Finite Group Databasebeta

← #14770574

Subgroups — #14770574

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13071575C211yesmaximal, characteristic, complemented
4#13069545C212yesmaximal
5#13069540C211yesmaximal, characteristic, complemented
6#13069424C212yesmaximal
7#13068629C212yesmaximal, complemented
8#13068613C211yesmaximal, characteristic
9#103×Dic11C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C11×#1956C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#67000C2212yes—
14C2×Q8×Dic11C2212yes—
15#10623263—24no—
16#10623263C418yescomplemented
17C2×#66951—22no—
18C2×#66950—21no—
19C2×#66945—21no—
20C2×C4×D44C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#384C2211yescharacteristic
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×Dic11⋊C8C2212yes—
31C2×C8×Dic11C2212yes—
32#10622591—22no—
33#10622590C2212yes—
34C4⋊C4×Dic11—21no—
35C4⋊C4×Dic11C2212yes—
36#10622587—21no—
37C2×#66873C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C8×Dic22—24no—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43#10622167C2212yes—
44C22×Q8×C11C2312yes—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×Dic22D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8C2×C414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11C2311yescharacteristic
58#67000—24no—
59#67000C2×C418yes—
60Q8×Dic11—24no—
61Q8×Dic11C2×C418yes—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4D412yes—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2312yes—
75C22×C11⋊C8C2312yes—
76#66951—216no—
77#66950—28no—
78#66945—28no—
79C4×D44—22no—
80C4×D44C2×C414yes—
81C4×Dic22C2×C414yes—
82C4×Dic22D414yes—
83C11×#103—24no—
84C11×#103—42no—
85C4×C8×C11—22no—
86#66899—24no—
87#66899—42no—
88C11⋊#95—21no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92#66885—22no—
93#66885—22no—
94Dic11⋊C8—24no—
95C8×Dic11—24no—
96#66873—42no—
97C4⋊(C11⋊C8)—22no—
98#22541—111nomaximal, Sylow
99C23×D11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11C22×C414yes—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11C2×D412yes—
115C22×Dic11C2×D412yes—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44C22×C412yes—
122C2×C4×D11—24no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22C22⋊C414yes—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11#4112yes—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—81no—
140C42×C11C22×C412yes—
141C42×C11C2×D412yes—
142(C2×D11)⋊C4—28no—
143(C2×D11)⋊C4—28no—
144(C2×D11)⋊C4—24no—
145C4⋊Dic11—28no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11C22⋊C414yes—
151C4⋊Dic11C22×C412yes—
152C4⋊Dic11#4112yes—
153Dic11⋊C4C22⋊C418yes—
154C4×Dic11—28no—
155C4×Dic11—42no—
156C4×Dic11—82no—
157C4×Dic11C22×C414yes—
158C4×Dic11C2×D414yes—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×#556—111no—
163C2×C8×Q8—111no—
164#2355—111no—
165#1983—112no—
166#1981—111no—
167#1958—112no—
168#1956D1111yescharacteristic, complemented
169#1805—112no—
170#1802—111no—
171C4×#103—112no—
172C4×#102—111no—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181Q8×C11—24no—
182Q8×C11—24no—
183Q8×C11—42no—
184Q8×C11—42no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—24no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
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×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11H(5,𝔽2)11yescharacteristic
202C2×C4×C112−1+411yescharacteristic
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11C2×C22⋊C414yes—
217C2×Dic11C2×C22⋊C414yes—
218D44—22no—
219D44—22no—
220D44—41no—
221D44—41no—
222C4×D11—48no—
223Dic22—28no—
224C8×C11—22no—
225C8×C11—41no—
226C11⋊C8—42no—
227#556—118no—
228#556—224no—
229C2×C4⋊Q8C2×D1111yescharacteristic
230C2×#126—222no—
231C2×#124—112no—
232C2×C22⋊Q8—221no—
233C2×C4×Q8—111no—
234C2×C4×Q8—112no—
235C2×C4×D4—111no—
236C2×#117—221no—
237C8×Q8—224no—
238C2×C4⋊C8—112no—
239C2×C4⋊C8—111no—
240C2×#103—112no—
241C2×#103—112no—
242C2×#103C2×D1112yes—
243C2×#103C2×D1112yes—
244C2×#102—111no—
245C2×#102—111no—
246C2×#102—112no—
247C2×C4×C8—112no—
248C2×C4×C8C2×D1111yescharacteristic
249#391—221no—
250#387—222no—
251#384C2×D1111yescharacteristic
252#382—112no—
253C4×C4⋊C4—112no—
254C4×C4⋊C4—111no—
255C4×C4⋊C4—221no—
256#340—111no—
257#340—111no—
258#340—112no—
259C22×C11C22×C22⋊C411yescharacteristic
260C22×C11#54811yescharacteristic
261C22×C11#55011yescharacteristic
262C22×C11C2×#13511yescharacteristic
263C22×C11C2×#13511yescharacteristic
264C22×C11#57711yescharacteristic
265C22×C11#57811yescharacteristic
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C2×D11—81no—
273C4×C11—22no—
274C4×C11—44no—
275C4×C11—82no—
276C4×C11#41614yes—
277C4×C11C4×#4111yescharacteristic
278C4×C11#52011yescharacteristic
279C4×C11#54811yescharacteristic
280C4×C11#55011yescharacteristic
281Dic11—24no—
282Dic11—24no—
283Dic11—42no—
284Dic11—42no—
285Dic11—81no—
286C22×Q8—111no—
287C22×Q8C22×D1112yes—
288C22×D4—111no—
289C23×C4—221no—
290C22×C8—112no—
291C22×C8C22×D1111yescharacteristic
292C22×C8C22×D1111yescharacteristic
293C4⋊Q8—22no—
294C4⋊Q8C4×D1114yes—
295#126—2216no—
296#124—118no—
297#124—224no—
298C22⋊Q8—228no—
299C4×Q8—114no—
300C4×Q8—114no—
301C4×Q8—118no—
302C4×Q8—224no—
303C4×D4—114no—
304C4×D4—222no—
305#117—228no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4C22×D1112yes—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—221no—
320C2×C42—112no—
321C2×C42—222no—
322C2×C42—221no—
323C2×C42—222no—
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—224no—
326C4⋊C8—222no—
327#103—24no—
328#103—42no—
329#103—224no—
330#103—442no—
331#102—222no—
332#102—222no—
333#102—442no—
334C4×C8—22no—
335C4×C8—224no—
336#95—222no—
337#95—222no—
338#95—222no—
339#95—221no—
340C2×C11#234111yescharacteristic
341C2×C11C2×#41611yescharacteristic
342C2×C11#289811yescharacteristic
343C2×C11#336011yescharacteristic
344C2×C11#336411yescharacteristic
345C2×C11#339311yescharacteristic
346C2×C11#339411yescharacteristic
347D11—82no—
348C24—221no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—114no—
355C2×Q8—222no—
356C2×Q8—222no—
357C2×Q8C2×C4×D1114yes—
358C2×D4—112no—
359C2×D4—221no—
360C2×D4—221no—
361C2×D4—221no—
362C2×D4—221no—
363C2×D4—221no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—112no—
367C22×C4—112no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—224no—
371C22×C4—221no—
372C22×C4—442no—
373C22×C4—442no—
374C22×C4D4×D1111yescharacteristic
375C22×C4D4×D1111yescharacteristic
376C22×C4C23×D1111yescharacteristic
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—222no—
385C2×C8#434112yes—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—42no—
391C4⋊C4—81no—
392C4⋊C4—114no—
393C4⋊C4—118no—
394C4⋊C4—112no—
395C4⋊C4—112no—
396C4⋊C4—228no—
397C4⋊C4—221no—
398C4⋊C4—221no—
399C4⋊C4—221no—
400C4⋊C4—221no—
401C22⋊C4—228no—
402C22⋊C4—228no—
403C22⋊C4—224no—
404C42—114no—
405C42—114no—
406C42—228no—
407C42—442no—
408C42—882no—
409C42C2×C4×D1112yes—
410C42D4×D1112yes—
411C11#2254111yescharacteristic, complemented, Sylow
412C23—222no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23—441no—
418C23—441no—
419C23C2×D4×D1111yescharacteristic
420Q8—24no—
421Q8—24no—
422Q8—42no—
423Q8—42no—
424Q8—228no—
425D4—222no—
426D4—222no—
427D4—441no—
428D4—441no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—24no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—114no—
438C2×C4—114no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—448no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4C22⋊C4×D1112yes—
454C2×C4C22⋊C4×D1112yes—
455C2×C4#6696912yes—
456C2×C4#6697212yes—
457C2×C4C22×C4×D1111yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4C2×#434111yescharacteristic
460C2×C4#6703711yescharacteristic
461C2×C4#41×D1111yescharacteristic
462C2×C4#6704311yescharacteristic
463C8—22no—
464C8—41no—
465C8—442no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22C2×C22⋊C4×D1111yescharacteristic
474C22#1062320811yescharacteristic
475C22#1062324911yescharacteristic
476C22C2×#6696911yescharacteristic
477C22#1062329311yescharacteristic
478C22C2×#6697211yescharacteristic
479C22#1062329711yescharacteristic
480C4—22no—
481C4—44no—
482C4—82no—
483C4—224no—
484C4—224no—
485C4—442no—
486C4—442no—
487C4—881no—
488C4#1062241714yes—
489C4C4×#434111yescharacteristic
490C4#1062307711yescharacteristic
491C4#1062312911yescharacteristic
492C4#1062313011yescharacteristic
493C2—882no—
494C2#1307145511yescharacteristic
495C2C2×#1062241711yescharacteristic
496C2#1307714411yescharacteristic
497C2#1308127011yescharacteristic
498C2#1308130611yescharacteristic
499C2#1308160611yescharacteristic
500C2#1308161711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1956D11
hypocenterC11#22541
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13071575C2semidirect
5. #13069540C2semidirect
7. #13068629C2semidirect
9. #103×Dic11C2semidirect
11. C11×#1956C2semidirect
16. #10623263C4semidirect
168. #1956D11semidirect
411. C11#22541semidirect

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×C8×Dic222
#130715752
#130695452
#130695402
#130694242
#130686292
#130686132
#103×Dic112
C4×#668852
C11×#19562
#2254111