Finite Group Databasebeta

← #14770609

Subgroups — #14770609

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×#10622637C211yesmaximal, characteristic, complemented
2#13071573C211yesmaximal, characteristic, complemented
3#13069544C211yesmaximal, characteristic, complemented
4#13069544C212yesmaximal, complemented
5#13069441C212yesmaximal, complemented
6#13069423C211yesmaximal, characteristic, complemented
7#13068626C212yesmaximal, complemented
8#13068616C211yesmaximal, characteristic, complemented
9#13068441C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×C11×#550C211yesmaximal, characteristic
12C22×C11×#41—21no—
13C11×#550—24no—
14C11×#550C418yescomplemented
15C2×C11×#127C2211yescharacteristic
16C2×C11×#127C2212yes—
17C2×C11×#121—21no—
18C2×C11×#121—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2212yes—
22#10622843—21no—
23C2×#66896C2212yes—
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30#10622637—24no—
31#10622594—22no—
32C4⋊C4×Dic11—21no—
33#10622549C2212yes—
34#10622548C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2212yes—
39C2×#66867C2212yes—
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C2×C11×#41—28no—
45C2×C11×#41—44no—
46C2×C11×#41—44no—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11C2312yes—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—22no—
55C23×C4×C11—21no—
56C11×#127—22no—
57C11×#127—24no—
58C11×#127C2×C414yes—
59C11×#127C2×C418yes—
60C11×#121—216no—
61C11×#121—28no—
62C4×Q8×C11C2×C414yes—
63C4×Q8×C11D414yes—
64C4×D4×C11—22no—
65C4×D4×C11—24no—
66C4×D4×C11C2×C414yes—
67C4×D4×C11C2×C418yes—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D412yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2312yes—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4×Dic11—21no—
81C2×C4×Dic11—22no—
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84C22×C11⋊C8C2311yescharacteristic
85#66896—22no—
86#66896—24no—
87#66896—24no—
88#66896—22no—
89#66896—42no—
90#66896—42no—
91#66896—42no—
92C11⋊#95—22no—
93C11⋊#95—21no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C4⋊(C11⋊C8)—24no—
97C4⋊(C11⋊C8)—22no—
98#66867—24no—
99C4×C11⋊C8—22no—
100#22545—111nomaximal, Sylow
101C24×C11—22no—
102C24×C11—21no—
103C11×#41—432no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11C22⋊C414yes—
107C2×D4×C11—28no—
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—28no—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—82no—
126C2×D4×C11—81no—
127C2×D4×C11—82no—
128C2×D4×C11—81no—
129C2×D4×C11C22×C412yes—
130C2×D4×C11C22×C414yes—
131C22×C4×C11—21no—
132C22×C4×C11—28no—
133C22×C4×C11—24no—
134C22×C4×C11—44no—
135C22×C4×C11—44no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4C22⋊C418yes—
148C11×C4⋊C4C22⋊C414yes—
149C11×C4⋊C4C22×C412yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—28no—
152C42×C11C22×C414yes—
153C42×C11C22×C412yes—
154C42×C11C2×D412yes—
155C42×C11C2×D414yes—
156C4⋊Dic11—22no—
157C4⋊Dic11—21no—
158C4⋊Dic11—22no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—42no—
162C4⋊Dic11—81no—
163C4⋊Dic11#4112yescomplemented
164C4×Dic11—42no—
165C4×Dic11—82no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8#4112yescomplemented
175C2×#550D1111yescharacteristic
176C2×#446—111no—
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×C11—24no—
187C23×C11—22no—
188C23×C11—42no—
189C23×C11—41no—
190C23×C11—42no—
191C23×C11—41no—
192C23×C11—42no—
193C23×C11—41no—
194C23×C11—42no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—41no—
200C23×C11C22×D411yescharacteristic
201Q8×C11—28no—
202D4×C11—24no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11—24no—
206D4×C11—416no—
207D4×C11—41no—
208D4×C11—42no—
209D4×C11—41no—
210D4×C11—42no—
211D4×C11—48no—
212D4×C11—88no—
213D4×C11—84no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—416no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—48no—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C2×C22⋊C414yes—
227C2×C4×C11C2×C22⋊C414yes—
228C2×C4×C11C2×C22⋊C412yes—
229C2×C4×C11AGL(1,ℤ/8)12yes—
230C2×C4×C11AGL(1,ℤ/8)12yes—
231C2×C4×C11C23×C411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×Dic11—22no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—42no—
242C2×Dic11—41no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—41no—
246C11⋊C8—22no—
247C11⋊C8—41no—
248C11⋊C8—42no—
249C22×#41—21no—
250#550—24no—
251#550Dic1118yescomplemented
252C2×#127C2×D1111yescharacteristic
253C2×#127C2×D1112yes—
254C2×#121—21no—
255C2×#121—22no—
256C2×C4×Q8C2×D1111yescharacteristic
257C2×C4×D4C2×D1111yescharacteristic
258C2×C4×D4C2×D1112yes—
259#446—224no—
260C2×C4⋊C8—111no—
261C2×C4⋊C8—112no—
262C2×#102—112no—
263C2×#102—111no—
264C2×#102—111no—
265C2×#102—112no—
266C2×#102—112no—
267C2×#102—112no—
268C2×#102—112no—
269C2×#97—112no—
270C2×C4×C8—111no—
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×C11—44no—
282C22×C11—42no—
283C22×C11—44no—
284C22×C11—42no—
285C22×C11—44no—
286C22×C11—42no—
287C22×C11—82no—
288C22×C11—81no—
289C22×C11—82no—
290C22×C11—81no—
291C22×C11—82no—
292C22×C11—81no—
293C22×C11—82no—
294C22×C11—81no—
295C22×C11C22×C22⋊C411yescharacteristic
296C22×C11#54811yescharacteristic
297C22×C11#55011yescharacteristic
298C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C11#57611yescharacteristic
301C22×C11#57711yescharacteristic
302C4×C11—24no—
303C4×C11—24no—
304C4×C11—22no—
305C4×C11—42no—
306C4×C11#41814yes—
307C4×C11C4×#4111yescharacteristic
308C4×C11#52011yescharacteristic
309C4×C11#54811yescharacteristic
310C4×C11#55011yescharacteristic
311Dic11—42no—
312Dic11—81no—
313Dic11—82no—
314C2×#41—28no—
315C2×#41—44no—
316C2×#41—44no—
317C22×Q8C22⋊D1111yescharacteristic
318C22×D4—22no—
319C22×D4—21no—
320C22×D4—22no—
321C22×D4—21no—
322C22×D4C22×D1111yescharacteristic
323C22×D4C22×D1112yes—
324C23×C4—22no—
325C23×C4—21no—
326C22×C8—111no—
327C22×C8—111no—
328C22×C8—112no—
329#127—22no—
330#127—24no—
331#127C2×Dic1114yes—
332#127C2×Dic1118yes—
333#121—216no—
334#121—28no—
335C4×Q8C2×Dic1114yes—
336C4×Q8C22⋊D1114yes—
337C4×D4—22no—
338C4×D4—24no—
339C4×D4C2×Dic1114yes—
340C4×D4C2×Dic1118yes—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4C22⋊D1111yescharacteristic
347C2×C4⋊C4C22⋊D1112yes—
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C42—221no—
352C2×C42—222no—
353C2×C42C22×D1112yes—
354C2×C42C22×D1111yescharacteristic
355C4⋊C8—222no—
356C4⋊C8—224no—
357#102—222no—
358#102—224no—
359#102—224no—
360#102—222no—
361#102—442no—
362#102—442no—
363#102—442no—
364#97—224no—
365C4×C8—222no—
366#95—221no—
367#95—222no—
368#95—222no—
369#95—222no—
370C2×C11—84no—
371C2×C11—82no—
372C2×C11#234111yescharacteristic
373C2×C11C2×#41811yescharacteristic
374C2×C11#289711yescharacteristic
375C2×C11#336611yescharacteristic
376C2×C11#336811yescharacteristic
377C2×C11#339711yescharacteristic
378C2×C11#339911yescharacteristic
379C24—22no—
380C24—21no—
381#41—432no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8C22⋊Dic1114yes—
385C2×D4—28no—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—28no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—44no—
400C2×D4—44no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—82no—
404C2×D4—81no—
405C2×D4—82no—
406C2×D4—81no—
407C2×D4C22×Dic1112yes—
408C2×D4C22×Dic1114yes—
409C22×C4—21no—
410C22×C4—28no—
411C22×C4—24no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4C2×C22⋊D1112yes—
420C22×C4C2×C22⋊D1112yes—
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C2×C22⋊D1111yescharacteristic
423C22×C4C23×D1111yescharacteristic
424C2×C8—112no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—221no—
428C2×C8—222no—
429C2×C8—221no—
430C2×C8—222no—
431C2×C8—221no—
432C2×C8—222no—
433C4⋊C4—21no—
434C4⋊C4—112no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C4⋊C4—222no—
438C4⋊C4—221no—
439C4⋊C4—222no—
440C4⋊C4—442no—
441C4⋊C4—881no—
442C4⋊C4C22⋊Dic1118yes—
443C4⋊C4C22⋊Dic1114yes—
444C4⋊C4C22×Dic1112yes—
445C22⋊C4—24no—
446C22⋊C4—28no—
447C42—442no—
448C42—882no—
449C42C22×Dic1114yes—
450C42C22×Dic1112yes—
451C42C2×C22⋊D1112yes—
452C42C2×C22⋊D1114yes—
453C11#2254511yescharacteristic, complemented, Sylow
454C23—24no—
455C23—22no—
456C23—42no—
457C23—41no—
458C23—42no—
459C23—41no—
460C23—42no—
461C23—41no—
462C23—42no—
463C23—41no—
464C23—41no—
465C23—42no—
466C23—42no—
467C23—41no—
468C23C22×C22⋊D1111yescharacteristic
469Q8—28no—
470D4—24no—
471D4—22no—
472D4—22no—
473D4—24no—
474D4—416no—
475D4—48no—
476D4—42no—
477D4—41no—
478D4—41no—
479D4—42no—
480D4—88no—
481D4—84no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—416no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—48no—
493C2×C4—222no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—442no—
498C2×C4—441no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—441no—
502C2×C4#6698512yes—
503C2×C4#6698512yes—
504C2×C4C2×C22⋊Dic1112yes—
505C2×C4C2×C22⋊Dic1114yes—
506C2×C4C2×C22⋊Dic1114yes—
507C2×C4C2×C22⋊Dic1112yes—
508C2×C4#41×D1111yescharacteristic
509C2×C4#41×D1111yescharacteristic
510C2×C4#6704211yescharacteristic
511C2×C4#6704311yescharacteristic
512C2×C4C23×Dic1111yescharacteristic
513C2×C4C22×C22⋊D1111yescharacteristic
514C8—222no—
515C8—441no—
516C8—442no—
517C22—44no—
518C22—42no—
519C22—44no—
520C22—42no—
521C22—44no—
522C22—42no—
523C22—82no—
524C22—81no—
525C22—82no—
526C22—81no—
527C22—82no—
528C22—81no—
529C22—82no—
530C22—81no—
531C22C2×#6698511yescharacteristic
532C22C2×#6698511yescharacteristic
533C22#1062336211yescharacteristic
534C22#1062336511yescharacteristic
535C22#1062336611yescharacteristic
536C22#1062336711yescharacteristic
537C22C22×C22⋊Dic1111yescharacteristic
538C4—24no—
539C4—24no—
540C4—22no—
541C4—42no—
542C4—442no—
543C4—881no—
544C4—882no—
545C4#1062282814yes—
546C4#41×Dic1111yescharacteristic
547C4#1062335811yescharacteristic
548C4#1062336211yescharacteristic
549C4#1062336511yescharacteristic
550C2—84no—
551C2—82no—
552C2#1307145711yescharacteristic
553C2C2×#1062282811yescharacteristic
554C2#1307714211yescharacteristic
555C2#1308131911yescharacteristic
556C2#1308134111yescharacteristic
557C2#1308163211yescharacteristic
558C2#1308165811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#550D11
hypocenterC11#22545
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10622637C2semidirect
2. #13071573C2semidirect
3. #13069544C2semidirect
4. #13069544C2semidirect
5. #13069441C2semidirect
6. #13069423C2semidirect
7. #13068626C2semidirect
8. #13068616C2semidirect
9. #13068441C2semidirect
10. C4×#66896C2semidirect
14. C11×#550C4semidirect
163. C4⋊Dic11#41semidirect
174. C2×C11⋊C8#41semidirect
251. #550Dic11semidirect
453. C11#22545semidirect

Maximal subgroups

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

subgroupindex
C2×#106226372
#130715732
#130695442
#130694412
#130694232
#130686262
#130686162
#130684412
C4×#668962
C2×C11×#5502
#2254511