Finite Group Databasebeta

← #14911405

Subgroups — #14911405

Order 2816.

482 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081036C211yesmaximal, characteristic
2#13081006C211yesmaximal, characteristic, complemented
3#13070890C211yesmaximal, characteristic, complemented
4#13070827C211yesmaximal, characteristic, complemented
5#13070824C211yesmaximal, characteristic, complemented
6#13070798C211yesmaximal, characteristic, complemented
7#13070796C211yesmaximal, characteristic, complemented
8#13070767C211yesmaximal, characteristic, complemented
9#13070762C211yesmaximal, characteristic, complemented
10#13070730C211yesmaximal, characteristic, complemented
11#13070729C211yesmaximal, characteristic, complemented
12#13070467C211yesmaximal, characteristic, complemented
13#13070446C211yesmaximal, characteristic, complemented
14#13070403C211yesmaximal, characteristic, complemented
15C11×#2159C211yesmaximal, characteristic, complemented
16#10623063—21no—
17#10623042—21no—
18C2×C11×M32C2211yescharacteristic
19C11×#427C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21#10622729C2211yescharacteristic
22#10622728C2211yescharacteristic
23C8×C22⋊D11C2211yescharacteristic
24#10622616—21no—
25#10622583—21no—
26C2×#66864C2211yescharacteristic
27C2×#66862C2211yescharacteristic
28#10622500C2211yescharacteristic
29#10622497—21no—
30#10622496C2211yescharacteristic
31#10622493C2211yescharacteristic
32D11×#107C2211yescharacteristic
33#10622488—21no—
34#10622487C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622486C2211yescharacteristic
37#10622485C2211yescharacteristic
38#10622483—21no—
39#10622479—21no—
40C11×#367C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622147C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47#10622142C2211yescharacteristic
48#10622141C2211yescharacteristic
49Dic11⋊C16C2211yescharacteristic
50C16×Dic11C2211yescharacteristic
51#10622130C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×#117—21no—
61C2×C11×C4⋊C4—21no—
62#66983—21no—
63C4×C22⋊D11—41no—
64C4×C22⋊D11D411yescharacteristic
65#66977—21no—
66#66977—41no—
67C2×Dic44C2311yescharacteristic
68C2×D88C2311yescharacteristic
69C2×C8×D11C2311yescharacteristic
70#66950—21no—
71#66949—41no—
72#66948—21no—
73#66946—21no—
74#66945—21no—
75C4⋊C4×D11—21no—
76#66942—41no—
77#66941—21no—
78#66941—21no—
79#66940—21no—
80#66938—41no—
81#66937—41no—
82#66928—41no—
83#66925—41no—
84C11×M32—22no—
85C2×C11×C16C2311yescharacteristic
86C2×C11×C16C2311yescharacteristic
87C11×#107—21no—
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
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#66872—21no—
108#66871—21no—
109#66871—21no—
110#66871—21no—
111#66864—22no—
112#66862—22no—
113#33924—111nomaximal, Sylow
114C22×C4×C11—41no—
115C22×C4×C11C2×D411yescharacteristic
116C2×C22⋊D11—41no—
117C2×C22⋊D11D811yescharacteristic
118C2×D44—21no—
119C2×D44—41no—
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11C2×D411yescharacteristic
123C2×Dic22—21no—
124C2×Dic22—41no—
125C2×Dic22—41no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—41no—
136C42×C11—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11D811yescharacteristic
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4D811yescharacteristic
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4D811yescharacteristic
154C4×Dic11—41no—
155C4×Dic11—41no—
156C4×Dic11C2×D411yescharacteristic
157C2×C11⋊C8C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159Dic44—21no—
160Dic44—21no—
161D88—21no—
162D88—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16#4112yes—
167C11⋊C16—21no—
168C11⋊C16—21no—
169#3341—111no—
170#3338—111no—
171#2252—111no—
172#2237—111no—
173#2237—111no—
174#2232—111no—
175#2232—111no—
176#2227—111no—
177#2226—111no—
178#2220—111no—
179#2220—111no—
180C4×SD32—111no—
181#2169—111no—
182#2159—111no—
183#2159D1111yescharacteristic, complemented
184C23×C11C2×D811yescharacteristic
185C22×D11—41no—
186C22×D11C2×D811yescharacteristic
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—161no—
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C22⋊D11—22no—
197C22⋊D11—161no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11C2×D811yescharacteristic
202C2×Dic11C2×D811yescharacteristic
203C2×Dic11C2×D811yescharacteristic
204D44—41no—
205D44—41no—
206D44—161no—
207C4×D11—21no—
208C4×D11—21no—
209C4×D11—82no—
210C4×D11—161no—
211Dic22—41no—
212Dic22—41no—
213Dic22—161no—
214Dic22—161no—
215C8×C11—21no—
216C8×C11C2×#4111yescharacteristic
217C8×C112−1+411yescharacteristic
218C11⋊C8—21no—
219C11⋊C8—21no—
220#555—221no—
221#554—221no—
222C2×SD32—111no—
223C2×M32—111no—
224C2×M32C2×D1111yescharacteristic
225#500—111no—
226#500—111no—
227#484—221no—
228#484—221no—
229#482—221no—
230#482—221no—
231#477—221no—
232#476—221no—
233#467—111no—
234#467—111no—
235#466—111no—
236#466—111no—
237C4×Q16—111no—
238C4×D8—111no—
239C8×D4—111no—
240#427—111no—
241#427C2×D1111yescharacteristic
242C2×#107—111no—
243C2×#107C2×D1111yescharacteristic
244#367—111no—
245#367C2×D1111yescharacteristic
246#367C2×D1111yescharacteristic
247#366—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251#366C2×D1111yescharacteristic
252#366C2×D1111yescharacteristic
253C4⋊C16—111no—
254#358—111no—
255#358—111no—
256#358—111no—
257#357—111no—
258#357—111no—
259#357—111no—
260C22⋊C16—111no—
261C22⋊C16—111no—
262C4×C16—111no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11C22×D811yescharacteristic
267C2×D11—21no—
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—81no—
271C2×D11—81no—
272C2×D11—81no—
273C4×C11—21no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11#54711yescharacteristic
279C4×C11#57811yescharacteristic
280Dic11—21no—
281Dic11—21no—
282Dic11—81no—
283Dic11—81no—
284Dic11—81no—
285Dic11#51012yes—
286C2×Q16—111no—
287C2×D8—111no—
288C22×C8—111no—
289C22×C8C22×D1111yescharacteristic
290C4⋊Q8—221no—
291C4⋊Q8—221no—
292#125—441no—
293#124—441no—
294#124—441no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297C22⋊Q8—441no—
298C22⋊Q8—441no—
299#121—221no—
300#121—221no—
301#121—441no—
302C4×Q8—221no—
303C4×D4—111no—
304C4×D4—221no—
305C4×D4—441no—
306#117—21no—
307#117—221no—
308#117—441no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—221no—
311SD32—222no—
312M32—22no—
313M32—222no—
314C2×C16—111no—
315C2×C16—111no—
316C2×C16C22×D1111yescharacteristic
317C2×C16C22×D1111yescharacteristic
318#107—21no—
319#107—111no—
320#107—111no—
321#107—221no—
322#107—221no—
323#107—221no—
324#107C22×D1111yescharacteristic
325#107C22×D1111yescharacteristic
326#107C22×D1111yescharacteristic
327#107C22×D1111yescharacteristic
328#106—21no—
329#106—221no—
330C4⋊C8—111no—
331#103—221no—
332#103—221no—
333#103—221no—
334#102—221no—
335#102—221no—
336#102—221no—
337C22⋊C8—111no—
338C22⋊C8—111no—
339C4×C8—111no—
340C2×C11—41no—
341C2×C11#333411yescharacteristic
342C2×C11C2×#51011yescharacteristic
343C2×C11#341511yescharacteristic
344D11—41no—
345D11—161no—
346C2×Q8—221no—
347C2×Q8—441no—
348C2×Q8—441no—
349C2×D4—111no—
350C2×D4—221no—
351C2×D4—441no—
352C2×D4—441no—
353C22×C4—41no—
354C22×C4—111no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4D4×D1111yescharacteristic
358Q16—221no—
359Q16—221no—
360D8—221no—
361D8—221no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—111no—
365C2×C8—111no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8D4×D1111yescharacteristic
369C2×C8C23×D1111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—111no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C22⋊C4—41no—
385C22⋊C4—111no—
386C22⋊C4—111no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C42—41no—
394C42—111no—
395C42—441no—
396C42—441no—
397C16—21no—
398C16—221no—
399C16—221no—
400C16#433912yes—
401C11#3392411yescharacteristic, complemented, Sylow
402C23—111no—
403C23—441no—
404C23D8×D1111yescharacteristic
405Q8—441no—
406Q8—441no—
407Q8—1761no—
408Q8—1761no—
409D4—222no—
410D4—441no—
411D4—441no—
412D4—1761no—
413D4—1761no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—111no—
421C2×C4—111no—
422C2×C4—111no—
423C2×C4—161no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—882no—
430C2×C4—1761no—
431C2×C4D8×D1111yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C8—21no—
434C8—221no—
435C8—221no—
436C8C2×#433911yescharacteristic
437C8#6704011yescharacteristic
438C22—21no—
439C22—21no—
440C22—21no—
441C22—221no—
442C22—221no—
443C22—221no—
444C22—881no—
445C22—881no—
446C22—881no—
447C22C2×D8×D1111yescharacteristic
448C4—21no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—112no—
454C4—221no—
455C4—221no—
456C4—881no—
457C4—881no—
458C4—881no—
459C4#1062303811yescharacteristic
460C4#1062329711yescharacteristic
461C2—41no—
462C2—441no—
463C2—1761no—
464C2#1308096111yescharacteristic
465C2D11×#51011yescharacteristic
466C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radical#13081036C2
hypercenter#2159D11
hypocenterC11#33924
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
2. #13081006C2semidirect
3. #13070890C2semidirect
4. #13070827C2semidirect
5. #13070824C2semidirect
6. #13070798C2semidirect
7. #13070796C2semidirect
8. #13070767C2semidirect
9. #13070762C2semidirect
10. #13070730C2semidirect
11. #13070729C2semidirect
12. #13070467C2semidirect
13. #13070446C2semidirect
14. #13070403C2semidirect
15. C11×#2159C2semidirect
183. #2159D11semidirect
401. C11#33924semidirect

Maximal subgroups

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

subgroupindex
#130810362
#130810062
#130708902
#130708272
#130708242
#130707982
#130707962
#130707672
#130707622
#130707302
#130707292
#130704672
#130704462
#130704032
C11×#21592
#3392411