Finite Group Databasebeta

← #14808209

Subgroups — #14808209

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079163C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13076972C211yesmaximal, characteristic, complemented
4#13069823C214yesmaximal, complemented
5#13069594C211yesmaximal, characteristic, complemented
6#13069457C211yesmaximal, characteristic, complemented
7#13068826C214yesmaximal, complemented
8C4×#66901C211yesmaximal, characteristic, complemented
9C11×#3508C211yesmaximal, characteristic
10C11×#559—21no—
11C11×#559—21no—
12C11×#550—21no—
13C11×#550—21no—
14C11×#546—22no—
15C11×#546—22no—
16C11×#540—22no—
17C11×#535C2212yes—
18C11×#533C2211yescharacteristic
19C11×#532—21no—
20C11×#532—21no—
21C2×C11×#127C2211yescharacteristic
22C11×#518C2212yes—
23C4×C11×#41C2211yescharacteristic
24C2×#66989—22no—
25C2×#66922C2211yescharacteristic
26C2×#66901C2212yes—
27#10622845C2212yes—
28#10622834—22no—
29#10622834C2214yes—
30C2×#66897C2214yes—
31#10622692—21no—
32#10622691—21no—
33#10622678—22no—
34#10622634—21no—
35#10622633—21no—
36#10622621—21no—
37#10622620—21no—
38#10622608C2212yes—
39#10622608C2214yes—
40C42×Dic11C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622170C2212yes—
44#10622170C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41C2311yescharacteristic
48C22×D4×C11D412yes—
49C22×D4×C11D412yes—
50C22×D4×C11C2312yes—
51C22×Dic22—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×#127—22no—
55C11×#127—21no—
56C11×#127—21no—
57C11×#127—21no—
58C11×#127—21no—
59C11×#125D412yes—
60C11×#124—22no—
61C11×#124—22no—
62C11×#124—22no—
63C11×#123—24no—
64C11×#123—24no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—21no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—24no—
70C11×#121—24no—
71C11×#121—22no—
72C11×#121—22no—
73C11×#120—24no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11D411yescharacteristic
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11D411yescharacteristic
87C4×D4×C11D411yescharacteristic
88C11×#117—21no—
89C11×#117C2311yescharacteristic
90C11×#117C2312yes—
91C2×C11×C22⋊C4—24no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11—28no—
95#66989—48no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2312yes—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2312yes—
101C2×#4318C2312yes—
102C2×#4318C2312yes—
103#66922—21no—
104#66922—21no—
105#66922—21no—
106#66922—21no—
107#66901—24no—
108#66899—22no—
109#66897—28no—
110#66896—22no—
111#66872—22no—
112#66872—24no—
113#66871—22no—
114#66871—24no—
115C4⋊(C11⋊C8)—21no—
116C4⋊(C11⋊C8)—21no—
117#66867—21no—
118C4×C11⋊C8—21no—
119#25687—111nomaximal, Sylow
120C24×C11C2×D414yes—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—84no—
124C11×#41—84no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11C2×D411yescharacteristic
128C2×D4×C11—21no—
129C2×D4×C11—24no—
130C2×D4×C11—24no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11C2×D411yescharacteristic
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—22no—
151C22×Dic11—22no—
152C2×Dic22—44no—
153C2×Dic22—41no—
154C2×Dic22—41no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4C2×D411yescharacteristic
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D411yescharacteristic
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—22no—
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C22⋊Dic11—416no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11—41no—
185C4⋊Dic11—41no—
186C4×Dic11—24no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—42no—
190#4318—24no—
191#4318—22no—
192#4318#4114yescomplemented
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195#3508D1111yescharacteristic
196#3165—111no—
197#3079—111no—
198#2858—111no—
199#2037—114no—
200#1994—111no—
201#1965—111no—
202#1856—114no—
203C4×#104—111no—
204C23×C11—24no—
205C23×C11—21no—
206C23×C11—28no—
207C23×C11—44no—
208C23×C11—44no—
209C23×C11C22×D411yescharacteristic
210Q8×C11—21no—
211Q8×C11—21no—
212Q8×C11—42no—
213Q8×C11—42no—
214D4×C11—21no—
215D4×C11—21no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—44no—
220D4×C11—44no—
221D4×C11—44no—
222D4×C11—82no—
223D4×C11—82no—
224D4×C11—84no—
225D4×C11—84no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—84no—
237C2×C4×C11—84no—
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4112yes—
245C2×C4×C112−1+412yes—
246C2×Dic11—24no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—44no—
250C2×Dic11—42no—
251Dic22—82no—
252Dic22—82no—
253C11⋊C8—24no—
254C11⋊C8—42no—
255#559—21no—
256#559—21no—
257#550—21no—
258#550—21no—
259#546—22no—
260#546—22no—
261#540—22no—
262#535C2×D1112yes—
263#533C2×D1111yescharacteristic
264#532—21no—
265#532—21no—
266C2×C4⋊Q8—111no—
267C2×#127C2×D1111yescharacteristic
268C2×#124—222no—
269#518C2×D1112yes—
270C4×#41C2×D1111yescharacteristic
271#501—222no—
272#500—221no—
273#498—221no—
274#477—221no—
275#476—221no—
276#475—221no—
277#474—221no—
278#428—112no—
279#428—114no—
280#423—111no—
281C2×#104—112no—
282#417—112no—
283C2×#100—114no—
284C4×M16—111no—
285#390—114no—
286#390—222no—
287C43—111no—
288#339—112no—
289#339—114no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—41no—
293C22×C11—44no—
294C22×C11—41no—
295C22×C11—44no—
296C22×C11—41no—
297C22×C11—44no—
298C22×C11—88no—
299C22×C11C2×#12011yescharacteristic
300C22×C11#54712yes—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—41no—
304C4×C11—41no—
305C4×C11—42no—
306C4×C11—41no—
307C4×C11—42no—
308C4×C11#45312yes—
309C4×C11#45512yes—
310C4×C11#53211yescharacteristic
311C4×C11#53611yescharacteristic
312C4×C11#54812yes—
313Dic11—44no—
314Dic11—82no—
315C2×#41—22no—
316C2×#41—22no—
317C2×#41C22×D1111yescharacteristic
318C22×Q8—221no—
319C22×D4C22⋊D1112yes—
320C22×D4C22⋊D1112yes—
321C22×D4C22×D1112yes—
322C2×M16—112no—
323C2×M16—112no—
324C4⋊Q8—221no—
325C4⋊Q8—221no—
326C4⋊Q8—221no—
327C4⋊Q8—221no—
328C4⋊Q8C22⋊D1111yescharacteristic
329C4⋊Q8C22⋊D1111yescharacteristic
330#127—22no—
331#127—21no—
332#127—21no—
333#127—21no—
334#127—21no—
335#125C22⋊D1112yes—
336#124—22no—
337#124—22no—
338#124—22no—
339#124—448no—
340#123—24no—
341#123—24no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344#121—22no—
345#121—22no—
346#121—24no—
347#121—24no—
348#121—22no—
349#121—22no—
350#120—24no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8C22⋊D1111yescharacteristic
354C4×Q8C22⋊D1111yescharacteristic
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4C22⋊D1111yescharacteristic
364C4×D4C22⋊D1111yescharacteristic
365#117—21no—
366#117C22×D1111yescharacteristic
367#117C22×D1112yes—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—221no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—228no—
372C2×C42—21no—
373C2×C42—112no—
374C2×C42—221no—
375C2×C42—221no—
376C2×C42C22×D1111yescharacteristic
377#107—222no—
378#107—224no—
379#106—222no—
380#106—224no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383#104—224no—
384#103—222no—
385#102—222no—
386#100—228no—
387#97—221no—
388C4×C8—221no—
389C2×C11—22no—
390C2×C11—81no—
391C2×C11—84no—
392C2×C11#243211yescharacteristic
393C2×C11C2×#45311yescharacteristic
394C2×C11C2×#45511yescharacteristic
395C24C2×C22⋊D1114yes—
396#41—22no—
397#41—22no—
398#41—84no—
399#41—84no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—444no—
403C2×Q8—441no—
404C2×Q8—441no—
405C2×Q8C2×C22⋊D1111yescharacteristic
406C2×D4—21no—
407C2×D4—24no—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4C2×C22⋊D1111yescharacteristic
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C23×D1111yescharacteristic
430M16—114no—
431M16—222no—
432M16—224no—
433C2×C8—222no—
434C2×C8—222no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—222no—
442C4⋊C4—222no—
443C4⋊C4—441no—
444C4⋊C4—441no—
445C4⋊C4C2×C22⋊D1111yescharacteristic
446C4⋊C4C2×C22⋊D1112yes—
447C4⋊C4C2×C22⋊D1111yescharacteristic
448C4⋊C4C2×C22⋊D1112yes—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—21no—
454C22⋊C4—22no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C22⋊C4—4416no—
458C42—21no—
459C42—21no—
460C42—21no—
461C42—22no—
462C42—224no—
463C42—222no—
464C42—222no—
465C42—442no—
466C42C2×C22⋊D1111yescharacteristic
467C42C2×C22⋊D1111yescharacteristic
468C42C2×C22⋊D1111yescharacteristic
469C42C2×C22⋊D1111yescharacteristic
470C11#2568711yescharacteristic, complemented, Sylow
471C23—24no—
472C23—21no—
473C23—28no—
474C23—44no—
475C23—44no—
476C23C22×C22⋊D1111yescharacteristic
477Q8—21no—
478Q8—21no—
479Q8—42no—
480Q8—42no—
481Q8—882no—
482Q8—882no—
483D4—21no—
484D4—21no—
485D4—42no—
486D4—42no—
487D4—44no—
488D4—42no—
489D4—44no—
490D4—44no—
491D4—82no—
492D4—82no—
493D4—84no—
494D4—84no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—84no—
506C2×C4—84no—
507C2×C4—224no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—444no—
511C2×C4—442no—
512C2×C4#6700611yescharacteristic
513C2×C4#6700611yescharacteristic
514C2×C4#6700611yescharacteristic
515C2×C4#6700611yescharacteristic
516C2×C4#41×D1112yes—
517C2×C4#6704312yes—
518C2×C4C22×C22⋊D1111yescharacteristic
519C2×C4C22×C22⋊D1111yescharacteristic
520C8—224no—
521C8—442no—
522C22—21no—
523C22—21no—
524C22—41no—
525C22—44no—
526C22—41no—
527C22—44no—
528C22—41no—
529C22—44no—
530C22—88no—
531C22#1062335512yes—
532C22C2×#6700611yescharacteristic
533C4—21no—
534C4—21no—
535C4—41no—
536C4—41no—
537C4—42no—
538C4—41no—
539C4—42no—
540C4—444no—
541C4—882no—
542C4#1062285412yes—
543C4#1062285512yes—
544C4#1062335611yescharacteristic
545C4#1062336212yes—
546C4#1062336311yescharacteristic
547C2—22no—
548C2—84no—
549C2—81no—
550C2#1307224011yescharacteristic
551C2C2×#1062285411yescharacteristic
552C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3508C2
socleC22×C11C2×#120
hypercenter#3508D11
hypocenterC11#25687
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13079163C2semidirect
2. #13078431C2semidirect
3. #13076972C2semidirect
4. #13069823C2semidirect
5. #13069594C2semidirect
6. #13069457C2semidirect
7. #13068826C2semidirect
8. C4×#66901C2semidirect
192. #4318#41semidirect
470. C11#25687semidirect

Maximal subgroups

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

subgroupindex
#130791632
#130784312
#130769722
#130698232
#130695942
#130694572
#130688262
C4×#669012
C11×#35082
#2568711