Finite Group Databasebeta

← #14911125

Subgroups — #14911125

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080961C211yesmaximal, characteristic, complemented
2#13080960C211yesmaximal, characteristic, complemented
3#13070890C211yesmaximal, characteristic, complemented
4#13070798C211yesmaximal, characteristic, complemented
5#13070797C211yesmaximal, characteristic, complemented
6#13070795C211yesmaximal, characteristic, complemented
7#13070752C211yesmaximal, characteristic, complemented
8#13070751C211yesmaximal, characteristic, complemented
9#13070701C211yesmaximal, characteristic, complemented
10#13070700C211yesmaximal, characteristic, complemented
11#13070460C211yesmaximal, characteristic, complemented
12(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
13C2×#10622127C211yesmaximal, characteristic, complemented
14D11×#366C211yesmaximal, characteristic, complemented
15C11×#2232C211yesmaximal, characteristic, complemented
16#10623142—21no—
17#10623038—21no—
18C11×#466C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20#10622770C2211yescharacteristic
21D8×Dic11C2211yescharacteristic
22C2×#66890C2211yescharacteristic
23#10622728C2211yescharacteristic
24C8×C22⋊D11C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C22×C11⋊C16C2211yescharacteristic
27#10622646—21no—
28#10622580—21no—
29C2×C16×D11C2211yescharacteristic
30#10622503—21no—
31#10622496C2211yescharacteristic
32#10622495—21no—
33D11×#107C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622485C2211yescharacteristic
38#10622387—21no—
39#10622372—21no—
40C11×#366C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622142C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4341—41no—
60C2×#4339—41no—
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#121—21no—
64C2×C11×C4⋊C4—21no—
65#66991—21no—
66#66988—41no—
67D4×Dic11—21no—
68#66983—21no—
69#66982—41no—
70C4×C22⋊D11D411yescharacteristic
71C2×C4⋊Dic11—21no—
72C2×D88C2311yescharacteristic
73C2×C8×D11C2311yescharacteristic
74#66949—41no—
75#66948—21no—
76#66947—41no—
77#66946—21no—
78C4⋊C4×D11—21no—
79C4⋊C4×D11—21no—
80#66941—21no—
81#66941—21no—
82#66936—41no—
83#66931—41no—
84C2×C11×C16C2311yescharacteristic
85C2×C11×C16C2311yescharacteristic
86C11×#107—21no—
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#102—21no—
91#66896—21no—
92#66896—21no—
93C22⋊(C11⋊C8)D411yescharacteristic
94#66890—22no—
95#66885—21no—
96(C2×D11)⋊C8D411yescharacteristic
97#66882—21no—
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101Dic11⋊C8D411yescharacteristic
102C8×Dic11C2311yescharacteristic
103C2×C11⋊C16—22no—
104C2×C11⋊C16C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106#66873—21no—
107#66873—21no—
108#66871—21no—
109#66871—21no—
110#66871—21no—
111#66871—21no—
112C16×D11—22no—
113#33901—111nomaximal, Sylow
114C2×D4×C11—21no—
115C2×D4×C11—41no—
116C22×C4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C2×C22⋊D11D811yescharacteristic
121C22×Dic11—41no—
122C22×Dic11—41no—
123#4341—84no—
124#4339—84no—
125C2×D44—21no—
126C2×D44—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×C4×D11C2×D411yescharacteristic
131C2×Dic22—41no—
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×C4⋊C4—41no—
143C11×C22⋊C4—41no—
144C22⋊Dic11—41no—
145C22⋊Dic11—41no—
146C22⋊Dic11D811yescharacteristic
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4D811yescharacteristic
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4D811yescharacteristic
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163D88—21no—
164D88—21no—
165C8×D11—21no—
166C8×D11—21no—
167C11×C16—21no—
168C11×C16—21no—
169C11⋊C16—21no—
170C11⋊C16#4112yescomplemented
171#3334—111no—
172#3334—111no—
173#2252—111no—
174#2232—111no—
175#2232—111no—
176#2232—111no—
177#2232D1111yescharacteristic, complemented
178#2224—111no—
179#2224—111no—
180#2215—111no—
181#2215—111no—
182C4×D16—111no—
183D4×C16—111no—
184C2×#366—111no—
185C2×#366—111no—
186C23×C11—41no—
187C23×C11C2×D811yescharacteristic
188C22×D11—41no—
189C22×D11C2×D811yescharacteristic
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—82no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—82no—
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C22⋊D11—82no—
202C22⋊D11—82no—
203C22⋊D11D1614yescomplemented
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—82no—
208C2×Dic11—82no—
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
212D44—41no—
213D44—41no—
214D44—82no—
215C4×D11—21no—
216C4×D11—21no—
217C4×D11—82no—
218C4×D11—82no—
219C4×D11—82no—
220Dic22—82no—
221Dic22—82no—
222C8×C11—21no—
223C8×C11C2×#4111yescharacteristic
224C8×C112−1+411yescharacteristic
225C11⋊C8—21no—
226C11⋊C8—21no—
227#547—221no—
228#547—221no—
229C2×D16—111no—
230C22×C16—111no—
231C22×C16—111no—
232#500—111no—
233#500—111no—
234#480—221no—
235#480—221no—
236#480—221no—
237#480—221no—
238#474—221no—
239#474—221no—
240#466—111no—
241#466—111no—
242#466—111no—
243#466C2×D1111yescharacteristic
244C4×D8—111no—
245C4×D8—111no—
246C8×D4—111no—
247C2×#107—111no—
248C2×#107—111no—
249C2×#107—111no—
250C2×#107C2×D1111yescharacteristic
251#366—111no—
252#366—111no—
253#366—111no—
254#366—111no—
255#366—111no—
256#366—111no—
257#366—111no—
258#366C2×D1111yescharacteristic
259#366C2×D1111yescharacteristic
260C4⋊C16—111no—
261#357—111no—
262#357—111no—
263#357—111no—
264#357—111no—
265#357C2×D1111yescharacteristic
266#357C2×D1111yescharacteristic
267C22⋊C16—111no—
268C22⋊C16C2×D1111yescharacteristic
269C4×C16—111no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11C2×D1612yes—
276C22×C11C22×D811yescharacteristic
277C2×D11—21no—
278C2×D11—21no—
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—81no—
282C2×D11C2×D1612yes—
283C4×C11—21no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11—81no—
287C4×C11#54711yescharacteristic
288C4×C11#57811yescharacteristic
289Dic11—21no—
290Dic11—21no—
291Dic11—81no—
292Dic11—81no—
293Dic11—81no—
294Dic11C2×D1612yes—
295C2×#41—441no—
296C2×#41—441no—
297C2×D8—111no—
298C2×D8C22×D1111yescharacteristic
299C22×C8—111no—
300C22×C8C22×D1111yescharacteristic
301C4⋊Q8—221no—
302C4⋊Q8—221no—
303#123—441no—
304#123—441no—
305#123—441no—
306#123—441no—
307C22⋊Q8—441no—
308C22⋊Q8—441no—
309#121—21no—
310#121—221no—
311#121—221no—
312#121—221no—
313C4×D4—111no—
314C4×D4—221no—
315C4×D4—221no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320D16—222no—
321C2×C16—111no—
322C2×C16—111no—
323C2×C16—222no—
324C2×C16—222no—
325C2×C16C22×D1111yescharacteristic
326C2×C16C22×D1111yescharacteristic
327#107—21no—
328#107—111no—
329#107—111no—
330#107—111no—
331#107—221no—
332#107—221no—
333#107—221no—
334#107—221no—
335#107—221no—
336#107C22×D1111yescharacteristic
337#107C22×D1111yescharacteristic
338#107C22×D1111yescharacteristic
339C4⋊C8—111no—
340#102—21no—
341#102—221no—
342#102—221no—
343#102—221no—
344#102—221no—
345#102—221no—
346C22⋊C8—111no—
347C22⋊C8—111no—
348C4×C8—111no—
349C2×C11—22no—
350C2×C11—161no—
351C2×C11#333411yescharacteristic
352C2×C11C22×D1611yescharacteristic
353C2×C11#341711yescharacteristic
354D11—22no—
355D11—161no—
356#41—884no—
357#41—884no—
358C2×Q8—441no—
359C2×Q8—441no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—111no—
363C2×D4—221no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—441no—
367C22×C4—41no—
368C22×C4—111no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4D4×D1111yescharacteristic
375D8—21no—
376D8—21no—
377D8—221no—
378D8—221no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—111no—
382C2×C8—111no—
383C2×C8—221no—
384C2×C8—221no—
385C2×C8D4×D1111yescharacteristic
386C2×C8C23×D1111yescharacteristic
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—41no—
391C4⋊C4—111no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C22⋊C4—41no—
401C22⋊C4—111no—
402C22⋊C4—111no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C42—111no—
409C16—21no—
410C16—21no—
411C16—112no—
412C16—221no—
413C11#3390111yescharacteristic, complemented, Sylow
414C23—41no—
415C23—111no—
416C23—441no—
417C23D8×D1111yescharacteristic
418Q8—882no—
419Q8—882no—
420D4—41no—
421D4—41no—
422D4—82no—
423D4—114no—
424D4—441no—
425D4—441no—
426D4—882no—
427D4—882no—
428D4—882no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—111no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—882no—
444C2×C4—882no—
445C2×C4—882no—
446C2×C4—882no—
447C2×C4—882no—
448C2×C4D8×D1111yescharacteristic
449C2×C4C2×D4×D1111yescharacteristic
450C8—21no—
451C8—221no—
452C8—221no—
453C8#41×D1111yescharacteristic
454C8#6704311yescharacteristic
455C22—21no—
456C22—21no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—112no—
461C22—221no—
462C22—221no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22D11×D1612yes—
467C22C2×D8×D1111yescharacteristic
468C4—21no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4—112no—
473C4—221no—
474C4—221no—
475C4—881no—
476C4—881no—
477C4—881no—
478C4#1062318611yescharacteristic
479C4#1062331011yescharacteristic
480C2—22no—
481C2—161no—
482C2—222no—
483C2—1761no—
484C2#1308095811yescharacteristic
485C2C2×D11×D1611yescharacteristic
486C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2232C2
socleC22×C11C22×D8
hypercenter#2232D11
hypocenterC11#33901
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
1. #13080961C2semidirect
2. #13080960C2semidirect
3. #13070890C2semidirect
4. #13070798C2semidirect
5. #13070797C2semidirect
6. #13070795C2semidirect
7. #13070752C2semidirect
8. #13070751C2semidirect
9. #13070701C2semidirect
10. #13070700C2semidirect
11. #13070460C2semidirect
12. (C22⋊D11)⋊C16C2semidirect
13. C2×#10622127C2semidirect
14. D11×#366C2semidirect
15. C11×#2232C2semidirect
170. C11⋊C16#41semidirect
177. #2232D11semidirect
203. C22⋊D11D16semidirect
413. C11#33901semidirect

Maximal subgroups

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

subgroupindex
#130809612
#130809602
#130708902
#130707982
#130707972
#130707952
#130707522
#130707512
#130707012
#130707002
#130704602
(C22⋊D11)⋊C162
C2×#106221272
D11×#3662
C11×#22322
#3390111