Finite Group Databasebeta

← #14729463

Subgroups — #14729463

Order 2816.

996 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078938C211yesmaximal, characteristic, complemented
2#13078687C212yesmaximal, complemented
3#13067830C212yesmaximal, complemented
4#13067823C212yesmaximal, complemented
5#13067802C212yesmaximal, complemented
6#13067795C212yesmaximal, complemented
7#13067278C211yesmaximal, characteristic, complemented
8#13066998C212yesmaximal, complemented
9C11×#3481C211yesmaximal, characteristic
10C11×#559C2211yescharacteristic
11C11×#554C2212yes—
12C11×#553—22no—
13C11×#551—22no—
14C11×#546—22no—
15D42×C11C2211yescharacteristic
16C11×#532C2211yescharacteristic
17C11×#529—22no—
18C11×#525—22no—
19C4×C11×#41C2212yes—
20C2×C4×D4×C11—22no—
21#10623001C2211yescharacteristic, complemented
22#10622852—22no—
23#10622846—22no—
24#10622694C2212yescomplemented
25#10622683C2212yes—
26#10622669—22no—
27#10622644C2212yescomplemented
28C4×#4326—22no—
29#10622633C2212yescomplemented
30#10622632C2212yes—
31C4×#4324—22no—
32#10622620C2212yes—
33#10622609—22no—
34#10622538C2212yescomplemented
35C2×C4×C11⋊C8C2211yescharacteristic, complemented
36#10622184C2211yescharacteristic, complemented
37#10622184C2211yescharacteristic, complemented
38#10622182C2212yes—
39Q8⋊(C11⋊C8)C2212yescomplemented
40Q8⋊(C11⋊C8)C2212yescomplemented
41D4⋊(C11⋊C8)C2212yes—
42D4⋊(C11⋊C8)C2212yes—
43C2×C11×#41D412yes—
44C2×C11×#41D412yes—
45C22×D4×C11—22no—
46C23×C4×C11—22no—
47C11×C4⋊Q8C2311yescharacteristic
48C11×#127C2311yescharacteristic
49C11×#126—24no—
50C11×#125—22no—
51C11×#124—22no—
52C11×#124D412yes—
53C11×#123—22no—
54C11×#123—24no—
55C11×#123—22no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—22no—
58C11×#121—24no—
59C11×#121—22no—
60C11×#121—22no—
61C11×#120—22no—
62C11×#120—22no—
63C4×Q8×C11D412yes—
64C4×Q8×C11C2312yes—
65C4×D4×C11—24no—
66C4×D4×C11—24no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11D412yes—
73C4×D4×C11C2312yes—
74C11×#117—22no—
75C11×#117—22no—
76C11×#117D412yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C22⋊C4—24no—
79C2×C42×C11—22no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326—22no—
82C2×#4324—22no—
83#66979—21no—
84#66977—22no—
85C22×C11⋊C8—21no—
86#66923—21no—
87#66922C2312yes—
88C4×Dic22—22no—
89#66899—24no—
90#66899—22no—
91#66896—24no—
92#66896—22no—
93C22⋊(C11⋊C8)—22no—
94#66874—22no—
95#66874—22no—
96#66872—22no—
97#66871—22no—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2312yes—
100C4×C11⋊C8—21no—
101C4×C11⋊C8—22no—
102C4×C11⋊C8C2312yes—
103#18485—111nomaximal, Sylow
104C24×C11—22no—
105C11×#41—24no—
106C11×#41—42no—
107C11×#41—44no—
108C2×Q8×C11C2×D412yes—
109C2×Q8×C11C2×D412yes—
110C2×D4×C11—24no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11C2×D412yes—
117C2×D4×C11C2×D412yes—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—84no—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C2×Dic22—22no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C2×D412yes—
134C11×C4⋊C4C2×D412yes—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—22no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11C2×D412yes—
147C42×C11C2×D411yescharacteristic
148C42×C11C2411yescharacteristic
149C22⋊Dic11—41no—
150#4326—44no—
151#4324—44no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154Dic11⋊C4—42no—
155C4×Dic11—41no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—42no—
160#3481D1111yescharacteristic
161#3131—111no—
162#3107—112no—
163#1644—112no—
164#1643—112no—
165#1640—112no—
166#1639—112no—
167#1543—111no—
168#1476—112no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—48no—
172C23×C11—82no—
173C23×C11#12011yescharacteristic
174Q8×C11—22no—
175Q8×C11—22no—
176Q8×C11—42no—
177D4×C11—22no—
178D4×C11—42no—
179D4×C11—44no—
180D4×C11—48no—
181D4×C11—42no—
182D4×C11—42no—
183D4×C11—82no—
184D4×C11#13514yes—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—44no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—44no—
196C2×C4×C11—44no—
197C2×C4×C11—82no—
198C2×C4×C11—84no—
199C2×C4×C11#12012yes—
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D412yes—
203C2×Dic11—42no—
204Dic22—42no—
205Dic22—42no—
206C11⋊C8—42no—
207C11⋊C8—42no—
208C11⋊C8—42no—
209#559C2×D1111yescharacteristic
210#554C2×D1112yes—
211#553—22no—
212#551—22no—
213#546—22no—
214D42C2×D1111yescharacteristic
215#533—111no—
216#532C2×D1111yescharacteristic
217#529—22no—
218#525—22no—
219C4×#41C2×D1112yes—
220C2×C4×D4—22no—
221#488—222no—
222#487—112no—
223#486—112no—
224#485—222no—
225#475—112no—
226#474—112no—
227#462—112no—
228#461—112no—
229#452—222no—
230C4×Q16—222no—
231C4×SD16—222no—
232#431—112no—
233#416—222no—
234C2×C4×C8—111no—
235#333—111no—
236#333—111no—
237#331—112no—
238Q8⋊C8—112no—
239Q8⋊C8—112no—
240D4⋊C8—112no—
241D4⋊C8—112no—
242C22×C11—22no—
243C22×C11—24no—
244C22×C11—21no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—44no—
248C22×C11—42no—
249C22×C11—88no—
250C22×C11C2×#12011yescharacteristic
251C4×C11—22no—
252C4×C11—21no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11#45512yes—
258C4×C11C2×#13512yes—
259C4×C11#57512yes—
260Dic11—82no—
261C2×#41C22⋊D1112yes—
262C2×#41C22⋊D1112yes—
263C22×D4—22no—
264C23×C4—22no—
265C2×Q16—222no—
266C2×SD16—222no—
267C22×C8—221no—
268C4⋊Q8—112no—
269C4⋊Q8C22×D1111yescharacteristic
270#127C22×D1111yescharacteristic
271#126—24no—
272#125—22no—
273#125—221no—
274#124—22no—
275#124C22⋊D1112yes—
276#123—22no—
277#123—24no—
278#123—22no—
279C22⋊Q8—24no—
280C22⋊Q8—22no—
281C22⋊Q8—222no—
282#121—24no—
283#121—22no—
284#121—22no—
285#120—22no—
286#120—22no—
287C4×Q8—222no—
288C4×Q8C22⋊D1112yes—
289C4×Q8C22×D1112yes—
290C4×D4—24no—
291C4×D4—24no—
292C4×D4—22no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—22no—
297C4×D4C22⋊D1112yes—
298C4×D4C22×D1112yes—
299#117—22no—
300#117—22no—
301#117—221no—
302#117C22⋊D1112yes—
303C2×C4⋊C4—22no—
304C2×C22⋊C4—24no—
305C2×C42—22no—
306C2×C42C22×D1111yescharacteristic
307#107—222no—
308#106—222no—
309C4⋊C8—112no—
310C4⋊C8—112no—
311#103—224no—
312#103—222no—
313#103—222no—
314#103—222no—
315#102—224no—
316#102—222no—
317C22⋊C8—222no—
318C4×C8—112no—
319C4×C8—221no—
320C4×C8—222no—
321C2×C11—41no—
322C2×C11—44no—
323C2×C11—82no—
324C2×C11#300212yes—
325C2×C11C2×#45511yescharacteristic
326C24—22no—
327#41—24no—
328#41—42no—
329#41—44no—
330C2×Q8—222no—
331C2×Q8C2×C22⋊D1112yes—
332C2×Q8C2×C22⋊D1112yes—
333C2×D4—24no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—44no—
338C2×D4—44no—
339C2×D4C2×C22⋊D1112yes—
340C2×D4C2×C22⋊D1112yes—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—84no—
348C22×C4C2×C22⋊D1112yes—
349C22×C4C2×C22⋊D1111yescharacteristic
350Q16—444no—
351SD16—444no—
352C2×C8—222no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—442no—
356C4⋊C4—24no—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C4⋊C4—442no—
364C4⋊C4C2×C22⋊D1112yes—
365C4⋊C4C2×C22⋊D1112yes—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—24no—
373C22⋊C4—22no—
374C22⋊C4—441no—
375C42—22no—
376C42—22no—
377C42—22no—
378C42—441no—
379C42C2×C22⋊D1111yescharacteristic
380C42C2×C22⋊D1112yes—
381C42C23×D1111yescharacteristic
382C11#1848511yescharacteristic, complemented, Sylow
383C23—22no—
384C23—22no—
385C23—48no—
386C23—82no—
387C23#6700611yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—42no—
391Q8—442no—
392Q8—442no—
393D4—22no—
394D4—42no—
395D4—44no—
396D4—48no—
397D4—42no—
398D4—42no—
399D4—82no—
400D4#6700314yes—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—82no—
414C2×C4—84no—
415C2×C4—442no—
416C2×C4#6700612yes—
417C2×C4#6700611yescharacteristic
418C2×C4C22×C22⋊D1111yescharacteristic
419C2×C4C22×C22⋊D1112yes—
420C8—442no—
421C8—442no—
422C8—442no—
423C22—22no—
424C22—24no—
425C22—21no—
426C22—42no—
427C22—42no—
428C22—44no—
429C22—42no—
430C22—88no—
431C22C2×#6700611yescharacteristic
432C4—22no—
433C4—21no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4—42no—
438C4—882no—
439C4#1062285512yes—
440C4C2×#6700312yes—
441C4#1062335312yes—
442C2—41no—
443C2—44no—
444C2—82no—
445C2#1307783412yes—
446C2C2×#1062285511yescharacteristic
subgroupG/H
centerC2×C4#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3481C2
socleC22×C11C2×#120
hypercenter#3481D11
hypocenterC11#18485
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #13078938C2semidirect
2. #13078687C2semidirect
3. #13067830C2semidirect
4. #13067823C2semidirect
5. #13067802C2semidirect
6. #13067795C2semidirect
7. #13067278C2semidirect
8. #13066998C2semidirect
21. #10623001C22semidirect
24. #10622694C22semidirect
27. #10622644C22semidirect
29. #10622633C22semidirect
34. #10622538C22semidirect
35. C2×C4×C11⋊C8C22semidirect
36. #10622184C22semidirect
37. #10622184C22semidirect
39. Q8⋊(C11⋊C8)C22semidirect
40. Q8⋊(C11⋊C8)C22semidirect
382. C11#18485semidirect

Maximal subgroups

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

subgroupindex
#130789382
#130786872
#130678302
#130678232
#130678022
#130677952
#130672782
#130669982
C11×#34812
#1848511