Finite Group Databasebeta

← #14908695

Subgroups — #14908695

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic, complemented
2C4×D8×D11C211yesmaximal, characteristic, complemented
3#13070798C211yesmaximal, characteristic, complemented
4#13070795C211yesmaximal, characteristic, complemented
5#13070752C211yesmaximal, characteristic, complemented
6#13070751C211yesmaximal, characteristic, complemented
7#13070650C211yesmaximal, characteristic, complemented
8#13070649C211yesmaximal, characteristic, complemented
9#13070529C211yesmaximal, characteristic, complemented
10#13070526C211yesmaximal, characteristic, complemented
11C4×D176C211yesmaximal, characteristic, complemented
12C4×#66890C211yesmaximal, characteristic, complemented
13C4×#66890C211yesmaximal, characteristic, complemented
14#13070413C211yesmaximal, characteristic, complemented
15C4×C11×D16C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17#10623079—21no—
18C4×D4×D11—21no—
19C2×C11×D16C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C4×C11×D8C2211yescharacteristic, complemented
22#10622770C2211yescharacteristic
23#10622764C2211yescharacteristic, complemented
24D8×Dic11C2211yescharacteristic
25C2×#66890C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27C4×#4323—21no—
28C4×#4323—21no—
29C2×D176C2211yescharacteristic
30#10622496C2211yescharacteristic
31D11×#107C2211yescharacteristic
32#10622487C2211yescharacteristic, complemented
33#10622485C2211yescharacteristic
34#10622388—21no—
35D11×#102—21no—
36#10622373—21no—
37#10622369—21no—
38C4×D88C2211yescharacteristic
39C4×D88C2211yescharacteristic, complemented
40C4×C8×D11C2211yescharacteristic
41C11×#366C2211yescharacteristic, complemented
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic, complemented
44C4×C11×C16C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic, complemented
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic, complemented
49(C2×D11)⋊C16C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622142C2211yescharacteristic, complemented
52Dic11⋊C16C2211yescharacteristic, complemented
53Dic11⋊C16C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic, complemented
56#10622127C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58C4×C11⋊C16C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×#4339—41no—
61C22×C4×D11—41no—
62C2×C11×D8C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66#66993—21no—
67#66991—21no—
68D4×Dic11—21no—
69C2×#4323—21no—
70C2×#4323—21no—
71C4×C22⋊D11—41no—
72C4×C22⋊D11—41no—
73D8×D11—22no—
74D8×D11—22no—
75C2×D88C2311yescharacteristic
76C2×D88C2311yescharacteristic
77C2×C8×D11D411yescharacteristic
78C2×C8×D11C2311yescharacteristic
79#66948—21no—
80#66946—21no—
81C4⋊C4×D11—21no—
82#66941—21no—
83#66938—41no—
84#66937—41no—
85(C22⋊D11)⋊C4—41no—
86C22⋊C4×D11—41no—
87C4×D44—21no—
88C4×D44—21no—
89C42×D11D411yescharacteristic
90C11×D16—22no—
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#102—21no—
96C11×#102—21no—
97C4×C8×C11C2311yescharacteristic
98#66896—21no—
99#66896—21no—
100#66890—22no—
101#66890—22no—
102#66885—21no—
103#66885—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106C8×Dic11D411yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66873—21no—
111#66873—21no—
112#66871—21no—
113#66871—21no—
114C4×C11⋊C8D411yescharacteristic
115D176—22no—
116#33660—111nomaximal, Sylow
117C23×D11—41no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C22×Dic11—41no—
127D4×D11—24no—
128D4×D11—42no—
129#4339—84no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—41no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11—84no—
138C2×C4×D11D811yescharacteristic
139C2×C4×D11D811yescharacteristic
140C2×C4×D11C2×D411yescharacteristic
141C2×Dic22—41no—
142C11×D8—21no—
143C11×D8—21no—
144C11×D8—21no—
145C11×D8#4112yescomplemented
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C42×C11C2×D411yescharacteristic
153C22⋊Dic11—41no—
154C22⋊Dic11—41no—
155#4323—24no—
156#4323—42no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165C4×Dic11D811yescharacteristic
166C4×Dic11D811yescharacteristic
167C4×Dic11C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170D88—21no—
171D88—21no—
172D88—21no—
173D88#4112yescomplemented
174C8×D11—21no—
175C8×D11—21no—
176C8×D11—41no—
177C11×C16—21no—
178C11×C16—21no—
179C11⋊C16—21no—
180C11⋊C16—21no—
181#3169—111no—
182C2×C4×D8—111no—
183#2232—111no—
184#2232—111no—
185#2224—111no—
186#2224—111no—
187#2206—111no—
188#2206—111no—
189#2184—111no—
190#2184—111no—
191C4×D16—111no—
192C4×D16—111no—
193C4×D16—111no—
194C4×D16D1111yescharacteristic, complemented
195#2162—111no—
196C23×C11—41no—
197C23×C11—41no—
198C22×D11—44no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—82no—
202C22×D11—82no—
203C22×D11C2×D811yescharacteristic
204D4×C11—22no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—82no—
211C2×C4×C11—82no—
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C22⋊D11—44no—
216C22⋊D11—82no—
217C22⋊D11—82no—
218C22⋊D11—82no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—82no—
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225D44—22no—
226D44—41no—
227D44—41no—
228D44—41no—
229D44—82no—
230C4×D11—21no—
231C4×D11—21no—
232C4×D11—41no—
233C4×D11—82no—
234C4×D11—82no—
235C4×D11—82no—
236C4×D11—82no—
237C4×D11D1614yescomplemented
238Dic22—82no—
239C8×C11—21no—
240C8×C11C2×#4111yescharacteristic
241C8×C11C2×#4111yescharacteristic
242C11⋊C8—21no—
243C11⋊C8—21no—
244C22×D8—111no—
245#532—221no—
246C2×C4×D4—221no—
247C2×D16—111no—
248C2×D16—111no—
249C2×D16—111no—
250C2×D16C2×D1111yescharacteristic
251#500—111no—
252#493—111no—
253#486—221no—
254#466—111no—
255#466—111no—
256#466—221no—
257C4×D8—111no—
258C4×D8—111no—
259C4×D8—111no—
260C4×D8—111no—
261C4×D8—221no—
262C4×D8—221no—
263C4×D8—221no—
264C4×D8C2×D1111yescharacteristic
265C4×D8C2×D1111yescharacteristic, complemented
266C2×#107—111no—
267C2×#102—221no—
268C2×C4×C8—111no—
269#366—111no—
270#366—111no—
271#366—111no—
272#366C2×D1111yescharacteristic, complemented
273C4⋊C16—111no—
274C4⋊C16—111no—
275#357—111no—
276#357—111no—
277#357—111no—
278#357—111no—
279#357—111no—
280#357—111no—
281#357C2×D1111yescharacteristic
282#357C2×D1111yescharacteristic, complemented
283C22⋊C16—111no—
284C22⋊C16—111no—
285C4×C16—111no—
286C4×C16C2×D1111yescharacteristic, complemented
287C22×C11—42no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11C22×D811yescharacteristic
294C2×D11—21no—
295C2×D11—21no—
296C2×D11—42no—
297C2×D11—88no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11C2×D1612yes—
304C4×C11—21no—
305C4×C11—81no—
306C4×C11—81no—
307C4×C11C2×D1612yes—
308C4×C11#52511yescharacteristic
309C4×C11#57511yescharacteristic
310Dic11—21no—
311Dic11—21no—
312Dic11—81no—
313Dic11—81no—
314Dic11C2×D1612yes—
315C2×#41—441no—
316C22×D4—221no—
317C23×C4—441no—
318C2×D8—111no—
319C2×D8—111no—
320C2×D8—221no—
321C2×D8—221no—
322C2×D8—222no—
323C2×D8—222no—
324C2×D8C22×D1111yescharacteristic
325C2×D8C22×D1111yescharacteristic
326C22×C8—111no—
327C22×C8—111no—
328C4⋊Q8—221no—
329#127—221no—
330#124—441no—
331#121—221no—
332#121—221no—
333#121—441no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—221no—
337C4×D4—221no—
338C4×D4—221no—
339C4×D4—221no—
340C4×D4—441no—
341C4×D4—441no—
342C4×D4—441no—
343C2×C4⋊C4—221no—
344C2×C22⋊C4—441no—
345C2×C42—111no—
346D16—22no—
347D16—222no—
348D16—222no—
349D16—222no—
350C2×C16—111no—
351C2×C16—111no—
352C2×C16C22×D1111yescharacteristic
353C2×C16C22×D1111yescharacteristic
354#107—111no—
355#107—111no—
356#107—221no—
357#107—221no—
358#107C22×D1111yescharacteristic
359#107C22×D1111yescharacteristic
360#102—21no—
361#102—21no—
362#102—221no—
363#102—221no—
364#102—221no—
365#102—221no—
366#102—221no—
367#102—221no—
368C4×C8—111no—
369C4×C8—111no—
370C4×C8—111no—
371C4×C8C22×D1111yescharacteristic
372C2×C11—82no—
373C2×C11—161no—
374C2×C11#310011yescharacteristic
375C2×C11C22×D1611yescharacteristic
376C2×C11#341411yescharacteristic
377D11—22no—
378D11—82no—
379D11—161no—
380C24—441no—
381#41—884no—
382C2×Q8—441no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—224no—
386C2×D4—221no—
387C2×D4—221no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4—441no—
392C2×D4—442no—
393C2×D4—441no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4—884no—
405D8—21no—
406D8—21no—
407D8—21no—
408D8—112no—
409D8—224no—
410D8—221no—
411D8—221no—
412D8—221no—
413D8—442no—
414D8#433912yescomplemented
415C2×C8—111no—
416C2×C8—111no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—441no—
420C2×C8D4×D1111yescharacteristic
421C2×C8C23×D1111yescharacteristic
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C42—111no—
437C42—111no—
438C42—111no—
439C42D4×D1111yescharacteristic
440C16—21no—
441C16—21no—
442C16—221no—
443C16—221no—
444C11#3366011yescharacteristic, complemented, Sylow
445C23—41no—
446C23—41no—
447C23—111no—
448C23—444no—
449C23—441no—
450C23—441no—
451C23—882no—
452C23—882no—
453Q8—882no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—222no—
459D4—444no—
460D4—441no—
461D4—441no—
462D4—441no—
463D4—882no—
464D4—882no—
465D4—882no—
466D4—882no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—111no—
472C2×C4—114no—
473C2×C4—111no—
474C2×C4—111no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—882no—
481C2×C4—882no—
482C2×C4—882no—
483C2×C4—882no—
484C2×C4—882no—
485C2×C4D8×D1111yescharacteristic
486C2×C4D8×D1111yescharacteristic
487C2×C4C2×D4×D1111yescharacteristic
488C8—21no—
489C8—221no—
490C8—221no—
491C8C2×#433911yescharacteristic
492C8#41×D1111yescharacteristic
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—112no—
500C22—221no—
501C22—221no—
502C22—442no—
503C22—888no—
504C22—881no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22—881no—
509C22C2×D8×D1111yescharacteristic
510C4—21no—
511C4—81no—
512C4—81no—
513C4—112no—
514C4—221no—
515C4—221no—
516C4—881no—
517C4—881no—
518C4D11×D1612yes—
519C4#1062307811yescharacteristic
520C4#1062329911yescharacteristic
521C2—82no—
522C2—161no—
523C2—222no—
524C2—882no—
525C2—1761no—
526C2#1307861411yescharacteristic
527C2C2×D11×D1611yescharacteristic
528C2#1308174911yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×D16C2
socleC22×C11C22×D8
hypercenterC4×D16D11
hypocenterC11#33660
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #13079192C2semidirect
2. C4×D8×D11C2semidirect
3. #13070798C2semidirect
4. #13070795C2semidirect
5. #13070752C2semidirect
6. #13070751C2semidirect
7. #13070650C2semidirect
8. #13070649C2semidirect
9. #13070529C2semidirect
10. #13070526C2semidirect
11. C4×D176C2semidirect
12. C4×#66890C2semidirect
13. C4×#66890C2semidirect
14. #13070413C2semidirect
15. C4×C11×D16C2semidirect
21. C4×C11×D8C22semidirect
23. #10622764C22semidirect
32. #10622487C22semidirect
39. C4×D88C22semidirect
41. C11×#366C22semidirect
43. C11×#357C22semidirect
44. C4×C11×C16C22semidirect
46. #10622200C22semidirect
48. #10622147C22semidirect
51. #10622142C22semidirect
52. Dic11⋊C16C22semidirect
53. Dic11⋊C16C22semidirect
55. #10622129C22semidirect
56. #10622127C22semidirect
57. #10622127C22semidirect
58. C4×C11⋊C16C22semidirect
145. C11×D8#41semidirect
173. D88#41semidirect
194. C4×D16D11semidirect
237. C4×D11D16semidirect
265. C4×D8C2×D11semidirect
272. #366C2×D11semidirect
282. #357C2×D11semidirect
286. C4×C16C2×D11semidirect
414. D8#4339semidirect
444. C11#33660semidirect

Maximal subgroups

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

subgroupindex
#130791922
C4×D8×D112
#130707982
#130707952
#130707522
#130707512
#130706502
#130706492
#130705292
#130705262
C4×D1762
C4×#668902
#130704132
C4×C11×D162
#3366011