Finite Group Databasebeta

← #14812570

Subgroups — #14812570

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622295C211yesmaximal, characteristic, complemented
2C2×#10622734C211yesmaximal, characteristic
3#13072318C211yesmaximal, characteristic
4#13072307C211yesmaximal, characteristic
5#13070099C211yesmaximal, characteristic, complemented
6#13070089C211yesmaximal, characteristic, complemented
7#13069950C211yesmaximal, characteristic, complemented
8#13069945C211yesmaximal, characteristic, complemented
9#13069354C211yesmaximal, characteristic, complemented
10#13069344C211yesmaximal, characteristic, complemented
11#13068817C211yesmaximal, characteristic
12#13068806C211yesmaximal, characteristic
13#13068784C211yesmaximal, characteristic, complemented
14#13068649C211yesmaximal, characteristic
15C11×#1753C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66931—21no—
20C2×#66922C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622825C2211yescharacteristic
28#10622734—24no—
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66881C2211yescharacteristic
39#10622563—21no—
40#10622561—21no—
41#10622560—21no—
42#10622549C2211yescharacteristic
43#10622548C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622295—24no—
49#10622274—21no—
50#10622269—21no—
51#10622268—21no—
52#10622259—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22—21no—
64C22×Dic22—21no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16Q814yescomplemented
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66979—22no—
80#66979—41no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—41no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101#66931—44no—
102#66922—22no—
103#66922—22no—
104#66922—41no—
105#66922—41no—
106C11×C22⋊C8Q814yescomplemented
107C11×#97—22no—
108C4×C8×C11—22no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#66882—22no—
120#66882—22no—
121#66882—22no—
122#66882—22no—
123#66882—41no—
124#66882D414yes—
125#66881—22no—
126#66881—22no—
127#66881—22no—
128#66881—41no—
129#26074—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×Q812yes—
141C22×C4×C11C2×Q812yes—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—81no—
154C2×Dic22—42no—
155C2×Dic22—42no—
156C2×Dic22—42no—
157C2×Dic22—42no—
158C2×Dic22—81no—
159C2×Dic22—81no—
160C11×M16—28no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C2×D412yes—
168C2×C8×C11C2×Q812yes—
169C2×C8×C11C2×Q812yes—
170C2×C8×C11C2×Q812yes—
171C2×C8×C11C2×Q812yes—
172C2×C8×C11#4112yes—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C22⋊Dic11—42no—
180C22⋊Dic11—42no—
181C22⋊Dic11—81no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11—81no—
201C4⋊Dic11C2×D412yes—
202C4⋊Dic11C2×D412yes—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—81no—
207C4×Dic11—42no—
208C2×#500—111no—
209C2×#428—111no—
210#2440—111no—
211#2439—111no—
212#2085—111no—
213#2083—111no—
214#2058—111no—
215#2057—111no—
216#1943—111no—
217#1941—111no—
218#1854—111no—
219#1852—111no—
220#1847—111no—
221#1809—111no—
222#1753D1111yescharacteristic
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11C4⋊Q812yes—
230C23×C11C22×D411yescharacteristic
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11C4⋊Q812yes—
248C2×C4×C11AGL(1,ℤ/8)12yes—
249C2×C4×C11#13712yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×Q811yescharacteristic
252C2×C4×C11C22×Q811yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
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×Dic11—84no—
281Dic22—84no—
282Dic22—84no—
283C8×C11—22no—
284C8×C11—22no—
285C8×C11—22no—
286C8×C11C22⋊Q814yescomplemented
287C22×M16C2×D1111yescharacteristic
288C2×C4⋊Q8—111no—
289C2×C4⋊Q8—111no—
290C2×C22⋊Q8—221no—
291C2×#117—111no—
292C22×C4⋊C4—111no—
293#500—224no—
294#428—224no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#107—111no—
298C2×#107—111no—
299C2×#107—111no—
300C2×#107—111no—
301C2×#106—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×#106—111no—
305C2×C22⋊C8C2×D1111yescharacteristic
306C2×#97C2×D1111yescharacteristic
307C2×C4×C8C2×D1111yescharacteristic
308#398—221no—
309#396—221no—
310#395—221no—
311#393—221no—
312#391—221no—
313#389—111no—
314#389—111no—
315#389—111no—
316#389—111no—
317#387—221no—
318#385—221no—
319#384—111no—
320#382—111no—
321#380—111no—
322#380—111no—
323C4×C22⋊C4C2×D1111yescharacteristic
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#336C2×D1111yescharacteristic
331#336C2×D1111yescharacteristic
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×C4⋊Q811yescharacteristic
340C22×C11D4211yescharacteristic
341C22×C11#54711yescharacteristic
342C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C11C2×#13711yescharacteristic
344C22×C11#57611yescharacteristic
345C22×C11#57811yescharacteristic
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11C2×C22⋊Q811yescharacteristic
352C4×C11#54411yescharacteristic
353C4×C11D4×Q811yescharacteristic
354C4×C11#55411yescharacteristic
355Dic11—42no—
356Dic11—42no—
357Dic11—81no—
358Dic11—81no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—221no—
364C22×Q8—221no—
365C23×C4—221no—
366C23×C4C22×D1111yescharacteristic
367C2×M16—22no—
368C2×M16—22no—
369C2×M16Dic2214yescomplemented
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C4⋊Q8—222no—
375C4⋊Q8—222no—
376C4⋊Q8—441no—
377C4⋊Q8—441no—
378C22⋊Q8—444no—
379#117—222no—
380#117—441no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
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—441no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4D4411yescharacteristic
404C2×C22⋊C4D4411yescharacteristic
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408#107—114no—
409#107—222no—
410#107—222no—
411#107—222no—
412#107—222no—
413#107—441no—
414#106—222no—
415#106—222no—
416#106—222no—
417#106—441no—
418C22⋊C8Dic2214yescomplemented
419#97—22no—
420C4×C8—22no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95D4411yescharacteristic
430#95D4411yescharacteristic
431C2×C11—42no—
432C2×C11#244011yescharacteristic
433C2×C11#316411yescharacteristic
434C2×C11#316511yescharacteristic
435C2×C11#326411yescharacteristic
436C2×C11#327011yescharacteristic
437C2×C11#335311yescharacteristic
438C2×C11#335711yescharacteristic
439C24C2×D4411yescharacteristic
440C2×Q8—442no—
441C2×Q8—442no—
442C2×Q8—442no—
443C2×Q8—442no—
444C2×Q8—881no—
445C2×Q8—881no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4—881no—
461C22×C4C2×Dic2212yes—
462C22×C4C2×Dic2212yes—
463C22×C4C2×D4411yescharacteristic
464C22×C4C2×D4411yescharacteristic
465C22×C4C2×D4411yescharacteristic
466C22×C4C2×D4411yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C23×D1111yescharacteristic
469M16—28no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8C2×Dic2212yes—
477C2×C8C2×Dic2212yes—
478C2×C8C2×Dic2212yes—
479C2×C8C2×Dic2212yes—
480C2×C8D4×D1112yes—
481C2×C8#434112yes—
482C4⋊C4—112no—
483C4⋊C4—112no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—881no—
506C4⋊C4—881no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—442no—
510C22⋊C4—442no—
511C22⋊C4—881no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—442no—
517C11#2607411yescharacteristic, complemented, Sylow
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23#6692212yes—
525C23C22×D4411yescharacteristic
526Q8—884no—
527Q8—884no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—884no—
569C2×C4#6692212yes—
570C2×C4#6696112yes—
571C2×C4#6696212yes—
572C2×C4C22×Dic2211yescharacteristic
573C2×C4C22×Dic2211yescharacteristic
574C2×C4C2×D4×D1111yescharacteristic
575C2×C4C2×#434111yescharacteristic
576C2×C4#6704211yescharacteristic
577C2×C4#6704311yescharacteristic
578C8—22no—
579C8—22no—
580C8—22no—
581C8#6693114yescomplemented
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22C2×#6692211yescharacteristic
590C22D4×D4411yescharacteristic
591C22#1062308611yescharacteristic
592C22C2×#6696111yescharacteristic
593C22C2×#6696211yescharacteristic
594C22#1062328311yescharacteristic
595C22#1062328411yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—41no—
600C4—41no—
601C4—442no—
602C4—442no—
603C4—881no—
604C4—881no—
605C4—881no—
606C4—881no—
607C4—881no—
608C4—881no—
609C4C2×#6693111yescharacteristic
610C4#1062305011yescharacteristic
611C4D4×Dic2211yescharacteristic
612C4#1062307411yescharacteristic
613C2—42no—
614C2#1307231811yescharacteristic
615C2#1307915511yescharacteristic
616C2#1307916211yescharacteristic
617C2#1308010111yescharacteristic
618C2#1308019111yescharacteristic
619C2#1308120111yescharacteristic
620C2#1308124311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1753D11
hypocenterC11#26074
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#10622295C2semidirect
5. #13070099C2semidirect
6. #13070089C2semidirect
7. #13069950C2semidirect
8. #13069945C2semidirect
9. #13069354C2semidirect
10. #13069344C2semidirect
13. #13068784C2semidirect
67. C2×C11×M16Q8semidirect
106. C11×C22⋊C8Q8semidirect
286. C8×C11C22⋊Q8semidirect
369. C2×M16Dic22semidirect
418. C22⋊C8Dic22semidirect
517. C11#26074semidirect
581. C8#66931semidirect

Maximal subgroups

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

subgroupindex
C2×#106222952
C2×#106227342
#130723182
#130723072
#130700992
#130700892
#130699502
#130699452
#130693542
#130693442
#130688172
#130688062
#130687842
#130686492
C11×#17532
#2607411