Finite Group Databasebeta

← #14909773

Subgroups — #14909773

Order 2816.

688 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#13079189C211yesmaximal, characteristic, complemented
2D11×#493C211yesmaximal, characteristic, complemented
3#13070881C212yesmaximal, complemented
4#13070856C212yesmaximal, complemented
5#13070656C211yesmaximal, characteristic, complemented
6#13070652C211yesmaximal, characteristic, complemented
7#13070648C211yesmaximal, characteristic, complemented
8#13070543C212yesmaximal, complemented
9#13070529C212yesmaximal, complemented
10#13070418C211yesmaximal, characteristic, complemented
11C11×#2207C211yesmaximal, characteristic, complemented
12C2×D8×D11—21no—
13C2×D8×D11C2212yes—
14D11×#127—21no—
15#10623111—21no—
16C2×C11×SD32C2212yescomplemented
17C11×#493C2211yescharacteristic
18C4×C11×Q16C2211yescharacteristic, complemented
19#10622804C2211yescharacteristic, complemented
20#10622801C2211yescharacteristic
21C2×#66892C2212yescomplemented
22#10622764—21no—
23#10622764C2212yes—
24C2×#66890C2212yescomplemented
25#10622686—21no—
26C4×#4325—21no—
27C2×D176C2212yescomplemented
28#10622496C2211yescharacteristic
29#10622491C2211yescharacteristic, complemented
30#10622420—21no—
31#10622413—21no—
32#10622308C2211yescharacteristic
33C4×D88C2211yescharacteristic, complemented
34C4×C8×D11C2211yescharacteristic
35C11×C4⋊C16C2211yescharacteristic, complemented
36C11×#357C2212yescomplemented
37#10622200C2212yescomplemented
38#10622147C2212yescomplemented
39(C2×D11)⋊C16C2212yes—
40#10622140C2212yescomplemented
41#10622129C2212yescomplemented
42C4⋊(C11⋊C16)C2211yescharacteristic, complemented
43C2×D4×D11—22no—
44C2×D4×D11—41no—
45C2×D4×D11—41no—
46C2×C11×Q16C2311yescharacteristic
47C2×C11×D8—21no—
48C2×C11×D8C2312yes—
49C11×#127—21no—
50C4×Q8×C11—21no—
51#67000—21no—
52#66999—21no—
53C2×#4325—21no—
54#66993—22no—
55#66993—41no—
56#66993—41no—
57C2×#4323—22no—
58C2×#4323—22no—
59D8×D11—42no—
60D8×D11—42no—
61D8×D11—44no—
62C2×D88—21no—
63C2×D88C2311yescharacteristic
64C2×D88C2312yes—
65C2×C8×D11D411yescharacteristic
66C2×C8×D11C2311yescharacteristic
67#66951—41no—
68#66948—21no—
69#66947—41no—
70#66943—21no—
71#66927—21no—
72C4×D44—21no—
73C4×D44—41no—
74#66925—41no—
75C42×D11D411yescharacteristic
76C11×SD32—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#103—21no—
80C4×C8×C11C2311yescharacteristic
81#66899—21no—
82#66892—42no—
83#66890—42no—
84#66885—21no—
85#66882C2311yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C2×C11⋊C16C2312yes—
89#66873—21no—
90#66872—21no—
91C4×C11⋊C8D411yescharacteristic
92D176—42no—
93#33783—111nomaximal, Sylow
94C23×D11—42no—
95C2×Q8×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×C22⋊D11—42no—
100C2×C22⋊D11—42no—
101C2×C22⋊D11—42no—
102D4×D11—44no—
103D4×D11—44no—
104D4×D11—84no—
105D4×D11—84no—
106C2×D44—21no—
107C2×D44—22no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×C4×D11—41no—
112C2×C4×D11D811yescharacteristic
113C2×C4×D11D811yescharacteristic
114C2×C4×D11C2×D411yescharacteristic
115C11×Q16—21no—
116C11×Q16—21no—
117C11×D8—22no—
118C11×D8—22no—
119C11×D8—42no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2411yescharacteristic
122C11×C4⋊C4—21no—
123C11×C4⋊C4—41no—
124C42×C11—41no—
125C42×C11C2×D411yescharacteristic
126#4325—42no—
127#4323—44no—
128#4323—44no—
129(C2×D11)⋊C4—41no—
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—
136Dic11⋊C4—41no—
137Dic11⋊C4—41no—
138C4×Dic11D811yescharacteristic
139C4×Dic11D811yescharacteristic
140C4×Dic11C2×D411yescharacteristic
141C2×C11⋊C8C2×D411yescharacteristic
142C2×C11⋊C8C2×D411yescharacteristic
143D88—21no—
144D88—22no—
145D88—21no—
146D88—22no—
147D88—42no—
148C8×D11—21no—
149C8×D11—21no—
150C8×D11—22no—
151C11×C16—22no—
152C11⋊C16—22no—
153#3168—111no—
154C2×#493—111no—
155#2250—112no—
156#2244—112no—
157#2207—111no—
158#2207D1111yescharacteristic, complemented
159#2206—111no—
160#2206—111no—
161#2187—112no—
162#2184—112no—
163#2163—111no—
164C23×C11—42no—
165C22×D11—41no—
166C22×D11—42no—
167C22×D11—84no—
168C22×D11—84no—
169C22×D11—84no—
170C22×D11C2×D811yescharacteristic
171Q8×C11—41no—
172Q8×C11—41no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—82no—
176D4×C11—82no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C22⋊D11—84no—
183C22⋊D11—84no—
184C22⋊D11—84no—
185C2×Dic11—41no—
186C2×Dic11C2×D811yescharacteristic
187C2×Dic11C2×D811yescharacteristic
188C2×Dic11C2×D811yescharacteristic
189D44—42no—
190D44—41no—
191D44—42no—
192D44—41no—
193D44—82no—
194D44—82no—
195D44—82no—
196C4×D11—22no—
197C4×D11—21no—
198C4×D11—21no—
199C4×D11—22no—
200C4×D11—82no—
201C8×C11—21no—
202C8×C11H(5,𝔽2)11yescharacteristic
203C8×C11H(5,𝔽2)11yescharacteristic
204C11⋊C8—21no—
205C11⋊C8AGL(1,ℤ/8)12yes—
206C22×D8—112no—
207C22×D8—221no—
208C2×#127—221no—
209#529—221no—
210C2×SD32—112no—
211C2×SD32C2×D1112yescomplemented
212C2×D16—112no—
213C2×D16—112no—
214#499—111no—
215#495—111no—
216#493—112no—
217#493—111no—
218#493—221no—
219#493—221no—
220#493C2×D1111yescharacteristic
221#488—221no—
222#467—111no—
223#466—111no—
224#465—221no—
225C4×Q16C2×D1111yescharacteristic, complemented
226C4×SD16—221no—
227C4×D8—111no—
228C2×C4×C8—111no—
229C4⋊C16—111no—
230C4⋊C16C2×D1111yescharacteristic, complemented
231#357—112no—
232#357—112no—
233#357—112no—
234#357C2×D1112yescomplemented
235C22⋊C16—112no—
236#346—112no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11C22×D811yescharacteristic
241C2×D11—21no—
242C2×D11—21no—
243C2×D11—82no—
244C2×D11—82no—
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—82no—
248C2×D11—81no—
249C2×D11—168no—
250C2×D11#50912yes—
251C4×C11—21no—
252C4×C11—81no—
253C4×C11—81no—
254C4×C11#50912yes—
255C4×C11#53511yescharacteristic
256C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
257Dic11—21no—
258Dic11—21no—
259Dic11—21no—
260Dic11—81no—
261C22×D4—222no—
262C22×D4—441no—
263C22×D4—441no—
264C2×Q16C22×D1111yescharacteristic
265C2×SD16—221no—
266C2×D8—21no—
267C2×D8—112no—
268C2×D8—111no—
269C2×D8—222no—
270C2×D8—222no—
271C2×D8—221no—
272C2×D8—442no—
273C2×D8—442no—
274C2×D8—444no—
275C2×D8C22×D1112yes—
276C22×C8—111no—
277C22×C8—111no—
278#127—21no—
279#127—222no—
280#127—221no—
281#127—441no—
282#127—441no—
283#126—441no—
284#125—221no—
285#124—221no—
286#123—441no—
287C22⋊Q8—221no—
288#121—221no—
289C4×Q8—21no—
290C4×D4—221no—
291C4×D4—441no—
292#117—441no—
293C2×C42—111no—
294SD32—42no—
295SD32—442no—
296D16—442no—
297D16—442no—
298C2×C16—112no—
299C2×C16C22×D1112yes—
300#107—111no—
301#107C22×D1111yescharacteristic
302#106—221no—
303#103—21no—
304#103—221no—
305#102—221no—
306#102—221no—
307C4×C8—111no—
308C4×C8—111no—
309C4×C8—111no—
310C4×C8C22×D1111yescharacteristic
311C2×C11—162no—
312C2×C11#320511yescharacteristic
313C2×C11C2×#50911yescharacteristic
314C2×C11C2×#50911yescharacteristic
315D11—22no—
316D11—161no—
317D11—162no—
318C24—442no—
319C2×Q8—21no—
320C2×D4—22no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—221no—
324C2×D4—222no—
325C2×D4—441no—
326C2×D4—442no—
327C2×D4—442no—
328C2×D4—442no—
329C2×D4—444no—
330C2×D4—444no—
331C2×D4—441no—
332C2×D4—441no—
333C2×D4—884no—
334C2×D4—884no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—111no—
338C22×C4—441no—
339Q16—21no—
340Q16—21no—
341SD16—442no—
342D8—22no—
343D8—22no—
344D8—42no—
345D8—221no—
346D8—222no—
347D8—221no—
348D8—222no—
349D8—442no—
350D8—444no—
351D8—444no—
352C2×C8—111no—
353C2×C8—111no—
354C2×C8—222no—
355C2×C8—221no—
356C2×C8—221no—
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—441no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C22⋊C4—441no—
370C42—41no—
371C42—111no—
372C42—111no—
373C42—111no—
374C42D4×D1111yescharacteristic
375C16—22no—
376C16—222no—
377C11#3378311yescharacteristic, complemented, Sylow
378C23—42no—
379C23—111no—
380C23—441no—
381C23—442no—
382C23—884no—
383C23—884no—
384C23—884no—
385Q8—41no—
386Q8—41no—
387D4—42no—
388D4—42no—
389D4—82no—
390D4—82no—
391D4—442no—
392D4—441no—
393D4—442no—
394D4—441no—
395D4—882no—
396D4—882no—
397D4—884no—
398D4—884no—
399D4—884no—
400D4—882no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—111no—
404C2×C4—111no—
405C2×C4—111no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—441no—
411C2×C4—882no—
412C2×C4D8×D1111yescharacteristic
413C2×C4D8×D1111yescharacteristic
414C2×C4C2×D4×D1111yescharacteristic
415C8—21no—
416C8—112no—
417C8—221no—
418C8#6703711yescharacteristic
419C8#6704211yescharacteristic
420C22—82no—
421C22—82no—
422C22—82no—
423C22—112no—
424C22—221no—
425C22—221no—
426C22—882no—
427C22—881no—
428C22—881no—
429C22—882no—
430C22—882no—
431C22—881no—
432C22—1768no—
433C22C2×D8×D1111yescharacteristic
434C4—21no—
435C4—81no—
436C4—81no—
437C4—221no—
438C4—221no—
439C4—221no—
440C4—881no—
441C4#1062252712yes—
442C4#1062313811yescharacteristic
443C4D11×AGL(1,ℤ/8)11yescharacteristic
444C2—162no—
445C2—222no—
446C2—1762no—
447C2—1761no—
448C2#1307953311yescharacteristic
449C2D11×#50911yescharacteristic
450C2C2×#1062252711yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2207C2
socleC22×C11C22×D8
hypercenter#2207D11
hypocenterC11#33783
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #13079189C2semidirect
2. D11×#493C2semidirect
3. #13070881C2semidirect
4. #13070856C2semidirect
5. #13070656C2semidirect
6. #13070652C2semidirect
7. #13070648C2semidirect
8. #13070543C2semidirect
9. #13070529C2semidirect
10. #13070418C2semidirect
11. C11×#2207C2semidirect
16. C2×C11×SD32C22semidirect
18. C4×C11×Q16C22semidirect
19. #10622804C22semidirect
21. C2×#66892C22semidirect
24. C2×#66890C22semidirect
27. C2×D176C22semidirect
29. #10622491C22semidirect
33. C4×D88C22semidirect
35. C11×C4⋊C16C22semidirect
36. C11×#357C22semidirect
37. #10622200C22semidirect
38. #10622147C22semidirect
40. #10622140C22semidirect
41. #10622129C22semidirect
42. C4⋊(C11⋊C16)C22semidirect
158. #2207D11semidirect
211. C2×SD32C2×D11semidirect
225. C4×Q16C2×D11semidirect
230. C4⋊C16C2×D11semidirect
234. #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
#130791892
D11×#4932
#130708812
#130708562
#130706562
#130706522
#130706482
#130705432
#130705292
#130704182
C11×#22072
#3378311