Finite Group Databasebeta

← #14813793

Subgroups — #14813793

Order 2816.

840 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
1C2×#10622779C211yesmaximal, characteristic
2C2×SD16×Dic11C211yesmaximal, characteristic
3#13072401C211yesmaximal, characteristic
4Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13070158C211yesmaximal, characteristic, complemented
6#13070116C211yesmaximal, characteristic, complemented
7#13070019C211yesmaximal, characteristic
8#13069856C211yesmaximal, characteristic
9#13069293C211yesmaximal, characteristic, complemented
10#13069174C211yesmaximal, characteristic, complemented
11#13068957C211yesmaximal, characteristic, complemented
12#13068955C211yesmaximal, characteristic, complemented
13#13068886C211yesmaximal, characteristic, complemented
14#13068879C211yesmaximal, characteristic
15C11×#1880C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66989C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622779—24no—
30SD16×Dic11—24no—
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622598—21no—
38#10622598—21no—
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622598C2211yescharacteristic
42#10622587C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44#10622566—21no—
45#10622566—21no—
46#10622563—21no—
47#10622556—21no—
48#10622548—21no—
49#10622548C2211yescharacteristic
50C4×C4⋊Dic11—21no—
51C4×C4⋊Dic11C2211yescharacteristic
52#10622542C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×Dic22C2311yescharacteristic
65C2×C11×SD16—22no—
66C2×C11×SD16—22no—
67C2×C11×SD16D414yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85Q8×Dic11—41no—
86C2×#4326—22no—
87C2×#4326—22no—
88C2×#4326—22no—
89#66989—22no—
90#66989—41no—
91D4×Dic11—22no—
92D4×Dic11—41no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11D411yescharacteristic
101C2×C4⋊Dic11D411yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C11×#103—22no—
112C11×#102—22no—
113#66899—22no—
114#66896—22no—
115#66896—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66881—22no—
126#66881—41no—
127#66880—22no—
128#66880—41no—
129Dic11⋊C8—22no—
130C8×Dic11—22no—
131#66874—22no—
132#26161—111nomaximal, Sylow
133C24×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×D412yes—
138C2×Q8×C11#4112yes—
139C2×Q8×C11#4112yes—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—81no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C11×SD16—28no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D412yes—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4#4112yes—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—81no—
183C42×C11—24no—
184C42×C11—21no—
185C42×C11—21no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189#4326—44no—
190C4⋊Dic11—22no—
191C4⋊Dic11—22no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11—42no—
201C4⋊Dic11—81no—
202C4⋊Dic11—81no—
203C4⋊Dic11—81no—
204C4⋊Dic11—81no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×#464—111no—
218C2×C4×SD16—111no—
219#2447—111no—
220Q8×C4⋊C4—111no—
221#2096—111no—
222#2088—111no—
223#2071—111no—
224#2042—111no—
225#1933—111no—
226#1916—111no—
227#1880D1111yescharacteristic
228#1878—111no—
229#1878—111no—
230#1865—111no—
231#1864—111no—
232C23×C11—22no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C22×D411yescharacteristic
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11#12314yes—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—41no—
247D4×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11#13512yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
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—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281C2×Dic11—41no—
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×Dic11#13712yes—
294Dic22—41no—
295Dic22—41no—
296Dic22—41no—
297Dic22—41no—
298C8×C11—22no—
299C8×C11—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C22×Q16—111no—
303C22×SD16C2×D1111yescharacteristic
304C2×#124—111no—
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×Q8C2×D1111yescharacteristic
308C2×C4×D4—111no—
309#464—224no—
310C4×SD16—224no—
311C2×#106—111no—
312C2×#106—111no—
313C2×C4⋊C8—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103C2×D1111yescharacteristic
319C2×#102—111no—
320C2×#102—111no—
321C2×#102C2×D1111yescharacteristic
322C2×C4×C8—111no—
323#397—221no—
324#397—221no—
325#391—111no—
326#391—111no—
327#390C2×D1111yescharacteristic
328#389—111no—
329#389—111no—
330#389—111no—
331#389—221no—
332#389—221no—
333#385—221no—
334#384—111no—
335#384—221no—
336#381—221no—
337C4×C4⋊C4—111no—
338C4×C4⋊C4—221no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#336—111no—
344#336—111no—
345#336—111no—
346#336C2×D1111yescharacteristic
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11#52511yescharacteristic
355C22×C11D4211yescharacteristic
356C22×C11#54811yescharacteristic
357C22×C11C2×#13511yescharacteristic
358C22×C11C2×#13711yescharacteristic
359C22×C11#57711yescharacteristic
360C22×C11#57711yescharacteristic
361C4×C11—22no—
362C4×C11—24no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—81no—
366C4×C11C2×#12311yescharacteristic
367C4×C11#53911yescharacteristic
368C4×C11#54711yescharacteristic
369C4×C11#55311yescharacteristic
370Dic11—22no—
371Dic11—41no—
372Dic11—41no—
373Dic11—41no—
374Dic11—81no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8—111no—
379C22×Q8C22×D1111yescharacteristic
380C22×D4C22×D1111yescharacteristic
381C23×C4—221no—
382C2×Q16—222no—
383C2×Q16—222no—
384C2×Q16—222no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16D4414yes—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392#124—222no—
393#124—441no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—222no—
397C4×Q8—222no—
398C4×Q8—441no—
399C4×Q8—441no—
400C4×D4—222no—
401C4×D4—441no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—21no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—221no—
426C2×C42—221no—
427C2×C42C22×D1111yescharacteristic
428#106—222no—
429#106—441no—
430C4⋊C8—222no—
431#103—22no—
432#103—222no—
433#103—222no—
434#103—222no—
435#103—441no—
436#102—22no—
437#102—222no—
438#102—222no—
439C4×C8—222no—
440#95—111no—
441#95—111no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449C2×C11—82no—
450C2×C11#244311yescharacteristic
451C2×C11#310811yescharacteristic
452C2×C11#312511yescharacteristic
453C2×C11#326611yescharacteristic
454C2×C11#328411yescharacteristic
455C2×C11#336511yescharacteristic
456C2×C11#336911yescharacteristic
457C24—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8C2×D4412yes—
468C2×Q8#434112yes—
469C2×Q8#434112yes—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4C2×D4412yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—881no—
490C22×C4D4×D1111yescharacteristic
491C22×C4D4×D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
493Q16—444no—
494SD16—28no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8C2×D4412yes—
507C4⋊C4—24no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—442no—
520C4⋊C4—442no—
521C4⋊C4—442no—
522C4⋊C4—881no—
523C4⋊C4—881no—
524C4⋊C4—881no—
525C4⋊C4—881no—
526C4⋊C4#434112yes—
527C22⋊C4—42no—
528C22⋊C4—81no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C42—24no—
533C42—21no—
534C42—21no—
535C42—221no—
536C42—221no—
537C42—221no—
538C42—221no—
539C42—442no—
540C42—442no—
541C11#2616111yescharacteristic, complemented, Sylow
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23C2×D4×D1111yescharacteristic
550Q8—22no—
551Q8—22no—
552Q8—22no—
553Q8—441no—
554Q8—441no—
555Q8—441no—
556Q8—441no—
557Q8#6693914yes—
558D4—22no—
559D4—22no—
560D4—41no—
561D4—41no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—112no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
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—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—884no—
601C2×C4#6696912yes—
602C2×C4C22×D4411yescharacteristic
603C2×C4C2×#434111yescharacteristic
604C2×C4C2×#434111yescharacteristic
605C2×C4C2×#434111yescharacteristic
606C2×C4#6704211yescharacteristic
607C2×C4#6704311yescharacteristic
608C8—22no—
609C8—41no—
610C8—441no—
611C8—441no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22D4×D4411yescharacteristic
620C22#1062311711yescharacteristic
621C22#1062312911yescharacteristic
622C22C2×#6696911yescharacteristic
623C22#1062330111yescharacteristic
624C22#1062330611yescharacteristic
625C22D11×#13711yescharacteristic
626C4—22no—
627C4—24no—
628C4—41no—
629C4—42no—
630C4—81no—
631C4—222no—
632C4—441no—
633C4—441no—
634C4—441no—
635C4—881no—
636C4—881no—
637C4—881no—
638C4—881no—
639C4C2×#6693911yescharacteristic
640C4#1062308611yescharacteristic
641C4#1062314911yescharacteristic
642C4#1062319611yescharacteristic
643C2—82no—
644C2#1307234911yescharacteristic
645C2#1307869111yescharacteristic
646C2#1307889411yescharacteristic
647C2#1308012811yescharacteristic
648C2#1308034711yescharacteristic
649C2#1308131611yescharacteristic
650C2#1308135111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1880C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1880D11
hypocenterC11#26161
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
4. Q8×C4⋊Dic11C2semidirect
5. #13070158C2semidirect
6. #13070116C2semidirect
9. #13069293C2semidirect
10. #13069174C2semidirect
11. #13068957C2semidirect
12. #13068955C2semidirect
13. #13068886C2semidirect
541. C11#26161semidirect

Maximal subgroups

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

subgroupindex
C2×#106227792
C2×SD16×Dic112
#130724012
Q8×C4⋊Dic112
#130701582
#130701162
#130700192
#130698562
#130692932
#130691742
#130689572
#130689552
#130688862
#130688792
C11×#18802
#2616111