Finite Group Databasebeta

← #14909691

Subgroups — #14909691

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079199C211yesmaximal, characteristic, complemented
2D11×#493C211yesmaximal, characteristic
3#13070870C212yesmaximal, complemented
4#13070838C212yesmaximal, complemented
5#13070657C211yesmaximal, characteristic, complemented
6#13070656C211yesmaximal, characteristic, complemented
7#13070653C211yesmaximal, characteristic, complemented
8#13070546C212yesmaximal, complemented
9#13070543C212yesmaximal, complemented
10#13070414C211yesmaximal, characteristic, complemented
11C11×#2207C211yesmaximal, characteristic, complemented
12C2×D8×D11—21no—
13C2×D8×D11C2212yes—
14D11×#127—21no—
15#10623109—21no—
16C2×C11×SD32C2212yescomplemented
17C11×#493C2211yescharacteristic
18C4×C11×Q16C2211yescharacteristic, complemented
19#10622801C2211yescharacteristic
20#10622794C2211yescharacteristic, complemented
21C2×#66892C2212yescomplemented
22#10622764—21no—
23#10622764C2212yes—
24C2×#66891C2212yescomplemented
25#10622686—21no—
26C4×#4326—21no—
27C2×#66864C2212yescomplemented
28#10622500C2211yescharacteristic
29#10622487C2211yescharacteristic, complemented
30#10622426—21no—
31#10622405—21no—
32C4×Dic44C2211yescharacteristic, complemented
33#10622308C2211yescharacteristic
34C4×C8×D11C2211yescharacteristic
35C11×C4⋊C16C2211yescharacteristic, complemented
36C11×#357C2212yescomplemented
37#10622200C2212yescomplemented
38#10622147C2212yescomplemented
39(C2×D11)⋊C16C2212yes—
40C16×Dic11C2212yescomplemented
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#66999—21no—
52#66997—21no—
53C2×#4326—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×Dic44C2311yescharacteristic
63C2×D88—21no—
64C2×D88C2312yes—
65C2×C8×D11D411yescharacteristic
66C2×C8×D11C2311yescharacteristic
67#66950—21no—
68#66949—41no—
69#66942—41no—
70#66941—21no—
71#66927—21no—
72#66925—41no—
73C42×D11D411yescharacteristic
74C4×Dic22—21no—
75C4×Dic22—41no—
76C11×SD32—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#103—21no—
80C4×C8×C11C2311yescharacteristic
81#66899—21no—
82#66892—42no—
83#66891—42no—
84#66882C2311yescharacteristic
85#66880—21no—
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C2×C11⋊C16C2312yes—
89#66874—21no—
90#66871—21no—
91C4×C11⋊C8D411yescharacteristic
92#66864—42no—
93#33774—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—22no—
107C2×D44—41no—
108C2×D44—41no—
109C2×C4×D11D811yescharacteristic
110C2×C4×D11D811yescharacteristic
111C2×C4×D11C2×D411yescharacteristic
112C2×Dic22—21no—
113C2×Dic22—41no—
114C11×Q16—21no—
115C11×Q16—21no—
116C11×D8—22no—
117C11×D8—22no—
118C11×D8—42no—
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2411yescharacteristic
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C42×C11—41no—
124C42×C11C2×D411yescharacteristic
125#4326—42no—
126#4323—44no—
127#4323—44no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—41no—
132Dic11⋊C4—41no—
133Dic11⋊C4—41no—
134Dic11⋊C4—41no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C4×Dic11—41no—
138C4×Dic11D811yescharacteristic
139C4×Dic11D811yescharacteristic
140C4×Dic11C2×D411yescharacteristic
141C2×C11⋊C8C2×D411yescharacteristic
142C2×C11⋊C8C2×D411yescharacteristic
143Dic44—21no—
144Dic44—21no—
145D88—22no—
146D88—22no—
147D88—42no—
148C8×D11—21no—
149C8×D11—21no—
150C8×D11—22no—
151C11×C16—22no—
152C11⋊C16—22no—
153#3170—111no—
154C2×#493—111no—
155#2248—112no—
156#2240—112no—
157#2207—111no—
158#2207—111no—
159#2207—111no—
160#2207D1111yescharacteristic, complemented
161#2187—112no—
162#2187—112no—
163#2162—111no—
164C23×C11—42no—
165C22×D11—42no—
166C22×D11—84no—
167C22×D11—84no—
168C22×D11—84no—
169C22×D11C2×D811yescharacteristic
170Q8×C11—41no—
171Q8×C11—41no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—82no—
175D4×C11—82no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C22⋊D11—84no—
182C22⋊D11—84no—
183C22⋊D11—84no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11C2×D811yescharacteristic
187C2×Dic11C2×D811yescharacteristic
188C2×Dic11C2×D811yescharacteristic
189D44—42no—
190D44—42no—
191D44—82no—
192D44—82no—
193C4×D11—21no—
194C4×D11—21no—
195C4×D11—22no—
196C4×D11SD3214yescomplemented
197Dic22—41no—
198Dic22—41no—
199Dic22—82no—
200C8×C11—21no—
201C8×C11H(5,𝔽2)11yescharacteristic
202C8×C11H(5,𝔽2)11yescharacteristic
203C11⋊C8—21no—
204C11⋊C8AGL(1,ℤ/8)12yes—
205C22×D8—112no—
206C22×D8—221no—
207#533—221no—
208C2×#127—221no—
209C2×SD32—112no—
210C2×SD32—112no—
211C2×SD32—112no—
212C2×SD32C2×D1112yescomplemented
213#500—111no—
214#494—111no—
215#493—112no—
216#493—111no—
217#493—221no—
218#493—221no—
219#493C2×D1111yescharacteristic
220#487—221no—
221#467—111no—
222#467—111no—
223#467—221no—
224C4×Q16—111no—
225C4×Q16—221no—
226C4×Q16C2×D1111yescharacteristic, complemented
227C2×C4×C8—111no—
228C4⋊C16—111no—
229C4⋊C16C2×D1111yescharacteristic, complemented
230#357—112no—
231#357—112no—
232#357—112no—
233#357C2×D1112yescomplemented
234C22⋊C16—112no—
235C4×C16—112no—
236C22×C11—82no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11C22×D811yescharacteristic
240C2×D11—21no—
241C2×D11—21no—
242C2×D11—82no—
243C2×D11—82no—
244C2×D11—82no—
245C2×D11—168no—
246C2×D11C2×SD3212yes—
247C4×C11—21no—
248C4×C11—81no—
249C4×C11—81no—
250C4×C11C2×SD3212yes—
251C4×C11#53511yescharacteristic
252C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
253Dic11—21no—
254Dic11—81no—
255Dic11—81no—
256Dic11C2×SD3212yes—
257Dic11#50912yes—
258C22×D4—222no—
259C22×D4—441no—
260C22×D4—441no—
261C2×Q16—111no—
262C2×Q16—221no—
263C2×Q16C22×D1111yescharacteristic
264C2×D8—21no—
265C2×D8—112no—
266C2×D8—222no—
267C2×D8—222no—
268C2×D8—221no—
269C2×D8—442no—
270C2×D8—442no—
271C2×D8—444no—
272C2×D8C22×D1112yes—
273C22×C8—111no—
274C22×C8—111no—
275C4⋊Q8—221no—
276C4⋊Q8—221no—
277#127—21no—
278#127—222no—
279#127—221no—
280#127—441no—
281#127—441no—
282#125—441no—
283C22⋊Q8—221no—
284C22⋊Q8—221no—
285C22⋊Q8—441no—
286C4×Q8—21no—
287C4×Q8—221no—
288C4×Q8—441no—
289#117—441no—
290C2×C42—111no—
291SD32—42no—
292SD32—442no—
293SD32—442no—
294SD32—442no—
295C2×C16—112no—
296C2×C16C22×D1112yes—
297#107—111no—
298#107—221no—
299#107C22×D1111yescharacteristic
300#103—21no—
301#103—221no—
302#103—221no—
303#103—221no—
304C4×C8—111no—
305C4×C8—111no—
306C4×C8—111no—
307C4×C8C22×D1111yescharacteristic
308C2×C11—162no—
309C2×C11#320511yescharacteristic
310C2×C11C22×SD3211yescharacteristic
311C2×C11C2×#50911yescharacteristic
312D11—22no—
313D11—162no—
314C24—442no—
315C2×Q8—21no—
316C2×Q8—221no—
317C2×Q8—441no—
318C2×D4—22no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—222no—
322C2×D4—442no—
323C2×D4—442no—
324C2×D4—442no—
325C2×D4—444no—
326C2×D4—444no—
327C2×D4—441no—
328C2×D4—441no—
329C2×D4—884no—
330C2×D4—884no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—111no—
334Q16—21no—
335Q16—21no—
336Q16—221no—
337Q16—221no—
338Q16—442no—
339D8—22no—
340D8—22no—
341D8—42no—
342D8—222no—
343D8—222no—
344D8—442no—
345D8—444no—
346D8—444no—
347C2×C8—111no—
348C2×C8—111no—
349C2×C8—222no—
350C2×C8—221no—
351C2×C8—221no—
352C2×C8D4×D1111yescharacteristic
353C2×C8C23×D1111yescharacteristic
354C4⋊C4—21no—
355C4⋊C4—41no—
356C4⋊C4—221no—
357C4⋊C4—441no—
358C4⋊C4—441no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C4⋊C4—441no—
362C4⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4—441no—
365C42—41no—
366C42—111no—
367C42—111no—
368C42—111no—
369C42—441no—
370C42D4×D1111yescharacteristic
371C16—22no—
372C16—222no—
373C11#3377411yescharacteristic, complemented, Sylow
374C23—42no—
375C23—111no—
376C23—442no—
377C23—884no—
378C23—884no—
379C23—884no—
380Q8—41no—
381Q8—41no—
382Q8—441no—
383Q8—441no—
384Q8—882no—
385D4—42no—
386D4—42no—
387D4—82no—
388D4—82no—
389D4—442no—
390D4—442no—
391D4—882no—
392D4—884no—
393D4—884no—
394D4—884no—
395D4—882no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—111no—
399C2×C4—111no—
400C2×C4—114no—
401C2×C4—111no—
402C2×C4—222no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4D8×D1111yescharacteristic
408C2×C4D8×D1111yescharacteristic
409C2×C4C2×D4×D1111yescharacteristic
410C8—21no—
411C8—112no—
412C8—221no—
413C8#6703711yescharacteristic
414C8#6704211yescharacteristic
415C22—82no—
416C22—82no—
417C22—82no—
418C22—112no—
419C22—221no—
420C22—221no—
421C22—882no—
422C22—882no—
423C22—882no—
424C22—1768no—
425C22C2×D8×D1111yescharacteristic
426C4—21no—
427C4—81no—
428C4—81no—
429C4—112no—
430C4—112no—
431C4—221no—
432C4—881no—
433C4—881no—
434C4D11×SD3212yes—
435C4#1062313811yescharacteristic
436C4D11×AGL(1,ℤ/8)11yescharacteristic
437C2—162no—
438C2—222no—
439C2—1762no—
440C2#1307953311yescharacteristic
441C2C2×D11×SD3211yescharacteristic
442C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2207C2
socleC22×C11C22×D8
prime radicalD11×#493C2
hypercenter#2207D11
hypocenterC11#33774
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. #13079199C2semidirect
3. #13070870C2semidirect
4. #13070838C2semidirect
5. #13070657C2semidirect
6. #13070656C2semidirect
7. #13070653C2semidirect
8. #13070546C2semidirect
9. #13070543C2semidirect
10. #13070414C2semidirect
11. C11×#2207C2semidirect
16. C2×C11×SD32C22semidirect
18. C4×C11×Q16C22semidirect
20. #10622794C22semidirect
21. C2×#66892C22semidirect
24. C2×#66891C22semidirect
27. C2×#66864C22semidirect
29. #10622487C22semidirect
32. C4×Dic44C22semidirect
35. C11×C4⋊C16C22semidirect
36. C11×#357C22semidirect
37. #10622200C22semidirect
38. #10622147C22semidirect
40. C16×Dic11C22semidirect
41. #10622129C22semidirect
42. C4⋊(C11⋊C16)C22semidirect
160. #2207D11semidirect
196. C4×D11SD32semidirect
212. C2×SD32C2×D11semidirect
226. C4×Q16C2×D11semidirect
229. C4⋊C16C2×D11semidirect
233. #357C2×D11semidirect
373. C11#33774semidirect

Maximal subgroups

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

subgroupindex
#130791992
D11×#4932
#130708702
#130708382
#130706572
#130706562
#130706532
#130705462
#130705432
#130704142
C11×#22072
#3377411