Finite Group Databasebeta

← #14911170

Subgroups — #14911170

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081006C211yesmaximal, characteristic
2#13081005C211yesmaximal, characteristic
3#13070890C211yesmaximal, characteristic, complemented
4#13070820C211yesmaximal, characteristic, complemented
5#13070819C211yesmaximal, characteristic, complemented
6#13070817C211yesmaximal, characteristic, complemented
7#13070767C211yesmaximal, characteristic, complemented
8#13070766C211yesmaximal, characteristic, complemented
9#13070706C211yesmaximal, characteristic, complemented
10#13070705C211yesmaximal, characteristic, complemented
11#13070472C211yesmaximal, characteristic, complemented
12(C22⋊D11)⋊C16C211yesmaximal, characteristic
13C2×#10622127C211yesmaximal, characteristic, complemented
14D11×#366C211yesmaximal, characteristic, complemented
15C11×#2236C211yesmaximal, characteristic, complemented
16#10623166—21no—
17#10623042—21no—
18C11×#467C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20#10622801C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22C2×#66893C2211yescharacteristic
23#10622729C2211yescharacteristic
24C8×C22⋊D11C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C22×C11⋊C16C2211yescharacteristic
27#10622657—21no—
28#10622583—21no—
29C2×C16×D11C2211yescharacteristic
30#10622500C2211yescharacteristic
31#10622497—21no—
32D11×#107C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622488—21no—
35#10622487C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622422—21no—
39#10622407—21no—
40C11×#366C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45#10622202C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47#10622142C2211yescharacteristic
48#10622142C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×C22⋊Q8—21no—
62C2×C11×C4⋊C4—21no—
63#66999—21no—
64Q8×Dic11—21no—
65C4×C22⋊D11—41no—
66C4×C22⋊D11D411yescharacteristic
67C2×C4⋊Dic11—21no—
68#66977—21no—
69#66977—41no—
70C2×Dic44C2311yescharacteristic
71C2×C8×D11C2311yescharacteristic
72#66950—21no—
73#66950—41no—
74#66949—41no—
75C4⋊C4×D11—21no—
76C4⋊C4×D11—21no—
77#66942—41no—
78#66942—41no—
79#66941—21no—
80#66941—21no—
81#66940—21no—
82(C22⋊D11)⋊C4—41no—
83#66931—41no—
84C2×C11×C16C2311yescharacteristic
85C2×C11×C16C2311yescharacteristic
86C11×#107—21no—
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#103—21no—
91#66899—21no—
92#66899—21no—
93C22⋊(C11⋊C8)D411yescharacteristic
94#66893—22no—
95(C2×D11)⋊C8D411yescharacteristic
96#66882—21no—
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66880—21no—
101Dic11⋊C8D411yescharacteristic
102C8×Dic11C2311yescharacteristic
103C2×C11⋊C16—22no—
104C2×C11⋊C16C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106#66874—21no—
107#66874—21no—
108#66871—21no—
109#66871—21no—
110#66871—21no—
111#66871—21no—
112C16×D11—22no—
113#33905—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C2×C22⋊D11D811yescharacteristic
118C22×Dic11—41no—
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×C4×D11C2×D411yescharacteristic
122C2×Dic22—21no—
123C2×Dic22—41no—
124C2×Dic22—41no—
125C11×Q16—21no—
126C11×Q16—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11D811yescharacteristic
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4D811yescharacteristic
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—41no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148Dic11⋊C4—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×Dic11—41no—
158C4×Dic11C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160C2×C11⋊C8C2×D411yescharacteristic
161Dic44—21no—
162Dic44—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3338—111no—
170#3338—111no—
171#2252—111no—
172#2236—111no—
173#2236—111no—
174#2236—111no—
175#2236D1111yescharacteristic, complemented
176#2227—111no—
177#2227—111no—
178#2216—111no—
179#2216—111no—
180C4×Q32—111no—
181D4×C16—111no—
182C2×#366—111no—
183C2×#366—111no—
184C23×C11C2×D811yescharacteristic
185C22×D11C2×D811yescharacteristic
186Q8×C11—41no—
187Q8×C11—41no—
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—161no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C22⋊D11Q3214yescomplemented
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—161no—
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205C2×Dic11C2×D811yescharacteristic
206C4×D11—21no—
207C4×D11—21no—
208C4×D11—161no—
209C4×D11—161no—
210Dic22—41no—
211Dic22—41no—
212Dic22—161no—
213Dic22—161no—
214C8×C11—21no—
215C8×C11C2×#4111yescharacteristic
216C8×C112−1+411yescharacteristic
217C11⋊C8—21no—
218C11⋊C8—21no—
219#554—221no—
220#554—221no—
221C2×Q32—111no—
222C22×C16—111no—
223C22×C16—111no—
224#500—111no—
225#500—111no—
226#484—221no—
227#484—221no—
228#484—221no—
229#484—221no—
230#477—221no—
231#477—221no—
232#467—111no—
233#467—111no—
234#467—111no—
235#467C2×D1111yescharacteristic
236C4×Q16—111no—
237C4×Q16—111no—
238C8×D4—111no—
239C2×#107—111no—
240C2×#107—111no—
241C2×#107—111no—
242C2×#107C2×D1111yescharacteristic
243#366—111no—
244#366—111no—
245#366—111no—
246#366—111no—
247#366—111no—
248#366—111no—
249#366—111no—
250#366C2×D1111yescharacteristic
251#366C2×D1111yescharacteristic
252C4⋊C16—111no—
253#358—111no—
254#358—111no—
255#358—111no—
256#358—111no—
257#358C2×D1111yescharacteristic
258#358C2×D1111yescharacteristic
259C22⋊C16—111no—
260C22⋊C16C2×D1111yescharacteristic
261C4×C16—111no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11C2×Q3212yes—
265C22×C11C22×D811yescharacteristic
266C2×D11—21no—
267C2×D11—21no—
268C2×D11C2×Q3212yes—
269C4×C11—21no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11—81no—
273C4×C11—81no—
274C4×C11#54711yescharacteristic
275C4×C11#57811yescharacteristic
276Dic11—21no—
277Dic11—21no—
278Dic11—81no—
279Dic11—81no—
280Dic11—81no—
281Dic11—81no—
282Dic11C2×Q3212yes—
283C2×Q16—111no—
284C2×Q16C22×D1111yescharacteristic
285C22×C8—111no—
286C22×C8C22×D1111yescharacteristic
287C4⋊Q8—221no—
288C4⋊Q8—221no—
289#125—441no—
290#125—441no—
291C22⋊Q8—21no—
292C22⋊Q8—221no—
293C22⋊Q8—221no—
294C22⋊Q8—221no—
295C22⋊Q8—441no—
296C22⋊Q8—441no—
297C22⋊Q8—441no—
298C22⋊Q8—441no—
299C4×Q8—221no—
300C4×Q8—221no—
301C4×D4—111no—
302C4×D4—441no—
303C4×D4—441no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308Q32—222no—
309C2×C16—111no—
310C2×C16—111no—
311C2×C16—222no—
312C2×C16—222no—
313C2×C16C22×D1111yescharacteristic
314C2×C16C22×D1111yescharacteristic
315#107—21no—
316#107—111no—
317#107—111no—
318#107—111no—
319#107—221no—
320#107—221no—
321#107—221no—
322#107—221no—
323#107—221no—
324#107C22×D1111yescharacteristic
325#107C22×D1111yescharacteristic
326#107C22×D1111yescharacteristic
327C4⋊C8—111no—
328#103—21no—
329#103—221no—
330#103—221no—
331#103—221no—
332#103—221no—
333#103—221no—
334C22⋊C8—111no—
335C22⋊C8—111no—
336C4×C8—111no—
337C2×C11—22no—
338C2×C11#333411yescharacteristic
339C2×C11C22×Q3211yescharacteristic
340C2×C11#341511yescharacteristic
341D11—22no—
342C2×Q8—21no—
343C2×Q8—221no—
344C2×Q8—441no—
345C2×Q8—441no—
346C2×D4—111no—
347C22×C4—41no—
348C22×C4—111no—
349C22×C4—441no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4D4×D1111yescharacteristic
353Q16—21no—
354Q16—21no—
355Q16—221no—
356Q16—221no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—111no—
360C2×C8—111no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8D4×D1111yescharacteristic
364C2×C8C23×D1111yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—111no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
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—
390C42—111no—
391C42—441no—
392C42—441no—
393C16—21no—
394C16—21no—
395C16—112no—
396C16—221no—
397C11#3390511yescharacteristic, complemented, Sylow
398C23—111no—
399C23D8×D1111yescharacteristic
400Q8—41no—
401Q8—41no—
402Q8—441no—
403Q8—441no—
404Q8—1761no—
405Q8—1761no—
406D4—114no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—111no—
414C2×C4—111no—
415C2×C4—111no—
416C2×C4—161no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—1761no—
424C2×C4—1761no—
425C2×C4—1761no—
426C2×C4D8×D1111yescharacteristic
427C2×C4C2×D4×D1111yescharacteristic
428C8—21no—
429C8—221no—
430C8—221no—
431C8#41×D1111yescharacteristic
432C8#6704311yescharacteristic
433C22—21no—
434C22—21no—
435C22—112no—
436C22—221no—
437C22—221no—
438C22D11×Q3212yes—
439C22C2×D8×D1111yescharacteristic
440C4—21no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4—112no—
446C4—221no—
447C4—221no—
448C4—881no—
449C4—881no—
450C4—881no—
451C4—881no—
452C4#1062318611yescharacteristic
453C4#1062331011yescharacteristic
454C2—22no—
455C2—222no—
456C2#1308095811yescharacteristic
457C2C2×D11×Q3211yescharacteristic
458C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2236C2
socleC22×C11C22×D8
prime radicalC2×C22⋊D11D8
hypercenter#2236D11
hypocenterC11#33905
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
3. #13070890C2semidirect
4. #13070820C2semidirect
5. #13070819C2semidirect
6. #13070817C2semidirect
7. #13070767C2semidirect
8. #13070766C2semidirect
9. #13070706C2semidirect
10. #13070705C2semidirect
11. #13070472C2semidirect
13. C2×#10622127C2semidirect
14. D11×#366C2semidirect
15. C11×#2236C2semidirect
175. #2236D11semidirect
197. C22⋊D11Q32semidirect
397. C11#33905semidirect

Maximal subgroups

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

subgroupindex
#130810062
#130810052
#130708902
#130708202
#130708192
#130708172
#130707672
#130707662
#130707062
#130707052
#130704722
(C22⋊D11)⋊C162
C2×#106221272
D11×#3662
C11×#22362
#3390511