Finite Group Databasebeta

← #14770971

Subgroups — #14770971

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66899C211yesmaximal, characteristic
2#13071495C211yesmaximal, characteristic
3Q8×C22⋊Dic11C211yesmaximal, characteristic
4#13069289C212yesmaximal, complemented
5#13069260C212yesmaximal, complemented
6#13068868C212yesmaximal, complemented
7#13068707C211yesmaximal, characteristic
8#13068643C211yesmaximal, characteristic
9#103×Dic11C212yesmaximal, complemented
10#13068390C211yesmaximal, characteristic
11C11×#1787C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C2×Q8×Dic11C2212yes—
14C22×C4⋊Dic11C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×C11×#103C2212yes—
17C2×C11×#103C2212yes—
18C2×C11×C22⋊C8C2211yescharacteristic
19C11×#380C2211yescharacteristic
20#10622843—22no—
21#10622843C2212yes—
22C2×#66899C418yescomplemented
23C2×#66899C2211yescharacteristic
24C2×#66899C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27#10622825—21no—
28#10622825C2211yescharacteristic
29C4×C22⋊Dic11—21no—
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C8×Dic11C2212yes—
32C4⋊C4×Dic11C2212yes—
33#10622586C2212yes—
34C2×#66871C2212yes—
35#10622555—21no—
36C22⋊C4×Dic11—21no—
37#10622266—22no—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42C22×Q8×C11—21no—
43C22×Q8×C11—22no—
44C22×Q8×C11—24no—
45C22×Q8×C11—42no—
46C22×Q8×C11C2×C414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C22×C8×C11C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—21no—
55C2×C22⋊Dic11—21no—
56C2×C22⋊Dic11D411yescharacteristic
57C2×C22⋊Dic11D411yescharacteristic
58Q8×Dic11—24no—
59Q8×Dic11—42no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11C2×C414yes—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8—42no—
72C22×C11⋊C8C2×C414yes—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C11×#103—24no—
76C11×#103—42no—
77C11×C22⋊C8—22no—
78C11×#95—21no—
79#66899C2×C414yes—
80#66899C2×C414yes—
81#66899C2×C414yes—
82#66899C2×C414yes—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95D412yes—
89C8×Dic11—42no—
90#66871—42no—
91#22575—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—24no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—28no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—44no—
101C2×Q8×C11—44no—
102C2×Q8×C11—48no—
103C2×Q8×C11C22×C412yes—
104C2×Q8×C11C22×C412yes—
105C2×Q8×C11#4114yes—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—44no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—24no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C22×Dic11—82no—
122C22×Dic11C2×D412yes—
123C22×Dic11C2×D412yes—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C22⋊C4—42no—
130C22⋊Dic11—22no—
131C22⋊Dic11—42no—
132C22⋊Dic11Q1614yes—
133C4⋊Dic11—24no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—44no—
139C4⋊Dic11C22×C412yes—
140C4⋊Dic11C22×C412yes—
141Dic11⋊C4—82no—
142C4×Dic11—22no—
143C4×Dic11—22no—
144C4×Dic11—44no—
145C4×Dic11—82no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—44no—
149C2×C11⋊C8C22×C412yes—
150C2×C11⋊C8C22×C412yes—
151C22×#103—111no—
152#2345—111no—
153Q8×C22⋊C4—111no—
154#1933—112no—
155#1928—112no—
156#1863—112no—
157#1824—111no—
158#1808—111no—
159#1787D1111yescharacteristic
160C4×#103—112no—
161C8×C22⋊C4—111no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11C4×D412yes—
165C23×C11C2×Q1612yes—
166C23×C11#13512yes—
167C23×C11C22×D411yescharacteristic
168Q8×C11—22no—
169Q8×C11—24no—
170Q8×C11—22no—
171Q8×C11—22no—
172Q8×C11—48no—
173Q8×C11—42no—
174Q8×C11#11714yes—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—22no—
182C2×C4×C11—48no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11C4×D412yes—
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C2×#4112yes—
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11H(5,𝔽2)12yes—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—84no—
205C2×Dic11C2×Q1614yes—
206C8×C11—42no—
207C11⋊C8—22no—
208C11⋊C8—22no—
209C23×Q8C2×D1111yescharacteristic
210C23×C8—111no—
211C2×C4×Q8—112no—
212C22×C4⋊C4—111no—
213C2×#107—112no—
214C2×#103—111no—
215C2×#103—111no—
216C2×#103—111no—
217C2×#103—111no—
218C2×#103—118no—
219C2×#103C2×D1112yes—
220C2×#103C2×D1112yes—
221C2×C22⋊C8C2×D1111yescharacteristic
222C2×C4×C8—112no—
223#391—112no—
224#391—222no—
225#389—112no—
226#387—222no—
227#380—111no—
228#380—221no—
229#380—221no—
230#380C2×D1111yescharacteristic
231C4×C4⋊C4—112no—
232C4×C22⋊C4—111no—
233C4×C22⋊C4—221no—
234C4×C22⋊C4—221no—
235#340—112no—
236#340—112no—
237#340—112no—
238#336—112no—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—24no—
242C22×C11—24no—
243C22×C11C4×Q1614yes—
244C22×C11C2×C4×D411yescharacteristic
245C22×C11#54612yes—
246C22×C11C22×Q1611yescharacteristic
247C22×C11C2×#13511yescharacteristic
248C22×C11#57712yes—
249C4×C11—22no—
250C4×C11—24no—
251C4×C11—42no—
252C4×C11—82no—
253C4×C11C2×#11711yescharacteristic
254C4×C11#51811yescharacteristic
255C4×C11#55112yes—
256Dic11—24no—
257Dic11—42no—
258Dic11—42no—
259Dic11—42no—
260Dic11—82no—
261C22×Q8—21no—
262C22×Q8—22no—
263C22×Q8—24no—
264C22×Q8—42no—
265C22×Q8C4×D1114yes—
266C22×Q8C22×D1111yescharacteristic
267C22×Q8C22×D1111yescharacteristic
268C23×C4—21no—
269C23×C4—221no—
270C23×C4C22×D1111yescharacteristic
271C22×C8—111no—
272C22×C8—111no—
273C22×C8—114no—
274C22×C8—442no—
275C22×C8C22×D1112yes—
276C4×Q8—224no—
277C4×Q8—442no—
278C2×C4⋊C4—114no—
279C2×C4⋊C4—111no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4C22×D1112yes—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—111no—
289C2×C22⋊C4—111no—
290C2×C22⋊C4—221no—
291C2×C42—112no—
292C2×C42—222no—
293C2×C42—222no—
294#107—442no—
295#103—24no—
296#103—42no—
297#103—114no—
298#103—114no—
299#103—114no—
300#103—114no—
301C22⋊C8—22no—
302C4×C8—442no—
303#95—21no—
304#95—112no—
305#95—222no—
306#95—222no—
307#95—222no—
308#95—222no—
309#95—221no—
310C2×C11—24no—
311C2×C11#234211yescharacteristic
312C2×C11C2×C4×Q1611yescharacteristic
313C2×C11#294911yescharacteristic
314C2×C11#329912yes—
315C2×C11#330112yes—
316C24D4×D1111yescharacteristic
317C2×Q8—24no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—22no—
321C2×Q8—28no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—44no—
325C2×Q8—44no—
326C2×Q8—48no—
327C2×Q8C2×C4×D1112yes—
328C2×Q8C2×C4×D1112yes—
329C2×Q8#434114yes—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—44no—
337C22×C4—112no—
338C22×C4—112no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—224no—
342C22×C4—222no—
343C22×C4—882no—
344C22×C4C2×C4×D1112yes—
345C22×C4D4×D1111yescharacteristic
346C22×C4#434112yes—
347C22×C4C23×D1111yescharacteristic
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—112no—
352C2×C8—112no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—444no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—112no—
359C4⋊C4—112no—
360C4⋊C4—224no—
361C4⋊C4—221no—
362C4⋊C4—221no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4—444no—
366C4⋊C4—882no—
367C22⋊C4—42no—
368C22⋊C4—114no—
369C22⋊C4—222no—
370C22⋊C4—442no—
371C42—222no—
372C42—222no—
373C42—444no—
374C42—882no—
375C11#2257511yescharacteristic, complemented, Sylow
376C23—22no—
377C23—22no—
378C23(C22⋊D11)⋊C412yes—
379C23#6696912yes—
380C23Q16×D1112yes—
381C23C2×D4×D1111yescharacteristic
382Q8—22no—
383Q8—24no—
384Q8—22no—
385Q8—22no—
386Q8—48no—
387Q8—42no—
388Q8#6693014yes—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—48no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—114no—
402C2×C4—222no—
403C2×C4—222no—
404C2×C4—222no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—884no—
415C2×C4(C22⋊D11)⋊C412yes—
416C2×C4C22×C4×D1111yescharacteristic
417C2×C4C2×#434112yes—
418C2×C4C2×#434111yescharacteristic
419C2×C4#6703712yes—
420C8—42no—
421C8—222no—
422C8—222no—
423C22—22no—
424C22—24no—
425C22—24no—
426C22—22no—
427C22#1062240314yes—
428C22C2×(C22⋊D11)⋊C411yescharacteristic
429C22#1062312212yes—
430C22C2×#6696911yescharacteristic
431C22C2×Q16×D1111yescharacteristic
432C22#1062330912yes—
433C4—22no—
434C4—24no—
435C4—42no—
436C4—82no—
437C4—224no—
438C4—442no—
439C4—442no—
440C4—442no—
441C4—882no—
442C4C2×#6693011yescharacteristic
443C4#1062301711yescharacteristic
444C4#1062311812yes—
445C2—24no—
446C2#1307146711yescharacteristic
447C2C2×#1062240311yescharacteristic
448C2#1307747111yescharacteristic
449C2#1308048512yes—
450C2#1308052212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#22575
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
4. #13069289C2semidirect
5. #13069260C2semidirect
6. #13068868C2semidirect
9. #103×Dic11C2semidirect
22. C2×#66899C4semidirect
375. C11#22575semidirect

Maximal subgroups

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

subgroupindex
C22×#668992
#130714952
Q8×C22⋊Dic112
#130692892
#130692602
#130688682
#130687072
#130686432
#103×Dic112
#130683902
C11×#17872
#2257511