Finite Group Databasebeta

← #14911243

Subgroups — #14911243

Order 2816.

472 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081010C211yesmaximal, characteristic
2#13080986C211yesmaximal, characteristic
3#13070902C211yesmaximal, characteristic, complemented
4#13070823C211yesmaximal, characteristic, complemented
5#13070817C211yesmaximal, characteristic, complemented
6#13070812C211yesmaximal, characteristic, complemented
7#13070812C211yesmaximal, characteristic, complemented
8#13070780C211yesmaximal, characteristic, complemented
9#13070758C211yesmaximal, characteristic, complemented
10#13070721C211yesmaximal, characteristic, complemented
11#13070704C211yesmaximal, characteristic, complemented
12#13070443C211yesmaximal, characteristic
13#13070403C211yesmaximal, characteristic, complemented
14D11×#367C211yesmaximal, characteristic, complemented
15C11×#2176C211yesmaximal, characteristic, complemented
16#10623112—21no—
17#10623110—21no—
18C2×C11×Q32C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622801C2211yescharacteristic
22#10622801C2211yescharacteristic
23#10622801C2211yescharacteristic
24#10622801C2211yescharacteristic
25#10622635—21no—
26#10622634—21no—
27C2×#66862C2211yescharacteristic
28C2×C16×D11C2211yescharacteristic
29#10622493C2211yescharacteristic
30D11×#107C2211yescharacteristic
31D11×#107C2211yescharacteristic
32D11×#107C2211yescharacteristic
33#10622428—21no—
34#10622422—21no—
35#10622422—21no—
36#10622418—21no—
37C8×D44C2211yescharacteristic
38#10622296C2211yescharacteristic
39#10622295C2211yescharacteristic
40C11×#367C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#346C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622142C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×Q16C2311yescharacteristic
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63#66999—21no—
64#66999—21no—
65#66999—21no—
66#66999—21no—
67C2×C8×D11C2311yescharacteristic
68C2×C8×D11C2311yescharacteristic
69#66949—41no—
70#66949—41no—
71#66947—41no—
72#66945—21no—
73C4⋊C4×D11—21no—
74C4⋊C4×D11—21no—
75C4⋊C4×D11—21no—
76#66942—41no—
77#66929—41no—
78C4×D44—41no—
79C4×D44D411yescharacteristic
80#66925—41no—
81#66923—21no—
82#66923—41no—
83#66922—21no—
84C11×Q32—22no—
85C2×C11×C16C2311yescharacteristic
86C2×C11×C16C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#103—21no—
90C11×#103—21no—
91C4×C8×C11C2311yescharacteristic
92#66899—21no—
93#66899—21no—
94#66899—21no—
95#66899—21no—
96(C2×D11)⋊C8D411yescharacteristic
97(C2×D11)⋊C8D411yescharacteristic
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66881—21no—
104C2×C11⋊C16C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106#66872—21no—
107#66871—21no—
108#66871—21no—
109#66871—21no—
110C4⋊(C11⋊C8)D411yescharacteristic
111#66862—22no—
112C16×D11—22no—
113#33911—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×D44D811yescharacteristic
117C2×C4×D11—41no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C2×C4×D11C2×D411yescharacteristic
121C2×C4×D11C2×D411yescharacteristic
122C2×Dic22—41no—
123C11×Q16—21no—
124C11×Q16—21no—
125C11×Q16—21no—
126C11×Q16—21no—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2411yescharacteristic
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C42×C11—41no—
134C42×C11—41no—
135C42×C11C2×D411yescharacteristic
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4D811yescharacteristic
142(C2×D11)⋊C4D811yescharacteristic
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—41no—
148C4⋊Dic11D811yescharacteristic
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158C4×Dic11—41no—
159C2×C11⋊C8C2×D411yescharacteristic
160C2×C11⋊C8C2×D411yescharacteristic
161C8×D11—21no—
162C8×D11—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16#4112yes—
167C11⋊C16—21no—
168C11⋊C16—21no—
169#3338—111no—
170#3336—111no—
171#2255—111no—
172#2237—111no—
173#2236—111no—
174#2235—111no—
175#2235—111no—
176#2229—111no—
177#2225—111no—
178#2219—111no—
179#2216—111no—
180#2176D1111yescharacteristic, complemented
181#2168—111no—
182#2159—111no—
183C2×#367—111no—
184C22×D11C2×D811yescharacteristic
185C22×D11C2×D811yescharacteristic
186Q8×C11—41no—
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11C2×D811yescharacteristic
202C2×Dic11C2×D811yescharacteristic
203D44—22no—
204C4×D11—21no—
205C4×D11—21no—
206C4×D11—21no—
207C4×D11—21no—
208C4×D11—82no—
209C4×D11—161no—
210C4×D11—161no—
211Dic22—161no—
212C8×C11—21no—
213C8×C11C2×#4111yescharacteristic
214C8×C112−1+411yescharacteristic
215C11⋊C8—21no—
216C11⋊C8—21no—
217#554—221no—
218#552—221no—
219C2×Q32C2×D1111yescharacteristic
220C2×M32—111no—
221C22×C16—111no—
222#500—111no—
223#499—111no—
224#485—221no—
225#484—221no—
226#484—221no—
227#483—221no—
228#479—221no—
229#477—221no—
230#467—111no—
231#467—111no—
232#467—111no—
233#467—111no—
234C4×Q16C2×D1111yescharacteristic
235C4×Q16C2×D1111yescharacteristic
236C8×D4—111no—
237#427—111no—
238C2×#107—111no—
239C2×#107—111no—
240C2×#107—111no—
241#367—111no—
242#367—111no—
243#367—111no—
244#367—111no—
245#367—111no—
246#367C2×D1111yescharacteristic
247#366—111no—
248#366—111no—
249#366—111no—
250C4⋊C16—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#358C2×D1111yescharacteristic
256#358C2×D1111yescharacteristic
257C22⋊C16—111no—
258C22⋊C16—111no—
259#346C2×D1111yescharacteristic
260C22×C11C22×D811yescharacteristic
261C2×D11—21no—
262C2×D11—21no—
263C2×D11—21no—
264C2×D11—21no—
265C2×D11—21no—
266C2×D11#51012yes—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11—81no—
273C4×C11#54711yescharacteristic
274C4×C11#57811yescharacteristic
275Dic11—21no—
276Dic11—21no—
277Dic11—81no—
278Dic11—81no—
279Dic11—81no—
280Dic11—81no—
281C2×Q16C22×D1111yescharacteristic
282C2×Q16C22×D1111yescharacteristic
283C22×C8—111no—
284C22×C8—111no—
285C4⋊Q8—221no—
286#126—441no—
287#125—221no—
288#125—441no—
289#125—441no—
290#123—441no—
291C22⋊Q8—221no—
292C22⋊Q8—221no—
293C22⋊Q8—221no—
294C22⋊Q8—221no—
295C22⋊Q8—441no—
296C22⋊Q8—441no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×D4—111no—
300C4×D4—441no—
301#117—221no—
302#117—441no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306Q32—22no—
307M32—222no—
308C2×C16—111no—
309C2×C16—111no—
310C2×C16—222no—
311C2×C16C22×D1111yescharacteristic
312C2×C16C22×D1111yescharacteristic
313#107—111no—
314#107—111no—
315#107—111no—
316#107—111no—
317#107—221no—
318#107—221no—
319#107—221no—
320#107—221no—
321#107C22×D1111yescharacteristic
322#107C22×D1111yescharacteristic
323#106—221no—
324#106—221no—
325C4⋊C8—111no—
326#103—21no—
327#103—21no—
328#103—221no—
329#103—221no—
330#103—221no—
331#103—221no—
332C22⋊C8—111no—
333C22⋊C8—111no—
334C4×C8C22×D1111yescharacteristic
335C2×C11#333411yescharacteristic
336C2×C11C2×#51011yescharacteristic
337C2×C11#341611yescharacteristic
338D11—22no—
339D11—41no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—441no—
343C2×D4—111no—
344C22×C4—111no—
345C22×C4—111no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—441no—
349Q16—21no—
350Q16—21no—
351Q16—21no—
352Q16—21no—
353C2×C8—111no—
354C2×C8—111no—
355C2×C8—221no—
356C2×C8—221no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8D4×D1111yescharacteristic
360C2×C8C23×D1111yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—111no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C22⋊C4—111no—
381C22⋊C4—111no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C42—41no—
388C42—41no—
389C42—441no—
390C42D4×D1111yescharacteristic
391C16—21no—
392C16—221no—
393C16—221no—
394C16#433912yes—
395C11#3391111yescharacteristic, complemented, Sylow
396C23—111no—
397C23—111no—
398Q8—41no—
399Q8—41no—
400Q8—41no—
401Q8—41no—
402Q8—1761no—
403D4—222no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—111no—
409C2×C4—111no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—882no—
419C2×C4—1761no—
420C2×C4—1761no—
421C2×C4D8×D1111yescharacteristic
422C2×C4D8×D1111yescharacteristic
423C2×C4C2×D4×D1111yescharacteristic
424C8—21no—
425C8—221no—
426C8—221no—
427C8C2×#433911yescharacteristic
428C8#6704311yescharacteristic
429C22—112no—
430C22—221no—
431C22—221no—
432C22—221no—
433C22—221no—
434C22—221no—
435C22C2×D8×D1111yescharacteristic
436C4—21no—
437C4—21no—
438C4—81no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—221no—
443C4—221no—
444C4—881no—
445C4—881no—
446C4—881no—
447C4—881no—
448C4#1062308211yescharacteristic
449C4#1062330211yescharacteristic
450C2—222no—
451C2—441no—
452C2#1308096511yescharacteristic
453C2D11×#51011yescharacteristic
454C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2176C2
socleC22×C11C22×D8
prime radicalC2×D44D8
hypercenter#2176D11
hypocenterC11#33911
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2176

Complements

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

NH ≅ G/Ntype
3. #13070902C2semidirect
4. #13070823C2semidirect
5. #13070817C2semidirect
6. #13070812C2semidirect
7. #13070812C2semidirect
8. #13070780C2semidirect
9. #13070758C2semidirect
10. #13070721C2semidirect
11. #13070704C2semidirect
13. #13070403C2semidirect
14. D11×#367C2semidirect
15. C11×#2176C2semidirect
180. #2176D11semidirect
395. C11#33911semidirect

Maximal subgroups

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

subgroupindex
#130810102
#130809862
#130709022
#130708232
#130708172
#130708122
#130707802
#130707582
#130707212
#130707042
#130704432
#130704032
D11×#3672
C11×#21762
#3391111