Finite Group Databasebeta

← #14909772

Subgroups — #14909772

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079187C211yesmaximal, characteristic, complemented
2C2×#10622764C211yesmaximal, characteristic, complemented
3#13070881C212yesmaximal, complemented
4#13070856C212yesmaximal, complemented
5#13070654C212yesmaximal, complemented
6#13070650C212yesmaximal, complemented
7#13070544C211yesmaximal, characteristic, complemented
8#13070530C211yesmaximal, characteristic, complemented
9#13070528C211yesmaximal, characteristic, complemented
10#13070416C211yesmaximal, characteristic, complemented
11C11×#2187C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×#66993—21no—
14C22×#4323—21no—
15C22×D88C2211yescharacteristic
16#10623155—21no—
17C2×C11×SD32C2212yescomplemented
18C11×#467C2211yescharacteristic
19#10622804C2211yescharacteristic, complemented
20Q16×Dic11C2211yescharacteristic, complemented
21C2×#66892C2212yescomplemented
22#10622764—21no—
23#10622764—21no—
24#10622764C2212yes—
25#10622764C2212yes—
26C2×#66890C2212yescomplemented
27#10622728C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622661—21no—
30C2×D176C2212yescomplemented
31#10622491C2211yescharacteristic, complemented
32#10622485C2211yescharacteristic, complemented
33#10622413—21no—
34#10622401—21no—
35C11×#357C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic
37#10622200C2212yescomplemented
38C22⋊(C11⋊C16)C2211yescharacteristic
39#10622147C2212yescomplemented
40#10622140C2212yescomplemented
41Dic11⋊C16C2212yescomplemented
42#10622129C2212yescomplemented
43C22×D4×C11—21no—
44C22×C22⋊D11—41no—
45C22×C22⋊D11—41no—
46C22×D44—21no—
47C2×C11×Q16C2311yescharacteristic
48C2×C11×D8—21no—
49C2×C11×D8—42no—
50C2×C11×D8C2312yes—
51C22×C8×C11C2311yescharacteristic
52C11×C22⋊Q8—21no—
53#67000—21no—
54Q8×Dic11—21no—
55C2×#4325—21no—
56#66993—22no—
57#66993—22no—
58#66993—41no—
59#66993—41no—
60C2×#4323—22no—
61C2×#4323—22no—
62C2×#4323—44no—
63#66983—21no—
64C2×C4×Dic11D411yescharacteristic
65C22×C11⋊C8D411yescharacteristic
66C2×D88—21no—
67C2×D88—42no—
68C2×D88C2311yescharacteristic
69C2×D88C2312yes—
70#66951—41no—
71#66946—21no—
72#66945—41no—
73#66943—21no—
74#66939—41no—
75(C22⋊D11)⋊C4—41no—
76C11×SD32—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#103—21no—
80#66899—21no—
81#66892—42no—
82#66890—42no—
83#66885—21no—
84#66882C2311yescharacteristic
85C8×Dic11D411yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C8×Dic11C2311yescharacteristic
89C2×C11⋊C16C2312yes—
90#66873—21no—
91#66872—21no—
92D176—42no—
93#33783—111nomaximal, Sylow
94C24×C11—41no—
95C23×D11—41no—
96C2×Q8×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—42no—
103C2×C22⋊D11—42no—
104C2×C22⋊D11—42no—
105C2×C22⋊D11—42no—
106C2×C22⋊D11—41no—
107C2×C22⋊D11—84no—
108C2×C22⋊D11—84no—
109C22×Dic11D811yescharacteristic
110C22×Dic11D811yescharacteristic
111C2×D44—21no—
112C2×D44—22no—
113C2×D44—42no—
114C2×D44—42no—
115C2×D44—41no—
116C2×C4×D11—41no—
117C11×Q16—22no—
118C11×D8—22no—
119C11×D8—22no—
120C11×D8—42no—
121C2×C8×C11—22no—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2411yescharacteristic
124C11×C4⋊C4—21no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—41no—
127#4325—42no—
128#4323—44no—
129#4323—44no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134C4⋊Dic11—21no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
137Dic11⋊C4—41no—
138C4×Dic11—41no—
139C4×Dic11D811yescharacteristic
140C4×Dic11D811yescharacteristic
141C4×Dic11C2×D411yescharacteristic
142C4×Dic11C2×D411yescharacteristic
143C2×C11⋊C8—22no—
144C2×C11⋊C8C2×D411yescharacteristic
145C2×C11⋊C8C2×D411yescharacteristic
146D88—22no—
147D88—22no—
148D88—22no—
149D88—42no—
150C11×C16—22no—
151C11⋊C16—22no—
152#3168—111no—
153C2×#493—111no—
154#2250—112no—
155#2244—112no—
156#2207—112no—
157#2206—112no—
158#2187—111no—
159#2187D1111yescharacteristic, complemented
160#2184—111no—
161#2184—111no—
162#2163—111no—
163C23×C11—42no—
164C23×C11—82no—
165C23×C11—82no—
166C23×C11—82no—
167C23×C11C2×D811yescharacteristic
168C22×D11—41no—
169C22×D11—42no—
170C22×D11—82no—
171C22×D11—82no—
172C22×D11—82no—
173Q8×C11—41no—
174Q8×C11—41no—
175D4×C11—42no—
176D4×C11—42no—
177D4×C11—82no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C22⋊D11—84no—
185C22⋊D11—84no—
186C22⋊D11—84no—
187C22⋊D11—82no—
188C22⋊D11—84no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—41no—
192C2×Dic11C2×D811yescharacteristic
193C2×Dic11C2×D811yescharacteristic
194C2×Dic11C2×D811yescharacteristic
195C2×Dic11C2×D811yescharacteristic
196D44—42no—
197D44—41no—
198D44—42no—
199D44—41no—
200D44—82no—
201C4×D11—82no—
202C8×C11—21no—
203C8×C11H(5,𝔽2)12yes—
204C11⋊C8—21no—
205C11⋊C8AGL(1,ℤ/8)12yes—
206C22×D8—111no—
207C22×D8—221no—
208C22×D8C2×D1111yescharacteristic
209C2×#127—221no—
210#529—221no—
211C2×SD32—112no—
212C2×SD32C2×D1112yescomplemented
213C2×D16—112no—
214C2×D16—112no—
215#499—111no—
216#495—111no—
217#493—112no—
218#493—112no—
219#493—221no—
220#493—221no—
221#488—221no—
222#467C2×D1111yescharacteristic
223#466—111no—
224#465—221no—
225C4×Q16—111no—
226C4×SD16—221no—
227C4×D8—111no—
228C2×C4×C8—111no—
229C4⋊C16—112no—
230#357—112no—
231#357—112no—
232#357—112no—
233#357C2×D1112yescomplemented
234C22⋊C16—111no—
235C22⋊C16C2×D1111yescharacteristic
236#346—112no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11—82no—
242C22×C11—164no—
243C22×C11#50912yes—
244C22×C11C22×D811yescharacteristic
245C2×D11—82no—
246C2×D11—82no—
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—82no—
250C2×D11—81no—
251C2×D11—164no—
252C4×C11—21no—
253C4×C11—81no—
254C4×C11—81no—
255C4×C11#53511yescharacteristic
256C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
257Dic11—21no—
258Dic11—21no—
259Dic11—21no—
260Dic11—81no—
261Dic11#50912yes—
262C22×D4—21no—
263C22×D4—221no—
264C22×D4—441no—
265C22×D4—441no—
266C2×Q16C22×D1111yescharacteristic
267C2×SD16—221no—
268C2×D8—21no—
269C2×D8—42no—
270C2×D8—112no—
271C2×D8—111no—
272C2×D8—222no—
273C2×D8—222no—
274C2×D8—221no—
275C2×D8—442no—
276C2×D8—444no—
277C2×D8C22×D1112yes—
278C22×C8—111no—
279C22×C8C22×D1111yescharacteristic
280#127—222no—
281#127—222no—
282#127—441no—
283#127—441no—
284#126—441no—
285#125—221no—
286#124—221no—
287#123—441no—
288C22⋊Q8—21no—
289#121—221no—
290C4×Q8—221no—
291C4×D4—221no—
292C4×D4—441no—
293#117—441no—
294C2×C42—111no—
295SD32—42no—
296SD32—442no—
297D16—442no—
298D16—442no—
299C2×C16—112no—
300C2×C16C22×D1112yes—
301#107—111no—
302#107C22×D1111yescharacteristic
303#106—221no—
304#103—21no—
305#103—221no—
306#102—221no—
307#102—221no—
308C4×C8—111no—
309C4×C8—111no—
310C4×C8—111no—
311C4×C8—111no—
312C2×C11—22no—
313C2×C11—162no—
314C2×C11#320511yescharacteristic
315C2×C11C2×#50911yescharacteristic
316C2×C11C2×#50911yescharacteristic
317D11—161no—
318D11—162no—
319C24—41no—
320C24—441no—
321C2×Q8—21no—
322C2×D4—22no—
323C2×D4—42no—
324C2×D4—42no—
325C2×D4—41no—
326C2×D4—221no—
327C2×D4—222no—
328C2×D4—442no—
329C2×D4—442no—
330C2×D4—442no—
331C2×D4—442no—
332C2×D4—442no—
333C2×D4—442no—
334C2×D4—441no—
335C2×D4—441no—
336C2×D4—884no—
337C2×D4—884no—
338C22×C4—111no—
339C22×C4—111no—
340C22×C4—441no—
341C22×C4D4×D1111yescharacteristic
342Q16—22no—
343SD16—442no—
344D8—22no—
345D8—22no—
346D8—42no—
347D8—222no—
348D8—222no—
349D8—222no—
350D8—442no—
351D8—444no—
352D8—444no—
353C2×C8—22no—
354C2×C8—111no—
355C2×C8—111no—
356C2×C8—222no—
357C2×C8D4×D1111yescharacteristic
358C2×C8C23×D1111yescharacteristic
359C4⋊C4—21no—
360C4⋊C4—41no—
361C4⋊C4—221no—
362C4⋊C4—441no—
363C4⋊C4—441no—
364C4⋊C4—441no—
365C22⋊C4—41no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C22⋊C4—441no—
370C42—111no—
371C42—111no—
372C42—111no—
373C42—111no—
374C42—441no—
375C16—22no—
376C16—222no—
377C11#3378311yescharacteristic, complemented, Sylow
378C23—42no—
379C23—82no—
380C23—82no—
381C23—82no—
382C23—441no—
383C23—442no—
384C23—882no—
385C23—882no—
386C23—882no—
387C23D8×D1111yescharacteristic
388Q8—41no—
389Q8—41no—
390D4—42no—
391D4—42no—
392D4—82no—
393D4—442no—
394D4—441no—
395D4—442no—
396D4—441no—
397D4—882no—
398D4—884no—
399D4—884no—
400D4—884no—
401D4—884no—
402D4—882no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—111no—
408C2×C4—111no—
409C2×C4—111no—
410C2×C4—111no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—441no—
414C2×C4—882no—
415C2×C4D8×D1111yescharacteristic
416C2×C4C2×D4×D1111yescharacteristic
417C8—21no—
418C8—112no—
419C8—221no—
420C8#6703712yes—
421C22—21no—
422C22—21no—
423C22—82no—
424C22—82no—
425C22—82no—
426C22—164no—
427C22—881no—
428C22—882no—
429C22—882no—
430C22—881no—
431C22—882no—
432C22—881no—
433C22—1764no—
434C22#1062252712yes—
435C22C2×D8×D1111yescharacteristic
436C4—21no—
437C4—81no—
438C4—81no—
439C4—112no—
440C4—221no—
441C4—221no—
442C4—221no—
443C4—881no—
444C4#1062312311yescharacteristic
445C4D11×AGL(1,ℤ/8)11yescharacteristic
446C2—22no—
447C2—162no—
448C2—1762no—
449C2—1761no—
450C2#1307953211yescharacteristic
451C2D11×#50911yescharacteristic
452C2C2×#1062252711yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2187C2
socleC22×C11C22×D8
hypercenter#2187D11
hypocenterC11#33783
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #13079187C2semidirect
2. C2×#10622764C2semidirect
3. #13070881C2semidirect
4. #13070856C2semidirect
5. #13070654C2semidirect
6. #13070650C2semidirect
7. #13070544C2semidirect
8. #13070530C2semidirect
9. #13070528C2semidirect
10. #13070416C2semidirect
11. C11×#2187C2semidirect
17. C2×C11×SD32C22semidirect
19. #10622804C22semidirect
20. Q16×Dic11C22semidirect
21. C2×#66892C22semidirect
26. C2×#66890C22semidirect
30. C2×D176C22semidirect
31. #10622491C22semidirect
32. #10622485C22semidirect
35. C11×#357C22semidirect
37. #10622200C22semidirect
39. #10622147C22semidirect
40. #10622140C22semidirect
41. Dic11⋊C16C22semidirect
42. #10622129C22semidirect
159. #2187D11semidirect
212. C2×SD32C2×D11semidirect
233. #357C2×D11semidirect
377. C11#33783semidirect

Maximal subgroups

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

subgroupindex
#130791872
C2×#106227642
#130708812
#130708562
#130706542
#130706502
#130705442
#130705302
#130705282
#130704162
C11×#21872
#3378311