Finite Group Databasebeta

← #14804253

Subgroups — #14804253

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×#10622629C212yesmaximal, complemented
3C2×#10622685C211yesmaximal, characteristic
4#13073611C211yesmaximal, characteristic, complemented
5#13069933C212yesmaximal, complemented
6#13069692C212yesmaximal, complemented
7#13069539C211yesmaximal, characteristic, complemented
8#13069335C211yesmaximal, characteristic, complemented
9#13068950C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#2366C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2212yes—
15C22×#4324C2212yes—
16C22×#4324C2212yes—
17C22×#4323C2212yes—
18C2×#66928C2212yes—
19C2×C4×D44C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C11×#390—21no—
22C11×#390C2212yes—
23C11×#386—22no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66896C2212yes—
27#10622689—24no—
28#10622685—24no—
29#10622629—28no—
30#10622600—21no—
31#10622600—21no—
32C2×#66874C2212yes—
33C2×#66874C2212yes—
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36#10622542C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2212yes—
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622287—22no—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43#10622162C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C23×C4×C11—22no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×Dic22C2312yes—
51C11×#127—22no—
52C11×#127D414yes—
53C4×D4×C11—24no—
54C4×D4×C11—42no—
55C4×D4×C11—44no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11—21no—
64C2×C42×C11C2312yes—
65C2×C42×C11C2311yescharacteristic
66C2×#4324—24no—
67C2×#4324—24no—
68C2×#4324—24no—
69C2×#4324—24no—
70C2×#4324—42no—
71C2×#4324—42no—
72C2×#4323—24no—
73C2×#4323—24no—
74C2×#4323—42no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66928—24no—
85#66928—42no—
86C4×D44—22no—
87C4×D44—22no—
88#66922—22no—
89#66922—22no—
90C11×#95—21no—
91C11×#95D412yes—
92#66896—24no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95#66874—24no—
96#66874—42no—
97#66873—22no—
98#66873D414yescomplemented
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)—24no—
101C4×C11⋊C8—22no—
102#25367—111nomaximal, Sylow
103C24×C11—22no—
104C23×D11—21no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11—81no—
115C2×D4×C11—81no—
116C2×D4×C11C2×D414yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—44no—
120C22×C4×C11—44no—
121C22×C4×C11—82no—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—22no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44C2×D412yes—
135C2×C4×D11—42no—
136C2×C4×D11—42no—
137C2×C4×D11—42no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4C2×D412yes—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—82no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11—42no—
156C42×C11C2×D412yes—
157C42×C11#4112yes—
158#4324—48no—
159#4324—48no—
160#4323—48no—
161(C2×D11)⋊C4—44no—
162(C2×D11)⋊C4—44no—
163(C2×D11)⋊C4—42no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—42no—
167C4⋊Dic11—42no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8C2×D412yes—
176C2×C11⋊C8#4112yes—
177C2×#492—111no—
178C2×#463—112no—
179C2×#459—111no—
180#2547—111no—
181#2366D1111yescharacteristic, complemented
182#2055—112no—
183#2012—112no—
184#1981—111no—
185#1939—111no—
186#1877—112no—
187C4×#102—111no—
188C23×C11—24no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11C22×D411yescharacteristic
196C22×D11—22no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—41no—
203D4×C11—24no—
204D4×C11—24no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—48no—
208D4×C11—84no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—88no—
224C2×C4×C11#12112yes—
225C2×C4×C11#12112yes—
226C2×C4×C11#13512yes—
227C2×C4×C11AGL(1,ℤ/8)12yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×Dic11—41no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240D44—22no—
241D44—22no—
242D44—41no—
243D44—41no—
244C4×D11—84no—
245Dic22—42no—
246Dic22—42no—
247Dic22—42no—
248Dic22—42no—
249C11⋊C8—22no—
250C11⋊C8—22no—
251C11⋊C8—42no—
252C22×SD16—112no—
253C22×SD16—112no—
254C22×D8—112no—
255C2×C4⋊Q8—111no—
256C2×#127C2×D1111yescharacteristic
257C2×#124—112no—
258C2×C4×D4—21no—
259C2×C4×D4—111no—
260C2×C4×D4C2×D1112yes—
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—111no—
269C2×#102—112no—
270C2×#102—111no—
271C2×C4×C8—111no—
272#397—222no—
273#391—112no—
274#390—21no—
275#390C2×D1112yes—
276#386—22no—
277#380—221no—
278#380—221no—
279C4×C4⋊C4C2×D1111yescharacteristic
280C4×C4⋊C4C2×D1111yescharacteristic
281#340—111no—
282#340—111no—
283#336—112no—
284C22×C11—44no—
285C22×C11—44no—
286C22×C11—44no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
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—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—81no—
310C4×C11#46314yescomplemented
311C4×C11#53211yescharacteristic
312C4×C11#54011yescharacteristic
313C4×C11D4211yescharacteristic
314C4×C11#54611yescharacteristic
315Dic11—82no—
316Dic11—81no—
317C22×Q8—112no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—111no—
321C22×D4C22×D1112yes—
322C23×C4—22no—
323C23×C4—221no—
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—111no—
334C22×C8—111no—
335C22×C8—112no—
336C4⋊Q8—222no—
337C4⋊Q8—222no—
338#127—22no—
339#127D4414yes—
340#124—224no—
341#124—442no—
342C4×D4—24no—
343C4×D4—42no—
344C4×D4—44no—
345C4×D4—222no—
346C4×D4—222no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4C22⋊D1111yescharacteristic
351C2×C4⋊C4C22⋊D1111yescharacteristic
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—21no—
361C2×C42C22×D1112yes—
362C2×C42C22×D1111yescharacteristic
363C4⋊C8—224no—
364C4⋊C8—222no—
365#103—224no—
366#103—442no—
367#102—114no—
368#102—222no—
369#102—224no—
370C4×C8—222no—
371#95—21no—
372#95—222no—
373#95—222no—
374#95C22⋊D1112yes—
375C2×C11—84no—
376C2×C11#242811yescharacteristic
377C2×C11C2×#46311yescharacteristic
378C2×C11#304211yescharacteristic
379C2×C11#327211yescharacteristic
380C2×C11#328411yescharacteristic
381C2×C11#339411yescharacteristic
382C2×C11#339711yescharacteristic
383D11—82no—
384C24—22no—
385C24—221no—
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—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—81no—
402C2×D4—81no—
403C2×D4—112no—
404C2×D4—221no—
405C2×D4—221no—
406C2×D4—221no—
407C2×D4—221no—
408C2×D4—221no—
409C2×D4C2×D4414yes—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—82no—
415C22×C4—221no—
416C22×C4—222no—
417C22×C4—442no—
418C22×C4—442no—
419C22×C4—442no—
420C22×C4C2×C22⋊D1112yes—
421C22×C4C2×C22⋊D1112yes—
422C22×C4C2×C22⋊D1111yescharacteristic
423C22×C4C2×C22⋊D1111yescharacteristic
424C22×C4C23×D1111yescharacteristic
425SD16—448no—
426SD16—448no—
427D8—448no—
428C2×C8—112no—
429C2×C8—112no—
430C2×C8—221no—
431C2×C8—221no—
432C2×C8—221no—
433C2×C8—221no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—222no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—221no—
443C4⋊C4—221no—
444C4⋊C4—442no—
445C4⋊C4—442no—
446C4⋊C4D4×D1112yes—
447C22⋊C4—44no—
448C22⋊C4—44no—
449C22⋊C4—82no—
450C22⋊C4—444no—
451C22⋊C4—444no—
452C22⋊C4—442no—
453C42—22no—
454C42—22no—
455C42—42no—
456C42C2×D4412yes—
457C42#433912yes—
458C11#2536711yescharacteristic, complemented, Sylow
459C23—24no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—222no—
467C23—441no—
468C23—441no—
469C23—441no—
470C23—441no—
471C23—441no—
472C23—441no—
473C23C22×C22⋊D1111yescharacteristic
474Q8—442no—
475Q8—442no—
476Q8—442no—
477Q8—442no—
478D4—24no—
479D4—24no—
480D4—42no—
481D4—42no—
482D4—48no—
483D4—84no—
484D4—222no—
485D4—222no—
486D4—441no—
487D4—441no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—88no—
503C2×C4—441no—
504C2×C4—442no—
505C2×C4—441no—
506C2×C4—442no—
507C2×C4—441no—
508C2×C4—442no—
509C2×C4—884no—
510C2×C4#6698312yes—
511C2×C4#6698312yes—
512C2×C4#6698512yes—
513C2×C4#6700312yes—
514C2×C4C22×D4411yescharacteristic
515C2×C4C2×#433911yescharacteristic
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4#6703711yescharacteristic
518C2×C4#41×D1111yescharacteristic
519C2×C4#6704211yescharacteristic
520C8—222no—
521C8—222no—
522C8—442no—
523C22—44no—
524C22—44no—
525C22—44no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22C2×#6698311yescharacteristic
538C22C2×#6698511yescharacteristic
539C22D4×C22⋊D1111yescharacteristic
540C22C2×#6700311yescharacteristic
541C22#1062336511yescharacteristic
542C22#1062336711yescharacteristic
543C22#1062336711yescharacteristic
544C4—22no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—81no—
549C4—881no—
550C4—882no—
551C4#1062262914yescomplemented
552C4#1062307911yescharacteristic
553C4D4×D4411yescharacteristic
554C4#1062308511yescharacteristic
555C4#1062309311yescharacteristic
556C2—84no—
557C2—882no—
558C2#1307219811yescharacteristic
559C2C2×#1062262911yescharacteristic
560C2#1307812811yescharacteristic
561C2#1308021211yescharacteristic
562C2#1308034611yescharacteristic
563C2#1308160811yescharacteristic
564C2#1308163211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2366C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenter#2366D11
hypocenterC11#25367
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. C2×#10622689C2semidirect
2. C2×#10622629C2semidirect
4. #13073611C2semidirect
5. #13069933C2semidirect
6. #13069692C2semidirect
7. #13069539C2semidirect
8. #13069335C2semidirect
9. #13068950C2semidirect
10. C4×#66873C2semidirect
11. C11×#2366C2semidirect
98. #66873D4semidirect
181. #2366D11semidirect
310. C4×C11#463semidirect
458. C11#25367semidirect
551. C4#10622629semidirect

Maximal subgroups

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

subgroupindex
C2×#106226892
C2×#106226292
C2×#106226852
#130736112
#130699332
#130696922
#130695392
#130693352
#130689502
C4×#668732
C11×#23662
#2536711