Finite Group Databasebeta

← #14746123

Subgroups — #14746123

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080423C212yesmaximal, complemented
2D8×D44C211yesmaximal, characteristic, complemented
3#13068223C211yesmaximal, characteristic, complemented
4#13068055C212yesmaximal, complemented
5#13067978C211yesmaximal, characteristic, complemented
6#13067971C211yesmaximal, characteristic, complemented
7#13067793C212yesmaximal, complemented
8#13067705C212yesmaximal, complemented
9D8×C11⋊C8C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11C11×#3283C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C11×#547C2212yescomplemented
14C2×D8×D11—21no—
15D4×D44C2212yes—
16C11×#494C2211yescharacteristic, complemented
17C11×#467—21no—
18C11×#461C2212yescomplemented
19C11×#452—22no—
20C4×C11×D8C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic, complemented
22#10622701C2212yescomplemented
23#10622701C2212yescomplemented
24#10622700C2212yes—
25#10622651—22no—
26#10622649—22no—
27#10622628C2212yes—
28#10622628C2212yescomplemented
29C4×#4323C2211yescharacteristic
30D4×C11⋊C8C2212yescomplemented
31#10622580—22no—
32C2×#66873—22no—
33#10622496—21no—
34#10622386—22no—
35#10622308C2211yescharacteristic
36C8×D44C2211yescharacteristic
37#10622185C2212yescomplemented
38D4⋊(C11⋊C8)C2212yescomplemented
39D4⋊(C11⋊C8)C2211yescharacteristic, complemented
40#10622123C2212yescomplemented
41#10622121C2211yescharacteristic
42#10622117C2211yescharacteristic, complemented
43#10622096C2211yescharacteristic, complemented
44C8×C11⋊C8C2211yescharacteristic, complemented
45C2×C11×#41—22no—
46C2×D4×D11—22no—
47C22×D44—22no—
48C11×#135—44no—
49C2×C11×Q16—21no—
50C2×C11×Q16—21no—
51C2×C11×SD16—22no—
52C2×C11×D8D411yescharacteristic
53C22×C8×C11—21no—
54C11×C4⋊Q8C2312yes—
55C11×#123—42no—
56C11×C22⋊Q8—22no—
57C11×#121—22no—
58C4×D4×C11C2312yes—
59C4×D4×C11C2311yescharacteristic
60C2×C11×C4⋊C4—22no—
61C2×#4323—22no—
62C2×#4323—22no—
63C2×#4323D411yescharacteristic
64#66983—22no—
65C22×C11⋊C8—22no—
66D8×D11—44no—
67C2×D88—21no—
68C2×D88—21no—
69C2×C8×D11—21no—
70#66948—22no—
71#66935—42no—
72#66927C2312yes—
73C4×D44C2311yescharacteristic
74C11×#107D411yescharacteristic
75C11×C4⋊C8C2311yescharacteristic
76C11×#103—22no—
77C11×#102D412yes—
78C11×C22⋊C8—21no—
79C4×C8×C11C2311yescharacteristic
80#66896D411yescharacteristic
81C22⋊(C11⋊C8)—22no—
82(C2×D11)⋊C8—21no—
83#66873—22no—
84#66873—22no—
85#66873—22no—
86#66873—22no—
87#66873—22no—
88#66873—42no—
89#66873D411yescharacteristic
90#66871—22no—
91#66871D411yescharacteristic
92C4⋊(C11⋊C8)C2311yescharacteristic
93C4⋊(C11⋊C8)C2312yes—
94C4×C11⋊C8C2311yescharacteristic
95C4×C11⋊C8C2311yescharacteristic
96#19968—111nomaximal, Sylow
97C23×D11—42no—
98C11×#41—44no—
99C11×#41—82no—
100C2×Q8×C11—22no—
101C2×D4×C11—42no—
102C2×D4×C11C2×D411yescharacteristic
103C2×D4×C11C2×D412yes—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—42no—
107C2×C22⋊D11—42no—
108D4×D11—44no—
109D4×D11—82no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—42no—
114C2×D44—44no—
115C2×D44—82no—
116C2×D44C2×D411yescharacteristic
117C2×C4×D11—21no—
118C11×Q16—42no—
119C11×Q16—81no—
120C11×SD16—44no—
121C11×D8D814yescomplemented
122C2×C8×C11—21no—
123C2×C8×C11—42no—
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4C2×D411yescharacteristic
130C11×C4⋊C4C2×D412yes—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—21no—
133C11×C22⋊C4—42no—
134C42×C11C2411yescharacteristic
135#4323—22no—
136#4323—44no—
137#4323—82no—
138(C2×D11)⋊C4—21no—
139(C2×D11)⋊C4—42no—
140C4⋊Dic11C2×D411yescharacteristic
141C2×C11⋊C8—22no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—82no—
145C2×C11⋊C8C2×D411yescharacteristic
146C2×C11⋊C8C2×D411yescharacteristic
147D88—42no—
148D88—81no—
149C8×D11—42no—
150#3294—112no—
151#3283D1111yescharacteristic, complemented
152D4×D8—111no—
153#1709—111no—
154#1681—112no—
155#1669—111no—
156#1667—111no—
157#1639—112no—
158#1625—112no—
159C8×D8—111no—
160C8×D8—111no—
161C23×C11—22no—
162C23×C11—21no—
163C22×D11—21no—
164C22×D11—42no—
165C22×D11—84no—
166C22×D11—84no—
167C22×D11—162no—
168Q8×C11—42no—
169Q8×C11—42no—
170D4×C11—21no—
171D4×C11—22no—
172D4×C11—21no—
173D4×C11—84no—
174D4×C11C2×D814yes—
175C2×C4×C11—22no—
176C2×C4×C11—21no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—84no—
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11H(5,𝔽2)11yescharacteristic
186C22⋊D11—84no—
187C2×Dic11—21no—
188D44—21no—
189D44—42no—
190D44—42no—
191D44—42no—
192D44—42no—
193D44—82no—
194D44—84no—
195D44#13512yescomplemented
196C4×D11—41no—
197C4×D11—41no—
198C8×C11—21no—
199C8×C11—41no—
200C8×C11C2×D812yes—
201C11⋊C8—21no—
202C11⋊C8—21no—
203C11⋊C8—41no—
204C11⋊C8—41no—
205C11⋊C8—42no—
206C2×#135—21no—
207C22×D8—221no—
208#547C2×D1112yescomplemented
209D42—112no—
210#494C2×D1111yescharacteristic, complemented
211#493—111no—
212#486—112no—
213#486—112no—
214#480—222no—
215#474—112no—
216#467—21no—
217#466—222no—
218#466—221no—
219#461C2×D1112yescomplemented
220#459—112no—
221#459—112no—
222#452—22no—
223#447—222no—
224#447—222no—
225C4×D8—111no—
226C4×D8C2×D1111yescharacteristic
227C8×D4—112no—
228C8×D4—111no—
229C8×D4C2×D1111yescharacteristic, complemented
230C2×#102—222no—
231#335—111no—
232#335—111no—
233#332—112no—
234#331—112no—
235D4⋊C8—111no—
236D4⋊C8—112no—
237D4⋊C8—111no—
238C82—111no—
239C22×C11—24no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11D4211yescharacteristic
246C2×D11—22no—
247C2×D11—41no—
248C2×D11—41no—
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—82no—
252C2×D11—168no—
253C4×C11—21no—
254C4×C11—41no—
255C4×C11—42no—
256C4×C11—82no—
257C4×C11C22×D811yescharacteristic
258C4×C11C2×#13511yescharacteristic
259C4×C11#57611yescharacteristic
260C4×C11#57611yescharacteristic
261Dic11—41no—
262C2×#41—22no—
263C22×D4—222no—
264C22×D4—222no—
265#135—44no—
266C2×Q16—21no—
267C2×Q16—21no—
268C2×SD16—22no—
269C2×D8—111no—
270C2×D8—222no—
271C2×D8—222no—
272C2×D8—221no—
273C2×D8—221no—
274C2×D8—444no—
275C2×D8C22⋊D1111yescharacteristic
276C22×C8—21no—
277C22×C8—222no—
278C22×C8—221no—
279C4⋊Q8C22×D1112yes—
280#127—112no—
281#123—42no—
282C22⋊Q8—22no—
283#121—22no—
284#121—222no—
285#121—222no—
286#120—442no—
287C4×D4—111no—
288C4×D4C22×D1111yescharacteristic
289C4×D4C22×D1112yes—
290C2×C4⋊C4—22no—
291#107—111no—
292#107—222no—
293#107C22⋊D1111yescharacteristic
294C4⋊C8—112no—
295C4⋊C8—111no—
296C4⋊C8C22×D1111yescharacteristic
297#103—22no—
298#102—111no—
299#102—111no—
300#102—222no—
301#102—222no—
302#102—222no—
303#102—222no—
304#102—222no—
305#102—442no—
306#102C22⋊D1112yes—
307C22⋊C8—21no—
308C22⋊C8—222no—
309C22⋊C8—221no—
310C4×C8—111no—
311C4×C8—111no—
312C4×C8C22×D1111yescharacteristic
313C2×C11—44no—
314C2×C11—81no—
315C2×C11D4×D811yescharacteristic
316C2×C11#328011yescharacteristic
317C2×C11#329011yescharacteristic
318D11—42no—
319D11—162no—
320C24—442no—
321#41—44no—
322#41—82no—
323C2×Q8—22no—
324C2×D4—42no—
325C2×D4—111no—
326C2×D4—222no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—442no—
330C2×D4—444no—
331C2×D4—442no—
332C2×D4—444no—
333C2×D4—882no—
334C2×D4—882no—
335C2×D4D4×D1111yescharacteristic
336C2×D4C2×C22⋊D1112yes—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—42no—
340C22×C4—221no—
341Q16—42no—
342Q16—81no—
343SD16—44no—
344D8—222no—
345D8—444no—
346D8—442no—
347D8—881no—
348D8—882no—
349D8#432314yescomplemented
350C2×C8—21no—
351C2×C8—42no—
352C2×C8—111no—
353C2×C8—111no—
354C2×C8—222no—
355C2×C8—221no—
356C2×C8—221no—
357C2×C8—442no—
358C2×C8—882no—
359C2×C8C2×C22⋊D1111yescharacteristic
360C2×C8C2×C22⋊D1111yescharacteristic
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—42no—
364C4⋊C4—111no—
365C4⋊C4D4×D1111yescharacteristic
366C4⋊C4C2×C22⋊D1112yes—
367C22⋊C4—22no—
368C22⋊C4—21no—
369C22⋊C4—42no—
370C22⋊C4—221no—
371C22⋊C4—442no—
372C42C23×D1111yescharacteristic
373C11#1996811yescharacteristic, complemented, Sylow
374C23—22no—
375C23—21no—
376C23—221no—
377C23—442no—
378C23—884no—
379C23—884no—
380C23—1762no—
381Q8—42no—
382Q8—42no—
383D4—21no—
384D4—21no—
385D4—22no—
386D4—84no—
387D4—112no—
388D4—221no—
389D4—442no—
390D4—442no—
391D4—442no—
392D4—442no—
393D4—882no—
394D4—884no—
395D4—884no—
396D4C2×#432314yes—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—84no—
405C2×C4—221no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4C2×D4×D1111yescharacteristic
409C2×C4#6703711yescharacteristic
410C2×C4C22×C22⋊D1111yescharacteristic
411C8—21no—
412C8—41no—
413C8—221no—
414C8—221no—
415C8—441no—
416C8—442no—
417C8—441no—
418C8C2×#432312yes—
419C22—24no—
420C22—42no—
421C22—42no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—222no—
426C22—441no—
427C22—441no—
428C22—882no—
429C22—882no—
430C22—882no—
431C22—1768no—
432C22D4×C22⋊D1111yescharacteristic
433C4—21no—
434C4—41no—
435C4—42no—
436C4—82no—
437C4—441no—
438C4D11×#13511yescharacteristic
439C4#1062330011yescharacteristic
440C4C22×#432311yescharacteristic
441C4#1062336611yescharacteristic
442C2—44no—
443C2—81no—
444C2—442no—
445C2—1762no—
446C2D4×#432311yescharacteristic
447C2#1308029511yescharacteristic
448C2#1308040211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3283C2
socleC22×C11D42
hypercenter#3283D11
hypocenterC11#19968
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #13080423C2semidirect
2. D8×D44C2semidirect
3. #13068223C2semidirect
4. #13068055C2semidirect
5. #13067978C2semidirect
6. #13067971C2semidirect
7. #13067793C2semidirect
8. #13067705C2semidirect
9. D8×C11⋊C8C2semidirect
10. C8×#4323C2semidirect
11. C11×#3283C2semidirect
13. C11×#547C22semidirect
16. C11×#494C22semidirect
18. C11×#461C22semidirect
21. C8×D4×C11C22semidirect
22. #10622701C22semidirect
23. #10622701C22semidirect
28. #10622628C22semidirect
30. D4×C11⋊C8C22semidirect
37. #10622185C22semidirect
38. D4⋊(C11⋊C8)C22semidirect
39. D4⋊(C11⋊C8)C22semidirect
40. #10622123C22semidirect
42. #10622117C22semidirect
43. #10622096C22semidirect
44. C8×C11⋊C8C22semidirect
121. C11×D8D8semidirect
151. #3283D11semidirect
195. D44#135semidirect
208. #547C2×D11semidirect
210. #494C2×D11semidirect
219. #461C2×D11semidirect
229. C8×D4C2×D11semidirect
349. D8#4323semidirect
373. C11#19968semidirect

Maximal subgroups

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

subgroupindex
#130804232
D8×D442
#130682232
#130680552
#130679782
#130679712
#130677932
#130677052
D8×C11⋊C82
C8×#43232
C11×#32832
#1996811