Finite Group Databasebeta

← #14736537

Subgroups — #14736537

Order 2816.

844 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079066C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic, complemented
3D4×#4318C211yesmaximal, characteristic, complemented
4#13068093C212yesmaximal, complemented
5#13068079C212yesmaximal, complemented
6#13067969C212yesmaximal, complemented
7#13067955C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067291C211yesmaximal, characteristic, complemented
10#13067284C211yesmaximal, characteristic, complemented
11C2×C11×#459C211yesmaximal, characteristic, complemented
12C22×C11×D8—21no—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66985—21no—
16C2×#66985—21no—
17C22×#4318—21no—
18#10623008C2211yescharacteristic
19C11×#459—21no—
20C11×#459—21no—
21C11×#459C2212yes—
22C11×#459C2212yes—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102—21no—
25#10622830—21no—
26#10622820—21no—
27#10622689C2212yescomplemented
28#10622687—22no—
29#10622686C2212yescomplemented
30#10622628C2211yescharacteristic, complemented
31#10622628C2211yescharacteristic, complemented
32C4×#4323—21no—
33C4×#4323—21no—
34#10622625C2212yescomplemented
35#10622624—22no—
36D4×C11⋊C8C2212yescomplemented
37#10622620C2211yescharacteristic, complemented
38#10622620C2211yescharacteristic, complemented
39#10622580—21no—
40#10622538C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622182C2212yescomplemented
44#10622182C2212yescomplemented
45#10622124C2212yescomplemented
46#10622123C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C2×#4339—21no—
55C2×C11×D8—22no—
56C2×C11×D8—22no—
57C2×C11×D8—44no—
58C22×C8×C11—21no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127—21no—
62C11×#127C2312yes—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11D411yescharacteristic
66C4×D4×C11D411yescharacteristic
67C4×D4×C11C2311yescharacteristic
68C4×D4×C11C2311yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4324—22no—
73C2×#4324—22no—
74#66985—44no—
75#66985—44no—
76C2×#4323—21no—
77C2×#4323—21no—
78C2×#4323—22no—
79C2×#4323—22no—
80#66983—21no—
81#66983—21no—
82C2×#4318—21no—
83C2×#4318—22no—
84C2×#4318—44no—
85C2×#4318D411yescharacteristic
86C2×#4318D411yescharacteristic
87C22×C11⋊C8—22no—
88#66928—21no—
89#66927C2311yescharacteristic
90C4×D44—21no—
91C4×D44—21no—
92#66922C2311yescharacteristic
93C11×C4⋊C8—21no—
94C11×C4⋊C8C2312yes—
95C11×#102—22no—
96C11×#102—22no—
97#66896—21no—
98#66896—21no—
99C22⋊(C11⋊C8)—21no—
100C22⋊(C11⋊C8)—22no—
101C22⋊(C11⋊C8)—22no—
102#66873—21no—
103#66873—21no—
104#66871—21no—
105#66871—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2311yescharacteristic
110#66867D412yes—
111C4×C11⋊C8—21no—
112C4×C11⋊C8C2312yes—
113#19162—111nomaximal, Sylow
114C24×C11—21no—
115C24×C11—41no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—41no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—82no—
130C2×D4×C11C2×D411yescharacteristic
131C2×D4×C11C2×D411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11#4111yescharacteristic
142C2×C22⋊D11—41no—
143#4339—42no—
144#4339—42no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×C4×D11—41no—
149C2×Dic22—21no—
150C11×D8—44no—
151C11×D8—44no—
152C2×C8×C11—22no—
153C2×C8×C11—42no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C2×D411yescharacteristic
156C11×C4⋊C4C2×D411yescharacteristic
157C11×C22⋊C4—21no—
158C11×C22⋊C4—21no—
159C11×C22⋊C4—21no—
160C11×C22⋊C4—21no—
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11#4111yescharacteristic
164C42×C11C2411yescharacteristic
165#4324—44no—
166#4324—44no—
167#4323—42no—
168#4323—44no—
169#4323—44no—
170#4323—42no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175#4318—22no—
176#4318—44no—
177#4318—42no—
178#4318D814yescomplemented
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—44no—
183C2×C11⋊C8C2×D412yes—
184C2×C11⋊C8C2×D412yes—
185#3151—111no—
186#3100—111no—
187C2×#459D1111yescharacteristic, complemented
188D4×M16—111no—
189#1687—112no—
190#1685—112no—
191#1667—112no—
192#1665—112no—
193#1565—111no—
194#1547—111no—
195#1545—111no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—81no—
202C23×C11—82no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11#12111yescharacteristic
206C22×D11—41no—
207D4×C11—21no—
208D4×C11—21no—
209D4×C11—21no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—82no—
216D4×C11—82no—
217D4×C11—82no—
218D4×C11—82no—
219D4×C11AGL(1,ℤ/8)12yescomplemented
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11#12111yescharacteristic
233C2×C4×C11#12111yescharacteristic
234C2×C4×C11#12111yescharacteristic
235C2×C4×C11C2×D812yes—
236C2×C4×C11AGL(1,ℤ/8)12yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C22⋊D11—82no—
241C2×Dic11—41no—
242D44—41no—
243D44—41no—
244D44—41no—
245D44—41no—
246D44—81no—
247C4×D11—82no—
248Dic22—41no—
249Dic22—41no—
250C8×C11—42no—
251C11⋊C8—22no—
252C11⋊C8—42no—
253C11⋊C8—41no—
254C11⋊C8—41no—
255C11⋊C8C2×D814yescomplemented
256C2×AGL(1,ℤ/8)—221no—
257C2×AGL(1,ℤ/8)—221no—
258C22×D8—21no—
259C22×M16—221no—
260#532—111no—
261C2×#127C2×D1111yescharacteristic
262C2×C4×D4C2×D1111yescharacteristic
263#496—222no—
264#493—112no—
265#492—112no—
266#480—221no—
267#474—111no—
268#474—111no—
269#459—21no—
270#459—21no—
271#459—111no—
272#459—111no—
273#459C2×D1112yes—
274#459C2×D1112yes—
275#447—221no—
276C4×D8—221no—
277C4×D8—221no—
278#436—112no—
279#435—222no—
280C8×D4—112no—
281#431—111no—
282#423—111no—
283C2×C4⋊C8C2×D1111yescharacteristic
284C2×#102—21no—
285#407—221no—
286C4×M16—111no—
287#335—112no—
288#334—112no—
289#332—112no—
290#331—112no—
291#331—112no—
292#331—112no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—22no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—84no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—164no—
306C22×C11#45912yes—
307C22×C11C2×#12111yescharacteristic
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—41no—
315C4×C11—41no—
316C4×C11#45912yes—
317C4×C11C22×D811yescharacteristic
318C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
319C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
320C4×C11#57511yescharacteristic
321Dic11—81no—
322C2×#41—221no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C22⋊D1111yescharacteristic
327C23×C4—21no—
328AGL(1,ℤ/8)—444no—
329AGL(1,ℤ/8)—444no—
330C2×SD16—222no—
331C2×SD16—222no—
332C2×D8—22no—
333C2×D8—22no—
334C2×D8—44no—
335C2×D8—222no—
336C2×D8—222no—
337C2×D8—221no—
338C2×D8—221no—
339C2×M16—111no—
340C2×M16—111no—
341C2×M16—222no—
342C2×M16—221no—
343C2×M16—444no—
344C22×C8—21no—
345C22×C8—222no—
346C4⋊Q8—111no—
347#127—21no—
348#127—21no—
349#127—21no—
350#127—111no—
351#127C22×D1112yes—
352#124—221no—
353#121—221no—
354#121—221no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—221no—
358C4×D4—221no—
359C4×D4C22⋊D1111yescharacteristic
360C4×D4C22⋊D1111yescharacteristic
361C4×D4C22×D1111yescharacteristic
362C4×D4C22×D1111yescharacteristic
363C2×C4⋊C4C22⋊D1111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C42C22×D1111yescharacteristic
366#107—221no—
367#107—221no—
368C4⋊C8—21no—
369C4⋊C8—112no—
370C4⋊C8—111no—
371C4⋊C8—111no—
372C4⋊C8—221no—
373C4⋊C8C22×D1112yes—
374#102—22no—
375#102—22no—
376#102—221no—
377#102—221no—
378#102—221no—
379#102—221no—
380C22⋊C8—222no—
381C22⋊C8—222no—
382C22⋊C8—221no—
383#97—112no—
384C4×C8—112no—
385C4×C8—221no—
386C2×C11—22no—
387C2×C11—42no—
388C2×C11—81no—
389C2×C11—162no—
390C2×C11C2×#45911yescharacteristic
391C2×C11#305511yescharacteristic
392C2×C11#306811yescharacteristic
393D11—161no—
394C24—21no—
395C24—41no—
396#41—442no—
397#41—442no—
398C2×Q8—221no—
399C2×D4—22no—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—41no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—82no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—441no—
417C2×D4C2×C22⋊D1111yescharacteristic
418C2×D4C2×C22⋊D1111yescharacteristic
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—441no—
427C22×C4D4×D1111yescharacteristic
428C22×C4#434111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430SD16—444no—
431SD16—444no—
432D8—44no—
433D8—44no—
434D8—444no—
435D8—444no—
436D8—442no—
437D8—442no—
438M16—114no—
439M16—222no—
440M16—444no—
441M16—442no—
442C2×C8—22no—
443C2×C8—42no—
444C2×C8—112no—
445C2×C8—112no—
446C2×C8—222no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—444no—
450C4⋊C4—21no—
451C4⋊C4—221no—
452C4⋊C4—221no—
453C4⋊C4C2×C22⋊D1111yescharacteristic
454C4⋊C4C2×C22⋊D1111yescharacteristic
455C22⋊C4—21no—
456C22⋊C4—21no—
457C22⋊C4—21no—
458C22⋊C4—21no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C42D4×D1111yescharacteristic
462C42#434111yescharacteristic
463C42C2×C22⋊D1111yescharacteristic
464C42C23×D1111yescharacteristic
465C11#1916211yescharacteristic, complemented, Sylow
466C23—21no—
467C23—21no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—81no—
472C23—82no—
473C23—82no—
474C23—82no—
475C23—441no—
476C23#6699211yescharacteristic
477Q8—441no—
478Q8—441no—
479D4—21no—
480D4—21no—
481D4—21no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—82no—
488D4—82no—
489D4—82no—
490D4—82no—
491D4—441no—
492D4—441no—
493D4—441no—
494D4—441no—
495D4—881no—
496D4—882no—
497D4#6698512yescomplemented
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—441no—
511C2×C4—882no—
512C2×C4D8×D1112yes—
513C2×C4#6696412yes—
514C2×C4#6699211yescharacteristic
515C2×C4#6699211yescharacteristic
516C2×C4#6699211yescharacteristic
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4C2×#434111yescharacteristic
519C2×C4C22×C22⋊D1111yescharacteristic
520C8—42no—
521C8—114no—
522C8—222no—
523C8—442no—
524C8—441no—
525C8—441no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—84no—
535C22—82no—
536C22—82no—
537C22—82no—
538C22—164no—
539C22—881no—
540C22—881no—
541C22—881no—
542C22#1062276312yes—
543C22C2×#6699211yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—881no—
550C4#1062276312yes—
551C4C2×D8×D1111yescharacteristic
552C4C2×#6696411yescharacteristic
553C4C2×#6698511yescharacteristic
554C4#1062335311yescharacteristic
555C2—22no—
556C2—42no—
557C2—81no—
558C2—162no—
559C2—1761no—
560C2C2×#1062276311yescharacteristic
561C2#1307823111yescharacteristic
562C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#459C2
socleC22×C11C2×#121
hypercenterC2×#459D11
hypocenterC11#19162
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #13079066C2semidirect
2. #13078616C2semidirect
3. D4×#4318C2semidirect
4. #13068093C2semidirect
5. #13068079C2semidirect
6. #13067969C2semidirect
7. #13067955C2semidirect
8. #13067366C2semidirect
9. #13067291C2semidirect
10. #13067284C2semidirect
11. C2×C11×#459C2semidirect
27. #10622689C22semidirect
29. #10622686C22semidirect
30. #10622628C22semidirect
31. #10622628C22semidirect
34. #10622625C22semidirect
36. D4×C11⋊C8C22semidirect
37. #10622620C22semidirect
38. #10622620C22semidirect
43. #10622182C22semidirect
44. #10622182C22semidirect
45. #10622124C22semidirect
46. #10622123C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
178. #4318D8semidirect
187. C2×#459D11semidirect
219. D4×C11AGL(1,ℤ/8)semidirect
255. C11⋊C8C2×D8semidirect
465. C11#19162semidirect
497. D4#66985semidirect

Maximal subgroups

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

subgroupindex
#130790662
#130786162
D4×#43182
#130680932
#130680792
#130679692
#130679552
#130673662
#130672912
#130672842
C2×C11×#4592
#1916211