Finite Group Databasebeta

← #14680422

Subgroups — #14680422

Order 2816.

1978 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
3#13066866C212yesmaximal, complemented
4#13066863C212yesmaximal, complemented
5#13066858C212yesmaximal, complemented
6#13066855C212yesmaximal
7#13066852C212yesmaximal, complemented
8#13066851C212yesmaximal, complemented
9C2×C11×#380C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C2×#66982—24no—
17C2×#66982—24no—
18C2×#66982C418yescomplemented
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2214yes—
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C11×#380—24no—
26C2×C11×#95C2212yes—
27C4×C22⋊Dic11—24no—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32C25×C11C2311yescharacteristic
33C24×D11C2311yescharacteristic
34C23×C4×C11—44no—
35C23×C4×C11C2×C414yes—
36C23×C4×C11D414yes—
37C23×C4×C11D414yes—
38C23×C4×C11C2314yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—22no—
42C22×C22⋊D11—22no—
43C22×C22⋊D11—44no—
44C22×C22⋊D11C2×C414yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2314yes—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4—44no—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—44no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—28no—
57C2×C22⋊Dic11C2×C414yes—
58#66982—232no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—28no—
64C2×(C2×D11)⋊C4—44no—
65C2×(C2×D11)⋊C4—44no—
66C2×(C2×D11)⋊C4C2×C414yes—
67C2×(C2×D11)⋊C4C2×C414yes—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4C2×C414yes—
73C2×Dic11⋊C4C2×C414yes—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—44no—
76C11×#95—24no—
77C11⋊#95—24no—
78C11⋊#95—28no—
79C11⋊#95—44no—
80C11⋊#95—44no—
81#14287—111nomaximal, Sylow
82C24×C11—24no—
83C24×C11—22no—
84C24×C11—24no—
85C24×C11—22no—
86C24×C11C22×C412yes—
87C24×C11C2×D412yes—
88C24×C11C2×D412yes—
89C24×C11C2411yescharacteristic
90C23×D11—21no—
91C23×D11—21no—
92C23×D11—24no—
93C23×D11—22no—
94C23×D11—24no—
95C23×D11—22no—
96C23×D11C22×C412yes—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—48no—
107C22×C4×C11—48no—
108C22×C4×C11—48no—
109C22×C4×C11C22⋊C4116yescomplemented
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C2×C22⋊D11—28no—
117C2×C22⋊D11—48no—
118C2×C22⋊D11—48no—
119C2×C22⋊D11—48no—
120C22×Dic11—24no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—22no—
130C22×Dic11—24no—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—22no—
135C22×Dic11—24no—
136C22×Dic11C22×C412yes—
137C22×Dic11C22×C412yes—
138C22×Dic11C22×C412yes—
139C22×Dic11#4118yes—
140C11×C4⋊C4—48no—
141C11×C22⋊C4—48no—
142C22⋊Dic11—216no—
143C22⋊Dic11—28no—
144(C2×D11)⋊C4—28no—
145(C2×D11)⋊C4—28no—
146(C2×D11)⋊C4—416no—
147Dic11⋊C4—28no—
148Dic11⋊C4—28no—
149C4×Dic11—48no—
150C22×#123—111no—
151C2×#380D1111yescharacteristic, complemented
152C2×C4×C22⋊C4—111no—
153#1441—112no—
154#1440—112no—
155#1439—112no—
156#1438—112no—
157#1437—112no—
158#1436—112no—
159C23×C11—24no—
160C23×C11—24no—
161C23×C11—24no—
162C23×C11—24no—
163C23×C11—24no—
164C23×C11—24no—
165C23×C11—24no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—44no—
170C23×C11—44no—
171C23×C11—44no—
172C23×C11—44no—
173C23×C11C2×C22⋊C414yes—
174C23×C11C23×C411yescharacteristic
175C23×C11C22×D411yescharacteristic
176C23×C11C22×D411yescharacteristic
177C23×C11C2×#4114yes—
178C23×C11H(5,𝔽2)14yes—
179C23×C11H(5,𝔽2)12yes—
180C23×C112−1+412yes—
181C22×D11—22no—
182C22×D11—24no—
183C22×D11—24no—
184C22×D11—24no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—42no—
192C22×D11—44no—
193C22×D11—44no—
194C22×D11—44no—
195C22×D11—44no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—416no—
203C2×C4×C11—44no—
204C2×C4×C11—44no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11—44no—
209C2×C4×C11—44no—
210C2×C4×C11C2×C22⋊C414yes—
211C2×C4×C11C2×C22⋊C414yes—
212C22⋊D11—416no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—28no—
220C2×Dic11—28no—
221C2×Dic11—28no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—44no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—44no—
231C2×Dic11—44no—
232C2×Dic11—44no—
233C23×D4—111no—
234C24×C4C2×D1111yescharacteristic
235C2×#123—118no—
236C2×#123—224no—
237C2×#123—224no—
238C22×C4⋊C4—111no—
239C22×C4⋊C4—111no—
240C22×C4⋊C4C2×D1112yes—
241C22×C22⋊C4—111no—
242C22×C22⋊C4—111no—
243C22×C22⋊C4—111no—
244C22×C22⋊C4—112no—
245C22×C22⋊C4—114no—
246C22×C22⋊C4C2×D1112yes—
247C22×C42—112no—
248#380—24no—
249C4×C22⋊C4—224no—
250C2×#95—114no—
251C2×#95—112no—
252C2×#95—114no—
253C2×#95—114no—
254C2×#95C2×D1112yes—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—24no—
258C22×C11—48no—
259C22×C11—48no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11C22×C22⋊C411yescharacteristic
263C22×C11C4×#4112yes—
264C22×C11#51812yes—
265C22×C11#52012yes—
266C22×C11#52512yes—
267C22×C11#53212yes—
268C22×C11#53412yes—
269C22×C11#53412yes—
270C22×C11#53511yescharacteristic
271C22×C11#53611yescharacteristic
272C22×C11#53712yes—
273C22×C11#53814yes—
274C22×C11#53914yes—
275C22×C11#54014yes—
276C22×C11#54214yes—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—48no—
280C2×D11—42no—
281C2×D11—84no—
282C2×D11—82no—
283C2×D11—82no—
284C4×C11—24no—
285C4×C11—24no—
286C4×C11—84no—
287Dic11—42no—
288Dic11—42no—
289Dic11—48no—
290Dic11—42no—
291C25—111no—
292C25C22×D1111yescharacteristic
293C22×D4—114no—
294C22×D4—222no—
295C22×D4—222no—
296C22×D4—444no—
297C23×C4—44no—
298C23×C4—111no—
299C23×C4—111no—
300C23×C4—114no—
301C23×C4—111no—
302C23×C4C4×D1114yes—
303C23×C4D4414yes—
304C23×C4C22⋊D1114yes—
305C23×C4C22×D1114yes—
306C23×C4C22×D1111yescharacteristic
307C23×C4C22×D1111yescharacteristic
308#123—2232no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—114no—
312C2×C4⋊C4—114no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—114no—
320C2×C22⋊C4—114no—
321C2×C22⋊C4—114no—
322C2×C22⋊C4—228no—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—224no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—228no—
331C2×C22⋊C4—444no—
332C2×C22⋊C4—444no—
333C2×C42—224no—
334C2×C42—444no—
335#95—24no—
336#95—228no—
337#95—224no—
338#95—444no—
339#95—444no—
340C2×C11—44no—
341C2×C11#229711yescharacteristic
342C2×C11#230811yescharacteristic
343C2×C11#231111yescharacteristic
344C2×C11#233514yes—
345C2×C11#263014yes—
346C2×C11#266112yes—
347C2×C11#266312yes—
348D11—82no—
349C24—22no—
350C24—24no—
351C24—22no—
352C24—24no—
353C24—112no—
354C24—221no—
355C24—222no—
356C24—224no—
357C24—222no—
358C24—224no—
359C24—221no—
360C24C2×C4×D1112yes—
361C24C2×D4412yes—
362C24C2×C22⋊D1112yes—
363C24C23×D1111yescharacteristic
364C2×D4—228no—
365C2×D4—448no—
366C2×D4—448no—
367C2×D4—448no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—48no—
378C22×C4—48no—
379C22×C4—48no—
380C22×C4—112no—
381C22×C4—112no—
382C22×C4—112no—
383C22×C4—118no—
384C22×C4—224no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—222no—
389C22×C4—224no—
390C22×C4—224no—
391C22×C4—224no—
392C22×C4—224no—
393C22×C4—222no—
394C22×C4—224no—
395C22×C4—224no—
396C22×C4—224no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4(C2×D11)⋊C4116yescomplemented
401C22×C4C2×C4×D1112yes—
402C22×C4C2×C4×D1112yes—
403C22×C4C2×D4412yes—
404C22×C4C2×D4412yes—
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1112yes—
407C4⋊C4—48no—
408C4⋊C4—228no—
409C4⋊C4—228no—
410C22⋊C4—48no—
411C22⋊C4—2216no—
412C22⋊C4—228no—
413C22⋊C4—228no—
414C22⋊C4—228no—
415C22⋊C4—4416no—
416C42—448no—
417C11#1428711yescharacteristic, complemented, Sylow
418C23—24no—
419C23—24no—
420C23—24no—
421C23—24no—
422C23—24no—
423C23—24no—
424C23—24no—
425C23—22no—
426C23—22no—
427C23—24no—
428C23—44no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—224no—
433C23—224no—
434C23—224no—
435C23—222no—
436C23—442no—
437C23—442no—
438C23—442no—
439C23—442no—
440C23—441no—
441C23—441no—
442C23—442no—
443C23—444no—
444C23—444no—
445C23—444no—
446C23—444no—
447C23C2×(C2×D11)⋊C414yes—
448C23C22×C4×D1111yescharacteristic
449C23C22×D4411yescharacteristic
450C23#6703714yes—
451C23#6703712yes—
452C23#6704012yes—
453C23#41×D1114yes—
454C23C22×C22⋊D1111yescharacteristic
455D4—4416no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—416no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—228no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—228no—
478C2×C4—228no—
479C2×C4—444no—
480C2×C4—442no—
481C2×C4—444no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—442no—
488C2×C4—444no—
489C2×C4—444no—
490C2×C4C2×(C2×D11)⋊C414yes—
491C2×C4C2×(C2×D11)⋊C414yes—
492C22—24no—
493C22—24no—
494C22—24no—
495C22—48no—
496C22—48no—
497C22—44no—
498C22—44no—
499C22—442no—
500C22—448no—
501C22—442no—
502C22—442no—
503C22—884no—
504C22—882no—
505C22—882no—
506C22#1062301712yes—
507C22#1062302412yes—
508C22#1062303512yes—
509C22#1062304112yes—
510C22#1062305312yes—
511C22#1062305512yes—
512C22#1062314414yes—
513C22#1062314614yes—
514C22#1062316914yes—
515C22#1062317114yes—
516C22C22×(C2×D11)⋊C411yescharacteristic
517C22#1062333512yes—
518C22#1062333611yescharacteristic
519C22#1062334711yescharacteristic
520C22#1062336312yes—
521C4—24no—
522C4—24no—
523C4—84no—
524C4—442no—
525C4—448no—
526C4—442no—
527C4—442no—
528C2—44no—
529C2—882no—
530C2#1307110411yescharacteristic
531C2#1307119111yescharacteristic
532C2#1307120911yescharacteristic
533C2#1307140214yes—
534C2#1307445714yes—
535C2#1307474512yes—
536C2#1307476712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#380D11
hypocenterC11#14287
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic11C2semidirect
3. #13066866C2semidirect
4. #13066863C2semidirect
5. #13066858C2semidirect
7. #13066852C2semidirect
8. #13066851C2semidirect
9. C2×C11×#380C2semidirect
18. C2×#66982C4semidirect
109. C22×C4×C11C22⋊C4semidirect
151. C2×#380D11semidirect
400. C22×C4(C2×D11)⋊C4semidirect
417. C11#14287semidirect

Maximal subgroups

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

subgroupindex
C22×#669822
C2×C4×C22⋊Dic112
#130668662
#130668632
#130668582
#130668552
#130668522
#130668512
C2×C11×#3802
#1428711