Finite Group Databasebeta

← #14758995

Subgroups — #14758995

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623222C211yesmaximal, characteristic
2C2×D11×#97C211yesmaximal, characteristic, complemented
3#13071021C211yesmaximal, characteristic, complemented
4#13069586C211yesmaximal, characteristic, complemented
5#13069432C211yesmaximal, characteristic, complemented
6#13069430C211yesmaximal, characteristic, complemented
7#13069043C212yesmaximal
8#13069038C212yesmaximal, complemented
9#13068445C212yesmaximal, complemented
10#13068440C212yesmaximal, complemented
11C11×#1992C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C22×C8×D11C2212yes—
14#10623222—24no—
15#10623222C418yescomplemented
16C2×#66951—21no—
17C2×#66950C2211yescharacteristic
18C2×#66948C2211yescharacteristic
19C2×#66947—21no—
20C2×#66946—21no—
21C2×#66946C2211yescharacteristic
22C2×#66945—21no—
23C2×#66945—21no—
24C2×#66940C2211yescharacteristic
25C2×#66928C2211yescharacteristic
26C2×C42×D11C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C11×#384C2211yescharacteristic
29C2×#66885C2212yes—
30C2×#66880C2212yes—
31C2×#66879C2212yes—
32#10622600—21no—
33#10622600C2212yes—
34#10622590—21no—
35C4⋊C4×Dic11—21no—
36C4⋊C4×Dic11C2212yes—
37C2×#66874C2212yes—
38C2×#66873C2212yes—
39#10622548C2211yescharacteristic
40C2×#66867C2211yescharacteristic
41D11×#97—24no—
42C11×#340C2212yes—
43C11×#340C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×D44—21no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×C4×D11C2311yescharacteristic
52C22×Dic22C2311yescharacteristic
53C22×C8×C11C2312yes—
54C11×#125—22no—
55C11×#125C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2312yes—
74C2×Dic11⋊C4—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C22×C11⋊C8C2312yes—
81C2×C8×D11—24no—
82C2×C8×D11—24no—
83C2×C8×D11—24no—
84#66951—28no—
85#66950—22no—
86#66950C2×C414yes—
87#66948—22no—
88#66948C2×C414yes—
89#66947—28no—
90#66946—28no—
91#66946—22no—
92#66946C2×C414yes—
93#66945—28no—
94#66945—44no—
95#66940—22no—
96#66940C2×C414yes—
97#66928—22no—
98#66928C2×C414yes—
99C42×D11C2×C414yes—
100C42×D11D414yes—
101C11×#97—22no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104#66885—24no—
105#66880—24no—
106#66879—24no—
107#66874—24no—
108#66873—24no—
109#66867—22no—
110#21406—111nomaximal, Sylow
111C23×D11—21no—
112C23×D11C2×D411yescharacteristic
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C22×Dic11—21no—
120C22×Dic11—22no—
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C22×Dic11C2×D411yescharacteristic
124C2×D44—24no—
125C2×D44—21no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—42no—
129C2×D44—42no—
130C2×D44C22×C412yes—
131C2×C4×D11—24no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×C4×D11C22⋊C414yes—
141C2×C4×D11C22⋊C414yes—
142C2×C4×D11C22×C412yes—
143C2×C4×D11C2×D412yes—
144C2×Dic22—21no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22C22×C412yes—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11#4114yes—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4C22×C412yes—
160C11×C4⋊C4C22×C412yes—
161C42×C11C22×C412yes—
162C42×C11C2×D412yes—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—44no—
169C4⋊Dic11—24no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—42no—
173C4⋊Dic11—42no—
174Dic11⋊C4—24no—
175C4×Dic11—24no—
176C4×Dic11—44no—
177C4×Dic11C22⋊C414yes—
178C4×Dic11C22⋊C414yes—
179C4×Dic11C22×C412yes—
180C4×Dic11C2×D412yes—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8#4114yes—
184C8×D11—216no—
185C2×#529—111no—
186C22×#97—111no—
187#2285—111no—
188#1992—111no—
189#1992D1111yescharacteristic, complemented
190#1959—111no—
191#1959—111no—
192#1893—112no—
193#1892—112no—
194#1763—112no—
195#1762—112no—
196C23×C11C22×D411yescharacteristic
197C22×D11—21no—
198C22×D11—21no—
199C22×D11—21no—
200C22×D11—21no—
201C22×D11—22no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11C2×C22⋊C412yes—
209C22×D11AGL(1,ℤ/8)12yes—
210C22×D11#13712yes—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11C2×C22⋊C412yes—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4112yes—
229C2×C4×C11C2×#4112yes—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—22no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11C2×C22⋊C412yes—
243C2×Dic11C2×C22⋊C412yes—
244C2×Dic11C2×C22⋊C412yes—
245D44—24no—
246D44—48no—
247D44—42no—
248C4×D11—28no—
249C4×D11—24no—
250C4×D11—24no—
251C4×D11—44no—
252C4×D11—48no—
253Dic22—24no—
254Dic22—42no—
255C8×C11—24no—
256C11⋊C8—24no—
257C23×C8—112no—
258#529—118no—
259#529—224no—
260C2×#126—221no—
261C2×#125C2×D1111yescharacteristic
262C2×#124—111no—
263C2×#123—221no—
264C2×C22⋊Q8—111no—
265C2×#121—111no—
266C2×C4×Q8—111no—
267C2×C4×D4—111no—
268C2×C4×D4—221no—
269C2×#117—221no—
270C2×#117—221no—
271C22×C42—111no—
272C2×#103—112no—
273C2×#103—112no—
274C2×#102—112no—
275C2×#102—112no—
276C2×#97—112no—
277C2×#97—111no—
278C2×#97—224no—
279C2×#97C2×D1111yescharacteristic
280#384—111no—
281#384C2×D1111yescharacteristic
282#382—221no—
283#380—112no—
284#380—221no—
285C4×C4⋊C4—112no—
286C4×C4⋊C4—221no—
287#340—112no—
288#340—112no—
289#340C2×D1112yes—
290#340C2×D1112yes—
291C22×C11C22×C22⋊C411yescharacteristic
292C22×C11#53211yescharacteristic
293C22×C11#53211yescharacteristic
294C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C11C2×#13711yescharacteristic
296C22×C11#57511yescharacteristic
297C22×C11#57511yescharacteristic
298C2×D11—22no—
299C2×D11—22no—
300C2×D11—22no—
301C2×D11—22no—
302C2×D11—22no—
303C2×D11—22no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—81no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C2×D11#41714yes—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—82no—
317C4×C11C4×#4112yes—
318C4×C11#52512yes—
319Dic11—22no—
320Dic11—22no—
321Dic11—22no—
322Dic11—42no—
323Dic11—82no—
324C22×Q8—111no—
325C22×D4—111no—
326C22×D4—221no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—221no—
331C22×C8—112no—
332C22×C8—224no—
333C22×C8—224no—
334C22×C8—224no—
335C22×C8C22×D1112yes—
336#126—228no—
337#125—22no—
338#125C4×D1114yes—
339#124—114no—
340#124—222no—
341#123—228no—
342C22⋊Q8—114no—
343C22⋊Q8—222no—
344#121—114no—
345#121—222no—
346C4×Q8—114no—
347C4×Q8—222no—
348C4×D4—114no—
349C4×D4—222no—
350C4×D4—228no—
351#117—228no—
352#117—444no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22×D1112yes—
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C22⋊C4—221no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—221no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—222no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—114no—
375C2×C42—114no—
376C2×C42—221no—
377C2×C42—222no—
378C2×C42C22×D1111yescharacteristic
379#103—224no—
380#103—224no—
381#102—224no—
382#102—224no—
383#97—22no—
384#97—224no—
385#97—222no—
386#95—222no—
387#95—222no—
388C2×C11#229711yescharacteristic
389C2×C11C2×#41711yescharacteristic
390C2×C11#289611yescharacteristic
391C2×C11#318011yescharacteristic
392C2×C11#318011yescharacteristic
393C2×C11#318111yescharacteristic
394C2×C11#318111yescharacteristic
395D11—24no—
396D11—82no—
397C24—111no—
398C24—221no—
399C2×Q8—112no—
400C2×Q8—221no—
401C2×Q8—222no—
402C2×Q8—222no—
403C2×D4—112no—
404C2×D4—224no—
405C2×D4—221no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—442no—
409C2×D4—442no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—114no—
417C22×C4—112no—
418C22×C4—112no—
419C22×C4—114no—
420C22×C4—224no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—221no—
426C22×C4—222no—
427C22×C4—441no—
428C22×C4—441no—
429C22×C4—442no—
430C22×C4—442no—
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433C22×C4C23×D1111yescharacteristic
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—114no—
437C2×C8—2216no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8#434314yes—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—42no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4—222no—
452C4⋊C4—222no—
453C4⋊C4—442no—
454C4⋊C4—442no—
455C4⋊C4C2×C4×D1112yes—
456C4⋊C4C2×C4×D1112yes—
457C22⋊C4—224no—
458C22⋊C4—224no—
459C22⋊C4—224no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C22⋊C4—444no—
463C42—114no—
464C42—114no—
465C42—112no—
466C42—112no—
467C42—224no—
468C42—444no—
469C42C2×C4×D1112yes—
470C42D4×D1112yes—
471C11#2140611yescharacteristic, complemented, Sylow
472C23—112no—
473C23—112no—
474C23—112no—
475C23—221no—
476C23—221no—
477C23—221no—
478C23—221no—
479C23—222no—
480C23—441no—
481C23—441no—
482C23—441no—
483C23—441no—
484C23—441no—
485C23—441no—
486C23C2×D4×D1111yescharacteristic
487Q8—224no—
488Q8—442no—
489D4—224no—
490D4—448no—
491D4—442no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—112no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—228no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—222no—
518C2×C4—444no—
519C2×C4—448no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4C22⋊C4×D1112yes—
526C2×C4C22⋊C4×D1112yes—
527C2×C4C22×C4×D1111yescharacteristic
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4C2×#434312yes—
530C2×C4#41×D1112yes—
531C8—24no—
532C8—224no—
533C22—114no—
534C22—222no—
535C22—222no—
536C22—222no—
537C22—222no—
538C22—222no—
539C22—222no—
540C22—442no—
541C22—442no—
542C22—442no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22C2×C22⋊C4×D1111yescharacteristic
548C22#1062319911yescharacteristic
549C22#1062325611yescharacteristic
550C22D11×AGL(1,ℤ/8)11yescharacteristic
551C22#1062330411yescharacteristic
552C22D11×#13711yescharacteristic
553C22#1062330811yescharacteristic
554C4—22no—
555C4—22no—
556C4—42no—
557C4—42no—
558C4—82no—
559C4—222no—
560C4—222no—
561C4—222no—
562C4—442no—
563C4—882no—
564C4C4×#434312yes—
565C4#1062315812yes—
566C2—224no—
567C2—882no—
568C2#1307110511yescharacteristic
569C2D11×#41711yescharacteristic
570C2#1307713211yescharacteristic
571C2#1307931311yescharacteristic
572C2#1307931611yescharacteristic
573C2#1307932411yescharacteristic
574C2#1307932711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1992C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
cosocleC22×C4×C11C24
hypercenter#1992D11
hypocenterC11#21406
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
2. C2×D11×#97C2semidirect
3. #13071021C2semidirect
4. #13069586C2semidirect
5. #13069432C2semidirect
6. #13069430C2semidirect
8. #13069038C2semidirect
9. #13068445C2semidirect
10. #13068440C2semidirect
11. C11×#1992C2semidirect
15. #10623222C4semidirect
189. #1992D11semidirect
471. C11#21406semidirect

Maximal subgroups

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

subgroupindex
C2×#106232222
C2×D11×#972
#130710212
#130695862
#130694322
#130694302
#130690432
#130690382
#130684452
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