Finite Group Databasebeta

← #14660183

Subgroups — #14660183

Order 2816.

916 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622752C211yesmaximal, characteristic
2#13077136C211yesmaximal, characteristic
3C2×#10622619C211yesmaximal, characteristic
4#13068348C211yesmaximal, characteristic, complemented
5#13068327C211yesmaximal, characteristic, complemented
6C2×#10622195C211yesmaximal, characteristic, complemented
7C11×#2873C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C11×#405—22no—
16C11×#405—22no—
17C4×C11×M16—22no—
18#10622752—22no—
19#10622752—22no—
20C2×#66889C414yescomplemented
21#10622746—22no—
22#10622744C412yescomplemented
23#10622733C412yescomplemented
24#10622726—22no—
25#10622619—22no—
26#10622619C414yescomplemented
27C2×#66870—22no—
28#10622195—22no—
29#10622193—22no—
30#10622165—22no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C2×#4339—21no—
34C2×#4339—21no—
35C2×#4339—21no—
36C2×#4339—21no—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339C2×C412yes—
44C2×#4339C2×C412yes—
45C22×D44C2×C411yescharacteristic
46C22×C4×D11—21no—
47C22×Dic22C2×C411yescharacteristic
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16C2×C412yes—
56C2×C11×M16C2×C412yes—
57C2×C11×M16D412yes—
58C2×C11×M16D412yes—
59C2×C11×M16D412yes—
60C22×C8×C11—21no—
61C22×C8×C11D412yes—
62C11×#117—21no—
63C11×#117—21no—
64C11×#117C2×C412yes—
65C11×#117D412yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75#66979—21no—
76#66979—21no—
77#66979—21no—
78#66979—21no—
79#66979—21no—
80#66979—21no—
81#66979—21no—
82#66979C2×C412yes—
83#66979C2×C412yes—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2×C412yes—
90C11×#97—24no—
91C4×C8×C11—24no—
92#66889—28no—
93#66885—24no—
94#66880—24no—
95#66870—28no—
96#10951—111nomaximal, Sylow
97C24×C11C2×D411yescharacteristic
98C23×D11—21no—
99C22×C4×C11—22no—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C2×C22⋊D11—22no—
115C2×C22⋊D11—22no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C22×Dic11—21no—
121C22×Dic11—22no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124#4339—22no—
125#4339—22no—
126#4339—22no—
127#4339—22no—
128#4339—22no—
129#4339—22no—
130#4339—22no—
131#4339—22no—
132#4339—41no—
133#4339—41no—
134#4339—41no—
135#4339—41no—
136#4339—41no—
137#4339—41no—
138#4339—41no—
139#4339—41no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44C4212yes—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—41no—
149C2×C4×D11—41no—
150C2×C4×D11—41no—
151C2×C4×D11—41no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22C4212yes—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16C22⋊C414yes—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11C22⋊C414yes—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4C22⋊C414yes—
176C42×C11—22no—
177C42×C11—22no—
178C22⋊Dic11—22no—
179C22⋊Dic11—22no—
180C22⋊Dic11—41no—
181C22⋊Dic11—41no—
182C22⋊Dic11—41no—
183C22⋊Dic11—41no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—41no—
187C4⋊Dic11—41no—
188C4⋊Dic11—41no—
189C4⋊Dic11—41no—
190C4×Dic11—22no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—22no—
194C4×Dic11—41no—
195C4×Dic11—41no—
196C2×#421—111no—
197#2896—111no—
198C2×#410—111no—
199#2873D1111yescharacteristic, complemented
200#1740—111no—
201#1733—111no—
202C2×H(3,ℤ/4)—111no—
203C23×C11—81no—
204C23×C11C2×C22⋊C411yescharacteristic
205C23×C11C4×D411yescharacteristic
206C23×C11C4×D411yescharacteristic
207C23×C11#12111yescharacteristic
208C23×C11#12111yescharacteristic
209C23×C11#12411yescharacteristic
210C23×C11#12711yescharacteristic
211C22×D11—22no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—82no—
215C2×C4×C11—24no—
216C2×C4×C11—82no—
217C2×C4×C11C2×C4211yescharacteristic
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11#11711yescharacteristic
221C2×C4×C11#11711yescharacteristic
222C2×C4×C11#11711yescharacteristic
223C2×C4×C11C4×D411yescharacteristic
224C2×C4×C11C4×D411yescharacteristic
225C2×C4×C11C4×D411yescharacteristic
226C2×C4×C11C4×D411yescharacteristic
227C2×C4×C11C4×D411yescharacteristic
228C2×C4×C11C4×D411yescharacteristic
229C2×C4×C11C4×D411yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12111yescharacteristic
235C2×C4×C11#12111yescharacteristic
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11#12111yescharacteristic
238C2×C4×C11#12311yescharacteristic
239C2×C4×C11#12311yescharacteristic
240C2×C4×C11#12311yescharacteristic
241C2×C4×C11#12411yescharacteristic
242C2×C4×C11#12411yescharacteristic
243C2×C4×C11#12611yescharacteristic
244C2×C4×C11#12611yescharacteristic
245C22⋊D11—42no—
246C22⋊D11—42no—
247C22⋊D11—42no—
248C22⋊D11—42no—
249C2×Dic11—22no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—82no—
256C2×Dic11—82no—
257C2×Dic11—82no—
258D44—22no—
259D44—22no—
260D44—41no—
261D44—41no—
262C4×D11—42no—
263C4×D11—42no—
264C4×D11—42no—
265C4×D11—42no—
266Dic22—22no—
267Dic22—22no—
268Dic22—41no—
269Dic22—41no—
270C8×C11—24no—
271C8×C11—24no—
272C22×#41—111no—
273C22×M16C2×D1111yescharacteristic
274C22×M16C2×D1111yescharacteristic
275C2×#117—111no—
276C2×#117—111no—
277C2×#117—111no—
278C2×#117C2×D1111yescharacteristic
279#421—222no—
280#421—222no—
281C2×#104—114no—
282#419—112no—
283#418—112no—
284#417—222no—
285#416—222no—
286#410—114no—
287#410—222no—
288C2×#99—222no—
289#405—22no—
290#405—22no—
291C4×M16—22no—
292#342—222no—
293#339—222no—
294H(3,ℤ/4)—222no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11C4×C22⋊C411yescharacteristic
303C22×C11#38611yescharacteristic
304C22×C11#38811yescharacteristic
305C22×C11#38811yescharacteristic
306C22×C11#39011yescharacteristic
307C22×C11#39011yescharacteristic
308C22×C11#39011yescharacteristic
309C2×D11—42no—
310C2×D11—82no—
311C2×D11—82no—
312C2×D11—82no—
313C4×C11—44no—
314C4×C11C4×C22⋊C411yescharacteristic
315C4×C11C4×C22⋊C411yescharacteristic
316C4×C11#38611yescharacteristic
317C4×C11#38611yescharacteristic
318C4×C11#38811yescharacteristic
319C4×C11#38811yescharacteristic
320C4×C11#38811yescharacteristic
321C4×C11#38811yescharacteristic
322Dic11—42no—
323Dic11—82no—
324Dic11—82no—
325Dic11—82no—
326C2×#41—112no—
327C2×#41—112no—
328C2×#41—221no—
329C2×#41—221no—
330C2×#41—221no—
331C2×#41—221no—
332C2×#41—221no—
333C2×#41—221no—
334C2×#41—221no—
335C2×#41—221no—
336C2×#41—221no—
337C2×#41—221no—
338C22×Q8—111no—
339C22×D4—111no—
340C22×D4—221no—
341C23×C4—221no—
342C23×C4C22×D1111yescharacteristic
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16C4×D1112yes—
351C2×M16C4×D1112yes—
352C2×M16D4412yes—
353C2×M16D4412yes—
354C2×M16C22⋊D1112yes—
355C22×C8—21no—
356C22×C8C22⋊D1112yes—
357#117—21no—
358#117—21no—
359#117—112no—
360#117—112no—
361#117—221no—
362#117—221no—
363#117—221no—
364#117—221no—
365#117—221no—
366#117—221no—
367#117—221no—
368#117—221no—
369#117—221no—
370#117—221no—
371#117C4×D1112yes—
372#117C22⋊D1112yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4D4412yes—
381C2×C42—21no—
382C2×C42—112no—
383C2×C42—221no—
384C2×C42—221no—
385#104—228no—
386#103—224no—
387#102—224no—
388#99—228no—
389#97—24no—
390C4×C8—24no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11#143711yescharacteristic
399D11—82no—
400C24—221no—
401C24C2×D4411yescharacteristic
402#41—222no—
403#41—222no—
404#41—222no—
405#41—222no—
406#41—222no—
407#41—222no—
408#41—222no—
409#41—222no—
410#41—441no—
411#41—441no—
412#41—441no—
413#41—441no—
414#41—441no—
415#41—441no—
416#41—441no—
417#41—441no—
418C2×Q8—112no—
419C2×Q8—221no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×D4—112no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—221no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—441no—
433C2×D4—441no—
434C2×D4—441no—
435C2×D4—441no—
436C22×C4—22no—
437C22×C4—221no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4C2×C4×D1111yescharacteristic
450C22×C4C2×D4411yescharacteristic
451C22×C4C2×D4411yescharacteristic
452C22×C4#433911yescharacteristic
453C22×C4#433911yescharacteristic
454C22×C4#433911yescharacteristic
455C22×C4#433911yescharacteristic
456C22×C4#433911yescharacteristic
457C22×C4#433911yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—22no—
467M16—22no—
468M16(C2×D11)⋊C414yes—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8(C2×D11)⋊C414yes—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—222no—
478C4⋊C4—222no—
479C4⋊C4—441no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C22⋊C4—22no—
484C22⋊C4—222no—
485C22⋊C4—222no—
486C22⋊C4—441no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4(C2×D11)⋊C414yes—
491C42—22no—
492C42—22no—
493C42—222no—
494C42—222no—
495C42—222no—
496C42—222no—
497C42—441no—
498C42—441no—
499C11#1095111yescharacteristic, complemented, Sylow
500C23—81no—
501C23—222no—
502C23—441no—
503C23—441no—
504C23—882no—
505C23C4×D4411yescharacteristic
506C23C4×D4411yescharacteristic
507C23#6692711yescharacteristic
508C23#6692811yescharacteristic
509C23C2×(C2×D11)⋊C411yescharacteristic
510C23#6698311yescharacteristic
511C23#6698311yescharacteristic
512Q8—222no—
513Q8—222no—
514Q8—441no—
515Q8—441no—
516D4—222no—
517D4—222no—
518D4—442no—
519D4—442no—
520D4—442no—
521D4—442no—
522D4—441no—
523D4—441no—
524C2×C4—24no—
525C2×C4—82no—
526C2×C4—222no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—882no—
537C2×C4—882no—
538C2×C4—882no—
539C2×C4C42×D1111yescharacteristic
540C2×C4#6692511yescharacteristic
541C2×C4#6692511yescharacteristic
542C2×C4#6692511yescharacteristic
543C2×C4C4×D4411yescharacteristic
544C2×C4C4×D4411yescharacteristic
545C2×C4C4×D4411yescharacteristic
546C2×C4C4×D4411yescharacteristic
547C2×C4#6692811yescharacteristic
548C2×C4#6692811yescharacteristic
549C2×C4#6692911yescharacteristic
550C2×C4#6692911yescharacteristic
551C2×C4C2×(C2×D11)⋊C411yescharacteristic
552C2×C4C2×(C2×D11)⋊C411yescharacteristic
553C2×C4C4×C22⋊D1111yescharacteristic
554C2×C4C4×C22⋊D1111yescharacteristic
555C2×C4C4×C22⋊D1111yescharacteristic
556C2×C4C4×C22⋊D1111yescharacteristic
557C2×C4C4×C22⋊D1111yescharacteristic
558C2×C4C4×C22⋊D1111yescharacteristic
559C2×C4#6698211yescharacteristic
560C2×C4#6698211yescharacteristic
561C2×C4#6698211yescharacteristic
562C2×C4#6698311yescharacteristic
563C2×C4#6698311yescharacteristic
564C2×C4#6698311yescharacteristic
565C2×C4#6698311yescharacteristic
566C2×C4#6700611yescharacteristic
567C8—24no—
568C8—24no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—442no—
577C22—882no—
578C22—882no—
579C22—882no—
580C22C4×(C2×D11)⋊C411yescharacteristic
581C22#1062255211yescharacteristic
582C22#1062255211yescharacteristic
583C22#1062255211yescharacteristic
584C22#1062255311yescharacteristic
585C22#1062255311yescharacteristic
586C22#1062282611yescharacteristic
587C4—44no—
588C4—442no—
589C4—882no—
590C4—882no—
591C4—882no—
592C4C4×(C2×D11)⋊C411yescharacteristic
593C4C4×(C2×D11)⋊C411yescharacteristic
594C4#1062255311yescharacteristic
595C4#1062255311yescharacteristic
596C4#1062255311yescharacteristic
597C4#1062255311yescharacteristic
598C4#1062282611yescharacteristic
599C4#1062282611yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—882no—
608C2#1306685411yescharacteristic
subgroupG/H
centerC4#10622826
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#2873C2
socleC2×C11#1437
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenter#2873D11
hypocenterC11#10951
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2873

Complements

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

NH ≅ G/Ntype
4. #13068348C2semidirect
5. #13068327C2semidirect
6. C2×#10622195C2semidirect
7. C11×#2873C2semidirect
20. C2×#66889C4semidirect
22. #10622744C4semidirect
23. #10622733C4semidirect
26. #10622619C4semidirect
199. #2873D11semidirect
499. C11#10951semidirect

Maximal subgroups

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

subgroupindex
C2×#106227522
#130771362
C2×#106226192
#130683482
#130683272
C2×#106221952
C11×#28732
#1095111