Finite Group Databasebeta

← #14660608

Subgroups — #14660608

Order 2816.

1242 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4326C211yesmaximal, characteristic
2C2×#10622733C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic
4C22×#66888C211yesmaximal, characteristic
5C2×#10622196C211yesmaximal, characteristic
6#13068314C211yesmaximal, characteristic
7C22×C11×#101C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×#4326—22no—
13C22×#4326—22no—
14C22×#4326—22no—
15C22×#4326—22no—
16C22×#4326—22no—
17C22×#4326—22no—
18C22×#4326C414yescomplemented
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×C11×#101—22no—
23C2×C11×#101—22no—
24C2×C11×#101—22no—
25#10622838—22no—
26#10622838—22no—
27C2×#66899—22no—
28C2×#66888—22no—
29C2×#66888—22no—
30C2×#66888—22no—
31#10622733—22no—
32#10622733—22no—
33C2×#66880—22no—
34#10622196—22no—
35#10622188—22no—
36C22×Q8×C11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11C2×C412yes—
48C22×Q8×C11D412yes—
49C22×Q8×C11D412yes—
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—21no—
53C22×Dic22—21no—
54C22×Dic22—21no—
55C22×Dic22—21no—
56C22×Dic22—21no—
57C22×Dic22—21no—
58C22×Dic22—21no—
59C22×Dic22—21no—
60C22×Dic22—21no—
61C22×Dic22—21no—
62C22×Dic22—21no—
63C22×Dic22—21no—
64C22×Dic22C2×C412yes—
65C22×Dic22D412yes—
66C22×Dic22D412yes—
67C2×C11×M16—21no—
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16—21no—
72C2×C11×M16—21no—
73C2×C11×M16—21no—
74C2×C11×M16—21no—
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C2×C11×M16D412yes—
78C2×C11×M16D412yes—
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C2×C22⋊Dic11—21no—
82C2×#4326—28no—
83C2×#4326—28no—
84C2×#4326—28no—
85C2×#4326—28no—
86C2×#4326—28no—
87C2×#4326—28no—
88C2×#4326—28no—
89#66979—21no—
90#66979—21no—
91#66979—21no—
92#66979—21no—
93C2×C4⋊Dic11D412yes—
94C2×C4×Dic11—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318D412yes—
101C22×C11⋊C8—21no—
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104C22×C11⋊C8—21no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8C2×C412yes—
107C22×C11⋊C8D412yes—
108C22×C11⋊C8D412yes—
109C11×#101—28no—
110#66899—28no—
111#66888—28no—
112#66880—28no—
113#11029—111nomaximal, Sylow
114C24×C11#4111yescharacteristic
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—41no—
131C2×Q8×C11—41no—
132C2×Q8×C11—41no—
133C2×Q8×C11—41no—
134C2×Q8×C11—41no—
135C2×Q8×C11—41no—
136C2×Q8×C11—41no—
137C2×Q8×C11—41no—
138C2×Q8×C11—41no—
139C2×Q8×C11—41no—
140C2×Q8×C11—41no—
141C2×Q8×C11—41no—
142C2×Q8×C11C22⋊C414yes—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—41no—
169C22×Dic11—41no—
170C22×Dic11—41no—
171C22×Dic11—41no—
172C2×Dic22—22no—
173C2×Dic22—22no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22—22no—
181C2×Dic22—22no—
182C2×Dic22—22no—
183C2×Dic22—22no—
184C2×Dic22—22no—
185C2×Dic22—22no—
186C2×Dic22—22no—
187C2×Dic22—41no—
188C2×Dic22—41no—
189C2×Dic22—41no—
190C2×Dic22—41no—
191C2×Dic22—41no—
192C2×Dic22—41no—
193C2×Dic22—41no—
194C2×Dic22—41no—
195C2×Dic22—41no—
196C2×Dic22—41no—
197C2×Dic22—41no—
198C2×Dic22—41no—
199C2×Dic22C22⋊C414yes—
200C11×M16—22no—
201C11×M16—22no—
202C11×M16—22no—
203C11×M16—22no—
204C11×M16—41no—
205C11×M16—41no—
206C11×M16—41no—
207C11×M16—41no—
208C2×C8×C11—22no—
209C2×C8×C11—22no—
210C2×C8×C11—41no—
211C2×C8×C11—41no—
212C2×C8×C11—41no—
213C2×C8×C11—41no—
214C22⋊Dic11—41no—
215C22⋊Dic11—41no—
216#4326—232no—
217C4⋊Dic11—22no—
218C4⋊Dic11—22no—
219C4×Dic11—41no—
220C4×Dic11—41no—
221#4318—22no—
222#4318—22no—
223#4318—41no—
224#4318—41no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—22no—
227C2×C11⋊C8—22no—
228C2×C11⋊C8—22no—
229C2×C11⋊C8—22no—
230C2×C11⋊C8—22no—
231C2×C11⋊C8—22no—
232C2×C11⋊C8—41no—
233C2×C11⋊C8—41no—
234C2×C11⋊C8C22⋊C414yes—
235C23×Q16—111no—
236C2×#419—111no—
237C2×#419—111no—
238C22×#101—111no—
239C22×#101D1111yescharacteristic
240C2×#341—111no—
241#1729—111no—
242C23×C11—24no—
243C23×C11C4×D411yescharacteristic
244C23×C11#12111yescharacteristic
245C23×C11#12111yescharacteristic
246C23×C11#12111yescharacteristic
247C23×C11#12311yescharacteristic
248C23×C11#12311yescharacteristic
249C23×C11#12411yescharacteristic
250Q8×C11—24no—
251Q8×C11—24no—
252Q8×C11—42no—
253Q8×C11—42no—
254Q8×C11—42no—
255Q8×C11—42no—
256Q8×C11—42no—
257Q8×C11—42no—
258C2×C4×C11—24no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C4×D411yescharacteristic
269C2×C4×C11C4×D411yescharacteristic
270C2×C4×C11C4×D411yescharacteristic
271C2×C4×C11#12011yescharacteristic
272C2×C4×C11#12011yescharacteristic
273C2×C4×C11#12011yescharacteristic
274C2×C4×C11#12011yescharacteristic
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11#12011yescharacteristic
277C2×C4×C11#12011yescharacteristic
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11#12111yescharacteristic
280C2×C4×C11#12111yescharacteristic
281C2×C4×C11#12111yescharacteristic
282C2×C4×C11#12111yescharacteristic
283C2×C4×C11#12111yescharacteristic
284C2×C4×C11#12111yescharacteristic
285C2×C4×C11#12111yescharacteristic
286C2×C4×C11#12111yescharacteristic
287C2×C4×C11#12111yescharacteristic
288C2×C4×C11#12311yescharacteristic
289C2×C4×C11#12311yescharacteristic
290C2×C4×C11#12411yescharacteristic
291C2×C4×C11#12711yescharacteristic
292C2×C4×C11#12711yescharacteristic
293C2×Dic11—24no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—44no—
302Dic22—24no—
303Dic22—24no—
304Dic22—42no—
305Dic22—42no—
306Dic22—42no—
307Dic22—42no—
308Dic22—42no—
309Dic22—42no—
310C8×C11—42no—
311C8×C11—42no—
312C11⋊C8—24no—
313C11⋊C8—42no—
314C23×Q8—111no—
315C23×Q8C2×D1111yescharacteristic
316C22×Q16—114no—
317C22×Q16—222no—
318C22×Q16—222no—
319C22×Q16—222no—
320C22×Q16—222no—
321C22×Q16—222no—
322C22×Q16—222no—
323C22×M16—111no—
324C22×M16C2×D1111yescharacteristic
325C22×M16C2×D1111yescharacteristic
326C23×C8—111no—
327C2×#117—111no—
328#419—222no—
329#419—222no—
330#419—222no—
331#419—222no—
332C2×#103—222no—
333C2×#103—222no—
334C2×#101—22no—
335C2×#101—22no—
336C2×#101—22no—
337C2×#101—222no—
338C2×#101—222no—
339C2×#101—222no—
340#341—222no—
341#336—222no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11#38611yescharacteristic
349C22×C11#38611yescharacteristic
350C22×C11#39011yescharacteristic
351C22×C11#39211yescharacteristic
352C22×C11#39411yescharacteristic
353C22×C11#39411yescharacteristic
354C22×C11#39411yescharacteristic
355C22×C11#47314yes—
356C4×C11—44no—
357C4×C11#37911yescharacteristic
358C4×C11#38611yescharacteristic
359C4×C11#38611yescharacteristic
360C4×C11#39011yescharacteristic
361C4×C11#39211yescharacteristic
362C4×C11#39211yescharacteristic
363C4×C11#39211yescharacteristic
364C4×C11#39411yescharacteristic
365Dic11—44no—
366Dic11—82no—
367C22×Q8—21no—
368C22×Q8—21no—
369C22×Q8—21no—
370C22×Q8—21no—
371C22×Q8—21no—
372C22×Q8—21no—
373C22×Q8—21no—
374C22×Q8—21no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—21no—
378C22×Q8—112no—
379C22×Q8—112no—
380C22×Q8—112no—
381C22×Q8—221no—
382C22×Q8—221no—
383C22×Q8—221no—
384C22×Q8—221no—
385C22×Q8—221no—
386C22×Q8—221no—
387C22×Q8—221no—
388C22×Q8—221no—
389C22×Q8—221no—
390C22×Q8—221no—
391C22×Q8—221no—
392C22×Q8C4×D1112yes—
393C22×Q8D4412yes—
394C22×Q8C22⋊D1112yes—
395C23×C4—21no—
396C23×C4—221no—
397C23×C4C22×D1111yescharacteristic
398C2×Q16—228no—
399C2×Q16—228no—
400C2×Q16—228no—
401C2×Q16—228no—
402C2×Q16—228no—
403C2×Q16—228no—
404C2×Q16—228no—
405C2×M16—21no—
406C2×M16—21no—
407C2×M16—21no—
408C2×M16—21no—
409C2×M16—21no—
410C2×M16—21no—
411C2×M16—21no—
412C2×M16—21no—
413C2×M16—21no—
414C2×M16—21no—
415C2×M16—112no—
416C2×M16—221no—
417C2×M16—221no—
418C2×M16—221no—
419C2×M16—221no—
420C2×M16—221no—
421C2×M16C22⋊D1112yes—
422C2×M16C22⋊D1112yes—
423C22×C8—21no—
424C22×C8—21no—
425C22×C8—112no—
426C22×C8—112no—
427C22×C8—112no—
428C22×C8—221no—
429C22×C8—221no—
430C22×C8—221no—
431C22×C8—221no—
432C22×C8—221no—
433#117—221no—
434#117—221no—
435#117—221no—
436#117—221no—
437C2×C4⋊C4—112no—
438C2×C22⋊C4—221no—
439C2×C42—221no—
440#103—228no—
441#103—228no—
442#101—28no—
443#101—228no—
444C2×C11—21no—
445C2×C11—21no—
446C2×C11—21no—
447C2×C11—21no—
448C2×C11#143811yescharacteristic
449C2×C11#197912yes—
450C2×C11#202012yes—
451C2×C11#204712yes—
452C24#433911yescharacteristic
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—41no—
469C2×Q8—41no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×Q8—41no—
473C2×Q8—41no—
474C2×Q8—41no—
475C2×Q8—41no—
476C2×Q8—41no—
477C2×Q8—41no—
478C2×Q8—41no—
479C2×Q8—41no—
480C2×Q8—114no—
481C2×Q8—222no—
482C2×Q8—222no—
483C2×Q8—222no—
484C2×Q8—222no—
485C2×Q8—222no—
486C2×Q8—222no—
487C2×Q8—222no—
488C2×Q8—222no—
489C2×Q8—222no—
490C2×Q8—222no—
491C2×Q8—222no—
492C2×Q8—222no—
493C2×Q8—222no—
494C2×Q8—222no—
495C2×Q8—222no—
496C2×Q8—441no—
497C2×Q8—441no—
498C2×Q8—441no—
499C2×Q8—441no—
500C2×Q8—441no—
501C2×Q8—441no—
502C2×Q8—441no—
503C2×Q8—441no—
504C2×Q8—441no—
505C2×Q8—441no—
506C2×Q8—441no—
507C2×Q8—441no—
508C2×Q8(C2×D11)⋊C414yes—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—441no—
521C22×C4—441no—
522C22×C4—441no—
523C22×C4—441no—
524C22×C4C2×C4×D1111yescharacteristic
525C22×C4C2×D4411yescharacteristic
526C22×C4#433911yescharacteristic
527C22×C4D4×D1111yescharacteristic
528C22×C4D4×D1111yescharacteristic
529C22×C4D4×D1111yescharacteristic
530C22×C4D4×D1111yescharacteristic
531C22×C4D4×D1111yescharacteristic
532C22×C4D4×D1111yescharacteristic
533C22×C4#434111yescharacteristic
534C22×C4#434111yescharacteristic
535C22×C4C2×C22⋊D1111yescharacteristic
536C22×C4C2×C22⋊D1111yescharacteristic
537C22×C4C2×C22⋊D1111yescharacteristic
538Q16—2232no—
539M16—22no—
540M16—22no—
541M16—22no—
542M16—22no—
543M16—41no—
544M16—41no—
545M16—41no—
546M16—41no—
547M16—222no—
548M16—222no—
549M16—441no—
550M16—441no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—114no—
558C2×C8—222no—
559C2×C8—222no—
560C2×C8—222no—
561C2×C8—222no—
562C2×C8—222no—
563C2×C8—222no—
564C2×C8—222no—
565C2×C8—441no—
566C2×C8—441no—
567C4⋊C4—222no—
568C4⋊C4—222no—
569C22⋊C4—441no—
570C22⋊C4—441no—
571C42—441no—
572C42—441no—
573C11#1102911yescharacteristic, complemented, Sylow
574C23—24no—
575C23#6693611yescharacteristic
576C23#6693711yescharacteristic
577C23#6693711yescharacteristic
578C23#6693811yescharacteristic
579C23C4×C22⋊D1111yescharacteristic
580C23#6698211yescharacteristic
581C23#6698311yescharacteristic
582Q8—24no—
583Q8—24no—
584Q8—42no—
585Q8—42no—
586Q8—42no—
587Q8—42no—
588Q8—42no—
589Q8—42no—
590Q8—224no—
591Q8—224no—
592Q8—442no—
593Q8—442no—
594Q8—442no—
595Q8—442no—
596Q8—442no—
597Q8—442no—
598C2×C4—24no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—224no—
606C2×C4—442no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—444no—
614C2×C4C22⋊C4×D1111yescharacteristic
615C2×C4C22⋊C4×D1111yescharacteristic
616C2×C4(C22⋊D11)⋊C411yescharacteristic
617C2×C4(C22⋊D11)⋊C411yescharacteristic
618C2×C4#6693511yescharacteristic
619C2×C4#6693511yescharacteristic
620C2×C4#6693511yescharacteristic
621C2×C4#6693611yescharacteristic
622C2×C4#6693711yescharacteristic
623C2×C4#6693711yescharacteristic
624C2×C4#6693811yescharacteristic
625C2×C4#6693911yescharacteristic
626C2×C4C2×(C2×D11)⋊C411yescharacteristic
627C2×C4C4×C22⋊D1111yescharacteristic
628C2×C4#6698311yescharacteristic
629C2×C4#6699011yescharacteristic
630C2×C4#6699011yescharacteristic
631C2×C4#6699011yescharacteristic
632C2×C4#6699011yescharacteristic
633C2×C4#6699111yescharacteristic
634C2×C4#6699111yescharacteristic
635C2×C4#6699211yescharacteristic
636C2×C4#6699211yescharacteristic
637C2×C4#6699211yescharacteristic
638C2×C4#6699211yescharacteristic
639C2×C4#6699311yescharacteristic
640C2×C4#6699311yescharacteristic
641C2×C4#6700611yescharacteristic
642C8—42no—
643C8—42no—
644C8—224no—
645C8—442no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22#1062236814yes—
653C22#1062256911yescharacteristic
654C22#1062257011yescharacteristic
655C22#1062257211yescharacteristic
656C22#1062257211yescharacteristic
657C22#1062257311yescharacteristic
658C22#1062257411yescharacteristic
659C22#1062282611yescharacteristic
660C4—44no—
661C4—444no—
662C4—882no—
663C4#1062256811yescharacteristic
664C4#1062256911yescharacteristic
665C4#1062257011yescharacteristic
666C4#1062257111yescharacteristic
667C4#1062257311yescharacteristic
668C4#1062257411yescharacteristic
669C4#1062283611yescharacteristic
670C4#1062283611yescharacteristic
671C2—21no—
672C2—21no—
673C2—21no—
674C2—21no—
675C2#1306685511yescharacteristic
676C2#1306952812yes—
677C2#1306973612yes—
678C2#1306988212yes—
subgroupG/H
centerC23#66937
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#101C2
socleC23×C11#121
prime radicalC24×C11#41
cosocleC23×C4×C11C23
hypercenterC22×#101D11
hypocenterC11#11029
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
18. C22×#4326C4semidirect
573. C11#11029semidirect

Maximal subgroups

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

subgroupindex
C23×#43262
C2×#106227332
C2×#106228382
C22×#668882
C2×#106221962
#130683142
C22×C11×#1012
#1102911