Finite Group Databasebeta

← #14770374

Subgroups — #14770374

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623261C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13071575C211yesmaximal, characteristic, complemented
4#13069579C212yesmaximal, complemented
5#13069570C212yesmaximal, complemented
6#13069565C211yesmaximal, characteristic, complemented
7#13068625C212yesmaximal
8#13068613C211yesmaximal, characteristic
9C4×#66885C211yesmaximal, characteristic
10#13068430C212yesmaximal
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—22no—
14#10623261—24no—
15#10623261C418yescomplemented
16C2×#66950—21no—
17C2×#66946C2212yes—
18C2×C4⋊C4×D11—21no—
19C2×#66943C2212yes—
20C2×C4×D44C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×Dic11⋊C8C2212yes—
27C2×C8×Dic11C2212yes—
28#10622591—22no—
29#10622590C2212yes—
30C4⋊C4×Dic11—21no—
31C4⋊C4×Dic11C2212yes—
32#10622587—21no—
33C2×#66873C2212yes—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C8×Dic22—24no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×Q8×C11—21no—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C4×D11—22no—
48C22×Dic22D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8C2×C414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C42×C11C2311yescharacteristic
59#66999—216no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4D412yes—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2312yes—
73#66950—28no—
74#66946—24no—
75#66946C2×C418yes—
76C4⋊C4×D11—28no—
77#66943—24no—
78#66943C2×C418yes—
79C4×D44—22no—
80C4×D44C2×C414yes—
81C4×Dic22C2×C414yes—
82C4×Dic22D414yes—
83C4×C8×C11—22no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66885—22no—
89#66885Q814yescomplemented
90Dic11⋊C8—24no—
91C8×Dic11—24no—
92#66873—24no—
93C4⋊(C11⋊C8)—22no—
94#22519—111nomaximal, Sylow
95C23×D11—21no—
96C2×Q8×C11—24no—
97C2×Q8×C11—81no—
98C2×Q8×C11—81no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11C2×D412yes—
108C22×Dic11C2×D412yes—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44C22×C412yes—
113C2×D44C2×Q812yes—
114C2×D44#4112yes—
115C2×C4×D11—28no—
116C2×C4×D11—24no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11—82no—
120C2×C4×D11—82no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22C22⋊C414yes—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C2×Q812yes—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—81no—
136C11×C4⋊C4C22×C414yes—
137C42×C11C22×C412yes—
138C42×C11C2×D412yes—
139(C2×D11)⋊C4—28no—
140(C2×D11)⋊C4—24no—
141C4⋊Dic11—28no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11C22⋊C414yes—
147C4⋊Dic11C22×C412yes—
148C4⋊Dic11C2×Q812yes—
149Dic11⋊C4—28no—
150Dic11⋊C4C22⋊C418yes—
151C4×Dic11—42no—
152C4×Dic11—82no—
153C4×Dic11C22×C414yes—
154C4×Dic11C2×D414yes—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×#554—111no—
159C2×C8×Q8—111no—
160#2355—111no—
161#1991—112no—
162#1990D1111yescharacteristic, complemented
163#1989—112no—
164#1987—111no—
165#1804—112no—
166#1802—111no—
167C4×#102—111no—
168C4×#102—112no—
169C23×C11C22×D411yescharacteristic
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177Q8×C11—84no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—24no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11C2×C22⋊C412yes—
187C2×C4×C11C2×C22⋊C412yes—
188C2×C4×C11#13512yes—
189C2×C4×C11#13512yes—
190C2×C4×C11C23×C411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C22×Q811yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C2×C4×C112−1+411yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11C2×C22⋊C414yes—
210C2×Dic11C2×C22⋊C414yes—
211D44—22no—
212D44—22no—
213D44—22no—
214D44C4×Q814yes—
215C4×D11—48no—
216C4×D11—88no—
217Dic22—28no—
218C8×C11—22no—
219C8×C11—41no—
220C11⋊C8—42no—
221#554—118no—
222#554—224no—
223C2×C4⋊Q8C2×D1111yescharacteristic
224C2×#125—112no—
225C2×C22⋊Q8—221no—
226C2×C22⋊Q8—222no—
227C2×C4×Q8—111no—
228C2×C4×D4—112no—
229C2×C4×D4—111no—
230C22×C4⋊C4—221no—
231C8×Q8—224no—
232C2×C4⋊C8—112no—
233C2×C4⋊C8—111no—
234C2×#102—111no—
235C2×#102—111no—
236C2×#102—112no—
237C2×C4×C8—112no—
238C2×C4×C8C2×D1111yescharacteristic
239#391—221no—
240#387—222no—
241#384C2×D1111yescharacteristic
242#382—112no—
243C4×C4⋊C4—112no—
244C4×C4⋊C4—111no—
245C4×C4⋊C4—221no—
246#340—111no—
247#340—111no—
248#340—112no—
249#340—112no—
250#340—112no—
251#340C2×D1112yes—
252#340C2×D1112yes—
253C22×C11C22×C22⋊C411yescharacteristic
254C22×C11#54811yescharacteristic
255C22×C11D4×Q811yescharacteristic
256C22×C11C2×#13511yescharacteristic
257C22×C11C2×#13511yescharacteristic
258C22×C11#57611yescharacteristic
259C22×C11#57711yescharacteristic
260C2×D11—24no—
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C4×C11—22no—
268C4×C11—44no—
269C4×C11—82no—
270C4×C11#41614yes—
271C4×C11C2×C4×Q811yescharacteristic
272C4×C11#51911yescharacteristic
273C4×C11#54811yescharacteristic
274C4×C11D4×Q811yescharacteristic
275Dic11—24no—
276Dic11—24no—
277Dic11—42no—
278Dic11—42no—
279Dic11—81no—
280C22×Q8—21no—
281C22×Q8—111no—
282C22×D4—111no—
283C23×C4—222no—
284C23×C4—221no—
285C22×C8—112no—
286C22×C8C22×D1111yescharacteristic
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—22no—
289C4⋊Q8C4×D1114yes—
290#125—118no—
291#125—224no—
292C22⋊Q8—228no—
293C22⋊Q8—2216no—
294C4×Q8—114no—
295C4×Q8—114no—
296C4×D4—118no—
297C4×D4—114no—
298C4×D4—224no—
299C4×D4—222no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—228no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4C22×D1112yes—
312C2×C4⋊C4C22×D1112yes—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—221no—
315C2×C42—112no—
316C2×C42—221no—
317C2×C42—222no—
318C2×C42C22×D1111yescharacteristic
319C4⋊C8—224no—
320C4⋊C8—222no—
321#102—114no—
322#102—224no—
323#102—222no—
324C4×C8—22no—
325C4×C8—224no—
326#95—222no—
327#95—222no—
328#95—222no—
329#95—221no—
330C2×C11Q8×C22⋊C411yescharacteristic
331C2×C11C2×#41611yescharacteristic
332C2×C11#289711yescharacteristic
333C2×C11#336011yescharacteristic
334C2×C11#336111yescharacteristic
335C2×C11#338011yescharacteristic
336C2×C11#338111yescharacteristic
337D11—44no—
338C24—221no—
339C2×Q8—24no—
340C2×Q8—81no—
341C2×Q8—81no—
342C2×Q8—114no—
343C2×Q8—222no—
344C2×Q8—222no—
345C2×D4—112no—
346C2×D4—112no—
347C2×D4—112no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—112no—
354C22×C4—112no—
355C22×C4—228no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—224no—
359C22×C4—221no—
360C22×C4—442no—
361C22×C4—442no—
362C22×C4—882no—
363C22×C4—882no—
364C22×C4D4×D1111yescharacteristic
365C22×C4D4×D1111yescharacteristic
366C22×C4C23×D1111yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—222no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8Q8×D1112yes—
376C4⋊C4—24no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—42no—
381C4⋊C4—81no—
382C4⋊C4—114no—
383C4⋊C4—118no—
384C4⋊C4—112no—
385C4⋊C4—112no—
386C4⋊C4—228no—
387C4⋊C4—228no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4C2×C4×D1114yes—
393C22⋊C4—228no—
394C22⋊C4—224no—
395C42—114no—
396C42—114no—
397C42—442no—
398C42—882no—
399C42C2×C4×D1112yes—
400C42D4×D1112yes—
401C11#2251911yescharacteristic, complemented, Sylow
402C23—222no—
403C23—222no—
404C23—222no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23C2×D4×D1111yescharacteristic
410Q8—84no—
411Q8—228no—
412D4—114no—
413D4—222no—
414D4—222no—
415D4—222no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—114no—
425C2×C4—114no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—448no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—888no—
441C2×C4C22⋊C4×D1112yes—
442C2×C4C22⋊C4×D1112yes—
443C2×C4#6696912yes—
444C2×C4#6697212yes—
445C2×C4C22×C4×D1111yescharacteristic
446C2×C4C2×D4×D1111yescharacteristic
447C2×C4C2×Q8×D1111yescharacteristic
448C2×C4#6704011yescharacteristic
449C2×C4#41×D1111yescharacteristic
450C2×C4#6704311yescharacteristic
451C8—22no—
452C8—41no—
453C8—442no—
454C22—224no—
455C22—442no—
456C22—442no—
457C22—442no—
458C22—442no—
459C22—442no—
460C22—442no—
461C22C2×C22⋊C4×D1111yescharacteristic
462C22#1062320811yescharacteristic
463C22#1062325811yescharacteristic
464C22#1062328811yescharacteristic
465C22C2×#6696911yescharacteristic
466C22#1062329311yescharacteristic
467C22C2×#6697211yescharacteristic
468C4—22no—
469C4—44no—
470C4—82no—
471C4—224no—
472C4—224no—
473C4—442no—
474C4—442no—
475C4—881no—
476C4#1062241714yes—
477C4C4×Q8×D1111yescharacteristic
478C4#1062310311yescharacteristic
479C4#1062316311yescharacteristic
480C4#1062316411yescharacteristic
481C2—444no—
482C2#1307145011yescharacteristic
483C2C2×#1062241711yescharacteristic
484C2#1307713711yescharacteristic
485C2#1308127011yescharacteristic
486C2#1308128111yescharacteristic
487C2#1308148511yescharacteristic
488C2#1308149611yescharacteristic
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#22519
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. C2×C8×Dic22C2semidirect
3. #13071575C2semidirect
4. #13069579C2semidirect
5. #13069570C2semidirect
6. #13069565C2semidirect
11. C11×#1990C2semidirect
15. #10623261C4semidirect
89. #66885Q8semidirect
162. #1990D11semidirect
401. C11#22519semidirect

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×C8×Dic222
#130715752
#130695792
#130695702
#130695652
#130686252
#130686132
C4×#668852
#130684302
C11×#19902
#2251911