Finite Group Databasebeta

← #14911136

Subgroups — #14911136

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081006C211yesmaximal, characteristic, complemented
2#13080961C211yesmaximal, characteristic
3#13070897C211yesmaximal, characteristic, complemented
4#13070815C211yesmaximal, characteristic, complemented
5#13070813C211yesmaximal, characteristic, complemented
6#13070803C211yesmaximal, characteristic, complemented
7#13070801C211yesmaximal, characteristic, complemented
8#13070762C211yesmaximal, characteristic, complemented
9#13070757C211yesmaximal, characteristic, complemented
10#13070713C211yesmaximal, characteristic, complemented
11#13070712C211yesmaximal, characteristic, complemented
12#13070467C211yesmaximal, characteristic, complemented
13C16×C22⋊D11C211yesmaximal, characteristic, complemented
14D11×#367C211yesmaximal, characteristic, complemented
15C2×C11×#367C211yesmaximal, characteristic, complemented
16#10623042—21no—
17#10623038—21no—
18C22×C11×C16C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21#10622729C2211yescharacteristic
22#10622728C2211yescharacteristic
23C8×C22⋊D11C2211yescharacteristic
24#10622583—21no—
25#10622580—21no—
26C2×#66864C2211yescharacteristic
27C2×C16×D11C2211yescharacteristic
28#10622503—21no—
29#10622500C2211yescharacteristic
30#10622497—21no—
31#10622496C2211yescharacteristic
32#10622495—21no—
33D11×#107C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622488—21no—
36#10622487C2211yescharacteristic
37#10622487C2211yescharacteristic
38#10622486C2211yescharacteristic
39#10622485C2211yescharacteristic
40C11×#367C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#367C2211yescharacteristic
43C11×#367C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622147C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47#10622143C2211yescharacteristic
48#10622141C2211yescharacteristic
49Dic11⋊C16C2211yescharacteristic
50C16×Dic11C2211yescharacteristic
51#10622130C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C2×#4339—41no—
60C22×C8×C11C2311yescharacteristic
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63#66983—21no—
64#66982—41no—
65C4×C22⋊D11—41no—
66C4×C22⋊D11D411yescharacteristic
67#66977—21no—
68#66977—41no—
69C2×Dic44C2311yescharacteristic
70C2×D88C2311yescharacteristic
71C2×C8×D11C2311yescharacteristic
72#66950—21no—
73#66949—41no—
74#66949—41no—
75#66948—21no—
76#66947—41no—
77#66946—21no—
78C4⋊C4×D11—21no—
79C4⋊C4×D11—21no—
80#66942—41no—
81#66941—21no—
82#66941—21no—
83#66940—21no—
84C2×C11×C16—22no—
85C2×C11×C16C2311yescharacteristic
86C2×C11×C16C2311yescharacteristic
87C11×#107—21no—
88C11×#107—21no—
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C22⋊(C11⋊C8)D411yescharacteristic
94#66885—21no—
95(C2×D11)⋊C8D411yescharacteristic
96#66882C2311yescharacteristic
97#66882C2311yescharacteristic
98#66880—21no—
99Dic11⋊C8D411yescharacteristic
100C8×Dic11C2311yescharacteristic
101C2×C11⋊C16C2311yescharacteristic
102C2×C11⋊C16C2311yescharacteristic
103#66874—21no—
104#66874—21no—
105#66873—21no—
106#66873—21no—
107#66871—21no—
108#66871—21no—
109#66871—21no—
110#66871—21no—
111#66864—22no—
112C16×D11—22no—
113#33902—111nomaximal, Sylow
114C22×C4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C2×C22⋊D11—41no—
118C2×C22⋊D11D811yescharacteristic
119#4339—84no—
120C2×D44—21no—
121C2×D44—41no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×C4×D11C2×D411yescharacteristic
126C2×Dic22—21no—
127C2×Dic22—41no—
128C2×Dic22—41no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11D811yescharacteristic
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4D811yescharacteristic
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4D811yescharacteristic
156C4×Dic11—41no—
157C4×Dic11C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160Dic44—21no—
161Dic44—21no—
162D88—21no—
163D88—21no—
164C8×D11—21no—
165C8×D11—21no—
166C11×C16—21no—
167C11×C16#4112yescomplemented
168C11⋊C16—21no—
169C11⋊C16—21no—
170#3338—111no—
171#3334—111no—
172#2254—111no—
173#2235—111no—
174#2235—111no—
175#2233—111no—
176#2233—111no—
177#2226—111no—
178#2225—111no—
179#2217—111no—
180#2217—111no—
181C4×SD32—111no—
182D4×C16—111no—
183C2×#367—111no—
184C2×#367D1111yescharacteristic, complemented
185C23×C11C2×D811yescharacteristic
186C22×D11—41no—
187C22×D11C2×D811yescharacteristic
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—82no—
195C2×C4×C11—161no—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C22⋊D11—82no—
199C22⋊D11SD3214yescomplemented
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205C2×Dic11C2×D811yescharacteristic
206D44—41no—
207D44—41no—
208D44—82no—
209C4×D11—21no—
210C4×D11—21no—
211C4×D11—82no—
212C4×D11—82no—
213C4×D11—161no—
214Dic22—41no—
215Dic22—41no—
216Dic22—82no—
217Dic22—161no—
218C8×C11—21no—
219C8×C11C2×#4111yescharacteristic
220C8×C112−1+411yescharacteristic
221C11⋊C8—21no—
222C11⋊C8—21no—
223#554—221no—
224#547—221no—
225C2×SD32—111no—
226C22×C16—111no—
227C22×C16C2×D1111yescharacteristic
228#500—111no—
229#500—111no—
230#484—221no—
231#484—221no—
232#480—221no—
233#480—221no—
234#477—221no—
235#474—221no—
236#467—111no—
237#467—111no—
238#466—111no—
239#466—111no—
240C4×Q16—111no—
241C4×D8—111no—
242C8×D4—111no—
243C2×#107—111no—
244C2×#107—111no—
245C2×#107C2×D1111yescharacteristic
246C2×#107C2×D1111yescharacteristic
247#367—111no—
248#367—111no—
249#367—111no—
250#367—111no—
251#367—111no—
252#367C2×D1111yescharacteristic
253#367C2×D1111yescharacteristic
254#367C2×D1111yescharacteristic
255#367C2×D1111yescharacteristic
256C4⋊C16—111no—
257#358—111no—
258#358—111no—
259#358—111no—
260#357—111no—
261#357—111no—
262#357—111no—
263C22⋊C16—111no—
264C22⋊C16—111no—
265C4×C16—111no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11C2×SD3212yes—
269C22×C11C22×D811yescharacteristic
270C2×D11—21no—
271C2×D11—21no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C2×D11C2×SD3212yes—
276C4×C11—21no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11#54711yescharacteristic
282C4×C11#57811yescharacteristic
283Dic11—21no—
284Dic11—21no—
285Dic11—81no—
286Dic11—81no—
287Dic11—81no—
288Dic11C2×SD3212yes—
289C2×#41—441no—
290C2×Q16—111no—
291C2×D8—111no—
292C22×C8—111no—
293C22×C8C22×D1111yescharacteristic
294C4⋊Q8—221no—
295C4⋊Q8—221no—
296#125—441no—
297#123—441no—
298#123—441no—
299C22⋊Q8—221no—
300C22⋊Q8—221no—
301C22⋊Q8—441no—
302C22⋊Q8—441no—
303C22⋊Q8—441no—
304#121—221no—
305#121—221no—
306C4×Q8—221no—
307C4×D4—111no—
308C4×D4—221no—
309C4×D4—441no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314SD32—222no—
315C2×C16—22no—
316C2×C16—111no—
317C2×C16—111no—
318C2×C16—222no—
319C2×C16C22×D1111yescharacteristic
320C2×C16C22×D1111yescharacteristic
321#107—21no—
322#107—21no—
323#107—111no—
324#107—111no—
325#107—221no—
326#107—221no—
327#107—221no—
328#107—221no—
329#107C22×D1111yescharacteristic
330#107C22×D1111yescharacteristic
331#107C22×D1111yescharacteristic
332#107C22×D1111yescharacteristic
333C4⋊C8—111no—
334#103—221no—
335#103—221no—
336#103—221no—
337#102—221no—
338#102—221no—
339#102—221no—
340C22⋊C8—111no—
341C22⋊C8—111no—
342C4×C8—111no—
343C2×C11—22no—
344C2×C11#333411yescharacteristic
345C2×C11C22×SD3211yescharacteristic
346C2×C11#341611yescharacteristic
347D11—22no—
348D11—161no—
349#41—884no—
350C2×Q8—221no—
351C2×Q8—441no—
352C2×Q8—441no—
353C2×D4—111no—
354C2×D4—221no—
355C2×D4—441no—
356C2×D4—441no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—111no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4D4×D1111yescharacteristic
364Q16—221no—
365Q16—221no—
366D8—221no—
367D8—221no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8D4×D1111yescharacteristic
375C2×C8C23×D1111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—111no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C22⋊C4—111no—
393C22⋊C4—111no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C42—111no—
400C42—441no—
401C16—21no—
402C16—221no—
403C16—221no—
404C16#433912yescomplemented
405C11#3390211yescharacteristic, complemented, Sylow
406C23—111no—
407C23—441no—
408C23D8×D1111yescharacteristic
409Q8—441no—
410Q8—441no—
411Q8—882no—
412Q8—1761no—
413D4—114no—
414D4—441no—
415D4—441no—
416D4—882no—
417D4—882no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—82no—
425C2×C4—111no—
426C2×C4—111no—
427C2×C4—111no—
428C2×C4—161no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—882no—
435C2×C4—882no—
436C2×C4—1761no—
437C2×C4D8×D1111yescharacteristic
438C2×C4C2×D4×D1111yescharacteristic
439C8—21no—
440C8—221no—
441C8—221no—
442C8C2×#433911yescharacteristic
443C8#6704011yescharacteristic
444C22—21no—
445C22—21no—
446C22—112no—
447C22—221no—
448C22—221no—
449C22—881no—
450C22—881no—
451C22—881no—
452C22D11×SD3212yes—
453C22C2×D8×D1111yescharacteristic
454C4—21no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4—112no—
460C4—221no—
461C4—221no—
462C4—881no—
463C4—881no—
464C4—881no—
465C4#1062303811yescharacteristic
466C4#1062329711yescharacteristic
467C2—22no—
468C2—222no—
469C2—1761no—
470C2#1308096111yescharacteristic
471C2C2×D11×SD3211yescharacteristic
472C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#367C2
socleC22×C11C22×D8
prime radical#13080961C2
hypercenterC2×#367D11
hypocenterC11#33902
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

Complements

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

NH ≅ G/Ntype
1. #13081006C2semidirect
3. #13070897C2semidirect
4. #13070815C2semidirect
5. #13070813C2semidirect
6. #13070803C2semidirect
7. #13070801C2semidirect
8. #13070762C2semidirect
9. #13070757C2semidirect
10. #13070713C2semidirect
11. #13070712C2semidirect
12. #13070467C2semidirect
13. C16×C22⋊D11C2semidirect
14. D11×#367C2semidirect
15. C2×C11×#367C2semidirect
167. C11×C16#41semidirect
184. C2×#367D11semidirect
199. C22⋊D11SD32semidirect
404. C16#4339semidirect
405. C11#33902semidirect

Maximal subgroups

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

subgroupindex
#130810062
#130809612
#130708972
#130708152
#130708132
#130708032
#130708012
#130707622
#130707572
#130707132
#130707122
#130704672
C16×C22⋊D112
D11×#3672
C2×C11×#3672
#3390211