Finite Group Databasebeta

← #14763516

Subgroups — #14763516

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623155C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic, complemented
3#13071019C211yesmaximal, characteristic, complemented
4#13069583C212yesmaximal, complemented
5#13069429C212yesmaximal, complemented
6#13068938C211yesmaximal, characteristic
7#13068936C211yesmaximal, characteristic
8#13068929C211yesmaximal, characteristic, complemented
9#13068629C212yesmaximal, complemented
10#13068625C212yesmaximal, complemented
11C11×#1873C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#67000C2211yescharacteristic
15C2×Q8×Dic11C2211yescharacteristic
16C2×#66983C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19#10623155—24no—
20#10623155C418yescomplemented
21C2×#66951—21no—
22C2×#66946C2211yescharacteristic
23C2×#66945—21no—
24C2×#66943C2211yescharacteristic
25C2×#66939—21no—
26C2×(C22⋊D11)⋊C4—21no—
27C2×C11×#103C2212yes—
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×#66899C2212yes—
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66885C2212yes—
32C2×#66879C2212yes—
33C2×Dic11⋊C8C2212yes—
34#10622590C2212yes—
35#10622589C2212yes—
36C2×#66873C2212yes—
37#10622555—21no—
38#10622555—21no—
39C4×Dic11⋊C4—21no—
40C4×Dic11⋊C4—21no—
41#10622332—24no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C23×Dic11D411yescharacteristic
50C23×Dic11D411yescharacteristic
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C22×C8×C11C2312yes—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8C2×C414yes—
56C11×#117—42no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—21no—
63C2×C22⋊Dic11—21no—
64#67000—22no—
65#67000C2×C414yes—
66Q8×Dic11—22no—
67Q8×Dic11C2×C414yes—
68#66983—22no—
69#66983C2×C414yes—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74#66979—42no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11C2×C414yes—
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D414yes—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2312yes—
91#66951—28no—
92#66946—22no—
93#66946C2×C414yes—
94#66945—28no—
95#66943—22no—
96#66943C2×C414yes—
97#66939—28no—
98(C22⋊D11)⋊C4—28no—
99C11×#103—42no—
100C11×C22⋊C8—22no—
101#66899—42no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C22⋊(C11⋊C8)—22no—
105#66885—42no—
106#66879—24no—
107Dic11⋊C8—24no—
108#66873—42no—
109#21868—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C23×D11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22×C412yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—24no—
126C2×C22⋊D11—44no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—42no—
130C22×Dic11—42no—
131C22×Dic11C22⋊C414yes—
132C22×Dic11C22⋊C414yes—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C2×D44—21no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44C22×C412yes—
141C2×C4×D11—24no—
142C2×C4×D11—44no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4C22×C412yes—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—42no—
153C42×C11—42no—
154C22⋊Dic11—42no—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—24no—
159C4⋊Dic11—24no—
160C4⋊Dic11—24no—
161C4⋊Dic11—21no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11C22×C412yes—
165Dic11⋊C4—24no—
166Dic11⋊C4—44no—
167Dic11⋊C4—44no—
168C4×Dic11—24no—
169C4×Dic11—42no—
170C4×Dic11C22⋊C414yes—
171C4×Dic11C22⋊C414yes—
172C4×Dic11C22×C412yes—
173C4×Dic11C22×C412yes—
174C4×Dic11C2×D412yes—
175C4×Dic11C2×D412yes—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×#529—111no—
180C2×#432—111no—
181#2285—111no—
182#1992—112no—
183#1959—112no—
184#1875—111no—
185#1875—111no—
186#1873—111no—
187#1873D1111yescharacteristic, complemented
188#1805—112no—
189#1804—112no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11C2×C22⋊C412yes—
195C23×C11C22×D411yescharacteristic
196C22×D11—22no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—42no—
200C22×D11—42no—
201Q8×C11—24no—
202Q8×C11—42no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11H(5,𝔽2)12yes—
219C2×C4×C112−1+412yes—
220C22⋊D11—48no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—44no—
227C2×Dic11—44no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11C2×C22⋊C412yes—
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×C22⋊C412yes—
235C2×Dic11C2×C22⋊C412yes—
236D44—24no—
237D44—42no—
238C4×D11—48no—
239C8×C11—42no—
240C11⋊C8—42no—
241#529—118no—
242#529—224no—
243C2×#126—221no—
244C2×#125—111no—
245C2×#124—111no—
246C2×#123—221no—
247C2×C22⋊Q8C2×D1111yescharacteristic
248C2×#121—111no—
249C2×C4×Q8—111no—
250C2×C4×D4—111no—
251C2×C4×D4—221no—
252C2×#117—111no—
253C2×#117—221no—
254C2×#117C2×D1111yescharacteristic
255C22×C42—111no—
256#432—224no—
257C2×C4⋊C8—112no—
258C2×#103—112no—
259C2×#103C2×D1112yes—
260C2×#102—112no—
261C2×#102—112no—
262C2×C22⋊C8—111no—
263C2×C22⋊C8C2×D1111yescharacteristic
264C2×#97—112no—
265#384—112no—
266#382—112no—
267#380—221no—
268#380—221no—
269C4×C4⋊C4—221no—
270C4×C4⋊C4—221no—
271#340—112no—
272#340—112no—
273#340—112no—
274#340C2×D1112yes—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11C22×C22⋊C411yescharacteristic
281C22×C11#53511yescharacteristic
282C22×C11#53611yescharacteristic
283C22×C11#57512yes—
284C22×C11#57512yes—
285C2×D11—42no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—82no—
289C2×D11—82no—
290C4×C11—22no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—82no—
294C4×C11#52012yes—
295C4×C11#53712yes—
296Dic11—22no—
297Dic11—22no—
298Dic11—22no—
299Dic11—22no—
300Dic11—42no—
301Dic11—82no—
302C22×Q8C22×D1111yescharacteristic
303C22×D4—111no—
304C22×D4—221no—
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—221no—
308C23×C4C22×D1111yescharacteristic
309C22×C8—112no—
310C22×C8C22×D1112yes—
311#126—228no—
312#125—114no—
313#125—222no—
314#124—114no—
315#124—222no—
316#123—228no—
317C22⋊Q8—22no—
318C22⋊Q8C4×D1114yes—
319#121—114no—
320#121—222no—
321C4×Q8—114no—
322C4×Q8—222no—
323C4×D4—114no—
324C4×D4—222no—
325C4×D4—228no—
326#117—42no—
327#117—228no—
328#117—442no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4C22×D1112yes—
338C2×C4⋊C4C22×D1111yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—221no—
342C2×C22⋊C4—221no—
343C2×C22⋊C4—221no—
344C2×C22⋊C4—221no—
345C2×C22⋊C4—221no—
346C2×C42—21no—
347C2×C42—114no—
348C2×C42—111no—
349C2×C42—111no—
350C2×C42—114no—
351C2×C42—111no—
352C2×C42—111no—
353C2×C42—221no—
354C2×C42—221no—
355C4⋊C8—224no—
356#103—42no—
357#103—442no—
358#102—442no—
359#102—442no—
360C22⋊C8—22no—
361C22⋊C8—222no—
362#97—224no—
363#95—222no—
364#95—222no—
365C2×C11—42no—
366C2×C11#231111yescharacteristic
367C2×C11#289611yescharacteristic
368C2×C11#289611yescharacteristic
369C2×C11#321912yes—
370C2×C11#324012yes—
371D11—82no—
372C24—221no—
373C24D4×D1111yescharacteristic
374C2×Q8—21no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8C2×C4×D1112yes—
378C2×D4—112no—
379C2×D4—224no—
380C2×D4—221no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—444no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—111no—
390C22×C4—111no—
391C22×C4—111no—
392C22×C4—111no—
393C22×C4—114no—
394C22×C4—114no—
395C22×C4—224no—
396C22×C4—221no—
397C22×C4—222no—
398C22×C4—444no—
399C22×C4—442no—
400C22×C4—442no—
401C22×C4C2×C4×D1112yes—
402C22×C4D4×D1111yescharacteristic
403C22×C4D4×D1112yes—
404C22×C4C23×D1111yescharacteristic
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—222no—
409C2×C8—222no—
410C2×C8—222no—
411C4⋊C4—24no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—112no—
416C4⋊C4—224no—
417C4⋊C4—224no—
418C4⋊C4—224no—
419C4⋊C4—221no—
420C4⋊C4—222no—
421C4⋊C4—222no—
422C4⋊C4—444no—
423C4⋊C4—444no—
424C4⋊C4C2×C4×D1112yes—
425C22⋊C4—24no—
426C22⋊C4—42no—
427C22⋊C4—224no—
428C22⋊C4—224no—
429C22⋊C4—224no—
430C22⋊C4—224no—
431C22⋊C4—442no—
432C42—42no—
433C42—114no—
434C42—114no—
435C42—112no—
436C42—112no—
437C42—112no—
438C42—112no—
439C42—224no—
440C42—442no—
441C11#2186811yescharacteristic, complemented, Sylow
442C23—22no—
443C23—22no—
444C23—21no—
445C23—21no—
446C23—222no—
447C23—442no—
448C23—442no—
449C23—441no—
450C23—441no—
451C23C22⋊C4×D1112yes—
452C23C2×D4×D1111yescharacteristic
453Q8—24no—
454Q8—42no—
455D4—224no—
456D4—448no—
457D4—442no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—112no—
471C2×C4—112no—
472C2×C4—112no—
473C2×C4—112no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—448no—
480C2×C4—444no—
481C2×C4—444no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4C22⋊C4×D1112yes—
487C2×C4C22×C4×D1111yescharacteristic
488C2×C4C2×D4×D1111yescharacteristic
489C2×C4#6703712yes—
490C2×C4#6704312yes—
491C8—42no—
492C8—442no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—42no—
497C22—42no—
498C22—442no—
499C22—442no—
500C22—442no—
501C22—882no—
502C22—882no—
503C22C2×C22⋊C4×D1111yescharacteristic
504C22#1062312311yescharacteristic
505C22#1062317911yescharacteristic
506C22#1062329912yes—
507C22#1062330812yes—
508C4—22no—
509C4—42no—
510C4—42no—
511C4—82no—
512C4—222no—
513C4—222no—
514C4—222no—
515C4—222no—
516C4—442no—
517C4—882no—
518C4#1062307712yes—
519C4#1062312812yes—
520C2—42no—
521C2—882no—
522C2#1307120311yescharacteristic
523C2#1307713111yescharacteristic
524C2#1307713411yescharacteristic
525C2#1307965712yes—
526C2#1307986012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1873D11
hypocenterC11#21868
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. C2×#10622332C2semidirect
3. #13071019C2semidirect
4. #13069583C2semidirect
5. #13069429C2semidirect
8. #13068929C2semidirect
9. #13068629C2semidirect
10. #13068625C2semidirect
11. C11×#1873C2semidirect
20. #10623155C4semidirect
187. #1873D11semidirect
441. C11#21868semidirect

Maximal subgroups

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

subgroupindex
C2×#106231552
C2×#106223322
#130710192
#130695832
#130694292
#130689382
#130689362
#130689292
#130686292
#130686252
C11×#18732
#2186811