Finite Group Databasebeta

← #14909246

Subgroups — #14909246

Order 2816.

826 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
1C2×#10622521C211yesmaximal, characteristic, complemented
2C2×#10622807C211yesmaximal, characteristic, complemented
3C22×#66892C211yesmaximal, characteristic, complemented
4#13079105C211yesmaximal, characteristic, complemented
5#13079103C211yesmaximal, characteristic, complemented
6#13070884C212yesmaximal, complemented
7#13070881C212yesmaximal, complemented
8#13070878C212yesmaximal, complemented
9#13070870C212yesmaximal, complemented
10#13070215C211yesmaximal, characteristic, complemented
11C2×C11×#510C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C22×C11×Q16C2211yescharacteristic
14#10623361—21no—
15C2×#67002—21no—
16#10623347—21no—
17C2×#66995—21no—
18C2×#66957C2211yescharacteristic
19C22×D88C2211yescharacteristic
20C11×#510—24no—
21C2×C11×Q32C2212yescomplemented
22C2×C11×SD32C2212yescomplemented
23C2×C11×M32C2211yescharacteristic
24#10622807—24no—
25#10622804C2212yes—
26#10622804C2212yescomplemented
27#10622803—22no—
28#10622794C2212yescomplemented
29C2×#66893C2211yescharacteristic, complemented
30C2×#66892—24no—
31C2×#66892C2212yes—
32C2×#66892C2212yes—
33C2×#66892C2211yescharacteristic, complemented
34#10622789—22no—
35#10622764C2212yes—
36C2×#66891C2211yescharacteristic, complemented
37C2×#66890C2211yescharacteristic, complemented
38#10622714C2211yescharacteristic
39C22×C11⋊C16C2211yescharacteristic
40#10622521—24no—
41C2×#66864C2212yes—
42C2×D176C2212yes—
43#10622140C2212yescomplemented
44C16×Dic11C2212yescomplemented
45C2×C11×#41—21no—
46C22×Q8×C11—21no—
47C2×#4339—21no—
48C22×D44—21no—
49C11×#135—22no—
50C11×#135—22no—
51C2×C11×Q16—22no—
52C2×C11×Q16—22no—
53C2×C11×Q16—21no—
54C2×C11×Q16C2312yes—
55C2×C11×Q16C2311yescharacteristic
56C2×C11×SD16—21no—
57C2×C11×D8C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59#67002—44no—
60#67000—22no—
61#67000—22no—
62#66999—42no—
63#66997—22no—
64C2×#4326—22no—
65#66995—44no—
66C2×#4325—22no—
67C2×#4325—22no—
68#66993—22no—
69#66990—42no—
70C2×#4323—22no—
71#66983—42no—
72#66982—42no—
73#66979D411yescharacteristic
74C2×#4318D411yescharacteristic
75C2×Dic44C2311yescharacteristic
76#66957—22no—
77#66957—22no—
78C2×D88—22no—
79C2×D88—22no—
80C2×D88—21no—
81C2×D88C2311yescharacteristic
82C2×D88C2312yes—
83C2×#4314—21no—
84C11×Q32—24no—
85C11×SD32—24no—
86C11×M32D414yescomplemented
87C2×C11×C16C2312yes—
88#66893—22no—
89#66892—24no—
90#66892—24no—
91#66892—22no—
92#66891—22no—
93#66890—22no—
94#66879D412yes—
95C8×Dic11C2312yes—
96C2×C11⋊C16D414yescomplemented
97C2×C11⋊C16C2311yescharacteristic
98C2×C11⋊C16C2311yescharacteristic
99#66864—24no—
100D176—24no—
101#33722—111nomaximal, Sylow
102C23×D11—41no—
103C11×#41—42no—
104C11×#41—42no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—41no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×D4×C11—21no—
111C2×D4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11C2×D411yescharacteristic
115C2×C22⋊D11—44no—
116C2×C22⋊D11—41no—
117#4339—42no—
118#4339—42no—
119C2×D44—21no—
120C2×D44—22no—
121C2×D44—42no—
122C2×D44—41no—
123C2×D44—42no—
124C2×C4×D11—41no—
125C2×Dic22—21no—
126C11×Q16—22no—
127C11×Q16—21no—
128C11×Q16—22no—
129C11×Q16—21no—
130C11×Q16—42no—
131C11×SD16—42no—
132C11×D8—21no—
133C11×D8—21no—
134C2×C8×C11C2×D412yes—
135C2×C8×C11C2×D412yes—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C22⋊Dic11D812yes—
139#4326—44no—
140#4325—44no—
141#4325—44no—
142#4323—44no—
143(C2×D11)⋊C4—44no—
144(C2×D11)⋊C4—44no—
145C4⋊Dic11D812yes—
146Dic11⋊C4—44no—
147C4×Dic11C2×D412yes—
148#4318D814yes—
149C2×C11⋊C8C2×D412yes—
150Dic44—21no—
151Dic44—21no—
152D88—21no—
153D88—22no—
154D88—21no—
155D88—22no—
156D88—42no—
157#4314—42no—
158C11×C16C2×D414yes—
159C11⋊C16C2×D412yes—
160C11⋊C16C2×D412yes—
161C2×#510D1111yescharacteristic, complemented
162C2×#509—111no—
163C2×#508—111no—
164C22×SD32—111no—
165#3156—111no—
166#3155—111no—
167#2251—112no—
168#2250—112no—
169#2249—112no—
170#2248—112no—
171#2108—111no—
172C23×C11—41no—
173C23×C11C2×D811yescharacteristic
174C22×D11—41no—
175C22×D11—42no—
176C22×D11—82no—
177C22×D11—162no—
178Q8×C11—41no—
179Q8×C11—42no—
180Q8×C11—41no—
181Q8×C11—42no—
182Q8×C11—82no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—82no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—82no—
189C2×C4×C11—82no—
190C2×C4×C11#12712yes—
191C2×C4×C11C2×D812yes—
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C22⋊D11—82no—
195C22⋊D11—164no—
196C2×Dic11—41no—
197C2×Dic11C2×D814yes—
198D44—41no—
199D44—42no—
200D44—42no—
201D44—41no—
202D44—82no—
203C4×D11—82no—
204Dic22—41no—
205Dic22—41no—
206C8×C11#12712yes—
207C8×C11C22×D411yescharacteristic
208C8×C11C22×D411yescharacteristic
209C11⋊C8C2×D814yes—
210C2×#137—221no—
211C2×AGL(1,ℤ/8)—221no—
212C2×#135—111no—
213C2×#135C2×D1111yescharacteristic
214C22×Q16C2×D1111yescharacteristic
215C22×D8—111no—
216#536—221no—
217#535—221no—
218#510—24no—
219#509—224no—
220#508—224no—
221C2×Q32—111no—
222C2×Q32C2×D1112yescomplemented
223C2×SD32—112no—
224C2×SD32—112no—
225C2×SD32—111no—
226C2×SD32—111no—
227C2×SD32—112no—
228C2×SD32—224no—
229C2×SD32C2×D1112yescomplemented
230C2×D16—111no—
231C2×D16—112no—
232C2×M32C2×D1111yescharacteristic
233C22×C16—111no—
234#497—222no—
235#496—222no—
236#495—112no—
237#495—112no—
238#494—112no—
239#493—112no—
240#405—111no—
241#346—112no—
242C4×C16—112no—
243C22×C11—22no—
244C22×C11—81no—
245C22×C11—82no—
246C22×C11#49312yes—
247C22×C11C22×D811yescharacteristic
248C2×D11—82no—
249C2×D11—81no—
250C2×D11—82no—
251C2×D11—84no—
252C2×D11—164no—
253C4×C11—81no—
254C4×C11—82no—
255C4×C11#49312yes—
256C4×C11C2×#12711yescharacteristic
257C4×C11C22×D811yescharacteristic
258Dic11—24no—
259Dic11—81no—
260C2×#41—21no—
261C2×#41—221no—
262C22×Q8—21no—
263C22×D4—221no—
264#137—444no—
265AGL(1,ℤ/8)—444no—
266#135—22no—
267#135—22no—
268#135—222no—
269#135—222no—
270C2×Q16—22no—
271C2×Q16—21no—
272C2×Q16—22no—
273C2×Q16—111no—
274C2×Q16—222no—
275C2×Q16C22×D1112yes—
276C2×Q16C22×D1111yescharacteristic
277C2×SD16—21no—
278C2×SD16—222no—
279C2×SD16—222no—
280C2×SD16—221no—
281C2×D8—112no—
282C2×D8—111no—
283C2×D8—222no—
284C2×D8—222no—
285C2×D8—221no—
286C2×D8—222no—
287C2×D8C22×D1111yescharacteristic
288C2×M16—111no—
289C22×C8C22×D1111yescharacteristic
290C4⋊Q8—222no—
291#127—222no—
292#124—222no—
293#124—222no—
294#123—442no—
295C22⋊Q8—442no—
296#121—442no—
297#120—442no—
298#117—111no—
299Q32—24no—
300Q32—222no—
301SD32—24no—
302SD32—222no—
303SD32—224no—
304SD32—224no—
305SD32—222no—
306SD32—224no—
307D16—222no—
308D16—224no—
309M32C22⋊D1114yescomplemented
310C2×C16—114no—
311C2×C16—111no—
312C2×C16—111no—
313C2×C16C22×D1112yes—
314#97—112no—
315C4×C8—112no—
316C2×C11—22no—
317C2×C11—161no—
318C2×C11C2×#49311yescharacteristic
319C2×C11#341612yes—
320D11—161no—
321D11—162no—
322C24—441no—
323#41—42no—
324#41—42no—
325#41—442no—
326#41—442no—
327C2×Q8—21no—
328C2×Q8—22no—
329C2×Q8—41no—
330C2×Q8—42no—
331C2×Q8—42no—
332C2×Q8—221no—
333C2×D4—21no—
334C2×D4—41no—
335C2×D4—221no—
336C2×D4—222no—
337C2×D4—444no—
338C2×D4—441no—
339C2×D4—442no—
340C2×D4—441no—
341C2×D4—442no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—441no—
345C22×C4D4×D1111yescharacteristic
346Q16—22no—
347Q16—21no—
348Q16—22no—
349Q16—21no—
350Q16—42no—
351Q16—221no—
352Q16—221no—
353Q16—444no—
354SD16—42no—
355SD16—444no—
356SD16—444no—
357SD16—442no—
358D8—21no—
359D8—21no—
360D8—221no—
361D8—222no—
362D8—221no—
363D8—222no—
364D8—444no—
365D8—442no—
366M16—114no—
367C2×C8—112no—
368C2×C8D4×D1111yescharacteristic
369C2×C8D4×D1112yes—
370C2×C8C2×C22⋊D1112yes—
371C2×C8C23×D1111yescharacteristic
372C4⋊C4—112no—
373C4⋊C4—444no—
374C22⋊C4—112no—
375C22⋊C4—444no—
376C22⋊C4—444no—
377C42—112no—
378C16—112no—
379C16—112no—
380C16C2×C22⋊D1114yes—
381C11#3372211yescharacteristic, complemented, Sylow
382C23—41no—
383C23—441no—
384C23—442no—
385C23—882no—
386C23—1762no—
387C23D8×D1111yescharacteristic
388Q8—41no—
389Q8—42no—
390Q8—41no—
391Q8—42no—
392Q8—82no—
393Q8—441no—
394Q8—441no—
395D4—41no—
396D4—41no—
397D4—82no—
398D4—442no—
399D4—441no—
400D4—442no—
401D4—441no—
402D4—882no—
403D4—882no—
404D4—1764no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—114no—
410C2×C4—441no—
411C2×C4—882no—
412C2×C4D8×D1111yescharacteristic
413C2×C4D8×D1112yes—
414C2×C4#6699312yes—
415C2×C4C2×D4×D1111yescharacteristic
416C8—114no—
417C8#6699312yes—
418C8C2×D4×D1111yescharacteristic
419C8C22×C22⋊D1111yescharacteristic
420C22—22no—
421C22—82no—
422C22—81no—
423C22—884no—
424C22—882no—
425C22—881no—
426C22—882no—
427C22—1764no—
428C22#1062276412yes—
429C22C2×D8×D1111yescharacteristic
430C4—81no—
431C4—82no—
432C4—224no—
433C4—881no—
434C4#1062276412yes—
435C4C2×D8×D1111yescharacteristic
436C4C2×#6699311yescharacteristic
437C2—22no—
438C2—161no—
439C2—1762no—
440C2—1761no—
441C2C2×#1062276411yescharacteristic
442C2#1308176112yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#510C2
socleC22×C11C22×D8
hypercenterC2×#510D11
hypocenterC11#33722
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. C2×#10622807C2semidirect
3. C22×#66892C2semidirect
4. #13079105C2semidirect
5. #13079103C2semidirect
6. #13070884C2semidirect
7. #13070881C2semidirect
8. #13070878C2semidirect
9. #13070870C2semidirect
10. #13070215C2semidirect
11. C2×C11×#510C2semidirect
21. C2×C11×Q32C22semidirect
22. C2×C11×SD32C22semidirect
26. #10622804C22semidirect
28. #10622794C22semidirect
29. C2×#66893C22semidirect
33. C2×#66892C22semidirect
36. C2×#66891C22semidirect
37. C2×#66890C22semidirect
43. #10622140C22semidirect
44. C16×Dic11C22semidirect
86. C11×M32D4semidirect
96. C2×C11⋊C16D4semidirect
161. C2×#510D11semidirect
222. C2×Q32C2×D11semidirect
229. C2×SD32C2×D11semidirect
309. M32C22⋊D11semidirect
381. C11#33722semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
C2×#106228072
C22×#668922
#130791052
#130791032
#130708842
#130708812
#130708782
#130708702
#130702152
C2×C11×#5102
#3372211