Finite Group Databasebeta

← #14660323

Subgroups — #14660323

Order 2816.

1334 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic
2C2×#10622838C211yesmaximal, characteristic
3C22×#66888C211yesmaximal, characteristic
4#13071200C211yesmaximal, characteristic
5C2×#10622193C211yesmaximal, characteristic
6C2×#10622170C211yesmaximal, characteristic
7C2×C11×#419C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66997—22no—
13C2×#66997—22no—
14C2×#66997—22no—
15C2×#66997—22no—
16C2×#66997—22no—
17C2×#66997C414yescomplemented
18C2×#66979C2211yescharacteristic
19C22×Dic11⋊C4—22no—
20C22×C4×Dic11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C11×#419—22no—
23C11×#419—22no—
24C2×C11×#103—22no—
25#10622838—22no—
26#10622838—22no—
27C2×#66899—22no—
28C2×#66888—22no—
29C2×#66888—22no—
30C2×#66888—22no—
31#10622587—22no—
32#10622556—22no—
33#10622542—22no—
34#10622193—22no—
35#10622170—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—
53C23×Dic11D412yes—
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×Dic22—21no—
65C22×Dic22—21no—
66C22×Dic22C2×C412yes—
67C22×Dic22D412yes—
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16—21no—
72C2×C11×M16—21no—
73C2×C11×M16D412yes—
74C22×C8×C11—21no—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C2×C11×C4⋊C4D412yes—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83#66997—28no—
84#66997—28no—
85#66997—28no—
86#66997—28no—
87#66979—21no—
88#66979—21no—
89#66979—21no—
90#66979—21no—
91C2×C4⋊Dic11D412yes—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—28no—
94C2×Dic11⋊C4—28no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2×C412yes—
100C2×C4×Dic11D412yes—
101C2×C4×Dic11D412yes—
102C2×#4318—21no—
103C2×#4318—21no—
104C2×#4318—21no—
105C2×#4318—21no—
106C2×#4318—21no—
107C2×#4318D412yes—
108C22×C11⋊C8—21no—
109C11×#103—28no—
110#66899—28no—
111C11⋊#95—28no—
112#66888—28no—
113#10978—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
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—22no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11C22×C411yescharacteristic
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×C4×C11#4111yescharacteristic
165C22×Dic11—28no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11C22⋊C414yes—
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—22no—
188C2×Dic22—22no—
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×Dic22—41no—
200C2×Dic22—41no—
201C2×Dic22—41no—
202C2×Dic22—41no—
203C2×Dic22—41no—
204C2×Dic22—41no—
205C11×M16—22no—
206C11×M16—22no—
207C11×M16—41no—
208C11×M16—41no—
209C2×C8×C11—22no—
210C2×C8×C11—41no—
211C2×C8×C11—41no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—22no—
214C11×C22⋊C4—41no—
215C11×C22⋊C4—41no—
216C42×C11—41no—
217C42×C11—41no—
218C22⋊Dic11—41no—
219C22⋊Dic11—41no—
220C4⋊Dic11—22no—
221C4⋊Dic11—22no—
222Dic11⋊C4—232no—
223C4×Dic11—22no—
224C4×Dic11—22no—
225C4×Dic11—22no—
226C4×Dic11—41no—
227C4×Dic11—41no—
228C4×Dic11C22⋊C414yes—
229#4318—22no—
230#4318—22no—
231#4318—41no—
232#4318—41no—
233C2×C11⋊C8—22no—
234C2×C11⋊C8—41no—
235C2×C11⋊C8—41no—
236C22×C4⋊Q8—111no—
237C2×#419—111no—
238C2×#419D1111yescharacteristic
239C22×#101—111no—
240#2310—111no—
241C2×#339—111no—
242C2×#339—111no—
243C23×C11—24no—
244C23×C11C2×C22⋊C411yescharacteristic
245C23×C11#12011yescharacteristic
246C23×C11#12011yescharacteristic
247C23×C11#12011yescharacteristic
248C23×C11#12111yescharacteristic
249C23×C11#12111yescharacteristic
250C23×C11#12311yescharacteristic
251Q8×C11—24no—
252Q8×C11—24no—
253Q8×C11—42no—
254Q8×C11—42no—
255Q8×C11—42no—
256Q8×C11—42no—
257Q8×C11—42no—
258Q8×C11—42no—
259C2×C4×C11—24no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—44no—
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C4×D411yescharacteristic
271C2×C4×C11C4×D411yescharacteristic
272C2×C4×C11C4×D411yescharacteristic
273C2×C4×C11C4×D411yescharacteristic
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#12111yescharacteristic
289C2×C4×C11#12311yescharacteristic
290C2×C4×C11#12311yescharacteristic
291C2×C4×C11#12311yescharacteristic
292C2×C4×C11#12411yescharacteristic
293C2×C4×C11#12411yescharacteristic
294C2×C4×C11#12711yescharacteristic
295C2×C4×C11#12711yescharacteristic
296C2×Dic11—28no—
297C2×Dic11—28no—
298C2×Dic11—28no—
299C2×Dic11—24no—
300C2×Dic11—24no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—44no—
309Dic22—42no—
310Dic22—42no—
311Dic22—42no—
312Dic22—42no—
313Dic22—42no—
314Dic22—42no—
315Dic22—42no—
316Dic22—42no—
317C8×C11—42no—
318C11⋊C8—42no—
319C23×Q8—111no—
320C23×Q8C2×D1111yescharacteristic
321C22×M16—111no—
322C22×M16C2×D1111yescharacteristic
323C2×C4⋊Q8—114no—
324C2×C4⋊Q8—222no—
325C2×C4⋊Q8—222no—
326C2×C4⋊Q8—222no—
327C2×C4⋊Q8—222no—
328C2×C4⋊Q8—222no—
329C2×#117—111no—
330C2×#117C2×D1111yescharacteristic
331C22×C4⋊C4—222no—
332C22×C42—111no—
333#419—22no—
334#419—22no—
335#419—222no—
336#419—222no—
337C2×#103—22no—
338C2×#103—222no—
339C2×#101—222no—
340C2×#101—222no—
341C2×#101—222no—
342#391—222no—
343#391—222no—
344#381—222no—
345#339—222no—
346#339—222no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11#37911yescharacteristic
354C22×C11#38611yescharacteristic
355C22×C11#38611yescharacteristic
356C22×C11#39211yescharacteristic
357C22×C11#39211yescharacteristic
358C22×C11#39411yescharacteristic
359C22×C11#39411yescharacteristic
360C22×C11#45614yes—
361C4×C11—44no—
362C4×C11—82no—
363C4×C11#38611yescharacteristic
364C4×C11#38611yescharacteristic
365C4×C11#39011yescharacteristic
366C4×C11#39011yescharacteristic
367C4×C11#39211yescharacteristic
368C4×C11#39211yescharacteristic
369C4×C11#39411yescharacteristic
370C4×C11#39411yescharacteristic
371Dic11—28no—
372Dic11—44no—
373Dic11—82no—
374C22×Q8—21no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—21no—
378C22×Q8—21no—
379C22×Q8—21no—
380C22×Q8—21no—
381C22×Q8—21no—
382C22×Q8—21no—
383C22×Q8—21no—
384C22×Q8—21no—
385C22×Q8—112no—
386C22×Q8—112no—
387C22×Q8—221no—
388C22×Q8—221no—
389C22×Q8—221no—
390C22×Q8—221no—
391C22×Q8—221no—
392C22×Q8—221no—
393C22×Q8—221no—
394C22×Q8—221no—
395C22×Q8—221no—
396C22×Q8—221no—
397C22×Q8—221no—
398C22×Q8—221no—
399C22×Q8C4×D1112yes—
400C22×Q8D4412yes—
401C22×Q8C22⋊D1112yes—
402C23×C4—21no—
403C23×C4—112no—
404C23×C4—221no—
405C23×C4C22×D1111yescharacteristic
406C2×M16—21no—
407C2×M16—21no—
408C2×M16—21no—
409C2×M16—21no—
410C2×M16—21no—
411C2×M16—112no—
412C2×M16—221no—
413C2×M16—221no—
414C2×M16—221no—
415C2×M16—221no—
416C2×M16—221no—
417C2×M16C22⋊D1112yes—
418C22×C8—21no—
419C22×C8—221no—
420C4⋊Q8—228no—
421C4⋊Q8—228no—
422C4⋊Q8—228no—
423C4⋊Q8—228no—
424#117—21no—
425#117—21no—
426#117—21no—
427#117—21no—
428#117—221no—
429#117—221no—
430#117—221no—
431#117—221no—
432C2×C4⋊C4—112no—
433C2×C4⋊C4—228no—
434C2×C4⋊C4—228no—
435C2×C4⋊C4—228no—
436C2×C4⋊C4C22⋊D1112yes—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—221no—
439C2×C42—21no—
440C2×C42—112no—
441C2×C42—112no—
442C2×C42—112no—
443C2×C42—221no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42—221no—
447#103—28no—
448#103—228no—
449#101—228no—
450#95—228no—
451C2×C11—21no—
452C2×C11—21no—
453C2×C11—21no—
454C2×C11—21no—
455C2×C11#143811yescharacteristic
456C2×C11#188612yes—
457C2×C11#200512yes—
458C2×C11#200512yes—
459C24D4×D1111yescharacteristic
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—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—41no—
476C2×Q8—41no—
477C2×Q8—41no—
478C2×Q8—41no—
479C2×Q8—41no—
480C2×Q8—41no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8—41no—
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—222no—
497C2×Q8—222no—
498C2×Q8—222no—
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—441no—
509C2×Q8—441no—
510C2×Q8—441no—
511C2×Q8—441no—
512C2×Q8—441no—
513C2×Q8—441no—
514C2×Q8—441no—
515C2×Q8(C2×D11)⋊C414yes—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—114no—
525C22×C4—228no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4—222no—
532C22×C4—222no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4C2×C4×D1111yescharacteristic
537C22×C4C2×D4411yescharacteristic
538C22×C4#433911yescharacteristic
539C22×C4#433911yescharacteristic
540C22×C4D4×D1111yescharacteristic
541C22×C4D4×D1111yescharacteristic
542C22×C4D4×D1111yescharacteristic
543C22×C4D4×D1111yescharacteristic
544C22×C4D4×D1111yescharacteristic
545C22×C4#434111yescharacteristic
546C22×C4#434111yescharacteristic
547C22×C4C2×C22⋊D1111yescharacteristic
548C22×C4C2×C22⋊D1111yescharacteristic
549C22×C4C2×C22⋊D1111yescharacteristic
550M16—22no—
551M16—22no—
552M16—41no—
553M16—41no—
554M16—222no—
555M16—222no—
556M16—441no—
557M16—441no—
558C2×C8—22no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—222no—
562C2×C8—441no—
563C2×C8—441no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—2232no—
567C4⋊C4—222no—
568C4⋊C4—222no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—441no—
572C22⋊C4—441no—
573C42—41no—
574C42—41no—
575C42—114no—
576C42—222no—
577C42—222no—
578C42—222no—
579C42—441no—
580C42—441no—
581C11#1097811yescharacteristic, complemented, Sylow
582C23—24no—
583C23C22⋊C4×D1111yescharacteristic
584C23#6693511yescharacteristic
585C23#6693611yescharacteristic
586C23#6693711yescharacteristic
587C23#6699011yescharacteristic
588C23#6699011yescharacteristic
589C23#6699111yescharacteristic
590Q8—24no—
591Q8—24no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595Q8—42no—
596Q8—42no—
597Q8—42no—
598Q8—442no—
599Q8—442no—
600Q8—442no—
601Q8—442no—
602Q8—442no—
603Q8—442no—
604Q8—442no—
605Q8—442no—
606C2×C4—24no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—44no—
614C2×C4—42no—
615C2×C4—228no—
616C2×C4—228no—
617C2×C4—228no—
618C2×C4—224no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—444no—
627C2×C4—442no—
628C2×C4C22⋊C4×D1111yescharacteristic
629C2×C4(C22⋊D11)⋊C411yescharacteristic
630C2×C4(C22⋊D11)⋊C411yescharacteristic
631C2×C4#6693511yescharacteristic
632C2×C4#6693511yescharacteristic
633C2×C4#6693611yescharacteristic
634C2×C4#6693711yescharacteristic
635C2×C4#6693711yescharacteristic
636C2×C4#6693711yescharacteristic
637C2×C4#6693811yescharacteristic
638C2×C4#6693811yescharacteristic
639C2×C4#6693911yescharacteristic
640C2×C4C2×(C2×D11)⋊C411yescharacteristic
641C2×C4C4×C22⋊D1111yescharacteristic
642C2×C4C4×C22⋊D1111yescharacteristic
643C2×C4#6698211yescharacteristic
644C2×C4#6698311yescharacteristic
645C2×C4#6698311yescharacteristic
646C2×C4#6699011yescharacteristic
647C2×C4#6699011yescharacteristic
648C2×C4#6699111yescharacteristic
649C2×C4#6699211yescharacteristic
650C2×C4#6699211yescharacteristic
651C2×C4#6699211yescharacteristic
652C2×C4#6699211yescharacteristic
653C2×C4#6699311yescharacteristic
654C2×C4#6699311yescharacteristic
655C2×C4#6700611yescharacteristic
656C8—42no—
657C8—442no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22#1062256811yescharacteristic
665C22#1062256911yescharacteristic
666C22#1062256911yescharacteristic
667C22#1062257211yescharacteristic
668C22#1062257311yescharacteristic
669C22#1062257411yescharacteristic
670C22#1062281814yes—
671C22#1062283611yescharacteristic
672C4—44no—
673C4—82no—
674C4—228no—
675C4—444no—
676C4—882no—
677C4#1062257011yescharacteristic
678C4#1062257011yescharacteristic
679C4#1062257111yescharacteristic
680C4#1062257211yescharacteristic
681C4#1062257311yescharacteristic
682C4#1062257411yescharacteristic
683C4#1062282611yescharacteristic
684C4#1062283611yescharacteristic
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2#1306685511yescharacteristic
690C2#1306900612yes—
691C2#1306964912yes—
692C2#1306965312yes—
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#419C2
socleC23×C11#120
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#419D11
hypocenterC11#10978
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
17. C2×#66997C4semidirect
581. C11#10978semidirect

Maximal subgroups

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

subgroupindex
C22×#669972
C2×#106228382
C22×#668882
#130712002
C2×#106221932
C2×#106221702
C2×C11×#4192
#1097811