Finite Group Databasebeta

← #14914250

Subgroups — #14914250

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2#13071715C214yesmaximal, complemented
3#13071709C214yesmaximal, complemented
4#13071492C214yesmaximal
5#13071490C214yesmaximal
6#13071358C211yesmaximal, characteristic, complemented
7#13071357C211yesmaximal, characteristic, complemented
8#13071355C211yesmaximal, characteristic, complemented
9#13071231C212yesmaximal
10#13071175C212yesmaximal, complemented
11C4×#66943C212yesmaximal, complemented
12#13071021C211yesmaximal, characteristic
13#13070970C212yesmaximal
14#13070955C211yesmaximal, characteristic
15C11×#2330C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17D11×#125C4116yescomplemented
18C2×#66945C2212yes—
19C2×C4⋊C4×D11C2212yes—
20C2×C4⋊C4×D11C2214yes—
21C2×#66943C2212yes—
22C2×#66942C2214yes—
23C2×#66925C2211yescharacteristic
24C2×#66925C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×#66923C2211yescharacteristic
27C11×#389C2212yes—
28C11×#389C2214yes—
29C11×#387C2214yes—
30C11×#384C2211yescharacteristic
31C4×C11×C4⋊C4C2212yes—
32C11×#376C2211yescharacteristic
33#10622600C2214yes—
34#10622600C2214yes—
35#10622598C2212yes—
36#10622598C2214yes—
37#10622594C2214yes—
38#10622591C2214yes—
39#10622591C2214yes—
40#10622590C2212yes—
41C4⋊C4×Dic11C2214yes—
42C4⋊C4×Dic11C2212yes—
43C4⋊C4×Dic11C2212yes—
44C4⋊C4×Dic11C2214yes—
45#10622586C2212yes—
46#10622585C2214yes—
47#10622585C2214yes—
48C4×(C2×D11)⋊C4C2214yes—
49#10622548C2211yescharacteristic
50C4×C4⋊Dic11C2214yes—
51C4×C4⋊Dic11C2212yes—
52#10622545C2211yescharacteristic
53C4×Dic11⋊C4C2214yes—
54C4×Dic11⋊C4C2214yes—
55C42×Dic11C2211yescharacteristic
56C42×Dic11C2211yescharacteristic
57#10622541C2212yes—
58#10622280C2214yes—
59#10622279C2212yes—
60#10622279C2212yes—
61#10622279C2214yes—
62#10622268C2214yes—
63#10622268C2214yes—
64#10622267C2214yes—
65#10622266C2214yes—
66#10622262C2214yes—
67#10622262C2212yes—
68#10622262C2214yes—
69#10622262C2212yes—
70#10622260C2214yes—
71#10622260C2214yes—
72C22×C4×D11C2312yes—
73C22×C4×D11C2314yes—
74C22×C4×D11C2311yescharacteristic
75C11×#125C2×C418yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2314yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×(C2×D11)⋊C4C2311yescharacteristic
86C2×(C2×D11)⋊C4C2311yescharacteristic
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2312yes—
89C2×C4⋊Dic11C2312yes—
90C2×C4⋊Dic11C2314yes—
91C2×C4⋊Dic11C2314yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2314yes—
94C2×Dic11⋊C4C2311yescharacteristic
95C2×Dic11⋊C4C2311yescharacteristic
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2312yes—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2314yes—
104C2×C4×Dic11C2314yes—
105C2×C4×Dic11C2312yes—
106C2×C4×Dic11C2314yes—
107C2×C4×Dic11C2312yes—
108C2×C4×Dic11C2312yes—
109C2×C4×Dic11C2312yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114#66945—28no—
115C4⋊C4×D11C2×C4132yes—
116C4⋊C4×D11C2×C4116yes—
117#66943C2×C4116yes—
118#66942C2×C4132yes—
119#66925—24no—
120#66925Q818yes—
121C42×D11C2×C418yes—
122#66923C2×C418yes—
123C11×#95C2312yes—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11×#95C2312yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2312yes—
132C11⋊#95C2312yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137#34217—111nomaximal, Sylow
138C23×D11C2411yescharacteristic
139C22×C4×C11C2414yes—
140C22×C4×C11C2411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11C2411yescharacteristic
147C22×Dic11C2411yescharacteristic
148C22×Dic11C2414yes—
149C22×Dic11C2412yes—
150C22×Dic11C2414yes—
151C22×Dic11C2412yes—
152C22×Dic11C2411yescharacteristic
153C2×C4×D11—44no—
154C2×C4×D11—42no—
155C2×C4×D11—44no—
156C2×C4×D11—42no—
157C2×C4×D11C22×C418yes—
158C2×C4×D11C22×C4116yes—
159C2×C4×D11C22×C414yes—
160C2×C4×D11C2×Q814yes—
161C2×C4×D11#4114yes—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—44no—
164C11×C4⋊C4—44no—
165C11×C4⋊C4C22×C4116yes—
166C11×C4⋊C4C22×C418yes—
167C42×C11—22no—
168C42×C11—44no—
169C42×C11C22×C414yes—
170C42×C11C2×Q814yes—
171(C2×D11)⋊C4—22no—
172(C2×D11)⋊C4—22no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4C2×Q818yes—
175C4⋊Dic11—24no—
176C4⋊Dic11—44no—
177C4⋊Dic11—44no—
178C4⋊Dic11C22×C418yes—
179C4⋊Dic11C22×C4116yes—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—44no—
183Dic11⋊C4—44no—
184Dic11⋊C4C22×C4116yes—
185Dic11⋊C4C22×C4116yes—
186Dic11⋊C4C22×C4116yes—
187Dic11⋊C4C2×Q818yes—
188C4×Dic11—28no—
189C4×Dic11—22no—
190C4×Dic11—42no—
191C4×Dic11—44no—
192C4×Dic11—44no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C4×Dic11—44no—
196C4×Dic11—42no—
197C4×Dic11C22×C418yes—
198C4×Dic11C22×C414yes—
199C4×Dic11C2×Q814yes—
200C22×#125—111no—
201#2370—114no—
202#2370—114no—
203#2345—114no—
204#2345—114no—
205#2330—111no—
206#2330—111no—
207#2330—111no—
208#2330D1111yescharacteristic, complemented
209#2316—112no—
210C4×#125—112no—
211C4×#125—112no—
212#2285—111no—
213#2274—112no—
214C4×#117—111no—
215C23×C11C2511yescharacteristic
216C22×D11—22no—
217C22×D11—22no—
218C22×D11C23×C412yes—
219C22×D11C22×Q812yes—
220C22×D11C2×#4112yes—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11C23×C414yes—
235C2×C4×C11C23×C418yes—
236C2×C4×C11C23×C412yes—
237C2×C4×C11C22×Q814yes—
238C2×C4×C11C22×Q812yes—
239C2×C4×C11C2×#4112yes—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11C23×C414yes—
254C2×Dic11C23×C418yes—
255C2×Dic11C23×C412yes—
256C2×Dic11C22×Q814yes—
257C2×Dic11C22×Q812yes—
258C2×Dic11C2×#4112yes—
259C4×D11—48no—
260C4×D11—416no—
261C4×D11C4×Q8116yes—
262C2×#125—1116no—
263C2×#125—112no—
264C2×#125—114no—
265C2×#125—111no—
266C2×#125C2×D1111yescharacteristic
267C2×#117—112no—
268C2×#117—111no—
269C2×#117—111no—
270C22×C4⋊C4—112no—
271C22×C4⋊C4—114no—
272C22×C42—111no—
273#389—112no—
274#389—112no—
275#389—114no—
276#389—114no—
277#389—114no—
278#389—112no—
279#389—114no—
280#389—114no—
281#389C2×D1112yes—
282#389C2×D1114yes—
283#387—114no—
284#387—114no—
285#387—114no—
286#387—114no—
287#387—114no—
288#387—114no—
289#387—114no—
290#387C2×D1114yes—
291#384—111no—
292#384C2×D1111yescharacteristic
293#382—112no—
294#380—114no—
295#380—114no—
296#380—114no—
297C4×C4⋊C4—112no—
298C4×C4⋊C4—112no—
299C4×C4⋊C4—114no—
300C4×C4⋊C4—114no—
301C4×C4⋊C4—112no—
302C4×C4⋊C4—114no—
303C4×C4⋊C4—114no—
304C4×C4⋊C4—114no—
305C4×C4⋊C4—114no—
306C4×C4⋊C4—112no—
307C4×C4⋊C4—112no—
308C4×C4⋊C4—114no—
309C4×C4⋊C4C2×D1112yes—
310C4×C22⋊C4—114no—
311C4×C22⋊C4—112no—
312C4×C22⋊C4—112no—
313C4×C22⋊C4—114no—
314#376—111no—
315#376C2×D1111yescharacteristic
316C43—111no—
317C43—111no—
318C22×C11C24×C411yescharacteristic
319C22×C11C23×Q811yescharacteristic
320C22×C11C22×#4111yescharacteristic
321C22×C11#58512yes—
322C22×C11#58512yes—
323C2×D11—24no—
324C2×D11—24no—
325C2×D11—22no—
326C2×D11—22no—
327C2×D11C2×C4×Q814yes—
328C4×C11—28no—
329C4×C11—24no—
330C4×C11—24no—
331C4×C11—44no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11C2×C4×Q814yes—
335Dic11—24no—
336Dic11—28no—
337Dic11—24no—
338Dic11—41no—
339Dic11—41no—
340Dic11—44no—
341Dic11C2×C4×Q814yes—
342C23×C4—111no—
343C23×C4—114no—
344C23×C4—112no—
345#125—1132no—
346#125—1116no—
347#125—118no—
348#125C4×D1118yes—
349#117—118no—
350#117—224no—
351#117—228no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—1116no—
359C2×C4⋊C4—1132no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4C22×D1112yes—
368C2×C4⋊C4C22×D1114yes—
369C2×C4⋊C4C22×D1114yes—
370C2×C4⋊C4C22×D1112yes—
371C2×C4⋊C4C22×D1114yes—
372C2×C22⋊C4—112no—
373C2×C22⋊C4—114no—
374C2×C22⋊C4—111no—
375C2×C22⋊C4—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—112no—
379C2×C42—118no—
380C2×C42—111no—
381C2×C42—114no—
382C2×C42—112no—
383C2×C42—112no—
384C2×C42—112no—
385C2×C42—112no—
386C2×C42—114no—
387C2×C42—114no—
388C2×C42—114no—
389C2×C42C22×D1111yescharacteristic
390C2×C42C22×D1114yes—
391C2×C42C22×D1111yescharacteristic
392C2×C42C22×D1111yescharacteristic
393#95—112no—
394#95—112no—
395#95—114no—
396#95—114no—
397#95—114no—
398#95—114no—
399#95—114no—
400#95—114no—
401#95—114no—
402#95—114no—
403#95C22×D1112yes—
404#95C22×D1112yes—
405#95C22×D1114yes—
406#95C22×D1114yes—
407C2×C11C22×C4×Q811yescharacteristic
408C2×C11#342812yes—
409C2×C11#350412yes—
410C2×C11#351211yescharacteristic
411C2×C11#351211yescharacteristic
412D11—24no—
413C24—111no—
414C22×C4—111no—
415C22×C4—114no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—114no—
421C22×C4—118no—
422C22×C4—1116no—
423C22×C4—111no—
424C22×C4—114no—
425C22×C4—111no—
426C22×C4—444no—
427C22×C4—442no—
428C22×C4—444no—
429C22×C4—442no—
430C22×C4C23×D1111yescharacteristic
431C22×C4C23×D1114yes—
432C22×C4C23×D1111yescharacteristic
433C22×C4C23×D1114yes—
434C22×C4C23×D1112yes—
435C22×C4C23×D1112yes—
436C22×C4C23×D1111yescharacteristic
437C4⋊C4—24no—
438C4⋊C4—44no—
439C4⋊C4—44no—
440C4⋊C4—1116no—
441C4⋊C4—1116no—
442C4⋊C4—1116no—
443C4⋊C4—1116no—
444C4⋊C4—118no—
445C4⋊C4—118no—
446C4⋊C4—222no—
447C4⋊C4—222no—
448C4⋊C4—224no—
449C4⋊C4—444no—
450C4⋊C4—444no—
451C4⋊C4—444no—
452C4⋊C4—444no—
453C4⋊C4C2×C4×D11116yes—
454C4⋊C4C2×C4×D1118yes—
455C22⋊C4—118no—
456C22⋊C4—222no—
457C22⋊C4—222no—
458C22⋊C4—228no—
459C42—22no—
460C42—44no—
461C42—118no—
462C42—114no—
463C42—114no—
464C42—228no—
465C42—222no—
466C42—442no—
467C42—442no—
468C42—444no—
469C42—444no—
470C42—444no—
471C42—442no—
472C42—442no—
473C42C2×C4×D1114yes—
474C42Q8×D1114yes—
475C11#3421711yescharacteristic, complemented, Sylow
476C23—112no—
477C23—112no—
478C23—112no—
479C23—222no—
480C23—222no—
481C23C24×D1111yescharacteristic
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—112no—
498C2×C4—1116no—
499C2×C4—114no—
500C2×C4—118no—
501C2×C4—114no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—224no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—224no—
508C2×C4—221no—
509C2×C4—224no—
510C2×C4—221no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—448no—
516C2×C4—4416no—
517C2×C4C22×C4×D1114yes—
518C2×C4C22×C4×D1118yes—
519C2×C4C22×C4×D1112yes—
520C2×C4C2×Q8×D1114yes—
521C2×C4C2×Q8×D1112yes—
522C2×C4#41×D1112yes—
523C22—114no—
524C22—224no—
525C22—222no—
526C22—222no—
527C22—224no—
528C22C23×C4×D1111yescharacteristic
529C22C22×Q8×D1111yescharacteristic
530C22C2×#41×D1111yescharacteristic
531C22#1062345512yes—
532C22#1062345712yes—
533C4—24no—
534C4—28no—
535C4—24no—
536C4—41no—
537C4—44no—
538C4—41no—
539C4—114no—
540C4—224no—
541C4—224no—
542C4—228no—
543C4—441no—
544C4—444no—
545C4—441no—
546C4C4×Q8×D1114yes—
547C2—224no—
548C2C2×C4×Q8×D1111yescharacteristic
549C2#1308181612yes—
550C2#1308243912yes—
551C2#1308253511yescharacteristic
552C2#1308253911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2330C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2330D11
hypocenterC11#34217
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2330

Complements

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

NH ≅ G/Ntype
2. #13071715C2semidirect
3. #13071709C2semidirect
6. #13071358C2semidirect
7. #13071357C2semidirect
8. #13071355C2semidirect
10. #13071175C2semidirect
11. C4×#66943C2semidirect
15. C11×#2330C2semidirect
17. D11×#125C4semidirect
208. #2330D11semidirect
475. C11#34217semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
#130717152
#130717092
#130714922
#130714902
#130713582
#130713572
#130713552
#130712312
#130711752
C4×#669432
#130710212
#130709702
#130709552
C11×#23302
#3421711