Finite Group Databasebeta

← #14810402

Subgroups — #14810402

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10622701C211yesmaximal, characteristic, complemented
3C2×#10622307C211yesmaximal, characteristic, complemented
4#13076962C211yesmaximal, characteristic
5#13069761C214yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13068937C214yesmaximal, complemented
8C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
9C11×#1990C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13#10623259—24no—
14#10623259—24no—
15C2×#66950—21no—
16C2×#66948—21no—
17C2×#66948—21no—
18C2×#66948C2212yes—
19C2×#66945C2212yes—
20C2×#66943C2212yes—
21C2×#66940—21no—
22C2×#66927C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×#66885C2214yes—
28C2×(C2×D11)⋊C8C2212yes—
29#10622701—24no—
30#10622601—21no—
31#10622601—21no—
32#10622601C2212yes—
33C2×#66873C2214yes—
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622307—24no—
36C11×#340C2214yes—
37#10622188C2212yes—
38#10622167C2214yes—
39C22×Q8×C11—21no—
40C22×D44—22no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44C2312yes—
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11C2311yescharacteristic
47C22×Dic22—21no—
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8D414yescomplemented
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11C2311yescharacteristic
57#66999—28no—
58Q8×Dic11—28no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C22×C11⋊C8C2312yes—
72#66950—28no—
73#66948—28no—
74#66948—44no—
75#66948—44no—
76#66945—24no—
77#66945—24no—
78#66943—24no—
79#66943—24no—
80#66940—28no—
81#66927—22no—
82#66927—22no—
83C42×D11—22no—
84C42×D11—22no—
85#66922—22no—
86#66922D414yescomplemented
87C4×C8×C11—22no—
88#66885—28no—
89(C2×D11)⋊C8—24no—
90#66873—28no—
91C4×C11⋊C8—22no—
92#25905—111nomaximal, Sylow
93C23×D11—22no—
94C23×D11C2×D411yescharacteristic
95C2×Q8×C11—24no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—24no—
110C2×D44—24no—
111C2×D44—44no—
112C2×D44—44no—
113C2×D44—44no—
114C2×D44—42no—
115C2×D44—42no—
116C2×D44—42no—
117C2×D44—42no—
118C2×D44—42no—
119C2×D44—42no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×C4×D11—22no—
129C2×C4×D11#4114yes—
130C2×Dic22—24no—
131C2×Dic22—42no—
132C2×Dic22—42no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4C2×D414yes—
142C42×C11C2×D412yes—
143C42×C11C2×D412yes—
144(C2×D11)⋊C4—28no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—44no—
147(C2×D11)⋊C4—44no—
148C4⋊Dic11—28no—
149C4⋊Dic11—24no—
150C4⋊Dic11—22no—
151C4⋊Dic11C2×D414yes—
152Dic11⋊C4—28no—
153C4×Dic11—28no—
154C4×Dic11—22no—
155C4×Dic11—22no—
156C4×Dic11—21no—
157C4×Dic11—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×#533—111no—
162C2×#486—111no—
163C2×#486—111no—
164#2856—111no—
165#2025—114no—
166#1990—111no—
167#1990D1111yescharacteristic, complemented
168#1875—114no—
169C4×C22⋊C8—111no—
170C23×C11C22×D411yescharacteristic
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11#12412yes—
185Q8×C11—48no—
186C2×C4×C11—24no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11#12012yes—
193C2×C4×C11#12012yes—
194C2×C4×C11#13512yes—
195C2×C4×C11#13512yes—
196C2×C4×C11AGL(1,ℤ/8)12yes—
197C2×C4×C11AGL(1,ℤ/8)12yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4112yes—
201C2×C4×C112−1+412yes—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—24no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11#12412yes—
214D44—44no—
215D44—44no—
216D44—88no—
217D44—84no—
218D44—84no—
219C4×D11—24no—
220C4×D11—24no—
221C4×D11—44no—
222C4×D11—44no—
223Dic22—48no—
224C8×C11—42no—
225C11⋊C8—42no—
226#533—224no—
227#533—224no—
228C2×C4⋊Q8—111no—
229C2×C4⋊Q8C2×D1111yescharacteristic
230C2×#127—111no—
231C2×#125—112no—
232C2×C22⋊Q8—221no—
233C2×C22⋊Q8—221no—
234C2×#121—112no—
235C2×#121—221no—
236C2×#121—221no—
237C2×C4×Q8—221no—
238C2×C4×Q8—221no—
239C2×#117—112no—
240C22×C42—111no—
241#486—224no—
242#486—224no—
243C2×#102—114no—
244C2×#102—114no—
245C2×C22⋊C8—112no—
246C2×C4×C8—111no—
247C2×C4×C8C2×D1111yescharacteristic
248#390—112no—
249#390—221no—
250#390—221no—
251#384C2×D1111yescharacteristic
252#340—114no—
253#340C2×D1114yes—
254#336—112no—
255C22×C11C2×#12011yescharacteristic
256C22×C11C2×#12411yescharacteristic
257C22×C11#53611yescharacteristic
258C22×C11C2×#13511yescharacteristic
259C22×C11C2×#13511yescharacteristic
260C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
262C2×D11—22no—
263C2×D11—22no—
264C2×D11—22no—
265C2×D11—41no—
266C2×D11—41no—
267C2×D11—41no—
268C2×D11—41no—
269C2×D11—82no—
270C2×D11—82no—
271C2×D11—82no—
272C2×D11—82no—
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—82no—
276C4×C11—44no—
277C4×C11—82no—
278C4×C11#44914yes—
279C4×C11#44914yes—
280C4×C11#54812yes—
281C4×C11#54812yes—
282Dic11—22no—
283Dic11—44no—
284Dic11—41no—
285Dic11—41no—
286C22×Q8—21no—
287C22×Q8—221no—
288C22×D4—112no—
289C22×D4—222no—
290C22×D4—221no—
291C22×D4—221no—
292C23×C4—111no—
293C23×C4—111no—
294C23×C4—111no—
295C22×C8—112no—
296C22×C8C22×D1112yes—
297C4⋊Q8—22no—
298C4⋊Q8—114no—
299C4⋊Q8—222no—
300C4⋊Q8D4414yescomplemented
301#127—222no—
302#127—222no—
303#125—224no—
304#125—224no—
305C22⋊Q8—228no—
306C22⋊Q8—228no—
307#121—228no—
308#121—444no—
309#121—444no—
310C4×Q8—228no—
311C4×Q8—228no—
312#117—224no—
313#117—224no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4C22×D1112yes—
322C2×C4⋊C4C22×D1112yes—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—222no—
327C2×C42—111no—
328C2×C42—111no—
329C2×C42—111no—
330C2×C42—222no—
331C2×C42—222no—
332C2×C42—222no—
333C2×C42C22×D1111yescharacteristic
334#102—228no—
335#102—228no—
336C22⋊C8—224no—
337C4×C8—22no—
338C4×C8—222no—
339C2×C11#243611yescharacteristic
340C2×C11C2×#44911yescharacteristic
341C2×C11C2×#44911yescharacteristic
342C2×C11#313111yescharacteristic
343C2×C11#313811yescharacteristic
344C2×C11#322811yescharacteristic
345C2×C11#322811yescharacteristic
346D11—42no—
347D11—162no—
348C24—111no—
349C24—222no—
350C2×Q8—24no—
351C2×Q8—42no—
352C2×Q8—42no—
353C2×Q8—224no—
354C2×Q8—442no—
355C2×Q8—442no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—224no—
359C2×D4—224no—
360C2×D4—444no—
361C2×D4—444no—
362C2×D4—444no—
363C2×D4—442no—
364C2×D4—442no—
365C2×D4—442no—
366C2×D4—442no—
367C2×D4—442no—
368C2×D4—442no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—111no—
372C22×C4—114no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4D4×D1111yescharacteristic
386C22×C4D4×D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C4⋊C4—114no—
400C4⋊C4—228no—
401C4⋊C4—228no—
402C4⋊C4—224no—
403C4⋊C4—222no—
404C4⋊C4C2×D4414yes—
405C22⋊C4—228no—
406C22⋊C4—444no—
407C22⋊C4—444no—
408C22⋊C4—444no—
409C42—228no—
410C42—222no—
411C42—222no—
412C42—221no—
413C42—221no—
414C42C2×D4412yes—
415C42D4×D1112yes—
416C11#2590511yescharacteristic, complemented, Sylow
417C23—112no—
418C23—221no—
419C23—221no—
420C23—221no—
421C23—221no—
422C23—221no—
423C23—221no—
424C23—442no—
425C23—442no—
426C23—442no—
427C23—442no—
428C23—442no—
429C23—442no—
430C23—442no—
431C23C2×D4×D1111yescharacteristic
432Q8—48no—
433Q8—448no—
434D4—444no—
435D4—444no—
436D4—888no—
437D4—884no—
438D4—884no—
439C2×C4—24no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—112no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—224no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—444no—
460C2×C4—444no—
461C2×C4#6693512yes—
462C2×C4#6693512yes—
463C2×C4#6696412yes—
464C2×C4#6696712yes—
465C2×C4#6696912yes—
466C2×C4#6697212yes—
467C2×C4C22×D4411yescharacteristic
468C2×C4C2×D4×D1111yescharacteristic
469C2×C4#6704012yes—
470C2×C4#41×D1112yes—
471C8—42no—
472C8—442no—
473C22—222no—
474C22—222no—
475C22—222no—
476C22—441no—
477C22—441no—
478C22—441no—
479C22—441no—
480C22—882no—
481C22—882no—
482C22—882no—
483C22—882no—
484C22—882no—
485C22—882no—
486C22—882no—
487C22C2×#6693511yescharacteristic
488C22D11×#12411yescharacteristic
489C22#1062325511yescharacteristic
490C22C2×#6696411yescharacteristic
491C22C2×#6696711yescharacteristic
492C22C2×#6696911yescharacteristic
493C22C2×#6697211yescharacteristic
494C4—44no—
495C4—82no—
496C4—222no—
497C4—441no—
498C4—441no—
499C4—444no—
500C4#1062239414yes—
501C4#1062242414yes—
502C4#1062310712yes—
503C4#1062316412yes—
504C2—442no—
505C2—1762no—
506C2#1307227311yescharacteristic
507C2C2×#1062239411yescharacteristic
508C2C2×#1062242411yescharacteristic
509C2#1307894011yescharacteristic
510C2#1307898711yescharacteristic
511C2#1307975311yescharacteristic
512C2#1307975511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radical#13076962C2
hypercenter#1990D11
hypocenterC11#25905
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
2. C2×#10622701C2semidirect
3. C2×#10622307C2semidirect
5. #13069761C2semidirect
6. #13069576C2semidirect
7. #13068937C2semidirect
8. C4×(C2×D11)⋊C8C2semidirect
9. C11×#1990C2semidirect
50. C11×C4⋊Q8D4semidirect
86. #66922D4semidirect
167. #1990D11semidirect
300. C4⋊Q8D44semidirect
416. C11#25905semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106227012
C2×#106223072
#130769622
#130697612
#130695762
#130689372
C4×(C2×D11)⋊C82
C11×#19902
#2590511