Finite Group Databasebeta

← #14804261

Subgroups — #14804261

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×#10622689C211yesmaximal, characteristic, complemented
2C2×#10622766C212yesmaximal, complemented
3#13073608C211yesmaximal, characteristic, complemented
4#13071681C211yesmaximal, characteristic, complemented
5#13069932C212yesmaximal, complemented
6#13069691C212yesmaximal, complemented
7#13069538C211yesmaximal, characteristic, complemented
8#13069332C211yesmaximal, characteristic, complemented
9#13068948C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×C11×#459C211yesmaximal, characteristic
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66989C2212yes—
16C2×D4×Dic11—21no—
17C2×D4×Dic11C2212yes—
18C22×#4324C2212yes—
19C22×#4324C2212yes—
20C2×#66922C2211yescharacteristic
21C11×#459—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2212yes—
24#10622834—21no—
25#10622834C2212yes—
26#10622833—22no—
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622825—21no—
30#10622825—21no—
31#10622766—28no—
32C2×#66880C2212yes—
33C2×#66880C2212yes—
34C2×Dic11⋊C8C2212yes—
35#10622689—24no—
36#10622587C2212yes—
37#10622566—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622188C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×Dic11—22no—
50C22×Dic22C2312yes—
51C2×C11×D8—24no—
52C2×C11×D8—24no—
53C2×C11×D8—42no—
54C22×C8×C11C2312yes—
55C11×#127—22no—
56C11×#127D414yes—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67#66989—24no—
68#66989—42no—
69D4×Dic11—24no—
70D4×Dic11—42no—
71D4×Dic11—44no—
72C2×#4324—24no—
73C2×#4324—24no—
74C2×#4324—24no—
75C2×#4324—24no—
76C2×#4324—42no—
77C2×#4324—42no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11D411yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4×Dic11—21no—
85C2×C4×Dic11C2312yes—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88#66922—22no—
89#66922—22no—
90C11×C4⋊C8—22no—
91C11×#102—24no—
92#66896—22no—
93#66896D414yescomplemented
94C11⋊#95—21no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C11⋊#95D412yes—
98#66880—24no—
99#66880—42no—
100Dic11⋊C8—24no—
101C4×C11⋊C8—22no—
102#25367—111nomaximal, Sylow
103C24×C11—21no—
104C24×C11—22no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—81no—
120C2×D4×C11—81no—
121C2×D4×C11C2×D412yes—
122C2×D4×C11C2×D414yes—
123C22×C4×C11—21no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—44no—
134C22×Dic11—44no—
135C22×Dic11—82no—
136C22×Dic11C2×D412yes—
137C22×Dic11C2×D412yes—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C11×D8—48no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C22⋊C4—42no—
151C42×C11C2×D412yes—
152C42×C11#4112yes—
153C22⋊Dic11—44no—
154C22⋊Dic11—44no—
155C22⋊Dic11—44no—
156C22⋊Dic11—44no—
157C22⋊Dic11—82no—
158#4324—48no—
159#4324—48no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—42no—
166C4⋊Dic11—42no—
167C4⋊Dic11C2×D412yes—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C4×Dic11—42no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8C2×D412yes—
176C2×C11⋊C8#4112yes—
177C2×#492—111no—
178C2×#463—112no—
179C2×#459D1111yescharacteristic
180#2547—111no—
181#2366—111no—
182#2055—112no—
183#2012—112no—
184#1981—111no—
185#1939—111no—
186#1877—112no—
187C4×#102—111no—
188C23×C11—24no—
189C23×C11—22no—
190C23×C11—41no—
191C23×C11—42no—
192C23×C11—41no—
193C23×C11—42no—
194C23×C11—41no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—41no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11C22×D411yescharacteristic
203D4×C11—22no—
204D4×C11—24no—
205D4×C11—22no—
206D4×C11—24no—
207D4×C11—42no—
208D4×C11—41no—
209D4×C11—42no—
210D4×C11—41no—
211D4×C11—48no—
212D4×C11—84no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
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—22no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—41no—
241C2×Dic11—42no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—88no—
245Dic22—42no—
246Dic22—42no—
247Dic22—42no—
248Dic22—42no—
249C8×C11—42no—
250C11⋊C8—22no—
251C11⋊C8—22no—
252C22×SD16—112no—
253C22×SD16—112no—
254C22×D8C2×D1112yes—
255C2×C4⋊Q8—111no—
256C2×#127C2×D1111yescharacteristic
257C2×#124—112no—
258C2×C4×D4—112no—
259C2×C4×D4—221no—
260C2×C4×D4C2×D1111yescharacteristic
261#492—224no—
262#463—228no—
263#459—24no—
264C2×C4⋊C8—112no—
265C2×C4⋊C8C2×D1111yescharacteristic
266C2×#103—112no—
267C2×#103—112no—
268C2×#102—111no—
269C2×#102—111no—
270C2×#102C2×D1112yes—
271C2×C4×C8—111no—
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⋊C4—111no—
281#340—111no—
282#340—111no—
283#336—112no—
284C22×C11—42no—
285C22×C11—44no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—44no—
289C22×C11—44no—
290C22×C11—81no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11—81no—
294C22×C11—82no—
295C22×C11—82no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11C2×#12111yescharacteristic
299C22×C11D4211yescharacteristic
300C22×C11#55011yescharacteristic
301C22×C11C2×#13511yescharacteristic
302C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C11#57711yescharacteristic
304C22×C11#57711yescharacteristic
305C4×C11—22no—
306C4×C11—81no—
307C4×C11#46314yescomplemented
308C4×C11#53211yescharacteristic
309C4×C11#54011yescharacteristic
310C4×C11D4211yescharacteristic
311C4×C11#54611yescharacteristic
312Dic11—42no—
313Dic11—42no—
314Dic11—42no—
315Dic11—81no—
316Dic11—82no—
317C22×Q8—112no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4C22×D1111yescharacteristic
321C22×D4C22×D1112yes—
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—24no—
331C2×D8—24no—
332C2×D8—42no—
333C22×C8—111no—
334C22×C8—111no—
335C22×C8C22×D1112yes—
336C4⋊Q8—222no—
337C4⋊Q8—222no—
338#127—22no—
339#127C22⋊D1114yes—
340#124—224no—
341#124—442no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—224no—
345C4×D4—442no—
346C4×D4—444no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—111no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
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—112no—
361C2×C42—221no—
362C2×C42C22×D1111yescharacteristic
363C4⋊C8—22no—
364C4⋊C8—224no—
365#103—224no—
366#103—442no—
367#102—24no—
368#102—114no—
369#102—222no—
370C4×C8—222no—
371#95—112no—
372#95—222no—
373#95—222no—
374#95—221no—
375C2×C11—82no—
376C2×C11—84no—
377C2×C11#242811yescharacteristic
378C2×C11C2×#46311yescharacteristic
379C2×C11#304211yescharacteristic
380C2×C11#327211yescharacteristic
381C2×C11#328411yescharacteristic
382C2×C11#339411yescharacteristic
383C2×C11#339711yescharacteristic
384C24—21no—
385C24—22no—
386C2×Q8—222no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—222no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—81no—
407C2×D4—81no—
408C2×D4D4×D1112yes—
409C2×D4C2×C22⋊D1114yes—
410C22×C4—21no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—221no—
417C22×C4—222no—
418C22×C4—221no—
419C22×C4—444no—
420C22×C4—444no—
421C22×C4—882no—
422C22×C4D4×D1111yescharacteristic
423C22×C4D4×D1111yescharacteristic
424C22×C4C23×D1111yescharacteristic
425SD16—448no—
426SD16—448no—
427D8—48no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—112no—
432C2×C8—112no—
433C2×C8—221no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—221no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—112no—
440C4⋊C4—222no—
441C4⋊C4—222no—
442C4⋊C4—221no—
443C4⋊C4—221no—
444C4⋊C4—221no—
445C4⋊C4—442no—
446C4⋊C4—442no—
447C22⋊C4—42no—
448C22⋊C4—444no—
449C22⋊C4—444no—
450C22⋊C4—444no—
451C22⋊C4—444no—
452C22⋊C4—882no—
453C42—222no—
454C42—222no—
455C42—442no—
456C42#434112yes—
457C42C2×C22⋊D1112yes—
458C11#2536711yescharacteristic, complemented, Sylow
459C23—24no—
460C23—22no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—42no—
472C23—42no—
473C23C2×D4×D1111yescharacteristic
474Q8—442no—
475Q8—442no—
476Q8—442no—
477Q8—442no—
478D4—22no—
479D4—24no—
480D4—24no—
481D4—22no—
482D4—48no—
483D4—41no—
484D4—42no—
485D4—41no—
486D4—42no—
487D4—84no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—84no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—442no—
506C2×C4—441no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—888no—
510C2×C4#6696412yes—
511C2×C4#6696512yes—
512C2×C4#6699212yes—
513C2×C4#6699212yes—
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×#434111yescharacteristic
516C2×C4#6703711yescharacteristic
517C2×C4#41×D1111yescharacteristic
518C2×C4#6704211yescharacteristic
519C2×C4C22×C22⋊D1111yescharacteristic
520C8—42no—
521C8—222no—
522C8—222no—
523C22—44no—
524C22—42no—
525C22—42no—
526C22—44no—
527C22—44no—
528C22—42no—
529C22—81no—
530C22—82no—
531C22—81no—
532C22—82no—
533C22—82no—
534C22—81no—
535C22—81no—
536C22—82no—
537C22#1062313011yescharacteristic
538C22#1062314011yescharacteristic
539C22C2×#6696411yescharacteristic
540C22C2×#6696511yescharacteristic
541C22#1062330611yescharacteristic
542C22#1062330611yescharacteristic
543C22C2×#6699211yescharacteristic
544C4—22no—
545C4—81no—
546C4—442no—
547C4—442no—
548C4—442no—
549C4—881no—
550C4—882no—
551C4#1062276614yescomplemented
552C4#1062312711yescharacteristic
553C4#1062315011yescharacteristic
554C4D4×C22⋊D1111yescharacteristic
555C4#1062336011yescharacteristic
556C2—84no—
557C2—82no—
558C2#1307220611yescharacteristic
559C2C2×#1062276611yescharacteristic
560C2#1307813011yescharacteristic
561C2#1308021111yescharacteristic
562C2#1308034911yescharacteristic
563C2#1308161611yescharacteristic
564C2#1308164011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11#25367
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10622689C2semidirect
2. C2×#10622766C2semidirect
3. #13073608C2semidirect
4. #13071681C2semidirect
5. #13069932C2semidirect
6. #13069691C2semidirect
7. #13069538C2semidirect
8. #13069332C2semidirect
9. #13068948C2semidirect
10. C4×#66896C2semidirect
93. #66896D4semidirect
307. C4×C11#463semidirect
458. C11#25367semidirect
551. C4#10622766semidirect

Maximal subgroups

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

subgroupindex
C2×#106226892
C2×#106227662
#130736082
#130716812
#130699322
#130696912
#130695382
#130693322
#130689482
C4×#668962
C2×C11×#4592
#2536711