Finite Group Databasebeta

← #14756166

Subgroups — #14756166

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622611C211yesmaximal, characteristic, complemented
2C2×#10622726C211yesmaximal, characteristic
3C2×#10622615C211yesmaximal, characteristic
4#13071104C211yesmaximal, characteristic
5#117×Dic11C211yesmaximal, characteristic, complemented
6#13069255C212yesmaximal, complemented
7#13069248C212yesmaximal, complemented
8#13069241C212yesmaximal, complemented
9#13069234C212yesmaximal, complemented
10C2×#10622188C211yesmaximal, characteristic, complemented
11C11×#1735C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19#10622726—24no—
20C2×#66885C2212yes—
21C2×#66880C2212yes—
22#10622615C418yescomplemented
23#10622611—24no—
24#10622601C2212yes—
25C4⋊C4×Dic11C2212yes—
26C4⋊C4×Dic11C2212yes—
27#10622587C2212yes—
28C2×#66874C2211yescharacteristic
29C2×#66874C2211yescharacteristic
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32C2×#66872C2212yes—
33C2×#66871C2212yes—
34#10622571—22no—
35C22⋊C4×Dic11—22no—
36C4×(C2×D11)⋊C4—21no—
37C4×(C2×D11)⋊C4—21no—
38#10622545—21no—
39C42×Dic11—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11—21no—
46C23×Dic11D412yes—
47C2×#4339—22no—
48C2×#4339—22no—
49C2×#4339—22no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339C2×C414yes—
53C22×D44C2311yescharacteristic
54C22×C4×D11—21no—
55C22×Dic22C2311yescharacteristic
56C22×C8×C11—22no—
57C22×C8×C11—22no—
58C22×C8×C11—22no—
59C22×C8×C11C2312yes—
60C11×#117—22no—
61C11×#117—22no—
62C11×#117—22no—
63C11×#117C2×C414yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11—21no—
70C2×C42×C11—21no—
71C2×C22⋊Dic11—21no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74#66979—22no—
75#66979D414yes—
76C2×C4⋊Dic11C2312yes—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2312yes—
85C22×C11⋊C8—22no—
86C22×C11⋊C8—22no—
87C22×C11⋊C8C2×C414yes—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94#66885—24no—
95#66880—24no—
96#66874C2×C414yescomplemented
97#66874C2×C414yescomplemented
98#66873C2×C414yescomplemented
99#66873C2×C414yescomplemented
100#66872—24no—
101#66871—24no—
102#21058—111nomaximal, Sylow
103C24×C11C2×D411yescharacteristic
104C23×D11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×C4×C11#4112yes—
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—24no—
117C2×C22⋊D11—42no—
118C2×C22⋊D11—42no—
119C22×Dic11—24no—
120C22×Dic11—24no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—42no—
124C22×Dic11C2×D412yes—
125C22×Dic11C2×D412yes—
126#4339—28no—
127#4339—28no—
128#4339—44no—
129#4339—44no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44C22×C412yes—
136C2×C4×D11—24no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C2×Dic22—21no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22C22×C412yes—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—44no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C22×C412yes—
154C11×C4⋊C4C22×C412yes—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—42no—
157C42×C11—24no—
158C42×C11—42no—
159C22⋊Dic11—24no—
160(C2×D11)⋊C4—44no—
161(C2×D11)⋊C4—44no—
162C4⋊Dic11—22no—
163C4⋊Dic11C2×D414yes—
164C4×Dic11—24no—
165C4×Dic11—22no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C4×Dic11—22no—
169C4×Dic11—44no—
170C4×Dic11—44no—
171C2×C11⋊C8—28no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8C22×C412yes—
177C2×C11⋊C8C22×C412yes—
178C2×#427—111no—
179C2×#416—111no—
180C2×#416—111no—
181#2297—111no—
182C4×#117—111no—
183#1928—112no—
184#1927—112no—
185#1926—112no—
186#1925—112no—
187#1735D1111yescharacteristic, complemented
188C2×#336—111no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11C4×D412yes—
192C23×C11#12112yes—
193C23×C11#12312yes—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—42no—
199C22×D11—42no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11#11714yes—
208C2×C4×C11C4×D412yes—
209C2×C4×C11C4×D414yes—
210C2×C4×C11#12112yes—
211C2×C4×C11#12312yes—
212C2×C4×C11#12414yes—
213C2×C4×C11#12614yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C22⋊D11—48no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—48no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11#13514yes—
234D44—22no—
235D44—22no—
236D44—41no—
237D44—41no—
238C4×D11—48no—
239Dic22—22no—
240Dic22—22no—
241Dic22—41no—
242Dic22—41no—
243C8×C11—42no—
244C11⋊C8—22no—
245C11⋊C8—22no—
246C22×#41—111no—
247C23×C8—111no—
248C23×C8C2×D1111yescharacteristic
249C2×#117—111no—
250C2×#117C2×D1111yescharacteristic
251C2×#117C2×D1111yescharacteristic
252C22×C42—111no—
253#427—224no—
254C2×#107—112no—
255C2×#106—112no—
256#416—118no—
257#416—224no—
258C2×#103—111no—
259C2×#103—111no—
260C2×#103—112no—
261C2×#102—111no—
262C2×#102—111no—
263C2×#102—112no—
264#391—112no—
265#390—112no—
266#386—222no—
267C4×C4⋊C4—112no—
268C4×C4⋊C4—112no—
269C4×C22⋊C4—221no—
270C4×C22⋊C4—221no—
271C4×C22⋊C4—222no—
272#376—221no—
273C43—221no—
274#340C2×D1112yes—
275#340C2×D1112yes—
276#336—112no—
277#336—112no—
278C22×C11—24no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—24no—
282C22×C11#38814yes—
283C22×C11C2×C4×D411yescharacteristic
284C22×C11C2×#12111yescharacteristic
285C22×C11C2×#12311yescharacteristic
286C22×C11C2×#13512yes—
287C22×C11#57512yes—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—82no—
292C2×D11—82no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—82no—
296C4×C11#38814yes—
297C4×C11C2×#11711yescharacteristic
298C4×C11C2×C4×D411yescharacteristic
299C4×C11C2×#12411yescharacteristic
300C4×C11C2×#12611yescharacteristic
301Dic11—24no—
302Dic11—42no—
303Dic11—44no—
304Dic11—42no—
305C2×#41—114no—
306C2×#41—222no—
307C2×#41—222no—
308C2×#41—222no—
309C2×#41—222no—
310C2×#41—222no—
311C22×Q8—111no—
312C22×D4—111no—
313C22×D4—221no—
314C23×C4—112no—
315C23×C4—221no—
316C23×C4C22×D1111yescharacteristic
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—114no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8—222no—
324C22×C8—222no—
325C22×C8C22×D1112yes—
326#117—22no—
327#117—22no—
328#117—22no—
329#117—114no—
330#117—222no—
331#117C4×D1114yes—
332C2×C4⋊C4—112no—
333C2×C4⋊C4C22×D1112yes—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—221no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—111no—
344C2×C42—111no—
345C2×C42—112no—
346C2×C42—222no—
347C2×C42—221no—
348C2×C42—222no—
349C2×C42—222no—
350C2×C42—222no—
351#107—224no—
352#106—224no—
353#103—114no—
354#103—114no—
355#103—224no—
356#102—114no—
357#102—114no—
358#102—224no—
359#95—222no—
360#95—222no—
361#95—222no—
362#95—222no—
363C2×C11—24no—
364C2×C11C2×#38811yescharacteristic
365C2×C11C4×#13511yescharacteristic
366C2×C11#294311yescharacteristic
367C2×C11#303512yes—
368C2×C11#309112yes—
369D11—82no—
370C24—221no—
371C24D4×D1111yescharacteristic
372#41—228no—
373#41—228no—
374#41—444no—
375#41—444no—
376C2×Q8—112no—
377C2×Q8—221no—
378C2×Q8—221no—
379C2×Q8—221no—
380C2×Q8—221no—
381C2×Q8—221no—
382C2×D4—112no—
383C2×D4—224no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—221no—
388C2×D4—221no—
389C2×D4—442no—
390C2×D4—442no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—224no—
397C22×C4—224no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4—224no—
401C22×C4—442no—
402C22×C4—442no—
403C22×C4—442no—
404C22×C4C2×C4×D1112yes—
405C22×C4#433912yes—
406C22×C4#433912yes—
407C22×C4D4×D1112yes—
408C22×C4D4×D1111yescharacteristic
409C22×C4#434112yes—
410C22×C4#434312yes—
411C22×C4C23×D1111yescharacteristic
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—44no—
416C2×C8—112no—
417C2×C8—112no—
418C2×C8—228no—
419C2×C8—221no—
420C2×C8—221no—
421C2×C8—221no—
422C2×C8—221no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—114no—
428C4⋊C4—222no—
429C4⋊C4C2×C4×D1112yes—
430C4⋊C4C2×C4×D1112yes—
431C22⋊C4—24no—
432C22⋊C4—42no—
433C22⋊C4—224no—
434C22⋊C4—444no—
435C22⋊C4—444no—
436C42—24no—
437C42—42no—
438C42—224no—
439C42—222no—
440C42—222no—
441C42—222no—
442C42—222no—
443C42—444no—
444C42—444no—
445C11#2105811yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—222no—
449C23—441no—
450C23—441no—
451C23—442no—
452C23—442no—
453C23(C22⋊D11)⋊C412yes—
454C23#6693712yes—
455C23#6694712yes—
456C23C2×D4×D1111yescharacteristic
457Q8—222no—
458Q8—222no—
459Q8—441no—
460Q8—441no—
461D4—222no—
462D4—222no—
463D4—448no—
464D4—441no—
465D4—441no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—114no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—224no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—448no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—448no—
487C2×C4#6692514yes—
488C2×C4(C22⋊D11)⋊C412yes—
489C2×C4#6693712yes—
490C2×C4#6693814yes—
491C2×C4#6694614yes—
492C2×C4#6694712yes—
493C2×C4#6695114yes—
494C2×C4C22×C4×D1111yescharacteristic
495C2×C4C2×#433911yescharacteristic
496C2×C4C2×#433911yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4C2×#434111yescharacteristic
499C2×C4C2×#434311yescharacteristic
500C8—42no—
501C8—222no—
502C8—222no—
503C22—24no—
504C22—24no—
505C22—22no—
506C22—22no—
507C22—442no—
508C22—442no—
509C22—442no—
510C22—882no—
511C22—882no—
512C22#1062228214yes—
513C22C2×(C22⋊D11)⋊C411yescharacteristic
514C22C2×#6693711yescharacteristic
515C22C2×#6694711yescharacteristic
516C22D11×#13512yes—
517C22#1062329912yes—
518C4—42no—
519C4—42no—
520C4—82no—
521C4—224no—
522C4—442no—
523C4—444no—
524C4—442no—
525C4#1062228214yes—
526C4C2×#6692511yescharacteristic
527C4C2×#6693811yescharacteristic
528C4C2×#6694611yescharacteristic
529C4C2×#6695111yescharacteristic
530C2—24no—
531C2—882no—
532C2C2×#1062228211yescharacteristic
533C2#1307738411yescharacteristic
534C2#1307741211yescharacteristic
535C2#1307806912yes—
536C2#1307853312yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1735C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1735D11
hypocenterC11#21058
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
1. C2×#10622611C2semidirect
5. #117×Dic11C2semidirect
6. #13069255C2semidirect
7. #13069248C2semidirect
8. #13069241C2semidirect
9. #13069234C2semidirect
10. C2×#10622188C2semidirect
11. C11×#1735C2semidirect
22. #10622615C4semidirect
96. #66874C2×C4semidirect
97. #66874C2×C4semidirect
98. #66873C2×C4semidirect
99. #66873C2×C4semidirect
187. #1735D11semidirect
445. C11#21058semidirect

Maximal subgroups

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

subgroupindex
C2×#106226112
C2×#106227262
C2×#106226152
#130711042
#117×Dic112
#130692552
#130692482
#130692412
#130692342
C2×#106221882
C11×#17352
#2105811