Finite Group Databasebeta

← #14767637

Subgroups — #14767637

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622671C211yesmaximal, characteristic
2#13071341C211yesmaximal, characteristic, complemented
3#13069428C211yesmaximal, characteristic, complemented
4#13069421C211yesmaximal, characteristic, complemented
5#13068971C212yesmaximal, complemented
6#13068967C212yesmaximal, complemented
7#13068964C212yesmaximal, complemented
8#13068953C212yesmaximal, complemented
9#13068751C211yesmaximal, characteristic, complemented
10#13068368C211yesmaximal, characteristic, complemented
11C11×#2326C211yesmaximal, characteristic, complemented
12C2×C11×#124C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C22×#4325C2212yes—
16C22×#4323C2212yes—
17C2×#66927C2211yescharacteristic
18C2×C4×D44C2212yes—
19C11×#391C2211yescharacteristic
20C11×#390C2211yescharacteristic
21C11×#388—22no—
22C11×#385—22no—
23C11×#384C2211yescharacteristic
24C11×#376C2211yescharacteristic
25C2×#66899C2212yes—
26C2×#66896C2212yes—
27#10622671C418yescomplemented
28C2×#66873C2212yes—
29C2×#66873C2212yes—
30#10622552C2212yes—
31#10622549C2211yescharacteristic
32C2×#66867C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622278—22no—
35#10622278—22no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622162C2212yes—
39#10622162C2212yes—
40C22×Q8×C11C2311yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C22×D44—22no—
44C22×D44C2312yes—
45C22×C4×D11—22no—
46C11×#124—22no—
47C11×#124C2×C414yescomplemented
48C4×Q8×C11—42no—
49C4×D4×C11—42no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—22no—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×#4325—42no—
62C2×#4325—42no—
63C2×#4325C2×C418yescomplemented
64C2×#4323—42no—
65C2×#4323—42no—
66C2×#4323C2×C418yescomplemented
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11C2312yes—
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2312yes—
73#66927—22no—
74#66927C2×C414yescomplemented
75C4×D44—42no—
76C4×D44—42no—
77C11×#95—22no—
78C11×#95D412yes—
79C11×#95D412yes—
80#66899—42no—
81#66896—42no—
82C11⋊#95—22no—
83#66873—42no—
84#66873—42no—
85#66867C2×C414yescomplemented
86C4×C11⋊C8—22no—
87#22279—111nomaximal, Sylow
88C24×C11—21no—
89C23×D11—22no—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11C22×C412yes—
94C2×D4×C11—21no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11C22×C412yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—42no—
102C22×C4×C11—82no—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—22no—
109C2×D44—28no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—82no—
116C2×D44—82no—
117C2×D44C22×C414yes—
118C2×C4×D11—44no—
119C2×C4×D11—82no—
120C2×C4×D11—82no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—82no—
125C11×C22⋊C4—28no—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—82no—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11—42no—
131C42×C11C22×C412yes—
132C42×C11#4112yes—
133#4325—48no—
134#4323—48no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—82no—
137(C2×D11)⋊C4—82no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8C22×C414yes—
146C2×#496—111no—
147#2328—111no—
148#2326D1111yescharacteristic, complemented
149#1958—111no—
150#1957—111no—
151#1880—112no—
152#1879—112no—
153#1879—112no—
154#1877—112no—
155#1836—111no—
156#1746—111no—
157C23×C11—22no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11C22×D411yescharacteristic
163C22×D11—24no—
164C22×D11—42no—
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—42no—
168C22×D11—42no—
169C22×D11—42no—
170Q8×C11—24no—
171Q8×C11—42no—
172D4×C11—24no—
173D4×C11—42no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—84no—
191C2×C4×C11C4×D414yes—
192C2×C4×C11C23×C411yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11H(5,𝔽2)12yes—
195C2×C4×C11H(5,𝔽2)12yes—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199D44—24no—
200D44—24no—
201D44—42no—
202D44—42no—
203D44—88no—
204C4×D11—88no—
205C11⋊C8—24no—
206C11⋊C8—42no—
207C22×SD16—112no—
208C22×D8—112no—
209C2×#127—111no—
210C2×#124C2×D1111yescharacteristic
211C2×C4×Q8C2×D1111yescharacteristic
212C2×C4×D4—112no—
213C2×C4×D4C2×D1111yescharacteristic
214#496—118no—
215C2×#103—112no—
216C2×#102—112no—
217C2×#102—112no—
218C2×#102—112no—
219C2×#97—111no—
220C2×C4×C8—111no—
221#391C2×D1111yescharacteristic
222#390—112no—
223#390C2×D1111yescharacteristic
224#388—22no—
225#386—222no—
226#386—222no—
227#385—22no—
228#384C2×D1111yescharacteristic
229#382—111no—
230#376C2×D1111yescharacteristic
231#340—112no—
232#340—112no—
233#336—112no—
234#336—112no—
235C22×C11—42no—
236C22×C11—44no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—82no—
240C22×C11C2×C4×D411yescharacteristic
241C22×C11#53511yescharacteristic
242C22×C11#53511yescharacteristic
243C22×C11#57612yes—
244C22×C11#57712yes—
245C2×D11—44no—
246C2×D11—44no—
247C2×D11—44no—
248C2×D11—82no—
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—82no—
252C4×C11—24no—
253C4×C11—42no—
254C4×C11—41no—
255C4×C11—41no—
256C4×C11—42no—
257C4×C11—81no—
258C4×C11—81no—
259C4×C11#51812yes—
260C4×C11#54012yes—
261Dic11—82no—
262C22×Q8C22×D1111yescharacteristic
263C22×D4—112no—
264C22×D4—222no—
265C22×D4C22×D1111yescharacteristic
266C23×C4—21no—
267C23×C4—222no—
268C2×SD16—118no—
269C2×SD16—442no—
270C2×SD16—442no—
271C2×D8—118no—
272C2×D8—442no—
273C2×D8—442no—
274C22×C8—112no—
275C22×C8—112no—
276#127—114no—
277#127—222no—
278#124—22no—
279#124C4×D1114yescomplemented
280C4×Q8—42no—
281C4×D4—42no—
282C4×D4—442no—
283C4×D4—442no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4C22×D1111yescharacteristic
288C2×C4⋊C4C22×D1111yescharacteristic
289C2×C22⋊C4—22no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—222no—
295C2×C42—21no—
296C2×C42C22×D1111yescharacteristic
297C2×C42C22×D1111yescharacteristic
298C2×C42C22×D1111yescharacteristic
299#103—442no—
300#102—442no—
301#102—442no—
302#102—442no—
303#97—114no—
304C4×C8—222no—
305#95—22no—
306#95—222no—
307#95C22⋊D1112yes—
308#95C22⋊D1112yes—
309C2×C11—82no—
310C2×C11#232811yescharacteristic
311C2×C11#294612yes—
312C2×C11#322011yescharacteristic
313C2×C11#322111yescharacteristic
314C2×C11#322412yes—
315D11—84no—
316C24—21no—
317C24—222no—
318C2×Q8—21no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8C2×C4×D1112yes—
322C2×D4—21no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—114no—
326C2×D4—228no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—882no—
333C2×D4—882no—
334C2×D4C2×C4×D1112yes—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—42no—
339C22×C4—82no—
340C22×C4—222no—
341C22×C4—444no—
342C22×C4—882no—
343C22×C4—882no—
344C22×C4C2×C22⋊D1112yes—
345C22×C4C2×C22⋊D1111yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347C22×C4C2×C22⋊D1112yes—
348C22×C4C23×D1111yescharacteristic
349SD16—448no—
350D8—448no—
351C2×C8—114no—
352C2×C8—222no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—222no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—42no—
360C4⋊C4—82no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C22⋊C4—28no—
364C22⋊C4—42no—
365C22⋊C4—82no—
366C22⋊C4—444no—
367C22⋊C4—882no—
368C22⋊C4—882no—
369C42—22no—
370C42—22no—
371C42—42no—
372C42C2×C4×D1112yes—
373C42#433912yes—
374C11#2227911yescharacteristic, complemented, Sylow
375C23—22no—
376C23—41no—
377C23—41no—
378C23—42no—
379C23—42no—
380C23—224no—
381C23—442no—
382C23—442no—
383C23—442no—
384C23—442no—
385C23—442no—
386C23—442no—
387C23C22×C22⋊D1111yescharacteristic
388Q8—24no—
389Q8—42no—
390D4—24no—
391D4—42no—
392D4—224no—
393D4—224no—
394D4—442no—
395D4—442no—
396D4—888no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—84no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—888no—
418C2×C4C4×C22⋊D1114yes—
419C2×C4C22×C4×D1111yescharacteristic
420C2×C4C2×#433911yescharacteristic
421C2×C4#6703712yes—
422C2×C4#6704212yes—
423C8—224no—
424C8—442no—
425C22—44no—
426C22—42no—
427C22—81no—
428C22—81no—
429C22—82no—
430C22—444no—
431C22—444no—
432C22—444no—
433C22—882no—
434C22—882no—
435C22—882no—
436C22—882no—
437C22C2×C4×C22⋊D1111yescharacteristic
438C22#1062333611yescharacteristic
439C22#1062336111yescharacteristic
440C22#1062336612yes—
441C22#1062336812yes—
442C4—24no—
443C4—41no—
444C4—41no—
445C4—42no—
446C4—42no—
447C4—81no—
448C4—81no—
449C4—882no—
450C4#1062307612yes—
451C4#1062309312yes—
452C2—82no—
453C2—884no—
454C2#1307133811yescharacteristic
455C2#1307744412yes—
456C2#1307966611yescharacteristic
457C2#1307967711yescharacteristic
458C2#1307970412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2326C2
socleC23×C11C22×D4
prime radicalC2×#10622671C2
cosocleC22×C4×C11C24
hypercenter#2326D11
hypocenterC11#22279
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #13071341C2semidirect
3. #13069428C2semidirect
4. #13069421C2semidirect
5. #13068971C2semidirect
6. #13068967C2semidirect
7. #13068964C2semidirect
8. #13068953C2semidirect
9. #13068751C2semidirect
10. #13068368C2semidirect
11. C11×#2326C2semidirect
27. #10622671C4semidirect
47. C11×#124C2×C4semidirect
63. C2×#4325C2×C4semidirect
66. C2×#4323C2×C4semidirect
74. #66927C2×C4semidirect
85. #66867C2×C4semidirect
148. #2326D11semidirect
279. #124C4×D11semidirect
374. C11#22279semidirect

Maximal subgroups

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

subgroupindex
C2×#106226712
#130713412
#130694282
#130694212
#130689712
#130689672
#130689642
#130689532
#130687512
#130683682
C11×#23262
#2227911