Finite Group Databasebeta

← #14770947

Subgroups — #14770947

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071501C211yesmaximal, characteristic, complemented
2#13071457C211yesmaximal, characteristic
3#13069301C212yesmaximal, complemented
4#13069238C212yesmaximal, complemented
5#13068872C212yesmaximal, complemented
6#13068711C211yesmaximal, characteristic, complemented
7#13068645C211yesmaximal, characteristic, complemented
8#13068556C211yesmaximal, characteristic
9#103×Dic11C212yesmaximal, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#416C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C11×#416C418yescomplemented
17C2×C11×#103C2211yescharacteristic
18C2×C11×#103C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×#66899C2212yes—
22#10622834—22no—
23#10622834C2212yes—
24C2×#66896C2212yes—
25#10622825—21no—
26#10622825C2211yescharacteristic
27#10622825C2211yescharacteristic
28C4×C22⋊Dic11—21no—
29C4×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66882C2212yes—
32C2×C8×Dic11C2212yes—
33#10622598C2212yes—
34C4⋊C4×Dic11C2212yes—
35#10622564—22no—
36#10622549—21no—
37#10622545—21no—
38#10622189C2212yes—
39#10622188C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C2×C11×#41—22no—
43C2×C11×#41—24no—
44C2×C11×#41—42no—
45C2×C11×#41C2×C414yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×C8×C11—42no—
52C22×C8×C11C2×C414yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×#117—22no—
56C11×#117C2×C414yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11—21no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11D412yes—
66Q8×Dic11—24no—
67Q8×Dic11—42no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2312yes—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2312yes—
75C22×C11⋊C8C2312yes—
76C11×#103C2×C414yes—
77C11×#103C2×C414yes—
78C11×#102C2×C414yes—
79C11×#102C2×C414yes—
80#66899—24no—
81#66896—42no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95D411yescharacteristic
87C11⋊#95D411yescharacteristic
88C22⋊(C11⋊C8)—22no—
89#66882—42no—
90C8×Dic11—42no—
91#22573—111nomaximal, Sylow
92C24×C11—21no—
93C24×C11C2×D411yescharacteristic
94C11×#41—28no—
95C11×#41—44no—
96C11×#41—48no—
97C2×Q8×C11—21no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22×C412yes—
100C2×Q8×C11#4114yes—
101C2×D4×C11—24no—
102C2×D4×C11—22no—
103C2×D4×C11—21no—
104C2×D4×C11—22no—
105C2×D4×C11—44no—
106C2×D4×C11C22×C412yes—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—44no—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4112yes—
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11C2×D412yes—
121C22×Dic11C2×D412yes—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—44no—
125C2×C8×C11C22×C412yes—
126C2×C8×C11C22×C412yes—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4C22×C412yes—
130C11×C4⋊C4C22×C412yes—
131C11×C22⋊C4—24no—
132C42×C11—24no—
133C22⋊Dic11—24no—
134C22⋊Dic11—44no—
135C22⋊Dic11—81no—
136C22⋊Dic11—81no—
137C22⋊Dic11—82no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—44no—
143C4⋊Dic11—82no—
144C4×Dic11—22no—
145C4×Dic11—22no—
146C4×Dic11—44no—
147C4×Dic11—44no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×#416D1111yescharacteristic
152#2346—111no—
153#2341—111no—
154#1934—112no—
155#1925—112no—
156#1863—112no—
157#1825—111no—
158#1808—111no—
159#1788—111no—
160C4×#103—112no—
161C8×C22⋊C4—111no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—22no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11C4×D412yes—
172C23×C11C22×D411yescharacteristic
173Q8×C11—22no—
174Q8×C11—24no—
175Q8×C11#11714yes—
176D4×C11—22no—
177D4×C11—22no—
178D4×C11—48no—
179D4×C11—42no—
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—48no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11C4×D412yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C2×#4112yes—
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11H(5,𝔽2)12yes—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11#13514yes—
209C8×C11—22no—
210C8×C11—22no—
211C11⋊C8—42no—
212C22×#41C2×D1111yescharacteristic
213C23×C8C2×D1111yescharacteristic
214C2×C4×Q8—112no—
215C2×#117C2×D1111yescharacteristic
216C2×#107—112no—
217#416Dic1118yescomplemented
218C2×#103—112no—
219C2×#103C2×D1111yescharacteristic
220C2×#103C2×D1111yescharacteristic
221C2×#102—112no—
222C2×#102C2×D1111yescharacteristic
223C2×#102C2×D1111yescharacteristic
224C2×C22⋊C8—111no—
225C2×C4×C8—112no—
226#390—112no—
227#390—222no—
228#389—112no—
229#388—222no—
230#382—221no—
231#380—111no—
232#380—111no—
233#380—221no—
234C4×C4⋊C4—112no—
235C4×C22⋊C4—111no—
236C4×C22⋊C4—221no—
237#376—221no—
238#340—112no—
239#340—112no—
240#340—112no—
241#336—112no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11C2×C4×D411yescharacteristic
253C22×C11#54612yes—
254C22×C11C2×#13512yes—
255C22×C11#57611yescharacteristic
256C22×C11#57811yescharacteristic
257C4×C11—22no—
258C4×C11—24no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11C2×#11711yescharacteristic
262C4×C11#51811yescharacteristic
263C4×C11#55112yes—
264Dic11—24no—
265Dic11—42no—
266Dic11—82no—
267Dic11—82no—
268C2×#41—22no—
269C2×#41—24no—
270C2×#41—42no—
271C2×#41C2×Dic1114yes—
272C22×Q8C22×D1111yescharacteristic
273C22×D4—21no—
274C22×D4C22×D1111yescharacteristic
275C23×C4—21no—
276C23×C4C22×D1111yescharacteristic
277C22×C8—42no—
278C22×C8—112no—
279C22×C8C2×Dic1114yes—
280C22×C8C22×D1111yescharacteristic
281C22×C8C22×D1111yescharacteristic
282C4×Q8—224no—
283C4×Q8—442no—
284#117—22no—
285#117C2×Dic1114yes—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4C22×D1111yescharacteristic
291C2×C4⋊C4C22×D1111yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—112no—
294C2×C22⋊C4—222no—
295C2×C22⋊C4—222no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C42—21no—
299C2×C42—112no—
300C2×C42—222no—
301C2×C42—222no—
302#107—442no—
303#103—224no—
304#103C2×Dic1114yes—
305#103C2×Dic1114yes—
306#102—442no—
307#102C2×Dic1114yes—
308#102C2×Dic1114yes—
309C22⋊C8—222no—
310C4×C8—442no—
311#95—111no—
312#95—111no—
313#95—222no—
314#95—222no—
315#95—221no—
316#95—221no—
317C2×C11—42no—
318C2×C11—82no—
319C2×C11#234211yescharacteristic
320C2×C11C4×#13511yescharacteristic
321C2×C11#295111yescharacteristic
322C2×C11#330012yes—
323C2×C11#330512yes—
324C24—21no—
325C24D4×D1111yescharacteristic
326#41—28no—
327#41—44no—
328#41—48no—
329C2×Q8—21no—
330C2×Q8—22no—
331C2×Q8#433914yes—
332C2×Q8C22×Dic1112yes—
333C2×D4—24no—
334C2×D4—22no—
335C2×D4—21no—
336C2×D4—22no—
337C2×D4—44no—
338C2×D4C22×Dic1112yes—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—24no—
345C22×C4—44no—
346C22×C4—112no—
347C22×C4—112no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4D4×D1111yescharacteristic
351C22×C4#434112yes—
352C22×C4C22×Dic1112yes—
353C22×C4C23×D1111yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—44no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8C22×Dic1112yes—
361C2×C8C22×Dic1112yes—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—444no—
369C4⋊C4—882no—
370C4⋊C4C22×Dic1112yes—
371C4⋊C4C22×Dic1112yes—
372C22⋊C4—24no—
373C22⋊C4—224no—
374C22⋊C4—444no—
375C22⋊C4—882no—
376C22⋊C4—881no—
377C22⋊C4—881no—
378C42—24no—
379C42—222no—
380C42—222no—
381C42—444no—
382C42—444no—
383C11#2257311yescharacteristic, complemented, Sylow
384C23—22no—
385C23—22no—
386C23—21no—
387C23—21no—
388C23—22no—
389C23—42no—
390C23—42no—
391C23—41no—
392C23—41no—
393C23D4×Dic1112yes—
394C23C2×D4×D1111yescharacteristic
395Q8—24no—
396Q8—22no—
397Q8#6697914yes—
398D4—22no—
399D4—22no—
400D4—48no—
401D4—42no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—48no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—114no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4D4×Dic1112yes—
427C2×C4C2×#433912yes—
428C2×C4C2×#434111yescharacteristic
429C2×C4#6703712yes—
430C2×C4C23×Dic1111yescharacteristic
431C8—22no—
432C8—22no—
433C8—442no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—82no—
443C22—82no—
444C22#1062302112yes—
445C22D11×#13512yes—
446C22#1062330011yescharacteristic
447C22#1062330211yescharacteristic
448C22C2×D4×Dic1111yescharacteristic
449C4—22no—
450C4—24no—
451C4—42no—
452C4—42no—
453C4—224no—
454C4—442no—
455C4—882no—
456C4—882no—
457C4#1062302612yes—
458C4C2×#6697911yescharacteristic
459C4#1062332911yescharacteristic
460C2—42no—
461C2—82no—
462C2#1307146511yescharacteristic
463C2#135×Dic1111yescharacteristic
464C2#1307749211yescharacteristic
465C2#1308050412yes—
466C2#1308056212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#416D11
hypocenterC11#22573
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. #13071501C2semidirect
3. #13069301C2semidirect
4. #13069238C2semidirect
5. #13068872C2semidirect
6. #13068711C2semidirect
7. #13068645C2semidirect
9. #103×Dic11C2semidirect
10. C8×C22⋊Dic11C2semidirect
16. C11×#416C4semidirect
217. #416Dic11semidirect
383. C11#22573semidirect

Maximal subgroups

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

subgroupindex
#130715012
#130714572
#130693012
#130692382
#130688722
#130687112
#130686452
#130685562
#103×Dic112
C8×C22⋊Dic112
C2×C11×#4162
#2257311