Finite Group Databasebeta

← #14769408

Subgroups — #14769408

Order 2816.

1426 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic22C211yesmaximal, characteristic
2C2×#10622625C211yesmaximal, characteristic
3C2×#10622617C212yesmaximal, complemented
4#13069539C211yesmaximal, characteristic, complemented
5#13069417C211yesmaximal, characteristic, complemented
6#13069047C212yesmaximal, complemented
7#13068928C212yesmaximal, complemented
8#13068618C211yesmaximal, characteristic, complemented
9#13068550C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#2354C211yesmaximal, characteristic
12C23×Dic22C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×C11×#117C2212yes—
15C2×D4×Dic11—21no—
16C2×#66977C2212yes—
17C22×#4318C2212yes—
18D4×Dic22—24no—
19D4×Dic22C418yescomplemented
20C2×#66941—21no—
21C2×#66931—22no—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#390—21no—
25C11×#388—22no—
26C11×#384C2211yescharacteristic
27C11×#380C2212yes—
28C4×C11×C4⋊C4—21no—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622625—24no—
32#10622617—28no—
33C2×#66874C2211yescharacteristic
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39C2×#66874C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C23×Dic11—22no—
48C22×Dic22—24no—
49C22×Dic22—24no—
50C22×Dic22—22no—
51C22×Dic22—24no—
52C22×Dic22—42no—
53C22×Dic22—42no—
54C22×Dic22C2×C418yes—
55C22×Dic22C2312yes—
56C22×Dic22C2311yescharacteristic
57C4×D4×C11C2×C414yes—
58C4×D4×C11D414yes—
59C11×#117—24no—
60C11×#117—42no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
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—
74D4×Dic11—28no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78#66977—24no—
79#66977C2×C418yes—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11—21no—
83C2×#4318—24no—
84C2×#4318—24no—
85C2×#4318—42no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89#66941—28no—
90#66931—216no—
91#66922—22no—
92#66922C2×C414yes—
93C4×Dic22—22no—
94C4×Dic22C2×C414yes—
95C11×#95—22no—
96C11×#95—21no—
97C22⋊(C11⋊C8)—24no—
98#66874—24no—
99#66874—22no—
100#66874—24no—
101#66874—24no—
102#66874—42no—
103#66874—42no—
104#66874D414yescomplemented
105C4⋊(C11⋊C8)—22no—
106C4×C11⋊C8—22no—
107#22430—111nomaximal, Sylow
108C24×C11C2×D412yes—
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×D411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—28no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—44no—
130C22×Dic11—44no—
131C2×Dic22—216no—
132C2×Dic22—28no—
133C2×Dic22—21no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—48no—
142C2×Dic22—48no—
143C2×Dic22—48no—
144C2×Dic22—44no—
145C2×Dic22—44no—
146C2×Dic22C22×C414yes—
147C2×Dic22C22×C412yes—
148C2×Dic22C2×D412yes—
149C2×Dic22#4112yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4C22⋊C414yes—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—82no—
161C11×C22⋊C4C22⋊C418yes—
162C42×C11—44no—
163C42×C11—42no—
164C42×C11C22×C412yes—
165C42×C11C2×D412yes—
166C22⋊Dic11—28no—
167C4⋊Dic11—24no—
168C4⋊Dic11—24no—
169C4⋊Dic11—21no—
170C4⋊Dic11C22×C412yes—
171Dic11⋊C4—24no—
172Dic11⋊C4—28no—
173C4×Dic11—24no—
174#4318—48no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8C2×D412yes—
184C2×D4×Q8—111no—
185C2×#436—111no—
186C2×#419—112no—
187#2354D1111yescharacteristic
188#1981—111no—
189#1956—111no—
190#1894—112no—
191#1873—112no—
192#1803—111no—
193#1787—112no—
194C4×#103—111no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11C2×C22⋊C414yes—
202C23×C11C22×D411yescharacteristic
203D4×C11—28no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C2×C22⋊C414yes—
223C2×C4×C11C2×C22⋊C412yes—
224C2×C4×C11#13712yes—
225C2×C4×C11#13712yes—
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11H(5,𝔽2)11yescharacteristic
231C2×C4×C11H(5,𝔽2)11yescharacteristic
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—416no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242Dic22—22no—
243Dic22—22no—
244Dic22—22no—
245Dic22—24no—
246Dic22—24no—
247Dic22—416no—
248Dic22—42no—
249Dic22—42no—
250Dic22C4×D414yes—
251C11⋊C8—22no—
252C11⋊C8—42no—
253C11⋊C8—41no—
254C23×Q8—112no—
255C22×M16—112no—
256D4×Q8—118no—
257D4×Q8—224no—
258C2×C4⋊Q8—111no—
259C2×C4⋊Q8—221no—
260C2×C22⋊Q8—112no—
261C2×C22⋊Q8—222no—
262C2×C4×Q8—111no—
263C2×C4×D4—221no—
264C2×C4×D4C2×D1111yescharacteristic
265C2×#117C2×D1112yes—
266#436—224no—
267C2×C4⋊C8—111no—
268#419—228no—
269C2×#103—111no—
270C2×#103—112no—
271C2×#103—112no—
272C2×#103—112no—
273C2×#103—111no—
274C2×#103—112no—
275C2×#103—112no—
276C2×C22⋊C8—112no—
277C2×C4×C8—111no—
278#390—21no—
279#388—22no—
280#384C2×D1111yescharacteristic
281#380C2×D1112yes—
282C4×C4⋊C4—21no—
283C4×C4⋊C4C2×D1111yescharacteristic
284#340—112no—
285#340—111no—
286#340—111no—
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—24no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11C22×C22⋊C411yescharacteristic
295C22×C11D4211yescharacteristic
296C22×C11#54611yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C22×C11#57711yescharacteristic
300C22×C11#57811yescharacteristic
301C4×C11—24no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—81no—
305C4×C11—82no—
306C4×C11#41914yescomplemented
307C4×C11C2×C4×D411yescharacteristic
308C4×C11#51811yescharacteristic
309C4×C11D4211yescharacteristic
310C4×C11#54611yescharacteristic
311Dic11—24no—
312Dic11—44no—
313Dic11—42no—
314C22×Q8—118no—
315C22×Q8—111no—
316C22×Q8—112no—
317C22×Q8—224no—
318C22×Q8—224no—
319C22×Q8—224no—
320C22×Q8—222no—
321C22×Q8—442no—
322C22×Q8—442no—
323C22×D4C22⋊D1111yescharacteristic
324C23×C4—222no—
325C23×C4C22×D1112yes—
326C2×M16—224no—
327C2×M16—224no—
328C2×M16—442no—
329C22×C8—111no—
330C22×C8—112no—
331C22×C8—111no—
332C4⋊Q8—114no—
333C4⋊Q8—228no—
334C4⋊Q8—222no—
335C22⋊Q8—118no—
336C22⋊Q8—224no—
337C22⋊Q8—2216no—
338C4×Q8—114no—
339C4×Q8—222no—
340C4×D4—228no—
341C4×D4C4×D1114yes—
342C4×D4D4414yes—
343#117—24no—
344#117—42no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4C22⋊D1111yescharacteristic
353C2×C4⋊C4C22×D1112yes—
354C2×C4⋊C4C22×D1111yescharacteristic
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4C22⋊D1112yes—
360C2×C42—22no—
361C2×C42—21no—
362C2×C42—221no—
363C2×C42C22×D1111yescharacteristic
364C4⋊C8—222no—
365#103—114no—
366#103—224no—
367#103—222no—
368#103—224no—
369#103—224no—
370#103—442no—
371#103—442no—
372C22⋊C8—224no—
373C4×C8—222no—
374#95—22no—
375#95—21no—
376C2×C11—44no—
377C2×C11D4×C22⋊C411yescharacteristic
378C2×C11C2×#41911yescharacteristic
379C2×C11#289811yescharacteristic
380C2×C11#327611yescharacteristic
381C2×C11#327811yescharacteristic
382C2×C11#332811yescharacteristic
383C2×C11#332911yescharacteristic
384C24C2×C22⋊D1112yes—
385C2×Q8—112no—
386C2×Q8—114no—
387C2×Q8—112no—
388C2×Q8—112no—
389C2×Q8—2216no—
390C2×Q8—228no—
391C2×Q8—221no—
392C2×Q8—222no—
393C2×Q8—221no—
394C2×Q8—221no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—444no—
400C2×Q8—444no—
401C2×Q8—448no—
402C2×Q8—448no—
403C2×Q8—448no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4(C2×D11)⋊C414yes—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—221no—
415C22×C4—228no—
416C22×C4—221no—
417C22×C4—222no—
418C22×C4—444no—
419C22×C4—444no—
420C22×C4C2×C4×D1114yes—
421C22×C4C2×D4414yes—
422C22×C4C2×C22⋊D1112yes—
423C22×C4C2×C22⋊D1111yescharacteristic
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C23×D1111yescharacteristic
426M16—448no—
427C2×C8—112no—
428C2×C8—221no—
429C2×C8—221no—
430C2×C8—221no—
431C2×C8—222no—
432C2×C8—222no—
433C2×C8—221no—
434C2×C8—221no—
435C2×C8—222no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—42no—
442C4⋊C4—81no—
443C4⋊C4—112no—
444C4⋊C4—224no—
445C4⋊C4—224no—
446C4⋊C4—228no—
447C4⋊C4—224no—
448C4⋊C4—221no—
449C4⋊C4(C2×D11)⋊C414yes—
450C4⋊C4D4×D1112yes—
451C22⋊C4—44no—
452C22⋊C4—82no—
453C22⋊C4—228no—
454C22⋊C4(C2×D11)⋊C418yes—
455C42—44no—
456C42—42no—
457C42—224no—
458C42C2×C4×D1112yes—
459C42C2×D4412yes—
460C11#2243011yescharacteristic, complemented, Sylow
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23C2×(C2×D11)⋊C414yes—
468C23C22×C22⋊D1111yescharacteristic
469Q8—114no—
470Q8—222no—
471Q8—222no—
472Q8—222no—
473Q8—224no—
474Q8—224no—
475Q8—4416no—
476Q8—442no—
477Q8—442no—
478D4—28no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—4416no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4C2×(C2×D11)⋊C412yes—
507C2×C4C2×(C2×D11)⋊C414yes—
508C2×C4C2×(C2×D11)⋊C412yes—
509C2×C4#6700412yes—
510C2×C4#6700412yes—
511C2×C4C22×C4×D1111yescharacteristic
512C2×C4C22×D4411yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4#6703711yescharacteristic
515C2×C4#41×D1111yescharacteristic
516C2×C4#6704211yescharacteristic
517C8—222no—
518C8—442no—
519C8—441no—
520C22—24no—
521C22—24no—
522C22—24no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22C22×(C2×D11)⋊C411yescharacteristic
528C22D4×C22⋊D1111yescharacteristic
529C22C2×#6700411yescharacteristic
530C22C2×#6700411yescharacteristic
531C22#1062336011yescharacteristic
532C22#1062336711yescharacteristic
533C22#1062336911yescharacteristic
534C4—24no—
535C4—22no—
536C4—42no—
537C4—81no—
538C4—82no—
539C4—224no—
540C4—444no—
541C4—442no—
542C4#1062261714yescomplemented
543C4C4×D4×D1111yescharacteristic
544C4#1062307611yescharacteristic
545C4D4×D4411yescharacteristic
546C4#1062308511yescharacteristic
547C2—44no—
548C2D4×(C2×D11)⋊C411yescharacteristic
549C2C2×#1062261711yescharacteristic
550C2#1307714611yescharacteristic
551C2#1308025811yescharacteristic
552C2#1308028211yescharacteristic
553C2#1308089311yescharacteristic
554C2#1308090411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenter#2354D11
hypocenterC11#22430
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
3. C2×#10622617C2semidirect
4. #13069539C2semidirect
5. #13069417C2semidirect
6. #13069047C2semidirect
7. #13068928C2semidirect
8. #13068618C2semidirect
9. #13068550C2semidirect
10. C4×#66874C2semidirect
19. D4×Dic22C4semidirect
104. #66874D4semidirect
306. C4×C11#419semidirect
460. C11#22430semidirect
542. C4#10622617semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×#106226252
C2×#106226172
#130695392
#130694172
#130690472
#130689282
#130686182
#130685502
C4×#668742
C11×#23542
#2243011