Finite Group Databasebeta

← #14816633

Subgroups — #14816633

Order 2816.

812 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622635C211yesmaximal, characteristic, complemented
2C2×#10622494C211yesmaximal, characteristic
3#13072331C211yesmaximal, characteristic
4#13071617C211yesmaximal, characteristic
5#13070152C211yesmaximal, characteristic, complemented
6#13070107C211yesmaximal, characteristic, complemented
7#13069995C211yesmaximal, characteristic, complemented
8#13069955C211yesmaximal, characteristic, complemented
9#13069371C211yesmaximal, characteristic, complemented
10#13069192C211yesmaximal, characteristic, complemented
11#13069046C211yesmaximal, characteristic
12#13068925C211yesmaximal, characteristic
13#13068805C211yesmaximal, characteristic
14#13068800C211yesmaximal, characteristic
15C11×#1863C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#389C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33#10622635—24no—
34#10622605—21no—
35#10622602—21no—
36#10622600C2211yescharacteristic
37#10622589C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622586C2211yescharacteristic
40#10622585—21no—
41#10622585—21no—
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C4×(C2×D11)⋊C4—21no—
46C4×(C2×D11)⋊C4C2211yescharacteristic
47#10622546—21no—
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622494—24no—
51#10622289—21no—
52#10622265—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75#66999—22no—
76#66999Q814yes—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4D411yescharacteristic
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×#4313—22no—
100C2×#4313—22no—
101C2×#4313—22no—
102#66945—22no—
103#66945—41no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—41no—
106#66923—22no—
107#66923—41no—
108C11×#107—22no—
109C11×#103—22no—
110C11×#103—41no—
111C11×#95—21no—
112#66899—22no—
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(C2×D11)⋊C8—22no—
123#66882—41no—
124#66881—22no—
125Dic11⋊C8—22no—
126#66872D414yes—
127#66871—22no—
128#66871—22no—
129C4⋊(C11⋊C8)—22no—
130#26362—111nomaximal, Sylow
131C23×D11C2×D411yescharacteristic
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×Dic11—21no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—81no—
159C2×C4×D11C2×Q812yes—
160C2×C4×D11#4112yes—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11#4112yes—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4C2×D412yes—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—42no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—24no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—81no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11C2×D412yes—
190C4⋊Dic11C2×Q812yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—81no—
198Dic11⋊C4—81no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—42no—
202C4×Dic11—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C2×D412yes—
209#4313—28no—
210C2×#479—111no—
211C2×#428—111no—
212#2441—111no—
213#2360—111no—
214#2095—111no—
215#2086—111no—
216#2066—111no—
217#2059—111no—
218#1947—111no—
219#1919—111no—
220#1894—111no—
221#1873—111no—
222#1863D1111yescharacteristic, complemented
223#1852—111no—
224#1851—111no—
225C23×C11C22×D411yescharacteristic
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11C22⋊Q812yes—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—41no—
236Q8×C11—41no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
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×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11C22⋊Q812yes—
281C2×Dic11#13712yes—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—84no—
287C8×C11—22no—
288C8×C11—41no—
289C11⋊C8—22no—
290C11⋊C8—41no—
291C22×M16—111no—
292C2×#125—111no—
293C2×C22⋊Q8—111no—
294C2×C4×Q8C2×D1111yescharacteristic
295C2×#117—111no—
296C22×C4⋊C4—111no—
297#479—224no—
298#428—224no—
299C2×#107—111no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#107C2×D1111yescharacteristic
303C2×#106—111no—
304C2×#106—111no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103C2×D1111yescharacteristic
310C2×#103C2×D1111yescharacteristic
311C2×C22⋊C8—111no—
312#399—221no—
313#396—221no—
314#391—111no—
315#389—111no—
316#389—111no—
317#389—221no—
318#389—221no—
319#389C2×D1111yescharacteristic
320#387—221no—
321#387—221no—
322#385—221no—
323#384—111no—
324#380—111no—
325C4×C4⋊C4—111no—
326C4×C22⋊C4—111no—
327C4×C22⋊C4—221no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340C2×D1111yescharacteristic
334#336—111no—
335#336C2×D1111yescharacteristic
336C22×C11C2×C22⋊Q811yescharacteristic
337C22×C11D4211yescharacteristic
338C22×C11#54711yescharacteristic
339C22×C11C2×#13711yescharacteristic
340C22×C11#57511yescharacteristic
341C22×C11#57611yescharacteristic
342C22×C11#57811yescharacteristic
343C2×D11—22no—
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11#52511yescharacteristic
357C4×C11#53911yescharacteristic
358C4×C11D4×Q811yescharacteristic
359C4×C11#55411yescharacteristic
360Dic11—22no—
361Dic11—22no—
362Dic11—42no—
363Dic11—41no—
364Dic11—42no—
365Dic11—81no—
366Dic11—81no—
367C22×Q8C22×D1111yescharacteristic
368C23×C4—111no—
369C23×C4—221no—
370C2×M16—222no—
371C2×M16—222no—
372C2×M16—222no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377#125—222no—
378#125—441no—
379C22⋊Q8—114no—
380C22⋊Q8—222no—
381C4×Q8—22no—
382C4×Q8—41no—
383#117—222no—
384#117—441no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—441no—
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—111no—
405C2×C22⋊C4—111no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C42—21no—
410C2×C42—111no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42C22×D1111yescharacteristic
414#107—22no—
415#107—222no—
416#107—222no—
417#107—441no—
418#106—114no—
419#106—222no—
420C4⋊C8—222no—
421C4⋊C8—222no—
422#103—22no—
423#103—41no—
424#103—222no—
425#103—222no—
426C22⋊C8—222no—
427#95—21no—
428#95—111no—
429#95—111no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436C2×C11#244911yescharacteristic
437C2×C11#307811yescharacteristic
438C2×C11#308311yescharacteristic
439C2×C11#326811yescharacteristic
440C2×C11#327611yescharacteristic
441C2×C11#334611yescharacteristic
442C2×C11#335211yescharacteristic
443D11—42no—
444C24—111no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8Q8×D1112yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—111no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4—881no—
471C22×C4D4×D1111yescharacteristic
472C22×C4D4×D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474M16—228no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—112no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8#433912yes—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—81no—
494C4⋊C4—112no—
495C4⋊C4—112no—
496C4⋊C4—224no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—881no—
509C4⋊C4—881no—
510C4⋊C4D4×D1112yes—
511C22⋊C4—222no—
512C22⋊C4—224no—
513C22⋊C4—441no—
514C22⋊C4—442no—
515C22⋊C4—881no—
516C42—21no—
517C42—21no—
518C42—42no—
519C42—221no—
520C42—221no—
521C42—442no—
522C42—881no—
523C11#2636211yescharacteristic, complemented, Sylow
524C23—112no—
525C23—221no—
526C23—221no—
527C23—221no—
528C23—221no—
529C23—221no—
530C23—221no—
531C23C2×D4×D1111yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—41no—
535Q8—41no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—884no—
580C2×C4C2×#433911yescharacteristic
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4#6703711yescharacteristic
583C2×C4C2×Q8×D1111yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#6704311yescharacteristic
586C8—22no—
587C8—41no—
588C8—222no—
589C8—441no—
590C22—222no—
591C22—222no—
592C22—222no—
593C22—441no—
594C22—441no—
595C22—441no—
596C22—441no—
597C22#1062308211yescharacteristic
598C22#1062312111yescharacteristic
599C22D11×C22⋊Q811yescharacteristic
600C22#1062329711yescharacteristic
601C22#1062329911yescharacteristic
602C22#1062330511yescharacteristic
603C22D11×#13711yescharacteristic
604C4—42no—
605C4—41no—
606C4—42no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4—222no—
611C4—222no—
612C4—441no—
613C4—442no—
614C4—442no—
615C4—881no—
616C4—881no—
617C4#1062304211yescharacteristic
618C4#1062307811yescharacteristic
619C4#1062316311yescharacteristic
620C4#1062319111yescharacteristic
621C2—442no—
622C2#1307242411yescharacteristic
623C2#1307841911yescharacteristic
624C2#1307846411yescharacteristic
625C2#1308016011yescharacteristic
626C2#1308025511yescharacteristic
627C2#1308110611yescharacteristic
628C2#1308119211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1863C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1863D11
hypocenterC11#26362
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
1. C2×#10622635C2semidirect
5. #13070152C2semidirect
6. #13070107C2semidirect
7. #13069995C2semidirect
8. #13069955C2semidirect
9. #13069371C2semidirect
10. #13069192C2semidirect
15. C11×#1863C2semidirect
222. #1863D11semidirect
523. C11#26362semidirect

Maximal subgroups

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

subgroupindex
C2×#106226352
C2×#106224942
#130723312
#130716172
#130701522
#130701072
#130699952
#130699552
#130693712
#130691922
#130690462
#130689252
#130688052
#130688002
C11×#18632
#2636211