Finite Group Databasebeta

← #14910591

Subgroups — #14910591

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080960C211yesmaximal, characteristic, complemented
2#13080290C211yesmaximal, characteristic, complemented
3#13070838C211yesmaximal, characteristic, complemented
4#13070798C211yesmaximal, characteristic, complemented
5#13070794C211yesmaximal, characteristic, complemented
6#13070752C211yesmaximal, characteristic, complemented
7#13070701C211yesmaximal, characteristic, complemented
8#13070649C211yesmaximal, characteristic, complemented
9#13070527C211yesmaximal, characteristic, complemented
10#13070526C211yesmaximal, characteristic, complemented
11#13070460C211yesmaximal, characteristic, complemented
12C16×C22⋊D11C211yesmaximal, characteristic, complemented
13C2×#10622147C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2215C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17C22×D88C2211yescharacteristic
18#10623142—21no—
19#10623140—21no—
20C2×C11×D16C2211yescharacteristic, complemented
21C22×C11×C16C2211yescharacteristic, complemented
22C11×#466C2211yescharacteristic
23C11×#466C2211yescharacteristic, complemented
24#10622770C2211yescharacteristic, complemented
25#10622764C2211yescharacteristic
26D8×Dic11C2211yescharacteristic, complemented
27C2×#66890C2211yescharacteristic
28C2×#66890C2211yescharacteristic, complemented
29C8×C22⋊D11C2211yescharacteristic
30C2×#66882C2211yescharacteristic, complemented
31#10622649—21no—
32#10622646—21no—
33C2×C16×D11C2211yescharacteristic, complemented
34#10622496C2211yescharacteristic
35D11×#107C2211yescharacteristic, complemented
36#10622487C2211yescharacteristic, complemented
37#10622485C2211yescharacteristic
38#10622399—21no—
39#10622387—21no—
40#10622386—21no—
41#10622372—21no—
42C11×#366C2211yescharacteristic, complemented
43C11×#357C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic, complemented
47C22⋊(C11⋊C16)C2211yescharacteristic, complemented
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic, complemented
51#10622147C2211yescharacteristic, complemented
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53Dic11⋊C16C2211yescharacteristic, complemented
54C16×Dic11C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×#4341—41no—
60C2×D4×D11—21no—
61C2×D4×D11—41no—
62C22×D44—21no—
63C2×C11×D8C2311yescharacteristic
64C2×C11×D8C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#121—21no—
67C11×#121—21no—
68#66993—21no—
69#66991—21no—
70#66990—41no—
71#66988—41no—
72D4×Dic11—21no—
73C2×#4323—21no—
74C2×#4323—21no—
75C4×C22⋊D11D411yescharacteristic
76C2×C4⋊Dic11—21no—
77D8×D11—22no—
78D8×D11—41no—
79C2×D88—22no—
80C2×D88—21no—
81C2×D88—41no—
82C2×D88C2311yescharacteristic
83C2×D88C2311yescharacteristic
84C2×C8×D11C2311yescharacteristic
85#66948—21no—
86#66946—21no—
87C4⋊C4×D11—21no—
88#66941—21no—
89#66937—41no—
90#66936—41no—
91#66935—41no—
92#66931—41no—
93C11×D16—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#102—21no—
100C11×#102—21no—
101#66896—21no—
102#66896—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66890—22no—
105#66890—41no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110Dic11⋊C8D411yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66873—21no—
115#66873—21no—
116#66871—21no—
117#66871—21no—
118C16×D11—41no—
119#33861—111nomaximal, Sylow
120C23×D11—41no—
121C23×D11—41no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C22×C4×C11C2×D411yescharacteristic
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11D811yescharacteristic
132C22×Dic11—41no—
133C22×Dic11—41no—
134#4341—84no—
135D4×D11—42no—
136D4×D11—81no—
137D4×D11—84no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—42no—
141C2×D44—41no—
142C2×D44—41no—
143C2×D44—81no—
144C2×C4×D11—41no—
145C2×C4×D11—41no—
146C2×C4×D11C2×D411yescharacteristic
147C2×Dic22—41no—
148C11×D8—21no—
149C11×D8—21no—
150C11×D8—21no—
151C11×D8—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C2×D411yescharacteristic
155C2×C8×C11C2411yescharacteristic
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C22⋊C4—41no—
159C11×C22⋊C4—41no—
160C22⋊Dic11—41no—
161C22⋊Dic11—41no—
162C22⋊Dic11D811yescharacteristic
163#4323—42no—
164#4323—81no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4D811yescharacteristic
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—41no—
171Dic11⋊C4—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4D811yescharacteristic
174C4×Dic11C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177D88—21no—
178D88—21no—
179D88—21no—
180D88—42no—
181D88#4112yescomplemented
182C8×D11—21no—
183C8×D11—21no—
184C11×C16—21no—
185C11×C16—21no—
186C11⋊C16—21no—
187C11⋊C16—21no—
188#3334—111no—
189D4×D8—111no—
190#2240—111no—
191#2232—111no—
192#2232—111no—
193#2224—111no—
194#2215—111no—
195#2215D1111yescharacteristic, complemented
196#2206—111no—
197#2184—111no—
198#2184—111no—
199C4×D16—111no—
200D4×C16—111no—
201C2×#357—111no—
202C2×#357—111no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11C2×D811yescharacteristic
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—82no—
209C22×D11—82no—
210C22×D11—82no—
211C22×D11—82no—
212C22×D11—161no—
213C22×D11—161no—
214C22×D11C2×D811yescharacteristic
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219D4×C11—82no—
220D4×C11—82no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C22⋊D11—82no—
228C22⋊D11—82no—
229C22⋊D11—82no—
230C22⋊D11—161no—
231C22⋊D11D1614yescomplemented
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—82no—
235C2×Dic11—82no—
236C2×Dic11C2×D811yescharacteristic
237C2×Dic11C2×D811yescharacteristic
238C2×Dic11C2×D811yescharacteristic
239D44—22no—
240D44—41no—
241D44—41no—
242D44—41no—
243D44—82no—
244D44—82no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—82no—
248C4×D11—82no—
249Dic22—82no—
250C8×C11—21no—
251C8×C11C2×#4111yescharacteristic
252C8×C11H(5,𝔽2)11yescharacteristic
253C11⋊C8—21no—
254C11⋊C8—21no—
255C22×D8—111no—
256C22×D8—111no—
257#547—221no—
258D42—221no—
259C2×D16—111no—
260C2×D16—111no—
261C2×D16C2×D1111yescharacteristic, complemented
262C22×C16—111no—
263C22×C16C2×D1111yescharacteristic, complemented
264#500—111no—
265#493—111no—
266#480—221no—
267#480—221no—
268#474—221no—
269#466—111no—
270#466—111no—
271#466C2×D1111yescharacteristic
272#466C2×D1111yescharacteristic, complemented
273#459—221no—
274#447—221no—
275#447—221no—
276C4×D8—111no—
277C4×D8—111no—
278C8×D4—111no—
279C2×#107—111no—
280C2×#107—111no—
281#366—111no—
282#366—111no—
283#366C2×D1111yescharacteristic, complemented
284C4⋊C16—111no—
285#357—111no—
286#357—111no—
287#357—111no—
288#357—111no—
289#357—111no—
290#357—111no—
291#357—111no—
292#357—111no—
293#357C2×D1111yescharacteristic, complemented
294#357C2×D1111yescharacteristic, complemented
295C22⋊C16—111no—
296C22⋊C16—111no—
297C4×C16—111no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11C2×D1612yes—
307C22×C11C22×D811yescharacteristic
308C2×D11—21no—
309C2×D11—21no—
310C2×D11—42no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—164no—
317C2×D11—164no—
318C2×D11C2×D1612yes—
319C4×C11—21no—
320C4×C11—81no—
321C4×C11—81no—
322C4×C11#54611yescharacteristic
323C4×C11#57711yescharacteristic
324Dic11—21no—
325Dic11—21no—
326Dic11—81no—
327Dic11—81no—
328Dic11C2×D1612yes—
329C2×#41—441no—
330C22×D4—221no—
331C22×D4—221no—
332C22×D4—441no—
333C2×D8—111no—
334C2×D8—111no—
335C2×D8—222no—
336C2×D8—221no—
337C2×D8—221no—
338C2×D8—222no—
339C2×D8—221no—
340C2×D8—441no—
341C2×D8—441no—
342C2×D8C22×D1111yescharacteristic
343C2×D8C22×D1111yescharacteristic
344C22×C8—111no—
345C22×C8C22×D1111yescharacteristic
346C4⋊Q8—221no—
347#127—221no—
348#123—441no—
349#123—441no—
350C22⋊Q8—441no—
351#121—21no—
352#121—21no—
353#121—221no—
354#121—221no—
355#121—441no—
356#120—441no—
357#120—441no—
358C4×D4—111no—
359C4×D4—221no—
360C4×D4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363D16—41no—
364D16—222no—
365D16—441no—
366C2×C16—41no—
367C2×C16—111no—
368C2×C16—111no—
369C2×C16—441no—
370C2×C16C22×D1111yescharacteristic
371C2×C16C22×D1111yescharacteristic
372#107—111no—
373#107—111no—
374#107—221no—
375#107—221no—
376#107—221no—
377#107C22×D1111yescharacteristic
378#107C22×D1111yescharacteristic
379C4⋊C8—111no—
380#102—21no—
381#102—21no—
382#102—221no—
383#102—221no—
384#102—221no—
385#102—221no—
386C22⋊C8—111no—
387C22⋊C8—111no—
388C4×C8—111no—
389C2×C11—22no—
390C2×C11—161no—
391C2×C11—161no—
392C2×C11#329411yescharacteristic
393C2×C11C22×D1611yescharacteristic
394C2×C11#341611yescharacteristic
395D11—22no—
396D11—82no—
397D11—161no—
398C24—441no—
399C24—441no—
400#41—884no—
401C2×Q8—441no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—111no—
407C2×D4—221no—
408C2×D4—221no—
409C2×D4—442no—
410C2×D4—441no—
411C2×D4—441no—
412C2×D4—441no—
413C2×D4—441no—
414C2×D4—442no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—881no—
418C2×D4—881no—
419C2×D4—884no—
420C22×C4—111no—
421C22×C4—441no—
422C22×C4—441no—
423C22×C4—441no—
424C22×C4—441no—
425C22×C4D4×D1111yescharacteristic
426D8—21no—
427D8—21no—
428D8—21no—
429D8—21no—
430D8—112no—
431D8—221no—
432D8—221no—
433D8—221no—
434D8—442no—
435D8—442no—
436D8—881no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—111no—
440C2×C8—111no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8D4×D1111yescharacteristic
444C2×C8C23×D1111yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—111no—
448C4⋊C4—221no—
449C4⋊C4—221no—
450C4⋊C4—441no—
451C4⋊C4—441no—
452C4⋊C4—441no—
453C22⋊C4—41no—
454C22⋊C4—41no—
455C22⋊C4—111no—
456C22⋊C4—111no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C42—111no—
462C16—21no—
463C16—21no—
464C16—221no—
465C16—221no—
466C11#3386111yescharacteristic, complemented, Sylow
467C23—41no—
468C23—41no—
469C23—111no—
470C23—441no—
471C23—441no—
472C23—882no—
473C23—882no—
474C23—882no—
475C23—882no—
476C23—1761no—
477C23—1761no—
478C23D8×D1111yescharacteristic
479Q8—882no—
480D4—41no—
481D4—41no—
482D4—41no—
483D4—41no—
484D4—82no—
485D4—82no—
486D4—114no—
487D4—222no—
488D4—441no—
489D4—441no—
490D4—441no—
491D4—882no—
492D4—882no—
493D4—882no—
494D4—882no—
495D4—882no—
496D4—1761no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—111no—
502C2×C4—111no—
503C2×C4—111no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—882no—
509C2×C4—882no—
510C2×C4—882no—
511C2×C4—882no—
512C2×C4D8×D1111yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C8—21no—
515C8—221no—
516C8—221no—
517C8#6703711yescharacteristic
518C8#41×D1111yescharacteristic
519C22—21no—
520C22—21no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—112no—
528C22—221no—
529C22—221no—
530C22—442no—
531C22—881no—
532C22—881no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—1764no—
537C22—1764no—
538C22D11×D1612yes—
539C22C2×D8×D1111yescharacteristic
540C4—21no—
541C4—81no—
542C4—81no—
543C4—112no—
544C4—221no—
545C4—221no—
546C4—881no—
547C4—881no—
548C4#1062314111yescharacteristic
549C4#1062330111yescharacteristic
550C2—22no—
551C2—161no—
552C2—161no—
553C2—222no—
554C2—882no—
555C2—1761no—
556C2#1308042411yescharacteristic
557C2C2×D11×D1611yescharacteristic
558C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2215C2
socleC22×C11C22×D8
hypercenter#2215D11
hypocenterC11#33861
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. #13080960C2semidirect
2. #13080290C2semidirect
3. #13070838C2semidirect
4. #13070798C2semidirect
5. #13070794C2semidirect
6. #13070752C2semidirect
7. #13070701C2semidirect
8. #13070649C2semidirect
9. #13070527C2semidirect
10. #13070526C2semidirect
11. #13070460C2semidirect
12. C16×C22⋊D11C2semidirect
13. C2×#10622147C2semidirect
14. D11×#357C2semidirect
15. C11×#2215C2semidirect
20. C2×C11×D16C22semidirect
21. C22×C11×C16C22semidirect
23. C11×#466C22semidirect
24. #10622770C22semidirect
26. D8×Dic11C22semidirect
28. C2×#66890C22semidirect
30. C2×#66882C22semidirect
33. C2×C16×D11C22semidirect
35. D11×#107C22semidirect
36. #10622487C22semidirect
42. C11×#366C22semidirect
43. C11×#357C22semidirect
44. C11×#357C22semidirect
45. #10622200C22semidirect
46. #10622200C22semidirect
47. C22⋊(C11⋊C16)C22semidirect
50. #10622147C22semidirect
51. #10622147C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. Dic11⋊C16C22semidirect
54. C16×Dic11C22semidirect
56. #10622129C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
181. D88#41semidirect
195. #2215D11semidirect
231. C22⋊D11D16semidirect
261. C2×D16C2×D11semidirect
263. C22×C16C2×D11semidirect
272. #466C2×D11semidirect
283. #366C2×D11semidirect
293. #357C2×D11semidirect
294. #357C2×D11semidirect
466. C11#33861semidirect

Maximal subgroups

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

subgroupindex
#130809602
#130802902
#130708382
#130707982
#130707942
#130707522
#130707012
#130706492
#130705272
#130705262
#130704602
C16×C22⋊D112
C2×#106221472
D11×#3572
C11×#22152
#3386111