Finite Group Databasebeta

← #14770611

Subgroups — #14770611

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623108C211yesmaximal, characteristic
2#13071573C211yesmaximal, characteristic, complemented
3#13069542C212yesmaximal, complemented
4#13069542C211yesmaximal, characteristic, complemented
5#13069440C212yesmaximal, complemented
6#13069422C211yesmaximal, characteristic, complemented
7#13068627C212yesmaximal, complemented
8#13068617C211yesmaximal, characteristic, complemented
9#13068442C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C2×C11×#446C211yesmaximal, characteristic, complemented
12C22×#4343—21no—
13C2×C4×Q8×C11C2211yescharacteristic
14#10623108—24no—
15#10623108C418yescomplemented
16C2×#66948—21no—
17C2×#66948—22no—
18C2×#66927C2211yescharacteristic
19C2×#66927C2212yes—
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2212yes—
22C11×#446—24no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#97C2212yes—
26C2×C4×C8×C11C2211yescharacteristic
27#10622843—21no—
28C2×#66885C2212yes—
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2212yes—
32C2×#66885C2212yes—
33C2×#66885C2212yes—
34C2×#66885C2212yes—
35#10622594—22no—
36C4⋊C4×Dic11—21no—
37#10622549C2212yes—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2212yes—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44C22×Q8×C11D411yescharacteristic
45C2×#4343—28no—
46C2×#4343—44no—
47C2×#4343—44no—
48C22×D44—22no—
49C22×D44—21no—
50C22×D44—22no—
51C22×D44—21no—
52C22×D44C2312yes—
53C22×D44C2311yescharacteristic
54C22×C4×D11—22no—
55C22×C4×D11—21no—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C4×Q8×C11C2×C414yes—
60C4×Q8×C11D414yes—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4D412yes—
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2312yes—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4×Dic11—21no—
74C2×C4×Dic11—22no—
75#66948—216no—
76#66948—28no—
77#66927—22no—
78#66927—24no—
79#66927C2×C414yes—
80#66927C2×C418yes—
81C4×D44—22no—
82C4×D44—24no—
83C4×D44C2×C414yes—
84C4×D44C2×C418yes—
85C11×C4⋊C8—22no—
86C11×C4⋊C8—24no—
87C11×#97—24no—
88C4×C8×C11—22no—
89C11⋊#95—22no—
90C11⋊#95—21no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93#66885—24no—
94#66885—22no—
95#66885—22no—
96#66885—24no—
97#66885—42no—
98#66885—42no—
99#66885—42no—
100#22545—111nomaximal, Sylow
101C23×D11—22no—
102C23×D11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11C22⋊C414yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—22no—
115#4343—432no—
116C2×D44—28no—
117C2×D44—24no—
118C2×D44—24no—
119C2×D44—28no—
120C2×D44—21no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—22no—
126C2×D44—21no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—21no—
130C2×D44—44no—
131C2×D44—44no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44—82no—
135C2×D44—81no—
136C2×D44—82no—
137C2×D44—81no—
138C2×D44C22×C412yes—
139C2×D44C22×C414yes—
140C2×C4×D11—28no—
141C2×C4×D11—24no—
142C2×C4×D11—44no—
143C2×C4×D11—44no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11—22no—
153C2×C8×C11—21no—
154C2×C8×C11#4112yescomplemented
155C11×C4⋊C4C22⋊C418yes—
156C11×C4⋊C4C22⋊C414yes—
157C42×C11C22×C414yes—
158C42×C11C22×C412yes—
159C42×C11C2×D412yes—
160C42×C11C2×D414yes—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—28no—
163C4⋊Dic11—21no—
164C4⋊Dic11—22no—
165C4⋊Dic11—21no—
166C4⋊Dic11—22no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—42no—
170C4⋊Dic11—81no—
171C4⋊Dic11C22×C412yes—
172C4⋊Dic11#4112yescomplemented
173C4×Dic11—42no—
174C4×Dic11—82no—
175C2×#550—111no—
176C2×#446D1111yescharacteristic, complemented
177#2355—111no—
178#1982—111no—
179#1982—112no—
180#1961—112no—
181#1957—111no—
182#1804—112no—
183#1802—111no—
184#1762—112no—
185C4×#102—111no—
186C23×C11C22×D411yescharacteristic
187C22×D11—24no—
188C22×D11—22no—
189C22×D11—42no—
190C22×D11—41no—
191C22×D11—42no—
192C22×D11—41no—
193C22×D11—42no—
194C22×D11—41no—
195C22×D11—42no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—41no—
201Q8×C11—28no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11C2×C22⋊C414yes—
210C2×C4×C11C2×C22⋊C414yes—
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11AGL(1,ℤ/8)12yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—41no—
232D44—24no—
233D44—22no—
234D44—22no—
235D44—24no—
236D44—416no—
237D44—41no—
238D44—42no—
239D44—41no—
240D44—42no—
241D44—48no—
242D44—88no—
243D44—84no—
244C4×D11—416no—
245C4×D11—48no—
246C8×C11—22no—
247C8×C11—41no—
248C8×C11—42no—
249C22×#41—221no—
250#550—118no—
251#550—224no—
252C2×#127—111no—
253C2×#127—112no—
254C2×#121—221no—
255C2×#121—222no—
256C2×C4×Q8C2×D1111yescharacteristic
257C2×C4×D4—111no—
258C2×C4×D4—112no—
259#446—24no—
260C2×C4⋊C8C2×D1111yescharacteristic
261C2×C4⋊C8C2×D1112yes—
262C2×#102—112no—
263C2×#102—111no—
264C2×#102—111no—
265C2×#102—112no—
266C2×#102—112no—
267C2×#102—112no—
268C2×#102—112no—
269C2×#97C2×D1112yes—
270C2×C4×C8C2×D1111yescharacteristic
271#391—221no—
272#387—222no—
273#384—111no—
274#382—112no—
275C4×C4⋊C4—111no—
276C4×C4⋊C4—112no—
277C4×C4⋊C4—221no—
278#340—112no—
279#340—111no—
280#340—111no—
281C22×C11C22×C22⋊C411yescharacteristic
282C22×C11#54811yescharacteristic
283C22×C11#55011yescharacteristic
284C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C11#57611yescharacteristic
287C22×C11#57711yescharacteristic
288C2×D11—44no—
289C2×D11—42no—
290C2×D11—44no—
291C2×D11—42no—
292C2×D11—44no—
293C2×D11—42no—
294C2×D11—82no—
295C2×D11—81no—
296C2×D11—82no—
297C2×D11—81no—
298C2×D11—82no—
299C2×D11—81no—
300C2×D11—82no—
301C2×D11—81no—
302C4×C11—24no—
303C4×C11—24no—
304C4×C11—22no—
305C4×C11#41814yes—
306C4×C11C4×#4111yescharacteristic
307C4×C11#52011yescharacteristic
308C4×C11#54811yescharacteristic
309C4×C11#55011yescharacteristic
310Dic11—42no—
311Dic11—42no—
312Dic11—81no—
313Dic11—82no—
314C2×#41—228no—
315C2×#41—444no—
316C2×#41—444no—
317C22×Q8D4411yescharacteristic
318C22×D4—111no—
319C22×D4—112no—
320C22×D4—222no—
321C22×D4—221no—
322C22×D4—222no—
323C22×D4—221no—
324C23×C4—222no—
325C23×C4—221no—
326C22×C8C22×D1111yescharacteristic
327C22×C8C22×D1112yes—
328C22×C8C22×D1111yescharacteristic
329#127—114no—
330#127—118no—
331#127—222no—
332#127—224no—
333#121—2216no—
334#121—228no—
335C4×Q8C4×D1114yes—
336C4×Q8C22⋊D1114yes—
337C4×D4—114no—
338C4×D4—118no—
339C4×D4—222no—
340C4×D4—224no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4D4411yescharacteristic
348C2×C4⋊C4D4412yes—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—221no—
351C2×C42—221no—
352C2×C42—222no—
353C2×C42C22×D1112yes—
354C2×C42C22×D1111yescharacteristic
355C4⋊C8—22no—
356C4⋊C8—24no—
357#102—222no—
358#102—224no—
359#102—224no—
360#102—222no—
361#102—442no—
362#102—442no—
363#102—442no—
364#97—24no—
365C4×C8—22no—
366#95—221no—
367#95—222no—
368#95—222no—
369#95—222no—
370C2×C11#234111yescharacteristic
371C2×C11C2×#41811yescharacteristic
372C2×C11#289711yescharacteristic
373C2×C11#336611yescharacteristic
374C2×C11#336811yescharacteristic
375C2×C11#339711yescharacteristic
376C2×C11#339911yescharacteristic
377D11—84no—
378D11—82no—
379C24—222no—
380C24—221no—
381#41—4432no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8(C2×D11)⋊C414yes—
385C2×D4—112no—
386C2×D4—114no—
387C2×D4—228no—
388C2×D4—224no—
389C2×D4—224no—
390C2×D4—228no—
391C2×D4—222no—
392C2×D4—221no—
393C2×D4—221no—
394C2×D4—222no—
395C2×D4—221no—
396C2×D4—222no—
397C2×D4—221no—
398C2×D4—222no—
399C2×D4—221no—
400C2×D4—222no—
401C2×D4—444no—
402C2×D4—444no—
403C2×D4—442no—
404C2×D4—442no—
405C2×D4—882no—
406C2×D4—881no—
407C2×D4—882no—
408C2×D4—881no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—228no—
412C22×C4—224no—
413C22×C4—221no—
414C22×C4—222no—
415C22×C4—444no—
416C22×C4—444no—
417C22×C4—442no—
418C22×C4—442no—
419C22×C4C2×D4412yes—
420C22×C4C2×D4412yes—
421C22×C4C2×D4411yescharacteristic
422C22×C4C2×D4411yescharacteristic
423C22×C4C23×D1111yescharacteristic
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—22no—
428C2×C8—21no—
429C2×C8—22no—
430C2×C8—21no—
431C2×C8—22no—
432C2×C8#434312yescomplemented
433C4⋊C4—112no—
434C4⋊C4—112no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C4⋊C4—221no—
438C4⋊C4—222no—
439C4⋊C4—221no—
440C4⋊C4—222no—
441C4⋊C4—442no—
442C4⋊C4—881no—
443C4⋊C4(C2×D11)⋊C418yes—
444C4⋊C4(C2×D11)⋊C414yes—
445C22⋊C4—224no—
446C22⋊C4—228no—
447C42—442no—
448C42—882no—
449C42C2×C4×D1114yes—
450C42C2×C4×D1112yes—
451C42C2×C22⋊D1112yes—
452C42C2×C22⋊D1114yes—
453C11#2254511yescharacteristic, complemented, Sylow
454C23—224no—
455C23—222no—
456C23—442no—
457C23—441no—
458C23—442no—
459C23—441no—
460C23—442no—
461C23—441no—
462C23—441no—
463C23—442no—
464C23—442no—
465C23—441no—
466C23—442no—
467C23—441no—
468C23C22×D4411yescharacteristic
469Q8—28no—
470D4—222no—
471D4—224no—
472D4—222no—
473D4—224no—
474D4—4416no—
475D4—448no—
476D4—442no—
477D4—441no—
478D4—441no—
479D4—442no—
480D4—888no—
481D4—884no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—4416no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—448no—
496C2×C4—441no—
497C2×C4—442no—
498C2×C4—441no—
499C2×C4—442no—
500C2×C4—441no—
501C2×C4—442no—
502C2×C4#6696112yes—
503C2×C4#6696112yes—
504C2×C4C2×(C2×D11)⋊C412yes—
505C2×C4C2×(C2×D11)⋊C414yes—
506C2×C4C2×(C2×D11)⋊C414yes—
507C2×C4C2×(C2×D11)⋊C412yes—
508C2×C4C22×C4×D1111yescharacteristic
509C2×C4C2×#434311yescharacteristic
510C2×C4#6704011yescharacteristic
511C2×C4#41×D1111yescharacteristic
512C2×C4#6704211yescharacteristic
513C2×C4C22×C22⋊D1111yescharacteristic
514C8—22no—
515C8—41no—
516C8—42no—
517C22—444no—
518C22—442no—
519C22—444no—
520C22—442no—
521C22—444no—
522C22—442no—
523C22—882no—
524C22—881no—
525C22—882no—
526C22—881no—
527C22—882no—
528C22—881no—
529C22—882no—
530C22—881no—
531C22#1062310711yescharacteristic
532C22#1062310811yescharacteristic
533C22C2×#6696111yescharacteristic
534C22C2×#6696111yescharacteristic
535C22#1062328211yescharacteristic
536C22#1062328311yescharacteristic
537C22C22×(C2×D11)⋊C411yescharacteristic
538C4—24no—
539C4—24no—
540C4—22no—
541C4—442no—
542C4—442no—
543C4—881no—
544C4—882no—
545C4#1062274414yes—
546C4C4×#434311yescharacteristic
547C4#1062310511yescharacteristic
548C4#1062334811yescharacteristic
549C4#1062336511yescharacteristic
550C2—884no—
551C2—882no—
552C2#1307145411yescharacteristic
553C2C2×#1062274411yescharacteristic
554C2#1307714311yescharacteristic
555C2#1308132511yescharacteristic
556C2#1308134711yescharacteristic
557C2#1308163811yescharacteristic
558C2#1308166011yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#446C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
cosocleC22×C4×C11C24
hypercenterC2×#446D11
hypocenterC11#22545
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #13071573C2semidirect
3. #13069542C2semidirect
4. #13069542C2semidirect
5. #13069440C2semidirect
6. #13069422C2semidirect
7. #13068627C2semidirect
8. #13068617C2semidirect
9. #13068442C2semidirect
10. C4×#66885C2semidirect
11. C2×C11×#446C2semidirect
15. #10623108C4semidirect
154. C2×C8×C11#41semidirect
172. C4⋊Dic11#41semidirect
176. C2×#446D11semidirect
432. C2×C8#4343semidirect
453. C11#22545semidirect

Maximal subgroups

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

subgroupindex
C2×#106231082
#130715732
#130695422
#130694402
#130694222
#130686272
#130686172
#130684422
C4×#668852
C2×C11×#4462
#2254511