Finite Group Databasebeta

← #14769628

Subgroups — #14769628

Order 2816.

1478 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×#66957C211yesmaximal, characteristic
2C2×C4×#4314C212yesmaximal, complemented
3#13071456C211yesmaximal, characteristic, complemented
4#13071447C211yesmaximal, characteristic, complemented
5#13069470C212yesmaximal, complemented
6#13068963C212yesmaximal, complemented
7#13068956C212yesmaximal, complemented
8#13068641C211yesmaximal, characteristic, complemented
9#13068557C211yesmaximal, characteristic, complemented
10#13068557C211yesmaximal, characteristic, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C22×Dic44C2211yescharacteristic
16C2×#66957—28no—
17C2×#66957C418yescomplemented
18C22×D88C2211yescharacteristic
19C22×#4314C2211yescharacteristic
20C22×#4314C2211yescharacteristic
21C2×C4×D44C2212yes—
22C2×C4×Dic22C2212yes—
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2212yes—
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×#66885C2212yes—
29C2×#66885C2212yes—
30C2×#66881C2212yes—
31C2×#66880C2212yes—
32C2×#66880C2212yes—
33#10622570—22no—
34#10622569—22no—
35#10622552C2212yes—
36#10622542C2212yes—
37C4×#4314—28no—
38#10622280—21no—
39#10622279—21no—
40#10622277—21no—
41D11×#95—21no—
42C11×#336C2212yes—
43#10622189C2212yes—
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11—21no—
46C22×C22⋊D11—21no—
47C2×#4339—22no—
48C2×#4339—22no—
49C2×#4339—24no—
50C2×#4339—24no—
51C2×#4339—42no—
52C2×#4339—42no—
53C2×#4339C2×C414yes—
54C2×#4339C2×C414yescomplemented
55C22×D44C2311yescharacteristic
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C22×C4×D11—21no—
59C22×C4×D11—22no—
60C22×Dic22C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11—24no—
63C22×C8×C11C2×C414yescomplemented
64C22×C8×C11C2312yes—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11C2312yes—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—22no—
77C2×C4×Dic11—22no—
78C2×Dic44—24no—
79C2×Dic44C2×C414yescomplemented
80#66957—232no—
81C2×D88—24no—
82C2×D88C2×C414yes—
83C2×#4314—24no—
84C2×#4314C2×C414yes—
85C2×#4314C2×C414yescomplemented
86C2×#4314D418yes—
87C4×D44—24no—
88C4×D44—42no—
89C4×Dic22—24no—
90C4×Dic22—42no—
91C11×C22⋊C8—22no—
92C4×C8×C11—24no—
93C11×#95D411yescharacteristic
94C11×#95D411yescharacteristic
95C11⋊#95—21no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—21no—
99#66885—24no—
100#66885—42no—
101#66881—24no—
102#66880—24no—
103#66880—42no—
104#22449—111nomaximal, Sylow
105C24×C11C2×D411yescharacteristic
106C23×D11—21no—
107C23×D11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—24no—
117C2×C22⋊D11—24no—
118C2×C22⋊D11—44no—
119C2×C22⋊D11—44no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124#4339—28no—
125#4339—28no—
126#4339—44no—
127#4339—44no—
128#4339—48no—
129#4339—48no—
130C2×D44—22no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44C22×C412yes—
136C2×D44C22×C412yes—
137C2×D44C2×D414yes—
138C2×C4×D11—24no—
139C2×C4×D11—24no—
140C2×C4×D11—44no—
141C2×C4×D11—44no—
142C2×C4×D11—44no—
143C2×C4×D11—44no—
144C2×C4×D11—82no—
145C2×Dic22—22no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22C22×C412yes—
151C2×Dic22C22×C412yes—
152C2×Dic22C2×D414yes—
153C2×C8×C11—28no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11C22×C412yes—
159C2×C8×C11C22×C412yes—
160C2×C8×C11C2×D414yes—
161C11×C22⋊C4—24no—
162C42×C11—22no—
163C42×C11—22no—
164C22⋊Dic11—81no—
165C22⋊Dic11—81no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—44no—
168(C2×D11)⋊C4—82no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173Dic11⋊C4—44no—
174C4×Dic11—44no—
175Dic44—28no—
176D88—28no—
177#4314—28no—
178#4314C22⋊C4116yescomplemented
179C22×#135—111no—
180C2×C4×SD16—112no—
181#2341—111no—
182#2339—111no—
183#1968—112no—
184#1879—112no—
185#1878—112no—
186#1807—111no—
187#1788—111no—
188#1788—111no—
189C8×C22⋊C4D1111yescharacteristic, complemented
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11C4×D412yes—
195C23×C11C22×D411yescharacteristic
196C22×D11—22no—
197C22×D11—24no—
198C22×D11—22no—
199C22×D11—42no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—41no—
205C22×D11—41no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11C4×D412yes—
216C2×C4×C11#13514yescomplemented
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C22×D412yes—
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)12yes—
221C22⋊D11—48no—
222C22⋊D11—48no—
223C2×Dic11—22no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233D44—22no—
234D44—22no—
235D44—22no—
236D44—24no—
237D44—42no—
238D44C2×C22⋊C414yes—
239C4×D11—48no—
240C4×D11—48no—
241C4×D11—88no—
242Dic22—22no—
243Dic22—24no—
244Dic22—22no—
245Dic22—22no—
246Dic22—42no—
247Dic22C2×C22⋊C414yes—
248C8×C11—22no—
249C8×C11—42no—
250C8×C11C2×C22⋊C414yes—
251C22×#41—111no—
252C22×#41—111no—
253C2×#135—118no—
254C2×#135—228no—
255C22×Q16—111no—
256C22×SD16—111no—
257C22×SD16—111no—
258C22×D8—111no—
259C23×C8C2×D1111yescharacteristic
260C2×C4×Q8—112no—
261C2×C4×D4—112no—
262C4×SD16—228no—
263C2×#106—112no—
264C2×#103—112no—
265C2×#103—112no—
266C2×#102—112no—
267C2×#102—112no—
268C2×C22⋊C8C2×D1111yescharacteristic
269C2×C4×C8C2×D1112yes—
270#391—112no—
271#390—112no—
272#390—222no—
273#386—222no—
274#381—221no—
275#380—111no—
276#380—111no—
277#380—221no—
278C4×C22⋊C4—221no—
279C4×C22⋊C4C2×D1111yescharacteristic
280C2×#95—221no—
281#340—112no—
282#336C2×D1112yes—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11C2×C4×D411yescharacteristic
289C22×C11D4212yes—
290C22×C11C2×#13512yes—
291C22×C11#57711yescharacteristic
292C22×C11#57711yescharacteristic
293C2×D11—24no—
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—44no—
297C2×D11—44no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—82no—
302C2×D11—82no—
303C4×C11—22no—
304C4×C11—24no—
305C4×C11—42no—
306C4×C11C22×C22⋊C411yescharacteristic
307C4×C11#51811yescharacteristic
308C4×C11#54612yes—
309Dic11—24no—
310Dic11—42no—
311Dic11—82no—
312Dic11—82no—
313C2×#41—114no—
314C2×#41—114no—
315C2×#41—224no—
316C2×#41—224no—
317C2×#41—222no—
318C2×#41—222no—
319C2×#41—442no—
320C2×#41—442no—
321C22×Q8—111no—
322C22×Q8—111no—
323C22×D4—111no—
324C22×D4—111no—
325C22×D4—221no—
326C22×D4—221no—
327C23×C4—221no—
328C23×C4—221no—
329C23×C4—222no—
330C23×C4C22×D1111yescharacteristic
331#135—2232no—
332C2×Q16—114no—
333C2×Q16—224no—
334C2×SD16—114no—
335C2×SD16—114no—
336C2×SD16—118no—
337C2×SD16—224no—
338C2×D8—114no—
339C2×D8—224no—
340C22×C8—24no—
341C22×C8C4×D1114yescomplemented
342C22×C8C22×D1112yes—
343C22×C8C22×D1111yescharacteristic
344C22×C8C22×D1111yescharacteristic
345C4×Q8—224no—
346C4×Q8—442no—
347C4×D4—224no—
348C4×D4—442no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—222no—
352C2×C22⋊C4—222no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—221no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4D4412yes—
358C2×C42—222no—
359C2×C42C22×D1112yes—
360#106—224no—
361#103—224no—
362#103—442no—
363#102—224no—
364#102—442no—
365C22⋊C8—22no—
366C4×C8—24no—
367#95—221no—
368#95—222no—
369#95—221no—
370#95—222no—
371#95D4411yescharacteristic
372#95D4411yescharacteristic
373C2×C11—42no—
374C2×C11D4×C22⋊C411yescharacteristic
375C2×C11C4×#13511yescharacteristic
376C2×C11#295211yescharacteristic
377C2×C11#328212yes—
378C2×C11#328412yes—
379D11—44no—
380D11—82no—
381C24—221no—
382C24—221no—
383C24C2×D4411yescharacteristic
384#41—228no—
385#41—228no—
386#41—444no—
387#41—444no—
388#41—448no—
389#41—448no—
390C2×Q8—112no—
391C2×Q8—112no—
392C2×Q8—114no—
393C2×Q8—221no—
394C2×Q8—221no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×D4—112no—
399C2×D4—112no—
400C2×D4—114no—
401C2×D4—224no—
402C2×D4—224no—
403C2×D4—221no—
404C2×D4—221no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—444no—
409C2×D4—444no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—221no—
413C22×C4—221no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—444no—
419C22×C4—444no—
420C22×C4—444no—
421C22×C4—444no—
422C22×C4—882no—
423C22×C4C2×C4×D1112yes—
424C22×C4C2×D4412yes—
425C22×C4C2×D4411yescharacteristic
426C22×C4C2×D4412yes—
427C22×C4#433912yes—
428C22×C4C23×D1111yescharacteristic
429Q16—228no—
430SD16—1116no—
431SD16—228no—
432D8—228no—
433C2×C8—22no—
434C2×C8—28no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8C2×C4×D1112yes—
439C2×C8C2×C4×D1112yes—
440C2×C8D4×D1114yes—
441C4⋊C4—222no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4—444no—
446C22⋊C4—24no—
447C22⋊C4—444no—
448C22⋊C4—444no—
449C22⋊C4—882no—
450C22⋊C4—881no—
451C22⋊C4—881no—
452C42—22no—
453C42—22no—
454C42—444no—
455C11#2244911yescharacteristic, complemented, Sylow
456C23—22no—
457C23—21no—
458C23—21no—
459C23—22no—
460C23—222no—
461C23—224no—
462C23—222no—
463C23—442no—
464C23—441no—
465C23—441no—
466C23—442no—
467C23—441no—
468C23—441no—
469C23—442no—
470C23C4×D4412yes—
471C23C22×D4411yescharacteristic
472Q8—114no—
473Q8—222no—
474Q8—224no—
475Q8—222no—
476Q8—222no—
477Q8—442no—
478D4—114no—
479D4—222no—
480D4—222no—
481D4—222no—
482D4—224no—
483D4—448no—
484D4—448no—
485D4—442no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—222no—
498C2×C4—448no—
499C2×C4—448no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—888no—
508C2×C4C4×D4412yes—
509C2×C4#6695714yescomplemented
510C2×C4C22×C4×D1111yescharacteristic
511C2×C4C2×#433911yescharacteristic
512C2×C4C2×D4×D1112yes—
513C2×C4#6704212yes—
514C8—22no—
515C8—42no—
516C8C22⋊C4×D1114yes—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—42no—
521C22—42no—
522C22—224no—
523C22—444no—
524C22—444no—
525C22—442no—
526C22—442no—
527C22—442no—
528C22—442no—
529C22—442no—
530C22—882no—
531C22—882no—
532C22C2×C4×D4411yescharacteristic
533C22D4×D4412yes—
534C22C2×#6695712yes—
535C22#1062328211yescharacteristic
536C22#1062328211yescharacteristic
537C4—24no—
538C4—22no—
539C4—42no—
540C4—224no—
541C4—442no—
542C4—882no—
543C4—882no—
544C4C2×C22⋊C4×D1111yescharacteristic
545C4#1062305211yescharacteristic
546C4#1062308112yes—
547C2—42no—
548C2—444no—
549C2—882no—
550C2C22⋊C4×D4411yescharacteristic
551C2C4×#6695711yescharacteristic
552C2#1307750111yescharacteristic
553C2#1308032812yes—
554C2#1308034812yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC22×#66957C2
cosocleC22×C4×C11C24
hypercenterC8×C22⋊C4D11
hypocenterC11#22449
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4314C2semidirect
3. #13071456C2semidirect
4. #13071447C2semidirect
5. #13069470C2semidirect
6. #13068963C2semidirect
7. #13068956C2semidirect
8. #13068641C2semidirect
9. #13068557C2semidirect
10. #13068557C2semidirect
11. C8×C11×C22⋊C4C2semidirect
17. C2×#66957C4semidirect
54. C2×#4339C2×C4semidirect
63. C22×C8×C11C2×C4semidirect
79. C2×Dic44C2×C4semidirect
85. C2×#4314C2×C4semidirect
178. #4314C22⋊C4semidirect
189. C8×C22⋊C4D11semidirect
216. C2×C4×C11#135semidirect
341. C22×C8C4×D11semidirect
455. C11#22449semidirect
509. C2×C4#66957semidirect

Maximal subgroups

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

subgroupindex
C22×#669572
C2×C4×#43142
#130714562
#130714472
#130694702
#130689632
#130689562
#130686412
#130685572
C8×C11×C22⋊C42
#2244911