Finite Group Databasebeta

← #14807090

Subgroups — #14807090

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic, complemented
3C2×#10622667C211yesmaximal, characteristic, complemented
4#13069624C212yesmaximal, complemented
5#13069619C212yesmaximal, complemented
6#13069564C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068939C212yesmaximal, complemented
9#13068929C212yesmaximal, 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×#66989—21no—
18C22×#4324C2211yescharacteristic
19C2×#66979C2212yes—
20C2×#66977C2212yes—
21#10623073—24no—
22#10623073—24no—
23C2×#66940—21no—
24C2×#66932—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—
50C22×Dic22—21no—
51C22×Dic22C2311yescharacteristic
52C11×#124—22no—
53C11×#124—22no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—42no—
56C11×#121—24no—
57C11×#121—42no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×#4326—22no—
73C2×#4326—42no—
74#66989—28no—
75C2×#4324—22no—
76C2×#4324—42no—
77#66979—24no—
78#66979—24no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2312yes—
82#66977—24no—
83#66977—24no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—22no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—22no—
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91#66940—28no—
92#66932—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#25580—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—22no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—42no—
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—21no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C2×Dic22—24no—
139C2×Dic22—21no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—44no—
143C2×Dic22C2×D412yes—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—44no—
147C11×C4⋊C4#4114yes—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—42no—
152C11×C22⋊C4—42no—
153C42×C11—81no—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156C22⋊Dic11—28no—
157C22⋊Dic11—28no—
158#4326—44no—
159#4324—44no—
160C4⋊Dic11—24no—
161C4⋊Dic11—21no—
162C4⋊Dic11—22no—
163C4⋊Dic11C2×D412yes—
164C4⋊Dic11C2×D414yes—
165Dic11⋊C4—28no—
166Dic11⋊C4—24no—
167C4×Dic11—28no—
168C4×Dic11—24no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×#556—111no—
177C2×#489—111no—
178C2×#464—111no—
179#2540D1111yescharacteristic
180#2001—112no—
181#2000—112no—
182#1987—111no—
183#1955—111no—
184#1875—112no—
185#1873—112no—
186#1763—111no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11C22×D411yescharacteristic
200Q8×C11—41no—
201Q8×C11—41no—
202Q8×C11—42no—
203D4×C11—44no—
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—42no—
207D4×C11—88no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11#12012yes—
224C2×C4×C11#12012yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4112yes—
228C2×C4×C11H(5,𝔽2)12yes—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—24no—
232C2×Dic11—42no—
233C2×Dic11—44no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236Dic22—22no—
237Dic22—22no—
238Dic22—48no—
239Dic22—42no—
240C11⋊C8—41no—
241C11⋊C8—41no—
242C11⋊C8—42no—
243C22×Q16—111no—
244C22×SD16—111no—
245#556—224no—
246#556—224no—
247C2×C4⋊Q8—111no—
248C2×#126—222no—
249C2×#124—221no—
250C2×#124C2×D1111yescharacteristic
251C2×C22⋊Q8—112no—
252C2×C22⋊Q8C2×D1112yes—
253C2×#121C2×D1112yes—
254C2×C4×Q8—111no—
255C2×C4×Q8—221no—
256C2×C4×D4C2×D1111yescharacteristic
257C2×#117—112no—
258#489—224no—
259#464—224no—
260C2×C4⋊C8—111no—
261C2×#103—112no—
262C2×#103—111no—
263C2×#103—112no—
264C2×#102—112no—
265C2×#102—111no—
266C2×C22⋊C8—112no—
267C2×C22⋊C8—112no—
268C2×#97—111no—
269#399—21no—
270#392—21no—
271#390—22no—
272C4×C4⋊C4C2×D1111yescharacteristic
273#340—112no—
274#340—112no—
275#340—112no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11C2×#12011yescharacteristic
289C22×C11#54612yes—
290C22×C11#57512yes—
291C22×C11#57711yescharacteristic
292C22×C11#57811yescharacteristic
293C4×C11—22no—
294C4×C11—22no—
295C4×C11—42no—
296C4×C11—44no—
297C4×C11—81no—
298C4×C11#53211yescharacteristic
299C4×C11#53511yescharacteristic
300C4×C11#55012yes—
301Dic11—42no—
302Dic11—44no—
303Dic11—42no—
304C22×Q8—111no—
305C22×Q8—221no—
306C22×Q8C22×D1111yescharacteristic
307C22×D4—22no—
308C22×D4C22⋊D1111yescharacteristic
309C22×D4C22×D1111yescharacteristic
310C23×C4C22×D1112yes—
311C2×Q16—222no—
312C2×Q16—442no—
313C2×SD16—222no—
314C2×SD16—442no—
315C22×C8—111no—
316C22×C8—111no—
317C22×C8—112no—
318C4⋊Q8—114no—
319C4⋊Q8—222no—
320#126—2216no—
321#124—22no—
322#124—22no—
323#124—228no—
324C22⋊Q8—24no—
325C22⋊Q8—42no—
326C22⋊Q8—224no—
327C22⋊Q8—224no—
328#121—24no—
329#121—42no—
330C4×Q8—114no—
331C4×Q8—228no—
332C4×Q8—222no—
333C4×D4—22no—
334C4×D4—22no—
335#117—224no—
336#117—224no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4C22⋊D1111yescharacteristic
344C2×C4⋊C4C22×D1112yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—222no—
351C2×C22⋊C4C22⋊D1112yes—
352C2×C42—21no—
353C2×C42—222no—
354C2×C42—221no—
355C2×C42C22×D1111yescharacteristic
356C4⋊C8—222no—
357#103—222no—
358#103—224no—
359#103—224no—
360#102—222no—
361#102—224no—
362C22⋊C8—442no—
363C22⋊C8—442no—
364#97—222no—
365#95—21no—
366C2×C11—82no—
367C2×C11—161no—
368C2×C11#243111yescharacteristic
369C2×C11#300511yescharacteristic
370C2×C11#301311yescharacteristic
371C2×C11#331112yes—
372C2×C11#331312yes—
373C24—21no—
374C24C2×C22⋊D1112yes—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—112no—
380C2×Q8—224no—
381C2×Q8—221no—
382C2×Q8—222no—
383C2×Q8—222no—
384C2×Q8—444no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—42no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—82no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4—221no—
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—444no—
410SD16—444no—
411C2×C8—222no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—222no—
417C2×C8—222no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—44no—
421C4⋊C4—112no—
422C4⋊C4—114no—
423C4⋊C4—228no—
424C4⋊C4—224no—
425C4⋊C4—224no—
426C4⋊C4—221no—
427C4⋊C4—222no—
428C4⋊C4#434114yes—
429C22⋊C4—24no—
430C22⋊C4—44no—
431C22⋊C4—44no—
432C22⋊C4—42no—
433C22⋊C4—42no—
434C22⋊C4—228no—
435C22⋊C4—228no—
436C42—81no—
437C42—228no—
438C42—224no—
439C42D4×D1112yes—
440C42D4×D1112yes—
441C11#2558011yescharacteristic, complemented, Sylow
442C23—22no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—41no—
450C23—42no—
451C23—42no—
452C23—41no—
453C23—41no—
454C23C22×C22⋊D1111yescharacteristic
455Q8—41no—
456Q8—41no—
457Q8—42no—
458Q8—222no—
459Q8—222no—
460Q8—448no—
461Q8—442no—
462D4—44no—
463D4—41no—
464D4—41no—
465D4—42no—
466D4—88no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—222no—
483C2×C4—224no—
484C2×C4—222no—
485C2×C4—442no—
486C2×C4—444no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4#6699012yes—
490C2×C4#6699012yes—
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4C2×D4×D1111yescharacteristic
493C2×C4C2×#434112yes—
494C2×C4#6703712yes—
495C8—441no—
496C8—441no—
497C8—442no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—82no—
506C22—81no—
507C22—81no—
508C22—82no—
509C22—81no—
510C22C2×#6699011yescharacteristic
511C22#1062333712yes—
512C22#1062335312yes—
513C22#1062336711yescharacteristic
514C22#1062336911yescharacteristic
515C4—22no—
516C4—22no—
517C4—44no—
518C4—42no—
519C4—81no—
520C4—444no—
521C4—442no—
522C4—442no—
523C4#1062324611yescharacteristic
524C4#1062324711yescharacteristic
525C4#1062324912yes—
526C2—82no—
527C2—161no—
528C2#1307223211yescharacteristic
529C2#1307785611yescharacteristic
530C2#1307792811yescharacteristic
531C2#1308065212yes—
532C2#1308068212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2540C2
socleC23×C11C22×D4
hypercenter#2540D11
hypocenterC11#25580
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×#10623073C2semidirect
2. C2×#10622668C2semidirect
3. C2×#10622667C2semidirect
4. #13069624C2semidirect
5. #13069619C2semidirect
6. #13069564C2semidirect
7. #13069415C2semidirect
8. #13068939C2semidirect
9. #13068929C2semidirect
10. #13068449C2semidirect
94. #66922D4semidirect
96. C4×Dic22D4semidirect
441. C11#25580semidirect

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×#106226682
C2×#106226672
#130696242
#130696192
#130695642
#130694152
#130689392
#130689292
#130684492
C11×#25402
#2558011