Finite Group Databasebeta

← #14754529

Subgroups — #14754529

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622608C211yesmaximal, characteristic, complemented
2C22×#66871C211yesmaximal, characteristic, complemented
3C2×#10622847C211yesmaximal, characteristic
4#13071208C211yesmaximal, characteristic
5#13068815C214yesmaximal, complemented
6#13068804C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068332C211yesmaximal, characteristic, complemented
9C2×C11×#520C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C11×#520—24no—
12C11×#520—24no—
13C2×C4×Q8×C11—21no—
14C2×C4×D4×C11—22no—
15C2×C4×D4×C11—21no—
16C2×C11×#117C2212yes—
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24#10622847C418yescomplemented
25#10622843—21no—
26#10622834—21no—
27#10622833—22no—
28#10622825C2214yes—
29C2×C22⋊(C11⋊C8)C2214yes—
30#10622608—24no—
31C2×#66872C2212yes—
32C2×#66871—24no—
33C2×#66871C2212yes—
34C2×#66871C2214yes—
35#10622167C2212yes—
36#10622167C2214yes—
37#10622167C2212yes—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41C2×C414yes—
43C2×C11×#41Q814yes—
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11D412yes—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—22no—
48C23×C4×C11—21no—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C4×Q8×C11—28no—
53C4×D4×C11—216no—
54C4×D4×C11—28no—
55C11×#117—22no—
56C11×#117—24no—
57C11×#117—24no—
58C11×#117D414yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4D414yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—22no—
71C2×C42×C11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—24no—
74#66979—22no—
75#66979—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2312yes—
81C2×C4×Dic11—21no—
82C2×#4318—22no—
83C2×#4318—22no—
84C2×#4318C2×C414yescomplemented
85C22×C11⋊C8—22no—
86C22×C11⋊C8—22no—
87C22×C11⋊C8C2×C414yescomplemented
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2312yes—
90C11⋊#95—24no—
91C22⋊(C11⋊C8)C2×C4116yescomplemented
92#66872—24no—
93#66871—28no—
94#66871—24no—
95#20847—111nomaximal, Sylow
96C24×C11C2×D412yes—
97C24×C11C2×D411yescharacteristic
98C11×#41—28no—
99C11×#41—28no—
100C11×#41—28no—
101C11×#41—28no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11C4⋊C414yes—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11C4⋊C418yes—
110C2×D4×C11C4⋊C414yes—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—28no—
119C22×C4×C11—24no—
120C22×C4×C11—82no—
121C22×C4×C11—84no—
122C22×C4×C11C22×C414yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×Q814yes—
129C22×C4×C11C2×Q812yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—42no—
136C22×Dic11—82no—
137C11×C4⋊C4—28no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4C2×D412yes—
143C11×C4⋊C4C2×D414yes—
144C11×C4⋊C4C2×D412yes—
145C11×C22⋊C4—28no—
146C11×C22⋊C4—24no—
147C42×C11—28no—
148C42×C11—24no—
149C22⋊Dic11—42no—
150C22⋊Dic11—84no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—42no—
156C4×Dic11—42no—
157#4318—28no—
158C2×C11⋊C8—28no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8C22×C414yes—
164C2×C11⋊C8C22×C414yes—
165C2×#520D1111yescharacteristic
166C2×#428—111no—
167C22×#107—111no—
168C2×#408—111no—
169#2311—111no—
170#1854—114no—
171#1852—114no—
172#1736—111no—
173#1735—111no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11C2×C4⋊C414yes—
181C23×C11C2×C4⋊C412yes—
182C23×C11#12012yes—
183C23×C11#12312yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—28no—
186D4×C11—216no—
187D4×C11—28no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—44no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—84no—
201C2×C4×C11—88no—
202C2×C4×C11C2×C4⋊C414yes—
203C2×C4×C11C2×C4⋊C412yes—
204C2×C4×C11C4×D414yes—
205C2×C4×C11C4×D414yes—
206C2×C4×C11#12012yes—
207C2×C4×C11C22⋊Q814yes—
208C2×C4×C11C22⋊Q814yes—
209C2×C4×C11#12312yes—
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×Q811yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—44no—
220C2×Dic11—42no—
221C2×Dic11—84no—
222C11⋊C8—24no—
223C11⋊C8—24no—
224C22×#41C2×D1111yescharacteristic
225C22×M16—111no—
226C23×C8—111no—
227#520—24no—
228#520—24no—
229C2×C4×Q8—21no—
230C2×C4×D4—22no—
231C2×C4×D4—21no—
232C2×#117—111no—
233C2×#117C2×D1112yes—
234C2×#117C2×D1111yescharacteristic
235C22×C4⋊C4—111no—
236C22×C4⋊C4C2×D1112yes—
237C22×C4⋊C4C2×D1111yescharacteristic
238#428—224no—
239C2×#107—112no—
240C2×#107—114no—
241C2×#107—224no—
242C2×#106—112no—
243#408—118no—
244C2×C22⋊C8—114no—
245#391—221no—
246#390—221no—
247#386—222no—
248#380—114no—
249#340—112no—
250#340—114no—
251#340—112no—
252C22×C11—24no—
253C22×C11—24no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—28no—
257C22×C11—24no—
258C22×C11—44no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11#38514yes—
262C22×C11C22×C4⋊C411yescharacteristic
263C22×C11C2×#12011yescharacteristic
264C22×C11C2×#12311yescharacteristic
265C22×C11#57612yes—
266C22×C11#57812yes—
267C4×C11—24no—
268C4×C11—44no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11#38514yes—
272C4×C11C2×C4×D411yescharacteristic
273C4×C11C2×C4×D411yescharacteristic
274C4×C11C2×C22⋊Q811yescharacteristic
275C4×C11C2×C22⋊Q811yescharacteristic
276Dic11—82no—
277Dic11—82no—
278C2×#41—22no—
279C2×#41—22no—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41Dic2214yes—
283C2×#41C4×D1114yes—
284C22×Q8C22⋊D1111yescharacteristic
285C22×D4C22⋊D1112yes—
286C22×D4C22⋊D1111yescharacteristic
287C23×C4—22no—
288C23×C4—21no—
289C23×C4—221no—
290C23×C4C22×D1112yes—
291C23×C4C22×D1111yescharacteristic
292C2×M16—114no—
293C2×M16—222no—
294C2×M16—222no—
295C22×C8—114no—
296C22×C8—112no—
297C22×C8—112no—
298C22×C8—222no—
299C22×C8—222no—
300C4×Q8—28no—
301C4×D4—216no—
302C4×D4—28no—
303#117—22no—
304#117—24no—
305#117—24no—
306#117—222no—
307#117—222no—
308#117C22⋊D1114yes—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4C22⋊D1114yes—
320C2×C4⋊C4C22×D1111yescharacteristic
321C2×C4⋊C4C22×D1112yes—
322C2×C4⋊C4C22×D1111yescharacteristic
323C2×C22⋊C4—22no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—224no—
327C2×C42—22no—
328C2×C42—21no—
329C2×C42—221no—
330#107—228no—
331#107—224no—
332#106—224no—
333C22⋊C8—1116no—
334#95—224no—
335C2×C11—24no—
336C2×C11—44no—
337C2×C11C2×#38511yescharacteristic
338C2×C11#291312yes—
339C2×C11#300811yescharacteristic
340C2×C11#301111yescharacteristic
341C2×C11#309812yes—
342C24C2×C22⋊D1112yes—
343C24C2×C22⋊D1111yescharacteristic
344#41—28no—
345#41—28no—
346#41—28no—
347#41—28no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8Dic11⋊C414yes—
351C2×D4—24no—
352C2×D4—24no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4Dic11⋊C418yes—
356C2×D4Dic11⋊C414yes—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—28no—
365C22×C4—24no—
366C22×C4—82no—
367C22×C4—84no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—442no—
371C22×C4—882no—
372C22×C4C2×Dic2214yes—
373C22×C4C2×Dic2212yes—
374C22×C4C2×C4×D1114yes—
375C22×C4C2×C4×D1112yes—
376C22×C4#433912yes—
377C22×C4#433912yes—
378C22×C4C2×C22⋊D1112yes—
379C22×C4C2×C22⋊D1111yescharacteristic
380C22×C4C2×C22⋊D1112yes—
381C22×C4C2×C22⋊D1112yes—
382C22×C4C23×D1111yescharacteristic
383M16—228no—
384C2×C8—114no—
385C2×C8—114no—
386C2×C8—228no—
387C2×C8—222no—
388C2×C8—222no—
389C2×C8—222no—
390C2×C8—222no—
391C4⋊C4—28no—
392C4⋊C4—24no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—222no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—442no—
401C4⋊C4C2×C22⋊D1112yes—
402C4⋊C4C2×C22⋊D1112yes—
403C4⋊C4C2×C22⋊D1114yes—
404C22⋊C4—28no—
405C22⋊C4—24no—
406C22⋊C4—442no—
407C22⋊C4—884no—
408C42—28no—
409C42—24no—
410C42—442no—
411C11#2084711yescharacteristic, complemented, Sylow
412C23—22no—
413C23—22no—
414C23—22no—
415C23—24no—
416C23—24no—
417C23—22no—
418C23C2×Dic11⋊C414yes—
419C23C2×Dic11⋊C412yes—
420C23#6698212yes—
421C23#6700612yes—
422C23C22×C22⋊D1111yescharacteristic
423Q8—28no—
424D4—216no—
425D4—28no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—84no—
439C2×C4—88no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—444no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—884no—
446C2×C4C2×Dic11⋊C414yes—
447C2×C4C2×Dic11⋊C412yes—
448C2×C4#6697714yes—
449C2×C4#6697714yes—
450C2×C4C4×C22⋊D1114yes—
451C2×C4C4×C22⋊D1114yes—
452C2×C4#6698212yes—
453C2×C4#6700612yes—
454C2×C4C22×Dic2211yescharacteristic
455C2×C4C22×C4×D1111yescharacteristic
456C2×C4C2×#433911yescharacteristic
457C2×C4C2×#433911yescharacteristic
458C2×C4C22×C22⋊D1111yescharacteristic
459C2×C4C22×C22⋊D1111yescharacteristic
460C8—224no—
461C8—224no—
462C22—24no—
463C22—22no—
464C22—22no—
465C22—24no—
466C22—24no—
467C22—28no—
468C22—44no—
469C22—42no—
470C22—42no—
471C22#1062282314yes—
472C22C22×Dic11⋊C411yescharacteristic
473C22C2×#6698211yescharacteristic
474C22#1062336612yes—
475C22#1062336912yes—
476C22C2×#6700611yescharacteristic
477C4—24no—
478C4—44no—
479C4—42no—
480C4—42no—
481C4—882no—
482C4—882no—
483C4#1062282314yes—
484C4C2×#6697711yescharacteristic
485C4C2×#6697711yescharacteristic
486C4C2×C4×C22⋊D1111yescharacteristic
487C4C2×C4×C22⋊D1111yescharacteristic
488C2—24no—
489C2—44no—
490C2C2×#1062282311yescharacteristic
491C2#1307721412yes—
492C2#1307788411yescharacteristic
493C2#1307791111yescharacteristic
494C2#1307859412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#520D11
hypocenterC11#20847
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#10622608C2semidirect
2. C22×#66871C2semidirect
5. #13068815C2semidirect
6. #13068804C2semidirect
7. #13068335C2semidirect
8. #13068332C2semidirect
24. #10622847C4semidirect
84. C2×#4318C2×C4semidirect
87. C22×C11⋊C8C2×C4semidirect
91. C22⋊(C11⋊C8)C2×C4semidirect
411. C11#20847semidirect

Maximal subgroups

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

subgroupindex
C2×#106226082
C22×#668712
C2×#106228472
#130712082
#130688152
#130688042
#130683352
#130683322
C2×C11×#5202
#2084711