Finite Group Databasebeta

← #14746129

Subgroups — #14746129

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#13080429C212yesmaximal, complemented
2#13080337C211yesmaximal, characteristic, complemented
3#13068221C211yesmaximal, characteristic, complemented
4#13068051C212yesmaximal, complemented
5#13067981C211yesmaximal, characteristic, complemented
6#13067968C211yesmaximal, characteristic, complemented
7#13067795C212yesmaximal, complemented
8#13067703C212yesmaximal, complemented
9D8×C11⋊C8C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11D4×C11×D8C211yesmaximal, characteristic, complemented
12C22×C11×D8—21no—
13D42×C11C2212yes—
14C2×#66965—21no—
15#10623086C2212yescomplemented
16C11×#493C2211yescharacteristic
17C11×#466—21no—
18C11×#459C2212yes—
19C11×#447—22no—
20C4×C11×D8C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622830—22no—
23C2×#66896—22no—
24#10622685C2212yescomplemented
25#10622683C2212yescomplemented
26#10622683C2212yescomplemented
27#10622651—22no—
28#10622646—22no—
29#10622632C2212yescomplemented
30C4×#4323C2211yescharacteristic
31D4×C11⋊C8C2212yescomplemented
32#10622620C2212yes—
33#10622500—21no—
34#10622396—22no—
35#10622312C2211yescharacteristic, complemented
36C8×D44C2211yescharacteristic, complemented
37#10622182C2212yescomplemented
38D4⋊(C11⋊C8)C2211yescharacteristic
39D4⋊(C11⋊C8)C2212yescomplemented
40#10622121C2211yescharacteristic, complemented
41#10622120C2212yescomplemented
42#10622117C2211yescharacteristic, complemented
43#10622096C2211yescharacteristic, complemented
44C8×C11⋊C8C2211yescharacteristic, complemented
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C2×#4341—22no—
48C2×C11×D8—22no—
49C2×C11×D8—21no—
50C2×C11×D8—21no—
51C2×C11×D8—44no—
52C2×C11×D8D411yescharacteristic
53C22×C8×C11—21no—
54C11×#127C2312yes—
55C11×#121—22no—
56C11×#121—22no—
57C11×#120—42no—
58C4×D4×C11C2312yes—
59C4×D4×C11C2311yescharacteristic
60C2×#4324—22no—
61C2×#4323—22no—
62C2×#4323D411yescharacteristic
63#66983—22no—
64C2×C4⋊Dic11—22no—
65C22×C11⋊C8—22no—
66#66965—44no—
67C2×Dic44—21no—
68C2×Dic44—21no—
69C2×C8×D11—21no—
70#66950—22no—
71#66939—42no—
72C4×D44C2311yescharacteristic
73#66922C2312yes—
74C11×#107D411yescharacteristic
75C11×C4⋊C8C2311yescharacteristic
76C11×#102—22no—
77C11×#102D412yes—
78C11×C22⋊C8—21no—
79C4×C8×C11C2311yescharacteristic
80#66896—22no—
81#66896—22no—
82#66896—22no—
83#66896—22no—
84#66896—42no—
85#66896D411yescharacteristic
86C22⋊(C11⋊C8)—22no—
87(C2×D11)⋊C8—21no—
88#66874—22no—
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
97C24×C11—42no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—42no—
102C2×D4×C11—42no—
103C2×D4×C11—44no—
104C2×D4×C11—44no—
105C2×D4×C11—82no—
106C2×D4×C11—82no—
107C2×D4×C11C2×D412yes—
108C2×D4×C11C2×D411yescharacteristic
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C2×C22⋊D11—42no—
112C22×Dic11—42no—
113#4341—44no—
114#4341—82no—
115C2×D44C2×D411yescharacteristic
116C2×C4×D11—21no—
117C2×Dic22—22no—
118C11×D8—42no—
119C11×D8—44no—
120C11×D8—81no—
121C11×D8D814yescomplemented
122C2×C8×C11—21no—
123C2×C8×C11—42no—
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C11×C4⋊C4C2×D411yescharacteristic
127C11×C4⋊C4C2×D412yes—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—21no—
130C11×C22⋊C4—42no—
131C42×C11C2411yescharacteristic
132#4324—44no—
133#4323—22no—
134#4323—82no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—42no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—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
147Dic44—42no—
148Dic44—81no—
149C8×D11—42no—
150#3294—112no—
151#3283—111no—
152D4×D8D1111yescharacteristic, complemented
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—
163C23×C11—42no—
164C23×C11—84no—
165C23×C11—84no—
166C23×C11—162no—
167C22×D11—21no—
168D4×C11—22no—
169D4×C11—21no—
170D4×C11—42no—
171D4×C11—42no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—82no—
175D4×C11—84no—
176D4×C11—84no—
177D4×C11C2×D814yes—
178D4×C11#13512yescomplemented
179C2×C4×C11—22no—
180C2×C4×C11—21no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11H(5,𝔽2)11yescharacteristic
188C22⋊D11—84no—
189C2×Dic11—21no—
190C2×Dic11—42no—
191C2×Dic11—84no—
192D44—21no—
193D44—21no—
194C4×D11—41no—
195C4×D11—41no—
196Dic22—42no—
197Dic22—42no—
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—221no—
207C22×D8—21no—
208#547—112no—
209D42C2×D1112yes—
210#494—111no—
211#493C2×D1111yescharacteristic
212#486—112no—
213#486—112no—
214#480—222no—
215#474—112no—
216#467—221no—
217#466—21no—
218#466—222no—
219#461—112no—
220#459—112no—
221#459C2×D1112yes—
222#452—222no—
223#447—22no—
224#447—222no—
225C4×D8—111no—
226C4×D8C2×D1111yescharacteristic
227C8×D4—112no—
228C8×D4—111no—
229C8×D4C2×D1111yescharacteristic
230C2×#102—222no—
231#335—111no—
232#335—111no—
233#332—112no—
234#331—112no—
235D4⋊C8—112no—
236D4⋊C8—111no—
237D4⋊C8—111no—
238C82—111no—
239C22×C11—24no—
240C22×C11—22no—
241C22×C11—41no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—41no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—168no—
249C22×C11D4211yescharacteristic
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—41no—
253C4×C11—21no—
254C4×C11—41no—
255C4×C11—42no—
256C4×C11C22×D811yescharacteristic
257C4×C11C2×#13511yescharacteristic
258C4×C11#57611yescharacteristic
259C4×C11#57611yescharacteristic
260Dic11—41no—
261Dic11—82no—
262C2×#41—222no—
263C22×D4—22no—
264C22×D4—22no—
265#135—444no—
266C2×Q16—221no—
267C2×Q16—221no—
268C2×SD16—222no—
269C2×D8—22no—
270C2×D8—21no—
271C2×D8—21no—
272C2×D8—44no—
273C2×D8—111no—
274C2×D8—222no—
275C2×D8C22⋊D1111yescharacteristic
276C22×C8—21no—
277C22×C8—222no—
278C22×C8—221no—
279C4⋊Q8—112no—
280#127C22×D1112yes—
281#123—442no—
282C22⋊Q8—222no—
283#121—22no—
284#121—22no—
285#121—222no—
286#120—42no—
287C4×D4—111no—
288C4×D4C22×D1111yescharacteristic
289C4×D4C22×D1112yes—
290C2×C4⋊C4—222no—
291#107—111no—
292#107—222no—
293#107C22⋊D1111yescharacteristic
294C4⋊C8—111no—
295C4⋊C8—112no—
296C4⋊C8C22×D1111yescharacteristic
297#103—222no—
298#102—22no—
299#102—111no—
300#102—111no—
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—42no—
315C2×C11—162no—
316C2×C11D4×D811yescharacteristic
317C2×C11#328011yescharacteristic
318C2×C11#329011yescharacteristic
319D11—81no—
320C24—42no—
321#41—444no—
322#41—882no—
323C2×Q8—222no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4—44no—
330C2×D4—44no—
331C2×D4—82no—
332C2×D4—82no—
333C2×D4—111no—
334C2×D4—442no—
335C2×D4D4×D1111yescharacteristic
336C2×D4C2×C22⋊D1112yes—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—221no—
340C22×C4—442no—
341Q16—442no—
342Q16—881no—
343SD16—444no—
344D8—44no—
345D8—42no—
346D8—81no—
347D8—222no—
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—111no—
362C4⋊C4—222no—
363C4⋊C4—222no—
364C4⋊C4—442no—
365C4⋊C4D4×D1111yescharacteristic
366C4⋊C4C2×C22⋊D1112yes—
367C22⋊C4—21no—
368C22⋊C4—22no—
369C22⋊C4—42no—
370C22⋊C4—221no—
371C22⋊C4—442no—
372C42C23×D1111yescharacteristic
373C11#1996811yescharacteristic, complemented, Sylow
374C23—22no—
375C23—21no—
376C23—42no—
377C23—84no—
378C23—84no—
379C23—162no—
380C23—221no—
381Q8—442no—
382Q8—442no—
383D4—21no—
384D4—22no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—82no—
390D4—84no—
391D4—84no—
392D4—221no—
393D4—221no—
394D4—884no—
395D4#6696512yescomplemented
396D4C2×#432314yes—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—221no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—442no—
407C2×C4—884no—
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—22no—
421C22—41no—
422C22—42no—
423C22—41no—
424C22—42no—
425C22—82no—
426C22—82no—
427C22—82no—
428C22—168no—
429C22—441no—
430C22—441no—
431C22—441no—
432C22D4×C22⋊D1111yescharacteristic
433C4—21no—
434C4—41no—
435C4—42no—
436C4—441no—
437C4—882no—
438C4C2×#6696511yescharacteristic
439C4#1062328811yescharacteristic
440C4C22×#432311yescharacteristic
441C4#1062336611yescharacteristic
442C2—42no—
443C2—44no—
444C2—162no—
445C2—881no—
446C2D4×#432311yescharacteristic
447C2#1308030111yescharacteristic
448C2#1308039811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingD4×C11×D8C2
socleC22×C11D42
hypercenterD4×D8D11
hypocenterC11#19968
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. #13080429C2semidirect
2. #13080337C2semidirect
3. #13068221C2semidirect
4. #13068051C2semidirect
5. #13067981C2semidirect
6. #13067968C2semidirect
7. #13067795C2semidirect
8. #13067703C2semidirect
9. D8×C11⋊C8C2semidirect
10. C8×#4323C2semidirect
11. D4×C11×D8C2semidirect
15. #10623086C22semidirect
24. #10622685C22semidirect
25. #10622683C22semidirect
26. #10622683C22semidirect
29. #10622632C22semidirect
31. D4×C11⋊C8C22semidirect
35. #10622312C22semidirect
36. C8×D44C22semidirect
37. #10622182C22semidirect
39. D4⋊(C11⋊C8)C22semidirect
40. #10622121C22semidirect
41. #10622120C22semidirect
42. #10622117C22semidirect
43. #10622096C22semidirect
44. C8×C11⋊C8C22semidirect
121. C11×D8D8semidirect
152. D4×D8D11semidirect
178. D4×C11#135semidirect
349. D8#4323semidirect
373. C11#19968semidirect
395. D4#66965semidirect

Maximal subgroups

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

subgroupindex
#130804292
#130803372
#130682212
#130680512
#130679812
#130679682
#130677952
#130677032
D8×C11⋊C82
C8×#43232
D4×C11×D82
#1996811