Finite Group Databasebeta

← #14660249

Subgroups — #14660249

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66887C211yesmaximal, characteristic
2C22×#66887C211yesmaximal, characteristic
3C2×M16×Dic11C211yesmaximal, characteristic, complemented
4C2×#10622601C211yesmaximal, characteristic
5C2×#10622168C211yesmaximal, characteristic, complemented
6#13068309C211yesmaximal, characteristic, complemented
7C2×C11×#343C211yesmaximal, characteristic, complemented
8C23×D44C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×(C2×D11)⋊C4C414yes—
13C22×C4×Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C2×#66887—22no—
17C2×#66887—22no—
18C2×#66887—22no—
19C2×#66887—22no—
20C2×#66887C414yescomplemented
21C2×#66887C414yescomplemented
22M16×Dic11—22no—
23M16×Dic11—22no—
24C2×#66879—21no—
25C2×C8×Dic11—21no—
26#10622601—22no—
27#10622601—21no—
28#10622601—21no—
29C11×#343—22no—
30#10622188—22no—
31#10622168—22no—
32C24×D11C2×C412yes—
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2×C412yes—
36C22×D44—21no—
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44—21no—
47C22×D44—21no—
48C22×D44C2×C412yes—
49C22×D44C2×C412yes—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16C2×C412yes—
59C2×C11×M16C2×C412yes—
60C2×C11×M16D412yes—
61C2×C11×M16D412yes—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—48no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11D412yes—
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318C2×C412yes—
89C2×#4318C2×C412yes—
90C2×#4318D412yes—
91C2×#4318D412yes—
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94#66887—28no—
95#66887—28no—
96#66879—24no—
97C8×Dic11—24no—
98#10962—111nomaximal, Sylow
99C24×C11C22×C411yescharacteristic
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—44no—
107C23×D11—44no—
108C23×D11C4214yes—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—44no—
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C22×Dic11—24no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—42no—
131C22×Dic11C22⋊C412yes—
132C22×Dic11C22⋊C412yes—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—41no—
146C2×D44—41no—
147C2×D44—41no—
148C2×D44—41no—
149C2×D44—41no—
150C2×D44—41no—
151C2×D44—41no—
152C2×D44—41no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44—41no—
157C2×D44—41no—
158C2×D44—41no—
159C2×D44—41no—
160C2×D44—41no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16C22⋊C414yescomplemented
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—41no—
174C2×C8×C11—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187#4318—22no—
188#4318—22no—
189#4318—22no—
190#4318—22no—
191#4318—22no—
192#4318—41no—
193#4318—41no—
194#4318C22⋊C414yescomplemented
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—41no—
200C2×C11⋊C8—41no—
201C22×#100—111no—
202C22×#100—111no—
203C2×C4×M16—111no—
204C2×#390—111no—
205C2×#343—111no—
206C2×#343D1111yescharacteristic, complemented
207#1728—111no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11C2×C4211yescharacteristic
211C23×C11C2×C22⋊C411yescharacteristic
212C23×C11#11711yescharacteristic
213C23×C11C4×D411yescharacteristic
214C23×C11C4×D411yescharacteristic
215C23×C11C4×D411yescharacteristic
216C23×C11C4×D411yescharacteristic
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—48no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—48no—
228C22×D11—84no—
229C22×D11—84no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—82no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11—82no—
237C2×C4×C11—82no—
238C2×C4×C11C2×C22⋊C411yescharacteristic
239C2×C4×C11C2×C22⋊C411yescharacteristic
240C2×C4×C11#11711yescharacteristic
241C2×C4×C11#11711yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12311yescharacteristic
258C2×C4×C11#12311yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12411yescharacteristic
261C2×C4×C11#12411yescharacteristic
262C2×C4×C11#12411yescharacteristic
263C2×C4×C11#12611yescharacteristic
264C2×C4×C11#12611yescharacteristic
265C2×C4×C11#12711yescharacteristic
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—44no—
272C2×Dic11—44no—
273C2×Dic11#10014yescomplemented
274D44—42no—
275D44—42no—
276D44—42no—
277D44—42no—
278D44—42no—
279D44—42no—
280D44—42no—
281D44—42no—
282C8×C11—24no—
283C8×C11—42no—
284C11⋊C8—24no—
285C11⋊C8—42no—
286C23×D4—111no—
287C22×M16—111no—
288C22×M16—111no—
289C22×M16C2×D1111yescharacteristic
290C22×M16C2×D1111yescharacteristic
291C22×C4⋊C4C2×D1111yescharacteristic
292C22×C22⋊C4—114no—
293C22×C42—111no—
294C2×#100—114no—
295C2×#100—114no—
296C2×#100—222no—
297C2×#100—222no—
298C2×#100—222no—
299C2×#100—222no—
300C4×M16—222no—
301C4×M16—222no—
302C2×#97—221no—
303C2×C4×C8—221no—
304#390—222no—
305#390—221no—
306#390—221no—
307#343—22no—
308#343—222no—
309#336—222no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11C4×C22⋊C411yescharacteristic
319C22×C11C4×C22⋊C411yescharacteristic
320C22×C11C4×C22⋊C411yescharacteristic
321C22×C11#38611yescharacteristic
322C22×C11#38811yescharacteristic
323C22×C11#38811yescharacteristic
324C22×C11#39011yescharacteristic
325C22×C11C2×#10012yes—
326C22×C11#41312yes—
327C2×D11—44no—
328C2×D11—48no—
329C2×D11—84no—
330C2×D11—84no—
331C2×D11—84no—
332C2×D11—82no—
333C2×D11—82no—
334C2×D11—84no—
335C2×D11—84no—
336C4×C11—82no—
337C4×C11#38611yescharacteristic
338C4×C11#38611yescharacteristic
339C4×C11#38811yescharacteristic
340C4×C11#38811yescharacteristic
341C4×C11#38811yescharacteristic
342C4×C11#38811yescharacteristic
343C4×C11#39011yescharacteristic
344C4×C11#39011yescharacteristic
345Dic11—24no—
346Dic11—42no—
347C25—112no—
348C22×D4—112no—
349C22×D4—112no—
350C22×D4—221no—
351C22×D4—221no—
352C22×D4—221no—
353C22×D4—221no—
354C22×D4—221no—
355C22×D4—221no—
356C22×D4—221no—
357C22×D4—221no—
358C22×D4—221no—
359C22×D4—221no—
360C22×D4—221no—
361C22×D4—221no—
362C23×C4—112no—
363C23×C4C4×D1112yes—
364C23×C4C22×D1111yescharacteristic
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—112no—
374C2×M16—112no—
375C2×M16—112no—
376C2×M16—112no—
377C2×M16—221no—
378C2×M16—221no—
379C2×M16—221no—
380C2×M16—221no—
381C2×M16—221no—
382C2×M16—221no—
383C2×M16—221no—
384C2×M16—221no—
385C2×M16C4×D1112yes—
386C2×M16C4×D1112yes—
387C2×M16D4412yes—
388C2×M16C22⋊D1112yes—
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—221no—
392C22×C8—221no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—448no—
402C2×C42—112no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42—221no—
409#100—228no—
410#100—228no—
411#97—224no—
412C4×C8—224no—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—21no—
416C2×C11—21no—
417C2×C11#143711yescharacteristic
418C2×C11C4×#10012yes—
419C2×C11#190012yes—
420C2×C11#196511yescharacteristic
421C2×C11#196711yescharacteristic
422D11—84no—
423C24—114no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—222no—
430C24—444no—
431C24—444no—
432C24C2×C4×D1111yescharacteristic
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—222no—
439C2×D4—222no—
440C2×D4—222no—
441C2×D4—222no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4—441no—
446C2×D4—441no—
447C2×D4—441no—
448C2×D4—441no—
449C2×D4—441no—
450C2×D4—441no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4—441no—
456C2×D4—441no—
457C2×D4—441no—
458C2×D4—441no—
459C2×D4—441no—
460C2×D4—441no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—44no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—224no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—442no—
471C22×C4C2×C4×D1111yescharacteristic
472C22×C4C2×C4×D1111yescharacteristic
473C22×C4C2×D4411yescharacteristic
474C22×C4#433911yescharacteristic
475C22×C4#433911yescharacteristic
476C22×C4D4×D1111yescharacteristic
477C22×C4D4×D1111yescharacteristic
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4#434111yescharacteristic
481C22×C4#434111yescharacteristic
482C22×C4#434311yescharacteristic
483C22×C4#434311yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—41no—
491M16—41no—
492M16—114no—
493M16—222no—
494M16—222no—
495M16—222no—
496M16—222no—
497M16—222no—
498M16—441no—
499M16—441no—
500M16(C2×D11)⋊C414yescomplemented
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—441no—
512C2×C8—441no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C22⋊C4—448no—
518C22⋊C4—448no—
519C42—221no—
520C42—221no—
521C42—222no—
522C42—221no—
523C42—221no—
524C42—222no—
525C11#1096211yescharacteristic, complemented, Sylow
526C23—22no—
527C23—22no—
528C23—224no—
529C23—224no—
530C23—224no—
531C23—448no—
532C23—448no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23—444no—
538C23—444no—
539C23—884no—
540C23—884no—
541C23—882no—
542C23—882no—
543C23—882no—
544C23—882no—
545C23C42×D1111yescharacteristic
546C23C4×D4411yescharacteristic
547C23C22⋊C4×D1111yescharacteristic
548C23(C22⋊D11)⋊C411yescharacteristic
549C23#6694511yescharacteristic
550C23#6694611yescharacteristic
551C23C4×C22⋊D1111yescharacteristic
552D4—442no—
553D4—442no—
554D4—442no—
555D4—442no—
556D4—442no—
557D4—442no—
558D4—442no—
559D4—442no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—114no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—444no—
571C2×C4—444no—
572C2×C4#6692511yescharacteristic
573C2×C4C4×D4411yescharacteristic
574C2×C4C22⋊C4×D1111yescharacteristic
575C2×C4(C22⋊D11)⋊C411yescharacteristic
576C2×C4(C22⋊D11)⋊C411yescharacteristic
577C2×C4(C22⋊D11)⋊C411yescharacteristic
578C2×C4#6693511yescharacteristic
579C2×C4#6693711yescharacteristic
580C2×C4#6693711yescharacteristic
581C2×C4#6693811yescharacteristic
582C2×C4#6693811yescharacteristic
583C2×C4#6693911yescharacteristic
584C2×C4#6694511yescharacteristic
585C2×C4#6694611yescharacteristic
586C2×C4#6694611yescharacteristic
587C2×C4#6694611yescharacteristic
588C2×C4#6694711yescharacteristic
589C2×C4#6694711yescharacteristic
590C2×C4#6694811yescharacteristic
591C2×C4#6694811yescharacteristic
592C2×C4#6695111yescharacteristic
593C2×C4#6695111yescharacteristic
594C2×C4C2×(C2×D11)⋊C411yescharacteristic
595C2×C4C4×C22⋊D1111yescharacteristic
596C2×C4#6699211yescharacteristic
597C2×C4#6699211yescharacteristic
598C2×C4#6699311yescharacteristic
599C2×C4#6700011yescharacteristic
600C8—24no—
601C8—42no—
602C8—224no—
603C8—442no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—444no—
613C22—448no—
614C22—884no—
615C22—884no—
616C22—884no—
617C22—884no—
618C22—884no—
619C22—882no—
620C22—882no—
621C22#1062227811yescharacteristic
622C22#1062227911yescharacteristic
623C22#1062227911yescharacteristic
624C22#1062228311yescharacteristic
625C22D11×#10012yes—
626C22#1062236412yes—
627C22C4×(C2×D11)⋊C411yescharacteristic
628C22#1062257011yescharacteristic
629C22#1062260311yescharacteristic
630C4—82no—
631C4—224no—
632C4—442no—
633C4#1062227811yescharacteristic
634C4#1062228211yescharacteristic
635C4#1062228211yescharacteristic
636C4#1062228311yescharacteristic
637C4#1062257011yescharacteristic
638C4#1062257111yescharacteristic
639C4#1062260111yescharacteristic
640C4#1062260311yescharacteristic
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—884no—
646C2#1306685211yescharacteristic
647C2#1306840712yes—
648C2#1306907812yes—
649C2#1306945411yescharacteristic
650C2#1306946411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#343C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D44C22
cosocleC23×C4×C11C23
hypercenterC2×#343D11
hypocenterC11#10962
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
3. C2×M16×Dic11C2semidirect
5. C2×#10622168C2semidirect
6. #13068309C2semidirect
7. C2×C11×#343C2semidirect
20. C2×#66887C4semidirect
21. C2×#66887C4semidirect
168. C11×M16C22⋊C4semidirect
194. #4318C22⋊C4semidirect
206. C2×#343D11semidirect
273. C2×Dic11#100semidirect
500. M16(C2×D11)⋊C4semidirect
525. C11#10962semidirect

Maximal subgroups

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

subgroupindex
C22×#668872
C2×M16×Dic112
C2×#106226012
C2×#106221682
#130683092
C2×C11×#3432
#1096211