441no—
425C42D4×D1111yescharacteristic
426C16—21no—
427C16—21no—
428C16—221no—
429C16—221no—
430C11#3366111yescharacteristic, complemented, Sylow
431C23—41no—
432C23—111no—
433C23—444no—
434C23—441no—
435C23—882no—
436C23—882no—
437Q8—41no—
438Q8—41no—
439Q8—441no—
440Q8—441no—
441Q8—882no—
442D4—22no—
443D4—41no—
444D4—222no—
445D4—444no—
446D4—441no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—82no—
451C2×C4—111no—
452C2×C4—114no—
453C2×C4—111no—
454C2×C4—111no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—882no—
462C2×C4—882no—
463C2×C4—882no—
464C2×C4—882no—
465C2×C4D8×D1111yescharacteristic
466C2×C4D8×D1111yescharacteristic
467C2×C4C2×D4×D1111yescharacteristic
468C8—21no—
469C8—221no—
470C8—221no—
471C8C2×#433911yescharacteristic
472C8#41×D1111yescharacteristic
473C22—42no—
474C22—81no—
475C22—81no—
476C22—112no—
477C22—221no—
478C22—221no—
479C22—442no—
480C22—888no—
481C22—881no—
482C22—881no—
483C22C2×D8×D1111yescharacteristic
484C4—21no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—112no—
489C4—221no—
490C4—221no—
491C4—881no—
492C4—881no—
493C4—881no—
494C4D11×SD3212yes—
495C4#1062307811yescharacteristic
496C4#1062329911yescharacteristic
497C2—82no—
498C2—222no—
499C2—882no—
500C2#1307861411yescharacteristic
501C2C2×D11×SD3211yescharacteristic
502C2#1308174911yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
hypercenterC4×SD32D11
hypocenterC11#33661
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #13079199C2semidirect
3. #13070815C2semidirect
4. #13070812C2semidirect
5. #13070762C2semidirect
6. #13070761C2semidirect
7. #13070660C2semidirect
8. #13070659C2semidirect
11. C4×#66864C2semidirect
12. C4×#66892C2semidirect
13. C4×#66891C2semidirect
14. #13070413C2semidirect
15. C4×C11×SD32C2semidirect
20. C4×C11×Q16C22semidirect
23. #10622794C22semidirect
32. #10622487C22semidirect
38. C4×Dic44C22semidirect
41. C11×#367C22semidirect
42. C11×#358C22semidirect
44. C4×C11×C16C22semidirect
45. #10622202C22semidirect
50. #10622143C22semidirect
51. #10622141C22semidirect
52. Dic11⋊C16C22semidirect
53. Dic11⋊C16C22semidirect
54. #10622130C22semidirect
56. #10622128C22semidirect
57. #10622128C22semidirect
58. C4×C11⋊C16C22semidirect
193. C4×SD32D11semidirect
228. C4×D11SD32semidirect
252. C4×Q16C2×D11semidirect
265. #367C2×D11semidirect
271. #358C2×D11semidirect
279. C4×C16C2×D11semidirect
430. C11#33661semidirect

Maximal subgroups

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

subgroupindex
#130791992
C4×D8×D112
#130708152
#130708122
#130707622
#130707612
#130706602
#130706592
#130705462
#130705432
C4×#668642
C4×#668922
C4×#668912
#130704132
C4×C11×SD322
#3366111