Finite Group Databasebeta

← #14908942

Subgroups — #14908942

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#13079267C211yesmaximal, characteristic, complemented
2#13077463C211yesmaximal, characteristic, complemented
3#13070810C211yesmaximal, characteristic, complemented
4#13070809C211yesmaximal, characteristic, complemented
5#13070770C211yesmaximal, characteristic, complemented
6#13070652C211yesmaximal, characteristic, complemented
7#13070651C211yesmaximal, characteristic, complemented
8#13070529C211yesmaximal, characteristic, complemented
9#13070529C211yesmaximal, characteristic, complemented
10#13070491C211yesmaximal, characteristic, complemented
11#13070489C211yesmaximal, characteristic, complemented
12#13070462C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14#13070422C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17#10623229—21no—
18#10623076—21no—
19C11×#499C2211yescharacteristic, complemented
20C4×C11×D8C2211yescharacteristic
21D8×Dic11C2211yescharacteristic
22C2×#66890C2211yescharacteristic
23C2×#66890C2211yescharacteristic
24#10622680—21no—
25#10622627—21no—
26C2×D176C2211yescharacteristic
27C2×D176C2211yescharacteristic
28#10622496C2211yescharacteristic
29#10622496C2211yescharacteristic
30#10622493C2211yescharacteristic
31#10622485C2211yescharacteristic
32#10622485C2211yescharacteristic, complemented
33#10622485C2211yescharacteristic, complemented
34#10622482—21no—
35#10622478—21no—
36#10622398—21no—
37#10622383—21no—
38#10622308C2211yescharacteristic, complemented
39C4×D88C2211yescharacteristic
40#10622302C2211yescharacteristic
41C11×#367C2211yescharacteristic, complemented
42C11×#366C2211yescharacteristic, complemented
43C11×C4⋊C16C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622147C2211yescharacteristic, complemented
47#10622147C2211yescharacteristic, complemented
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622140C2211yescharacteristic, complemented
51C16×Dic11C2211yescharacteristic, complemented
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic, complemented
56#10622128C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58C4⋊(C11⋊C16)C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×C11×D8C2311yescharacteristic
61C11×#125—21no—
62C4×D4×C11—21no—
63D4×Dic11—21no—
64C2×#4323—21no—
65C4×C22⋊D11—41no—
66C2×(C2×D11)⋊C4—41no—
67D8×D11—22no—
68D8×D11—22no—
69C2×D88—21no—
70C2×D88C2311yescharacteristic
71C2×D88C2311yescharacteristic
72C2×D88C2311yescharacteristic
73C2×#4313D411yescharacteristic
74C2×C8×D11C2311yescharacteristic
75#66948—21no—
76#66948—21no—
77#66948—41no—
78#66948—41no—
79#66947—41no—
80#66947—41no—
81#66946—21no—
82#66946—21no—
83#66946—21no—
84#66945—21no—
85(C22⋊D11)⋊C4—41no—
86C22⋊C4×D11—41no—
87#66927—21no—
88C4×D44—21no—
89#66925D411yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#106—21no—
96C11×#102—21no—
97C4×C8×C11C2311yescharacteristic
98#66896—21no—
99#66890—22no—
100#66890—22no—
101#66885—21no—
102#66882C2311yescharacteristic
103#66879D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107#66873—21no—
108#66873—21no—
109#66873—21no—
110#66873—21no—
111#66873—21no—
112#66872—21no—
113#66867D411yescharacteristic
114D176—22no—
115D176—22no—
116#33682—111nomaximal, Sylow
117C23×D11—41no—
118C2×D4×C11—21no—
119C22×C4×C11—41no—
120C2×C22⋊D11—41no—
121C22×Dic11—41no—
122D4×D11—24no—
123D4×D11—42no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—41no—
128C2×D44—41no—
129C2×D44—41no—
130C2×D44—41no—
131C2×C4×D11—41no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11C2×D411yescharacteristic
136C11×D8—21no—
137C11×D8#4112yes—
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2411yescharacteristic
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C22⋊C4—41no—
146C42×C11C2×D411yescharacteristic
147C22⋊Dic11—41no—
148#4323—24no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
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—
159Dic11⋊C4D811yescharacteristic
160Dic11⋊C4D811yescharacteristic
161C4×Dic11—41no—
162C4×Dic11C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165D88—21no—
166D88—21no—
167D88—21no—
168D88—21no—
169D88—21no—
170D88—42no—
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#2228D1111yescharacteristic, complemented
185#2206—111no—
186#2206—111no—
187#2184—111no—
188#2184—111no—
189#2177—111no—
190#2177—111no—
191C4×D16—111no—
192C4×D16—111no—
193#2164—111no—
194C23×C11—41no—
195C22×D11—44no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—161no—
200C22×D11—161no—
201C22×D11C2×D811yescharacteristic
202D4×C11—22no—
203D4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—161no—
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C22⋊D11—44no—
212C2×Dic11—41no—
213C2×Dic11—161no—
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217D44—22no—
218D44—41no—
219D44—41no—
220D44—41no—
221D44—41no—
222D44—41no—
223D44—161no—
224D44—161no—
225D44—161no—
226D44—161no—
227C4×D11—21no—
228C4×D11—21no—
229C4×D11—161no—
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×D16—111no—
245#499C2×D1111yescharacteristic, complemented
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×D8—111no—
259C4×D8C2×D1111yescharacteristic
260#427—111no—
261#418—221no—
262#405—111no—
263#367—111no—
264#367C2×D1111yescharacteristic, complemented
265#366—111no—
266#366C2×D1111yescharacteristic, complemented
267C4⋊C16—111no—
268C4⋊C16C2×D1111yescharacteristic, complemented
269#357—111no—
270#357—111no—
271#357—111no—
272#357—111no—
273#357—111no—
274#357—111no—
275#357C2×D1111yescharacteristic
276#357C2×D1111yescharacteristic
277C22⋊C16—111no—
278C22⋊C16—111no—
279#346—111no—
280C4×C16—111no—
281C22×C11—42no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11C22×D811yescharacteristic
285C2×D11—21no—
286C2×D11—21no—
287C2×D11—21no—
288C2×D11—42no—
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—81no—
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—81no—
303C4×C11#52511yescharacteristic
304C4×C11#57511yescharacteristic
305Dic11—21no—
306Dic11—21no—
307Dic11—21no—
308Dic11—81no—
309C22×D4—221no—
310C2×D8—111no—
311C2×D8—111no—
312C2×D8—111no—
313C2×D8—221no—
314C2×D8—222no—
315C2×D8—222no—
316C2×D8—221no—
317C2×D8C22×D1111yescharacteristic
318C2×M16—111no—
319C22×C8—111no—
320#127—221no—
321#125—21no—
322#123—441no—
323#123—441no—
324#121—221no—
325#121—221no—
326#121—441no—
327#121—441no—
328C4×D4—21no—
329C4×D4—221no—
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—222no—
341D16—222no—
342D16—222no—
343D16—222no—
344C2×C16—111no—
345C2×C16—111no—
346C2×C16C22×D1111yescharacteristic
347C2×C16C22×D1111yescharacteristic
348#107—111no—
349#107C22×D1111yescharacteristic
350#107C22×D1111yescharacteristic
351#107C22×D1111yescharacteristic
352#106—21no—
353#106—221no—
354#102—21no—
355#102—221no—
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#310011yescharacteristic
368C2×C11#341511yescharacteristic
369C2×C11#341511yescharacteristic
370D11—41no—
371D11—82no—
372D11—161no—
373D11—161no—
374C24—441no—
375C2×D4—21no—
376C2×D4—224no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—221no—
380C2×D4—441no—
381C2×D4—441no—
382C2×D4—441no—
383C2×D4—442no—
384C2×D4—441no—
385C2×D4—441no—
386C22×C4—41no—
387C22×C4—111no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4—441no—
393D8—21no—
394D8—112no—
395D8—224no—
396D8—221no—
397D8—221no—
398D8—221no—
399D8—221no—
400D8—221no—
401D8—442no—
402D8#434312yes—
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—21no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—111no—
416C4⋊C4—111no—
417C4⋊C4—221no—
418C22⋊C4—41no—
419C22⋊C4—111no—
420C22⋊C4—111no—
421C22⋊C4—441no—
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—111no—
439C23—444no—
440C23—441no—
441C23—441no—
442C23—441no—
443C23—1761no—
444C23—1761no—
445D4—22no—
446D4—41no—
447D4—222no—
448D4—444no—
449D4—441no—
450D4—441no—
451D4—441no—
452D4—441no—
453D4—441no—
454D4—1761no—
455D4—1761no—
456D4—1761no—
457D4—1761no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—111no—
462C2×C4—111no—
463C2×C4—111no—
464C2×C4—161no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—441no—
468C2×C4—1761no—
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×#434311yescharacteristic
480C8#41×D1111yescharacteristic
481C22—42no—
482C22—81no—
483C22—81no—
484C22—221no—
485C22—221no—
486C22—221no—
487C22—442no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22—881no—
492C22—881no—
493C22—881no—
494C22—881no—
495C22—881no—
496C22—1764no—
497C22C2×D8×D1111yescharacteristic
498C4—21no—
499C4—21no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—221no—
504C4—221no—
505C4—221no—
506C4—881no—
507C4#1062315811yescharacteristic
508C4#1062330811yescharacteristic
509C2—82no—
510C2—441no—
511C2—882no—
512C2—1761no—
513C2—1761no—
514C2#1307861811yescharacteristic
515C2#1308175411yescharacteristic
516C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
hypercenter#2228D11
hypocenterC11#33682
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #13079267C2semidirect
2. #13077463C2semidirect
3. #13070810C2semidirect
4. #13070809C2semidirect
5. #13070770C2semidirect
6. #13070652C2semidirect
7. #13070651C2semidirect
8. #13070529C2semidirect
9. #13070529C2semidirect
10. #13070491C2semidirect
11. #13070489C2semidirect
12. #13070462C2semidirect
13. #13070460C2semidirect
14. #13070422C2semidirect
15. C11×#2228C2semidirect
19. C11×#499C22semidirect
32. #10622485C22semidirect
33. #10622485C22semidirect
38. #10622308C22semidirect
41. C11×#367C22semidirect
42. C11×#366C22semidirect
43. C11×C4⋊C16C22semidirect
46. #10622147C22semidirect
47. #10622147C22semidirect
50. #10622140C22semidirect
51. C16×Dic11C22semidirect
54. #10622129C22semidirect
55. #10622129C22semidirect
56. #10622128C22semidirect
57. #10622127C22semidirect
58. C4⋊(C11⋊C16)C22semidirect
184. #2228D11semidirect
245. #499C2×D11semidirect
264. #367C2×D11semidirect
266. #366C2×D11semidirect
268. C4⋊C16C2×D11semidirect
436. C11#33682semidirect

Maximal subgroups

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

subgroupindex
#130792672
#130774632
#130708102
#130708092
#130707702
#130706522
#130706512
#130705292
#130704912
#130704892
#130704622
#130704602
#130704222
C11×#22282
#3368211