Finite Group Databasebeta

← #14774642

Subgroups — #14774642

Order 2816.

996 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077964C211yesmaximal, characteristic
2#13077523C212yesmaximal, complemented
3#13077162C212yesmaximal, complemented
4#13069449C211yesmaximal, characteristic, complemented
5#13069288C212yesmaximal, complemented
6#13069114C212yesmaximal, complemented
7#13068857C212yesmaximal, complemented
8#13068425C212yesmaximal, complemented
9C11×#1884C211yesmaximal, characteristic, complemented
10#10623453C2211yescharacteristic
11C11×#568C2211yescharacteristic, complemented
12C11×#532C2211yescharacteristic
13#10623353C2212yes—
14#10623276C2212yes—
15#10623053C2212yes—
16C11×#421C2212yes—
17C11×#410C2211yescharacteristic, complemented
18#10622850C2211yescharacteristic
19C2×#66901C2212yes—
20C2×#66901C2212yescomplemented
21#10622758—24no—
22#10622757—24no—
23C2×#66889C2212yes—
24#10622737C2212yescomplemented
25M16×Dic11C2212yescomplemented
26#10622708C412yescomplemented
27#10622690C412yescomplemented
28#10622675C412yescomplemented
29#10622674C412yescomplemented
30#10622618C2212yes—
31#10622545C2211yescharacteristic, complemented
32C2×#66869C2212yes—
33#10622537C2211yescharacteristic, complemented
34#10622434—24no—
35D11×#104—24no—
36C11×#339C2212yescomplemented
37#10622171C2212yescomplemented
38#10622170C2212yescomplemented
39C2×C11×#41C2311yescharacteristic
40C2×C11×#41C2311yescharacteristic
41#67043—22no—
42#67042—22no—
43#41×D11—24no—
44#67040C2×C412yes—
45#67037—41no—
46#67037C2×C412yes—
47C2×#4339—41no—
48C2×#4339C2312yes—
49C11×#131—24no—
50C2×C11×M16—41no—
51C2×C11×M16C2312yes—
52C11×C4⋊Q8C2×C411yescharacteristic, complemented
53C11×#127C2×C411yescharacteristic, complemented
54C11×#124C2×C411yescharacteristic, complemented
55C11×#124C2×C411yescharacteristic, complemented
56C11×#121—41no—
57C4×D4×C11—41no—
58C11×#117C2312yes—
59C2×C42×C11C2311yescharacteristic
60#67004—22no—
61#67003—24no—
62#67002—22no—
63#66995C2×C414yescomplemented
64#66985C2×C414yescomplemented
65C2×C4×Dic11C2312yes—
66C2×#4318C2312yes—
67C2×#4318C2312yes—
68#66960—42no—
69M16×D11—24no—
70#66954—24no—
71#66946—22no—
72#66940—22no—
73(C22⋊D11)⋊C4—42no—
74#66925—22no—
75C42×D11—22no—
76C11×#104—24no—
77C11×#99—41no—
78#66901—22no—
79#66901—22no—
80#66901—22no—
81#66901—22no—
82#66900C2×C412yescomplemented
83#66897C2×C412yescomplemented
84C11⋊#95—41no—
85#66889D414yescomplemented
86#66889D414yescomplemented
87#66886—24no—
88#66879—22no—
89C8×Dic11—22no—
90#66869—24no—
91#66869C2×C414yescomplemented
92#66869C2×C414yescomplemented
93C4⋊(C11⋊C8)—41no—
94#22898—111nomaximal, Sylow
95C11×#41—22no—
96C11×#41—22no—
97C11×#41—22no—
98C11×#41—22no—
99C2×Q8×C11C22×C411yescharacteristic
100C2×Q8×C11C22×C411yescharacteristic
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—41no—
104C2×D4×C11C22×C411yescharacteristic
105C2×D4×C11C22×C411yescharacteristic
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—22no—
111C2×C22⋊D11—42no—
112C22×Dic11—22no—
113#4343—24no—
114Q8×D11—24no—
115#4341—24no—
116#4341—44no—
117D4×D11—24no—
118D4×D11—44no—
119#4339—22no—
120#4339—22no—
121#4339—42no—
122#4339—42no—
123#4339—42no—
124#4339C22×C414yes—
125#4339C2×D414yes—
126C2×D44—41no—
127C2×D44#4112yes—
128C2×C4×D11—22no—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×Dic22—41no—
132C2×Dic22#4112yes—
133C11×M16—22no—
134C11×M16—42no—
135C11×M16C2×D414yes—
136C2×C8×C11—22no—
137C2×C8×C11—42no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—41no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11—21no—
144C42×C11—22no—
145C42×C11C22×C411yescharacteristic
146C42×C11C22×C411yescharacteristic
147#4326—24no—
148#4325—24no—
149#4324—24no—
150#4323—24no—
151(C2×D11)⋊C4—42no—
152Dic11⋊C4—42no—
153C4×Dic11—22no—
154C4×Dic11—42no—
155C4×Dic11C2×D412yes—
156C4×Dic11C2×D412yes—
157#4318—22no—
158#4318—22no—
159#4318—22no—
160#4318C22×C414yes—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163#4313—44no—
164C8×D11—44no—
165#3018—111no—
166#2956—112no—
167#2901—112no—
168#1963—111no—
169#1932—112no—
170#1906—112no—
171#1884D1111yescharacteristic, complemented
172#1861—112no—
173#1759—112no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11H(5,𝔽2)11yescharacteristic
177C22×D11—22no—
178C22×D11—42no—
179Q8×C11—22no—
180Q8×C11—22no—
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—42no—
184D4×C11—42no—
185D4×C11—82no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—81no—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C22×D412yes—
198C2×C4×C11C2×#4112yes—
199C2×C4×C11H(5,𝔽2)11yescharacteristic
200C22⋊D11—24no—
201C22⋊D11—24no—
202C22⋊D11—44no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—82no—
208D44—22no—
209D44—42no—
210D44C4×D414yes—
211C4×D11—24no—
212C4×D11—24no—
213C4×D11—44no—
214C4×D11—84no—
215Dic22—22no—
216Dic22—42no—
217Dic22C4×D414yes—
218C8×C11—24no—
219C11⋊C8—24no—
220C11⋊C8—42no—
221#585—111no—
222#575—112no—
223#568—112no—
224#568C2×D1111yescharacteristic, complemented
225#532C2×D1111yescharacteristic
226C4×#41—112no—
227#456—112no—
228#455—112no—
229#454—112no—
230#453—112no—
231#444—224no—
232#443—224no—
233#430—112no—
234#423—111no—
235#421—112no—
236#421—224no—
237#421C2×D1112yes—
238C2×#104—112no—
239C2×#104—112no—
240C2×#104—112no—
241C2×#104—112no—
242C2×#104—224no—
243#413—111no—
244#410C2×D1111yescharacteristic, complemented
245C4×M16—112no—
246#376—111no—
247#344—112no—
248#339—112no—
249#339C2×D1112yescomplemented
250C22×C11—41no—
251C22×C11—41no—
252C22×C11—41no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11#51811yescharacteristic
256C22×C11#54612yes—
257C2×D11—24no—
258C2×D11—82no—
259C2×D11—162no—
260C4×C11—41no—
261C4×C11—41no—
262C4×C11—41no—
263C4×C11—41no—
264C4×C11—82no—
265C4×C11C2×C4×D412yes—
266C4×C11D4211yescharacteristic
267C4×C11#55111yescharacteristic
268Dic11—24no—
269Dic11—42no—
270Dic11—42no—
2712−1+4—112no—
2722−1+4—222no—
273H(5,𝔽2)—112no—
274H(5,𝔽2)—222no—
275H(5,𝔽2)—441no—
276C2×#41—112no—
277C2×#41—224no—
278C2×#41—441no—
279C2×#41C22×D1111yescharacteristic
280C2×#41C22×D1111yescharacteristic
281#137—114no—
282#137—222no—
283AGL(1,ℤ/8)—114no—
284AGL(1,ℤ/8)—222no—
285#135—224no—
286#131—24no—
287#131—224no—
288#131—442no—
289C2×M16—41no—
290C2×M16—112no—
291C2×M16—112no—
292C2×M16—224no—
293C2×M16C22×D1112yes—
294C4⋊Q8C4×D1111yescharacteristic, complemented
295#127C4×D1111yescharacteristic, complemented
296#124C4×D1111yescharacteristic, complemented
297#124C4×D1111yescharacteristic, complemented
298#121—41no—
299C4×Q8—222no—
300C4×D4—41no—
301C4×D4—222no—
302C4×D4—442no—
303#117—222no—
304#117C22×D1112yes—
305C2×C42—112no—
306C2×C42—222no—
307C2×C42C22×D1111yescharacteristic
308#108—224no—
309C4⋊C8—441no—
310#104—24no—
311#104—114no—
312#104—114no—
313#104—114no—
314#104—114no—
315#104—224no—
316#104—222no—
317#104—222no—
318#104—222no—
319#104—222no—
320#101—112no—
321#100—112no—
322#99—41no—
323#97—222no—
324C4×C8—222no—
325#95—441no—
326C2×C11—22no—
327C2×C11—21no—
328C2×C11—81no—
329C2×C11—81no—
330C2×C11#235811yescharacteristic
331D11—44no—
332#41—22no—
333#41—22no—
334#41—22no—
335#41—22no—
336#41—114no—
337#41—114no—
338#41—222no—
339#41—222no—
340#41—224no—
341#41—224no—
342#41—442no—
343#41—442no—
344#41—442no—
345#41—444no—
346C2×Q8—112no—
347C2×Q8—224no—
348C2×Q8—441no—
349C2×Q8C2×C4×D1111yescharacteristic
350C2×Q8C2×C4×D1111yescharacteristic
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—41no—
354C2×D4—112no—
355C2×D4—224no—
356C2×D4—222no—
357C2×D4—441no—
358C2×D4—444no—
359C2×D4—442no—
360C2×D4C2×C4×D1111yescharacteristic
361C2×D4C2×C4×D1111yescharacteristic
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4C23×D1111yescharacteristic
370Q16—224no—
371SD16—224no—
372SD16—224no—
373D8—224no—
374M16—22no—
375M16—42no—
376M16—114no—
377M16—222no—
378M16—222no—
379M16—222no—
380M16—444no—
381M16D4×D1114yes—
382C2×C8—22no—
383C2×C8—42no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—444no—
387C4⋊C4—22no—
388C4⋊C4—41no—
389C4⋊C4—442no—
390C22⋊C4—22no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—442no—
394C42—21no—
395C42—22no—
396C42—112no—
397C42—112no—
398C42—222no—
399C42—442no—
400C42C2×C4×D1111yescharacteristic
401C42C2×C4×D1111yescharacteristic
402C11#2289811yescharacteristic, complemented, Sylow
403C23—21no—
404C23—21no—
405C23—222no—
406C23—442no—
407C23#6703711yescharacteristic
408Q8—22no—
409Q8—22no—
410Q8—114no—
411Q8—222no—
412Q8—442no—
413D4—22no—
414D4—22no—
415D4—42no—
416D4—42no—
417D4—82no—
418D4—114no—
419D4—224no—
420D4—224no—
421D4—222no—
422D4—442no—
423D4—444no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—81no—
434C2×C4—222no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—444no—
440C2×C4—442no—
441C2×C4—884no—
442C2×C4—882no—
443C2×C4C22×C4×D1111yescharacteristic
444C2×C4C2×D4×D1112yes—
445C2×C4#6703711yescharacteristic
446C2×C4#41×D1112yes—
447C8—24no—
448C8—224no—
449C8—442no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22—81no—
455C22—224no—
456C22—882no—
457C22—1762no—
458C22#1062301711yescharacteristic
459C22#1062314312yes—
460C4—41no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—82no—
465C4—224no—
466C4—442no—
467C4—442no—
468C4C4×D4×D1112yes—
469C4#1062312111yescharacteristic
470C4#1062319011yescharacteristic
471C2—21no—
472C2—22no—
473C2—81no—
474C2—81no—
475C2—444no—
476C2#1307159911yescharacteristic
subgroupG/H
centerC4#10623121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1884C2
socleC2×C11#2358
prime radical#13077964C2
cosocleC22×C4×C11C24
hypercenter#1884D11
hypocenterC11#22898
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1884

Complements

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

NH ≅ G/Ntype
2. #13077523C2semidirect
3. #13077162C2semidirect
4. #13069449C2semidirect
5. #13069288C2semidirect
6. #13069114C2semidirect
7. #13068857C2semidirect
8. #13068425C2semidirect
9. C11×#1884C2semidirect
11. C11×#568C22semidirect
17. C11×#410C22semidirect
20. C2×#66901C22semidirect
24. #10622737C22semidirect
25. M16×Dic11C22semidirect
26. #10622708C4semidirect
27. #10622690C4semidirect
28. #10622675C4semidirect
29. #10622674C4semidirect
31. #10622545C22semidirect
33. #10622537C22semidirect
36. C11×#339C22semidirect
37. #10622171C22semidirect
38. #10622170C22semidirect
52. C11×C4⋊Q8C2×C4semidirect
53. C11×#127C2×C4semidirect
54. C11×#124C2×C4semidirect
55. C11×#124C2×C4semidirect
63. #66995C2×C4semidirect
64. #66985C2×C4semidirect
82. #66900C2×C4semidirect
83. #66897C2×C4semidirect
85. #66889D4semidirect
86. #66889D4semidirect
91. #66869C2×C4semidirect
92. #66869C2×C4semidirect
171. #1884D11semidirect
224. #568C2×D11semidirect
244. #410C2×D11semidirect
249. #339C2×D11semidirect
294. C4⋊Q8C4×D11semidirect
295. #127C4×D11semidirect
296. #124C4×D11semidirect
297. #124C4×D11semidirect
402. C11#22898semidirect

Maximal subgroups

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

subgroupindex
#130779642
#130775232
#130771622
#130694492
#130692882
#130691142
#130688572
#130684252
C11×#18842
#2289811