Finite Group Databasebeta

← #14908124

Subgroups — #14908124

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic, complemented
2C2×#10622807C211yesmaximal, characteristic, complemented
3#13079102C211yesmaximal, characteristic, complemented
4#13070678C212yesmaximal, complemented
5#13070671C212yesmaximal, complemented
6#13070656C212yesmaximal, complemented
7#13070651C212yesmaximal, complemented
8#13070375C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic, complemented
10C2×#10622129C211yesmaximal, characteristic, complemented
11C11×#2951C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C11×#520—21no—
14C2×#66961—21no—
15C2×#66957C2211yescharacteristic
16C22×D88C2211yescharacteristic
17#10623056—21no—
18C11×#440—22no—
19C4×C11×Q16C2212yescomplemented
20C4×C11×D8C2212yescomplemented
21C2×C11×#107C2211yescharacteristic
22C11×#417—21no—
23C11×#405C2211yescharacteristic
24#10622807—24no—
25#10622806—24no—
26C2×#66893C2211yescharacteristic, complemented
27C2×#66892C2212yes—
28C2×#66892C2211yescharacteristic, complemented
29C2×#66891C2211yescharacteristic, complemented
30C2×#66890C2212yes—
31C2×#66890C2211yescharacteristic, complemented
32C2×#66876C2211yescharacteristic
33C22×C11⋊C16C2211yescharacteristic
34#10622325—22no—
35#10622309C2212yes—
36#10622308C2212yes—
37#10622130C2212yescomplemented
38#10622129C2212yes—
39#10622129C2212yes—
40#10622129C2212yescomplemented
41C4⋊(C11⋊C16)C2212yescomplemented
42C4⋊(C11⋊C16)C2212yescomplemented
43C2×C11×#41—21no—
44C2×#4339—21no—
45C22×D44—21no—
46C11×#135—22no—
47C11×#135D414yescomplemented
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic
51C2×C11×M16D411yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C4×Q8×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—42no—
56C11×#117—41no—
57C11×#117D411yescharacteristic
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—41no—
60#66961—44no—
61C2×Dic44C2311yescharacteristic
62#66957—22no—
63#66957—22no—
64C2×D88—22no—
65C2×D88—22no—
66C2×D88—21no—
67C2×D88—22no—
68C2×D88C2312yes—
69C2×D88C2311yescharacteristic
70C2×#4314—21no—
71C2×#4314—22no—
72#66948—41no—
73#66948—41no—
74#66935—42no—
75#66928—22no—
76#66927—22no—
77C11×#107—21no—
78C11×#107C2312yes—
79C11×#103—22no—
80C11×#102—22no—
81C11×#97D412yes—
82C4×C8×C11C2312yes—
83#66893—22no—
84#66892—24no—
85#66892—22no—
86#66891—22no—
87#66890—24no—
88#66890—22no—
89#66876—22no—
90C2×C11⋊C16—22no—
91C2×C11⋊C16C2312yes—
92C2×C11⋊C16C2311yescharacteristic
93C2×C11⋊C16C2311yescharacteristic
94#33589—111nomaximal, Sylow
95C23×D11—41no—
96C11×#41—24no—
97C11×#41—42no—
98C2×Q8×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—42no—
104C22×C4×C11C2×D411yescharacteristic
105C2×C22⋊D11—41no—
106#4339—42no—
107#4339—42no—
108C2×D44—21no—
109C2×D44—22no—
110C2×D44—42no—
111C2×D44—41no—
112C2×D44—42no—
113C2×D44—42no—
114C2×D44—42no—
115C2×C4×D11—41no—
116C2×Dic22—21no—
117C11×Q16—21no—
118C11×Q16C2×D412yes—
119C11×SD16—24no—
120C11×D8—21no—
121C11×D8C2×D412yes—
122C11×M16—22no—
123C2×C8×C11C2×D412yes—
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11#4112yes—
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—22no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4D811yescharacteristic
132C11×C4⋊C4D811yescharacteristic
133C11×C22⋊C4—42no—
134C11×C22⋊C4D812yes—
135C42×C11—42no—
136C42×C11C2×D412yes—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139Dic44—21no—
140Dic44—21no—
141D88—22no—
142D88—21no—
143D88—22no—
144D88—21no—
145D88—44no—
146D88—42no—
147#4314—44no—
148#4314—42no—
149C11⋊C16—21no—
150C11⋊C16—21no—
151C11⋊C16—22no—
152C2×#509—111no—
153C2×#508—111no—
154#3155—111no—
155#2951D1111yescharacteristic, complemented
156#2211—112no—
157#2210—112no—
158#2207—112no—
159#2206—112no—
160#2151—111no—
161#2139—111no—
162C2×#357—111no—
163C23×C11—41no—
164C23×C11C2×D811yescharacteristic
165C22×D11—42no—
166C22×D11—41no—
167C22×D11—82no—
168C22×D11—161no—
169C22×D11—161no—
170Q8×C11—22no—
171Q8×C11—41no—
172D4×C11—22no—
173D4×C11—44no—
174D4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—44no—
177C2×C4×C11—42no—
178C2×C4×C11—162no—
179C2×C4×C11—161no—
180C2×C4×C11#12112yes—
181C2×C4×C11C2×D812yes—
182C2×C4×C11C2×D812yes—
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)12yes—
185C2×C4×C11C22×D411yescharacteristic
186C22⋊D11—82no—
187C2×Dic11—41no—
188D44—41no—
189D44—42no—
190D44—42no—
191D44—41no—
192D44—82no—
193D44—162no—
194D44—162no—
195C4×D11—82no—
196Dic22—41no—
197Dic22—41no—
198C8×C11—22no—
199C8×C11#12112yes—
200C8×C11C22×D411yescharacteristic
201C8×C11C2×#4111yescharacteristic
202C2×AGL(1,ℤ/8)—221no—
203C2×#135—111no—
204C2×#135C2×D1111yescharacteristic
205C22×D8—111no—
206#535—221no—
207#520—21no—
208#509—224no—
209#508—224no—
210C2×Q32—111no—
211C2×SD32—112no—
212C2×SD32—111no—
213C2×SD32—111no—
214C2×D16—112no—
215C2×D16—111no—
216C2×M32—111no—
217C22×C16—111no—
218#496—222no—
219#495—112no—
220#493—112no—
221#440—22no—
222C4×Q16C2×D1112yescomplemented
223C4×D8C2×D1112yescomplemented
224C2×#107C2×D1111yescharacteristic
225#417—21no—
226#405C2×D1111yescharacteristic
227C4⋊C16—112no—
228C4⋊C16—112no—
229#358—112no—
230#357—112no—
231#357—112no—
232#357—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—42no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11#45912yes—
239C22×C11C22×D811yescharacteristic
240C2×D11—82no—
241C2×D11—81no—
242C2×D11—82no—
243C2×D11—81no—
244C2×D11—82no—
245C2×D11—81no—
246C2×D11—164no—
247C4×C11—22no—
248C4×C11—22no—
249C4×C11—42no—
250C4×C11—82no—
251C4×C11#45912yes—
252C4×C11C2×#12111yescharacteristic
253C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
254Dic11—81no—
255C2×#41—21no—
256C2×#41—221no—
257C22×D4—221no—
258AGL(1,ℤ/8)—444no—
259#135—22no—
260#135—222no—
261#135—222no—
262#135D4414yescomplemented
263C2×Q16—111no—
264C2×Q16C22×D1111yescharacteristic
265C2×SD16—21no—
266C2×SD16—221no—
267C2×SD16—222no—
268C2×D8—112no—
269C2×D8—111no—
270C2×D8—222no—
271C2×D8—222no—
272C2×D8—221no—
273C2×D8—222no—
274C2×D8C22×D1111yescharacteristic
275C2×M16C22⋊D1111yescharacteristic
276C22×C8C22×D1111yescharacteristic
277#127—222no—
278#124—222no—
279#121—441no—
280#121—441no—
281#120—442no—
282C4×Q8—22no—
283C4×D4—22no—
284C4×D4—42no—
285#117—41no—
286#117C22⋊D1111yescharacteristic
287C2×C4⋊C4—21no—
288C2×C4⋊C4—41no—
289Q32—222no—
290SD32—222no—
291SD32—224no—
292SD32—222no—
293D16—222no—
294D16—224no—
295M32—222no—
296C2×C16—111no—
297C2×C16—111no—
298C2×C16—112no—
299C2×C16—222no—
300#107—21no—
301#107C22×D1112yes—
302#103—22no—
303#102—22no—
304#97C22⋊D1112yes—
305C4×C8C22×D1112yes—
306C2×C11—22no—
307C2×C11—82no—
308C2×C11C2×#45911yescharacteristic
309C2×C11#341511yescharacteristic
310C2×C11#341611yescharacteristic
311D11—161no—
312D11—162no—
313C24—441no—
314#41—24no—
315#41—42no—
316#41—442no—
317#41—442no—
318C2×Q8—21no—
319C2×Q8—221no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4—222no—
323C2×D4—221no—
324C2×D4—441no—
325C2×D4—442no—
326C2×D4—441no—
327C2×D4—442no—
328C2×D4—442no—
329C2×D4—442no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—441no—
334C22×C4C2×C22⋊D1111yescharacteristic
335Q16—21no—
336Q16—221no—
337Q16—221no—
338Q16C2×D4412yes—
339SD16—24no—
340SD16—444no—
341SD16—442no—
342D8—21no—
343D8—222no—
344D8—221no—
345D8—222no—
346D8—221no—
347D8—444no—
348D8—442no—
349D8C2×D4412yes—
350M16—22no—
351C2×C8C2×D4412yes—
352C2×C8#433912yes—
353C2×C8C2×C22⋊D1112yes—
354C2×C8C2×C22⋊D1111yescharacteristic
355C2×C8C23×D1111yescharacteristic
356C4⋊C4—22no—
357C4⋊C4—41no—
358C4⋊C4—42no—
359C4⋊C4#432311yescharacteristic
360C4⋊C4#432311yescharacteristic
361C22⋊C4—42no—
362C22⋊C4—442no—
363C22⋊C4—442no—
364C22⋊C4#432312yes—
365C42—42no—
366C42C2×C22⋊D1112yes—
367C16—221no—
368C16—221no—
369C16—222no—
370C11#3358911yescharacteristic, complemented, Sylow
371C23—41no—
372C23—442no—
373C23—441no—
374C23—882no—
375C23—1761no—
376C23—1761no—
377C23C2×#432311yescharacteristic
378Q8—22no—
379Q8—41no—
380Q8—441no—
381Q8—441no—
382D4—22no—
383D4—44no—
384D4—41no—
385D4—442no—
386D4—441no—
387D4—441no—
388D4—442no—
389D4—882no—
390D4—882no—
391D4—1762no—
392D4—1762no—
393C2×C4—41no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—162no—
397C2×C4—161no—
398C2×C4—441no—
399C2×C4—882no—
400C2×C4#6698312yes—
401C2×C4C2×#432312yes—
402C2×C4C2×#432312yes—
403C2×C4C2×#432311yescharacteristic
404C2×C4#6700212yes—
405C2×C4C22×C22⋊D1111yescharacteristic
406C8—22no—
407C8#6698312yes—
408C8C22×D4411yescharacteristic
409C8C2×#433911yescharacteristic
410C22—21no—
411C22—21no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—881no—
416C22—882no—
417C22—881no—
418C22—882no—
419C22—881no—
420C22—882no—
421C22—1764no—
422C22#1062262812yes—
423C22C22×#432311yescharacteristic
424C4—22no—
425C4—22no—
426C4—42no—
427C4—82no—
428C4—881no—
429C4#1062262812yes—
430C4C2×#6698311yescharacteristic
431C4C2×#6700211yescharacteristic
432C2—22no—
433C2—82no—
434C2—1762no—
435C2—1761no—
436C2C2×#1062262811yescharacteristic
437C2#1308175511yescharacteristic
438C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2951C2
socleC22×C11C22×D8
hypercenter#2951D11
hypocenterC11#33589
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. C2×#10622807C2semidirect
3. #13079102C2semidirect
4. #13070678C2semidirect
5. #13070671C2semidirect
6. #13070656C2semidirect
7. #13070651C2semidirect
8. #13070375C2semidirect
9. #13070326C2semidirect
10. C2×#10622129C2semidirect
11. C11×#2951C2semidirect
19. C4×C11×Q16C22semidirect
20. C4×C11×D8C22semidirect
26. C2×#66893C22semidirect
28. C2×#66892C22semidirect
29. C2×#66891C22semidirect
31. C2×#66890C22semidirect
37. #10622130C22semidirect
40. #10622129C22semidirect
41. C4⋊(C11⋊C16)C22semidirect
42. C4⋊(C11⋊C16)C22semidirect
47. C11×#135D4semidirect
155. #2951D11semidirect
222. C4×Q16C2×D11semidirect
223. C4×D8C2×D11semidirect
262. #135D44semidirect
370. C11#33589semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
C2×#106228072
#130791022
#130706782
#130706712
#130706562
#130706512
#130703752
#130703262
C2×#106221292
C11×#29512
#3358911