Finite Group Databasebeta

← #14731368

Subgroups — #14731368

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079958C211yesmaximal, characteristic, complemented
2#13079198C211yesmaximal, characteristic, complemented
3#13078413C211yesmaximal, characteristic
4#13067865C212yesmaximal, complemented
5#13067830C212yesmaximal, complemented
6#13067781C212yesmaximal, complemented
7#13067750C212yesmaximal, complemented
8#13067306C211yesmaximal, characteristic, complemented
9#13067071C211yesmaximal, characteristic, complemented
10C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
11C11×#3501C211yesmaximal, characteristic
12C11×#554—21no—
13C11×#554—22no—
14C11×#554—22no—
15C11×#554C2212yes—
16D4×Q8×C11—21no—
17D4×Q8×C11C2212yes—
18C11×#544—21no—
19C11×#543—22no—
20C11×#533C2211yescharacteristic
21C11×#533C2211yescharacteristic
22C2×C11×C22⋊Q8—22no—
23C11×#518—21no—
24C2×C4×D4×C11C2211yescharacteristic
25#10623001C2211yescharacteristic
26#10622828—21no—
27#10622706C2211yescharacteristic, complemented
28#10622705C2211yescharacteristic, complemented
29#10622704—21no—
30#10622703—21no—
31#10622694C2211yescharacteristic, complemented
32#10622691C2211yescharacteristic, complemented
33#10622664—22no—
34#10622664—22no—
35#10622644C2212yescomplemented
36C4×#4326—22no—
37#10622634C2212yescomplemented
38#10622622—22no—
39#10622621C2212yes—
40#10622620C2212yes—
41#10622577—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622185C2212yescomplemented
46#10622184C2212yescomplemented
47Q8⋊(C11⋊C8)C2212yescomplemented
48Q8⋊(C11⋊C8)C2212yescomplemented
49D4⋊(C11⋊C8)C2212yes—
50D4⋊(C11⋊C8)C2212yes—
51C22×Q8×C11—22no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×#125—22no—
61C11×#125—22no—
62C11×#125—21no—
63C11×#125—21no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8D412yes—
75C11×C22⋊Q8D412yes—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11D412yes—
79C4×Q8×C11C2312yes—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D412yes—
87C4×D4×C11C2312yes—
88C11×#117—21no—
89C11×#117—21no—
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—21no—
95C2×C42×C11C2311yescharacteristic
96C2×#4326—22no—
97C2×#4326—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#66899—22no—
111#66896—22no—
112#66896—22no—
113#66874—22no—
114#66874—22no—
115#66872—22no—
116#66871—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#18665—111nomaximal, Sylow
127C24×C11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—82no—
132C2×Q8×C11—82no—
133C2×Q8×C11C2×D412yes—
134C2×Q8×C11C2×D412yes—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11Q1614yescomplemented
138C2×D4×C11C2×D412yes—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—81no—
145C22×C4×C11—81no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C2×Dic22—21no—
150C2×Dic22—21no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
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—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11C2411yescharacteristic
180C22⋊Dic11—41no—
181#4326—44no—
182#4326—82no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187Dic11⋊C4—41no—
188Dic11⋊C4—41no—
189C4×Dic11—41no—
190#4318—42no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—42no—
196C2×C11⋊C8—81no—
197#3501D1111yescharacteristic
198#3249—111no—
199#3170—111no—
200#3077—111no—
201#1649—112no—
202#1644—112no—
203#1637—112no—
204#1632—112no—
205#1550—111no—
206#1493—111no—
207C2×D4⋊C8—111no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—81no—
211C23×C11—81no—
212C23×C11#12011yescharacteristic
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—42no—
216Q8×C11—41no—
217Q8×C11—41no—
218Q8×C11—81no—
219Q8×C11—84no—
220D4×C11—22no—
221D4×C11—24no—
222D4×C11C2×Q1614yes—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—82no—
234C2×C4×C11—81no—
235C2×C4×C11—84no—
236C2×C4×C11—84no—
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11C2×Q1612yes—
241C2×C4×C11#13712yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×Dic11—41no—
246C2×Dic11—41no—
247Dic22—42no—
248Dic22—41no—
249Dic22—41no—
250C11⋊C8—22no—
251C11⋊C8—41no—
252C11⋊C8—42no—
253C11⋊C8—42no—
254#554—21no—
255#554—22no—
256#554—22no—
257#554C2×D1112yes—
258D4×Q8—21no—
259D4×Q8C2×D1112yes—
260#544—21no—
261#543—22no—
262#533—111no—
263#533C2×D1111yescharacteristic
264#533C2×D1111yescharacteristic
265C2×C22⋊Q8—22no—
266#518—21no—
267C2×C4×D4C2×D1111yescharacteristic
268#500—111no—
269#494—111no—
270#487—111no—
271#487—111no—
272#478—222no—
273#477—112no—
274#477—221no—
275#476—112no—
276#474—112no—
277#467—222no—
278#467—222no—
279#462—112no—
280#462—221no—
281C4×Q16—222no—
282#428—221no—
283#423—111no—
284C2×C4⋊C8—111no—
285#418—221no—
286C2×C4×C8—111no—
287#333—112no—
288#332—112no—
289Q8⋊C8—112no—
290Q8⋊C8—112no—
291D4⋊C8—112no—
292D4⋊C8—112no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—24no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—84no—
299C22×C11#45112yes—
300C22×C11C2×#12011yescharacteristic
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11#45112yes—
310C4×C11C22×Q1611yescharacteristic
311C4×C11C2×#13711yescharacteristic
312C4×C11#57611yescharacteristic
313C4×C11#57711yescharacteristic
314Dic11—81no—
315Dic11—81no—
316C22×Q8—22no—
317C22×D4C22⋊D1111yescharacteristic
318C23×C4—21no—
319C2×Q16—222no—
320C2×Q16—222no—
321C2×M16—221no—
322C22×C8—221no—
323C22×C8—221no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—111no—
327C4⋊Q8—111no—
328C4⋊Q8C22⋊D1111yescharacteristic
329C4⋊Q8C22⋊D1111yescharacteristic
330C4⋊Q8C22×D1111yescharacteristic
331C4⋊Q8C22×D1111yescharacteristic
332#125—22no—
333#125—22no—
334#125—21no—
335#125—21no—
336#125—221no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—22no—
342C22⋊Q8—24no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8—22no—
346C22⋊Q8—24no—
347C22⋊Q8—221no—
348C22⋊Q8—221no—
349C22⋊Q8C22⋊D1112yes—
350C22⋊Q8C22⋊D1112yes—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8—221no—
354C4×Q8—221no—
355C4×Q8C22⋊D1112yes—
356C4×Q8C22×D1112yes—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4C22⋊D1112yes—
364C4×D4C22×D1112yes—
365#117—21no—
366#117—21no—
367#117—221no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4C22⋊D1111yescharacteristic
371C2×C22⋊C4—24no—
372C2×C22⋊C4—21no—
373C2×C42C22×D1111yescharacteristic
374#107—222no—
375#107—222no—
376#107—222no—
377#106—222no—
378C4⋊C8—112no—
379C4⋊C8—112no—
380C4⋊C8—221no—
381C4⋊C8—221no—
382#103—222no—
383#103—222no—
384#103—222no—
385#103—222no—
386#102—222no—
387#102—222no—
388C4×C8—111no—
389C4×C8—111no—
390C4×C8—221no—
391C2×C11—22no—
392C2×C11—44no—
393C2×C11C2×#45111yescharacteristic
394C2×C11#301211yescharacteristic
395C2×C11#301811yescharacteristic
396C24—21no—
397C2×Q8—24no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—82no—
401C2×Q8—82no—
402C2×Q8—221no—
403C2×Q8—221no—
404C2×Q8C2×C22⋊D1112yes—
405C2×Q8C2×C22⋊D1112yes—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4#432614yescomplemented
409C2×D4C2×C22⋊D1112yes—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—81no—
416C22×C4—81no—
417C22×C4C2×C22⋊D1111yescharacteristic
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C2×C22⋊D1111yescharacteristic
420Q16—444no—
421Q16—882no—
422M16—442no—
423C2×C8—221no—
424C2×C8—221no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8—442no—
428C2×C8—881no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—221no—
444C4⋊C4—221no—
445C4⋊C4—221no—
446C4⋊C4—221no—
447C4⋊C4—441no—
448C4⋊C4—441no—
449C4⋊C4C2×C22⋊D1112yes—
450C4⋊C4C2×C22⋊D1112yes—
451C4⋊C4C2×C22⋊D1112yes—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—441no—
459C42—22no—
460C42—22no—
461C42—441no—
462C42C2×C22⋊D1111yescharacteristic
463C42C2×C22⋊D1111yescharacteristic
464C42C2×C22⋊D1111yescharacteristic
465C42C23×D1111yescharacteristic
466C11#1866511yescharacteristic, complemented, Sylow
467C23—22no—
468C23—24no—
469C23—81no—
470C23—81no—
471C23#6700611yescharacteristic
472Q8—22no—
473Q8—22no—
474Q8—42no—
475Q8—41no—
476Q8—41no—
477Q8—81no—
478Q8—84no—
479Q8—442no—
480Q8—441no—
481Q8—441no—
482D4—22no—
483D4—24no—
484D4C2×#432614yes—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—82no—
496C2×C4—81no—
497C2×C4—84no—
498C2×C4—84no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4#6699512yes—
502C2×C4C2×#432612yes—
503C2×C4#6700611yescharacteristic
504C2×C4#6700611yescharacteristic
505C2×C4#6700611yescharacteristic
506C2×C4C22×C22⋊D1111yescharacteristic
507C2×C4C22×C22⋊D1111yescharacteristic
508C2×C4C22×C22⋊D1111yescharacteristic
509C8—222no—
510C8—441no—
511C8—442no—
512C8—442no—
513C22—21no—
514C22—21no—
515C22—24no—
516C22—42no—
517C22—42no—
518C22—84no—
519C22#1062284112yes—
520C22C2×#6700611yescharacteristic
521C4—21no—
522C4—21no—
523C4—21no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—42no—
529C4—881no—
530C4—881no—
531C4#1062284112yes—
532C4C2×#6699511yescharacteristic
533C4C22×#432611yescharacteristic
534C4#1062336611yescharacteristic
535C4#1062336711yescharacteristic
536C2—22no—
537C2—44no—
538C2C2×#1062284111yescharacteristic
539C2#1307792011yescharacteristic
540C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenter#3501D11
hypocenterC11#18665
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13079958C2semidirect
2. #13079198C2semidirect
4. #13067865C2semidirect
5. #13067830C2semidirect
6. #13067781C2semidirect
7. #13067750C2semidirect
8. #13067306C2semidirect
9. #13067071C2semidirect
27. #10622706C22semidirect
28. #10622705C22semidirect
31. #10622694C22semidirect
32. #10622691C22semidirect
35. #10622644C22semidirect
37. #10622634C22semidirect
45. #10622185C22semidirect
46. #10622184C22semidirect
47. Q8⋊(C11⋊C8)C22semidirect
48. Q8⋊(C11⋊C8)C22semidirect
137. C2×D4×C11Q16semidirect
408. C2×D4#4326semidirect
466. C11#18665semidirect

Maximal subgroups

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

subgroupindex
#130799582
#130791982
#130784132
#130678652
#130678302
#130677812
#130677502
#130673062
#130670712
C2×D4⋊(C11⋊C8)2
C11×#35012
#1866511