Finite Group Databasebeta

← #14911312

Subgroups — #14911312

Order 2816.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081046C211yesmaximal, characteristic
2#13080983C211yesmaximal, characteristic
3#13070827C211yesmaximal, characteristic, complemented
4#13070827C211yesmaximal, characteristic, complemented
5#13070826C211yesmaximal, characteristic, complemented
6#13070820C211yesmaximal, characteristic, complemented
7#13070777C211yesmaximal, characteristic, complemented
8#13070765C211yesmaximal, characteristic, complemented
9#13070725C211yesmaximal, characteristic, complemented
10#13070708C211yesmaximal, characteristic, complemented
11#13070488C211yesmaximal, characteristic, complemented
12#13070443C211yesmaximal, characteristic
13#13070401C211yesmaximal, characteristic, complemented
14#13070399C211yesmaximal, characteristic, complemented
15C11×#2255C211yesmaximal, characteristic, complemented
16#10623263—21no—
17#10623225—21no—
18C11×#500C2211yescharacteristic
19C11×#499C2211yescharacteristic
20#10622707—21no—
21#10622676—21no—
22C2×Dic88C2211yescharacteristic
23C2×#66862C2211yescharacteristic
24C2×C16×D11C2211yescharacteristic
25#10622501—21no—
26#10622501—21no—
27#10622500C2211yescharacteristic
28#10622500C2211yescharacteristic
29#10622500C2211yescharacteristic
30#10622500C2211yescharacteristic
31#10622493C2211yescharacteristic
32#10622493C2211yescharacteristic
33#10622493C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622480—21no—
36#10622475—21no—
37C4×Dic44C2211yescharacteristic
38C4×Dic44C2211yescharacteristic
39C8×D44C2211yescharacteristic
40C11×#367C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C11×#346C2211yescharacteristic
45(C2×D11)⋊C16C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47#10622143C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622130C2211yescharacteristic
51#10622130C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C11×C4⋊Q8—21no—
60C11×#125—21no—
61#67000—41no—
62Q8×Dic11—41no—
63C2×Dic44C2311yescharacteristic
64C2×Dic44C2311yescharacteristic
65C2×C8×D11C2311yescharacteristic
66C2×C8×D11C2311yescharacteristic
67#66951—41no—
68#66951—41no—
69#66951—41no—
70#66950—21no—
71#66950—21no—
72#66950—21no—
73#66950—21no—
74#66947—41no—
75#66945—21no—
76#66945—21no—
77#66945—21no—
78#66945—41no—
79C4⋊C4×D11—21no—
80#66943—41no—
81C4×D44D411yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C2×C11×C16C2311yescharacteristic
85C2×C11×C16C2311yescharacteristic
86C11×#107—21no—
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#106—21no—
92C4×C8×C11C2311yescharacteristic
93(C2×D11)⋊C8D411yescharacteristic
94(C2×D11)⋊C8D411yescharacteristic
95#66882C2311yescharacteristic
96#66882C2311yescharacteristic
97#66880—21no—
98#66880—21no—
99C2×C11⋊C16C2311yescharacteristic
100C2×C11⋊C16C2311yescharacteristic
101#66874—21no—
102#66874—21no—
103#66874—21no—
104#66874—21no—
105#66872—21no—
106#66872—21no—
107#66872—21no—
108#66871—21no—
109C4⋊(C11⋊C8)D411yescharacteristic
110Dic88—22no—
111#66862—22no—
112C16×D11—22no—
113#33916—111nomaximal, Sylow
114C2×Q8×C11—41no—
115C2×D44D811yescharacteristic
116C2×C4×D11—41no—
117C2×C4×D11C2×D411yescharacteristic
118C2×C4×D11C2×D411yescharacteristic
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C42×C11C2×D411yescharacteristic
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4D811yescharacteristic
139(C2×D11)⋊C4D811yescharacteristic
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—41no—
143C4⋊Dic11—41no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146C4⋊Dic11D811yescharacteristic
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150C4×Dic11—41no—
151C4×Dic11—41no—
152C4×Dic11—41no—
153C4×Dic11—41no—
154C4×Dic11—41no—
155C2×C11⋊C8C2×D411yescharacteristic
156C2×C11⋊C8C2×D411yescharacteristic
157Dic44—21no—
158Dic44—21no—
159Dic44—21no—
160Dic44—21no—
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#3342—111no—
170#3336—111no—
171#2255D1111yescharacteristic, complemented
172#2237—111no—
173#2237—111no—
174#2237—111no—
175#2236—111no—
176#2229—111no—
177#2227—111no—
178#2219—111no—
179#2216—111no—
180#2176—111no—
181#2168—111no—
182#2159—111no—
183#2158—111no—
184C22×D11C2×D811yescharacteristic
185C22×D11C2×D811yescharacteristic
186Q8×C11—82no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11C2×D811yescharacteristic
199C2×Dic11C2×D811yescharacteristic
200D44—41no—
201C4×D11—21no—
202C4×D11—21no—
203C4×D11—21no—
204C4×D11—21no—
205C4×D11—82no—
206Dic22—41no—
207Dic22—41no—
208Dic22—41no—
209Dic22—41no—
210C8×C11—21no—
211C8×C11C2×#4111yescharacteristic
212C8×C112−1+411yescharacteristic
213C11⋊C8—21no—
214C11⋊C8—21no—
215#556—221no—
216#552—221no—
217C2×Q32—111no—
218C2×M32—111no—
219C22×C16—111no—
220#500C2×D1111yescharacteristic
221#499C2×D1111yescharacteristic
222#485—221no—
223#485—221no—
224#485—221no—
225#483—221no—
226#479—221no—
227#475—221no—
228#467—111no—
229#467—111no—
230#467—111no—
231#467—111no—
232C4×Q16—111no—
233C4×Q16—111no—
234C8×D4—111no—
235#427—111no—
236#427—111no—
237#427—111no—
238C2×#107—111no—
239#367—111no—
240#367—111no—
241#367C2×D1111yescharacteristic
242#367C2×D1111yescharacteristic
243#366—111no—
244#366—111no—
245#366—111no—
246#366C2×D1111yescharacteristic
247#366C2×D1111yescharacteristic
248C4⋊C16—111no—
249#358—111no—
250#358—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255C22⋊C16—111no—
256C22⋊C16—111no—
257#346C2×D1111yescharacteristic
258C22×C11C22×D811yescharacteristic
259C2×D11—21no—
260C2×D11—21no—
261C2×D11—21no—
262C2×D11—21no—
263C2×D11—21no—
264C2×D11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—81no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11#54711yescharacteristic
272C4×C11#57811yescharacteristic
273Dic11—21no—
274Dic11—21no—
275Dic11—81no—
276Dic11—81no—
277Dic11—81no—
278Dic11—81no—
279C2×Q16—111no—
280C2×Q16—111no—
281C22×C8—111no—
282C22×C8—111no—
283C4⋊Q8—21no—
284#126—441no—
285#126—441no—
286#126—441no—
287#125—21no—
288#125—441no—
289#124—441no—
290#123—441no—
291C22⋊Q8—221no—
292C22⋊Q8—221no—
293C22⋊Q8—221no—
294C22⋊Q8—221no—
295C4×Q8—221no—
296C4×Q8—221no—
297C4×Q8—441no—
298C4×D4—111no—
299#117—221no—
300#117—221no—
301#117—221no—
302#117—441no—
303C2×C4⋊C4—221no—
304Q32—222no—
305M32—222no—
306C2×C16—111no—
307C2×C16—111no—
308C2×C16—222no—
309C2×C16C22×D1111yescharacteristic
310C2×C16C22×D1111yescharacteristic
311#107—21no—
312#107—111no—
313#107—111no—
314#107—221no—
315#107C22×D1111yescharacteristic
316#107C22×D1111yescharacteristic
317#107C22×D1111yescharacteristic
318#107C22×D1111yescharacteristic
319#106—21no—
320#106—221no—
321#106—221no—
322#106—221no—
323C4⋊C8—111no—
324#103—221no—
325#103—221no—
326#103—221no—
327#103—221no—
328#103—221no—
329#103—221no—
330C22⋊C8—111no—
331C22⋊C8—111no—
332C4×C8C22×D1111yescharacteristic
333C2×C11#333411yescharacteristic
334C2×C11#341411yescharacteristic
335C2×C11#341711yescharacteristic
336D11—41no—
337D11—41no—
338C2×Q8—41no—
339C2×Q8—221no—
340C2×Q8—221no—
341C2×D4—111no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—441no—
345Q16—221no—
346Q16—221no—
347Q16—221no—
348Q16—221no—
349C2×C8—111no—
350C2×C8—111no—
351C2×C8—221no—
352C2×C8—221no—
353C2×C8—221no—
354C2×C8—221no—
355C2×C8D4×D1111yescharacteristic
356C2×C8C23×D1111yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—111no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—441no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C22⋊C4—111no—
375C22⋊C4—111no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C42—441no—
384C42—441no—
385C42—441no—
386C42—441no—
387C42—441no—
388C42D4×D1111yescharacteristic
389C16—21no—
390C16—221no—
391C16—221no—
392C16#434312yes—
393C11#3391611yescharacteristic, complemented, Sylow
394C23—111no—
395C23—111no—
396Q8—82no—
397Q8—441no—
398Q8—441no—
399Q8—441no—
400Q8—441no—
401D4—441no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—111no—
407C2×C4—111no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—882no—
417C2×C4D8×D1111yescharacteristic
418C2×C4D8×D1111yescharacteristic
419C2×C4C2×D4×D1111yescharacteristic
420C8—21no—
421C8—221no—
422C8—221no—
423C8C2×#434311yescharacteristic
424C8#6704011yescharacteristic
425C22—221no—
426C22—221no—
427C22—221no—
428C22—221no—
429C22—221no—
430C22—221no—
431C22C2×D8×D1111yescharacteristic
432C4—21no—
433C4—21no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—221no—
439C4—221no—
440C4—881no—
441C4—881no—
442C4—881no—
443C4—881no—
444C4#1062325711yescharacteristic
445C4#1062329711yescharacteristic
446C2—441no—
447C2—441no—
448C2#1308096311yescharacteristic
449C2#1308174811yescharacteristic
450C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2255C2
socleC22×C11C22×D8
prime radicalC2×D44D8
hypercenter#2255D11
hypocenterC11#33916
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #13070827C2semidirect
4. #13070827C2semidirect
5. #13070826C2semidirect
6. #13070820C2semidirect
7. #13070777C2semidirect
8. #13070765C2semidirect
9. #13070725C2semidirect
10. #13070708C2semidirect
11. #13070488C2semidirect
13. #13070401C2semidirect
14. #13070399C2semidirect
15. C11×#2255C2semidirect
171. #2255D11semidirect
393. C11#33916semidirect

Maximal subgroups

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

subgroupindex
#130810462
#130809832
#130708272
#130708262
#130708202
#130707772
#130707652
#130707252
#130707082
#130704882
#130704432
#130704012
#130703992
C11×#22552
#3391611