Finite Group Databasebeta

← #14807079

Subgroups — #14807079

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic, complemented
3C2×#10622667C211yesmaximal, characteristic, complemented
4#13069624C212yesmaximal, complemented
5#13069619C212yesmaximal, complemented
6#13069568C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068934C212yesmaximal, complemented
9#13068924C212yesmaximal, complemented
10#13068449C211yesmaximal, characteristic, complemented
11C11×#2540C211yesmaximal, characteristic
12C2×C11×#124C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×C11×#121C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4326C2211yescharacteristic
17C2×D4×Dic11—21no—
18C22×#4324C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C2×#66977C2212yes—
21#10623074—24no—
22#10623074—24no—
23C2×#66943—21no—
24C2×#66931—22no—
25C2×#66922C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#399—21no—
28C11×#392—21no—
29C11×#390—22no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2212yes—
33C2×#66896C2211yescharacteristic
34C2×#66896C2212yes—
35C2×C22⋊(C11⋊C8)C2212yes—
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622668—24no—
38#10622667—24no—
39C2×#66874C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11D411yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×Dic11—22no—
51C22×Dic22—21no—
52C22×Dic22C2311yescharacteristic
53C11×#124—22no—
54C11×#124—22no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—42no—
57C11×#121—24no—
58C11×#121—42no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4D412yes—
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—22no—
72C2×#4326—22no—
73C2×#4326—42no—
74D4×Dic11—28no—
75C2×#4324—22no—
76C2×#4324—42no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—24no—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2312yes—
83#66977—24no—
84#66977—24no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—21no—
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91#66943—28no—
92#66931—216no—
93#66922—22no—
94#66922D414yescomplemented
95C4×Dic22—22no—
96C4×Dic22D414yescomplemented
97C11×#95—21no—
98#66899—22no—
99#66899—24no—
100#66896—22no—
101#66896—24no—
102C22⋊(C11⋊C8)—42no—
103C22⋊(C11⋊C8)—42no—
104#66874—24no—
105C4⋊(C11⋊C8)—22no—
106#66867—22no—
107#25579—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11C2×D412yes—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×D4×C11—24no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—82no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—28no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—82no—
140C22×Dic11—82no—
141C2×Dic22—24no—
142C2×Dic22—21no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—81no—
146C2×Dic22—81no—
147C2×Dic22C2×D412yes—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—44no—
151C11×C4⋊C4#4114yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—44no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—42no—
157C42×C11—81no—
158C42×C11C2×D412yes—
159C42×C11C2×D412yes—
160C22⋊Dic11—28no—
161#4326—44no—
162#4324—44no—
163C4⋊Dic11—28no—
164C4⋊Dic11—24no—
165C4⋊Dic11—21no—
166C4⋊Dic11—22no—
167C4⋊Dic11C2×D412yes—
168C4⋊Dic11C2×D414yes—
169Dic11⋊C4—28no—
170Dic11⋊C4—24no—
171C4×Dic11—24no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×#554—111no—
180C2×#489—111no—
181C2×#464—111no—
182#2540D1111yescharacteristic
183#2001—112no—
184#2000—112no—
185#1988—111no—
186#1955—111no—
187#1874—112no—
188#1872—112no—
189#1763—111no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11#13714yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—41no—
204Q8×C11—41no—
205Q8×C11—42no—
206D4×C11—28no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—42no—
210D4×C11—88no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11#12012yes—
227C2×C4×C11#12012yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4112yes—
231C2×C4×C11H(5,𝔽2)12yes—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—88no—
241Dic22—22no—
242Dic22—22no—
243Dic22—42no—
244Dic22—84no—
245C11⋊C8—41no—
246C11⋊C8—41no—
247C11⋊C8—42no—
248C22×Q16—111no—
249C22×SD16—111no—
250#554—224no—
251#554—224no—
252C2×C4⋊Q8—111no—
253C2×#125—221no—
254C2×#124C2×D1111yescharacteristic
255C2×C22⋊Q8—112no—
256C2×C22⋊Q8—222no—
257C2×C22⋊Q8C2×D1112yes—
258C2×#121C2×D1112yes—
259C2×C4×Q8—111no—
260C2×C4×D4—221no—
261C2×C4×D4C2×D1111yescharacteristic
262C22×C4⋊C4—112no—
263#489—224no—
264#464—224no—
265C2×C4⋊C8—111no—
266C2×#103—112no—
267C2×#103—111no—
268C2×#103—112no—
269C2×#102—112no—
270C2×#102—111no—
271C2×C22⋊C8—112no—
272C2×C22⋊C8—112no—
273C2×#97—111no—
274#399—21no—
275#392—21no—
276#390—22no—
277C4×C4⋊C4C2×D1111yescharacteristic
278#340—112no—
279#340—112no—
280#340—112no—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11C2×#12011yescharacteristic
294C22×C11#54612yes—
295C22×C11C2×#13712yes—
296C22×C11#57611yescharacteristic
297C22×C11#57711yescharacteristic
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—44no—
302C4×C11—81no—
303C4×C11#53211yescharacteristic
304C4×C11#53511yescharacteristic
305C4×C11#55012yes—
306Dic11—42no—
307Dic11—44no—
308Dic11—42no—
309C22×Q8—111no—
310C22×Q8—221no—
311C22×Q8C22×D1111yescharacteristic
312C22×D4—22no—
313C22×D4C22⋊D1111yescharacteristic
314C22×D4C22×D1111yescharacteristic
315C23×C4—222no—
316C23×C4C22×D1112yes—
317C2×Q16—222no—
318C2×Q16—442no—
319C2×SD16—222no—
320C2×SD16—442no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8—112no—
324C4⋊Q8—114no—
325C4⋊Q8—222no—
326#125—228no—
327#124—22no—
328#124—22no—
329C22⋊Q8—24no—
330C22⋊Q8—42no—
331C22⋊Q8—2216no—
332C22⋊Q8—224no—
333C22⋊Q8—224no—
334#121—24no—
335#121—42no—
336C4×Q8—114no—
337C4×Q8—222no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—228no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4C22⋊D1111yescharacteristic
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4C22⋊D1112yes—
358C2×C42—21no—
359C2×C42—221no—
360C2×C42C22×D1111yescharacteristic
361C4⋊C8—222no—
362#103—222no—
363#103—224no—
364#103—224no—
365#102—222no—
366#102—224no—
367C22⋊C8—442no—
368C22⋊C8—442no—
369#97—222no—
370#95—21no—
371C2×C11—44no—
372C2×C11—161no—
373C2×C11#243111yescharacteristic
374C2×C11#300411yescharacteristic
375C2×C11#301211yescharacteristic
376C2×C11#331412yes—
377C2×C11#331612yes—
378C24—21no—
379C24C2×C22⋊D1112yes—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—112no—
385C2×Q8—224no—
386C2×Q8—221no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—881no—
390C2×Q8—881no—
391C2×D4—24no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—44no—
398C2×D4—44no—
399C2×D4—82no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—222no—
411C22×C4—228no—
412C22×C4—882no—
413C22×C4—882no—
414C22×C4C2×C22⋊D1112yes—
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C23×D1111yescharacteristic
418Q16—444no—
419SD16—444no—
420C2×C8—222no—
421C2×C8—221no—
422C2×C8—221no—
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—222no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—44no—
430C4⋊C4—112no—
431C4⋊C4—114no—
432C4⋊C4—228no—
433C4⋊C4—228no—
434C4⋊C4—224no—
435C4⋊C4—224no—
436C4⋊C4—221no—
437C4⋊C4—222no—
438C4⋊C4#434114yes—
439C22⋊C4—24no—
440C22⋊C4—44no—
441C22⋊C4—44no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—228no—
445C42—81no—
446C42—224no—
447C42D4×D1112yes—
448C42D4×D1112yes—
449C11#2557911yescharacteristic, complemented, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—41no—
460C23—41no—
461C23#6700414yes—
462C23C22×C22⋊D1111yescharacteristic
463Q8—41no—
464Q8—41no—
465Q8—42no—
466Q8—222no—
467Q8—222no—
468Q8—442no—
469Q8—884no—
470D4—28no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—88no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—224no—
493C2×C4—442no—
494C2×C4—441no—
495C2×C4—442no—
496C2×C4—441no—
497C2×C4—442no—
498C2×C4—888no—
499C2×C4#6699012yes—
500C2×C4#6699012yes—
501C2×C4C2×D4×D1111yescharacteristic
502C2×C4C2×D4×D1111yescharacteristic
503C2×C4C2×#434112yes—
504C2×C4#6703712yes—
505C8—441no—
506C8—441no—
507C8—442no—
508C22—24no—
509C22—24no—
510C22—24no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—81no—
516C22—81no—
517C22—82no—
518C22—82no—
519C22—81no—
520C22C2×#6699011yescharacteristic
521C22#1062333712yes—
522C22C2×#6700412yes—
523C22#1062336611yescharacteristic
524C22#1062336811yescharacteristic
525C4—22no—
526C4—22no—
527C4—42no—
528C4—44no—
529C4—81no—
530C4—442no—
531C4—442no—
532C4—444no—
533C4#1062324611yescharacteristic
534C4#1062324711yescharacteristic
535C4#1062324912yes—
536C2—44no—
537C2—161no—
538C2#1307223211yescharacteristic
539C2#1307784911yescharacteristic
540C2#1307791711yescharacteristic
541C2#1308069712yes—
542C2#1308072712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2540C2
socleC23×C11C22×D4
hypercenter#2540D11
hypocenterC11#25579
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. C2×#10622668C2semidirect
3. C2×#10622667C2semidirect
4. #13069624C2semidirect
5. #13069619C2semidirect
6. #13069568C2semidirect
7. #13069415C2semidirect
8. #13068934C2semidirect
9. #13068924C2semidirect
10. #13068449C2semidirect
94. #66922D4semidirect
96. C4×Dic22D4semidirect
449. C11#25579semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106226682
C2×#106226672
#130696242
#130696192
#130695682
#130694152
#130689342
#130689242
#130684492
C11×#25402
#2557911