Finite Group Databasebeta

← #14909886

Subgroups — #14909886

Order 2816.

504 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic
2#13079129C211yesmaximal, characteristic, complemented
3#13070897C211yesmaximal, characteristic, complemented
4#13070890C211yesmaximal, characteristic, complemented
5#13070838C211yesmaximal, characteristic, complemented
6#13070838C211yesmaximal, characteristic, complemented
7#13070810C211yesmaximal, characteristic, complemented
8#13070809C211yesmaximal, characteristic, complemented
9#13070806C211yesmaximal, characteristic, complemented
10#13070805C211yesmaximal, characteristic, complemented
11#13070774C211yesmaximal, characteristic, complemented
12#13070773C211yesmaximal, characteristic, complemented
13#13070770C211yesmaximal, characteristic, complemented
14#13070414C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16#10623219—21no—
17#10623079—21no—
18C11×#499C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20#10622770C2211yescharacteristic
21#10622764C2211yescharacteristic
22#10622677—21no—
23C4×#4323—21no—
24#10622496C2211yescharacteristic
25#10622493C2211yescharacteristic
26#10622493C2211yescharacteristic
27#10622487C2211yescharacteristic
28#10622487C2211yescharacteristic
29#10622487C2211yescharacteristic
30#10622473—21no—
31#10622468—21no—
32#10622388—21no—
33#10622373—21no—
34C4×D88C2211yescharacteristic
35C4×C8×D11C2211yescharacteristic
36#10622296C2211yescharacteristic
37C11×#367C2211yescharacteristic
38C11×#366C2211yescharacteristic
39C11×C4⋊C16C2211yescharacteristic
40C11×#357C2211yescharacteristic
41C11×#357C2211yescharacteristic
42#10622200C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622147C2211yescharacteristic
45#10622147C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622142C2211yescharacteristic
50C16×Dic11C2211yescharacteristic
51C16×Dic11C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×#4339—41no—
60C2×C11×D8C2311yescharacteristic
61C11×#125—21no—
62C4×D4×C11—21no—
63#66993—21no—
64#66991—21no—
65C2×#4323—21no—
66C4×C22⋊D11—41no—
67C2×D88C2311yescharacteristic
68C2×C8×D11D411yescharacteristic
69C2×C8×D11C2311yescharacteristic
70#66949—41no—
71#66949—41no—
72#66948—21no—
73#66945—21no—
74#66945—21no—
75#66941—21no—
76#66941—21no—
77#66941—21no—
78#66940—41no—
79#66940—41no—
80#66938—41no—
81#66937—41no—
82C4×D44—21no—
83C42×D11D411yescharacteristic
84#66923—21no—
85C2×C11×C16C2311yescharacteristic
86C2×C11×C16C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#106—21no—
91C11×#102—21no—
92C4×C8×C11C2311yescharacteristic
93#66896—21no—
94#66885—21no—
95#66882C2311yescharacteristic
96#66882C2311yescharacteristic
97#66882C2311yescharacteristic
98#66881—21no—
99C8×Dic11D411yescharacteristic
100C8×Dic11C2311yescharacteristic
101C2×C11⋊C16C2311yescharacteristic
102C2×C11⋊C16C2311yescharacteristic
103#66873—21no—
104#66872—21no—
105#66872—21no—
106#66871—21no—
107#66871—21no—
108#66871—21no—
109C4×C11⋊C8D411yescharacteristic
110#33794—111nomaximal, Sylow
111C2×D4×C11—21no—
112C22×C4×C11—41no—
113C2×C22⋊D11—41no—
114C2×C22⋊D11—41no—
115C2×C22⋊D11—41no—
116#4339—84no—
117C2×D44—21no—
118C2×D44—41no—
119C2×C4×D11—41no—
120C2×C4×D11D811yescharacteristic
121C2×C4×D11D811yescharacteristic
122C2×C4×D11C2×D411yescharacteristic
123C2×Dic22—41no—
124C2×Dic22—41no—
125C2×Dic22—41no—
126C11×D8—21no—
127C11×D8—21no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—41no—
136C42×C11C2×D411yescharacteristic
137C22⋊Dic11—41no—
138#4323—42no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146Dic11⋊C4—41no—
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151C4×Dic11—41no—
152C4×Dic11—41no—
153C4×Dic11D811yescharacteristic
154C4×Dic11D811yescharacteristic
155C4×Dic11C2×D411yescharacteristic
156C2×C11⋊C8C2×D411yescharacteristic
157C2×C11⋊C8C2×D411yescharacteristic
158D88—21no—
159D88—21no—
160C8×D11—21no—
161C8×D11—21no—
162C8×D11—22no—
163C11×C16—21no—
164C11×C16—21no—
165C11⋊C16—21no—
166C11⋊C16—21no—
167#3169—111no—
168#3160—111no—
169#2254—111no—
170#2252—111no—
171#2240—111no—
172#2240—111no—
173#2234—111no—
174#2234—111no—
175#2234—111no—
176#2234—111no—
177#2228—111no—
178#2228—111no—
179#2228—111no—
180#2228D1111yescharacteristic, complemented
181#2162—111no—
182C23×C11—41no—
183C22×D11—41no—
184C22×D11C2×D811yescharacteristic
185D4×C11—41no—
186D4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—82no—
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C22⋊D11—82no—
195C22⋊D11—82no—
196C22⋊D11—82no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11C2×D811yescharacteristic
201C2×Dic11C2×D811yescharacteristic
202C2×Dic11C2×D811yescharacteristic
203D44—41no—
204D44—41no—
205D44—82no—
206C4×D11—21no—
207C4×D11—21no—
208C4×D11—22no—
209C4×D11—22no—
210C4×D11—82no—
211Dic22—82no—
212Dic22—82no—
213Dic22—82no—
214C8×C11—21no—
215C8×C112−1+411yescharacteristic
216C8×C112−1+411yescharacteristic
217C11⋊C8—21no—
218C11⋊C8#13712yes—
219#533—221no—
220#532—221no—
221#500—111no—
222#500—111no—
223#500—111no—
224#499—111no—
225#499—221no—
226#499C2×D1111yescharacteristic
227#498—221no—
228#493—111no—
229#486—221no—
230#466—111no—
231#466—111no—
232#466—221no—
233C4×D8—111no—
234C4×D8—221no—
235C4×D8C2×D1111yescharacteristic
236#427—111no—
237#427—111no—
238#427—221no—
239C2×C4×C8—111no—
240#367—111no—
241#367—111no—
242#367—111no—
243#367C2×D1111yescharacteristic
244#366—111no—
245#366—111no—
246#366—111no—
247#366C2×D1111yescharacteristic
248C4⋊C16—111no—
249C4⋊C16C2×D1111yescharacteristic
250#357—111no—
251#357—111no—
252#357—111no—
253#357—111no—
254#357—111no—
255#357—111no—
256#357C2×D1111yescharacteristic
257#357C2×D1111yescharacteristic
258C22⋊C16—111no—
259C22⋊C16—111no—
260C4×C16—111no—
261C4×C16—111no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11C22×D811yescharacteristic
266C2×D11—21no—
267C2×D11—21no—
268C2×D11—21no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11#53611yescharacteristic
278C4×C11C2×#13711yescharacteristic
279Dic11—21no—
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11#50812yes—
284Dic11#50912yes—
285C2×#41—441no—
286C2×D8—111no—
287C2×D8—221no—
288C2×D8C22×D1111yescharacteristic
289C22×C8—111no—
290C22×C8—111no—
291C4⋊Q8—221no—
292C4⋊Q8—221no—
293C4⋊Q8—221no—
294#127—221no—
295#125—21no—
296#125—221no—
297#124—441no—
298C22⋊Q8—441no—
299C22⋊Q8—441no—
300#121—221no—
301#121—221no—
302#121—441no—
303C4×Q8—441no—
304C4×Q8—441no—
305C4×D4—21no—
306C4×D4—221no—
307C4×D4—441no—
308#117—221no—
309#117—221no—
310C2×C42—111no—
311C2×C16—111no—
312C2×C16—111no—
313C2×C16C22×D1111yescharacteristic
314C2×C16C22×D1111yescharacteristic
315#107—111no—
316#107—111no—
317#107—111no—
318#107—221no—
319#107—221no—
320#107—221no—
321#107C22×D1111yescharacteristic
322#107C22×D1111yescharacteristic
323#107C22×D1111yescharacteristic
324#106—21no—
325#106—221no—
326#106—221no—
327#106—221no—
328#102—21no—
329#102—221no—
330#102—221no—
331#102—221no—
332C4×C8—111no—
333C4×C8—111no—
334C4×C8—111no—
335C4×C8C22×D1111yescharacteristic
336C2×C11—161no—
337C2×C11#322611yescharacteristic
338C2×C11C2×#50811yescharacteristic
339C2×C11C2×#50911yescharacteristic
340D11—41no—
341D11—161no—
342#41—884no—
343C2×Q8—441no—
344C2×Q8—441no—
345C2×Q8—441no—
346C2×D4—21no—
347C2×D4—221no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—441no—
352C22×C4—41no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—441no—
357D8—21no—
358D8—21no—
359D8—221no—
360D8—221no—
361D8—442no—
362C2×C8—111no—
363C2×C8—111no—
364C2×C8—222no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8D4×D1111yescharacteristic
368C2×C8C23×D1111yescharacteristic
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C22⋊C4—41no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C42—111no—
389C42—111no—
390C42—111no—
391C42—441no—
392C42—441no—
393C42D4×D1111yescharacteristic
394C16—21no—
395C16—21no—
396C16—221no—
397C16—221no—
398C11#3379411yescharacteristic, complemented, Sylow
399C23—41no—
400C23—111no—
401C23—441no—
402Q8—882no—
403Q8—882no—
404Q8—882no—
405D4—41no—
406D4—41no—
407D4—441no—
408D4—441no—
409D4—882no—
410D4—882no—
411D4—882no—
412D4—882no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—82no—
417C2×C4—111no—
418C2×C4—111no—
419C2×C4—111no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—882no—
428C2×C4D8×D1111yescharacteristic
429C2×C4D8×D1111yescharacteristic
430C2×C4C2×D4×D1111yescharacteristic
431C8—21no—
432C8—112no—
433C8—221no—
434C8#6704011yescharacteristic
435C8#6704311yescharacteristic
436C22—81no—
437C22—81no—
438C22—81no—
439C22—221no—
440C22—221no—
441C22—221no—
442C22—881no—
443C22—881no—
444C22—881no—
445C22C2×D8×D1111yescharacteristic
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—112no—
452C4—112no—
453C4—221no—
454C4—881no—
455C4—881no—
456C4—881no—
457C4#1062315911yescharacteristic
458C4D11×#13711yescharacteristic
459C2—161no—
460C2—441no—
461C2—1761no—
462C2#1307973611yescharacteristic
463C2D11×#50811yescharacteristic
464C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
prime radical#13079192C2
hypercenter#2228D11
hypocenterC11#33794
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
2. #13079129C2semidirect
3. #13070897C2semidirect
4. #13070890C2semidirect
5. #13070838C2semidirect
6. #13070838C2semidirect
7. #13070810C2semidirect
8. #13070809C2semidirect
9. #13070806C2semidirect
10. #13070805C2semidirect
11. #13070774C2semidirect
12. #13070773C2semidirect
13. #13070770C2semidirect
14. #13070414C2semidirect
15. C11×#2228C2semidirect
180. #2228D11semidirect
398. C11#33794semidirect

Maximal subgroups

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

subgroupindex
#130791922
#130791292
#130708972
#130708902
#130708382
#130708102
#130708092
#130708062
#130708052
#130707742
#130707732
#130707702
#130704142
C11×#22282
#3379411