Finite Group Databasebeta

← #14731538

Subgroups — #14731538

Order 2816.

946 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#13079958C211yesmaximal, characteristic, complemented
2#13079171C211yesmaximal, characteristic, complemented
3#13078413C211yesmaximal, characteristic, complemented
4#13067886C212yesmaximal, complemented
5#13067809C212yesmaximal, complemented
6#13067788C212yesmaximal, complemented
7#13067743C212yesmaximal, complemented
8#13067293C211yesmaximal, characteristic, complemented
9#13067071C211yesmaximal, characteristic, complemented
10C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3506C211yesmaximal, characteristic
12C11×#559—22no—
13C11×#556C2212yes—
14C11×#555—21no—
15C11×#553—22no—
16C11×#550C2212yes—
17C11×#547—21no—
18C11×#538—22no—
19C11×#535—21no—
20C11×#533C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#525—22no—
23C11×#520—21no—
24C2×C4×D4×C11C2211yescharacteristic
25#10623001C2211yescharacteristic
26#10622828—21no—
27#10622706C2211yescharacteristic, complemented
28#10622704—21no—
29#10622703—21no—
30#10622692C2211yescharacteristic, complemented
31#10622689C2211yescharacteristic, complemented
32#10622683C2211yescharacteristic, complemented
33#10622664—22no—
34#10622654—22no—
35#10622644C2212yescomplemented
36#10622634C2212yescomplemented
37C4×#4324—22no—
38#10622622—22no—
39#10622621C2212yes—
40#10622620C2212yes—
41#10622577—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622185C2212yescomplemented
46#10622182C2212yescomplemented
47Q8⋊(C11⋊C8)C2212yescomplemented
48Q8⋊(C11⋊C8)C2212yescomplemented
49D4⋊(C11⋊C8)C2212yes—
50D4⋊(C11⋊C8)C2212yes—
51C2×C11×#41—22no—
52C2×C11×#41—21no—
53C22×D4×C11D411yescharacteristic
54C23×C4×C11—21no—
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×#127—22no—
59C11×#127C2311yescharacteristic
60C11×#126—24no—
61C11×#125—21no—
62C11×#124—24no—
63C11×#124—22no—
64C11×#124—21no—
65C11×#123—24no—
66C11×#123—24no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8D412yes—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—24no—
73C11×#121—21no—
74C11×#121—22no—
75C11×#121D412yes—
76C11×#120—24no—
77C4×Q8×C11—22no—
78C4×Q8×C11—21no—
79C4×Q8×C11C2312yes—
80C4×D4×C11—24no—
81C4×D4×C11—24no—
82C4×D4×C11—22no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D412yes—
87C4×D4×C11D412yes—
88C4×D4×C11C2312yes—
89C11×#117—22no—
90C11×#117—21no—
91C11×#117—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C42×C11C2311yescharacteristic
96C2×#4326—22no—
97C2×#4324—22no—
98#66979—21no—
99#66977—21no—
100#66977—21no—
101C2×#4318—21no—
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104#66923—21no—
105#66922C2311yescharacteristic
106#66922C2311yescharacteristic
107C4×Dic22—21no—
108C4×Dic22—21no—
109#66899—22no—
110#66896—22no—
111#66896—22no—
112#66896—22no—
113#66874—22no—
114#66874—22no—
115#66872—22no—
116#66872—22no—
117#66871—22no—
118#66871—22no—
119C4⋊(C11⋊C8)—21no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)C2312yes—
122C4⋊(C11⋊C8)C2312yes—
123C4×C11⋊C8—21no—
124C4×C11⋊C8C2311yescharacteristic
125C4×C11⋊C8C2311yescharacteristic
126#18679—111nomaximal, Sylow
127C24×C11—21no—
128C11×#41—42no—
129C11×#41—42no—
130C11×#41—82no—
131C11×#41—82no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11C2×D412yes—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11C2×D412yes—
144C2×D4×C11C2×D412yes—
145C22×C4×C11—24no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—81no—
151C22×C4×C11—81no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C2×Dic22—21no—
156C2×Dic22—21no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4C2×D412yes—
167C11×C4⋊C4C2×D412yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C42×C11—24no—
177C42×C11—22no—
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2411yescharacteristic
182C22⋊Dic11—41no—
183#4326—82no—
184#4324—44no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189Dic11⋊C4—41no—
190Dic11⋊C4—41no—
191C4×Dic11—41no—
192#4318—42no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—42no—
198C2×C11⋊C8—81no—
199#3506D1111yescharacteristic
200#3249—111no—
201#3167—111no—
202#3077—111no—
203#1652—112no—
204#1641—112no—
205#1638—112no—
206#1631—112no—
207#1547—111no—
208#1493—111no—
209C2×D4⋊C8—111no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—42no—
213C23×C11—81no—
214C23×C11—81no—
215C23×C11#12011yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220Q8×C11—81no—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—42no—
224D4×C11—44no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—41no—
229D4×C11—42no—
230D4×C11—84no—
231D4×C11—84no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—44no—
242C2×C4×C11—82no—
243C2×C4×C11—81no—
244C2×C4×C11—84no—
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11#13512yes—
249C2×C4×C11#13712yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×Dic11—41no—
254C2×Dic11—41no—
255Dic22—42no—
256Dic22—41no—
257Dic22—41no—
258C11⋊C8—22no—
259C11⋊C8—41no—
260C11⋊C8—42no—
261C11⋊C8—42no—
262#559—22no—
263#556C2×D1112yes—
264#555—21no—
265#553—22no—
266#550C2×D1112yes—
267#547—21no—
268#538—22no—
269#535—21no—
270#533—111no—
271#533C2×D1111yescharacteristic
272#532C2×D1111yescharacteristic
273#525—22no—
274#520—21no—
275C2×C4×D4C2×D1111yescharacteristic
276#498—111no—
277#492—111no—
278#487—111no—
279#486—111no—
280#478—222no—
281#477—112no—
282#477—221no—
283#476—112no—
284#474—112no—
285#467—222no—
286#465—222no—
287#462—112no—
288#462—221no—
289C4×SD16—222no—
290#428—221no—
291#423—111no—
292C2×C4⋊C8—111no—
293#418—221no—
294C2×C4×C8—111no—
295#332—112no—
296#331—112no—
297Q8⋊C8—112no—
298Q8⋊C8—112no—
299D4⋊C8—112no—
300D4⋊C8—112no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—84no—
310C22×C11#45212yes—
311C22×C11C2×#12011yescharacteristic
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11#45212yes—
320C4×C11C2×#13511yescharacteristic
321C4×C11C2×#13711yescharacteristic
322C4×C11#57611yescharacteristic
323C4×C11#57711yescharacteristic
324Dic11—81no—
325Dic11—81no—
326C2×#41—22no—
327C2×#41—21no—
328C22×D4C22⋊D1111yescharacteristic
329C23×C4—21no—
330C2×Q16—222no—
331C2×SD16—222no—
332C2×M16—221no—
333C22×C8—221no—
334C22×C8—221no—
335C4⋊Q8—111no—
336C4⋊Q8—111no—
337C4⋊Q8C22⋊D1111yescharacteristic
338C4⋊Q8C22⋊D1111yescharacteristic
339C4⋊Q8C22×D1111yescharacteristic
340#127—22no—
341#127C22×D1111yescharacteristic
342#126—24no—
343#125—21no—
344#125—221no—
345#124—24no—
346#124—22no—
347#124—21no—
348#123—24no—
349#123—24no—
350C22⋊Q8—22no—
351C22⋊Q8—21no—
352C22⋊Q8—221no—
353C22⋊Q8—221no—
354C22⋊Q8C22⋊D1112yes—
355#121—22no—
356#121—22no—
357#121—24no—
358#121—21no—
359#121—22no—
360#121C22⋊D1112yes—
361#120—24no—
362C4×Q8—22no—
363C4×Q8—21no—
364C4×Q8—221no—
365C4×Q8—221no—
366C4×Q8C22×D1112yes—
367C4×D4—24no—
368C4×D4—24no—
369C4×D4—22no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4C22⋊D1112yes—
374C4×D4C22⋊D1112yes—
375C4×D4C22×D1112yes—
376#117—22no—
377#117—21no—
378#117—22no—
379#117—221no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4C22⋊D1111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C42C22×D1111yescharacteristic
384#107—222no—
385#107—222no—
386#106—222no—
387#106—222no—
388C4⋊C8—112no—
389C4⋊C8—112no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392#103—222no—
393#103—222no—
394#103—222no—
395#102—222no—
396#102—222no—
397#102—222no—
398C4×C8—111no—
399C4×C8—111no—
400C4×C8—221no—
401C2×C11—22no—
402C2×C11—82no—
403C2×C11—82no—
404C2×C11C2×#45211yescharacteristic
405C2×C11#301211yescharacteristic
406C2×C11#301811yescharacteristic
407C24—21no—
408#41—42no—
409#41—42no—
410#41—82no—
411#41—82no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—221no—
415C2×Q8—221no—
416C2×Q8C2×C22⋊D1112yes—
417C2×D4—22no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4C2×C22⋊D1112yes—
426C2×D4C2×C22⋊D1112yes—
427C22×C4—24no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437Q16—882no—
438SD16—444no—
439M16—442no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—442no—
445C2×C8—881no—
446C4⋊C4—24no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—441no—
459C4⋊C4—441no—
460C4⋊C4C2×C22⋊D1112yes—
461C4⋊C4C2×C22⋊D1112yes—
462C4⋊C4C2×C22⋊D1112yes—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—441no—
472C42—24no—
473C42—22no—
474C42—441no—
475C42C2×C22⋊D1111yescharacteristic
476C42C2×C22⋊D1111yescharacteristic
477C42C2×C22⋊D1111yescharacteristic
478C42C23×D1111yescharacteristic
479C11#1867911yescharacteristic, complemented, Sylow
480C23—22no—
481C23—22no—
482C23—42no—
483C23—81no—
484C23—81no—
485C23#6700611yescharacteristic
486Q8—22no—
487Q8—22no—
488Q8—41no—
489Q8—41no—
490Q8—81no—
491Q8—442no—
492Q8—441no—
493Q8—441no—
494D4—22no—
495D4—22no—
496D4—42no—
497D4—44no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—41no—
502D4—41no—
503D4—84no—
504D4—84no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—81no—
517C2×C4—84no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4#6700312yes—
521C2×C4#6700412yes—
522C2×C4#6700611yescharacteristic
523C2×C4#6700611yescharacteristic
524C2×C4#6700611yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C2×C4C22×C22⋊D1111yescharacteristic
527C2×C4C22×C22⋊D1111yescharacteristic
528C8—222no—
529C8—441no—
530C8—442no—
531C8—442no—
532C22—21no—
533C22—21no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—84no—
541C22#1062285212yes—
542C22C2×#6700611yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—42no—
550C4—881no—
551C4—881no—
552C4#1062285212yes—
553C4C2×#6700311yescharacteristic
554C4C2×#6700411yescharacteristic
555C4#1062336611yescharacteristic
556C4#1062336711yescharacteristic
557C2—22no—
558C2—82no—
559C2—82no—
560C2C2×#1062285211yescharacteristic
561C2#1307792011yescharacteristic
562C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3506C2
socleC22×C11C2×#120
hypercenter#3506D11
hypocenterC11#18679
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13079958C2semidirect
2. #13079171C2semidirect
3. #13078413C2semidirect
4. #13067886C2semidirect
5. #13067809C2semidirect
6. #13067788C2semidirect
7. #13067743C2semidirect
8. #13067293C2semidirect
9. #13067071C2semidirect
10. C2×D4⋊(C11⋊C8)C2semidirect
27. #10622706C22semidirect
30. #10622692C22semidirect
31. #10622689C22semidirect
32. #10622683C22semidirect
35. #10622644C22semidirect
36. #10622634C22semidirect
45. #10622185C22semidirect
46. #10622182C22semidirect
47. Q8⋊(C11⋊C8)C22semidirect
48. Q8⋊(C11⋊C8)C22semidirect
479. C11#18679semidirect

Maximal subgroups

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

subgroupindex
#130799582
#130791712
#130784132
#130678862
#130678092
#130677882
#130677432
#130672932
#130670712
C2×D4⋊(C11⋊C8)2
C11×#35062
#1867911