Finite Group Databasebeta

← #14660475

Subgroups — #14660475

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622849C212yesmaximal, complemented
2C2×#10622828C212yesmaximal, complemented
3#13068355C211yesmaximal, characteristic, complemented
4#13068349C211yesmaximal, characteristic, complemented
5C2×C11×#535C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C23×D4×C11C2211yescharacteristic
8C11×#535—24no—
9C11×#535—24no—
10C2×C11×#127C412yescomplemented
11C2×C11×#124C412yescomplemented
12C2×C11×#121—22no—
13C2×C11×#120—22no—
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2212yes—
16C22×#4318C2212yes—
17#10622849—24no—
18#10622849—24no—
19C2×#66901—24no—
20#10622828—24no—
21#10622828—24no—
22C2×#66896—24no—
23#10622168—22no—
24#10622164—22no—
25C25×C11—21no—
26C2×C11×#41—22no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41D414yes—
32C22×Q8×C11C2×C411yescharacteristic
33C22×D4×C11—21no—
34C22×D4×C11—24no—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—21no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11C2×C412yes—
42C22×D4×C11C2×C411yescharacteristic
43C22×D4×C11D414yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C11×#127—24no—
47C11×#127—24no—
48C11×#124—24no—
49C11×#124—24no—
50C11×#121—216no—
51C11×#120—216no—
52C11×#117—22no—
53C11×#117—22no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4D412yes—
57C2×C42×C11C2×C412yes—
58C2×C22⋊Dic11—22no—
59#66979—22no—
60#66979—22no—
61#66979—22no—
62#66979D414yescomplemented
63C2×C4⋊Dic11—22no—
64C2×C4×Dic11—22no—
65C2×#4318—22no—
66C2×#4318—22no—
67C2×#4318—22no—
68C2×#4318—22no—
69C2×#4318—22no—
70C2×#4318D414yescomplemented
71C22×C11⋊C8—22no—
72#66901—216no—
73#66896—216no—
74#11006—111nomaximal, Sylow
75C24×C11—22no—
76C24×C11—21no—
77C24×C11—24no—
78C24×C11—42no—
79C24×C11—41no—
80C24×C11—41no—
81C24×C11—84no—
82C24×C11C2×D411yescharacteristic
83C11×#41—24no—
84C11×#41—24no—
85C11×#41—24no—
86C11×#41—24no—
87C11×#41—42no—
88C11×#41—42no—
89C11×#41—42no—
90C11×#41—42no—
91C2×Q8×C11—21no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11C22⋊C412yes—
95C2×D4×C11—24no—
96C2×D4×C11—216no—
97C2×D4×C11—22no—
98C2×D4×C11—21no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—24no—
108C2×D4×C11—42no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—41no—
117C2×D4×C11—41no—
118C2×D4×C11—88no—
119C2×D4×C11C22⋊C414yes—
120C2×D4×C11C22⋊C412yes—
121C22×C4×C11—21no—
122C22×C4×C11—24no—
123C22×C4×C11—42no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11C22⋊C414yes—
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×Dic11—42no—
136C11×C4⋊C4—24no—
137C11×C22⋊C4—216no—
138C11×C22⋊C4—24no—
139C42×C11—22no—
140C42×C11—22no—
141C22⋊Dic11—24no—
142C22⋊Dic11—42no—
143C4⋊Dic11—24no—
144C4⋊Dic11—42no—
145C4×Dic11—24no—
146C4×Dic11—42no—
147#4318—24no—
148#4318—24no—
149#4318—42no—
150#4318—42no—
151C2×C11⋊C8—24no—
152C2×C11⋊C8—42no—
153C2×C11⋊C8—42no—
154C2×#535D1111yescharacteristic
155C2×#421—112no—
156C2×#418—112no—
157#1742—111no—
158#1740—111no—
159C23×C11—24no—
160C23×C11—22no—
161C23×C11—42no—
162C23×C11—44no—
163C23×C11—48no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—88no—
171C23×C11—88no—
172C23×C11—84no—
173C23×C11—84no—
174C23×C11C2×C22⋊C411yescharacteristic
175C23×C11#12012yes—
176C23×C11#12112yes—
177C23×C11#12411yescharacteristic
178C23×C11#12711yescharacteristic
179Q8×C11—24no—
180Q8×C11—42no—
181D4×C11—28no—
182D4×C11—24no—
183D4×C11—44no—
184D4×C11—44no—
185D4×C11—44no—
186D4×C11—42no—
187D4×C11—44no—
188D4×C11—44no—
189D4×C11—816no—
190C2×C4×C11—24no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—44no—
195C2×C4×C11—44no—
196C2×C4×C11—44no—
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11C2×C22⋊C411yescharacteristic
199C2×C4×C11C4×D412yes—
200C2×C4×C11C4×D412yes—
201C2×C4×C11#12012yes—
202C2×C4×C11#12012yes—
203C2×C4×C11#12012yes—
204C2×C4×C11#12112yes—
205C2×C4×C11#12112yes—
206C2×C4×C11#12112yes—
207C2×C4×C11#12112yes—
208C2×C4×C11#12112yes—
209C2×C4×C11#12312yes—
210C2×C4×C11#12312yes—
211C2×C4×C11#12411yescharacteristic
212C2×C4×C11#12711yescharacteristic
213C2×Dic11—44no—
214C2×Dic11—84no—
215C11⋊C8—44no—
216C22×#41C2×D1111yescharacteristic
217C23×D4C2×D1111yescharacteristic
218C22×M16—112no—
219#535—24no—
220#535—24no—
221C2×#127Dic1112yescomplemented
222C2×#124Dic1112yescomplemented
223C2×#121—22no—
224C2×#120—22no—
225C2×#117—112no—
226C2×#117C2×D1111yescharacteristic
227#421—224no—
228#421—224no—
229C2×#104—224no—
230#418—224no—
231#418—224no—
232C2×#102—224no—
233#343—222no—
234#342—222no—
235C22×C11—22no—
236C22×C11—24no—
237C22×C11—42no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—44no—
241C22×C11—48no—
242C22×C11—42no—
243C22×C11—44no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11—84no—
247C22×C11—84no—
248C22×C11—88no—
249C22×C11—88no—
250C22×C11#37911yescharacteristic
251C22×C11#39011yescharacteristic
252C22×C11#39011yescharacteristic
253C22×C11#39212yes—
254C22×C11#39412yes—
255C4×C11—44no—
256C4×C11—42no—
257C4×C11#38612yes—
258C4×C11#38612yes—
259C4×C11#39212yes—
260C4×C11#39412yes—
261Dic11—84no—
262C25—21no—
263C2×#41—22no—
264C2×#41—22no—
265C2×#41—22no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41C22⋊D1114yes—
269C22×Q8C2×Dic1111yescharacteristic
270C22×D4—21no—
271C22×D4—24no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—21no—
277C22×D4—22no—
278C22×D4C2×Dic1112yes—
279C22×D4C2×Dic1111yescharacteristic
280C22×D4C22⋊D1114yes—
281C23×C4—21no—
282C23×C4C22×D1111yescharacteristic
283C2×M16—114no—
284C2×M16—222no—
285C2×M16—222no—
286C2×M16—222no—
287C2×M16—222no—
288C2×M16—222no—
289C22×C8—222no—
290#127—24no—
291#127—24no—
292#124—24no—
293#124—24no—
294#121—216no—
295#120—216no—
296#117—22no—
297#117—22no—
298#117—114no—
299#117—222no—
300#117—222no—
301#117—222no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4C22⋊D1112yes—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4C22⋊D1112yes—
307C2×C42—222no—
308C2×C42C2×Dic1112yes—
309#104—2216no—
310#102—2216no—
311C2×C11—22no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—22no—
315C2×C11—82no—
316C2×C11—84no—
317C2×C11#143811yescharacteristic
318C2×C11#179512yes—
319C24—22no—
320C24—21no—
321C24—24no—
322C24—41no—
323C24—42no—
324C24—41no—
325C24—84no—
326C24C2×C22⋊D1111yescharacteristic
327#41—24no—
328#41—24no—
329#41—24no—
330#41—24no—
331#41—42no—
332#41—42no—
333#41—42no—
334#41—42no—
335C2×Q8—21no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8C22⋊Dic1112yes—
339C2×D4—24no—
340C2×D4—216no—
341C2×D4—24no—
342C2×D4—24no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—24no—
349C2×D4—22no—
350C2×D4—21no—
351C2×D4—24no—
352C2×D4—41no—
353C2×D4—42no—
354C2×D4—41no—
355C2×D4—42no—
356C2×D4—41no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—41no—
362C2×D4—88no—
363C2×D4C22⋊Dic1114yes—
364C2×D4C22⋊Dic1112yes—
365C22×C4—21no—
366C22×C4—24no—
367C22×C4—41no—
368C22×C4—42no—
369C22×C4—41no—
370C22×C4—442no—
371C22×C4C22⋊Dic1114yes—
372C22×C4D4×D1112yes—
373C22×C4D4×D1112yes—
374C22×C4#434112yes—
375C22×C4#434112yes—
376C22×C4C22×Dic1111yescharacteristic
377C22×C4C2×C22⋊D1112yes—
378C22×C4C2×C22⋊D1112yes—
379C22×C4C2×C22⋊D1111yescharacteristic
380M16—224no—
381M16—224no—
382M16—442no—
383M16—442no—
384C2×C8—224no—
385C2×C8—442no—
386C2×C8—442no—
387C4⋊C4—24no—
388C4⋊C4—224no—
389C4⋊C4—442no—
390C22⋊C4—216no—
391C22⋊C4—24no—
392C22⋊C4—224no—
393C22⋊C4—442no—
394C42—22no—
395C42—22no—
396C42—224no—
397C42—442no—
398C11#1100611yescharacteristic, complemented, Sylow
399C23—24no—
400C23—22no—
401C23—42no—
402C23—44no—
403C23—48no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—42no—
408C23—44no—
409C23—44no—
410C23—88no—
411C23—84no—
412C23—88no—
413C23—84no—
414C23#6698911yescharacteristic
415C23#6699112yes—
416C23#6699311yescharacteristic
417C23C2×C22⋊Dic1111yescharacteristic
418C23#6700612yes—
419Q8—24no—
420Q8—42no—
421D4—28no—
422D4—24no—
423D4—44no—
424D4—44no—
425D4—44no—
426D4—42no—
427D4—44no—
428D4—44no—
429D4—816no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4—444no—
438C2×C4—884no—
439C2×C4D4×Dic1112yes—
440C2×C4D4×Dic1112yes—
441C2×C4#6698812yes—
442C2×C4#6698812yes—
443C2×C4#6698911yescharacteristic
444C2×C4#6699012yes—
445C2×C4#6699012yes—
446C2×C4#6699112yes—
447C2×C4#6699212yes—
448C2×C4#6699212yes—
449C2×C4#6699212yes—
450C2×C4#6699212yes—
451C2×C4#6699311yescharacteristic
452C2×C4C2×C22⋊Dic1111yescharacteristic
453C2×C4C2×C22⋊Dic1111yescharacteristic
454C2×C4#6700612yes—
455C8—444no—
456C22—22no—
457C22—24no—
458C22—41no—
459C22—42no—
460C22—41no—
461C22—44no—
462C22—48no—
463C22—42no—
464C22—44no—
465C22—84no—
466C22—84no—
467C22—82no—
468C22—82no—
469C22—88no—
470C22—88no—
471C22#1062283411yescharacteristic
472C22#1062283411yescharacteristic
473C22#1062283512yes—
474C22#1062283612yes—
475C22#1062286011yescharacteristic
476C4—44no—
477C4—42no—
478C4—884no—
479C4#1062283312yes—
480C4#1062283312yes—
481C4#1062283512yes—
482C4#1062283612yes—
483C2—22no—
484C2—21no—
485C2—21no—
486C2—22no—
487C2—84no—
488C2—82no—
489C2#1306685711yescharacteristic
490C2#1306858612yes—
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC2×C11×#535C2
socleC22×C11#379
cosocleC23×C4×C11C23
hypercenterC2×#535D11
hypocenterC11#11006
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#10622849C2semidirect
2. C2×#10622828C2semidirect
3. #13068355C2semidirect
4. #13068349C2semidirect
10. C2×C11×#127C4semidirect
11. C2×C11×#124C4semidirect
62. #66979D4semidirect
70. C2×#4318D4semidirect
221. C2×#127Dic11semidirect
222. C2×#124Dic11semidirect
398. C11#11006semidirect

Maximal subgroups

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

subgroupindex
C2×#106228492
C2×#106228282
#130683552
#130683492
C2×C11×#5352
#1100611