Finite Group Databasebeta

← #14813801

Subgroups — #14813801

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×#10622798C211yesmaximal, characteristic
2C2×#10622401C211yesmaximal, characteristic
3#13072406C211yesmaximal, characteristic
4Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13070159C211yesmaximal, characteristic, complemented
6#13070120C211yesmaximal, characteristic, complemented
7#13070021C211yesmaximal, characteristic
8#13069854C211yesmaximal, characteristic
9#13069294C211yesmaximal, characteristic, complemented
10#13069172C211yesmaximal, characteristic, complemented
11#13068971C211yesmaximal, characteristic
12#13068959C211yesmaximal, characteristic, complemented
13#13068882C211yesmaximal, characteristic, complemented
14#13068878C211yesmaximal, characteristic
15C11×#1878C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C2×#66946C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#391C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622798—24no—
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622598—21no—
36#10622598—21no—
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622552C2211yescharacteristic
44#10622548—21no—
45#10622548C2211yescharacteristic
46C4×C4⋊Dic11—21no—
47C4×C4⋊Dic11C2211yescharacteristic
48#10622401—24no—
49#10622288—21no—
50#10622287—21no—
51#10622281—21no—
52#10622277—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
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×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77#67000—22no—
78#67000—41no—
79Q8×Dic11—22no—
80Q8×Dic11—22no—
81Q8×Dic11—41no—
82Q8×Dic11—41no—
83C2×#4325—22no—
84C2×#4325—22no—
85C2×#4325D414yes—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11D411yescharacteristic
98C2×C4⋊Dic11D411yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66946—22no—
110#66946—41no—
111C11×#103—22no—
112C11×#103—22no—
113C11×#95—21no—
114C11×#95—21no—
115#66899—22no—
116#66899—22no—
117#66899—41no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66885—22no—
126#66885—22no—
127Dic11⋊C8—22no—
128C8×Dic11—22no—
129#66873—22no—
130#66872—22no—
131#66872—41no—
132#26161—111nomaximal, Sylow
133C23×D11—21no—
134C2×Q8×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×C11C2×D412yes—
144C2×Q8×C11#4112yes—
145C2×Q8×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44C2×D412yes—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—81no—
169C11×Q16—44no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4#4112yes—
181C42×C11—24no—
182C42×C11—21no—
183C42×C11—21no—
184#4325—28no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—81no—
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—
204Dic11⋊C4—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⋊C8C2×D412yes—
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#1880—111no—
228#1878—111no—
229#1878D1111yescharacteristic, complemented
230#1865—111no—
231#1864—111no—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11#12314yes—
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—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11#13512yes—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C112−1+411yescharacteristic
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—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
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#13712yes—
293D44—22no—
294D44—22no—
295D44—41no—
296D44—41no—
297C4×D11—84no—
298C8×C11—41no—
299C8×C11—41no—
300C11⋊C8—22no—
301C11⋊C8—41no—
302C22×Q16C2×D1111yescharacteristic
303C22×SD16—111no—
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×#103C2×D1111yescharacteristic
318C2×#103C2×D1111yescharacteristic
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×C4×C8—111no—
323#397—221no—
324#397—221no—
325#391—111no—
326#391C2×D1111yescharacteristic
327#390—111no—
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#52511yescharacteristic
348C22×C11D4211yescharacteristic
349C22×C11#54811yescharacteristic
350C22×C11C2×#13511yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C22×C11#57711yescharacteristic
353C22×C11#57711yescharacteristic
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C4×C11—22no—
362C4×C11—24no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—81no—
366C4×C11—81no—
367C4×C11C2×#12311yescharacteristic
368C4×C11#53911yescharacteristic
369C4×C11#54711yescharacteristic
370C4×C11#55311yescharacteristic
371Dic11—22no—
372Dic11—41no—
373Dic11—41no—
374Dic11—41no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8C22×D1111yescharacteristic
379C22×Q8C22×D1111yescharacteristic
380C22×D4—111no—
381C23×C4—221no—
382C2×Q16—22no—
383C2×Q16—22no—
384C2×Q16—22no—
385C2×SD16—114no—
386C2×SD16—222no—
387C2×SD16—222no—
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—221no—
418C2×C22⋊C4—221no—
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—22no—
433#103—222no—
434#103—222no—
435#103—441no—
436#102—222no—
437#102—222no—
438#102—222no—
439C4×C8—222no—
440#95—21no—
441#95—21no—
442#95—111no—
443#95—111no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449C2×C11#244311yescharacteristic
450C2×C11#310811yescharacteristic
451C2×C11#312511yescharacteristic
452C2×C11#326611yescharacteristic
453C2×C11#328411yescharacteristic
454C2×C11#336511yescharacteristic
455C2×C11#336911yescharacteristic
456D11—82no—
457C24—221no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8#433912yes—
468C2×Q8D4×D1112yes—
469C2×Q8#434112yes—
470C2×D4—112no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
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—44no—
494SD16—228no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—112no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
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—442no—
528C22⋊C4—442no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C22⋊C4—881no—
532C42—24no—
533C42—21no—
534C42—21no—
535C42—221no—
536C42—221no—
537C42—221no—
538C42—221no—
539C42—442no—
540C42—442no—
541C11#2616111yescharacteristic, complemented, Sylow
542C23—222no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23C2×D4×D1111yescharacteristic
550Q8—22no—
551Q8—22no—
552Q8—22no—
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—41no—
557Q8#6693614yes—
558D4—222no—
559D4—222no—
560D4—441no—
561D4—441no—
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—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—112no—
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—221no—
589C2×C4—221no—
590C2×C4—221no—
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#6697212yes—
602C2×C4C2×#433911yescharacteristic
603C2×C4C2×D4×D1111yescharacteristic
604C2×C4C2×#434111yescharacteristic
605C2×C4C2×#434111yescharacteristic
606C2×C4#6704211yescharacteristic
607C2×C4#6704311yescharacteristic
608C8—41no—
609C8—41no—
610C8—222no—
611C8—441no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22—881no—
616C22—881no—
617C22—881no—
618C22—881no—
619C22#1062308311yescharacteristic
620C22#1062311711yescharacteristic
621C22#1062314011yescharacteristic
622C22C2×#6697211yescharacteristic
623C22#1062330111yescharacteristic
624C22D11×#13711yescharacteristic
625C22#1062330911yescharacteristic
626C4—22no—
627C4—24no—
628C4—41no—
629C4—42no—
630C4—81no—
631C4—81no—
632C4—222no—
633C4—441no—
634C4—441no—
635C4—441no—
636C4—881no—
637C4—881no—
638C4—881no—
639C4C2×#6693611yescharacteristic
640C4#1062309611yescharacteristic
641C4#1062314211yescharacteristic
642C4#1062319611yescharacteristic
643C2—882no—
644C2#1307235711yescharacteristic
645C2#1307869711yescharacteristic
646C2#1307888611yescharacteristic
647C2#1308012111yescharacteristic
648C2#1308034111yescharacteristic
649C2#1308131011yescharacteristic
650C2#1308135711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1878D11
hypocenterC11#26161
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
4. Q8×C4⋊Dic11C2semidirect
5. #13070159C2semidirect
6. #13070120C2semidirect
9. #13069294C2semidirect
10. #13069172C2semidirect
12. #13068959C2semidirect
13. #13068882C2semidirect
15. C11×#1878C2semidirect
229. #1878D11semidirect
541. C11#26161semidirect

Maximal subgroups

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

subgroupindex
C2×#106227982
C2×#106224012
#130724062
Q8×C4⋊Dic112
#130701592
#130701202
#130700212
#130698542
#130692942
#130691722
#130689712
#130689592
#130688822
#130688782
C11×#18782
#2616111