Finite Group Databasebeta

← #14813866

Subgroups — #14813866

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic11C211yesmaximal, characteristic
2#13072388C211yesmaximal, characteristic, complemented
3D4×Dic11⋊C4C211yesmaximal, characteristic
4#13070157C211yesmaximal, characteristic, complemented
5#13070114C211yesmaximal, characteristic, complemented
6#13070027C211yesmaximal, characteristic, complemented
7#13069859C211yesmaximal, characteristic, complemented
8#13069289C211yesmaximal, characteristic, complemented
9#13069170C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic
11#13068952C211yesmaximal, characteristic
12#13068952C211yesmaximal, characteristic
13#13068882C211yesmaximal, characteristic, complemented
14#13068877C211yesmaximal, characteristic
15C2×C11×#461C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C22×Dic11⋊C4—21no—
24C11×#461—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30#10622843C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622823—21no—
38SD16×Dic11—24no—
39C2×#66881C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622599—21no—
42#10622596—21no—
43#10622591—21no—
44#10622591—21no—
45#10622589C2211yescharacteristic
46#10622586C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48#10622559—21no—
49#10622555—21no—
50C4×Dic11⋊C4C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622541C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×Dic11—21no—
66C23×Dic11—21no—
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16—22no—
72C2×C11×SD16D414yes—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8—41no—
77C4×D4×C11—22no—
78C4×D4×C11—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86Q8×Dic11—22no—
87Q8×Dic11—41no—
88D4×Dic11—22no—
89D4×Dic11—22no—
90D4×Dic11—22no—
91D4×Dic11—41no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—44no—
103C2×Dic11⋊C4D411yescharacteristic
104C2×Dic11⋊C4D411yescharacteristic
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×C4⋊C8—22no—
111C11×#103—22no—
112C11×#103—22no—
113#66899—22no—
114#66899—22no—
115#66899—22no—
116#66899—41no—
117#66896—22no—
118#66896—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130#66881—22no—
131C8×Dic11—22no—
132#66872—41no—
133#26166—111nomaximal, Sylow
134C24×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11C2×D412yes—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11C2×D412yes—
151C2×D4×C11#4112yes—
152C2×D4×C11#4112yes—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—81no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—24no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11—42no—
170C22×Dic11—42no—
171C22×Dic11—81no—
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176C11×SD16—28no—
177C11×SD16—44no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11C2×D412yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4—42no—
188C11×C22⋊C4—42no—
189C42×C11—21no—
190C42×C11—21no—
191C22⋊Dic11—24no—
192C22⋊Dic11—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—42no—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—41no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—81no—
208Dic11⋊C4SD1614yescomplemented
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—42no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×#461D1111yescharacteristic
221C2×C4×SD16—111no—
222#2446—111no—
223D4×C4⋊C4—111no—
224#2096—111no—
225#2088—111no—
226#2072—111no—
227#2043—111no—
228#1933—111no—
229#1916—111no—
230#1877—111no—
231#1877—111no—
232#1877—111no—
233#1865—111no—
234#1864—111no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11C22×D411yescharacteristic
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11—41no—
250Q8×C11—41no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11#12314yes—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—84no—
270C2×C4×C11C2×SD1612yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—48no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—84no—
301C2×Dic11C2×SD1612yes—
302C2×Dic11C2×SD1612yes—
303C8×C11—22no—
304C8×C11—41no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C22×SD16C2×D1111yescharacteristic
308C22×SD16C2×D1111yescharacteristic
309C2×C4⋊Q8C2×D1111yescharacteristic
310C2×C4×Q8—111no—
311C2×C4×D4—111no—
312C2×C4×D4—111no—
313C2×C4×D4C2×D1111yescharacteristic
314C22×C4⋊C4—221no—
315#461—24no—
316C4×SD16—224no—
317C2×#106—111no—
318C2×#106—111no—
319C2×C4⋊C8C2×D1111yescharacteristic
320C2×#103—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103C2×D1111yescharacteristic
325C2×#103C2×D1111yescharacteristic
326C2×#102—111no—
327C2×#102—111no—
328C2×C4×C8—111no—
329#400—221no—
330#398—221no—
331#391—111no—
332#391—111no—
333#391—111no—
334#389—111no—
335#389—111no—
336#389—111no—
337#387—221no—
338#387—221no—
339#385—221no—
340#385—221no—
341#384—111no—
342#380—221no—
343C4×C4⋊C4—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#336—111no—
349#336—111no—
350#336—111no—
351#336—111no—
352C22×C11—24no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11#52511yescharacteristic
360C22×C11D4211yescharacteristic
361C22×C11#54811yescharacteristic
362C22×C11C22×SD1611yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57711yescharacteristic
365C22×C11#57811yescharacteristic
366C4×C11—22no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11C2×#12311yescharacteristic
372C4×C11#53911yescharacteristic
373C4×C11#54711yescharacteristic
374C4×C11#55311yescharacteristic
375Dic11—22no—
376Dic11—22no—
377Dic11—42no—
378Dic11—41no—
379Dic11—41no—
380Dic11—81no—
381Dic11—81no—
382Dic11—81no—
383C22×Q8C22×D1111yescharacteristic
384C22×Q8C22×D1111yescharacteristic
385C22×D4C22×D1111yescharacteristic
386C23×C4—21no—
387C23×C4—221no—
388C23×C4—221no—
389C2×SD16—22no—
390C2×SD16—22no—
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—22no—
394C2×SD16C22⋊D1114yes—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C4⋊Q8—22no—
400C4⋊Q8—41no—
401C4×Q8—222no—
402C4×Q8—441no—
403C4×D4—22no—
404C4×D4—41no—
405C4×D4—222no—
406C4×D4—222no—
407C4×D4—222no—
408C4×D4—441no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—444no—
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432#106—222no—
433#106—441no—
434C4⋊C8—22no—
435#103—22no—
436#103—22no—
437#103—222no—
438#103—222no—
439#103—222no—
440#103—441no—
441#102—222no—
442#102—222no—
443C4×C8—222no—
444#95—111no—
445#95—111no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455C2×C11—44no—
456C2×C11#244311yescharacteristic
457C2×C11#310111yescharacteristic
458C2×C11#312011yescharacteristic
459C2×C11#326911yescharacteristic
460C2×C11D4×SD1611yescharacteristic
461C2×C11#335911yescharacteristic
462C2×C11#337611yescharacteristic
463C24—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8C2×C22⋊D1112yes—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4#434112yes—
480C2×D4#434112yes—
481C2×D4C2×C22⋊D1112yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—81no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—224no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—881no—
502C22×C4D4×D1111yescharacteristic
503C22×C4D4×D1111yescharacteristic
504C22×C4C23×D1111yescharacteristic
505SD16—28no—
506SD16—44no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8C2×C22⋊D1112yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—114no—
524C4⋊C4—112no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—441no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4—881no—
539C22⋊C4—42no—
540C22⋊C4—224no—
541C22⋊C4—442no—
542C42—21no—
543C42—21no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—442no—
549C11#2616611yescharacteristic, complemented, Sylow
550C23—22no—
551C23—22no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C2×D4×D1111yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—41no—
561Q8—41no—
562Q8—41no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566D4—22no—
567D4—22no—
568D4—22no—
569D4#6698814yes—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—84no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—222no—
598C2×C4—448no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—884no—
611C2×C4SD16×D1112yes—
612C2×C4C2×#434111yescharacteristic
613C2×C4C2×#434111yescharacteristic
614C2×C4#6703711yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#6704311yescharacteristic
617C2×C4C22×C22⋊D1111yescharacteristic
618C8—22no—
619C8—41no—
620C8—441no—
621C8—441no—
622C22—24no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22#1062312911yescharacteristic
630C22#1062313711yescharacteristic
631C22C2×SD16×D1111yescharacteristic
632C22#1062329311yescharacteristic
633C22#1062330811yescharacteristic
634C22#1062331011yescharacteristic
635C22D4×C22⋊D1111yescharacteristic
636C4—22no—
637C4—41no—
638C4—42no—
639C4—81no—
640C4—81no—
641C4—222no—
642C4—222no—
643C4—441no—
644C4—442no—
645C4—441no—
646C4—881no—
647C4—881no—
648C4—881no—
649C4#1062313211yescharacteristic
650C4#1062313311yescharacteristic
651C4C2×#6698811yescharacteristic
652C4#1062335511yescharacteristic
653C2—44no—
654C2#1307234711yescharacteristic
655C2#1307862311yescharacteristic
656C2#1307882711yescharacteristic
657C2#1308016511yescharacteristic
658C2SD16×C22⋊D1111yescharacteristic
659C2#1308125311yescharacteristic
660C2#1308143611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#461D11
hypocenterC11#26166
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. #13072388C2semidirect
4. #13070157C2semidirect
5. #13070114C2semidirect
6. #13070027C2semidirect
7. #13069859C2semidirect
8. #13069289C2semidirect
9. #13069170C2semidirect
13. #13068882C2semidirect
208. Dic11⋊C4SD16semidirect
549. C11#26166semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic112
#130723882
D4×Dic11⋊C42
#130701572
#130701142
#130700272
#130698592
#130692892
#130691702
#130689522
#130688822
#130688772
C2×C11×#4612
#2616611