Finite Group Databasebeta

← #14908571

Subgroups — #14908571

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078195C211yesmaximal, characteristic
2D11×#427C211yesmaximal, characteristic, complemented
3#13070825C211yesmaximal, characteristic, complemented
4#13070824C211yesmaximal, characteristic, complemented
5#13070820C211yesmaximal, characteristic, complemented
6#13070815C211yesmaximal, characteristic, complemented
7#13070804C211yesmaximal, characteristic, complemented
8#13070800C211yesmaximal, characteristic, complemented
9#13070795C211yesmaximal, characteristic, complemented
10#13070399C211yesmaximal, characteristic, complemented
11#13070397C211yesmaximal, characteristic, complemented
12#13070320C211yesmaximal, characteristic, complemented
13#13070320C211yesmaximal, characteristic, complemented
14D11×C22⋊C16C211yesmaximal, characteristic, complemented
15C11×#2234C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18#10623137—21no—
19D11×#117—21no—
20C11×#466C2211yescharacteristic
21C11×#427C2211yescharacteristic
22#10622770C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622719C2211yescharacteristic
25#10622654—21no—
26#10622611—21no—
27C2×C16×D11C2211yescharacteristic
28C2×C16×D11C2211yescharacteristic
29#10622500C2211yescharacteristic
30#10622493C2211yescharacteristic
31#10622493C2211yescharacteristic
32#10622493C2211yescharacteristic
33D11×#107C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622473—21no—
36D11×#106—21no—
37#10622391—21no—
38#10622385—21no—
39C11×#367C2211yescharacteristic, complemented
40C11×#366C2211yescharacteristic, complemented
41C11×#357C2211yescharacteristic, complemented
42C11×#357C2211yescharacteristic, complemented
43C11×C22⋊C16C2211yescharacteristic
44#10622200C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic, complemented
46C22⋊(C11⋊C16)C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622143C2211yescharacteristic, complemented
50#10622142C2211yescharacteristic, complemented
51#10622141C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622130C2211yescharacteristic, complemented
55#10622128C2211yescharacteristic, complemented
56#10622128C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×#4341—21no—
60C22×C4×D11D411yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#121—21no—
64C11×#117—21no—
65#66991—21no—
66#66990—41no—
67D4×Dic11—41no—
68C2×#4324—21no—
69#66979—21no—
70#66977—21no—
71C22×C11⋊C8D411yescharacteristic
72#66965—22no—
73#66965—22no—
74C2×Dic44C2311yescharacteristic
75C2×C8×D11—22no—
76C2×C8×D11—22no—
77C2×C8×D11D411yescharacteristic
78C2×C8×D11D411yescharacteristic
79C2×C8×D11C2311yescharacteristic
80C2×C8×D11C2311yescharacteristic
81#66950—21no—
82#66945—21no—
83#66945—21no—
84#66945—21no—
85C4⋊C4×D11—21no—
86C4⋊C4×D11—21no—
87#66936—41no—
88(C22⋊D11)⋊C4—41no—
89C22⋊C4×D11—41no—
90#66930—41no—
91#66925—41no—
92C42×D11—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#106—21no—
99C11×#102—21no—
100#66896—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66881—21no—
105#66880—21no—
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66872—21no—
110#66872—21no—
111#66872—21no—
112#66871—21no—
113#66871—21no—
114C16×D11—22no—
115C16×D11—22no—
116#33645—111nomaximal, Sylow
117C23×D11D811yescharacteristic
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C22×Dic11—41no—
124C22×Dic11D811yescharacteristic
125#4341—42no—
126#4341—42no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—41no—
130C2×C4×D11—41no—
131C2×C4×D11D811yescharacteristic
132C2×C4×D11D811yescharacteristic
133C2×C4×D11C2×D411yescharacteristic
134C2×C4×D11C2×D411yescharacteristic
135C2×Dic22—21no—
136C11×D8—21no—
137C11×D8—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C42×C11—41no—
148C22⋊Dic11—41no—
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151#4324—42no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170Dic44—21no—
171Dic44—21no—
172C8×D11—22no—
173C8×D11—21no—
174C8×D11—21no—
175C8×D11—22no—
176C8×D11#4112yes—
177C8×D11#4112yes—
178C11×C16—21no—
179C11×C16—21no—
180C11⋊C16—21no—
181C11⋊C16—21no—
182#3050—111no—
183C2×#427—111no—
184#2237—111no—
185#2237—111no—
186#2236—111no—
187#2235—111no—
188#2234—111no—
189#2234D1111yescharacteristic, complemented
190#2233—111no—
191#2232—111no—
192#2158—111no—
193#2158—111no—
194#2138—111no—
195#2138—111no—
196C2×C22⋊C16—111no—
197C23×C11—41no—
198C23×C11C2×D811yescharacteristic
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—41no—
202C22×D11C2×D811yescharacteristic
203C22×D11C2×D811yescharacteristic
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—82no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—82no—
215C22⋊D11—82no—
216C2×Dic11—22no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—82no—
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224C4×D11—22no—
225C4×D11—21no—
226C4×D11—21no—
227C4×D11—22no—
228C4×D11—82no—
229C4×D11—82no—
230C4×D11#12312yes—
231C4×D11#13712yes—
232Dic22—41no—
233Dic22—41no—
234C8×C11—21no—
235C8×C11C2×#4111yescharacteristic
236C8×C11C2×#4111yescharacteristic
237C11⋊C8—21no—
238C11⋊C8#12312yes—
239C2×#135—111no—
240C23×C8—111no—
241#525—221no—
242C2×#117—221no—
243C22×C16—111no—
244C22×C16—111no—
245#467—111no—
246#467—111no—
247#466—111no—
248#466C2×D1111yescharacteristic
249#465—221no—
250#465—221no—
251#427—111no—
252#427—111no—
253#427—111no—
254#427—111no—
255#427—221no—
256#427—221no—
257#427C2×D1111yescharacteristic
258C2×#107—111no—
259C2×#107—111no—
260C2×#106—221no—
261#416—221no—
262#367—111no—
263#367—111no—
264#367—111no—
265#367C2×D1111yescharacteristic, complemented
266#366—111no—
267#366—111no—
268#366—111no—
269#366C2×D1111yescharacteristic, complemented
270#358—111no—
271#358—111no—
272#358—111no—
273#358—111no—
274#357—111no—
275#357—111no—
276#357C2×D1111yescharacteristic, complemented
277#357C2×D1111yescharacteristic, complemented
278C22⋊C16—111no—
279C22⋊C16—111no—
280C22⋊C16—111no—
281C22⋊C16C2×D1111yescharacteristic
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11C22×D811yescharacteristic
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—21no—
292C2×D11—21no—
293C2×D11—44no—
294C2×D11#48012yes—
295C2×D11#50812yes—
296C4×C11—21no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11—81no—
300C4×C11C2×#12311yescharacteristic
301C4×C11C2×#13711yescharacteristic
302Dic11—21no—
303Dic11—81no—
304Dic11—81no—
305Dic11—81no—
306Dic11—81no—
307Dic11#48012yes—
308C2×#41—221no—
309C23×C4—111no—
310#135—222no—
311#135—222no—
312C2×Q16—111no—
313C2×SD16—221no—
314C2×D8C22×D1111yescharacteristic
315C22×C8—111no—
316C22×C8—111no—
317C22×C8—111no—
318C22×C8—111no—
319C22×C8—111no—
320C22×C8—222no—
321C22×C8—222no—
322C22×C8C22×D1111yescharacteristic
323#123—441no—
324C22⋊Q8—221no—
325C22⋊Q8—221no—
326#121—21no—
327#121—221no—
328#120—441no—
329C4×D4—441no—
330C4×D4—441no—
331#117—21no—
332#117—221no—
333#117—221no—
334#117—221no—
335#117—221no—
336#117—441no—
337#117—441no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C22⋊C4—441no—
341C2×C42—441no—
342C2×C16—111no—
343C2×C16—111no—
344C2×C16—222no—
345C2×C16—222no—
346C2×C16C22×D1111yescharacteristic
347C2×C16C22×D1111yescharacteristic
348#107—111no—
349#107—111no—
350#107—111no—
351#107—221no—
352#107—221no—
353#107C22×D1111yescharacteristic
354#107C22×D1111yescharacteristic
355#107C22×D1111yescharacteristic
356#106—21no—
357#106—221no—
358#106—221no—
359#106—221no—
360#106—221no—
361#103—221no—
362#103—221no—
363#102—21no—
364#102—221no—
365C2×C11—41no—
366C2×C11—161no—
367C2×C11C2×#48011yescharacteristic
368C2×C11C2×#50811yescharacteristic
369C2×C11#341411yescharacteristic
370D11—22no—
371D11—22no—
372C24—111no—
373#41—442no—
374#41—442no—
375C2×Q8—221no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—441no—
379C2×D4—441no—
380C22×C4—111no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—111no—
384C22×C4—111no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4D4×D1111yescharacteristic
391Q16—221no—
392Q16—221no—
393SD16—442no—
394D8—21no—
395D8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—111no—
399C2×C8—112no—
400C2×C8—112no—
401C2×C8—111no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—221no—
406C2×C8—221no—
407C2×C8D4×D1111yescharacteristic
408C2×C8C23×D1111yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C4⋊C4—441no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C42—41no—
429C42—441no—
430C42—441no—
431C42—441no—
432C42—441no—
433C16—21no—
434C16—21no—
435C16—221no—
436C16—221no—
437C11#3364511yescharacteristic, complemented, Sylow
438C23—41no—
439C23—111no—
440C23—111no—
441C23—222no—
442C23—222no—
443C23—441no—
444C23D8×D1111yescharacteristic
445Q8—441no—
446Q8—441no—
447D4—41no—
448D4—41no—
449D4—82no—
450D4—882no—
451D4—882no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—111no—
458C2×C4—112no—
459C2×C4—112no—
460C2×C4—111no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—882no—
471C2×C4—882no—
472C2×C4—882no—
473C2×C4D8×D1111yescharacteristic
474C2×C4C2×D4×D1111yescharacteristic
475C8—21no—
476C8—112no—
477C8—221no—
478C8#41×D1111yescharacteristic
479C8#41×D1111yescharacteristic
480C22—21no—
481C22—21no—
482C22—21no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—112no—
487C22—112no—
488C22—221no—
489C22—221no—
490C22—221no—
491C22—221no—
492C22—444no—
493C22C2×D8×D1111yescharacteristic
494C4—21no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—112no—
499C4—221no—
500C4—881no—
501C4—881no—
502C4—881no—
503C4—881no—
504C4D11×#12311yescharacteristic
505C4D11×#13711yescharacteristic
506C2—41no—
507C2—161no—
508C2—222no—
509C2—222no—
510C2D11×#48011yescharacteristic
511C2D11×#50811yescharacteristic
512C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2234C2
socleC22×C11C22×D8
prime radical#13078195C2
hypercenter#2234D11
hypocenterC11#33645
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
2. D11×#427C2semidirect
3. #13070825C2semidirect
4. #13070824C2semidirect
5. #13070820C2semidirect
6. #13070815C2semidirect
7. #13070804C2semidirect
8. #13070800C2semidirect
9. #13070795C2semidirect
10. #13070399C2semidirect
11. #13070397C2semidirect
12. #13070320C2semidirect
13. #13070320C2semidirect
14. D11×C22⋊C16C2semidirect
15. C11×#2234C2semidirect
39. C11×#367C22semidirect
40. C11×#366C22semidirect
41. C11×#357C22semidirect
42. C11×#357C22semidirect
44. #10622200C22semidirect
45. #10622200C22semidirect
49. #10622143C22semidirect
50. #10622142C22semidirect
51. #10622141C22semidirect
52. #10622141C22semidirect
53. #10622130C22semidirect
54. #10622130C22semidirect
55. #10622128C22semidirect
56. #10622128C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
189. #2234D11semidirect
265. #367C2×D11semidirect
269. #366C2×D11semidirect
276. #357C2×D11semidirect
277. #357C2×D11semidirect
437. C11#33645semidirect

Maximal subgroups

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

subgroupindex
#130781952
D11×#4272
#130708252
#130708242
#130708202
#130708152
#130708042
#130708002
#130707952
#130703992
#130703972
#130703202
D11×C22⋊C162
C11×#22342
#3364511