Finite Group Databasebeta

← #14807991

Subgroups — #14807991

Order 2816.

1020 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079009C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13076993C211yesmaximal, characteristic, complemented
4#13069842C214yesmaximal, complemented
5#13069606C211yesmaximal, characteristic, complemented
6#13069445C211yesmaximal, characteristic, complemented
7#13068849C214yesmaximal, complemented
8C4×#66901C211yesmaximal, characteristic, complemented
9C11×#3511C211yesmaximal, characteristic
10C11×#556—21no—
11C11×#555—21no—
12C11×#554—21no—
13C11×#553—22no—
14C11×#548—22no—
15C11×#547—21no—
16C11×#542—22no—
17C11×#537C2212yes—
18C11×#533—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520C2212yes—
23C4×C11×#41C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×#66901C2212yes—
26C2×#66901C2214yes—
27#10622845C2212yes—
28#10622845C2214yes—
29#10622843—22no—
30#10622694—21no—
31#10622683—21no—
32#10622668—22no—
33#10622634—21no—
34#10622633—21no—
35#10622621—21no—
36#10622620—21no—
37#10622608C2212yes—
38#10622590C2214yes—
39#10622587—22no—
40C42×Dic11C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622170C2212yes—
44#10622168C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41C2311yescharacteristic
47C2×C11×#41C2312yes—
48C22×Q8×C11D412yes—
49C22×Dic22—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8D411yescharacteristic
55C11×#127D411yescharacteristic
56C11×#126—24no—
57C11×#125—22no—
58C11×#124—22no—
59C11×#124—24no—
60C11×#124D412yes—
61C11×#123—24no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—21no—
70C11×#121—21no—
71C11×#121—24no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11D411yescharacteristic
75C4×Q8×C11D411yescharacteristic
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—24no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11D411yescharacteristic
84C4×D4×C11D411yescharacteristic
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—21no—
88C11×#117C2311yescharacteristic
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4D412yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2312yes—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2312yes—
99C2×#4318C2312yes—
100C2×#4318C2312yes—
101#66922—21no—
102#66922—21no—
103#66922—21no—
104#66922—21no—
105#66901—24no—
106#66901—28no—
107#66899—22no—
108#66899—24no—
109#66896—22no—
110#66896—24no—
111C11⋊#95—28no—
112#66872—22no—
113#66871—22no—
114C4⋊(C11⋊C8)—21no—
115C4⋊(C11⋊C8)—21no—
116#66867—21no—
117C4×C11⋊C8—21no—
118#25667—111nomaximal, Sylow
119C11×#41—24no—
120C11×#41—22no—
121C11×#41—24no—
122C11×#41—22no—
123C11×#41—84no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—44no—
127C2×Q8×C11C2×D412yes—
128C2×Q8×C11C2×D411yescharacteristic
129C2×D4×C11—21no—
130C2×D4×C11—22no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11C2×D412yes—
135C2×D4×C11C2×D411yescharacteristic
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—22no—
146C22×Dic11—22no—
147C2×Dic22—44no—
148C2×Dic22—41no—
149C2×Dic22—41no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C2×D411yescharacteristic
161C11×C4⋊C4C2×D411yescharacteristic
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—21no—
166C11×C22⋊C4—21no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C42×C11—24no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—41no—
181C4⋊Dic11—41no—
182C4×Dic11—22no—
183C4×Dic11—42no—
184C4×Dic11—42no—
185C4×Dic11#4114yescomplemented
186#4318—24no—
187#4318—22no—
188#4318—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191#3511D1111yescharacteristic
192#3141—111no—
193#3079—111no—
194#2862—111no—
195#2040—114no—
196#1997—111no—
197#1962—111no—
198#1860—114no—
199C4×#104—111no—
200C23×C11—21no—
201C23×C11—22no—
202C23×C11C22×D411yescharacteristic
203Q8×C11—21no—
204Q8×C11—21no—
205Q8×C11—24no—
206Q8×C11—44no—
207Q8×C11—82no—
208D4×C11—21no—
209D4×C11—21no—
210D4×C11—24no—
211D4×C11—44no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—84no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—24no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—44no—
229C2×C4×C11—84no—
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4112yes—
237C2×C4×C112−1+412yes—
238C2×Dic11—24no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—44no—
242C2×Dic11—42no—
243Dic22—82no—
244Dic22—82no—
245C11⋊C8—42no—
246C11⋊C8—42no—
247#556—21no—
248#555—21no—
249#554—21no—
250#553—22no—
251#548—22no—
252#547—21no—
253#542—22no—
254#537C2×D1112yes—
255#533—21no—
256#532—21no—
257#532C2×D1111yescharacteristic
258C2×C4⋊Q8—111no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260#520C2×D1112yes—
261C4×#41C2×D1111yescharacteristic
262#489—222no—
263#487—221no—
264#486—221no—
265#477—221no—
266#476—221no—
267#475—221no—
268#474—221no—
269#428—112no—
270#423—111no—
271C2×#104—114no—
272C2×#104—112no—
273#417—112no—
274#417—114no—
275C4×M16—111no—
276#391—222no—
277#391—222no—
278#382—114no—
279C43—111no—
280#343—114no—
281#339—112no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—42no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—42no—
288C22×C11—41no—
289C22×C11—42no—
290C22×C11C2×#12011yescharacteristic
291C22×C11#54812yes—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11—41no—
296C4×C11—41no—
297C4×C11—44no—
298C4×C11—41no—
299C4×C11#45412yes—
300C4×C11#45512yes—
301C4×C11#53211yescharacteristic
302C4×C11#53611yescharacteristic
303C4×C11#54712yes—
304Dic11—44no—
305Dic11—82no—
306C2×#41—22no—
307C2×#41C22×D1111yescharacteristic
308C2×#41C22×D1112yes—
309C22×Q8—221no—
310C22×Q8C22⋊D1112yes—
311C2×M16—112no—
312C2×M16—112no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—221no—
318C4⋊Q8—221no—
319C4⋊Q8—221no—
320C4⋊Q8—221no—
321C4⋊Q8C22⋊D1111yescharacteristic
322#127C22⋊D1111yescharacteristic
323#126—24no—
324#125—22no—
325#124—22no—
326#124—24no—
327#124C22⋊D1112yes—
328#123—24no—
329C22⋊Q8—22no—
330C22⋊Q8—24no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333#121—22no—
334#121—22no—
335#121—22no—
336#121—21no—
337#121—21no—
338#121—24no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8C22⋊D1111yescharacteristic
342C4×Q8C22⋊D1111yescharacteristic
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—24no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4C22⋊D1111yescharacteristic
351C4×D4C22⋊D1111yescharacteristic
352#117—22no—
353#117—22no—
354#117—21no—
355#117C22×D1111yescharacteristic
356C2×C4⋊C4—22no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22⋊D1112yes—
360C2×C4⋊C4C22×D1112yes—
361C2×C42—21no—
362C2×C42—112no—
363C2×C42—221no—
364C2×C42—221no—
365C2×C42C22×D1111yescharacteristic
366#107—222no—
367#106—222no—
368C4⋊C8—221no—
369C4⋊C8—221no—
370#104—228no—
371#104—224no—
372#103—222no—
373#103—224no—
374#102—222no—
375#102—224no—
376#97—221no—
377C4×C8—221no—
378#95—228no—
379C2×C11—22no—
380C2×C11—81no—
381C2×C11—82no—
382C2×C11#243211yescharacteristic
383C2×C11C2×#45511yescharacteristic
384C2×C11C2×#45411yescharacteristic
385#41—22no—
386#41—24no—
387#41—22no—
388#41—24no—
389#41—84no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—44no—
393C2×Q8—444no—
394C2×Q8—441no—
395C2×Q8—441no—
396C2×Q8C2×C22⋊D1112yes—
397C2×Q8C2×C22⋊D1111yescharacteristic
398C2×D4—21no—
399C2×D4—22no—
400C2×D4—24no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4C2×C22⋊D1112yes—
404C2×D4C2×C22⋊D1111yescharacteristic
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4C2×C22⋊D1111yescharacteristic
413C22×C4C2×C22⋊D1111yescharacteristic
414C22×C4C2×C22⋊D1114yes—
415C22×C4C23×D1111yescharacteristic
416M16—222no—
417M16—224no—
418M16—222no—
419C2×C8—222no—
420C2×C8—222no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—222no—
432C4⋊C4—222no—
433C4⋊C4—441no—
434C4⋊C4—441no—
435C4⋊C4C2×C22⋊D1111yescharacteristic
436C4⋊C4C2×C22⋊D1111yescharacteristic
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C42—24no—
446C42—21no—
447C42—21no—
448C42—21no—
449C42—114no—
450C42—222no—
451C42—442no—
452C42—442no—
453C42C2×C22⋊D1111yescharacteristic
454C42C2×C22⋊D1111yescharacteristic
455C42C2×C22⋊D1111yescharacteristic
456C42C2×C22⋊D1111yescharacteristic
457C11#2566711yescharacteristic, complemented, Sylow
458C23—21no—
459C23—22no—
460C23C22×C22⋊D1111yescharacteristic
461Q8—24no—
462Q8—21no—
463Q8—21no—
464Q8—44no—
465Q8—82no—
466Q8—882no—
467Q8—882no—
468D4—24no—
469D4—21no—
470D4—21no—
471D4—42no—
472D4—44no—
473D4—42no—
474D4—42no—
475D4—84no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—24no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—44no—
489C2×C4—84no—
490C2×C4—224no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—444no—
494C2×C4—442no—
495C2×C4#6700611yescharacteristic
496C2×C4#6700611yescharacteristic
497C2×C4#6700611yescharacteristic
498C2×C4#6700611yescharacteristic
499C2×C4#41×D1112yes—
500C2×C4#6704312yes—
501C2×C4C22×C22⋊D1111yescharacteristic
502C2×C4C22×C22⋊D1111yescharacteristic
503C8—442no—
504C8—442no—
505C22—21no—
506C22—21no—
507C22—41no—
508C22—42no—
509C22—41no—
510C22—42no—
511C22—41no—
512C22—42no—
513C22#1062336212yes—
514C22C2×#6700611yescharacteristic
515C4—21no—
516C4—21no—
517C4—41no—
518C4—42no—
519C4—41no—
520C4—44no—
521C4—41no—
522C4—444no—
523C4—882no—
524C4#1062285512yes—
525C4#1062285812yes—
526C4#1062335512yes—
527C4#1062335611yescharacteristic
528C4#1062336311yescharacteristic
529C2—22no—
530C2—81no—
531C2—82no—
532C2#1307224011yescharacteristic
533C2C2×#1062285511yescharacteristic
534C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11C2×#120
hypercenter#3511D11
hypocenterC11#25667
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13079009C2semidirect
2. #13078431C2semidirect
3. #13076993C2semidirect
4. #13069842C2semidirect
5. #13069606C2semidirect
6. #13069445C2semidirect
7. #13068849C2semidirect
8. C4×#66901C2semidirect
185. C4×Dic11#41semidirect
457. C11#25667semidirect

Maximal subgroups

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

subgroupindex
#130790092
#130784312
#130769932
#130698422
#130696062
#130694452
#130688492
C4×#669012
C11×#35112
#2566711