Finite Group Databasebeta

← #14775587

Subgroups — #14775587

Order 2816.

898 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#13071706C211yesmaximal, characteristic, complemented
2D4×C4⋊Dic11C211yesmaximal, characteristic
3#13069578C211yesmaximal, characteristic, complemented
4#13069380C211yesmaximal, characteristic, complemented
5#13069345C212yesmaximal, complemented
6#13069196C212yesmaximal, complemented
7#13068879C212yesmaximal
8#13068481C211yesmaximal, characteristic, complemented
9#102×Dic11C212yesmaximal
10C4×#66896C211yesmaximal, characteristic
11C2×C11×#476C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×D4×Dic11C2212yes—
15C22×C4⋊Dic11—21no—
16C11×#476C418yescomplemented
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2212yes—
20#10622843—22no—
21C2×#66896C2211yescharacteristic
22C2×#66896C2211yescharacteristic
23#10622825—21no—
24C2×#66881C2212yes—
25C2×C8×Dic11C2212yes—
26#10622598—21no—
27#10622598C2212yes—
28#10622598C2212yes—
29C4⋊C4×Dic11—21no—
30C4⋊C4×Dic11C2212yes—
31#10622563—22no—
32#10622548C2211yescharacteristic
33C4×C4⋊Dic11C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622189C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×Q8×C11—21no—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×Dic11—22no—
46C22×C8×C11C2312yes—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8C2×C414yescomplemented
49C4×D4×C11—22no—
50C4×D4×C11C2×C414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57D4×Dic11—24no—
58D4×Dic11—42no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—44no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2312yes—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C11×#106C2×C418yescomplemented
75C11×C4⋊C8C2×C414yescomplemented
76C11×#102C2×C418yes—
77#66896—22no—
78#66896Q814yescomplemented
79C11⋊#95—21no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95D412yes—
84#66881—42no—
85C8×Dic11—42no—
86C4×C11⋊C8—22no—
87#22963—111nomaximal, Sylow
88C24×C11—21no—
89C2×Q8×C11—24no—
90C2×Q8×C11—81no—
91C2×Q8×C11—81no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11C22×C412yes—
96C2×D4×C11C2×Q812yes—
97C2×D4×C11#4112yes—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—24no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C22×Dic11—44no—
110C22×Dic11—44no—
111C22×Dic11—82no—
112C22×Dic11C2×D412yes—
113C22×Dic11C2×D412yes—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11C22×C414yes—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4C22×C414yes—
121C11×C4⋊C4C22×C412yes—
122C11×C22⋊C4—24no—
123C42×C11C22×C412yes—
124C42×C11#4112yes—
125C22⋊Dic11—44no—
126C4⋊Dic11—22no—
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11—21no—
130C4⋊Dic11—22no—
131C4⋊Dic11—21no—
132C4⋊Dic11—44no—
133C4⋊Dic11—42no—
134C4⋊Dic11—81no—
135C4⋊Dic11—82no—
136C4⋊Dic11SD1614yes—
137C4⋊Dic11C2×Q812yes—
138C4×Dic11—22no—
139C4×Dic11—22no—
140C4×Dic11—42no—
141C4×Dic11—82no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8C2×Q812yes—
148C2×#476D1111yescharacteristic
149#2369—111no—
150D4×C4⋊C4—111no—
151#1990—111no—
152#1948—111no—
153#1941—112no—
154#1919—112no—
155#1864—112no—
156C8×C4⋊C4—111no—
157C4×#102—112no—
158C4×#102—111no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11C22×D411yescharacteristic
167Q8×C11—84no—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—22no—
171D4×C11C4×Q814yes—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—48no—
181C2×C4×C11C4×D412yes—
182C2×C4×C11C4×D412yes—
183C2×C4×C11C2×SD1612yes—
184C2×C4×C11#13512yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×Q811yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11H(5,𝔽2)11yescharacteristic
190C2×C4×C112−1+411yescharacteristic
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205C2×Dic11—88no—
206C2×Dic11C2×SD1614yes—
207C8×C11—24no—
208C11⋊C8—22no—
209C11⋊C8—41no—
210C2×C4⋊Q8C2×D1111yescharacteristic
211C2×C4×D4—112no—
212C2×C4×D4C2×D1111yescharacteristic
213C22×C4⋊C4—221no—
214#476Dic1118yescomplemented
215C2×#106—112no—
216C2×#106C2×D1112yes—
217C2×C4⋊C8C2×D1111yescharacteristic
218C2×#102—111no—
219C2×#102—111no—
220C2×#102C2×D1112yes—
221C2×C4×C8—111no—
222C2×C4×C8—112no—
223#391—222no—
224#389—112no—
225#389—112no—
226#389—221no—
227#385—222no—
228#384—111no—
229#380—221no—
230C4×C4⋊C4—111no—
231C4×C4⋊C4—112no—
232C4×C4⋊C4—111no—
233C4×C4⋊C4—221no—
234#340—112no—
235#340—112no—
236#340—111no—
237#340—111no—
238#340—112no—
239#336—112no—
240C22×C11—24no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11C2×C4×D411yescharacteristic
248C22×C11#54611yescharacteristic
249C22×C11D4×Q811yescharacteristic
250C22×C11C22×SD1611yescharacteristic
251C22×C11C2×#13511yescharacteristic
252C22×C11#57611yescharacteristic
253C22×C11#57711yescharacteristic
254C4×C11—22no—
255C4×C11—42no—
256C4×C11—44no—
257C4×C11C4×SD1614yes—
258C4×C11C2×C4×Q811yescharacteristic
259C4×C11#52011yescharacteristic
260C4×C11#55211yescharacteristic
261C4×C11#55411yescharacteristic
262Dic11—24no—
263Dic11—42no—
264Dic11—42no—
265Dic11—82no—
266Dic11—81no—
267C22×Q8—21no—
268C22×D4C22×D1111yescharacteristic
269C23×C4—21no—
270C23×C4—222no—
271C22×C8—111no—
272C22×C8—111no—
273C22×C8C22×D1112yes—
274C4⋊Q8—22no—
275C4⋊Q8C2×Dic1114yescomplemented
276C4×D4—22no—
277C4×D4—224no—
278C4×D4—442no—
279C4×D4C2×Dic1114yes—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—111no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—444no—
291C2×C4⋊C4C22×D1111yescharacteristic
292C2×C4⋊C4C22×D1112yes—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—222no—
295C2×C42—112no—
296C2×C42—221no—
297C2×C42—222no—
298C2×C42C22×D1111yescharacteristic
299#106—442no—
300#106C2×Dic1118yescomplemented
301C4⋊C8C2×Dic1114yescomplemented
302#102—114no—
303#102—222no—
304#102C2×Dic1118yes—
305C4×C8—222no—
306C4×C8—442no—
307#95—112no—
308#95—222no—
309#95—222no—
310#95—222no—
311#95—221no—
312C2×C11—44no—
313C2×C11#236011yescharacteristic
314C2×C11C2×C4×SD1611yescharacteristic
315C2×C11#294611yescharacteristic
316C2×C11#329511yescharacteristic
317C2×C11#330311yescharacteristic
318C2×C11Q8×SD1611yescharacteristic
319C2×C11#338011yescharacteristic
320C24—21no—
321C2×Q8—24no—
322C2×Q8—81no—
323C2×Q8—81no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4Q8×D1112yes—
328C2×D4#434312yes—
329C2×D4C22×Dic1112yes—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—24no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—112no—
336C22×C4—112no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—222no—
340C22×C4—444no—
341C22×C4—444no—
342C22×C4—882no—
343C22×C4D4×D1111yescharacteristic
344C22×C4D4×D1111yescharacteristic
345C22×C4C23×D1111yescharacteristic
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—112no—
349C2×C8—221no—
350C2×C8—221no—
351C2×C8—221no—
352C2×C8—221no—
353C2×C8—221no—
354C2×C8C22×Dic1114yes—
355C4⋊C4—24no—
356C4⋊C4—21no—
357C4⋊C4—22no—
358C4⋊C4—114no—
359C4⋊C4—112no—
360C4⋊C4—222no—
361C4⋊C4—221no—
362C4⋊C4—221no—
363C4⋊C4—222no—
364C4⋊C4—221no—
365C4⋊C4—222no—
366C4⋊C4—444no—
367C4⋊C4—442no—
368C4⋊C4—881no—
369C4⋊C4—882no—
370C4⋊C4C22×Dic1114yes—
371C4⋊C4C22×Dic1112yes—
372C22⋊C4—24no—
373C22⋊C4—444no—
374C42—222no—
375C42—222no—
376C42—442no—
377C42—882no—
378C42#434112yes—
379C42C22×Dic1112yes—
380C11#2296311yescharacteristic, complemented, Sylow
381C23—22no—
382C23—22no—
383C23—22no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23C2×D4×D1111yescharacteristic
389Q8—84no—
390D4—22no—
391D4—22no—
392D4—22no—
393D4Q8×Dic1114yes—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—48no—
403C2×C4—114no—
404C2×C4—222no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—442no—
413C2×C4—441no—
414C2×C4—442no—
415C2×C4—441no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—888no—
419C2×C4SD16×D1112yes—
420C2×C4#6696912yes—
421C2×C4D4×Dic1112yes—
422C2×C4D4×Dic1112yes—
423C2×C4C2×#434111yescharacteristic
424C2×C4C2×Q8×D1111yescharacteristic
425C2×C4C2×#434311yescharacteristic
426C2×C4#6704211yescharacteristic
427C2×C4#6704311yescharacteristic
428C2×C4C23×Dic1111yescharacteristic
429C8—24no—
430C8—222no—
431C8—441no—
432C22—24no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22#1062316111yescharacteristic
440C22#1062316311yescharacteristic
441C22C2×SD16×D1111yescharacteristic
442C22C2×#6696911yescharacteristic
443C22#1062330511yescharacteristic
444C22#1062330611yescharacteristic
445C22C2×D4×Dic1111yescharacteristic
446C4—22no—
447C4—42no—
448C4—44no—
449C4—224no—
450C4—442no—
451C4—442no—
452C4—882no—
453C4—881no—
454C4SD16×Dic1114yes—
455C4#1062316611yescharacteristic
456C4#1062317311yescharacteristic
457C4C2×Q8×Dic1111yescharacteristic
458C4#1062335811yescharacteristic
459C2—44no—
460C2#1307162511yescharacteristic
461C2C2×SD16×Dic1111yescharacteristic
462C2#1307744911yescharacteristic
463C2#1308043711yescharacteristic
464C2#1308054111yescharacteristic
465C2#1308147111yescharacteristic
466C2#1308148211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#476D11
hypocenterC11#22963
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #13071706C2semidirect
3. #13069578C2semidirect
4. #13069380C2semidirect
5. #13069345C2semidirect
6. #13069196C2semidirect
8. #13068481C2semidirect
16. C11×#476C4semidirect
48. C11×C4⋊Q8C2×C4semidirect
74. C11×#106C2×C4semidirect
75. C11×C4⋊C8C2×C4semidirect
78. #66896Q8semidirect
214. #476Dic11semidirect
275. C4⋊Q8C2×Dic11semidirect
300. #106C2×Dic11semidirect
301. C4⋊C8C2×Dic11semidirect
380. C11#22963semidirect

Maximal subgroups

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

subgroupindex
#130717062
D4×C4⋊Dic112
#130695782
#130693802
#130693452
#130691962
#130688792
#130684812
#102×Dic112
C4×#668962
C2×C11×#4762
#2296311