Finite Group Databasebeta

← #14807435

Subgroups — #14807435

Order 2816.

1116 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622673C211yesmaximal, characteristic, complemented
2C2×#10622706C211yesmaximal, characteristic, complemented
3#13074382C211yesmaximal, characteristic, complemented
4#13069624C212yesmaximal, complemented
5#13069619C212yesmaximal
6#13069590C211yesmaximal, characteristic, complemented
7#13069428C211yesmaximal, characteristic, complemented
8#13068957C212yesmaximal, complemented
9#13068950C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic, complemented
11C2×C11×#542C211yesmaximal, characteristic
12C11×#542—24no—
13C11×#542—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—21no—
16C2×C11×#124—21no—
17C2×C11×#124C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C22×#4326C2212yes—
26C22×#4324C2212yes—
27C2×#66977C2212yes—
28C2×#66922C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66896C2212yes—
31C2×C22⋊(C11⋊C8)C2212yes—
32#10622706—24no—
33#10622673—24no—
34#10622596—21no—
35#10622596—21no—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38#10622566—21no—
39#10622566—21no—
40#10622549C2211yescharacteristic
41#10622542C2212yes—
42C2×#66867C2211yescharacteristic
43C2×C4×C11⋊C8C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C22×Dic22C2312yes—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8D414yes—
56C11×#126—28no—
57C11×#124—28no—
58C11×#124—22no—
59C11×#124D414yes—
60C11×#123—28no—
61C11×C22⋊Q8—28no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×#121—22no—
65C11×#121—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C11×#117—22no—
71C11×#117—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90C2×#4326—24no—
91C2×#4326—24no—
92C2×#4326—42no—
93C2×#4324—24no—
94C2×#4324—24no—
95C2×#4324—42no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2312yes—
99#66977—42no—
100#66977—42no—
101C2×Dic11⋊C4—22no—
102C22×C11⋊C8C2312yes—
103C22×C11⋊C8C2312yes—
104#66922—22no—
105#66922—22no—
106#66899—42no—
107#66896—42no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C22⋊(C11⋊C8)—24no—
113#66874—24no—
114#66874—24no—
115#66867—22no—
116C4×C11⋊C8—22no—
117#25613—111nomaximal, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C2×Q8×C11—24no—
121C2×Q8×C11—21no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—82no—
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—24no—
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—82no—
131C2×D4×C11C2×D412yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—82no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—22no—
148C22×Dic11—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C42×C11—24no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11C2×D412yes—
175C42×C11C2×D412yes—
176C22⋊Dic11—44no—
177#4326—48no—
178#4324—48no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—42no—
182C4⋊Dic11—42no—
183Dic11⋊C4—44no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8#4114yes—
190C2×#542D1111yescharacteristic
191C2×#497—111no—
192C2×#487—111no—
193#2621—111no—
194#2001—112no—
195#2000—112no—
196#1993—111no—
197#1958—111no—
198#1878—112no—
199#1877—112no—
200#1750—111no—
201C23×C11—21no—
202C23×C11—22no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C22×D411yescharacteristic
212Q8×C11—24no—
213Q8×C11—42no—
214Q8×C11—84no—
215D4×C11—24no—
216D4×C11—42no—
217D4×C11—84no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—84no—
237C2×C4×C11#12012yes—
238C2×C4×C11#12012yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4112yes—
242C2×C4×C11H(5,𝔽2)12yes—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249Dic22—42no—
250Dic22—42no—
251Dic22—42no—
252Dic22—42no—
253C11⋊C8—24no—
254C11⋊C8—42no—
255C22×Q16—112no—
256C22×SD16—112no—
257#542—24no—
258#542—24no—
259C2×C4⋊Q8—111no—
260C2×C4⋊Q8C2×D1111yescharacteristic
261C2×#126—21no—
262C2×#124—21no—
263C2×#124C2×D1111yescharacteristic
264C2×#123—21no—
265C2×C22⋊Q8—21no—
266C2×C22⋊Q8—112no—
267C2×C22⋊Q8C2×D1111yescharacteristic
268C2×#121C2×D1111yescharacteristic
269C2×C4×Q8C2×D1111yescharacteristic
270C2×C4×D4C2×D1111yescharacteristic
271C2×#117C2×D1111yescharacteristic
272#497—224no—
273#487—224no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#103—112no—
277C2×#102—112no—
278C2×C22⋊C8—112no—
279C2×#97—111no—
280C2×C4×C8—111no—
281#398—221no—
282#398—221no—
283#397—221no—
284#397—221no—
285#391—112no—
286#382—111no—
287#340—112no—
288#340—112no—
289#336—112no—
290C22×C11—42no—
291C22×C11—41no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—42no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11C2×#12011yescharacteristic
301C22×C11#53211yescharacteristic
302C22×C11#53511yescharacteristic
303C22×C11#57712yes—
304C22×C11#57812yes—
305C4×C11—22no—
306C4×C11—22no—
307C4×C11—41no—
308C4×C11—42no—
309C4×C11—41no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—41no—
313C4×C11#54612yes—
314C4×C11#55012yes—
315Dic11—82no—
316Dic11—82no—
317C22×Q8—21no—
318C22×Q8—112no—
319C22×Q8C22×D1111yescharacteristic
320C22×D4—21no—
321C22×D4C22×D1111yescharacteristic
322C23×C4—21no—
323C23×C4C22×D1111yescharacteristic
324C2×Q16—224no—
325C2×Q16—224no—
326C2×Q16—442no—
327C2×SD16—224no—
328C2×SD16—224no—
329C2×SD16—442no—
330C22×C8—112no—
331C22×C8—112no—
332C4⋊Q8—22no—
333C4⋊Q8—222no—
334C4⋊Q8—222no—
335C4⋊Q8C22⋊D1114yes—
336#126—28no—
337#124—28no—
338#124—22no—
339#124C22⋊D1114yes—
340#123—28no—
341C22⋊Q8—28no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—442no—
345C22⋊Q8—442no—
346#121—22no—
347#121—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×D4—22no—
351C4×D4—22no—
352#117—22no—
353#117—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4C22⋊D1111yescharacteristic
362C2×C4⋊C4C22⋊D1111yescharacteristic
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4C22⋊D1111yescharacteristic
372C2×C22⋊C4C22⋊D1111yescharacteristic
373C2×C42—21no—
374C2×C42C22×D1111yescharacteristic
375C2×C42C22×D1111yescharacteristic
376#103—224no—
377#103—224no—
378#103—442no—
379#102—442no—
380C22⋊C8—224no—
381#97—222no—
382C4×C8—222no—
383#95—221no—
384#95—221no—
385#95—222no—
386#95—222no—
387C2×C11—81no—
388C2×C11—82no—
389C2×C11#243111yescharacteristic
390C2×C11#300911yescharacteristic
391C2×C11#301111yescharacteristic
392C2×C11#317812yes—
393C2×C11#322512yes—
394C24—21no—
395C24C2×C22⋊D1111yescharacteristic
396C2×Q8—24no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—82no—
401C2×Q8—222no—
402C2×Q8—222no—
403C2×Q8—222no—
404C2×Q8—222no—
405C2×Q8—222no—
406C2×Q8—222no—
407C2×Q8C2×C22⋊D1112yes—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—82no—
413C2×D4C2×C22⋊D1112yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—82no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431Q16—448no—
432SD16—448no—
433C2×C8—114no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—222no—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—222no—
447C4⋊C4—222no—
448C4⋊C4—444no—
449C4⋊C4—442no—
450C4⋊C4—442no—
451C4⋊C4C2×C22⋊D1112yes—
452C4⋊C4C2×C22⋊D1112yes—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—444no—
461C42—24no—
462C42—21no—
463C42—21no—
464C42C2×C22⋊D1112yes—
465C42C2×C22⋊D1112yes—
466C11#2561311yescharacteristic, complemented, Sylow
467C23—21no—
468C23—21no—
469C23—22no—
470C23—22no—
471C23—21no—
472C23—22no—
473C23—41no—
474C23—41no—
475C23—42no—
476C23—42no—
477C23C22×C22⋊D1111yescharacteristic
478Q8—24no—
479Q8—42no—
480Q8—84no—
481Q8—442no—
482Q8—442no—
483Q8—442no—
484Q8—442no—
485D4—24no—
486D4—42no—
487D4—84no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—84no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4#6700612yes—
514C2×C4#6700612yes—
515C2×C4#41×D1112yes—
516C2×C4#6704212yes—
517C2×C4C22×C22⋊D1111yescharacteristic
518C2×C4C22×C22⋊D1111yescharacteristic
519C8—224no—
520C8—442no—
521C22—41no—
522C22—42no—
523C22—42no—
524C22—41no—
525C22—41no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—82no—
530C22—82no—
531C22#1062336111yescharacteristic
532C22#1062336311yescharacteristic
533C22#1062336712yes—
534C22#1062336912yes—
535C22C2×#6700611yescharacteristic
536C4—22no—
537C4—22no—
538C4—41no—
539C4—42no—
540C4—41no—
541C4—42no—
542C4—42no—
543C4—41no—
544C4—882no—
545C4—882no—
546C4#1062336012yes—
547C4#1062336512yes—
548C2—81no—
549C2—82no—
550C2#1307223111yescharacteristic
551C2#1307789311yescharacteristic
552C2#1307791111yescharacteristic
553C2#1307927812yes—
554C2#1307971912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#542C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#542D11
hypocenterC11#25613
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#10622673C2semidirect
2. C2×#10622706C2semidirect
3. #13074382C2semidirect
4. #13069624C2semidirect
6. #13069590C2semidirect
7. #13069428C2semidirect
8. #13068957C2semidirect
9. #13068950C2semidirect
10. #13068382C2semidirect
466. C11#25613semidirect

Maximal subgroups

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

subgroupindex
C2×#106226732
C2×#106227062
#130743822
#130696242
#130696192
#130695902
#130694282
#130689572
#130689502
#130683822
C2×C11×#5422
#2561311