Finite Group Databasebeta

← #14914163

Subgroups — #14914163

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10623103C212yesmaximal
3#13071675C214yesmaximal, complemented
4#13071669C214yesmaximal, complemented
5#13071484C214yesmaximal
6#13071481C214yesmaximal
7#13071334C212yesmaximal, complemented
8#13071332C212yesmaximal, complemented
9#13071199C212yesmaximal
10C4⋊Q8×Dic11C211yesmaximal, characteristic, complemented
11C4×#66922C211yesmaximal, characteristic, complemented
12#13071183C211yesmaximal, characteristic, complemented
13#13071021C211yesmaximal, characteristic
14C4×#66925C211yesmaximal, characteristic
15C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2212yes—
19C2×Q8×Dic11C2212yes—
20C2×#66997C2212yes—
21D11×C4⋊Q8C4116yescomplemented
22#10623103—216no—
23C2×#66945C2212yes—
24C2×#66945C2214yes—
25C2×C4⋊C4×D11C2214yes—
26C2×#66941C2214yes—
27C2×#66940C2214yes—
28C2×#66940C2212yes—
29C2×#66925C2211yescharacteristic
30C2×#66925C2214yes—
31C2×#66925C2211yescharacteristic
32C2×C42×D11C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2214yes—
35C2×C4×Dic22C2212yes—
36C11×#391C2212yes—
37C11×#389C2214yes—
38C11×#384C2211yescharacteristic
39C4×C11×C4⋊C4C2214yes—
40C43×C11C2211yescharacteristic
41#10622843C2212yes—
42#10622600C2214yes—
43#10622598C2214yes—
44#10622591C2218yes—
45#10622590C2212yes—
46C4⋊C4×Dic11C2214yes—
47C4⋊C4×Dic11C2214yes—
48C4⋊C4×Dic11C2214yes—
49#10622587C2212yes—
50#10622586C2214yes—
51C4×(C2×D11)⋊C4C2212yes—
52C4×(C2×D11)⋊C4C2212yes—
53#10622548C2211yescharacteristic
54C4×C4⋊Dic11C2214yes—
55#10622546C2218yes—
56#10622545C2211yescharacteristic
57#10622545C2211yescharacteristic
58C4×Dic11⋊C4C2212yes—
59C4×Dic11⋊C4C2212yes—
60C42×Dic11C2211yescharacteristic
61#10622542C2212yes—
62#10622541C2214yes—
63#10622277C2218yes—
64#10622268C2218yes—
65#10622265C2218yes—
66#10622259C2218yes—
67C22×Q8×C11C2312yes—
68C2×Q8×D11—28no—
69C2×Q8×D11—28no—
70C2×Q8×D11C2×C4116yes—
71C22×C4×D11C2312yes—
72C22×C4×D11C2314yes—
73C22×C4×D11C2311yescharacteristic
74C22×Dic22C2312yes—
75C22×Dic22C2314yes—
76C11×C4⋊Q8C2×C418yes—
77C4×Q8×C11—28no—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C42×C11C2314yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2312yes—
85C2×C42×C11C2312yes—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88Q8×Dic11—28no—
89#66997C2×C4116yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2312yes—
92C2×(C2×D11)⋊C4C2311yescharacteristic
93C2×(C2×D11)⋊C4C2311yescharacteristic
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2312yes—
96C2×C4⋊Dic11C2314yes—
97C2×C4⋊Dic11C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2312yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2318yes—
102C2×Dic11⋊C4C2311yescharacteristic
103C2×Dic11⋊C4C2311yescharacteristic
104C2×C4×Dic11C2314yes—
105C2×C4×Dic11C2314yes—
106C2×C4×Dic11C2314yes—
107C2×C4×Dic11C2314yes—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2312yes—
110C2×C4×Dic11C2312yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114#66945—28no—
115#66945—216no—
116C4⋊C4×D11C2×C4132yes—
117#66941C2×C4132yes—
118#66940—216no—
119#66940—28no—
120#66925—24no—
121#66925—216no—
122#66925D418yes—
123C42×D11C2×C418yes—
124#66922C2×C418yes—
125C4×Dic22—28no—
126C4×Dic22—216no—
127C11×#95C2318yes—
128C11⋊#95C2318yes—
129C11⋊#95C2318yes—
130C11⋊#95C2318yes—
131C11⋊#95C2312yes—
132C11⋊#95C2318yes—
133C11⋊#95C2312yes—
134C11⋊#95C2312yes—
135C11⋊#95C2312yes—
136#34209—111nomaximal, Sylow
137C23×D11C2411yescharacteristic
138C2×Q8×C11—24no—
139C2×Q8×C11—24no—
140C2×Q8×C11C22×C418yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×C4×C11C2412yes—
148C22×Dic11C2412yes—
149C22×Dic11C2414yes—
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152C22×Dic11C2411yescharacteristic
153C22×Dic11C2411yescharacteristic
154C22×Dic11C2411yescharacteristic
155Q8×D11—264no—
156C2×C4×D11—28no—
157C2×C4×D11—28no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11C22×C418yes—
161C2×C4×D11C22×C4116yes—
162C2×C4×D11C22×C414yes—
163C2×C4×D11C2×D414yes—
164C2×C4×D11#4114yes—
165C2×Dic22—28no—
166C2×Dic22—28no—
167C2×Dic22—24no—
168C2×Dic22—24no—
169C2×Dic22C22×C418yes—
170C2×Dic22C22×C4116yes—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4C22×C4116yes—
175C42×C11—28no—
176C42×C11—22no—
177C42×C11—24no—
178C42×C11—24no—
179C42×C11C22×C414yes—
180C42×C11C2×D414yes—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4C2×D414yes—
184(C2×D11)⋊C4C2×D414yes—
185C4⋊Dic11—28no—
186C4⋊Dic11—24no—
187C4⋊Dic11—28no—
188C4⋊Dic11C22×C4116yes—
189Dic11⋊C4—28no—
190Dic11⋊C4—24no—
191Dic11⋊C4—28no—
192Dic11⋊C4C22×C4132yes—
193Dic11⋊C4C2×D414yes—
194Dic11⋊C4C2×D414yes—
195C4×Dic11—28no—
196C4×Dic11—28no—
197C4×Dic11—28no—
198C4×Dic11—28no—
199C4×Dic11—22no—
200C4×Dic11—24no—
201C4×Dic11—24no—
202C4×Dic11C22×C418yes—
203C4×Dic11C22×C414yes—
204C4×Dic11C2×D414yes—
205C22×C4⋊Q8—111no—
206C2×#519—112no—
207#2365—114no—
208#2365—114no—
209#2344—114no—
210#2344—114no—
211#2327—112no—
212#2327—112no—
213#2310—112no—
214C4×C4⋊Q8—111no—
215C4×C4⋊Q8—111no—
216C4×C4⋊Q8—111no—
217C4×C4⋊Q8D1111yescharacteristic, complemented
218#2285—111no—
219C4×#117—111no—
220C23×C11C2511yescharacteristic
221C22×D11—22no—
222C22×D11—22no—
223C22×D11C23×C412yes—
224C22×D11C22×D412yes—
225C22×D11C2×#4112yes—
226Q8×C11—216no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—28no—
236C2×C4×C11C23×C418yes—
237C2×C4×C11C23×C412yes—
238C2×C4×C11C23×C414yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C2×#4112yes—
243C2×C4×C112−1+414yes—
244C2×C4×C112−1+414yes—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—28no—
256C2×Dic11C23×C414yes—
257C2×Dic11C23×C418yes—
258C2×Dic11C23×C412yes—
259C2×Dic11C22×D412yes—
260C2×Dic11C22×D412yes—
261C2×Dic11C22×D412yes—
262C2×Dic11C2×#4112yes—
263C4×D11—232no—
264C4×D11—216no—
265C4×D11C4×D4116yes—
266Dic22—216no—
267Dic22—232no—
268C23×Q8—112no—
269C2×C4⋊Q8—112no—
270C2×C4⋊Q8—1116no—
271C2×C4⋊Q8—114no—
272C2×C4⋊Q8—111no—
273C2×C4⋊Q8C2×D1111yescharacteristic
274#519—2216no—
275C2×C4×Q8—112no—
276C2×C4×Q8—112no—
277C2×C4×Q8—114no—
278C2×C4×Q8—112no—
279C2×C4×Q8—114no—
280C2×C4×Q8C2×D1112yes—
281C2×#117—112no—
282C2×#117—114no—
283C2×#117—111no—
284C2×#117—111no—
285C2×#117—114no—
286C22×C4⋊C4—114no—
287C22×C42—111no—
288#391—112no—
289#391—112no—
290#391—112no—
291#391—118no—
292#391C2×D1112yes—
293#389—114no—
294#389—114no—
295#389—114no—
296#389C2×D1114yes—
297#387—118no—
298#387—118no—
299#387—118no—
300#387—118no—
301#384—111no—
302#384C2×D1111yescharacteristic
303#382—112no—
304#381—118no—
305#380—114no—
306C4×C4⋊C4—114no—
307C4×C4⋊C4—114no—
308C4×C4⋊C4—114no—
309C4×C4⋊C4—114no—
310C4×C4⋊C4—112no—
311C4×C4⋊C4—112no—
312C4×C4⋊C4C2×D1114yes—
313C4×C22⋊C4—112no—
314C4×C22⋊C4—112no—
315#376—111no—
316#376—111no—
317C43—111no—
318C43C2×D1111yescharacteristic
319C22×C11C24×C411yescharacteristic
320C22×C11C23×D411yescharacteristic
321C22×C11C22×#4111yescharacteristic
322C22×C11C2×2−1+412yes—
323C22×C11C2×2−1+412yes—
324C2×D11—24no—
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—24no—
328C2×D11C2×C4×D414yes—
329C4×C11—28no—
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—44no—
333C4×C11—42no—
334C4×C11C2×C4×D414yes—
335C4×C11#51918yescomplemented
336Dic11—28no—
337Dic11—24no—
338Dic11—22no—
339Dic11—22no—
340Dic11—44no—
341Dic11—42no—
342Dic11C2×C4×D414yes—
343C22×Q8—1116no—
344C22×Q8—114no—
345C22×Q8—112no—
346C22×Q8—228no—
347C22×Q8—228no—
348C22×Q8C22×D1112yes—
349C23×C4—111no—
350C23×C4—114no—
351C23×C4—112no—
352C4⋊Q8—1116no—
353C4⋊Q8—1132no—
354C4⋊Q8—118no—
355C4⋊Q8C4×D1118yes—
356C4×Q8—28no—
357C4×Q8—2216no—
358C4×Q8—228no—
359C4×Q8—228no—
360C4×Q8—2216no—
361C4×Q8—228no—
362#117—118no—
363#117—2216no—
364#117—224no—
365#117—2216no—
366#117—228no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—118no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—1132no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—114no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4C22×D1112yes—
379C2×C4⋊C4C22×D1114yes—
380C2×C4⋊C4C22×D1114yes—
381C2×C4⋊C4C22×D1114yes—
382C2×C22⋊C4—111no—
383C2×C22⋊C4—111no—
384C2×C22⋊C4—114no—
385C2×C22⋊C4—112no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—112no—
389C2×C42—118no—
390C2×C42—114no—
391C2×C42—114no—
392C2×C42—114no—
393C2×C42—114no—
394C2×C42—111no—
395C2×C42—112no—
396C2×C42—112no—
397C2×C42C22×D1114yes—
398C2×C42C22×D1111yescharacteristic
399C2×C42C22×D1112yes—
400C2×C42C22×D1112yes—
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1111yescharacteristic
403#95—112no—
404#95—112no—
405#95—112no—
406#95—112no—
407#95—118no—
408#95—118no—
409#95—118no—
410#95—118no—
411#95C22×D1118yes—
412C2×C11C22×C4×D411yescharacteristic
413C2×C11C2×#51912yes—
414C2×C11#349911yescharacteristic
415C2×C11#349911yescharacteristic
416C2×C11#350912yes—
417D11—24no—
418C24—111no—
419C2×Q8—24no—
420C2×Q8—24no—
421C2×Q8—1116no—
422C2×Q8—118no—
423C2×Q8—228no—
424C2×Q8—228no—
425C2×Q8—2264no—
426C2×Q8—224no—
427C2×Q8—224no—
428C2×Q8C2×C4×D1118yes—
429C22×C4—111no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—118no—
438C22×C4—1116no—
439C22×C4—112no—
440C22×C4—114no—
441C22×C4—228no—
442C22×C4—228no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4C23×D1112yes—
446C22×C4C23×D1114yes—
447C22×C4C23×D1114yes—
448C22×C4C23×D1111yescharacteristic
449C22×C4C23×D1111yescharacteristic
450C22×C4C23×D1111yescharacteristic
451C22×C4C23×D1112yes—
452C4⋊C4—28no—
453C4⋊C4—24no—
454C4⋊C4—28no—
455C4⋊C4—1132no—
456C4⋊C4—1116no—
457C4⋊C4—114no—
458C4⋊C4—114no—
459C4⋊C4—228no—
460C4⋊C4—228no—
461C4⋊C4—224no—
462C4⋊C4—228no—
463C4⋊C4—224no—
464C4⋊C4—228no—
465C4⋊C4C2×C4×D11116yes—
466C22⋊C4—114no—
467C22⋊C4—114no—
468C22⋊C4—228no—
469C22⋊C4—224no—
470C42—28no—
471C42—24no—
472C42—22no—
473C42—24no—
474C42—118no—
475C42—114no—
476C42—114no—
477C42—228no—
478C42—228no—
479C42—228no—
480C42—228no—
481C42—224no—
482C42—222no—
483C42—224no—
484C42C2×C4×D1114yes—
485C42D4×D1114yes—
486C11#3420911yescharacteristic, complemented, Sylow
487C23—112no—
488C23—112no—
489C23—112no—
490C23—222no—
491C23—222no—
492C23C24×D1111yescharacteristic
493Q8—216no—
494Q8—2232no—
495Q8—2216no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—28no—
505C2×C4—112no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—1116no—
509C2×C4—114no—
510C2×C4—118no—
511C2×C4—112no—
512C2×C4—112no—
513C2×C4—2232no—
514C2×C4—224no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—2216no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—228no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4C22×C4×D1118yes—
527C2×C4C22×C4×D1112yes—
528C2×C4C22×C4×D1114yes—
529C2×C4C2×D4×D1112yes—
530C2×C4C2×D4×D1112yes—
531C2×C4C2×D4×D1112yes—
532C2×C4#6704014yes—
533C2×C4#41×D1112yes—
534C2×C4#6704314yes—
535C22—114no—
536C22—222no—
537C22—222no—
538C22—224no—
539C22—224no—
540C22C23×C4×D1111yescharacteristic
541C22C22×D4×D1111yescharacteristic
542C22C2×#6704012yes—
543C22C2×#41×D1111yescharacteristic
544C22C2×#6704312yes—
545C4—22no—
546C4—22no—
547C4—28no—
548C4—44no—
549C4—42no—
550C4—114no—
551C4—222no—
552C4—222no—
553C4—228no—
554C4—224no—
555C4—444no—
556C4—442no—
557C4C4×D4×D1114yes—
558C4#1062310318yescomplemented
559C2—224no—
560C2C2×C4×D4×D1111yescharacteristic
561C2C2×#1062310312yes—
562C2#1308239611yescharacteristic
563C2#1308239911yescharacteristic
564C2#1308249512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×C4⋊Q8C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterC4×C4⋊Q8D11
hypocenterC11#34209
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13071675C2semidirect
4. #13071669C2semidirect
7. #13071334C2semidirect
8. #13071332C2semidirect
10. C4⋊Q8×Dic11C2semidirect
11. C4×#66922C2semidirect
12. #13071183C2semidirect
15. C4×C11×C4⋊Q8C2semidirect
21. D11×C4⋊Q8C4semidirect
217. C4×C4⋊Q8D11semidirect
335. C4×C11#519semidirect
486. C11#34209semidirect
558. C4#10623103semidirect

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
#130716752
#130716692
#130714842
#130714812
#130713342
#130713322
#130711992
C4⋊Q8×Dic112
C4×#669222
#130711832
#130710212
C4×#669252
C4×C11×C4⋊Q82
#3420911