Finite Group Databasebeta

← #14816787

Subgroups — #14816787

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622503C211yesmaximal, characteristic
2C2×#10622401C211yesmaximal, characteristic
3#13072458C211yesmaximal, characteristic, complemented
4#13071524C211yesmaximal, characteristic
5#13070098C211yesmaximal, characteristic, complemented
6#13070009C211yesmaximal, characteristic, complemented
7#13069947C211yesmaximal, characteristic, complemented
8#13069347C211yesmaximal, characteristic, complemented
9#13069174C211yesmaximal, characteristic, complemented
10#13068953C211yesmaximal, characteristic
11#13068947C211yesmaximal, characteristic
12#13068874C211yesmaximal, characteristic
13#13068868C211yesmaximal, characteristic, complemented
14#13068866C211yesmaximal, characteristic
15C11×#2097C211yesmaximal, characteristic, complemented
16C2×Q8×Dic11C2211yescharacteristic
17C22×#4325C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#382C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622503—24no—
44#10622401—24no—
45#10622281—21no—
46#10622281—21no—
47#10622280—21no—
48D11×#95—21no—
49#10622270—21no—
50#10622269—21no—
51#10622267—21no—
52#10622259—21no—
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×Dic22—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73Q8×Dic11—22no—
74Q8×Dic11—41no—
75C2×#4325—22no—
76C2×#4325—22no—
77C2×#4325Q814yescomplemented
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66946—22no—
98#66946—22no—
99#66946—41no—
100#66946—41no—
101#66941—22no—
102#66941—41no—
103C4×D44—22no—
104C4×D44—22no—
105C11×#107—22no—
106C11×#106—41no—
107C11×#103—22no—
108C11×#103—41no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113#66899—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66885—22no—
123#66885D414yes—
124#66882—22no—
125Dic11⋊C8—22no—
126C8×Dic11—22no—
127#66873—22no—
128#66872—22no—
129#66871—22no—
130#26372—111nomaximal, Sylow
131C23×D11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×Q812yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C2×D412yes—
156C2×D44C2×Q812yes—
157C2×D44#4112yes—
158C2×C4×D11—24no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×Dic22—42no—
168C2×Dic22—42no—
169C2×Dic22—81no—
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—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C42×C11—21no—
183C42×C11—21no—
184#4325—28no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188C4⋊Dic11—22no—
189C4⋊Dic11—22no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—42no—
195C4⋊Dic11C2×D412yes—
196C4⋊Dic11#4112yes—
197Dic11⋊C4—42no—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201Dic11⋊C4—81no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×Q812yes—
213C2×#474—111no—
214C2×C4×SD16—111no—
215#2451—111no—
216#2349—111no—
217#2097D1111yescharacteristic, complemented
218#2085—111no—
219#2068—111no—
220#2058—111no—
221#1942—111no—
222#1916—111no—
223#1877—111no—
224#1877—111no—
225#1864—111no—
226#1863—111no—
227#1862—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—41no—
239Q8×C11—41no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×Q811yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—22no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11#13512yes—
284C2×Dic11#13712yes—
285D44—22no—
286D44—22no—
287D44—22no—
288D44C22⋊Q814yes—
289C4×D11—84no—
290C4×D11—84no—
291C4×D11—84no—
292Dic22—84no—
293C8×C11—22no—
294C8×C11—41no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C22×SD16—111no—
298C2×C4⋊Q8—111no—
299C2×C4×Q8—111no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4—111no—
303#474—224no—
304C4×SD16—224no—
305C2×#107—111no—
306C2×#107—111no—
307C2×#107C2×D1111yescharacteristic
308C2×#106—111no—
309C2×#106C2×D1111yescharacteristic
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103C2×D1111yescharacteristic
313C2×#103C2×D1111yescharacteristic
314C2×#102—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×C4×C8—111no—
318#398—221no—
319#395—221no—
320#391—111no—
321#391—221no—
322#391C2×D1111yescharacteristic
323#389—111no—
324#389—111no—
325#389—111no—
326#389—111no—
327#387—221no—
328#385—221no—
329#385—221no—
330#382C2×D1111yescharacteristic
331#380—221no—
332C4×C4⋊C4—111no—
333C2×#95—221no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336C2×D1111yescharacteristic
342C22×C11#52511yescharacteristic
343C22×C11D4211yescharacteristic
344C22×C11D4×Q811yescharacteristic
345C22×C11C2×#13511yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C22×C11#57611yescharacteristic
348C22×C11#57711yescharacteristic
349C2×D11—24no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11C2×C22⋊Q811yescharacteristic
363C4×C11#53911yescharacteristic
364C4×C11#54711yescharacteristic
365C4×C11#55411yescharacteristic
366Dic11—22no—
367Dic11—22no—
368Dic11—42no—
369Dic11—41no—
370Dic11—42no—
371Dic11—41no—
372Dic11—81no—
373C22×Q8—221no—
374C22×Q8C22×D1111yescharacteristic
375C22×D4—111no—
376C23×C4—221no—
377C23×C4—221no—
378C23×C4—221no—
379C2×SD16—114no—
380C2×SD16—222no—
381C2×SD16—222no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386C4⋊Q8—222no—
387C4⋊Q8—441no—
388C4×Q8—222no—
389C4×Q8—441no—
390C4×D4—222no—
391C4×D4—222no—
392C4×D4—222no—
393C4×D4—222no—
394C4×D4—441no—
395C4×D4—441no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#107—22no—
418#107—222no—
419#107—222no—
420#106—41no—
421#106—222no—
422C4⋊C8—222no—
423#103—22no—
424#103—41no—
425#103—222no—
426#102—114no—
427#102—222no—
428#102—222no—
429C4×C8—222no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—111no—
435#95—111no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442C2×C11#244911yescharacteristic
443C2×C11#310711yescharacteristic
444C2×C11#311811yescharacteristic
445C2×C11#326611yescharacteristic
446C2×C11#328011yescharacteristic
447C2×C11#338111yescharacteristic
448C2×C11#338511yescharacteristic
449D11—44no—
450C24—221no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—442no—
457C2×Q8—442no—
458C2×Q8—881no—
459C2×Q8Q8×D1112yes—
460C2×D4—112no—
461C2×D4—112no—
462C2×D4—112no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—224no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4—881no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489SD16—228no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8D4×D1112yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—112no—
509C4⋊C4—112no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C4⋊C4—881no—
521C4⋊C4—881no—
522C22⋊C4—224no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C42—21no—
526C42—21no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—442no—
532C11#2637211yescharacteristic, complemented, Sylow
533C23—222no—
534C23—222no—
535C23—222no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23C2×D4×D1111yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—884no—
546D4—114no—
547D4—222no—
548D4—222no—
549D4—222no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—112no—
569C2×C4—112no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—222no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—222no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—884no—
590C2×C4—884no—
591C2×C4—884no—
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4#6703711yescharacteristic
594C2×C4C2×Q8×D1111yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#41×D1111yescharacteristic
597C2×C4#6704311yescharacteristic
598C8—22no—
599C8—41no—
600C8—222no—
601C8—441no—
602C22—224no—
603C22—442no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—442no—
608C22—442no—
609C22#1062316311yescharacteristic
610C22#1062318711yescharacteristic
611C22#1062324811yescharacteristic
612C22D11×#13511yescharacteristic
613C22#1062330011yescharacteristic
614C22D11×#13711yescharacteristic
615C22#1062330911yescharacteristic
616C4—41no—
617C4—42no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—222no—
623C4—222no—
624C4—442no—
625C4—441no—
626C4—441no—
627C4—442no—
628C4—881no—
629C4D11×C22⋊Q811yescharacteristic
630C4#1062316711yescharacteristic
631C4#1062318611yescharacteristic
632C4#1062319111yescharacteristic
633C2—444no—
634C2#1307242811yescharacteristic
635C2#1307868211yescharacteristic
636C2#1307880311yescharacteristic
637C2#1308012511yescharacteristic
638C2#1308030011yescharacteristic
639C2#1308149411yescharacteristic
640C2#1308152911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2097C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2097D11
hypocenterC11#26372
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2097

Complements

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

NH ≅ G/Ntype
3. #13072458C2semidirect
5. #13070098C2semidirect
6. #13070009C2semidirect
7. #13069947C2semidirect
8. #13069347C2semidirect
9. #13069174C2semidirect
13. #13068868C2semidirect
15. C11×#2097C2semidirect
77. C2×#4325Q8semidirect
217. #2097D11semidirect
532. C11#26372semidirect

Maximal subgroups

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

subgroupindex
C2×#106225032
C2×#106224012
#130724582
#130715242
#130700982
#130700092
#130699472
#130693472
#130691742
#130689532
#130689472
#130688742
#130688682
#130688662
C11×#20972
#2637211