Finite Group Databasebeta

← #14908876

Subgroups — #14908876

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079248C211yesmaximal, characteristic, complemented
2#13077467C211yesmaximal, characteristic, complemented
3#13070824C211yesmaximal, characteristic, complemented
4#13070762C211yesmaximal, characteristic, complemented
5#13070752C211yesmaximal, characteristic, complemented
6#13070670C211yesmaximal, characteristic, complemented
7#13070670C211yesmaximal, characteristic, complemented
8#13070547C211yesmaximal, characteristic, complemented
9#13070527C211yesmaximal, characteristic
10#13070489C211yesmaximal, characteristic, complemented
11#13070479C211yesmaximal, characteristic, complemented
12#13070467C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2234C211yesmaximal, characteristic, complemented
16C22×D88C2211yescharacteristic
17#10623134—21no—
18#10623052—21no—
19C11×#466C2211yescharacteristic
20C11×#427C2211yescharacteristic
21#10622768C2211yescharacteristic, complemented
22D8×Dic11C2211yescharacteristic, complemented
23C2×#66890C2211yescharacteristic
24C2×#66890C2211yescharacteristic
25#10622729C2211yescharacteristic
26#10622714C2211yescharacteristic
27#10622655—21no—
28#10622614—21no—
29C2×#66864C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31#10622487C2211yescharacteristic, complemented
32#10622486C2211yescharacteristic, complemented
33#10622485C2211yescharacteristic
34#10622485C2211yescharacteristic
35#10622485C2211yescharacteristic
36#10622485C2211yescharacteristic
37#10622482—21no—
38#10622482—21no—
39#10622378—21no—
40#10622370—21no—
41C11×#367C2211yescharacteristic, complemented
42C11×#366C2211yescharacteristic, complemented
43C11×#357C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic, complemented
45C11×C22⋊C16C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622140C2211yescharacteristic, complemented
50Dic11⋊C16C2211yescharacteristic, complemented
51Dic11⋊C16C2211yescharacteristic, complemented
52C16×Dic11C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622130C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C22×D44—21no—
60C2×C11×D8C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#121—21no—
63C11×#117—21no—
64#66989—21no—
65#66989—41no—
66#66988—41no—
67D4×Dic11—21no—
68C2×#4324—21no—
69#66979D411yescharacteristic
70#66977—21no—
71C2×#4318D411yescharacteristic
72C2×Dic44C2311yescharacteristic
73C2×D88—21no—
74C2×D88—22no—
75C2×D88—22no—
76C2×D88C2311yescharacteristic
77C2×D88C2311yescharacteristic
78#66946—21no—
79#66946—21no—
80#66946—21no—
81#66946—21no—
82#66941—21no—
83#66940—21no—
84C22⋊C4×D11—41no—
85C22⋊C4×D11—41no—
86#66932—41no—
87#66931—41no—
88C4×D44—41no—
89C4×D44—41no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#106—21no—
96C11×#102—21no—
97#66896—21no—
98#66890—22no—
99#66890—22no—
100#66882C2311yescharacteristic
101#66880—21no—
102#66879D411yescharacteristic
103#66879D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66873—21no—
110#66873—21no—
111#66873—21no—
112#66873—21no—
113#66871—21no—
114#66864—22no—
115#66864—22no—
116#33678—111nomaximal, Sylow
117C23×D11—41no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×Dic11—41no—
122C2×D44—24no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—42no—
126C2×D44—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×C4×D11—41no—
131C2×Dic22—21no—
132C2×Dic22—41no—
133C11×D8—21no—
134C11×D8—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2411yescharacteristic
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4—41no—
144C42×C11—41no—
145C22⋊Dic11—41no—
146C22⋊Dic11—41no—
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149C22⋊Dic11D811yescharacteristic
150C22⋊Dic11D811yescharacteristic
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⋊Dic11D811yescharacteristic
158C4⋊Dic11D811yescharacteristic
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163C4×Dic11C2×D411yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165#4318—41no—
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168Dic44—21no—
169Dic44—21no—
170D88—24no—
171D88—21no—
172D88—21no—
173D88#4112yes—
174D88#4112yes—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3175—111no—
180#2948—111no—
181#2237—111no—
182#2234D1111yescharacteristic, complemented
183#2226—111no—
184#2224—111no—
185#2210—111no—
186#2210—111no—
187#2187—111no—
188#2184—111no—
189#2177—111no—
190#2175—111no—
191C4×SD32—111no—
192C4×D16—111no—
193#2164—111no—
194C23×C11—41no—
195C23×C11C2×D811yescharacteristic
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—44no—
199C22×D11—161no—
200C22×D11—161no—
201D4×C11—41no—
202D4×C11—41no—
203D4×C11—161no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—161no—
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218D44—22no—
219D44—22no—
220D44—44no—
221D44—41no—
222D44—41no—
223C4×D11—161no—
224C4×D11—161no—
225C4×D11—161no—
226C4×D11—161no—
227Dic22—41no—
228Dic22—41no—
229Dic22—161no—
230C8×C11—21no—
231C8×C11C2×#4111yescharacteristic
232C8×C11C2×#4111yescharacteristic
233C11⋊C8—21no—
234C11⋊C8—21no—
235C22×D8—111no—
236#542—221no—
237#518—221no—
238C2×SD32—111no—
239C2×SD32—111no—
240C2×D16—111no—
241C2×D16—111no—
242#500—111no—
243#495—111no—
244#489—221no—
245#468—221no—
246#467—111no—
247#466C2×D1111yescharacteristic
248#442—221no—
249#442—221no—
250#440—221no—
251C4×Q16—111no—
252C4×D8—111no—
253C4×D8—111no—
254C4×D8—111no—
255C4×D8—111no—
256C4×D8—111no—
257#427C2×D1111yescharacteristic
258#418—221no—
259#405—111no—
260#367—111no—
261#367C2×D1111yescharacteristic, complemented
262#366—111no—
263#366C2×D1111yescharacteristic, complemented
264C4⋊C16—111no—
265C4⋊C16—111no—
266#358—111no—
267#358—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271#357—111no—
272#357C2×D1111yescharacteristic, complemented
273#357C2×D1111yescharacteristic, complemented
274C22⋊C16—111no—
275C22⋊C16C2×D1111yescharacteristic
276#346—111no—
277C4×C16—111no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11C22×D811yescharacteristic
285C2×D11—42no—
286C2×D11—42no—
287C2×D11—81no—
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—164no—
292C4×C11—21no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11—81no—
296C4×C11#52511yescharacteristic
297C4×C11#57511yescharacteristic
298Dic11—21no—
299Dic11—21no—
300Dic11—21no—
301Dic11—21no—
302Dic11—81no—
303Dic11—81no—
304C22×D4—221no—
305C2×Q16—111no—
306C2×SD16—221no—
307C2×D8—111no—
308C2×D8—111no—
309C2×D8—222no—
310C2×D8—222no—
311C2×D8—221no—
312C2×D8C22×D1111yescharacteristic
313C2×M16—111no—
314C22×C8C22×D1111yescharacteristic
315C4⋊Q8—221no—
316#126—441no—
317#124—221no—
318#124—441no—
319#123—441no—
320C22⋊Q8—221no—
321C22⋊Q8—441no—
322#121—21no—
323C4×Q8—221no—
324C4×D4—221no—
325C4×D4—221no—
326C4×D4—221no—
327C4×D4—221no—
328C4×D4—221no—
329C4×D4—441no—
330C4×D4—441no—
331#117—21no—
332#117—111no—
333C2×C22⋊C4—441no—
334C2×C22⋊C4—441no—
335SD32—222no—
336SD32—222no—
337D16—222no—
338D16—222no—
339C2×C16—111no—
340C2×C16—111no—
341C2×C16C22×D1111yescharacteristic
342C2×C16C22×D1111yescharacteristic
343#107—111no—
344#107—221no—
345#107C22×D1111yescharacteristic
346#107C22×D1111yescharacteristic
347#107C22×D1111yescharacteristic
348#106—21no—
349#103—221no—
350#103—221no—
351#102—21no—
352#102—221no—
353#102—221no—
354#102—221no—
355#102—221no—
356#102—221no—
357#97—111no—
358#97—111no—
359C4×C8—111no—
360C4×C8—111no—
361C2×C11—41no—
362C2×C11—161no—
363C2×C11#310011yescharacteristic
364C2×C11#341511yescharacteristic
365C2×C11#341611yescharacteristic
366D11—82no—
367D11—82no—
368C24—441no—
369C2×Q8—221no—
370C2×Q8—441no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—224no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—442no—
377C2×D4—441no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4D4×D1111yescharacteristic
384Q16—221no—
385Q16—221no—
386SD16—442no—
387D8—21no—
388D8—21no—
389D8—112no—
390D8—112no—
391D8—224no—
392D8—221no—
393D8—221no—
394M16—441no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—111no—
398C2×C8—111no—
399C2×C8D4×D1111yescharacteristic
400C2×C8C23×D1111yescharacteristic
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—111no—
405C4⋊C4—111no—
406C4⋊C4—221no—
407C4⋊C4—441no—
408C4⋊C4—441no—
409C4⋊C4—441no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—111no—
413C22⋊C4—111no—
414C22⋊C4—441no—
415C22⋊C4—441no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—441no—
422C42—41no—
423C42—111no—
424C42—111no—
425C42—441no—
426C16—21no—
427C16—21no—
428C16—221no—
429C16—221no—
430C11#3367811yescharacteristic, complemented, Sylow
431C23—41no—
432C23—444no—
433C23—441no—
434C23—441no—
435C23—1761no—
436C23—1761no—
437C23D8×D1111yescharacteristic
438Q8—441no—
439Q8—441no—
440Q8—1761no—
441D4—41no—
442D4—41no—
443D4—161no—
444D4—222no—
445D4—222no—
446D4—444no—
447D4—441no—
448D4—441no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—111no—
455C2×C4—111no—
456C2×C4—111no—
457C2×C4—111no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—1761no—
461C2×C4—1761no—
462C2×C4—1761no—
463C2×C4—1761no—
464C2×C4—1761no—
465C2×C4D8×D1111yescharacteristic
466C2×C4C2×D4×D1111yescharacteristic
467C8—21no—
468C8—221no—
469C8—221no—
470C8#41×D1111yescharacteristic
471C8#41×D1111yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—442no—
479C22—442no—
480C22—881no—
481C22—881no—
482C22—881no—
483C22—881no—
484C22—1764no—
485C22C2×D8×D1111yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—221no—
491C4—221no—
492C4—221no—
493C4—221no—
494C4—881no—
495C4—881no—
496C4#1062318711yescharacteristic
497C4#1062330811yescharacteristic
498C2—41no—
499C2—161no—
500C2—882no—
501C2—882no—
502C2#1307861311yescharacteristic
503C2#1308175611yescharacteristic
504C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2234C2
socleC22×C11C22×D8
prime radical#13070527C2
hypercenter#2234D11
hypocenterC11#33678
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
1. #13079248C2semidirect
2. #13077467C2semidirect
3. #13070824C2semidirect
4. #13070762C2semidirect
5. #13070752C2semidirect
6. #13070670C2semidirect
7. #13070670C2semidirect
8. #13070547C2semidirect
10. #13070489C2semidirect
11. #13070479C2semidirect
12. #13070467C2semidirect
13. #13070460C2semidirect
14. #13070420C2semidirect
15. C11×#2234C2semidirect
21. #10622768C22semidirect
22. D8×Dic11C22semidirect
31. #10622487C22semidirect
32. #10622486C22semidirect
41. C11×#367C22semidirect
42. C11×#366C22semidirect
43. C11×#357C22semidirect
44. C11×#357C22semidirect
49. #10622140C22semidirect
50. Dic11⋊C16C22semidirect
51. Dic11⋊C16C22semidirect
52. C16×Dic11C22semidirect
53. #10622130C22semidirect
54. #10622130C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
182. #2234D11semidirect
261. #367C2×D11semidirect
263. #366C2×D11semidirect
272. #357C2×D11semidirect
273. #357C2×D11semidirect
430. C11#33678semidirect

Maximal subgroups

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

subgroupindex
#130792482
#130774672
#130708242
#130707622
#130707522
#130706702
#130705472
#130705272
#130704892
#130704792
#130704672
#130704602
#130704202
C11×#22342
#3367811