Finite Group Databasebeta

← #14676000

Subgroups — #14676000

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C211yesmaximal, characteristic
2C2×#10622277C214yesmaximal
3C2×#10622280C211yesmaximal, characteristic
4C2×#10622279C211yesmaximal, characteristic
5#13066885C211yesmaximal, characteristic, complemented
6#13066884C211yesmaximal, characteristic, complemented
7#13066883C211yesmaximal, characteristic, complemented
8Dic11⋊#95C214yesmaximal, complemented
9C11×#1445C211yesmaximal, characteristic, complemented
10C23×C4×D11C2212yes—
11C23×C4×D11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2212yes—
18C22×C4×Dic11C2212yes—
19C2×C4⋊C4×D11—24no—
20C2×C4⋊C4×D11—24no—
21C2×C4⋊C4×D11C418yescomplemented
22C2×C11×#95C2214yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30#10622280—24no—
31#10622279—24no—
32#10622277—216no—
33C24×D11C2311yescharacteristic
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2311yescharacteristic
42C22×C4×D11—28no—
43C22×C4×D11—24no—
44C22×C4×D11—24no—
45C22×C4×D11—28no—
46C22×C4×D11—28no—
47C22×C4×D11C2×C418yes—
48C22×C4×D11C2×C414yes—
49C22×C4×D11D414yes—
50C22×C4×D11D414yes—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4—28no—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4D418yes—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11C2×C414yes—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—28no—
66C2×Dic11⋊C4C2×C418yes—
67C2×C4×Dic11—24no—
68C2×C4×Dic11—28no—
69C4⋊C4×D11—232no—
70C11×#95—28no—
71C11×#95—22no—
72C11×#95—22no—
73C11⋊#95—28no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—28no—
77C11⋊#95—28no—
78#13904—111nomaximal, Sylow
79C24×C11C2411yescharacteristic
80C23×D11—24no—
81C23×D11—22no—
82C23×D11—22no—
83C23×D11C22×C412yes—
84C23×D11C2×D412yes—
85C23×D11C2×D412yes—
86C23×D11C2×D414yes—
87C23×D11#4114yes—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—22no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11C22×C414yes—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×D414yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×Dic11—24no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—24no—
112C22×Dic11—22no—
113C22×Dic11—24no—
114C22×Dic11—22no—
115C22×Dic11—24no—
116C22×Dic11—24no—
117C22×Dic11—24no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11C22×C414yes—
121C22×Dic11C22×C412yes—
122C22×Dic11C2×D414yes—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×D412yes—
125C22×Dic11#4118yes—
126C2×C4×D11—216no—
127C2×C4×D11—216no—
128C2×C4×D11—216no—
129C2×C4×D11—216no—
130C2×C4×D11—232no—
131C2×C4×D11—416no—
132C2×C4×D11—48no—
133C2×C4×D11—48no—
134C2×C4×D11C22⋊C4116yes—
135C11×C4⋊C4—28no—
136(C2×D11)⋊C4—216no—
137(C2×D11)⋊C4—48no—
138C4⋊Dic11—28no—
139Dic11⋊C4—216no—
140Dic11⋊C4—48no—
141C4×Dic11—48no—
142C23×C4⋊C4—111no—
143C2×#381—114no—
144C2×#380—111no—
145C2×C4×C22⋊C4—111no—
146#1445—111no—
147#1445—111no—
148#1445—111no—
149#1445D1111yescharacteristic, complemented
150C4⋊#95—114no—
151C23×C11C23×C411yescharacteristic
152C23×C11C22×D411yescharacteristic
153C23×C11C22×D411yescharacteristic
154C23×C11C22×D412yes—
155C23×C11C2×#4114yes—
156C23×C11C2×#4112yes—
157C23×C112−1+412yes—
158C23×C112−1+412yes—
159C22×D11—24no—
160C22×D11—24no—
161C22×D11—24no—
162C22×D11—24no—
163C22×D11—22no—
164C22×D11—24no—
165C22×D11—22no—
166C22×D11—28no—
167C22×D11—28no—
168C22×D11—28no—
169C22×D11—28no—
170C22×D11C2×C22⋊C414yes—
171C22×D11C4×D418yes—
172C22×D11#12118yes—
173C22×D11#12414yes—
174C22×D11#12714yes—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—28no—
180C2×C4×C11—24no—
181C2×C4×C11—28no—
182C2×C4×C11—44no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—44no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—44no—
192C2×C4×C11—44no—
193C2×C4×C11C2×C22⋊C414yes—
194C2×Dic11—24no—
195C2×Dic11—28no—
196C2×Dic11—24no—
197C2×Dic11—28no—
198C2×Dic11—44no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—44no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—44no—
208C2×Dic11—44no—
209C2×Dic11C2×C22⋊C414yes—
210C2×Dic11#11718yes—
211C2×Dic11#12318yes—
212C2×Dic11#12318yes—
213C4×D11—232no—
214C4×D11—432no—
215C24×C4—111no—
216C24×C4—112no—
217C22×C4⋊C4—112no—
218C22×C4⋊C4—111no—
219C22×C4⋊C4—118no—
220C22×C4⋊C4—112no—
221C22×C4⋊C4—224no—
222C22×C4⋊C4—224no—
223C22×C4⋊C4C2×D1111yescharacteristic
224C22×C22⋊C4—112no—
225C22×C22⋊C4—112no—
226C22×C42—112no—
227#381—2216no—
228#380—224no—
229C4×C22⋊C4—224no—
230C2×#95—114no—
231C2×#95—114no—
232C2×#95—114no—
233C2×#95—111no—
234C2×#95—111no—
235C2×#95C2×D1114yes—
236C2×#95C2×D1111yescharacteristic
237C2×#95C2×D1111yescharacteristic
238C22×C11C22×C22⋊C411yescharacteristic
239C22×C11C2×#11712yes—
240C22×C11C2×C4×D412yes—
241C22×C11#51912yes—
242C22×C11C2×#12112yes—
243C22×C11C2×#12312yes—
244C22×C11C2×#12312yes—
245C22×C11C2×#12411yescharacteristic
246C22×C11C2×#12711yescharacteristic
247C22×C11#53611yescharacteristic
248C22×C11#53612yes—
249C22×C11#53611yescharacteristic
250C22×C11#54714yes—
251C22×C11#54714yes—
252C22×C11#55214yes—
253C22×C11#55214yes—
254C2×D11—24no—
255C2×D11—216no—
256C2×D11—28no—
257C2×D11—28no—
258C2×D11—28no—
259C2×D11—28no—
260C2×D11—24no—
261C2×D11#39018yes—
262C4×C11—24no—
263C4×C11—44no—
264C4×C11—44no—
265C4×C11—82no—
266Dic11—44no—
267Dic11—44no—
268Dic11—82no—
269Dic11#38118yescomplemented
270C25—111no—
271C23×C4—111no—
272C23×C4—114no—
273C23×C4—114no—
274C23×C4—114no—
275C23×C4—112no—
276C23×C4—112no—
277C23×C4—118no—
278C23×C4—112no—
279C23×C4—228no—
280C23×C4—224no—
281C23×C4—224no—
282C23×C4—228no—
283C23×C4—228no—
284C23×C4C22×D1112yes—
285C23×C4C22×D1112yes—
286C23×C4C22×D1112yes—
287C23×C4C22×D1111yescharacteristic
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—118no—
291C2×C4⋊C4—114no—
292C2×C4⋊C4—2232no—
293C2×C4⋊C4—224no—
294C2×C4⋊C4—224no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—224no—
298C2×C4⋊C4—228no—
299C2×C4⋊C4C4×D1114yes—
300C2×C22⋊C4—118no—
301C2×C22⋊C4—224no—
302C2×C22⋊C4—224no—
303C2×C22⋊C4—224no—
304C2×C22⋊C4—228no—
305C2×C42—224no—
306C2×C42—228no—
307#95—22no—
308#95—22no—
309#95—28no—
310#95—228no—
311#95—228no—
312#95—222no—
313#95—222no—
314#95—228no—
315C2×C11C2×#38111yescharacteristic
316C2×C11C2×#39011yescharacteristic
317C2×C11#231011yescharacteristic
318C2×C11#234414yes—
319C2×C11#248612yes—
320C2×C11#248612yes—
321C2×C11#250112yes—
322C2×C11#250312yes—
323D11—28no—
324C24—112no—
325C24—114no—
326C24—112no—
327C24—112no—
328C24—114no—
329C24—222no—
330C24—224no—
331C24—222no—
332C24C23×D1111yescharacteristic
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—112no—
348C22×C4—112no—
349C22×C4—112no—
350C22×C4—118no—
351C22×C4—1116no—
352C22×C4—114no—
353C22×C4—114no—
354C22×C4—2216no—
355C22×C4—2216no—
356C22×C4—2216no—
357C22×C4—2216no—
358C22×C4—2232no—
359C22×C4—224no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—224no—
364C22×C4—224no—
365C22×C4—222no—
366C22×C4—224no—
367C22×C4—224no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—224no—
371C22×C4—222no—
372C22×C4—448no—
373C22×C4—4416no—
374C22×C4—448no—
375C22×C4C2×C4×D1114yes—
376C22×C4C2×C4×D1112yes—
377C22×C4D4×D1114yes—
378C22×C4D4×D1112yes—
379C22×C4D4×D1112yes—
380C4⋊C4—28no—
381C4⋊C4—2216no—
382C4⋊C4—228no—
383C4⋊C4—448no—
384C22⋊C4—2216no—
385C22⋊C4—448no—
386C42—448no—
387C11#1390411yescharacteristic, complemented, Sylow
388C23—114no—
389C23—114no—
390C23—118no—
391C23—118no—
392C23—114no—
393C23—228no—
394C23—222no—
395C23—224no—
396C23—224no—
397C23—224no—
398C23—228no—
399C23—224no—
400C23—224no—
401C23—228no—
402C23—222no—
403C23—228no—
404C23C22×C4×D1111yescharacteristic
405C23C2×D4×D1111yescharacteristic
406C23C2×D4×D1112yes—
407C23C2×D4×D1111yescharacteristic
408C23#6704012yes—
409C23#41×D1112yes—
410C23#41×D1114yes—
411C23#6704312yes—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—28no—
417C2×C4—24no—
418C2×C4—28no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—114no—
431C2×C4—118no—
432C2×C4—118no—
433C2×C4—118no—
434C2×C4—2232no—
435C2×C4—224no—
436C2×C4—228no—
437C2×C4—224no—
438C2×C4—228no—
439C2×C4—4432no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—444no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—444no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—444no—
449C2×C4—442no—
450C2×C4—444no—
451C2×C4C22⋊C4×D1114yes—
452C22—118no—
453C22—228no—
454C22—228no—
455C22—224no—
456C22—2216no—
457C22—224no—
458C22—228no—
459C22—228no—
460C22C2×C22⋊C4×D1111yescharacteristic
461C22D11×#11712yes—
462C22C4×D4×D1112yes—
463C22#1062310312yes—
464C22D11×#12112yes—
465C22#1062315912yes—
466C22#1062316214yes—
467C22D11×#12312yes—
468C22D11×#12312yes—
469C22#1062318614yes—
470C22D11×#12411yescharacteristic
471C22#1062320611yescharacteristic
472C22#1062322414yes—
473C22#1062323914yes—
474C22D11×#12711yescharacteristic
475C22#1062325511yescharacteristic
476C4—24no—
477C4—44no—
478C4—44no—
479C4—82no—
480C4—118no—
481C4—444no—
482C4—444no—
483C4—882no—
484C2—228no—
485C2D11×#38111yescharacteristic
486C2D11×#39011yescharacteristic
487C2#1307119911yescharacteristic
488C2#1307148214yes—
489C2#1307291712yes—
490C2#1307291912yes—
491C2#1307308212yes—
492C2#1307309612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1445D11
hypocenterC11#13904
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
5. #13066885C2semidirect
6. #13066884C2semidirect
7. #13066883C2semidirect
8. Dic11⋊#95C2semidirect
9. C11×#1445C2semidirect
21. C2×C4⋊C4×D11C4semidirect
149. #1445D11semidirect
269. Dic11#381semidirect
387. C11#13904semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
C2×#106222772
C2×#106222802
C2×#106222792
#130668852
#130668842
#130668832
Dic11⋊#952
C11×#14452
#1390411