Finite Group Databasebeta

← #14914166

Subgroups — #14914166

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10623103C212yesmaximal
3#13071671C218yesmaximal, complemented
4#13071482C218yesmaximal
5#13071336C211yesmaximal, characteristic, complemented
6#13071335C211yesmaximal, characteristic, complemented
7#13071333C211yesmaximal, characteristic, complemented
8#13071199C212yesmaximal
9#13071185C212yesmaximal, complemented
10C4×#66997C212yesmaximal, complemented
11#13071022C211yesmaximal, characteristic
12#13070955C211yesmaximal, characteristic
13C11×#2327C211yesmaximal, characteristic, complemented
14C22×Q8×D11C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2212yes—
17C2×Q8×Dic11C2212yes—
18C2×#66997C2212yes—
19D11×C4⋊Q8C4116yescomplemented
20#10623103—216no—
21C2×#66945C2212yes—
22C2×#66945C2214yes—
23C2×C4⋊C4×D11C2214yes—
24C2×#66941C2214yes—
25C2×#66940C2214yes—
26C2×#66940C2212yes—
27C2×#66925C2211yescharacteristic
28C2×#66925C2214yes—
29C2×#66925C2211yescharacteristic
30C2×C42×D11C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2214yes—
33C2×C4×Dic22C2212yes—
34C11×#391C2212yes—
35C11×#387C2218yes—
36C11×#382C2211yescharacteristic
37C11×#376C2211yescharacteristic
38#10622843C2212yes—
39#10622594C2218yes—
40#10622589C2212yes—
41#10622587C2212yes—
42#10622585C2218yes—
43#10622549C2211yescharacteristic
44#10622545C2211yescharacteristic
45C4×Dic11⋊C4C2218yes—
46C42×Dic11C2211yescharacteristic
47C42×Dic11C2211yescharacteristic
48#10622542C2212yes—
49#10622280C2214yes—
50#10622279C2214yes—
51#10622277C2218yes—
52#10622267C2218yes—
53#10622266C2218yes—
54#10622262C2214yes—
55#10622262C2214yes—
56#10622262C2218yes—
57#10622260C2218yes—
58#10622259C2218yes—
59C22×Q8×C11C2312yes—
60C2×Q8×D11—28no—
61C2×Q8×D11—28no—
62C2×Q8×D11C2×C4116yes—
63C22×C4×D11C2312yes—
64C22×C4×D11C2314yes—
65C22×C4×D11C2311yescharacteristic
66C22×Dic22C2312yes—
67C22×Dic22C2314yes—
68C11×C4⋊Q8C2×C418yes—
69C4×Q8×C11—28no—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C42×C11C2314yes—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77Q8×Dic11—28no—
78#66997C2×C4116yes—
79C2×(C2×D11)⋊C4C2314yes—
80C2×(C2×D11)⋊C4C2312yes—
81C2×(C2×D11)⋊C4C2312yes—
82C2×C4⋊Dic11C2314yes—
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2314yes—
85C2×Dic11⋊C4C2314yes—
86C2×Dic11⋊C4C2312yes—
87C2×Dic11⋊C4C2314yes—
88C2×Dic11⋊C4C2318yes—
89C2×Dic11⋊C4C2318yes—
90C2×Dic11⋊C4C2312yes—
91C2×C4×Dic11C2314yes—
92C2×C4×Dic11C2314yes—
93C2×C4×Dic11C2314yes—
94C2×C4×Dic11C2314yes—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2314yes—
97C2×C4×Dic11C2314yes—
98C2×C4×Dic11C2312yes—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101#66945—28no—
102#66945—216no—
103C4⋊C4×D11C2×C4132yes—
104#66941C2×C4132yes—
105#66940—216no—
106#66940—28no—
107#66925—24no—
108#66925—216no—
109#66925D418yes—
110C42×D11C2×C418yes—
111#66922C2×C418yes—
112C4×Dic22—28no—
113C4×Dic22—216no—
114C11×#95C2318yes—
115C11×#95C2314yes—
116C11×#95C2314yes—
117C11⋊#95C2318yes—
118C11⋊#95C2318yes—
119C11⋊#95C2318yes—
120C11⋊#95C2314yes—
121C11⋊#95C2314yes—
122#34209—111nomaximal, Sylow
123C23×D11C2411yescharacteristic
124C2×Q8×C11—24no—
125C2×Q8×C11—24no—
126C2×Q8×C11C22×C418yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2412yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2411yescharacteristic
133C22×Dic11C2412yes—
134C22×Dic11C2414yes—
135C22×Dic11C2414yes—
136C22×Dic11C2412yes—
137C22×Dic11C2411yescharacteristic
138C22×Dic11C2412yes—
139Q8×D11—264no—
140C2×C4×D11—28no—
141C2×C4×D11—28no—
142C2×C4×D11—28no—
143C2×C4×D11C22×C418yes—
144C2×C4×D11C22×C4116yes—
145C2×C4×D11C22×C414yes—
146C2×C4×D11C2×D414yes—
147C2×C4×D11#4114yes—
148C2×Dic22—28no—
149C2×Dic22—28no—
150C2×Dic22—24no—
151C2×Dic22—24no—
152C2×Dic22C22×C418yes—
153C2×Dic22C22×C4116yes—
154C11×C4⋊C4—28no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4C22×C4116yes—
157C42×C11—28no—
158C42×C11—22no—
159C42×C11C22×C414yes—
160C42×C11C2×D414yes—
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4C2×D418yes—
164C4⋊Dic11—28no—
165C4⋊Dic11—24no—
166C4⋊Dic11C22×C4116yes—
167Dic11⋊C4—28no—
168Dic11⋊C4—24no—
169Dic11⋊C4—216no—
170Dic11⋊C4—28no—
171Dic11⋊C4C22×C4132yes—
172Dic11⋊C4C2×D418yes—
173C4×Dic11—28no—
174C4×Dic11—28no—
175C4×Dic11—28no—
176C4×Dic11—28no—
177C4×Dic11—28no—
178C4×Dic11—28no—
179C4×Dic11—22no—
180C4×Dic11C22×C418yes—
181C4×Dic11C22×C414yes—
182C4×Dic11C2×D414yes—
183C22×C4⋊Q8—111no—
184C2×#519—112no—
185#2365—118no—
186#2344—118no—
187#2327—111no—
188#2327—111no—
189#2327—111no—
190#2327D1111yescharacteristic, complemented
191#2310—112no—
192C4×C4⋊Q8—112no—
193C4×C4⋊Q8—112no—
194#2285—111no—
195C4×#117—111no—
196C23×C11C2511yescharacteristic
197C22×D11—24no—
198C22×D11C23×C412yes—
199C22×D11C22×D412yes—
200C22×D11C2×#4112yes—
201Q8×C11—216no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—28no—
210C2×C4×C11C23×C414yes—
211C2×C4×C11C23×C418yes—
212C2×C4×C11C23×C412yes—
213C2×C4×C11C22×D414yes—
214C2×C4×C11C22×D412yes—
215C2×C4×C11C2×#4112yes—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—22no—
221C2×Dic11—24no—
222C2×Dic11—28no—
223C2×Dic11C23×C418yes—
224C2×Dic11C23×C412yes—
225C2×Dic11C23×C414yes—
226C2×Dic11C22×D414yes—
227C2×Dic11C22×D412yes—
228C2×Dic11C2×#4112yes—
229C2×Dic112−1+418yes—
230C4×D11—232no—
231C4×D11—216no—
232C4×D11C4×D4116yes—
233Dic22—216no—
234Dic22—232no—
235C23×Q8—112no—
236C2×C4⋊Q8—112no—
237C2×C4⋊Q8—1116no—
238C2×C4⋊Q8—114no—
239C2×C4⋊Q8—111no—
240C2×C4⋊Q8C2×D1111yescharacteristic
241#519—2216no—
242C2×C4×Q8—112no—
243C2×C4×Q8—112no—
244C2×C4×Q8—114no—
245C2×C4×Q8—112no—
246C2×C4×Q8—114no—
247C2×C4×Q8C2×D1112yes—
248C2×#117—112no—
249C2×#117—114no—
250C2×#117—111no—
251C2×#117—111no—
252C2×#117—114no—
253C22×C4⋊C4—114no—
254C22×C42—111no—
255#391—112no—
256#391—112no—
257#391—112no—
258#391—118no—
259#391C2×D1112yes—
260#389—118no—
261#389—118no—
262#387—118no—
263#387—118no—
264#387—118no—
265#387C2×D1118yes—
266#384—112no—
267#382—111no—
268#382C2×D1111yescharacteristic
269#381—118no—
270#380—114no—
271C4×C4⋊C4—118no—
272C4×C4⋊C4—118no—
273C4×C4⋊C4—114no—
274C4×C4⋊C4—114no—
275C4×C22⋊C4—114no—
276#376—111no—
277#376C2×D1111yescharacteristic
278C43—111no—
279C43—111no—
280C22×C11C24×C411yescharacteristic
281C22×C11C23×D411yescharacteristic
282C22×C11C22×#4111yescharacteristic
283C22×C11C2×2−1+414yes—
284C2×D11—24no—
285C2×D11—24no—
286C2×D11—24no—
287C2×D11C2×C4×D414yes—
288C4×C11—28no—
289C4×C11—24no—
290C4×C11—24no—
291C4×C11—44no—
292C4×C11—42no—
293C4×C11C2×C4×D414yes—
294Dic11—28no—
295Dic11—24no—
296Dic11—44no—
297Dic11—42no—
298Dic11C2×C4×D414yes—
299Dic11#51918yescomplemented
300C22×Q8—1116no—
301C22×Q8—114no—
302C22×Q8—112no—
303C22×Q8—228no—
304C22×Q8—228no—
305C22×Q8C22×D1112yes—
306C23×C4—111no—
307C23×C4—114no—
308C23×C4—112no—
309C4⋊Q8—1116no—
310C4⋊Q8—1132no—
311C4⋊Q8—118no—
312C4⋊Q8C4×D1118yes—
313C4×Q8—28no—
314C4×Q8—2216no—
315C4×Q8—228no—
316C4×Q8—228no—
317C4×Q8—2216no—
318C4×Q8—228no—
319#117—118no—
320#117—2216no—
321#117—224no—
322#117—2216no—
323#117—228no—
324C2×C4⋊C4—118no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—1132no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4—112no—
333C2×C4⋊C4—118no—
334C2×C4⋊C4C22×D1112yes—
335C2×C4⋊C4C22×D1114yes—
336C2×C4⋊C4C22×D1114yes—
337C2×C22⋊C4—112no—
338C2×C22⋊C4—114no—
339C2×C22⋊C4—112no—
340C2×C42—111no—
341C2×C42—111no—
342C2×C42—112no—
343C2×C42—118no—
344C2×C42—114no—
345C2×C42—114no—
346C2×C42—114no—
347C2×C42—114no—
348C2×C42—111no—
349C2×C42—114no—
350C2×C42—114no—
351C2×C42C22×D1114yes—
352C2×C42C22×D1111yescharacteristic
353C2×C42C22×D1111yescharacteristic
354C2×C42C22×D1111yescharacteristic
355#95—114no—
356#95—114no—
357#95—118no—
358#95—118no—
359#95—118no—
360#95C22×D1114yes—
361#95C22×D1114yes—
362#95C22×D1118yes—
363C2×C11C22×C4×D411yescharacteristic
364C2×C11C2×#51912yes—
365C2×C11#349912yes—
366C2×C11#350912yes—
367D11—24no—
368C24—111no—
369C2×Q8—24no—
370C2×Q8—24no—
371C2×Q8—1116no—
372C2×Q8—118no—
373C2×Q8—228no—
374C2×Q8—228no—
375C2×Q8—2264no—
376C2×Q8—224no—
377C2×Q8—224no—
378C2×Q8C2×C4×D1118yes—
379C22×C4—112no—
380C22×C4—111no—
381C22×C4—114no—
382C22×C4—114no—
383C22×C4—114no—
384C22×C4—114no—
385C22×C4—112no—
386C22×C4—118no—
387C22×C4—1116no—
388C22×C4—112no—
389C22×C4—114no—
390C22×C4—228no—
391C22×C4—228no—
392C22×C4—228no—
393C22×C4C23×D1112yes—
394C22×C4C23×D1114yes—
395C22×C4C23×D1112yes—
396C22×C4C23×D1114yes—
397C22×C4C23×D1112yes—
398C22×C4C23×D1111yescharacteristic
399C4⋊C4—28no—
400C4⋊C4—24no—
401C4⋊C4—1132no—
402C4⋊C4—1116no—
403C4⋊C4—118no—
404C4⋊C4—228no—
405C4⋊C4—228no—
406C4⋊C4—224no—
407C4⋊C4—2216no—
408C4⋊C4—228no—
409C4⋊C4—224no—
410C4⋊C4C2×C4×D11116yes—
411C22⋊C4—118no—
412C22⋊C4—228no—
413C22⋊C4—224no—
414C42—28no—
415C42—22no—
416C42—114no—
417C42—118no—
418C42—114no—
419C42—228no—
420C42—228no—
421C42—228no—
422C42—228no—
423C42—228no—
424C42—228no—
425C42—222no—
426C42C2×C4×D1114yes—
427C42D4×D1114yes—
428C11#3420911yescharacteristic, complemented, Sylow
429C23—112no—
430C23—112no—
431C23—112no—
432C23—224no—
433C23C24×D1111yescharacteristic
434Q8—216no—
435Q8—2232no—
436Q8—2216no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—28no—
445C2×C4—114no—
446C2×C4—112no—
447C2×C4—112no—
448C2×C4—112no—
449C2×C4—118no—
450C2×C4—1116no—
451C2×C4—118no—
452C2×C4—114no—
453C2×C4—2216no—
454C2×C4—2232no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—222no—
460C2×C4—224no—
461C2×C4—228no—
462C2×C4C22×C4×D1114yes—
463C2×C4C22×C4×D1118yes—
464C2×C4C22×C4×D1112yes—
465C2×C4C2×D4×D1114yes—
466C2×C4C2×D4×D1112yes—
467C2×C4#41×D1112yes—
468C22—114no—
469C22—224no—
470C22—224no—
471C22—224no—
472C22C23×C4×D1111yescharacteristic
473C22C22×D4×D1111yescharacteristic
474C22C2×#41×D1111yescharacteristic
475C22D11×2−1+414yes—
476C4—24no—
477C4—28no—
478C4—24no—
479C4—44no—
480C4—42no—
481C4—114no—
482C4—118no—
483C4—224no—
484C4—228no—
485C4—444no—
486C4—442no—
487C4C4×D4×D1114yes—
488C2—224no—
489C2C2×C4×D4×D1111yescharacteristic
490C2D11×#51912yes—
491C2#1308239812yes—
492C2#1308249812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2327C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2327D11
hypocenterC11#34209
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2327

Complements

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

NH ≅ G/Ntype
3. #13071671C2semidirect
5. #13071336C2semidirect
6. #13071335C2semidirect
7. #13071333C2semidirect
9. #13071185C2semidirect
10. C4×#66997C2semidirect
13. C11×#2327C2semidirect
19. D11×C4⋊Q8C4semidirect
190. #2327D11semidirect
299. Dic11#519semidirect
428. C11#34209semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106231032
#130716712
#130714822
#130713362
#130713352
#130713332
#130711992
#130711852
C4×#669972
#130710222
#130709552
C11×#23272
#3420911