Finite Group Databasebeta

← #14804259

Subgroups — #14804259

Order 2816.

1118 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×#10622306C211yesmaximal, characteristic, complemented
2C2×#10622400C212yesmaximal, complemented
3C2×#10622628C211yesmaximal, characteristic
4#13073608C211yesmaximal, characteristic, complemented
5#13071680C211yesmaximal, characteristic, complemented
6#13069935C212yesmaximal, complemented
7#13069695C212yesmaximal, complemented
8#13069539C211yesmaximal, characteristic, complemented
9#13069334C211yesmaximal, characteristic, complemented
10#13068951C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66989C2212yes—
14C22×#4323C2212yes—
15C22×#4314C2212yes—
16C22×#4314C2212yes—
17C2×#66946C2212yes—
18C2×#66927C2211yescharacteristic
19C2×C4×D44—21no—
20C2×#66922C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622825—21no—
26#10622825—21no—
27C2×Dic11⋊C8C2212yes—
28#10622628—24no—
29#10622601C2212yes—
30#10622587C2212yes—
31C2×#66874C2212yes—
32C2×#66874C2212yes—
33C2×#66873C2212yes—
34#10622566—22no—
35#10622552—21no—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622400—28no—
39#10622306—24no—
40#10622278—22no—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43#10622188C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×D44—21no—
47C22×D44—21no—
48C22×D44C2312yes—
49C22×C4×D11—22no—
50C22×Dic22C2312yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63#66989—24no—
64#66989—42no—
65C2×#4323—24no—
66C2×#4323—24no—
67C2×#4323—42no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4×Dic11C2312yes—
76C22×C11⋊C8C2312yes—
77C2×#4314—24no—
78C2×#4314—24no—
79C2×#4314—24no—
80C2×#4314—24no—
81C2×#4314—42no—
82C2×#4314—42no—
83#66946—24no—
84#66946—42no—
85#66927—22no—
86#66927D414yes—
87C4×D44—44no—
88#66922—22no—
89#66922—22no—
90C11×#102—22no—
91C11×#102D414yescomplemented
92C4×C8×C11—22no—
93C11×#95—21no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95D412yes—
97Dic11⋊C8—24no—
98#66874—24no—
99#66874—42no—
100#66873—24no—
101C4⋊(C11⋊C8)—22no—
102#25367—111nomaximal, Sylow
103C24×C11—21no—
104C23×D11—22no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11C2×D412yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—22no—
121C22×Dic11C2×D412yes—
122C22×Dic11C2×D412yes—
123C2×D44—24no—
124C2×D44—24no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—42no—
131C2×D44—42no—
132C2×D44—81no—
133C2×D44—81no—
134C2×D44C2×D414yes—
135C2×C4×D11—44no—
136C2×C4×D11—44no—
137C2×C4×D11—82no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11C2×D412yes—
149C2×C8×C11#4112yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C2×D412yes—
156C11×C22⋊C4—42no—
157C42×C11—42no—
158C42×C11C2×D412yes—
159C42×C11#4112yes—
160C22⋊Dic11—44no—
161C22⋊Dic11—44no—
162#4323—48no—
163(C2×D11)⋊C4—44no—
164(C2×D11)⋊C4—44no—
165(C2×D11)⋊C4—82no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—42no—
169C4⋊Dic11—42no—
170C4×Dic11—22no—
171C4×Dic11—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175#4314—48no—
176#4314—48no—
177C2×#492—111no—
178C2×#463—112no—
179C2×#459—111no—
180#2547—111no—
181#2366—111no—
182#2055—112no—
183#2012—112no—
184#1981—111no—
185#1939—111no—
186#1877—112no—
187C4×#102D1111yescharacteristic, complemented
188C23×C11—22no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11C22×D411yescharacteristic
196C22×D11—24no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11—41no—
206D4×C11—41no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—84no—
219C2×C4×C11#12112yes—
220C2×C4×C11#12112yes—
221C2×C4×C11#13512yes—
222C2×C4×C11AGL(1,ℤ/8)12yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238D44—24no—
239D44—24no—
240D44—42no—
241D44—42no—
242D44—48no—
243D44—84no—
244C4×D11—88no—
245Dic22—42no—
246Dic22—42no—
247Dic22—42no—
248Dic22—42no—
249C8×C11—22no—
250C8×C11—22no—
251C11⋊C8—42no—
252C22×SD16—112no—
253C22×SD16—112no—
254C22×D8—112no—
255C2×C4⋊Q8—111no—
256C2×#127—111no—
257C2×#124—112no—
258C2×C4×D4—112no—
259C2×C4×D4—221no—
260C2×C4×D4C2×D1111yescharacteristic
261#492—224no—
262#463—228no—
263#459—224no—
264C2×C4⋊C8—112no—
265C2×C4⋊C8—111no—
266C2×#103—112no—
267C2×#103—112no—
268C2×#102—112no—
269C2×#102C2×D1111yescharacteristic
270C2×#102C2×D1111yescharacteristic
271C2×C4×C8C2×D1111yescharacteristic
272#397—222no—
273#391—112no—
274#390—112no—
275#390—221no—
276#386—222no—
277#380—221no—
278#380—221no—
279C4×C4⋊C4—111no—
280C4×C4⋊C4C2×D1111yescharacteristic
281#340C2×D1111yescharacteristic
282#340C2×D1111yescharacteristic
283#336—112no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11C2×#12111yescharacteristic
292C22×C11D4211yescharacteristic
293C22×C11#55011yescharacteristic
294C22×C11C2×#13511yescharacteristic
295C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C11#57711yescharacteristic
297C22×C11#57711yescharacteristic
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—44no—
301C2×D11—82no—
302C2×D11—82no—
303C2×D11—82no—
304C2×D11—82no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—81no—
308C4×C11—81no—
309C4×C11#46314yescomplemented
310C4×C11#53211yescharacteristic
311C4×C11#54011yescharacteristic
312C4×C11D4211yescharacteristic
313C4×C11#54611yescharacteristic
314Dic11—42no—
315Dic11—42no—
316Dic11—82no—
317C22×Q8—112no—
318C22×D4—112no—
319C22×D4—221no—
320C22×D4—221no—
321C22×D4C22×D1111yescharacteristic
322C23×C4—21no—
323C23×C4—222no—
324C2×SD16—224no—
325C2×SD16—224no—
326C2×SD16—224no—
327C2×SD16—224no—
328C2×SD16—442no—
329C2×SD16—442no—
330C2×D8—224no—
331C2×D8—224no—
332C2×D8—442no—
333C22×C8—112no—
334C22×C8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C4⋊Q8—222no—
337C4⋊Q8—222no—
338#127—114no—
339#127—222no—
340#124—224no—
341#124—442no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—224no—
345C4×D4—444no—
346C4×D4—442no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—21no—
361C2×C42—112no—
362C2×C42C22×D1111yescharacteristic
363C4⋊C8—224no—
364C4⋊C8—222no—
365#103—224no—
366#103—442no—
367#102—22no—
368#102—224no—
369#102D4414yescomplemented
370C4×C8—22no—
371#95—21no—
372#95—112no—
373#95—222no—
374#95—222no—
375C2×C11—82no—
376C2×C11#242811yescharacteristic
377C2×C11C2×#46311yescharacteristic
378C2×C11#304211yescharacteristic
379C2×C11#327211yescharacteristic
380C2×C11#328411yescharacteristic
381C2×C11#339411yescharacteristic
382C2×C11#339711yescharacteristic
383D11—84no—
384C24—21no—
385C24—222no—
386C2×Q8—222no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—222no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—114no—
398C2×D4—224no—
399C2×D4—224no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—442no—
406C2×D4—442no—
407C2×D4—881no—
408C2×D4—881no—
409C2×D4C2×D4412yes—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—222no—
419C22×C4—444no—
420C22×C4—444no—
421C22×C4—882no—
422C22×C4D4×D1111yescharacteristic
423C22×C4D4×D1111yescharacteristic
424C22×C4C23×D1111yescharacteristic
425SD16—448no—
426SD16—448no—
427D8—448no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8C2×D4412yes—
436C2×C8#433912yes—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—442no—
445C4⋊C4—442no—
446C4⋊C4C2×D4412yes—
447C22⋊C4—42no—
448C22⋊C4—444no—
449C22⋊C4—444no—
450C22⋊C4—444no—
451C22⋊C4—444no—
452C22⋊C4—882no—
453C42—42no—
454C42—222no—
455C42—222no—
456C42#433912yes—
457C42D4×D1112yes—
458C11#2536711yescharacteristic, complemented, Sylow
459C23—22no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—224no—
467C23—442no—
468C23—442no—
469C23—442no—
470C23—442no—
471C23—442no—
472C23—442no—
473C23C2×D4×D1111yescharacteristic
474Q8—442no—
475Q8—442no—
476Q8—442no—
477Q8—442no—
478D4—22no—
479D4—22no—
480D4—41no—
481D4—41no—
482D4—224no—
483D4—224no—
484D4—442no—
485D4—442no—
486D4—448no—
487D4—884no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—84no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—888no—
510C2×C4#6693712yes—
511C2×C4#6693712yes—
512C2×C4#6696412yes—
513C2×C4#6696912yes—
514C2×C4C22×D4411yescharacteristic
515C2×C4C2×#433911yescharacteristic
516C2×C4C2×#433911yescharacteristic
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4#6704211yescharacteristic
519C2×C4#6704211yescharacteristic
520C8—22no—
521C8—22no—
522C8—442no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—444no—
531C22—444no—
532C22—444no—
533C22—882no—
534C22—882no—
535C22—882no—
536C22—882no—
537C22C2×#6693711yescharacteristic
538C22D4×D4411yescharacteristic
539C22#1062308411yescharacteristic
540C22C2×#6696411yescharacteristic
541C22C2×#6696911yescharacteristic
542C22#1062330111yescharacteristic
543C22#1062330111yescharacteristic
544C4—22no—
545C4—42no—
546C4—81no—
547C4—81no—
548C4—442no—
549C4—442no—
550C4—882no—
551C4#1062240014yescomplemented
552C4#1062300811yescharacteristic
553C4#1062306611yescharacteristic
554C4D4×D4411yescharacteristic
555C4#1062308111yescharacteristic
556C2—82no—
557C2—884no—
558C2#1307220411yescharacteristic
559C2C2×#1062240011yescharacteristic
560C2#1307813111yescharacteristic
561C2#1308021711yescharacteristic
562C2#1308034711yescharacteristic
563C2#1308161011yescharacteristic
564C2#1308163411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenterC4×#102D11
hypocenterC11#25367
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. C2×#10622306C2semidirect
2. C2×#10622400C2semidirect
4. #13073608C2semidirect
5. #13071680C2semidirect
6. #13069935C2semidirect
7. #13069695C2semidirect
8. #13069539C2semidirect
9. #13069334C2semidirect
10. #13068951C2semidirect
11. C4×C11×#102C2semidirect
91. C11×#102D4semidirect
187. C4×#102D11semidirect
309. C4×C11#463semidirect
369. #102D44semidirect
458. C11#25367semidirect
551. C4#10622400semidirect

Maximal subgroups

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

subgroupindex
C2×#106223062
C2×#106224002
C2×#106226282
#130736082
#130716802
#130699352
#130696952
#130695392
#130693342
#130689512
C4×C11×#1022
#2536711