Finite Group Databasebeta

← #14769512

Subgroups — #14769512

Order 2816.

1466 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
1C22×#67003C211yesmaximal, characteristic
2C2×#10622639C212yesmaximal, complemented
3#13071447C211yesmaximal, characteristic, complemented
4#13069496C212yesmaximal, complemented
5#13068967C212yesmaximal, complemented
6#13068957C212yesmaximal, complemented
7#13068643C211yesmaximal, characteristic, complemented
8#13068556C211yesmaximal, characteristic, complemented
9#13068554C211yesmaximal, characteristic, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C11×#2341C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×#67003—28no—
16C2×#67003C418yescomplemented
17C22×#4326C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×C4×D44C2212yes—
23C11×#390—22no—
24C11×#390C2212yes—
25C11×#380—21no—
26C11×#380C2211yescharacteristic
27C4×C11×C22⋊C4—21no—
28C4×C11×C22⋊C4C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66896C2212yes—
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622639—28no—
34C2×#66874C2212yes—
35C2×#66873C2212yes—
36C2×#66871C2212yes—
37#10622569—22no—
38#10622542C2212yes—
39C2×#66867C2212yes—
40#10622277—21no—
41D11×#95—21no—
42#10622167C2212yes—
43#10622162C2212yes—
44C2×C11×#41—22no—
45C2×C11×#41—24no—
46C2×C11×#41—42no—
47C2×C11×#41C2×C414yescomplemented
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—21no—
54C2×#4339—22no—
55C2×#4339—24no—
56C2×#4339—42no—
57C2×#4339C2×C414yes—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11—22no—
61C22×Dic22C2311yescharacteristic
62C4×Q8×C11—24no—
63C4×Q8×C11—42no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C2×C22⋊Dic11—21no—
73#67003—232no—
74C2×#4326—24no—
75C2×#4326C2×C414yescomplemented
76C2×#4325C2×C414yes—
77C2×#4325D418yes—
78C2×#4324—24no—
79C2×#4324C2×C414yescomplemented
80C2×#4323—24no—
81C2×#4323C2×C414yes—
82C2×(C2×D11)⋊C4—22no—
83C2×C4⋊Dic11C2312yes—
84C22×C11⋊C8—24no—
85C22×C11⋊C8C2×C414yescomplemented
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C4×D44—24no—
90C4×D44—42no—
91C11×#95—21no—
92C11×#95D411yescharacteristic
93C11×#95D411yescharacteristic
94#66899—24no—
95#66896—42no—
96C11⋊#95—21no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C22⋊(C11⋊C8)—22no—
100#66874—42no—
101#66873—24no—
102#66871—24no—
103#66867—24no—
104#22439—111nomaximal, Sylow
105C24×C11—21no—
106C24×C11C2×D411yescharacteristic
107C23×D11—21no—
108C11×#41—28no—
109C11×#41—44no—
110C11×#41—48no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11C22×C412yes—
114C2×Q8×C11C2×D414yes—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—44no—
120C2×D4×C11C22×C412yes—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—44no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11#4112yes—
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—24no—
134C2×C22⋊D11—44no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137#4339—28no—
138#4339—44no—
139#4339—48no—
140C2×D44—21no—
141C2×D44—22no—
142C2×D44C22×C412yes—
143C2×D44C2×D414yes—
144C2×C4×D11—24no—
145C2×C4×D11—44no—
146C2×C4×D11—44no—
147C2×C4×D11—44no—
148C2×C4×D11—82no—
149C2×Dic22—22no—
150C2×Dic22—21no—
151C2×Dic22—22no—
152C2×Dic22C22×C412yes—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—44no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—82no—
159C11×C22⋊C4—81no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—44no—
163C22⋊Dic11—81no—
164#4326—28no—
165#4325C22⋊C4116yescomplemented
166#4324—28no—
167#4323—28no—
168(C2×D11)⋊C4—44no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C2×C11⋊C8—28no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8C22×C412yes—
177C2×C11⋊C8C22×C412yes—
178C2×C11⋊C8C2×D414yes—
179C22×#135—111no—
180C2×#440—112no—
181#2341D1111yescharacteristic, complemented
182#2339—111no—
183#1973—112no—
184#1879—112no—
185#1878—112no—
186#1808—111no—
187#1788—111no—
188#1788—111no—
189#1752—111no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11C4×D412yes—
200C23×C11C22×D411yescharacteristic
201C22×D11—22no—
202C22×D11—24no—
203C22×D11—42no—
204C22×D11—41no—
205C22×D11—41no—
206Q8×C11—22no—
207Q8×C11—24no—
208Q8×C11C2×C22⋊C414yes—
209D4×C11—22no—
210D4×C11—22no—
211D4×C11—48no—
212D4×C11—42no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—48no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11C4×D412yes—
230C2×C4×C11C23×C411yescharacteristic
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)12yes—
234C22⋊D11—48no—
235C2×Dic11—22no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240D44—22no—
241D44—24no—
242D44C2×C22⋊C414yes—
243C4×D11—48no—
244C4×D11—88no—
245Dic22—22no—
246Dic22—22no—
247Dic22—42no—
248C11⋊C8—22no—
249C11⋊C8—42no—
250C11⋊C8C2×C22⋊C414yes—
251C22×#41—111no—
252C22×#41C2×D1111yescharacteristic
253C2×#135—118no—
254C2×#135—228no—
255C22×Q16—111no—
256C22×SD16—111no—
257C22×SD16—111no—
258C22×D8—111no—
259C23×C8—111no—
260C2×C4×Q8C2×D1112yes—
261C2×C4×D4—112no—
262#440—228no—
263C2×#107—112no—
264C2×#103—112no—
265C2×#103—112no—
266C2×#102—112no—
267C2×#102—112no—
268C2×C22⋊C8—111no—
269C2×#97—112no—
270#391—112no—
271#390—22no—
272#390C2×D1112yes—
273#386—222no—
274#381—221no—
275#380—21no—
276#380—111no—
277#380C2×D1111yescharacteristic
278C4×C22⋊C4—21no—
279C4×C22⋊C4C2×D1111yescharacteristic
280C2×#95—221no—
281#340—112no—
282#336—112no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11C2×C4×D411yescharacteristic
294C22×C11D4212yes—
295C22×C11#57512yes—
296C22×C11#57611yescharacteristic
297C22×C11#57811yescharacteristic
298C2×D11—24no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—44no—
302C2×D11—44no—
303C4×C11—22no—
304C4×C11—24no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—82no—
308C4×C11C22×C22⋊C411yescharacteristic
309C4×C11#51811yescharacteristic
310C4×C11#54612yes—
311Dic11—42no—
312Dic11—82no—
313C2×#41—22no—
314C2×#41—24no—
315C2×#41—42no—
316C2×#41—114no—
317C2×#41—224no—
318C2×#41—222no—
319C2×#41—442no—
320C2×#41C4×D1114yescomplemented
321C22×Q8—111no—
322C22×Q8C22×D1111yescharacteristic
323C22×D4—21no—
324C22×D4—111no—
325C22×D4—221no—
326C22×D4C22×D1111yescharacteristic
327C23×C4—21no—
328C23×C4—221no—
329C23×C4—222no—
330C23×C4C22×D1111yescharacteristic
331#135—2232no—
332C2×Q16—114no—
333C2×Q16—224no—
334C2×SD16—114no—
335C2×SD16—118no—
336C2×SD16—114no—
337C2×SD16—224no—
338C2×D8—114no—
339C2×D8—224no—
340C22×C8—111no—
341C22×C8—114no—
342C22×C8—111no—
343C22×C8—112no—
344C22×C8—224no—
345C4×Q8—24no—
346C4×Q8—42no—
347C4×D4—224no—
348C4×D4—442no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4C22⋊D1112yes—
358C2×C42—22no—
359C2×C42C22×D1112yes—
360#107—224no—
361#103—224no—
362#103—442no—
363#102—224no—
364#102—442no—
365C22⋊C8—222no—
366#97—224no—
367#95—21no—
368#95—221no—
369#95—222no—
370#95—222no—
371#95C22⋊D1111yescharacteristic
372#95C22⋊D1111yescharacteristic
373C2×C11—42no—
374C2×C11—82no—
375C2×C11D4×C22⋊C411yescharacteristic
376C2×C11#294311yescharacteristic
377C2×C11#295111yescharacteristic
378C2×C11#326812yes—
379C2×C11#326912yes—
380D11—44no—
381C24—21no—
382C24—221no—
383C24C2×C22⋊D1111yescharacteristic
384#41—28no—
385#41—44no—
386#41—48no—
387#41—228no—
388#41—444no—
389#41—448no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—112no—
393C2×Q8—221no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×Q8C2×C4×D1112yes—
397C2×Q8D4×D1114yes—
398C2×D4—24no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—44no—
403C2×D4—112no—
404C2×D4—114no—
405C2×D4—224no—
406C2×D4—221no—
407C2×D4—222no—
408C2×D4—444no—
409C2×D4C2×C4×D1112yes—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—44no—
416C22×C4—221no—
417C22×C4—224no—
418C22×C4—222no—
419C22×C4—444no—
420C22×C4—444no—
421C22×C4—444no—
422C22×C4—882no—
423C22×C4C2×C4×D1112yes—
424C22×C4#433912yes—
425C22×C4C2×C22⋊D1112yes—
426C22×C4C2×C22⋊D1112yes—
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429Q16—228no—
430SD16—1116no—
431SD16—228no—
432D8—228no—
433C2×C8—112no—
434C2×C8—114no—
435C2×C8—112no—
436C2×C8—228no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—222no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—44no—
444C4⋊C4—222no—
445C4⋊C4—222no—
446C22⋊C4—42no—
447C22⋊C4—44no—
448C22⋊C4—82no—
449C22⋊C4—81no—
450C22⋊C4—444no—
451C22⋊C4—881no—
452C42—22no—
453C42—22no—
454C42—44no—
455C11#2243911yescharacteristic, complemented, Sylow
456C23—22no—
457C23—22no—
458C23—21no—
459C23—21no—
460C23—22no—
461C23—42no—
462C23—42no—
463C23—41no—
464C23—41no—
465C23—222no—
466C23—224no—
467C23—442no—
468C23—441no—
469C23—441no—
470C23C4×C22⋊D1112yes—
471C23C22×C22⋊D1111yescharacteristic
472Q8—22no—
473Q8—24no—
474Q8—222no—
475Q8—222no—
476Q8—442no—
477Q8C22⋊C4×D1114yes—
478D4—22no—
479D4—22no—
480D4—48no—
481D4—42no—
482D4—114no—
483D4—222no—
484D4—224no—
485D4—448no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—48no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—222no—
503C2×C4—448no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—888no—
509C2×C4C4×C22⋊D1112yes—
510C2×C4C22×C4×D1111yescharacteristic
511C2×C4C2×#433911yescharacteristic
512C2×C4C2×D4×D1112yes—
513C2×C4#6703712yes—
514C8—114no—
515C8—222no—
516C8—442no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—82no—
526C22—82no—
527C22—224no—
528C22—444no—
529C22—444no—
530C22—442no—
531C22—442no—
532C22C2×C4×C22⋊D1111yescharacteristic
533C22D4×C22⋊D1112yes—
534C22#1062335312yes—
535C22#1062336611yescharacteristic
536C22#1062336911yescharacteristic
537C4—22no—
538C4—24no—
539C4—42no—
540C4—42no—
541C4—82no—
542C4—442no—
543C4—882no—
544C4C2×C22⋊C4×D1111yescharacteristic
545C4#1062301711yescharacteristic
546C4#1062302112yes—
547C2—42no—
548C2—82no—
549C2—444no—
550C2C22⋊C4×C22⋊D1111yescharacteristic
551C2#1307741411yescharacteristic
552C2#1307748911yescharacteristic
553C2#1308015712yes—
554C2#1308017212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2341C2
socleC23×C11C22×D4
prime radicalC22×#67003C2
cosocleC22×C4×C11C24
hypercenter#2341D11
hypocenterC11#22439
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
3. #13071447C2semidirect
4. #13069496C2semidirect
5. #13068967C2semidirect
6. #13068957C2semidirect
7. #13068643C2semidirect
8. #13068556C2semidirect
9. #13068554C2semidirect
10. #13068394C2semidirect
11. C11×#2341C2semidirect
16. C2×#67003C4semidirect
47. C2×C11×#41C2×C4semidirect
75. C2×#4326C2×C4semidirect
79. C2×#4324C2×C4semidirect
85. C22×C11⋊C8C2×C4semidirect
165. #4325C22⋊C4semidirect
181. #2341D11semidirect
320. C2×#41C4×D11semidirect
455. C11#22439semidirect

Maximal subgroups

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

subgroupindex
C22×#670032
C2×#106226392
#130714472
#130694962
#130689672
#130689572
#130686432
#130685562
#130685542
#130683942
C11×#23412
#2243911