Finite Group Databasebeta

← #14772076

Subgroups — #14772076

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622430C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic
3C2×#10622401C211yesmaximal, characteristic
4#13071534C211yesmaximal, characteristic, complemented
5#13071525C211yesmaximal, characteristic
6#13069358C211yesmaximal, characteristic, complemented
7#13069356C211yesmaximal, characteristic, complemented
8#13068886C211yesmaximal, characteristic, complemented
9#13068880C211yesmaximal, characteristic
10#13068874C211yesmaximal, characteristic
11#13068777C211yesmaximal, characteristic, complemented
12#13068629C211yesmaximal, characteristic, complemented
13#13068625C211yesmaximal, characteristic
14#13068482C211yesmaximal, characteristic, complemented
15C11×#1865C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622639—24no—
35#10622602—21no—
36#10622600—21no—
37#10622598C2211yescharacteristic
38#10622590—21no—
39#10622590C2211yescharacteristic
40#10622590C2211yescharacteristic
41#10622586—21no—
42#10622586C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541—21no—
50#10622541C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52#10622430—24no—
53#10622401C418yescomplemented
54#10622281—21no—
55D11×#95—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78Q8×Dic11—22no—
79Q8×Dic11—22no—
80Q8×Dic11—41no—
81Q8×Dic11C2×C414yescomplemented
82C2×#4325C2×C414yes—
83C2×#4325D414yes—
84C2×#4325Q814yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4D411yescharacteristic
97C2×Dic11⋊C4D411yescharacteristic
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66946—22no—
105#66946—22no—
106#66946—41no—
107#66946C2×C414yes—
108C4×D44—22no—
109C4×D44—41no—
110C11×#106—41no—
111C11×#103—22no—
112C11×#103C2×C414yescomplemented
113C11×#95—21no—
114#66899—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124#66885—22no—
125#66885C2×C414yes—
126#66881—41no—
127#66879—22no—
128Dic11⋊C8—22no—
129C8×Dic11C2×C414yescomplemented
130#66873—22no—
131#66872C2×C414yescomplemented
132#66871—22no—
133#66871—22no—
134#66867—22no—
135#22673—111nomaximal, Sylow
136C23×D11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11C22×C412yes—
141C2×Q8×C11C2×D412yes—
142C2×Q8×C11C2×Q812yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44C22×C412yes—
161C2×D44C2×D412yes—
162C2×D44C2×Q812yes—
163C2×C4×D11—24no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—81no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×C4×D11—81no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C22×C412yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—81no—
185C11×C4⋊C4C22×C412yes—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—42no—
189#4325C4⋊C4116yescomplemented
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—24no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11—81no—
201C4⋊Dic11C22×C412yes—
202Dic11⋊C4—41no—
203Dic11⋊C4—41no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206C4×Dic11—24no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C4×Dic11C22×C412yes—
211C4×Dic11#4112yes—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C22×C412yes—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8C2×Q812yes—
218C2×#440—111no—
219C2×#440—111no—
220C2×C4×SD16—111no—
221#2351—111no—
222#2349—111no—
223#1944—111no—
224#1944—111no—
225#1865—111no—
226#1865D1111yescharacteristic, complemented
227#1864—111no—
228#1864—111no—
229#1846—111no—
230#1805—111no—
231#1804—111no—
232#1770—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11C2×C4⋊C414yes—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
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—41no—
262C2×C4×C11—41no—
263C2×C4×C11C23×C411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×Q811yescharacteristic
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—22no—
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×Dic11C4×D412yes—
289C2×Dic11C4×D412yes—
290D44—22no—
291D44—22no—
292D44—22no—
293D44C2×C4⋊C414yes—
294C4×D11—84no—
295C4×D11—84no—
296C4×D11—84no—
297C8×C11—22no—
298C8×C11—41no—
299C11⋊C8—41no—
300C11⋊C8C2×C4⋊C414yes—
301C22×SD16—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×Q8C2×D1111yescharacteristic
305C2×C4×D4—111no—
306C2×C4×D4—111no—
307C2×C4×D4—111no—
308#440—224no—
309#440—224no—
310C4×SD16—118no—
311C2×#107—111no—
312C2×#107—111no—
313C2×#106—111no—
314C2×#106—111no—
315C2×#106C2×D1111yescharacteristic
316C2×C4⋊C8—111no—
317C2×#103—111no—
318C2×#103C2×D1111yescharacteristic
319C2×#103C2×D1111yescharacteristic
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#97—111no—
324C2×#97—111no—
325C2×C4×C8—111no—
326#389—111no—
327#389—111no—
328#389—111no—
329#389—221no—
330#389—221no—
331#389C2×D1111yescharacteristic
332#385—221no—
333#385—221no—
334#382—111no—
335#382—111no—
336#382—221no—
337#380—221no—
338C4×C4⋊C4—111no—
339C4×C4⋊C4—221no—
340C2×#95—221no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340C2×D1111yescharacteristic
345#336—111no—
346#336C2×D1111yescharacteristic
347C22×C11C2×C4×D411yescharacteristic
348C22×C11D4211yescharacteristic
349C22×C11D4×Q811yescharacteristic
350C22×C11#57511yescharacteristic
351C22×C11#57511yescharacteristic
352C22×C11#57711yescharacteristic
353C22×C11#57711yescharacteristic
354C2×D11—24no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C4×C11—24no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—81no—
366C4×C11—81no—
367C4×C11C22×C4⋊C411yescharacteristic
368C4×C11#52011yescharacteristic
369C4×C11#54711yescharacteristic
370C4×C11#55411yescharacteristic
371Dic11—22no—
372Dic11—22no—
373Dic11—42no—
374Dic11—41no—
375Dic11—41no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8C22×D1111yescharacteristic
379C22×D4—111no—
380C23×C4—221no—
381C23×C4—221no—
382C23×C4—221no—
383C2×SD16—114no—
384C2×SD16—114no—
385C2×SD16—114no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390C4×Q8—22no—
391C4×Q8—41no—
392C4×Q8—114no—
393C4×Q8—222no—
394C4×Q8—222no—
395C4×Q8—441no—
396C4×D4—114no—
397C4×D4—222no—
398C4×D4—222no—
399C4×D4—222no—
400C4×D4—441no—
401C4×D4—441no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C42—21no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426#107—222no—
427#107—222no—
428#106—41no—
429#106—114no—
430#106—441no—
431C4⋊C8—222no—
432#103—22no—
433#103—222no—
434#103C4×D1114yescomplemented
435#102—114no—
436#102—222no—
437#102—222no—
438#97—222no—
439#97—222no—
440C4×C8—114no—
441#95—21no—
442#95—111no—
443#95—111no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11D4×C4⋊C411yescharacteristic
452C2×C11#294311yescharacteristic
453C2×C11#294911yescharacteristic
454C2×C11#327511yescharacteristic
455C2×C11#327511yescharacteristic
456C2×C11#338811yescharacteristic
457C2×C11#338811yescharacteristic
458D11—44no—
459C24—221no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8C2×C4×D1112yes—
464C2×Q8D4×D1112yes—
465C2×Q8Q8×D1112yes—
466C2×D4—112no—
467C2×D4—112no—
468C2×D4—112no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
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—442no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—881no—
489C22×C4—881no—
490C22×C4—881no—
491C22×C4—881no—
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495SD16—1116no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—112no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8C2×C4×D1112yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—42no—
514C4⋊C4—81no—
515C4⋊C4—112no—
516C4⋊C4—224no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—441no—
523C4⋊C4—441no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—881no—
528C4⋊C4C2×C4×D1112yes—
529C22⋊C4—224no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C42—21no—
533C42—21no—
534C42—42no—
535C42—112no—
536C42—112no—
537C42—224no—
538C42—221no—
539C42—221no—
540C42—442no—
541C11#2267311yescharacteristic, complemented, Sylow
542C23—222no—
543C23—222no—
544C23—222no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23C2×D4×D1111yescharacteristic
550Q8—22no—
551Q8—22no—
552Q8—22no—
553Q8C4⋊C4×D1114yes—
554D4—114no—
555D4—222no—
556D4—222no—
557D4—222no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—112no—
577C2×C4—112no—
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—222no—
587C2×C4—221no—
588C2×C4—221no—
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—884no—
598C2×C4—884no—
599C2×C4—884no—
600C2×C4C22×C4×D1111yescharacteristic
601C2×C4C2×D4×D1111yescharacteristic
602C2×C4#6703711yescharacteristic
603C2×C4C2×Q8×D1111yescharacteristic
604C2×C4#41×D1111yescharacteristic
605C2×C4#6704311yescharacteristic
606C8—22no—
607C8—41no—
608C8—114no—
609C8—441no—
610C22—224no—
611C22—442no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22C4×D4×D1111yescharacteristic
618C22#1062312111yescharacteristic
619C22#1062316311yescharacteristic
620C22#1062329311yescharacteristic
621C22#1062330111yescharacteristic
622C22#1062330811yescharacteristic
623C22#1062330811yescharacteristic
624C4—24no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—222no—
631C4—222no—
632C4—442no—
633C4—441no—
634C4—441no—
635C4—881no—
636C4—881no—
637C4C2×C4⋊C4×D1111yescharacteristic
638C4#1062307711yescharacteristic
639C4#1062316711yescharacteristic
640C4#1062318611yescharacteristic
641C2—444no—
642C2#1307151411yescharacteristic
643C2#1307741511yescharacteristic
644C2#1307747011yescharacteristic
645C2#1308024011yescharacteristic
646C2#1308025011yescharacteristic
647C2#1308156411yescharacteristic
648C2#1308156811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1865C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1865D11
hypocenterC11#22673
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
4. #13071534C2semidirect
6. #13069358C2semidirect
7. #13069356C2semidirect
8. #13068886C2semidirect
11. #13068777C2semidirect
12. #13068629C2semidirect
14. #13068482C2semidirect
15. C11×#1865C2semidirect
53. #10622401C4semidirect
81. Q8×Dic11C2×C4semidirect
112. C11×#103C2×C4semidirect
129. C8×Dic11C2×C4semidirect
131. #66872C2×C4semidirect
189. #4325C4⋊C4semidirect
226. #1865D11semidirect
434. #103C4×D11semidirect
541. C11#22673semidirect

Maximal subgroups

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

subgroupindex
C2×#106224302
C2×#106226392
C2×#106224012
#130715342
#130715252
#130693582
#130693562
#130688862
#130688802
#130688742
#130687772
#130686292
#130686252
#130684822
C11×#18652
#2267311