Finite Group Databasebeta

← #14775588

Subgroups — #14775588

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
1C2×#10622697C211yesmaximal, characteristic
2#13071706C211yesmaximal, characteristic, complemented
3#13071516C211yesmaximal, characteristic
4#13069377C211yesmaximal, characteristic, complemented
5#13069343C212yesmaximal, complemented
6#13069192C212yesmaximal, complemented
7#13068878C212yesmaximal
8C8×C4⋊Dic11C211yesmaximal, characteristic, complemented
9C4×#66885C211yesmaximal, characteristic
10#13068430C212yesmaximal
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66946C2212yes—
14C2×C4⋊C4×D11—21no—
15C2×C4×D44C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C11×#384C2211yescharacteristic
18#10622843—22no—
19C2×#66885C2211yescharacteristic
20C2×#66885C2211yescharacteristic
21C2×C8×Dic11C2212yes—
22#10622697C418yescomplemented
23#10622602—22no—
24#10622600—21no—
25#10622598—21no—
26#10622598C2212yes—
27C4⋊C4×Dic11—21no—
28C4⋊C4×Dic11C2212yes—
29#10622586C2212yes—
30C2×#66873C2212yes—
31C2×#66872C2212yes—
32C2×#66872C2212yes—
33C4×C4⋊Dic11C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C11×#340C2212yes—
37C11×#340C2212yes—
38#10622189C2211yescharacteristic
39#10622189C2211yescharacteristic
40#10622188C2212yes—
41#10622167C2212yes—
42C22×Q8×C11—21no—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×C4×D11—22no—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8C2×C414yescomplemented
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11C2311yescharacteristic
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11D411yescharacteristic
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11C2312yes—
68C22×C11⋊C8C2312yes—
69#66946—24no—
70#66946—42no—
71C4⋊C4×D11—44no—
72C4×D44—22no—
73C4×D44C2×C414yes—
74C4×C8×C11—22no—
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95D412yes—
80#66885—22no—
81#66885Q814yescomplemented
82C8×Dic11—42no—
83#66873C2×C418yes—
84#66872—42no—
85#66872C2×C418yescomplemented
86C4⋊(C11⋊C8)C2×C414yescomplemented
87#22963—111nomaximal, Sylow
88C23×D11—21no—
89C2×Q8×C11—24no—
90C2×Q8×C11—81no—
91C2×Q8×C11—81no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11C2×D412yes—
101C22×Dic11C2×D412yes—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44C22×C412yes—
106C2×D44C2×Q812yes—
107C2×D44#4112yes—
108C2×C4×D11—24no—
109C2×C4×D11—44no—
110C2×C4×D11—44no—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×C4×D11—82no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11C2×Q812yes—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—81no—
126C11×C4⋊C4C22×C414yes—
127C42×C11C22×C412yes—
128C42×C11#4112yes—
129(C2×D11)⋊C4—24no—
130(C2×D11)⋊C4—44no—
131C4⋊Dic11—22no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—82no—
137C4⋊Dic11SD1614yes—
138C4⋊Dic11C22×C412yes—
139C4⋊Dic11C2×Q812yes—
140Dic11⋊C4—44no—
141C4×Dic11—22no—
142C4×Dic11—22no—
143C4×Dic11—42no—
144C4×Dic11—82no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8C22×C414yes—
148C2×#476—111no—
149#2369—111no—
150D4×C4⋊C4—111no—
151#1990D1111yescharacteristic, complemented
152#1948—111no—
153#1941—112no—
154#1919—112no—
155#1864—112no—
156C8×C4⋊C4—111no—
157C4×#102—111no—
158C4×#102—112no—
159C23×C11C22×D411yescharacteristic
160C22×D11—22no—
161C22×D11—22no—
162C22×D11—22no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167Q8×C11—84no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—24no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11C4×D412yes—
177C2×C4×C11C4×D412yes—
178C2×C4×C11C2×SD1612yes—
179C2×C4×C11#13512yes—
180C2×C4×C11C23×C411yescharacteristic
181C2×C4×C11C22×Q811yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C11H(5,𝔽2)11yescharacteristic
185C2×C4×C112−1+411yescharacteristic
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11C2×SD1614yes—
201D44—22no—
202D44—22no—
203D44—22no—
204D44C4×Q814yes—
205C4×D11—48no—
206C4×D11—88no—
207C8×C11—22no—
208C8×C11—41no—
209C11⋊C8—24no—
210C2×C4⋊Q8C2×D1111yescharacteristic
211C2×C4×D4—112no—
212C2×C4×D4—111no—
213C22×C4⋊C4—221no—
214#476—118no—
215C2×#106—112no—
216C2×#106—112no—
217C2×C4⋊C8—111no—
218C2×#102—111no—
219C2×#102—112no—
220C2×#102—111no—
221C2×C4×C8—112no—
222C2×C4×C8C2×D1111yescharacteristic
223#391—222no—
224#389—112no—
225#389—112no—
226#389—221no—
227#385—222no—
228#384C2×D1111yescharacteristic
229#380—221no—
230C4×C4⋊C4—111no—
231C4×C4⋊C4—112no—
232C4×C4⋊C4—111no—
233C4×C4⋊C4—221no—
234#340—111no—
235#340—111no—
236#340—112no—
237#340C2×D1112yes—
238#340C2×D1112yes—
239#336—112no—
240C22×C11C2×C4×D411yescharacteristic
241C22×C11#54611yescharacteristic
242C22×C11D4×Q811yescharacteristic
243C22×C11C22×SD1611yescharacteristic
244C22×C11C2×#13511yescharacteristic
245C22×C11#57611yescharacteristic
246C22×C11#57711yescharacteristic
247C2×D11—24no—
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C4×C11—22no—
255C4×C11—44no—
256C4×C11—82no—
257C4×C11C4×SD1614yes—
258C4×C11C2×C4×Q811yescharacteristic
259C4×C11#52011yescharacteristic
260C4×C11#55211yescharacteristic
261C4×C11#55411yescharacteristic
262Dic11—24no—
263Dic11—42no—
264Dic11—42no—
265Dic11—42no—
266Dic11—81no—
267C22×Q8—21no—
268C22×D4—111no—
269C23×C4—222no—
270C23×C4—221no—
271C22×C8—112no—
272C22×C8C22×D1111yescharacteristic
273C22×C8C22×D1111yescharacteristic
274C4⋊Q8—22no—
275C4⋊Q8C4×D1114yescomplemented
276C4×D4—114no—
277C4×D4—224no—
278C4×D4—222no—
279C4×D4—442no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—444no—
291C2×C4⋊C4C22×D1112yes—
292C2×C4⋊C4C22×D1112yes—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—222no—
295C2×C42—112no—
296C2×C42—221no—
297C2×C42—222no—
298C2×C42C22×D1111yescharacteristic
299#106—118no—
300#106—442no—
301C4⋊C8—114no—
302#102—114no—
303#102—118no—
304#102—222no—
305C4×C8—22no—
306C4×C8—442no—
307#95—112no—
308#95—222no—
309#95—222no—
310#95—222no—
311#95—221no—
312C2×C11#236011yescharacteristic
313C2×C11C2×C4×SD1611yescharacteristic
314C2×C11#294611yescharacteristic
315C2×C11#329511yescharacteristic
316C2×C11#330311yescharacteristic
317C2×C11Q8×SD1611yescharacteristic
318C2×C11#338011yescharacteristic
319D11—44no—
320C24—221no—
321C2×Q8—24no—
322C2×Q8—81no—
323C2×Q8—81no—
324C2×D4—112no—
325C2×D4—112no—
326C2×D4—112no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—112no—
333C22×C4—112no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4—224no—
337C22×C4—221no—
338C22×C4—444no—
339C22×C4—444no—
340C22×C4—442no—
341C22×C4—442no—
342C22×C4—882no—
343C22×C4D4×D1111yescharacteristic
344C22×C4D4×D1111yescharacteristic
345C22×C4C23×D1111yescharacteristic
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—114no—
352C2×C8—222no—
353C2×C8—222no—
354C2×C8Q8×D1112yes—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—42no—
360C4⋊C4—81no—
361C4⋊C4—114no—
362C4⋊C4—112no—
363C4⋊C4—112no—
364C4⋊C4—222no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—444no—
370C4⋊C4—882no—
371C4⋊C4C2×C4×D1114yes—
372C22⋊C4—224no—
373C22⋊C4—444no—
374C42—222no—
375C42—222no—
376C42—442no—
377C42—882no—
378C42C2×C4×D1112yes—
379C42#434112yes—
380C11#2296311yescharacteristic, complemented, Sylow
381C23—222no—
382C23—222no—
383C23—222no—
384C23—441no—
385C23—441no—
386C23—441no—
387C23—441no—
388C23C2×D4×D1111yescharacteristic
389Q8—84no—
390D4—114no—
391D4—222no—
392D4—222no—
393D4—222no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—24no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—114no—
403C2×C4—222no—
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—441no—
413C2×C4—441no—
414C2×C4—448no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—888no—
419C2×C4(C22⋊D11)⋊C412yes—
420C2×C4(C22⋊D11)⋊C412yes—
421C2×C4SD16×D1112yes—
422C2×C4#6697212yes—
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C2×#434111yescharacteristic
425C2×C4C2×Q8×D1111yescharacteristic
426C2×C4#6704011yescharacteristic
427C2×C4#41×D1111yescharacteristic
428C2×C4#6704211yescharacteristic
429C8—22no—
430C8—41no—
431C8—224no—
432C22—224no—
433C22—442no—
434C22—442no—
435C22—442no—
436C22—442no—
437C22—442no—
438C22—442no—
439C22C2×(C22⋊D11)⋊C411yescharacteristic
440C22#1062320711yescharacteristic
441C22#1062325811yescharacteristic
442C22#1062328811yescharacteristic
443C22C2×SD16×D1111yescharacteristic
444C22#1062329311yescharacteristic
445C22C2×#6697211yescharacteristic
446C4—22no—
447C4—44no—
448C4—82no—
449C4—224no—
450C4—442no—
451C4—442no—
452C4—442no—
453C4—881no—
454C4#1062240114yes—
455C4C4×Q8×D1111yescharacteristic
456C4#1062310511yescharacteristic
457C4#1062316611yescharacteristic
458C4#1062317011yescharacteristic
459C2—444no—
460C2#1307162611yescharacteristic
461C2C2×#1062240111yescharacteristic
462C2#1307744211yescharacteristic
463C2#1308043911yescharacteristic
464C2#1308054311yescharacteristic
465C2#1308147311yescharacteristic
466C2#1308148511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1990D11
hypocenterC11#22963
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. #13071706C2semidirect
4. #13069377C2semidirect
5. #13069343C2semidirect
6. #13069192C2semidirect
8. C8×C4⋊Dic11C2semidirect
11. C11×#1990C2semidirect
22. #10622697C4semidirect
49. C11×C4⋊Q8C2×C4semidirect
81. #66885Q8semidirect
85. #66872C2×C4semidirect
86. C4⋊(C11⋊C8)C2×C4semidirect
151. #1990D11semidirect
275. C4⋊Q8C4×D11semidirect
380. C11#22963semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
#130717062
#130715162
#130693772
#130693432
#130691922
#130688782
C8×C4⋊Dic112
C4×#668852
#130684302
C11×#19902
#2296311