Finite Group Databasebeta

← #14763560

Subgroups — #14763560

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623066C211yesmaximal, characteristic
2C2×#10622613C211yesmaximal, characteristic, complemented
3#13069584C211yesmaximal, characteristic, complemented
4#13069580C211yesmaximal, characteristic, complemented
5#13069439C211yesmaximal, characteristic, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13068938C212yesmaximal, complemented
8#13068933C212yesmaximal, complemented
9#13068623C212yesmaximal, complemented
10#13068613C212yesmaximal, complemented
11C11×#2317C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66983C2212yes—
16#10623066—24no—
17#10623066C418yescomplemented
18C2×#66947—22no—
19C2×#66937—22no—
20C2×#66927C2211yescharacteristic
21C2×C4×D44C2212yes—
22C2×#66923C2211yescharacteristic
23C11×#389—22no—
24C11×#385—22no—
25C11×#384C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C11×#382C2211yescharacteristic
28C11×#382C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2212yes—
30#10622613—24no—
31C2×#66873C2212yes—
32C2×#66873C2212yes—
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×#66867C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—22no—
45C22×D44—22no—
46C22×D44C2312yes—
47C22×C4×D11—22no—
48C11×#117—42no—
49C11×#117C2×C414yes—
50C11×#117D414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—42no—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4D412yes—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65#66983—24no—
66#66983C2×C418yes—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—22no—
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2312yes—
73#66947—216no—
74#66937—216no—
75#66927—22no—
76#66927C2×C414yescomplemented
77C4×D44—24no—
78C4×D44C2×C418yescomplemented
79#66923—22no—
80#66923C2×C414yescomplemented
81C11×#95—22no—
82C11×#95—22no—
83C22⋊(C11⋊C8)—24no—
84#66873—42no—
85#66873—42no—
86#66873—42no—
87#66873—42no—
88C4⋊(C11⋊C8)—24no—
89#66867—22no—
90C4×C11⋊C8—22no—
91#21872—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C23×D11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—42no—
101C22×C4×C11—82no—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2411yescharacteristic
108C2×C22⋊D11—28no—
109C2×C22⋊D11—82no—
110C2×C22⋊D11—82no—
111C22×Dic11—22no—
112C2×D44—28no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—82no—
119C2×D44—82no—
120C2×D44C22×C414yes—
121C2×C4×D11—28no—
122C2×C4×D11—82no—
123C2×C4×D11—82no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—82no—
130C11×C4⋊C4—82no—
131C11×C4⋊C4C22⋊C418yes—
132C11×C22⋊C4—42no—
133C11×C22⋊C4C22⋊C418yes—
134C42×C11—42no—
135C42×C11C22×C412yes—
136C42×C11C22×C412yes—
137C42×C11C2×D412yes—
138C42×C11C2×D412yes—
139(C2×D11)⋊C4—28no—
140(C2×D11)⋊C4—28no—
141C4⋊Dic11—22no—
142C4⋊Dic11C22×C414yes—
143Dic11⋊C4—28no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×#540—111no—
151C2×#433—111no—
152#2317D1111yescharacteristic, complemented
153#1992—111no—
154#1991—111no—
155#1961—111no—
156#1957—111no—
157#1875—112no—
158#1874—112no—
159#1804—112no—
160#1802—112no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11C2×C22⋊C412yes—
166C23×C11C22×D411yescharacteristic
167C22×D11—24no—
168C22×D11—42no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11—42no—
172C22×D11—42no—
173C22×D11—42no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—84no—
191C2×C4×C11C2×C22⋊C414yes—
192C2×C4×C11C2×C22⋊C412yes—
193C2×C4×C11C2×C22⋊C414yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11H(5,𝔽2)12yes—
197C2×C4×C112−1+412yes—
198C22⋊D11—88no—
199C2×Dic11—24no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202D44—24no—
203D44—24no—
204D44—42no—
205D44—42no—
206D44—88no—
207C4×D11—88no—
208C11⋊C8—42no—
209C11⋊C8—42no—
210#540—118no—
211#540—224no—
212C2×#127—111no—
213C2×#125—111no—
214C2×#123—222no—
215C2×#121—112no—
216C2×#121—222no—
217C2×C4×D4—112no—
218C2×#117C2×D1111yescharacteristic
219C2×#117C2×D1111yescharacteristic
220C22×C4⋊C4C2×D1111yescharacteristic
221#433—224no—
222C2×C4⋊C8—112no—
223C2×#102—112no—
224C2×#102—112no—
225C2×#102—112no—
226C2×#102—112no—
227C2×C22⋊C8—112no—
228C2×#97—111no—
229C2×C4×C8—111no—
230#389—22no—
231#385—22no—
232#384C2×D1111yescharacteristic
233#384C2×D1111yescharacteristic
234#382C2×D1111yescharacteristic
235#382C2×D1111yescharacteristic
236#340—112no—
237#340—112no—
238#340—112no—
239#340—112no—
240C22×C11—22no—
241C22×C11—24no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—42no—
245C22×C11C22×C22⋊C411yescharacteristic
246C22×C11#53511yescharacteristic
247C22×C11#53611yescharacteristic
248C22×C11#57612yes—
249C22×C11#57712yes—
250C2×D11—44no—
251C2×D11—44no—
252C2×D11—44no—
253C2×D11—82no—
254C2×D11—82no—
255C2×D11—82no—
256C2×D11—82no—
257C4×C11—22no—
258C4×C11—24no—
259C4×C11—24no—
260C4×C11—81no—
261C4×C11—81no—
262C4×C11—81no—
263C4×C11—81no—
264C4×C11#52012yes—
265C4×C11#53712yes—
266Dic11—44no—
267C22×D4—112no—
268C22×D4—222no—
269C22×D4—222no—
270C23×C4—21no—
271C23×C4—222no—
272C23×C4C22×D1111yescharacteristic
273C22×C8—112no—
274C22×C8—112no—
275#127—114no—
276#127—222no—
277#125—114no—
278#125—222no—
279#123—2216no—
280#121—118no—
281#121—224no—
282#121—2216no—
283C4×D4—118no—
284C4×D4—224no—
285#117—42no—
286#117C4×D1114yes—
287#117D4414yes—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4C22⋊D1112yes—
295C2×C4⋊C4C22×D1111yescharacteristic
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C4⋊C4C22×D1111yescharacteristic
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—222no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4C22⋊D1112yes—
303C2×C42—21no—
304C2×C42C22×D1111yescharacteristic
305C2×C42C22×D1111yescharacteristic
306C4⋊C8—224no—
307#102—442no—
308#102—442no—
309#102—442no—
310#102—442no—
311C22⋊C8—224no—
312#97—222no—
313C4×C8—222no—
314#95—22no—
315#95—22no—
316C2×C11—42no—
317C2×C11#231111yescharacteristic
318C2×C11#289712yes—
319C2×C11#322011yescharacteristic
320C2×C11#322111yescharacteristic
321C2×C11#324112yes—
322D11—84no—
323C24—222no—
324C24C2×C22⋊D1111yescharacteristic
325C2×D4—114no—
326C2×D4—228no—
327C2×D4—228no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—882no—
334C2×D4—882no—
335C2×D4—882no—
336C2×D4—882no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—82no—
345C22×C4—222no—
346C22×C4—228no—
347C22×C4—882no—
348C22×C4—882no—
349C22×C4C2×C4×D1112yes—
350C22×C4C2×D4412yes—
351C22×C4C2×C22⋊D1112yes—
352C22×C4C2×C22⋊D1112yes—
353C22×C4C2×C22⋊D1111yescharacteristic
354C22×C4C23×D1111yescharacteristic
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—222no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—42no—
366C4⋊C4—82no—
367C4⋊C4—82no—
368C4⋊C4—114no—
369C4⋊C4—228no—
370C4⋊C4—222no—
371C4⋊C4(C2×D11)⋊C418yes—
372C22⋊C4—42no—
373C22⋊C4—228no—
374C22⋊C4—228no—
375C22⋊C4(C2×D11)⋊C418yes—
376C42—42no—
377C42C2×C4×D1112yes—
378C42C2×C4×D1112yes—
379C42C2×D4412yes—
380C42C2×D4412yes—
381C11#2187211yescharacteristic, complemented, Sylow
382C23—21no—
383C23—21no—
384C23—22no—
385C23—22no—
386C23—224no—
387C23—442no—
388C23—442no—
389C23—442no—
390C23—442no—
391C23—442no—
392C23—442no—
393C23C2×(C2×D11)⋊C412yes—
394C23C22×C22⋊D1111yescharacteristic
395D4—224no—
396D4—224no—
397D4—442no—
398D4—442no—
399D4—888no—
400D4—888no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—84no—
418C2×C4—224no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—888no—
422C2×C4C2×(C2×D11)⋊C414yes—
423C2×C4C2×(C2×D11)⋊C414yes—
424C2×C4C2×(C2×D11)⋊C412yes—
425C2×C4C22×C4×D1111yescharacteristic
426C2×C4C22×D4411yescharacteristic
427C2×C4#6703712yes—
428C2×C4#6704012yes—
429C8—442no—
430C8—442no—
431C22—22no—
432C22—24no—
433C22—42no—
434C22—41no—
435C22—41no—
436C22—444no—
437C22—444no—
438C22—444no—
439C22—882no—
440C22—882no—
441C22—882no—
442C22—882no—
443C22C22×(C2×D11)⋊C411yescharacteristic
444C22#1062333611yescharacteristic
445C22#1062334711yescharacteristic
446C22#1062336612yes—
447C22#1062336812yes—
448C4—22no—
449C4—24no—
450C4—24no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—444no—
456C4#1062303512yes—
457C4#1062304112yes—
458C2—42no—
459C2—884no—
460C2#1307120911yescharacteristic
461C2#1307713912yes—
462C2#1307966611yescharacteristic
463C2#1307967711yescharacteristic
464C2#1307986912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2317C2
socleC23×C11C22×D4
prime radicalC2×#10623066C2
cosocleC22×C4×C11C24
hypercenter#2317D11
hypocenterC11#21872
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. C2×#10622613C2semidirect
3. #13069584C2semidirect
4. #13069580C2semidirect
5. #13069439C2semidirect
6. #13069421C2semidirect
7. #13068938C2semidirect
8. #13068933C2semidirect
9. #13068623C2semidirect
10. #13068613C2semidirect
11. C11×#2317C2semidirect
17. #10623066C4semidirect
76. #66927C2×C4semidirect
78. C4×D44C2×C4semidirect
80. #66923C2×C4semidirect
152. #2317D11semidirect
381. C11#21872semidirect

Maximal subgroups

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

subgroupindex
C2×#106230662
C2×#106226132
#130695842
#130695802
#130694392
#130694212
#130689382
#130689332
#130686232
#130686132
C11×#23172
#2187211