Finite Group Databasebeta

← #14909350

Subgroups — #14909350

Order 2816.

510 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#13079197C211yesmaximal, characteristic, complemented
2#13079187C211yesmaximal, characteristic
3#13070901C211yesmaximal, characteristic, complemented
4#13070884C211yesmaximal, characteristic, complemented
5#13070860C211yesmaximal, characteristic, complemented
6#13070854C211yesmaximal, characteristic, complemented
7#13070731C211yesmaximal, characteristic
8#13070729C211yesmaximal, characteristic
9#13070722C211yesmaximal, characteristic, complemented
10Q32×Dic11C211yesmaximal, characteristic, complemented
11#13070472C211yesmaximal, characteristic, complemented
12#13070467C211yesmaximal, characteristic, complemented
13#13070465C211yesmaximal, characteristic, complemented
14M32×Dic11C211yesmaximal, characteristic, complemented
15C11×#2219C211yesmaximal, characteristic, complemented
16#10623155—21no—
17#10623153—21no—
18C2×C11×Q32C2211yescharacteristic
19C2×C11×M32C2211yescharacteristic
20C11×#467C2211yescharacteristic
21C11×#467C2211yescharacteristic
22#10622804C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic
25#10622794C2211yescharacteristic
26C2×#66893C2211yescharacteristic
27C2×#66892C2211yescharacteristic
28#10622729C2211yescharacteristic
29#10622728C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622664—21no—
33#10622661—21no—
34C2×#66864C2211yescharacteristic
35#10622491C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622413—21no—
40#10622405—21no—
41#10622403—21no—
42#10622401—21no—
43C11×#367C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#358C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622140C2211yescharacteristic
52#10622140C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×Q16C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64#67000—21no—
65Q8×Dic11—21no—
66Q8×Dic11—21no—
67#66997—21no—
68C2×#4326—21no—
69C2×#4325—21no—
70#66983—21no—
71#66977—21no—
72C2×C4×Dic11D411yescharacteristic
73C22×C11⋊C8D411yescharacteristic
74C2×Dic44C2311yescharacteristic
75C2×D88C2311yescharacteristic
76#66951—41no—
77#66946—21no—
78#66945—41no—
79#66943—21no—
80#66942—41no—
81#66941—21no—
82#66940—21no—
83#66940—41no—
84#66939—41no—
85(C22⋊D11)⋊C4—41no—
86#66931—41no—
87#66930—41no—
88C11×Q32—22no—
89C11×M32—22no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#103—21no—
95C11×#103—21no—
96#66899—21no—
97#66899—21no—
98#66893—22no—
99#66892—22no—
100#66885—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66880—21no—
104C8×Dic11D411yescharacteristic
105C8×Dic11D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108#66876—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111#66874—21no—
112#66873—21no—
113#66872—21no—
114#66871—21no—
115#66864—22no—
116#33738—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C22×C4×C11C2×D411yescharacteristic
120C2×C22⋊D11—41no—
121C22×Dic11D811yescharacteristic
122C22×Dic11D811yescharacteristic
123C2×D44—21no—
124C2×C4×D11—41no—
125C2×Dic22—21no—
126C2×Dic22—41no—
127C11×Q16—21no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×Q16—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2411yescharacteristic
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C22⋊Dic11—41no—
142#4326—42no—
143#4325—42no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11D811yescharacteristic
163C4×Dic11D811yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165C4×Dic11C2×D411yescharacteristic
166C2×C11⋊C8—22no—
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169Dic44—21no—
170Dic44—21no—
171D88—21no—
172D88—21no—
173C11×C16—21no—
174C11×C16#4112yes—
175C11⋊C16—21no—
176C11⋊C16#4112yes—
177#3170—111no—
178#3168—111no—
179#2255—111no—
180#2251—111no—
181#2245—111no—
182#2243—111no—
183#2220—111no—
184#2220—111no—
185#2219—111no—
186#2219D1111yescharacteristic, complemented
187C4×Q32—111no—
188C4×Q32—111no—
189C4×SD32—111no—
190C4×SD32—111no—
191C4×M32—111no—
192C23×C11C2×D811yescharacteristic
193C22×D11—41no—
194Q8×C11—41no—
195Q8×C11—41no—
196Q8×C11—41no—
197Q8×C11—41no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C22⋊D11—82no—
207C2×Dic11—22no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11C2×D811yescharacteristic
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216D44—41no—
217D44—41no—
218C4×D11—82no—
219Dic22—41no—
220Dic22—41no—
221Dic22—82no—
222C8×C11—21no—
223C8×C11C2×#4111yescharacteristic
224C8×C11C2×#4111yescharacteristic
225C11⋊C8—21no—
226C11⋊C8#13512yes—
227#533—221no—
228#529—221no—
229C2×Q32—111no—
230C2×Q32C2×D1111yescharacteristic
231C2×SD32—111no—
232C2×SD32—111no—
233C2×M32—111no—
234C2×M32C2×D1111yescharacteristic
235#500—111no—
236#499—111no—
237#495—111no—
238#494—111no—
239#488—221no—
240#487—221no—
241#467—111no—
242#467—221no—
243#467C2×D1111yescharacteristic
244#467C2×D1111yescharacteristic
245#466—111no—
246#465—221no—
247C4×Q16—111no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×Q16—221no—
251C4×SD16—221no—
252C4×D8—111no—
253C2×C4×C8—111no—
254#367—111no—
255#367C2×D1111yescharacteristic
256#366—111no—
257#366—111no—
258#358—111no—
259#358—111no—
260#358—111no—
261#358—111no—
262#358C2×D1111yescharacteristic
263#358C2×D1111yescharacteristic
264#357—111no—
265#357—111no—
266#346—111no—
267#346—111no—
268C4×C16—111no—
269C4×C16—111no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11C22×D811yescharacteristic
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—21no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11#53211yescharacteristic
283C4×C11C2×#13511yescharacteristic
284Dic11—21no—
285Dic11—21no—
286Dic11—21no—
287Dic11—81no—
288Dic11—81no—
289Dic11—81no—
290Dic11#51012yes—
291C2×Q16—111no—
292C2×Q16—221no—
293C2×Q16C22×D1111yescharacteristic
294C2×Q16C22×D1111yescharacteristic
295C2×SD16—221no—
296C2×D8—111no—
297C22×C8—111no—
298C22×C8C22×D1111yescharacteristic
299C4⋊Q8—221no—
300C4⋊Q8—221no—
301#126—441no—
302#125—221no—
303#125—441no—
304#124—221no—
305#123—441no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—221no—
309C22⋊Q8—441no—
310#121—221no—
311C4×Q8—221no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8—441no—
315C4×D4—221no—
316C4×D4—441no—
317#117—441no—
318#117—441no—
319C2×C42—111no—
320Q32—22no—
321Q32—222no—
322SD32—222no—
323SD32—222no—
324M32—22no—
325M32—222no—
326C2×C16—111no—
327C2×C16—111no—
328C2×C16C22×D1111yescharacteristic
329C2×C16C22×D1111yescharacteristic
330#107—111no—
331#107—111no—
332#107—221no—
333#107C22×D1111yescharacteristic
334#107C22×D1111yescharacteristic
335#106—221no—
336#103—21no—
337#103—21no—
338#103—221no—
339#103—221no—
340#103—221no—
341#103—221no—
342#102—221no—
343#102—221no—
344C4×C8—111no—
345C4×C8—111no—
346C4×C8—111no—
347C4×C8—111no—
348C2×C11—41no—
349C2×C11#316911yescharacteristic
350C2×C11C2×#51011yescharacteristic
351C2×C11#341411yescharacteristic
352D11—161no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—221no—
356C2×Q8—441no—
357C2×D4—221no—
358C2×D4—441no—
359C22×C4—111no—
360C22×C4—111no—
361C22×C4—441no—
362C22×C4D4×D1111yescharacteristic
363Q16—21no—
364Q16—21no—
365Q16—21no—
366Q16—21no—
367Q16—221no—
368Q16—221no—
369Q16—442no—
370SD16—442no—
371D8—221no—
372D8—221no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—111no—
376C2×C8—111no—
377C2×C8—222no—
378C2×C8D4×D1111yescharacteristic
379C2×C8C23×D1111yescharacteristic
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C42—111no—
403C42—111no—
404C42—111no—
405C42—111no—
406C42—441no—
407C42—441no—
408C42—441no—
409C16—21no—
410C16—112no—
411C16—221no—
412C16#434112yes—
413C11#3373811yescharacteristic, complemented, Sylow
414C23—441no—
415C23D8×D1111yescharacteristic
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—441no—
421Q8—441no—
422Q8—882no—
423D4—441no—
424D4—441no—
425D4—882no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—111no—
433C2×C4—111no—
434C2×C4—111no—
435C2×C4—111no—
436C2×C4—222no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—882no—
442C2×C4D8×D1111yescharacteristic
443C2×C4C2×D4×D1111yescharacteristic
444C8—21no—
445C8—112no—
446C8—221no—
447C8C2×#434111yescharacteristic
448C8#41×D1111yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—881no—
453C22—881no—
454C22—881no—
455C22C2×D8×D1111yescharacteristic
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—112no—
462C4—221no—
463C4—221no—
464C4—221no—
465C4—881no—
466C4—881no—
467C4—881no—
468C4#1062312711yescharacteristic
469C4D11×#13511yescharacteristic
470C2—41no—
471C2—1761no—
472C2#1307919011yescharacteristic
473C2D11×#51011yescharacteristic
474C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2219C2
socleC22×C11C22×D8
prime radical#10622728C22
hypercenter#2219D11
hypocenterC11#33738
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
1. #13079197C2semidirect
3. #13070901C2semidirect
4. #13070884C2semidirect
5. #13070860C2semidirect
6. #13070854C2semidirect
9. #13070722C2semidirect
10. Q32×Dic11C2semidirect
11. #13070472C2semidirect
12. #13070467C2semidirect
13. #13070465C2semidirect
14. M32×Dic11C2semidirect
15. C11×#2219C2semidirect
186. #2219D11semidirect
413. C11#33738semidirect

Maximal subgroups

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

subgroupindex
#130791972
#130791872
#130709012
#130708842
#130708602
#130708542
#130707312
#130707292
#130707222
Q32×Dic112
#130704722
#130704672
#130704652
M32×Dic112
C11×#22192
#3373811