Finite Group Databasebeta

← #14770528

Subgroups — #14770528

Order 2816.

1172 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
1#13071493C212yesmaximal, complemented
2#13069453C212yesmaximal, complemented
3#13069453C214yesmaximal, complemented
4#13068604C212yesmaximal, complemented
5#13068604C211yesmaximal, characteristic, complemented
6C4×#66898C211yesmaximal, characteristic, complemented
7C4×#66898C212yesmaximal, complemented
8C2×C11×#553C211yesmaximal, characteristic
9C11×#553—22no—
10C11×#553—24no—
11C11×#553—22no—
12C2×C11×#126C412yescomplemented
13C2×C11×#125C411yescharacteristic, complemented
14C2×C11×#123C412yescomplemented
15C2×C11×#121C411yescharacteristic, complemented
16C2×C11×#121C2212yes—
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11C411yescharacteristic, complemented
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C411yescharacteristic, complemented
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×#66898C2212yes—
24C2×#66898C2214yes—
25C2×#66898C2214yes—
26C2×#66898C2212yes—
27#10622825C2214yes—
28#10622825C2212yes—
29C4×C22⋊Dic11C2212yes—
30C4×C22⋊Dic11C2214yes—
31#10622598—22no—
32#10622594—24no—
33C4⋊C4×Dic11—22no—
34#10622164C2211yescharacteristic
35#10622164C2212yes—
36#10622164C2211yescharacteristic
37C22×D4×C11C2×C411yescharacteristic
38C22×D4×C11C2×C412yes—
39C22×D4×C11C2312yes—
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11C2×C412yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C11×#126—24no—
46C11×#126—24no—
47C11×#125—22no—
48C11×#125—22no—
49C11×#123—24no—
50C11×#123—24no—
51C11×#121—24no—
52C11×#121—24no—
53C11×#121—22no—
54C11×#121—22no—
55C11×#121—22no—
56C11×#121—22no—
57C4×D4×C11—24no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C11×#117—22no—
65C11×#117—21no—
66C11×#117—21no—
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C11×C4⋊C4C2×C412yes—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C412yes—
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C4⋊C4C2×C412yes—
74C2×C11×C4⋊C4D412yes—
75C2×C11×C4⋊C4D414yes—
76C2×C11×C4⋊C4D412yes—
77C2×C11×C22⋊C4C2×C412yes—
78C2×C11×C22⋊C4C2×C412yes—
79C2×C11×C22⋊C4C2×C412yes—
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C412yes—
82C2×C11×C22⋊C4C2311yescharacteristic
83C2×C42×C11C2×C412yes—
84C2×C42×C11C2×C411yescharacteristic
85C2×C22⋊Dic11C2312yes—
86C2×C22⋊Dic11C2314yes—
87C2×C22⋊Dic11C2312yes—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—24no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—24no—
92#66898—24no—
93#66898—28no—
94#66898—44no—
95#66898—42no—
96C11⋊#95—22no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—22no—
100#22535—111nomaximal, Sylow
101C24×C11C22×C411yescharacteristic
102C24×C11C22×C412yes—
103C24×C11C2411yescharacteristic
104C2×D4×C11—24no—
105C2×D4×C11—22no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—24no—
115C2×D4×C11—42no—
116C2×D4×C11—82no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—82no—
124C22×C4×C11—82no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2×D414yes—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4C22⋊C412yes—
146C11×C4⋊C4C22⋊C411yescharacteristic
147C11×C4⋊C4C22⋊C411yescharacteristic
148C11×C4⋊C4C22⋊C412yes—
149C11×C4⋊C4C22⋊C412yes—
150C11×C4⋊C4C22⋊C414yes—
151C11×C4⋊C4C22⋊C414yes—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—21no—
163C42×C11—21no—
164C22⋊Dic11—22no—
165C22⋊Dic11—24no—
166C22⋊Dic11—22no—
167C22⋊Dic11—24no—
168C22⋊Dic11—22no—
169C22⋊Dic11#4114yes—
170C4⋊Dic11—44no—
171C4⋊Dic11—84no—
172C4×Dic11—44no—
173C4×Dic11—84no—
174C2×#553D1111yescharacteristic
175#2345—112no—
176#1964—114no—
177#1964—112no—
178#1799—112no—
179#1799—111no—
180C4×#99—112no—
181C4×#99—111no—
182C23×C11—21no—
183C23×C11—22no—
184C23×C11—21no—
185C23×C11—22no—
186C23×C11—21no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—41no—
194C23×C11C23×C411yescharacteristic
195C23×C11C22×D412yes—
196C23×C11C2×#4112yes—
197C23×C11H(5,𝔽2)11yescharacteristic
198C23×C112−1+411yescharacteristic
199D4×C11—42no—
200D4×C11—44no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—84no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—21no—
216C2×C4×C11—44no—
217C2×C4×C11—44no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—82no—
227C2×C4×C11—82no—
228C2×C4×C11C2×C22⋊C412yes—
229C2×C4×C11C2×C22⋊C412yes—
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C2×C22⋊C414yes—
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×Dic11—24no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—44no—
239C2×Dic11—44no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—44no—
243#553—22no—
244#553—24no—
245#553—22no—
246C2×#126Dic1112yescomplemented
247C2×#125Dic1111yescharacteristic, complemented
248C2×#123Dic1112yescomplemented
249C2×#121Dic1111yescharacteristic, complemented
250C2×#121C2×D1112yes—
251C2×#121C2×D1111yescharacteristic
252C2×C4×D4Dic1111yescharacteristic, complemented
253C2×C4×D4C2×D1112yes—
254C2×C4×D4C2×D1111yescharacteristic
255C2×#117Dic1111yescharacteristic, complemented
256C22×C4⋊C4C2×D1111yescharacteristic
257C2×#99—112no—
258C2×#99—114no—
259C2×#99—114no—
260C2×#99—112no—
261#389—222no—
262#387—224no—
263#380—114no—
264#380—112no—
265C4×C4⋊C4—222no—
266C4×C22⋊C4—112no—
267C4×C22⋊C4—114no—
268#342—111no—
269#342—112no—
270#342—111no—
271C22×C11—21no—
272C22×C11—22no—
273C22×C11—21no—
274C22×C11—22no—
275C22×C11—42no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—42no—
280C22×C11—41no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—41no—
284C22×C11—81no—
285C22×C11—82no—
286C22×C11—81no—
287C22×C11—82no—
288C22×C11C22×C22⋊C411yescharacteristic
289C22×C11C4×#4111yescharacteristic
290C22×C11#52011yescharacteristic
291C22×C11#54812yes—
292C22×C11#55012yes—
293C4×C11—21no—
294C4×C11—22no—
295C4×C11—22no—
296C4×C11—22no—
297C4×C11—24no—
298C4×C11—42no—
299C4×C11—41no—
300C4×C11—41no—
301C4×C11—41no—
302C4×C11#41012yes—
303Dic11—44no—
304Dic11—82no—
305Dic11—84no—
306C22×D4C2×Dic1111yescharacteristic
307C22×D4C2×Dic1112yes—
308C22×D4C22×D1112yes—
309C22×D4C22×D1111yescharacteristic
310C23×C4C2×Dic1111yescharacteristic
311C23×C4C2×Dic1112yes—
312C23×C4C22×D1111yescharacteristic
313C23×C4C22×D1112yes—
314#126—24no—
315#126—24no—
316#125—22no—
317#125—22no—
318#123—24no—
319#123—24no—
320#121—24no—
321#121—24no—
322#121—22no—
323#121—22no—
324#121—22no—
325#121—22no—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—21no—
332C4×D4—21no—
333#117—22no—
334#117—21no—
335#117—21no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4C2×Dic1111yescharacteristic
339C2×C4⋊C4C2×Dic1112yes—
340C2×C4⋊C4C2×Dic1111yescharacteristic
341C2×C4⋊C4C2×Dic1112yes—
342C2×C4⋊C4C2×Dic1111yescharacteristic
343C2×C4⋊C4C2×Dic1111yescharacteristic
344C2×C4⋊C4C2×Dic1112yes—
345C2×C4⋊C4C22⋊D1112yes—
346C2×C4⋊C4C22⋊D1114yes—
347C2×C4⋊C4C22⋊D1112yes—
348C2×C22⋊C4—112no—
349C2×C22⋊C4—112no—
350C2×C22⋊C4—114no—
351C2×C22⋊C4C2×Dic1112yes—
352C2×C22⋊C4C2×Dic1112yes—
353C2×C22⋊C4C2×Dic1112yes—
354C2×C22⋊C4C2×Dic1111yescharacteristic
355C2×C22⋊C4C2×Dic1112yes—
356C2×C22⋊C4C22×D1111yescharacteristic
357C2×C42—222no—
358C2×C42—224no—
359C2×C42C2×Dic1112yes—
360C2×C42C2×Dic1111yescharacteristic
361#99—224no—
362#99—228no—
363#99—444no—
364#99—442no—
365#95—222no—
366#95—224no—
367#95—224no—
368#95—222no—
369C2×C11—22no—
370C2×C11—22no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—81no—
374C2×C11—82no—
375C2×C11#234111yescharacteristic
376C2×C11C2×#41011yescharacteristic
377C2×C11#288311yescharacteristic
378C24C22×Dic1111yescharacteristic
379C24C22×Dic1112yes—
380C24C23×D1111yescharacteristic
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—24no—
392C2×D4—42no—
393C2×D4—82no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—82no—
401C22×C4—82no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—224no—
405C22×C4C22×Dic1112yes—
406C22×C4C22×Dic1111yescharacteristic
407C22×C4C22×Dic1111yescharacteristic
408C22×C4C22×Dic1111yescharacteristic
409C22×C4C22×Dic1111yescharacteristic
410C22×C4C22×Dic1112yes—
411C22×C4C22×Dic1111yescharacteristic
412C22×C4C22×Dic1112yes—
413C22×C4C2×C22⋊D1112yes—
414C22×C4C2×C22⋊D1112yes—
415C22×C4C2×C22⋊D1114yes—
416C22×C4C2×C22⋊D1114yes—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—24no—
422C4⋊C4—444no—
423C4⋊C4—884no—
424C4⋊C4C22⋊Dic1112yes—
425C4⋊C4C22⋊Dic1111yescharacteristic
426C4⋊C4C22⋊Dic1111yescharacteristic
427C4⋊C4C22⋊Dic1112yes—
428C4⋊C4C22⋊Dic1112yes—
429C4⋊C4C22⋊Dic1114yes—
430C4⋊C4C22⋊Dic1114yes—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—24no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—24no—
439C22⋊C4—114no—
440C22⋊C4—222no—
441C22⋊C4—222no—
442C22⋊C4—224no—
443C22⋊C4—222no—
444C22⋊C4—224no—
445C42—22no—
446C42—22no—
447C42—21no—
448C42—21no—
449C42—444no—
450C42—884no—
451C11#2253511yescharacteristic, complemented, Sylow
452C23—21no—
453C23—22no—
454C23—21no—
455C23—22no—
456C23—21no—
457C23—22no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—42no—
463C23—41no—
464C23#41×D1112yes—
465C23#6704211yescharacteristic
466C23#6704311yescharacteristic
467C23C23×Dic1111yescharacteristic
468C23C22×C22⋊D1112yes—
469D4—42no—
470D4—44no—
471D4—42no—
472D4—44no—
473D4—42no—
474D4—42no—
475D4—84no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—82no—
497C2×C4—82no—
498C2×C4—224no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—444no—
503C2×C4—444no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—444no—
507C2×C4C2×C22⋊Dic1112yes—
508C2×C4C2×C22⋊Dic1112yes—
509C2×C4C2×C22⋊Dic1111yescharacteristic
510C2×C4C2×C22⋊Dic1112yes—
511C2×C4C2×C22⋊Dic1114yes—
512C2×C4C2×C22⋊Dic1111yescharacteristic
513C22—21no—
514C22—22no—
515C22—21no—
516C22—22no—
517C22—42no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—42no—
522C22—42no—
523C22—41no—
524C22—41no—
525C22—42no—
526C22—81no—
527C22—82no—
528C22—81no—
529C22—82no—
530C22#41×Dic1111yescharacteristic
531C22#1062335811yescharacteristic
532C22#1062336212yes—
533C22#1062336512yes—
534C22C22×C22⋊Dic1111yescharacteristic
535C4—21no—
536C4—22no—
537C4—22no—
538C4—22no—
539C4—24no—
540C4—41no—
541C4—41no—
542C4—42no—
543C4—41no—
544C4—444no—
545C4—882no—
546C4—884no—
547C4#1062285312yes—
548C2—22no—
549C2—22no—
550C2—21no—
551C2—21no—
552C2—81no—
553C2—82no—
554C2#1307145711yescharacteristic
555C2C2×#1062285311yescharacteristic
556C2#1307707711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
Fitting, prime radicalC2×C11×#553C2
socleC22×C11C22×C22⋊C4
cosocleC24×C11C24
hypercenterC2×#553D11
hypocenterC11#22535
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. #13071493C2semidirect
2. #13069453C2semidirect
3. #13069453C2semidirect
4. #13068604C2semidirect
5. #13068604C2semidirect
6. C4×#66898C2semidirect
7. C4×#66898C2semidirect
12. C2×C11×#126C4semidirect
13. C2×C11×#125C4semidirect
14. C2×C11×#123C4semidirect
15. C2×C11×#121C4semidirect
18. C2×C4×D4×C11C4semidirect
21. C2×C11×#117C4semidirect
246. C2×#126Dic11semidirect
247. C2×#125Dic11semidirect
248. C2×#123Dic11semidirect
249. C2×#121Dic11semidirect
252. C2×C4×D4Dic11semidirect
255. C2×#117Dic11semidirect
451. C11#22535semidirect

Maximal subgroups

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

subgroupindex
#130714932
#130694532
#130686042
C4×#668982
C2×C11×#5532
#2253511