Finite Group Databasebeta

← #14770373

Subgroups — #14770373

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×#10622443C211yesmaximal, characteristic, complemented
3#13071575C211yesmaximal, characteristic, complemented
4#13069579C212yesmaximal, complemented
5#13069576C211yesmaximal, characteristic, complemented
6#13069572C212yesmaximal, complemented
7#13069563C211yesmaximal, characteristic, complemented
8#13068624C212yesmaximal
9#102×Dic11C212yesmaximal
10C4×#66896C211yesmaximal, characteristic
11C11×#1802C211yesmaximal, 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×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2212yes—
24C11×#384C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×Dic11⋊C8C2212yes—
28C2×C8×Dic11C2212yes—
29#10622591—22no—
30#10622590C2212yes—
31C4⋊C4×Dic11—21no—
32C4⋊C4×Dic11C2212yes—
33#10622587—21no—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622443—24no—
37C11×#340C2212yes—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×Dic11—22no—
47C22×Dic22—21no—
48C22×Dic22D411yescharacteristic
49C22×C8×C11C2312yes—
50C4×D4×C11—22no—
51C4×D4×C11C2×C414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—22no—
59D4×Dic11—24no—
60D4×Dic11C2×C418yes—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—28no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68#66977—28no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4D412yes—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76#66943—24no—
77#66943C2×C418yes—
78#66931—216no—
79#66922—22no—
80#66922C2×C414yes—
81C4×Dic22C2×C414yes—
82C4×Dic22D414yes—
83C11×C4⋊C8—22no—
84C11×#102—24no—
85#66896—22no—
86#66896Q814yescomplemented
87C11⋊#95—21no—
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—24no—
104C22×C4×C11—22no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—28no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—21no—
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—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—81no—
132C11×C4⋊C4C22×C412yes—
133C11×C22⋊C4—24no—
134C42×C11C22×C412yes—
135C42×C11C2×D412yes—
136C22⋊Dic11—28no—
137C4⋊Dic11—28no—
138C4⋊Dic11—24no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11C22⋊C414yes—
144C4⋊Dic11C22×C414yes—
145C4⋊Dic11C2×Q812yes—
146Dic11⋊C4—28no—
147Dic11⋊C4C22⋊C418yes—
148C4×Dic11—42no—
149C4×Dic11—82no—
150C4×Dic11C22×C414yes—
151C4×Dic11C2×D414yes—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8C2×Q812yes—
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#1802D1111yescharacteristic
167C4×#102—112no—
168C4×#102—111no—
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—41no—
185C2×C4×C11—41no—
186C2×C4×C11—48no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11C2×C22⋊C412yes—
191C2×C4×C11C2×C22⋊C412yes—
192C2×C4×C11#13512yes—
193C2×C4×C11#13512yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×Q811yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×C4×C112−1+411yescharacteristic
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—24no—
205C2×Dic11—22no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—88no—
214C2×Dic11C2×C22⋊C414yes—
215C2×Dic11C2×C22⋊C414yes—
216Dic22—28no—
217Dic22—84no—
218C8×C11—42no—
219C11⋊C8—22no—
220C11⋊C8—41no—
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⋊C8C2×D1111yescharacteristic
234C2×#102—111no—
235C2×#102—111no—
236C2×#102C2×D1112yes—
237C2×C4×C8—112no—
238C2×C4×C8—111no—
239#391—221no—
240#387—222no—
241#384C2×D1111yescharacteristic
242#382—112no—
243C4×C4⋊C4—112no—
244C4×C4⋊C4—111no—
245C4×C4⋊C4—221no—
246#340—112no—
247#340—112no—
248#340—112no—
249#340—111no—
250#340—112no—
251#340—111no—
252#340C2×D1112yes—
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—82no—
270C4×C11#41614yes—
271C4×C11C2×C4×Q811yescharacteristic
272C4×C11#51911yescharacteristic
273C4×C11#54811yescharacteristic
274C4×C11D4×Q811yescharacteristic
275Dic11—24no—
276Dic11—24no—
277Dic11—42no—
278Dic11—44no—
279Dic11—81no—
280C22×Q8—111no—
281C22×Q8—221no—
282C22×D4C22×D1111yescharacteristic
283C23×C4—21no—
284C23×C4—222no—
285C22×C8—111no—
286C22×C8—111no—
287C22×C8C22×D1112yes—
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—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—228no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4C22×D1112yes—
312C2×C4⋊C4C22×D1111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—222no—
315C2×C42—112no—
316C2×C42—221no—
317C2×C42—222no—
318C2×C42C22×D1111yescharacteristic
319C4⋊C8—22no—
320C4⋊C8—224no—
321#102—24no—
322#102—114no—
323#102—222no—
324C4×C8—224no—
325C4×C8—222no—
326#95—222no—
327#95—222no—
328#95—222no—
329#95—221no—
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×C4×D1112yes—
349C2×D4#434112yes—
350C2×D4Q8×D1112yes—
351C22×C4—21no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—112no—
357C22×C4—112no—
358C22×C4—228no—
359C22×C4—221no—
360C22×C4—222no—
361C22×C4—221no—
362C22×C4—882no—
363C22×C4—882no—
364C22×C4D4×D1111yescharacteristic
365C22×C4D4×D1111yescharacteristic
366C22×C4C23×D1111yescharacteristic
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—112no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—42no—
380C4⋊C4—81no—
381C4⋊C4—114no—
382C4⋊C4—118no—
383C4⋊C4—114no—
384C4⋊C4—112no—
385C4⋊C4—228no—
386C4⋊C4—228no—
387C4⋊C4—224no—
388C4⋊C4—222no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4C2×C4×D1112yes—
393C22⋊C4—24no—
394C22⋊C4—228no—
395C42—114no—
396C42—114no—
397C42—442no—
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—
415D4#6694014yes—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—48no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—114no—
426C2×C4—114no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—224no—
432C2×C4—222no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—888no—
441C2×C4C22⋊C4×D1112yes—
442C2×C4C22⋊C4×D1112yes—
443C2×C4#6696512yes—
444C2×C4#6696912yes—
445C2×C4C22×C4×D1111yescharacteristic
446C2×C4C2×D4×D1111yescharacteristic
447C2×C4C2×#434111yescharacteristic
448C2×C4C2×Q8×D1111yescharacteristic
449C2×C4#6704311yescharacteristic
450C2×C4#6704311yescharacteristic
451C8—42no—
452C8—222no—
453C8—441no—
454C22—24no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22C2×C22⋊C4×D1111yescharacteristic
462C22#1062312911yescharacteristic
463C22#1062316311yescharacteristic
464C22C2×#6696511yescharacteristic
465C22C2×#6696911yescharacteristic
466C22#1062330511yescharacteristic
467C22#1062330911yescharacteristic
468C4—22no—
469C4—42no—
470C4—82no—
471C4—224no—
472C4—224no—
473C4—442no—
474C4—444no—
475C4—881no—
476C4#1062238514yes—
477C4C2×#6694011yescharacteristic
478C4#1062304711yescharacteristic
479C4#1062312911yescharacteristic
480C4#1062316311yescharacteristic
481C2—44no—
482C2#1307144811yescharacteristic
483C2C2×#1062238511yescharacteristic
484C2#1307714011yescharacteristic
485C2#1308126911yescharacteristic
486C2#1308128011yescharacteristic
487C2#1308148211yescharacteristic
488C2#1308149511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1802D11
hypocenterC11#22519
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#10622443C2semidirect
3. #13071575C2semidirect
4. #13069579C2semidirect
5. #13069576C2semidirect
6. #13069572C2semidirect
7. #13069563C2semidirect
17. #10623074C4semidirect
86. #66896Q8semidirect
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×#106224432
#130715752
#130695792
#130695762
#130695722
#130695632
#130686242
#102×Dic112
C4×#668962
C11×#18022
#2251911