Finite Group Databasebeta

← #14816848

Subgroups — #14816848

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622621C211yesmaximal, characteristic
2C2×SD16×Dic11C211yesmaximal, characteristic
3#13072457C211yesmaximal, characteristic, complemented
4D4×Dic11⋊C4C211yesmaximal, characteristic
5#13070157C211yesmaximal, characteristic, complemented
6#13070096C211yesmaximal, characteristic, complemented
7#13069997C211yesmaximal, characteristic, complemented
8#13069950C211yesmaximal, characteristic, complemented
9#13069343C211yesmaximal, characteristic, complemented
10#13069176C211yesmaximal, characteristic, complemented
11#13068952C211yesmaximal, characteristic
12#13068882C211yesmaximal, characteristic, complemented
13#13068879C211yesmaximal, characteristic
14#13068875C211yesmaximal, characteristic
15C11×#1877C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C22×Dic11⋊C4—21no—
22C2×#66922C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#391C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31#10622823—21no—
32SD16×Dic11—24no—
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622621—24no—
37#10622598C2211yescharacteristic
38#10622589C2211yescharacteristic
39#10622586C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44#10622559—21no—
45#10622555—21no—
46C4×Dic11⋊C4C2211yescharacteristic
47#10622541C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622274—21no—
50#10622269—21no—
51#10622268—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22—21no—
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16Q814yescomplemented
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×D4×C11—22no—
73C4×D4×C11—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80Q8×Dic11—22no—
81Q8×Dic11—41no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—22no—
85D4×Dic11—41no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—44no—
99C2×Dic11⋊C4D411yescharacteristic
100C2×Dic11⋊C4D411yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66922—22no—
107#66922—41no—
108C11×#103—41no—
109C11×#102—22no—
110C11×#95—21no—
111C11×#95—21no—
112#66899—22no—
113#66899—22no—
114#66896—22no—
115#66896D414yes—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124#66881—22no—
125#66881—41no—
126C8×Dic11—22no—
127#66872—22no—
128#66872—22no—
129#66872—22no—
130C4⋊(C11⋊C8)—22no—
131#26376—111nomaximal, Sylow
132C24×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11C2×Q812yes—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11C2×D412yes—
143C2×D4×C11C2×Q812yes—
144C2×D4×C11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—81no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—24no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—81no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C2×Dic22—42no—
169C2×Dic22—42no—
170C2×Dic22—81no—
171C11×SD16—28no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C2×Q812yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C22⋊C4—42no—
183C42×C11—21no—
184C42×C11—21no—
185C22⋊Dic11—24no—
186C22⋊Dic11—42no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—42no—
194C4⋊Dic11—42no—
195C4⋊Dic11—81no—
196C4⋊Dic11C2×D412yes—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—41no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—81no—
203Dic11⋊C4—81no—
204Dic11⋊C4SD1614yescomplemented
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C2×D412yes—
216C2×#476—111no—
217C2×C4×SD16—111no—
218#2451—111no—
219D4×C4⋊C4—111no—
220#2096—111no—
221#2084—111no—
222#2066—111no—
223#2058—111no—
224#1941—111no—
225#1916—111no—
226#1877—111no—
227#1877D1111yescharacteristic
228#1865—111no—
229#1864—111no—
230#1864—111no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C22×D411yescharacteristic
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—41no—
242Q8×C11—41no—
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11C22⋊Q814yes—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—84no—
262C2×C4×C11C2×SD1612yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×Q811yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—48no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—84no—
293C2×Dic11C2×SD1612yes—
294C2×Dic11C2×SD1612yes—
295Dic22—84no—
296C8×C11—22no—
297C8×C11—41no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C22×SD16C2×D1111yescharacteristic
301C2×C4⋊Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×D4—111no—
304C2×C4×D4—111no—
305C2×C4×D4C2×D1111yescharacteristic
306C22×C4⋊C4—221no—
307#476—224no—
308C4×SD16—224no—
309C2×#106—111no—
310C2×#106—111no—
311C2×#106—111no—
312C2×#106—111no—
313C2×#106—111no—
314C2×C4⋊C8—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103C2×D1111yescharacteristic
318C2×#102—111no—
319C2×#102—111no—
320C2×#102C2×D1111yescharacteristic
321C2×C4×C8—111no—
322#398—221no—
323#395—221no—
324#391—111no—
325#391—221no—
326#391C2×D1111yescharacteristic
327#389—111no—
328#389—111no—
329#389—111no—
330#389—111no—
331#387—221no—
332#385—221no—
333#385—221no—
334#384—111no—
335#380—221no—
336C4×C4⋊C4—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340C2×D1111yescharacteristic
341#336—111no—
342#336—111no—
343#336—111no—
344#336C2×D1111yescharacteristic
345C22×C11—24no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11#52511yescharacteristic
353C22×C11D4211yescharacteristic
354C22×C11D4×Q811yescharacteristic
355C22×C11C22×SD1611yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57711yescharacteristic
358C22×C11#57711yescharacteristic
359C4×C11—22no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—81no—
363C4×C11—81no—
364C4×C11C2×C22⋊Q811yescharacteristic
365C4×C11#53911yescharacteristic
366C4×C11#54711yescharacteristic
367C4×C11#55411yescharacteristic
368Dic11—22no—
369Dic11—22no—
370Dic11—42no—
371Dic11—41no—
372Dic11—42no—
373Dic11—41no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8—221no—
377C22×Q8C22×D1111yescharacteristic
378C22×D4C22×D1111yescharacteristic
379C23×C4—21no—
380C23×C4—221no—
381C23×C4—221no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16Dic2214yescomplemented
385C22×C8—111no—
386C22×C8—111no—
387C22×C8C22×D1111yescharacteristic
388C22×C8C22×D1111yescharacteristic
389C4⋊Q8—222no—
390C4⋊Q8—441no—
391C4×Q8—222no—
392C4×Q8—441no—
393C4×D4—22no—
394C4×D4—41no—
395C4×D4—222no—
396C4×D4—222no—
397C4×D4—222no—
398C4×D4—441no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—444no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423#106—222no—
424#106—222no—
425#106—222no—
426#106—222no—
427#106—441no—
428C4⋊C8—222no—
429#103—41no—
430#103—222no—
431#103—222no—
432#102—22no—
433#102—114no—
434#102—222no—
435C4×C8—222no—
436#95—21no—
437#95—21no—
438#95—111no—
439#95—111no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446C2×C11—44no—
447C2×C11#244911yescharacteristic
448C2×C11#310111yescharacteristic
449C2×C11#312511yescharacteristic
450C2×C11#326711yescharacteristic
451C2×C11D4×SD1611yescharacteristic
452C2×C11Q8×SD1611yescharacteristic
453C2×C11#338811yescharacteristic
454C24—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—442no—
461C2×Q8—442no—
462C2×Q8—881no—
463C2×Q8C2×Dic2212yes—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4C2×Dic2212yes—
468C2×D4D4×D1112yes—
469C2×D4#434112yes—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—81no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—224no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—881no—
490C22×C4D4×D1111yescharacteristic
491C22×C4D4×D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
493SD16—28no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—112no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8C2×Dic2212yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—114no—
511C4⋊C4—112no—
512C4⋊C4—112no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—441no—
520C4⋊C4—442no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—881no—
526C4⋊C4—881no—
527C4⋊C4—881no—
528C22⋊C4—42no—
529C22⋊C4—224no—
530C22⋊C4—442no—
531C42—21no—
532C42—21no—
533C42—221no—
534C42—221no—
535C42—221no—
536C42—221no—
537C42—442no—
538C11#2637611yescharacteristic, complemented, Sylow
539C23—22no—
540C23—22no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C2×D4×D1111yescharacteristic
547Q8—22no—
548Q8—22no—
549Q8—41no—
550Q8—41no—
551Q8—884no—
552D4—22no—
553D4—22no—
554D4—22no—
555D4#6693114yes—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—84no—
571C2×C4—112no—
572C2×C4—112no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—222no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—448no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—884no—
597C2×C4SD16×D1112yes—
598C2×C4C22×Dic2211yescharacteristic
599C2×C4C2×D4×D1111yescharacteristic
600C2×C4C2×#434111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#6704311yescharacteristic
604C8—22no—
605C8—41no—
606C8—222no—
607C8—441no—
608C22—24no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22D4×Dic2211yescharacteristic
616C22#1062312111yescharacteristic
617C22#1062313711yescharacteristic
618C22C2×SD16×D1111yescharacteristic
619C22#1062330111yescharacteristic
620C22#1062330611yescharacteristic
621C22#1062330811yescharacteristic
622C4—22no—
623C4—42no—
624C4—41no—
625C4—81no—
626C4—81no—
627C4—222no—
628C4—222no—
629C4—441no—
630C4—442no—
631C4—442no—
632C4—441no—
633C4—881no—
634C4—881no—
635C4C2×#6693111yescharacteristic
636C4#1062307011yescharacteristic
637C4#1062313311yescharacteristic
638C4#1062318611yescharacteristic
639C2—44no—
640C2#1307242911yescharacteristic
641C2#1307862311yescharacteristic
642C2#1307889011yescharacteristic
643C2#1308014411yescharacteristic
644C2#1308031011yescharacteristic
645C2SD16×Dic2211yescharacteristic
646C2#1308156211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1877C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1877D11
hypocenterC11#26376
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
3. #13072457C2semidirect
5. #13070157C2semidirect
6. #13070096C2semidirect
7. #13069997C2semidirect
8. #13069950C2semidirect
9. #13069343C2semidirect
10. #13069176C2semidirect
12. #13068882C2semidirect
69. C2×C11×SD16Q8semidirect
204. Dic11⋊C4SD16semidirect
384. C2×SD16Dic22semidirect
538. C11#26376semidirect

Maximal subgroups

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

subgroupindex
C2×#106226212
C2×SD16×Dic112
#130724572
D4×Dic11⋊C42
#130701572
#130700962
#130699972
#130699502
#130693432
#130691762
#130689522
#130688822
#130688792
#130688752
C11×#18772
#2637611