Finite Group Databasebeta

← #14908939

Subgroups — #14908939

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079262C211yesmaximal, characteristic, complemented
2#13077463C211yesmaximal, characteristic, complemented
3#13070809C211yesmaximal, characteristic, complemented
4#13070806C211yesmaximal, characteristic, complemented
5#13070775C211yesmaximal, characteristic, complemented
6#13070772C211yesmaximal, characteristic, complemented
7#13070650C211yesmaximal, characteristic, complemented
8#13070649C211yesmaximal, characteristic, complemented
9#13070529C211yesmaximal, characteristic, complemented
10#13070526C211yesmaximal, characteristic, complemented
11#13070493C211yesmaximal, characteristic, complemented
12C4×#66890C211yesmaximal, characteristic, complemented
13C4×#66890C211yesmaximal, characteristic, complemented
14#13070424C211yesmaximal, characteristic, complemented
15C11×#2177C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17#10623093—21no—
18#10623076—21no—
19C2×C11×D16C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C4×C11×D8C2211yescharacteristic, complemented
22#10622770C2211yescharacteristic
23#10622764C2211yescharacteristic, complemented
24D8×Dic11C2211yescharacteristic
25C2×#66890C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27#10622627—21no—
28#10622627—21no—
29C2×D176C2211yescharacteristic
30#10622496C2211yescharacteristic
31#10622493C2211yescharacteristic
32#10622491C2211yescharacteristic, complemented
33#10622485C2211yescharacteristic
34#10622398—21no—
35#10622395—21no—
36#10622383—21no—
37#10622377—21no—
38C4×D88C2211yescharacteristic
39C4×D88C2211yescharacteristic, complemented
40#10622302C2211yescharacteristic
41C11×#367C2211yescharacteristic, complemented
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic, complemented
44C11×#346C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic, complemented
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic, complemented
49(C2×D11)⋊C16C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622143C2211yescharacteristic, 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×C11×D8C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64#66993—21no—
65#66991—21no—
66D4×Dic11—21no—
67C2×#4323—21no—
68C2×#4323—21no—
69#66983—41no—
70#66982—41no—
71C4×C22⋊D11—41no—
72C2×(C2×D11)⋊C4—41no—
73D8×D11—22no—
74D8×D11—22no—
75C2×D88C2311yescharacteristic
76C2×D88C2311yescharacteristic
77C2×#4313D411yescharacteristic
78C2×C8×D11C2311yescharacteristic
79#66948—21no—
80#66946—21no—
81#66945—21no—
82#66943—21no—
83#66937—41no—
84#66936—41no—
85(C22⋊D11)⋊C4—41no—
86C22⋊C4×D11—41no—
87C4×D44—21no—
88C4×D44—21no—
89#66925D411yescharacteristic
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
106#66879D411yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66873—21no—
111#66873—21no—
112#66872—21no—
113#66872—21no—
114#66867D411yescharacteristic
115D176—22no—
116#33682—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—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—41no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11C2×D411yescharacteristic
136C11×D8—21no—
137C11×D8—21no—
138C11×D8—21no—
139C11×D8#4112yes—
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C42×C11C2×D411yescharacteristic
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149#4323—24no—
150#4323—42no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4D811yescharacteristic
157(C2×D11)⋊C4D811yescharacteristic
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4D811yescharacteristic
163Dic11⋊C4D811yescharacteristic
164C4×Dic11—41no—
165C4×Dic11C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168D88—21no—
169D88—21no—
170D88—21no—
171D88#4112yes—
172#4313—41no—
173C8×D11—21no—
174C8×D11—21no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3176—111no—
180#2948—111no—
181#2234—111no—
182#2234—111no—
183#2228—111no—
184#2228—111no—
185#2206—111no—
186#2206—111no—
187#2184—111no—
188#2184—111no—
189#2177—111no—
190#2177D1111yescharacteristic, complemented
191C4×D16—111no—
192C4×D16—111no—
193#2164—111no—
194C23×C11—41no—
195C23×C11—41no—
196C22×D11—44no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—161no—
200C22×D11—161no—
201C22×D11C2×D811yescharacteristic
202D4×C11—22no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—161no—
209C2×C4×C11—161no—
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C22⋊D11—44no—
214C22⋊D11—161no—
215C22⋊D11—161no—
216C22⋊D11—161no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—161no—
220C2×Dic11C2×D811yescharacteristic
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223D44—22no—
224D44—41no—
225D44—41no—
226D44—41no—
227D44—161no—
228C4×D11—21no—
229C4×D11—21no—
230C4×D11—161no—
231C4×D11—161no—
232C4×D11—161no—
233C8×C11—21no—
234C8×C11C2×#4111yescharacteristic
235C8×C11C2×#4111yescharacteristic
236C11⋊C8—21no—
237C11⋊C8—21no—
238C22×D8—111no—
239#540—221no—
240#518—221no—
241C2×D16—111no—
242C2×D16—111no—
243C2×D16—111no—
244C2×D16C2×D1111yescharacteristic
245#499—111no—
246#493—111no—
247#490—221no—
248#469—221no—
249#466—111no—
250#466—111no—
251#442—221no—
252#442—221no—
253#442—221no—
254C4×D8—111no—
255C4×D8—111no—
256C4×D8—111no—
257C4×D8—111no—
258C4×D8C2×D1111yescharacteristic
259C4×D8C2×D1111yescharacteristic, complemented
260#427—111no—
261#418—221no—
262#405—111no—
263#367—111no—
264#367C2×D1111yescharacteristic, complemented
265#366—111no—
266#366—111no—
267C4⋊C16—111no—
268C4⋊C16—111no—
269#357—111no—
270#357—111no—
271#357—111no—
272#357—111no—
273#357—111no—
274#357—111no—
275#357C2×D1111yescharacteristic
276#357C2×D1111yescharacteristic, complemented
277C22⋊C16—111no—
278C22⋊C16—111no—
279#346C2×D1111yescharacteristic, complemented
280C4×C16—111no—
281C22×C11—42no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11C22×D811yescharacteristic
288C2×D11—21no—
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—42no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—164no—
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—81no—
301C4×C11—81no—
302C4×C11#52511yescharacteristic
303C4×C11#57511yescharacteristic
304Dic11—21no—
305Dic11—21no—
306Dic11—21no—
307Dic11—81no—
308Dic11—81no—
309C22×D4—221no—
310C2×D8—111no—
311C2×D8—111no—
312C2×D8—221no—
313C2×D8—221no—
314C2×D8—222no—
315C2×D8—222no—
316C2×D8C22×D1111yescharacteristic
317C2×D8C22×D1111yescharacteristic
318C2×M16—111no—
319C22×C8—111no—
320#127—221no—
321#125—221no—
322#123—441no—
323#123—441no—
324#121—221no—
325#121—221no—
326#121—441no—
327#121—441no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—221no—
331C4×D4—221no—
332C4×D4—221no—
333C4×D4—221no—
334C4×D4—441no—
335C4×D4—441no—
336#117—111no—
337#117—221no—
338C2×C22⋊C4—441no—
339C2×C22⋊C4—441no—
340D16—22no—
341D16—222no—
342D16—222no—
343D16—222no—
344C2×C16—111no—
345C2×C16—111no—
346C2×C16C22×D1111yescharacteristic
347C2×C16C22×D1111yescharacteristic
348#107—111no—
349#107—111no—
350#107C22×D1111yescharacteristic
351#107C22×D1111yescharacteristic
352#106—221no—
353#106—221no—
354#102—21no—
355#102—21no—
356#102—221no—
357#102—221no—
358#102—221no—
359#102—221no—
360#102—221no—
361#102—221no—
362#97—111no—
363#97—111no—
364C4×C8—111no—
365C4×C8C22×D1111yescharacteristic
366C2×C11—82no—
367C2×C11—161no—
368C2×C11#310011yescharacteristic
369C2×C11#341511yescharacteristic
370C2×C11#341511yescharacteristic
371D11—41no—
372D11—82no—
373D11—161no—
374C24—441no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—224no—
378C2×D4—221no—
379C2×D4—221no—
380C2×D4—441no—
381C2×D4—441no—
382C2×D4—441no—
383C2×D4—441no—
384C2×D4—442no—
385C2×D4—441no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—111no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4—441no—
393D8—21no—
394D8—21no—
395D8—21no—
396D8—112no—
397D8—224no—
398D8—221no—
399D8—221no—
400D8—221no—
401D8—442no—
402D8#433912yes—
403M16—441no—
404C2×C8—111no—
405C2×C8—111no—
406C2×C8—221no—
407C2×C8—221no—
408C2×C8D4×D1111yescharacteristic
409C2×C8C23×D1111yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—111no—
413C4⋊C4—111no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—111no—
421C22⋊C4—111no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C22⋊C4—441no—
429C42—111no—
430C42—441no—
431C42D4×D1111yescharacteristic
432C16—21no—
433C16—21no—
434C16—221no—
435C16—221no—
436C11#3368211yescharacteristic, complemented, Sylow
437C23—41no—
438C23—41no—
439C23—111no—
440C23—444no—
441C23—441no—
442C23—441no—
443C23—1761no—
444C23—1761no—
445D4—22no—
446D4—41no—
447D4—41no—
448D4—41no—
449D4—222no—
450D4—444no—
451D4—441no—
452D4—441no—
453D4—441no—
454D4—1761no—
455D4—1761no—
456D4—1761no—
457D4—1761no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—111no—
461C2×C4—111no—
462C2×C4—111no—
463C2×C4—161no—
464C2×C4—161no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—1761no—
470C2×C4—1761no—
471C2×C4—1761no—
472C2×C4—1761no—
473C2×C4D8×D1111yescharacteristic
474C2×C4D8×D1111yescharacteristic
475C2×C4C2×D4×D1111yescharacteristic
476C8—21no—
477C8—221no—
478C8—221no—
479C8C2×#433911yescharacteristic
480C8#41×D1111yescharacteristic
481C22—42no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—221no—
488C22—221no—
489C22—221no—
490C22—442no—
491C22—881no—
492C22—881no—
493C22—881no—
494C22—881no—
495C22—881no—
496C22—1764no—
497C22C2×D8×D1111yescharacteristic
498C4—21no—
499C4—21no—
500C4—81no—
501C4—81no—
502C4—221no—
503C4—221no—
504C4—221no—
505C4—881no—
506C4—881no—
507C4#1062307811yescharacteristic
508C4#1062329911yescharacteristic
509C2—82no—
510C2—161no—
511C2—441no—
512C2—882no—
513C2—1761no—
514C2#1307861411yescharacteristic
515C2#1308175611yescharacteristic
516C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2177C2
socleC22×C11C22×D8
hypercenter#2177D11
hypocenterC11#33682
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2177

Complements

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

NH ≅ G/Ntype
1. #13079262C2semidirect
2. #13077463C2semidirect
3. #13070809C2semidirect
4. #13070806C2semidirect
5. #13070775C2semidirect
6. #13070772C2semidirect
7. #13070650C2semidirect
8. #13070649C2semidirect
9. #13070529C2semidirect
10. #13070526C2semidirect
11. #13070493C2semidirect
12. C4×#66890C2semidirect
13. C4×#66890C2semidirect
14. #13070424C2semidirect
15. C11×#2177C2semidirect
21. C4×C11×D8C22semidirect
23. #10622764C22semidirect
32. #10622491C22semidirect
39. C4×D88C22semidirect
41. C11×#367C22semidirect
43. C11×#357C22semidirect
44. C11×#346C22semidirect
46. #10622200C22semidirect
48. #10622147C22semidirect
51. #10622143C22semidirect
52. Dic11⋊C16C22semidirect
53. Dic11⋊C16C22semidirect
55. #10622129C22semidirect
56. #10622127C22semidirect
57. #10622127C22semidirect
58. C4×C11⋊C16C22semidirect
190. #2177D11semidirect
259. C4×D8C2×D11semidirect
264. #367C2×D11semidirect
276. #357C2×D11semidirect
279. #346C2×D11semidirect
436. C11#33682semidirect

Maximal subgroups

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

subgroupindex
#130792622
#130774632
#130708092
#130708062
#130707752
#130707722
#130706502
#130706492
#130705292
#130705262
#130704932
C4×#668902
#130704242
C11×#21772
#3368211