Finite Group Databasebeta

← #14770050

Subgroups — #14770050

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C11⋊C8C211yesmaximal, characteristic
2#13071565C211yesmaximal, characteristic
3#13069578C211yesmaximal, characteristic, complemented
4#13069569C211yesmaximal, characteristic, complemented
5#13069040C212yesmaximal, complemented
6#13068929C212yesmaximal, complemented
7#13068711C212yesmaximal, complemented
8#13068621C211yesmaximal, characteristic, complemented
9C4×#66899C211yesmaximal, characteristic, complemented
10#13068332C212yesmaximal, complemented
11C2×C11×#556C211yesmaximal, characteristic
12C11×#556—24no—
13C11×#556C418yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124—21no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C2212yes—
22C2×#66979C2212yes—
23C23×C11⋊C8C2212yes—
24C2×#66899C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2212yes—
27#10622834—21no—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30D4×C11⋊C8—24no—
31C4⋊C4×Dic11—21no—
32#10622564—22no—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44C22×Q8×C11—21no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11D411yescharacteristic
47C23×C4×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8C2×C414yes—
50C11×#126—216no—
51C11×#124—28no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8C2×C418yes—
54C4×Q8×C11—28no—
55C4×Q8×C11—22no—
56C4×Q8×C11C2×C414yes—
57C4×D4×C11C2×C414yes—
58C4×D4×C11D414yes—
59C11×#117—24no—
60C11×#117C2×C418yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11—22no—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75#66979—24no—
76#66979—42no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2312yes—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4×Dic11—21no—
83C2×C4×Dic11—22no—
84C22×C11⋊C8—24no—
85C22×C11⋊C8—24no—
86C22×C11⋊C8—42no—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90#66899—22no—
91#66899—22no—
92#66899—42no—
93C11⋊#95—21no—
94C11⋊#95—22no—
95C22⋊(C11⋊C8)—24no—
96C4⋊(C11⋊C8)—22no—
97C4×C11⋊C8—22no—
98#22490—111nomaximal, Sylow
99C24×C11C2×D412yes—
100C2×Q8×C11—24no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—42no—
107C2×Q8×C11—42no—
108C2×Q8×C11C22×C412yes—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11C22⋊C414yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11C22×C414yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C11×C4⋊C4—28no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C22⋊C414yes—
134C11×C4⋊C4C22×C412yes—
135C11×C4⋊C4C22×C414yes—
136C11×C22⋊C4—28no—
137C11×C22⋊C4—28no—
138C11×C22⋊C4C22⋊C418yes—
139C42×C11—28no—
140C42×C11—24no—
141C42×C11C22×C412yes—
142C42×C11C2×D412yes—
143C22⋊Dic11—44no—
144C22⋊Dic11—82no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—42no—
151C4⋊Dic11—81no—
152C4⋊Dic11#4112yes—
153C4×Dic11—44no—
154C4×Dic11—42no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—48no—
164C2×C11⋊C8#4112yes—
165C2×#556D1111yescharacteristic
166C2×C8×D4—111no—
167#2354—111no—
168#1990—111no—
169#1988—111no—
170#1892—112no—
171#1873—112no—
172#1825—112no—
173#1803—111no—
174C4×#103—111no—
175#1735—112no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11C2×C22⋊C414yes—
183C23×C11C22×D411yescharacteristic
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—41no—
187Q8×C11—41no—
188Q8×C11—48no—
189D4×C11—28no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11C2×C22⋊C414yes—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11#13512yes—
211C2×C4×C11#13512yes—
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C2×Dic11—22no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—41no—
227C11⋊C8—22no—
228C11⋊C8—42no—
229C11⋊C8—41no—
230C23×C8—112no—
231#556—24no—
232#556Dic1118yescomplemented
233C2×C4⋊Q8C2×D1111yescharacteristic
234C2×#126—22no—
235C2×#124—21no—
236C2×C22⋊Q8C2×D1112yes—
237C2×C4×Q8—21no—
238C2×C4×Q8C2×D1111yescharacteristic
239C2×C4×D4C2×D1111yescharacteristic
240C2×#117—112no—
241C2×#117C2×D1112yes—
242C8×D4—224no—
243C2×C4⋊C8—111no—
244C2×#103—111no—
245C2×#103—111no—
246C2×#103—112no—
247C2×C22⋊C8—112no—
248C2×C4×C8—111no—
249#390—221no—
250#388—222no—
251#384—111no—
252#380—112no—
253C4×C4⋊C4—111no—
254C4×C4⋊C4—221no—
255#340—112no—
256#340—111no—
257#340—112no—
258#340—112no—
259#340—112no—
260#340—112no—
261#340—111no—
262C22×C11—24no—
263C22×C11—24no—
264C22×C11—24no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11#54611yescharacteristic
271C22×C11#54711yescharacteristic
272C22×C11C2×#13511yescharacteristic
273C22×C11C2×#13511yescharacteristic
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C4×C11—24no—
277C4×C11—22no—
278C4×C11—42no—
279C4×C11—44no—
280C4×C11—42no—
281C4×C11#41614yes—
282C4×C11C4×#4111yescharacteristic
283C4×C11#52011yescharacteristic
284C4×C11#54611yescharacteristic
285C4×C11#54711yescharacteristic
286Dic11—42no—
287Dic11—81no—
288Dic11—82no—
289C22×Q8—21no—
290C22×Q8C22×D1111yescharacteristic
291C22×D4C22⋊D1111yescharacteristic
292C23×C4C22×D1112yes—
293C22×C8—111no—
294C22×C8—112no—
295C22×C8—111no—
296C22×C8—224no—
297C22×C8—224no—
298C22×C8—442no—
299C4⋊Q8—22no—
300C4⋊Q8C2×Dic1114yes—
301#126—216no—
302#124—28no—
303C22⋊Q8—24no—
304C22⋊Q8C2×Dic1118yes—
305C4×Q8—28no—
306C4×Q8—22no—
307C4×Q8C2×Dic1114yes—
308C4×D4C2×Dic1114yes—
309C4×D4C22⋊D1114yes—
310#117—24no—
311#117—224no—
312#117—442no—
313#117C2×Dic1118yes—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4C22⋊D1111yescharacteristic
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C4⋊C4C22×D1112yes—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C22⋊C4C22⋊D1112yes—
330C2×C42—22no—
331C2×C42—21no—
332C2×C42—222no—
333C2×C42—221no—
334C2×C42C22×D1111yescharacteristic
335C4⋊C8—222no—
336#103—222no—
337#103—222no—
338#103—442no—
339C22⋊C8—224no—
340C4×C8—222no—
341#95—221no—
342#95—222no—
343C2×C11—44no—
344C2×C11#233911yescharacteristic
345C2×C11C2×#41611yescharacteristic
346C2×C11#289811yescharacteristic
347C2×C11#330211yescharacteristic
348C2×C11#330411yescharacteristic
349C2×C11#334011yescharacteristic
350C2×C11#334211yescharacteristic
351C24C2×C22⋊D1112yes—
352C2×Q8—24no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—42no—
359C2×Q8—42no—
360C2×Q8C22×Dic1112yes—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4C22⋊Dic1114yes—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—222no—
374C22×C4C22×Dic1114yes—
375C22×C4C2×C22⋊D1112yes—
376C22×C4C2×C22⋊D1111yescharacteristic
377C22×C4C2×C22⋊D1114yes—
378C22×C4C2×C22⋊D1111yescharacteristic
379C22×C4C23×D1111yescharacteristic
380C2×C8—112no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8—222no—
389C2×C8—448no—
390C4⋊C4—28no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—112no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—221no—
401C4⋊C4—442no—
402C4⋊C4—881no—
403C4⋊C4C22⋊Dic1114yes—
404C4⋊C4C22×Dic1112yes—
405C4⋊C4C22×Dic1114yes—
406C22⋊C4—28no—
407C22⋊C4—28no—
408C22⋊C4—444no—
409C22⋊C4—882no—
410C22⋊C4C22⋊Dic1118yes—
411C42—28no—
412C42—24no—
413C42—444no—
414C42—442no—
415C42C22×Dic1112yes—
416C42C2×C22⋊D1112yes—
417C11#2249011yescharacteristic, complemented, Sylow
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23C2×C22⋊Dic1114yes—
425C23C22×C22⋊D1111yescharacteristic
426Q8—22no—
427Q8—22no—
428Q8—41no—
429Q8—48no—
430Q8—41no—
431D4—28no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—222no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—442no—
454C2×C4—441no—
455C2×C4—442no—
456C2×C4—441no—
457C2×C4—442no—
458C2×C4#6700312yes—
459C2×C4#6700312yes—
460C2×C4C2×C22⋊Dic1114yes—
461C2×C4C2×C22⋊Dic1112yes—
462C2×C4C2×C22⋊Dic1112yes—
463C2×C4#41×D1111yescharacteristic
464C2×C4#41×D1111yescharacteristic
465C2×C4#6704211yescharacteristic
466C2×C4#6704311yescharacteristic
467C2×C4C23×Dic1111yescharacteristic
468C2×C4C22×C22⋊D1111yescharacteristic
469C8—222no—
470C8—441no—
471C8—442no—
472C22—24no—
473C22—24no—
474C22—24no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22C2×#6700311yescharacteristic
480C22C2×#6700311yescharacteristic
481C22#1062335511yescharacteristic
482C22#1062336011yescharacteristic
483C22#1062336811yescharacteristic
484C22#1062336911yescharacteristic
485C22C22×C22⋊Dic1111yescharacteristic
486C4—24no—
487C4—22no—
488C4—42no—
489C4—44no—
490C4—42no—
491C4—442no—
492C4—881no—
493C4—882no—
494C4#1062284614yes—
495C4#1062335511yescharacteristic
496C4#41×Dic1111yescharacteristic
497C4#1062335811yescharacteristic
498C4#1062336011yescharacteristic
499C2—44no—
500C2#1307144611yescharacteristic
501C2C2×#1062284611yescharacteristic
502C2#1307714911yescharacteristic
503C2#1308052711yescharacteristic
504C2#1308054911yescharacteristic
505C2#1308102311yescharacteristic
506C2#1308104211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenterC2×#556D11
hypocenterC11#22490
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
3. #13069578C2semidirect
4. #13069569C2semidirect
5. #13069040C2semidirect
6. #13068929C2semidirect
7. #13068711C2semidirect
8. #13068621C2semidirect
9. C4×#66899C2semidirect
10. #13068332C2semidirect
13. C11×#556C4semidirect
232. #556Dic11semidirect
417. C11#22490semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C11⋊C82
#130715652
#130695782
#130695692
#130690402
#130689292
#130687112
#130686212
C4×#668992
#130683322
C2×C11×#5562
#2249011