Finite Group Databasebeta

← #14770367

Subgroups — #14770367

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13071571C211yesmaximal, characteristic, complemented
4#13069579C212yesmaximal, complemented
5#13069577C211yesmaximal, characteristic, complemented
6#13069572C212yesmaximal, complemented
7#13069564C211yesmaximal, characteristic, complemented
8#13068624C212yesmaximal
9#13068616C211yesmaximal, characteristic
10#102×Dic11C212yesmaximal
11C4×C11×#102C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11C2212yes—
14C22×C4⋊Dic11—21no—
15C2×#66977—21no—
16#10623074—24no—
17#10623074C418yescomplemented
18C2×#66943C2212yes—
19C2×#66931—22no—
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66896C2212yes—
27C2×Dic11⋊C8C2212yes—
28C2×C8×Dic11C2212yes—
29#10622590C2212yes—
30C4⋊C4×Dic11C2212yes—
31#10622548C2211yescharacteristic
32C4×C4⋊Dic11—21no—
33#10622542—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C8×Dic22—24no—
36#10622268—22no—
37C11×#340C2211yescharacteristic
38C11×#340C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×Dic11—22no—
47C22×Dic22—21no—
48C22×Dic22D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×D4×C11—22no—
52C4×D4×C11C2×C414yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—22no—
60D4×Dic11—24no—
61D4×Dic11C2×C418yes—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—28no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2312yes—
70#66977—28no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4D412yes—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2312yes—
75C22×C11⋊C8C2312yes—
76#66943—24no—
77#66943C2×C418yes—
78#66931—216no—
79#66922—22no—
80#66922C2×C414yes—
81C4×Dic22C2×C414yes—
82C4×Dic22D414yes—
83C11×#102—22no—
84C11×#102Q814yescomplemented
85C4×C8×C11—22no—
86C11×#95—21no—
87#66896—24no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91Dic11⋊C8—24no—
92C8×Dic11—24no—
93C4⋊(C11⋊C8)—22no—
94#22519—111nomaximal, Sylow
95C24×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11C22×C412yes—
100C2×D4×C11C2×Q812yes—
101C2×D4×C11#4112yes—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—24no—
105C22×C4×C11—21no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—28no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—82no—
115C22×Dic11—82no—
116C22×Dic11C2×D412yes—
117C22×Dic11C2×D412yes—
118C2×Dic22—24no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—81no—
122C2×Dic22—81no—
123C2×Dic22C22⋊C414yes—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C2×Q812yes—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4C22×C412yes—
135C11×C4⋊C4C2×Q812yes—
136C11×C22⋊C4—24no—
137C42×C11—42no—
138C42×C11C22×C412yes—
139C42×C11C2×D412yes—
140C22⋊Dic11—28no—
141C4⋊Dic11—28no—
142C4⋊Dic11—24no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—42no—
147C4⋊Dic11—81no—
148C4⋊Dic11C22⋊C414yes—
149C4⋊Dic11C22×C414yes—
150Dic11⋊C4—28no—
151Dic11⋊C4C22⋊C418yes—
152C4×Dic11—82no—
153C4×Dic11C22×C414yes—
154C4×Dic11C2×D414yes—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×#554—111no—
159C2×C8×Q8—111no—
160#2355—111no—
161#1991—112no—
162#1990—111no—
163#1989—112no—
164#1987—111no—
165#1804—112no—
166#1802—111no—
167C4×#102—112no—
168C4×#102D1111yescharacteristic
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11C22×D411yescharacteristic
177D4×C11—22no—
178D4×C11—22no—
179D4×C11—22no—
180D4×C11C4×Q814yes—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—48no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11C2×C22⋊C412yes—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11#13512yes—
196C2×C4×C11#13512yes—
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×Q811yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C112−1+411yescharacteristic
202C2×C4×C112−1+411yescharacteristic
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—24no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—88no—
214C2×Dic11C2×C22⋊C414yes—
215C2×Dic11C2×C22⋊C414yes—
216Dic22—28no—
217Dic22—84no—
218C8×C11—22no—
219C8×C11—41no—
220C11⋊C8—42no—
221#554—118no—
222#554—224no—
223C2×C4⋊Q8—111no—
224C2×#125—112no—
225C2×C22⋊Q8—222no—
226C2×C22⋊Q8—221no—
227C2×C4×Q8—111no—
228C2×C4×D4—112no—
229C2×C4×D4C2×D1111yescharacteristic
230C22×C4⋊C4—221no—
231C8×Q8—224no—
232C2×C4⋊C8—112no—
233C2×C4⋊C8—111no—
234C2×#102—112no—
235C2×#102C2×D1111yescharacteristic
236C2×#102C2×D1111yescharacteristic
237C2×C4×C8—112no—
238C2×C4×C8C2×D1111yescharacteristic
239#391—221no—
240#387—222no—
241#384—111no—
242#382—112no—
243C4×C4⋊C4—112no—
244C4×C4⋊C4—221no—
245C4×C4⋊C4C2×D1111yescharacteristic
246#340—112no—
247#340—112no—
248#340—112no—
249#340—112no—
250#340—112no—
251#340C2×D1111yescharacteristic
252#340C2×D1111yescharacteristic
253C22×C11—24no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11C22×C22⋊C411yescharacteristic
261C22×C11#54811yescharacteristic
262C22×C11D4×Q811yescharacteristic
263C22×C11C2×#13511yescharacteristic
264C22×C11C2×#13511yescharacteristic
265C22×C11#57611yescharacteristic
266C22×C11#57711yescharacteristic
267C4×C11—22no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—81no—
271C4×C11#41614yes—
272C4×C11C2×C4×Q811yescharacteristic
273C4×C11#51911yescharacteristic
274C4×C11#54811yescharacteristic
275C4×C11D4×Q811yescharacteristic
276Dic11—24no—
277Dic11—24no—
278Dic11—44no—
279Dic11—82no—
280C22×Q8—111no—
281C22×Q8—221no—
282C22×D4C22×D1111yescharacteristic
283C23×C4—21no—
284C23×C4—222no—
285C22×C8—112no—
286C22×C8C22×D1111yescharacteristic
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—114no—
289C4⋊Q8—222no—
290#125—118no—
291#125—224no—
292C22⋊Q8—2216no—
293C22⋊Q8—228no—
294C4×Q8—114no—
295C4×Q8—114no—
296C4×D4—22no—
297C4×D4—118no—
298C4×D4—224no—
299C4×D4C4×D1114yes—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—228no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C4⋊C4C22×D1111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—222no—
315C2×C42—21no—
316C2×C42—112no—
317C2×C42—222no—
318C2×C42C22×D1111yescharacteristic
319C4⋊C8—224no—
320C4⋊C8—222no—
321#102—22no—
322#102—224no—
323#102Dic2214yescomplemented
324C4×C8—22no—
325C4×C8—224no—
326#95—21no—
327#95—222no—
328#95—222no—
329#95—222no—
330C2×C11—44no—
331C2×C11Q8×C22⋊C411yescharacteristic
332C2×C11C2×#41611yescharacteristic
333C2×C11#289711yescharacteristic
334C2×C11#336011yescharacteristic
335C2×C11#336111yescharacteristic
336C2×C11#338011yescharacteristic
337C2×C11#338111yescharacteristic
338C24—21no—
339C2×Q8—114no—
340C2×Q8—224no—
341C2×Q8—222no—
342C2×Q8—222no—
343C2×Q8—881no—
344C2×Q8—881no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4C2×Dic2212yes—
349C2×D4C2×C4×D1112yes—
350C2×D4#433912yes—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—24no—
354C22×C4—21no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—228no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—882no—
363C22×C4—882no—
364C22×C4D4×D1111yescharacteristic
365C22×C4D4×D1111yescharacteristic
366C22×C4C23×D1111yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—222no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8C2×Dic2212yes—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—114no—
381C4⋊C4—118no—
382C4⋊C4—114no—
383C4⋊C4—228no—
384C4⋊C4—228no—
385C4⋊C4—224no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—442no—
390C4⋊C4—881no—
391C4⋊C4C2×Dic2212yes—
392C4⋊C4C2×C4×D1112yes—
393C22⋊C4—24no—
394C22⋊C4—228no—
395C42—42no—
396C42—114no—
397C42—114no—
398C42—882no—
399C42C2×C4×D1112yes—
400C42D4×D1112yes—
401C11#2251911yescharacteristic, complemented, Sylow
402C23—22no—
403C23—22no—
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23C2×D4×D1111yescharacteristic
410Q8—228no—
411Q8—884no—
412D4—22no—
413D4—22no—
414D4—22no—
415D4C4×Dic2214yes—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—48no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—114no—
429C2×C4—114no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—224no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—888no—
441C2×C4C22⋊C4×D1112yes—
442C2×C4C22⋊C4×D1112yes—
443C2×C4#6696512yes—
444C2×C4#6696912yes—
445C2×C4C22×Dic2211yescharacteristic
446C2×C4C22×C4×D1111yescharacteristic
447C2×C4C2×#433911yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4#6704311yescharacteristic
450C2×C4#6704311yescharacteristic
451C8—22no—
452C8—41no—
453C8—442no—
454C22—24no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22C2×C22⋊C4×D1111yescharacteristic
462C22D4×Dic2211yescharacteristic
463C22#1062308311yescharacteristic
464C22C2×#6696511yescharacteristic
465C22C2×#6696911yescharacteristic
466C22#1062330011yescharacteristic
467C22#1062330111yescharacteristic
468C4—22no—
469C4—42no—
470C4—42no—
471C4—81no—
472C4—224no—
473C4—224no—
474C4—444no—
475C4—882no—
476C4#1062238514yes—
477C4C2×C4×Dic2211yescharacteristic
478C4#1062304711yescharacteristic
479C4D4×Dic2211yescharacteristic
480C4#1062308311yescharacteristic
481C2—44no—
482C2C22⋊C4×Dic2211yescharacteristic
483C2C2×#1062238511yescharacteristic
484C2#1307713811yescharacteristic
485C2#1308126311yescharacteristic
486C2#1308127411yescharacteristic
487C2#1308148111yescharacteristic
488C2#1308148911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#22519
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13071571C2semidirect
4. #13069579C2semidirect
5. #13069577C2semidirect
6. #13069572C2semidirect
7. #13069564C2semidirect
17. #10623074C4semidirect
84. C11×#102Q8semidirect
323. #102Dic22semidirect
401. C11#22519semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×C8×Dic222
#130715712
#130695792
#130695772
#130695722
#130695642
#130686242
#130686162
#102×Dic112
C4×C11×#1022
#2251911