Finite Group Databasebeta

← #14911535

Subgroups — #14911535

Order 2816.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081625C211yesmaximal, characteristic, complemented
2#13081485C211yesmaximal, characteristic, complemented
3#13070856C211yesmaximal, characteristic, complemented
4#13070849C211yesmaximal, characteristic, complemented
5#13070778C211yesmaximal, characteristic, complemented
6#13070775C211yesmaximal, characteristic, complemented
7#13070750C211yesmaximal, characteristic, complemented
8#13070674C211yesmaximal, characteristic, complemented
9#13070668C211yesmaximal, characteristic, complemented
10#13070650C211yesmaximal, characteristic
11#13070522C211yesmaximal, characteristic, complemented
12#13070493C211yesmaximal, characteristic, complemented
13#13070483C211yesmaximal, characteristic, complemented
14#13070460C211yesmaximal, characteristic, complemented
15C11×#2243C211yesmaximal, characteristic, complemented
16#10623261—21no—
17#10623212—21no—
18C11×#500C2211yescharacteristic
19C11×#495C2211yescharacteristic
20#10622804C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22C2×#66892C2211yescharacteristic
23#10622778—21no—
24#10622776—21no—
25#10622764C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66890C2211yescharacteristic
28#10622697—21no—
29#10622670—21no—
30C2×D176C2211yescharacteristic
31#10622504—21no—
32#10622504—21no—
33#10622491C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622485C2211yescharacteristic
36#10622485C2211yescharacteristic
37C4×D88C2211yescharacteristic
38C4×D88C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×#358C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#346C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622140C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×D8C2311yescharacteristic
62C11×C4⋊Q8—21no—
63C11×#124—21no—
64#67000—21no—
65#66999—41no—
66#66999—41no—
67Q8×Dic11—21no—
68C2×#4325—21no—
69#66993—21no—
70D4×Dic11—21no—
71C2×#4323—21no—
72C2×D88C2311yescharacteristic
73C2×D88C2311yescharacteristic
74#66950—41no—
75#66946—21no—
76#66946—21no—
77C4⋊C4×D11—41no—
78#66943—21no—
79#66943—21no—
80#66939—41no—
81#66938—41no—
82#66936—41no—
83(C22⋊D11)⋊C4—41no—
84C4×D44—21no—
85C4×D44—21no—
86C4×Dic22D411yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C11×#107—21no—
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C4×C8×C11C2311yescharacteristic
93#66899—21no—
94#66896—21no—
95#66892—22no—
96#66890—22no—
97#66885—21no—
98#66885—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101Dic11⋊C8D411yescharacteristic
102Dic11⋊C8D411yescharacteristic
103C8×Dic11C2311yescharacteristic
104C8×Dic11C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107#66873—21no—
108#66873—21no—
109#66872—21no—
110#66872—21no—
111C4⋊(C11⋊C8)D411yescharacteristic
112D176—22no—
113#33937—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—41no—
116C2×D4×C11—21no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C22×Dic11—41no—
120C2×D44—21no—
121C2×D44—21no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×Dic22D811yescharacteristic
127C11×Q16—21no—
128C11×Q16—21no—
129C11×SD16—81no—
130C11×D8—21no—
131C11×D8—21no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2411yescharacteristic
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C42×C11C2×D411yescharacteristic
140C22⋊Dic11—41no—
141#4325—81no—
142#4323—81no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154C4⋊Dic11D811yescharacteristic
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4D811yescharacteristic
158Dic11⋊C4D811yescharacteristic
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C4×Dic11C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164D88—21no—
165D88—21no—
166D88—21no—
167D88#4112yes—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3396—111no—
173#3380—111no—
174#2244—111no—
175#2243D1111yescharacteristic, complemented
176#2242—111no—
177#2229—111no—
178#2228—111no—
179#2224—111no—
180#2210—111no—
181#2210—111no—
182#2206—111no—
183#2183—111no—
184#2177—111no—
185#2175—111no—
186C4×D16—111no—
187C23×C11—41no—
188C22×D11—41no—
189C22×D11—41no—
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—161no—
193D4×C11—41no—
194D4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C22⋊D11—82no—
202C22⋊D11—161no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—161no—
206C2×Dic11C2×D811yescharacteristic
207C2×Dic11C2×D811yescharacteristic
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210D44—22no—
211D44—41no—
212D44—41no—
213D44—41no—
214C4×D11—82no—
215C4×D11—161no—
216C4×D11—161no—
217C4×D11—161no—
218Dic22—41no—
219C8×C11—21no—
220C8×C11C2×#4111yescharacteristic
221C8×C112−1+411yescharacteristic
222C11⋊C8—21no—
223C11⋊C8—21no—
224#559—221no—
225#554—221no—
226C2×SD32—111no—
227C2×D16—111no—
228C2×D16—111no—
229#500C2×D1111yescharacteristic
230#499—111no—
231#499—111no—
232#495—111no—
233#495C2×D1111yescharacteristic
234#493—111no—
235#478—221no—
236#478—221no—
237#476—221no—
238#463—221no—
239#463—221no—
240#460—221no—
241C8×Q8—111no—
242C4×Q16—111no—
243C4×D8—111no—
244C4×D8—111no—
245C4×D8—111no—
246C4×D8—111no—
247C4×D8—111no—
248#367—111no—
249#366—111no—
250#366—111no—
251C4⋊C16—111no—
252C4⋊C16—111no—
253C4⋊C16—111no—
254#358—111no—
255#358C2×D1111yescharacteristic
256#358C2×D1111yescharacteristic
257#357—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261#357—111no—
262#357C2×D1111yescharacteristic
263#357C2×D1111yescharacteristic
264#346—111no—
265#346C2×D1111yescharacteristic
266C4×C16—111no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11C22×D811yescharacteristic
271C2×D11—42no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11#54811yescharacteristic
283C4×C11#57711yescharacteristic
284Dic11—21no—
285Dic11—21no—
286Dic11—21no—
287Dic11—21no—
288Dic11—81no—
289Dic11—81no—
290C2×Q16C22×D1111yescharacteristic
291C2×SD16—21no—
292C2×SD16—221no—
293C2×D8—111no—
294C2×D8—111no—
295C2×D8—221no—
296C2×D8C22×D1111yescharacteristic
297C4⋊Q8—21no—
298#127—221no—
299#125—221no—
300#125—221no—
301#124—21no—
302#124—221no—
303#124—441no—
304#123—441no—
305#123—441no—
306C22⋊Q8—441no—
307C22⋊Q8—441no—
308C22⋊Q8—441no—
309C4×Q8—111no—
310C4×Q8—221no—
311C4×D4—221no—
312C4×D4—221no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4—221no—
316C4×D4—441no—
317C2×C4⋊C4—441no—
318SD32—222no—
319D16—222no—
320D16—222no—
321C2×C16—111no—
322C2×C16—111no—
323C2×C16C22×D1111yescharacteristic
324C2×C16C22×D1111yescharacteristic
325#107—21no—
326#107—111no—
327#107—111no—
328#107C22×D1111yescharacteristic
329#107C22×D1111yescharacteristic
330#106—221no—
331#106—221no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—111no—
335#103—221no—
336#102—221no—
337#102—221no—
338#102—221no—
339#102—221no—
340#102—221no—
341C4×C8—111no—
342C4×C8—111no—
343C4×C8C22×D1111yescharacteristic
344C2×C11—161no—
345C2×C11#335811yescharacteristic
346C2×C11#341411yescharacteristic
347C2×C11#341511yescharacteristic
348D11—82no—
349D11—161no—
350C2×Q8—21no—
351C2×Q8—41no—
352C2×Q8—111no—
353C2×D4—21no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—441no—
357C2×D4—441no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4—441no—
363Q16—21no—
364Q16—21no—
365SD16—81no—
366SD16—881no—
367D8—21no—
368D8—21no—
369D8—112no—
370D8—221no—
371D8—221no—
372D8—221no—
373D8—881no—
374C2×C8—111no—
375C2×C8—111no—
376C2×C8D4×D1111yescharacteristic
377C2×C8C23×D1111yescharacteristic
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—111no—
382C4⋊C4—111no—
383C4⋊C4—111no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C42—111no—
401C42—111no—
402C42—441no—
403C42D4×D1111yescharacteristic
404C16—21no—
405C16—21no—
406C16—221no—
407C16—221no—
408C11#3393711yescharacteristic, complemented, Sylow
409C23—41no—
410C23—441no—
411C23—441no—
412Q8—41no—
413Q8—41no—
414Q8—161no—
415Q8—441no—
416D4—41no—
417D4—41no—
418D4—222no—
419D4—441no—
420D4—441no—
421D4—441no—
422D4—882no—
423D4—1761no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—111no—
428C2×C4—111no—
429C2×C4—111no—
430C2×C4—111no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—882no—
434C2×C4—1761no—
435C2×C4—1761no—
436C2×C4—1761no—
437C2×C4—1761no—
438C2×C4D8×D1111yescharacteristic
439C2×C4D8×D1111yescharacteristic
440C2×C4C2×D4×D1111yescharacteristic
441C8—21no—
442C8—221no—
443C8—221no—
444C8#41×D1111yescharacteristic
445C8#6704311yescharacteristic
446C22—81no—
447C22—81no—
448C22—81no—
449C22—442no—
450C22—881no—
451C22—881no—
452C22—881no—
453C22—881no—
454C22—881no—
455C22C2×D8×D1111yescharacteristic
456C4—21no—
457C4—21no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—221no—
462C4—221no—
463C4—221no—
464C4—221no—
465C4—881no—
466C4—881no—
467C4#1062320811yescharacteristic
468C4#1062329311yescharacteristic
469C2—161no—
470C2—882no—
471C2—1761no—
472C2#1308124811yescharacteristic
473C2#1308175111yescharacteristic
474C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2243C2
socleC22×C11C22×D8
prime radical#13070650C2
hypercenter#2243D11
hypocenterC11#33937
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
1. #13081625C2semidirect
2. #13081485C2semidirect
3. #13070856C2semidirect
4. #13070849C2semidirect
5. #13070778C2semidirect
6. #13070775C2semidirect
7. #13070750C2semidirect
8. #13070674C2semidirect
9. #13070668C2semidirect
11. #13070522C2semidirect
12. #13070493C2semidirect
13. #13070483C2semidirect
14. #13070460C2semidirect
15. C11×#2243C2semidirect
175. #2243D11semidirect
408. C11#33937semidirect

Maximal subgroups

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

subgroupindex
#130816252
#130814852
#130708562
#130708492
#130707782
#130707752
#130707502
#130706742
#130706682
#130706502
#130705222
#130704932
#130704832
#130704602
C11×#22432
#3393711