Finite Group Databasebeta

← #14788702

Subgroups — #14788702

Order 2816.

1380 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic, complemented
3#13073978C211yesmaximal, characteristic, complemented
4#13069848C212yesmaximal, complemented
5#13069702C212yesmaximal, complemented
6#13069556C211yesmaximal, characteristic, complemented
7#13069440C211yesmaximal, characteristic, complemented
8#13068947C212yesmaximal, complemented
9#13068860C212yesmaximal, complemented
10#13068626C211yesmaximal, characteristic, complemented
11C2×C11×#440C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C22×C11×SD16C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4325C2212yes—
17C2×#66993C2212yes—
18C2×#66983—21no—
19#10623084—24no—
20#10623084—24no—
21C2×#66946C2212yes—
22C2×#66937—22no—
23C2×#66927C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#440—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30#10622843C2212yes—
31C2×#66896C2212yes—
32C2×#66885C2212yes—
33C2×#66885C2212yes—
34#10622640—24no—
35#10622599—21no—
36#10622592—21no—
37#10622586C2212yes—
38C2×#66873C2212yes—
39#10622549C2211yescharacteristic
40#10622546—22no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C2×#4339—28no—
51C2×#4339—48no—
52C22×D44—21no—
53C22×D44—21no—
54C22×D44C2312yes—
55C22×C4×D11—22no—
56C22×Dic22D411yescharacteristic
57C2×C11×SD16—22no—
58C2×C11×SD16—22no—
59C2×C11×SD16—22no—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11D414yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4325—24no—
73C2×#4325—24no—
74C2×#4325—42no—
75#66993—24no—
76#66993—24no—
77#66983—28no—
78C2×(C2×D11)⋊C4—22no—
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11C2312yes—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4D412yes—
83C2×C4×Dic11C2312yes—
84C22×C11⋊C8C2312yes—
85#66946—24no—
86#66946—24no—
87#66937—216no—
88#66927—22no—
89#66927D414yes—
90C4×Dic22—22no—
91C4×Dic22—22no—
92C11×#107—22no—
93C11×#103—22no—
94C11×#102—22no—
95C11×#97—22no—
96#66896—42no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102#66885—24no—
103#66885—42no—
104#66873—24no—
105C4⋊(C11⋊C8)—22no—
106#24200—111nomaximal, Sylow
107C24×C11—21no—
108C23×D11—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11#4112yescomplemented
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11C2×D412yes—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—24no—
124C22×C4×C11—21no—
125C22×C4×C11—44no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—28no—
130C2×C22⋊D11—28no—
131C2×C22⋊D11—44no—
132C2×C22⋊D11—44no—
133C2×C22⋊D11—82no—
134C2×C22⋊D11—82no—
135C22×Dic11—22no—
136C22×Dic11C2×D412yes—
137C22×Dic11C2×D412yes—
138#4339—432no—
139C2×D44—24no—
140C2×D44—24no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—44no—
147C2×D44—82no—
148C2×D44C2×D414yes—
149C2×C4×D11—28no—
150C2×C4×D11—44no—
151C2×C4×D11—44no—
152C2×Dic22—24no—
153C2×Dic22—22no—
154C11×SD16—28no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11#4112yescomplemented
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C2×D412yes—
166C11×C22⋊C4—24no—
167C42×C11—42no—
168C42×C11C2×D412yes—
169C42×C11C2×D412yes—
170#4325—48no—
171(C2×D11)⋊C4—28no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175Dic11⋊C4—24no—
176Dic11⋊C4—44no—
177C4×Dic11—22no—
178C4×Dic11—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×#550—111no—
183C2×#460—111no—
184C2×#440D1111yescharacteristic, complemented
185#2581—111no—
186#2041—112no—
187#2014—112no—
188#1985—111no—
189#1961—111no—
190#1877—112no—
191#1862—112no—
192#1804—111no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11C22×D411yescharacteristic
199C22×D11—24no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—41no—
209Q8×C11—41no—
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—41no—
213D4×C11—41no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—48no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11#12012yes—
225C2×C4×C11#12012yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11H(5,𝔽2)11yescharacteristic
231C2×C4×C112−1+411yescharacteristic
232C22⋊D11—416no—
233C22⋊D11—88no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11AGL(1,ℤ/8)14yes—
243D44—24no—
244D44—24no—
245D44—48no—
246D44—42no—
247D44—42no—
248D44—84no—
249C4×D11—416no—
250Dic22—28no—
251C8×C11—22no—
252C8×C11—41no—
253C11⋊C8—42no—
254C22×#41—221no—
255C22×SD16—112no—
256C22×SD16C2×D1111yescharacteristic
257#550—224no—
258#550—224no—
259C2×#127—112no—
260C2×#127—111no—
261C2×#121—222no—
262C2×#121—221no—
263C2×C4×Q8—111no—
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×D4—112no—
266C2×C4×D4C2×D1111yescharacteristic
267#460—224no—
268#440—24no—
269C2×#107C2×D1111yescharacteristic
270C2×C4⋊C8—111no—
271C2×#103C2×D1111yescharacteristic
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—112no—
275C2×#102—112no—
276C2×#102C2×D1111yescharacteristic
277C2×#97C2×D1111yescharacteristic
278#400—221no—
279#395—221no—
280#391—112no—
281#389—112no—
282#387—222no—
283#382—111no—
284#340—112no—
285#336—112no—
286#336—112no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—82no—
291C22×C11—82no—
292C22×C11C2×#12011yescharacteristic
293C22×C11#54811yescharacteristic
294C22×C11#55011yescharacteristic
295C22×C11C2×AGL(1,ℤ/8)12yes—
296C22×C11#57712yes—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—82no—
301C2×D11—82no—
302C2×D11—82no—
303C2×D11—82no—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—81no—
309C4×C11#52511yescharacteristic
310C4×C11#53711yescharacteristic
311C4×C11#54611yescharacteristic
312C4×C11#54711yescharacteristic
313Dic11—24no—
314Dic11—42no—
315Dic11—82no—
316C2×#41—228no—
317C2×#41—448no—
318C22×Q8—111no—
319C22×Q8C22×D1111yescharacteristic
320C22×D4—112no—
321C22×D4—222no—
322C22×D4—222no—
323C22×D4—221no—
324C22×D4—221no—
325C22×D4C22×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—222no—
328C2×SD16—22no—
329C2×SD16—22no—
330C2×SD16—22no—
331C2×SD16—224no—
332C2×SD16—224no—
333C2×SD16—442no—
334C22×C8—112no—
335C22×C8C22×D1111yescharacteristic
336C22×C8C22×D1111yescharacteristic
337#127—114no—
338#127—224no—
339#127—224no—
340#127—222no—
341#121—2216no—
342#121—228no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—222no—
346C4×Q8—222no—
347C4×D4—22no—
348C4×D4—224no—
349C4×D4—224no—
350C4×D4C22⋊D1114yes—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4C22×D1111yescharacteristic
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—222no—
360C2×C42—21no—
361C2×C42—112no—
362C2×C42C22×D1111yescharacteristic
363#107—22no—
364C4⋊C8—222no—
365#103—22no—
366#102—22no—
367#102—224no—
368#102—224no—
369#102—442no—
370#102—442no—
371#97—22no—
372#95—222no—
373#95—222no—
374#95—222no—
375#95—221no—
376#95—221no—
377C2×C11—82no—
378C2×C11#240711yescharacteristic
379C2×C11#300311yescharacteristic
380C2×C11#300911yescharacteristic
381C2×C11#336812yes—
382C2×C11#339712yes—
383D11—84no—
384C24—21no—
385C24—222no—
386#41—4432no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—224no—
393C2×Q8—222no—
394C2×Q8#433912yescomplemented
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—114no—
401C2×D4—228no—
402C2×D4—228no—
403C2×D4—224no—
404C2×D4—224no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—444no—
411C2×D4—444no—
412C2×D4—444no—
413C2×D4—882no—
414C2×D4—882no—
415C2×D4—882no—
416C2×D4C2×C22⋊D1112yes—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—44no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—228no—
425C22×C4—222no—
426C22×C4—444no—
427C22×C4—444no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431SD16—28no—
432SD16—448no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8#433912yescomplemented
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—42no—
446C4⋊C4—224no—
447C4⋊C4—222no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—444no—
451C4⋊C4C2×C22⋊D1112yes—
452C22⋊C4—24no—
453C22⋊C4—228no—
454C42—42no—
455C42—222no—
456C42—222no—
457C42D4×D1112yes—
458C42C2×C22⋊D1112yes—
459C11#2420011yescharacteristic, complemented, Sylow
460C23—22no—
461C23—42no—
462C23—42no—
463C23—41no—
464C23—41no—
465C23—224no—
466C23—442no—
467C23—442no—
468C23—442no—
469C23—442no—
470C23—442no—
471C23—442no—
472C23C2×D4×D1111yescharacteristic
473Q8—22no—
474Q8—22no—
475Q8—41no—
476Q8—41no—
477Q8—228no—
478D4—22no—
479D4—22no—
480D4—41no—
481D4—41no—
482D4—224no—
483D4—224no—
484D4—448no—
485D4—4416no—
486D4—442no—
487D4—442no—
488D4—884no—
489D4—888no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—48no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—114no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—4416no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4#6699012yes—
511C2×C4#6699012yes—
512C2×C4C2×#433911yescharacteristic
513C2×C4C2×#433911yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4#6704211yescharacteristic
516C2×C4#6704311yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—22no—
519C8—41no—
520C8—442no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—82no—
525C22—82no—
526C22—444no—
527C22—444no—
528C22—444no—
529C22—882no—
530C22—882no—
531C22—882no—
532C22—882no—
533C22#1062308311yescharacteristic
534C22#1062308411yescharacteristic
535C22D11×AGL(1,ℤ/8)12yes—
536C22#1062330912yes—
537C22C2×#6699011yescharacteristic
538C4—22no—
539C4—22no—
540C4—42no—
541C4—42no—
542C4—81no—
543C4—224no—
544C4—442no—
545C4—882no—
546C4#1062308111yescharacteristic
547C4#1062308211yescharacteristic
548C4#1062332211yescharacteristic
549C4#1062336411yescharacteristic
550C2—82no—
551C2—884no—
552C2#1307196111yescharacteristic
553C2#1307784111yescharacteristic
554C2#1307789211yescharacteristic
555C2#1308134612yes—
556C2#1308163712yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
hypercenterC2×#440D11
hypocenterC11#24200
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#10622640C2semidirect
3. #13073978C2semidirect
4. #13069848C2semidirect
5. #13069702C2semidirect
6. #13069556C2semidirect
7. #13069440C2semidirect
8. #13068947C2semidirect
9. #13068860C2semidirect
10. #13068626C2semidirect
11. C2×C11×#440C2semidirect
114. C2×Q8×C11#41semidirect
160. C2×C8×C11#41semidirect
184. C2×#440D11semidirect
394. C2×Q8#4339semidirect
441. C2×C8#4339semidirect
459. C11#24200semidirect

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106226402
#130739782
#130698482
#130697022
#130695562
#130694402
#130689472
#130688602
#130686262
C2×C11×#4402
#2420011