Finite Group Databasebeta

← #14812629

Subgroups — #14812629

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622469C211yesmaximal, characteristic, complemented
2C2×#10622577C211yesmaximal, characteristic
3#13072330C211yesmaximal, characteristic
4#13072312C211yesmaximal, characteristic
5#13070095C211yesmaximal, characteristic, complemented
6#13070091C211yesmaximal, characteristic, complemented
7#13069956C211yesmaximal, characteristic, complemented
8#13069948C211yesmaximal, characteristic, complemented
9#13069353C211yesmaximal, characteristic, complemented
10#13069348C211yesmaximal, characteristic, complemented
11#13068817C211yesmaximal, characteristic
12#13068771C211yesmaximal, characteristic, complemented
13#13068647C211yesmaximal, characteristic
14#13068402C211yesmaximal, characteristic
15C11×#1853C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66977—21no—
19C22×#4318C2211yescharacteristic
20C2×#66943C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C11×#380C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622823—21no—
28C4×C22⋊Dic11C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622597—21no—
36#10622592—21no—
37#10622589C2211yescharacteristic
38#10622589C2211yescharacteristic
39#10622586C2211yescharacteristic
40#10622586C2211yescharacteristic
41#10622577—24no—
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622562—21no—
49#10622561—21no—
50#10622469—24no—
51#10622268—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×Dic22—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11D411yescharacteristic
77C2×C22⋊Dic11D411yescharacteristic
78#66979—22no—
79#66979—41no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87#66977—44no—
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×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318Q814yescomplemented
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66943—22no—
105#66943—41no—
106#66941—22no—
107#66941—41no—
108C11×#106—22no—
109C11×#106—41no—
110C11×C22⋊C8Q814yescomplemented
111C11×#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119#66882—22no—
120#66881—41no—
121#66879—22no—
122C8×Dic11—22no—
123#66872—22no—
124#66872—22no—
125#66872—22no—
126#66871—22no—
127#66871—22no—
128#66871D414yes—
129#26078—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—81no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×Q812yes—
144C22×C4×C11C2×Q812yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×Dic22—42no—
155C2×Dic22—42no—
156C2×Dic22—81no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C2×Q812yes—
162C2×C8×C11C2×Q812yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4C2×D412yes—
172C11×C22⋊C4—81no—
173C22⋊Dic11—22no—
174C22⋊Dic11—22no—
175C22⋊Dic11—42no—
176C22⋊Dic11—42no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—42no—
185C4⋊Dic11—42no—
186C4⋊Dic11—81no—
187C4⋊Dic11C2×D412yes—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—42no—
201#4318—28no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C2×D412yes—
205C2×C11⋊C8C2×Q812yes—
206C2×C11⋊C8C2×Q812yes—
207C2×C11⋊C8#4112yes—
208C2×#501—111no—
209C2×#428—111no—
210#2441—111no—
211#2440—111no—
212#2084—111no—
213#2083—111no—
214#2059—111no—
215#2058—111no—
216#1943—111no—
217#1942—111no—
218#1854—111no—
219#1853D1111yescharacteristic
220#1844—111no—
221#1809—111no—
222#1753—111no—
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—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—84no—
250C2×C4×C11C4⋊Q812yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×Q811yescharacteristic
253C2×C4×C11C22×Q811yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
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×Dic11AGL(1,ℤ/8)12yes—
280C2×Dic11#13712yes—
281Dic22—84no—
282C8×C11—22no—
283C8×C11—22no—
284C11⋊C8—22no—
285C11⋊C8C22⋊Q814yescomplemented
286C22×M16—111no—
287C2×C4⋊Q8—111no—
288C2×#125—111no—
289C2×C22⋊Q8—221no—
290C2×#117—111no—
291C22×C4⋊C4C2×D1111yescharacteristic
292#501—224no—
293#428—224no—
294C2×#107—111no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#107—111no—
298C2×#106—111no—
299C2×#106—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×#106C2×D1111yescharacteristic
303C2×#106C2×D1111yescharacteristic
304C2×C22⋊C8C2×D1111yescharacteristic
305C2×#97—111no—
306C2×C4×C8—111no—
307#399—221no—
308#398—221no—
309#396—221no—
310#395—221no—
311#389—111no—
312#389—111no—
313#389—111no—
314#389—111no—
315#389—221no—
316#387—221no—
317#385—221no—
318#384—111no—
319#384—111no—
320#380—111no—
321#380C2×D1111yescharacteristic
322C4×C22⋊C4—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340C2×D1111yescharacteristic
328#340C2×D1111yescharacteristic
329#336—111no—
330#336—111no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11C2×C4⋊Q811yescharacteristic
339C22×C11D4211yescharacteristic
340C22×C11#54711yescharacteristic
341C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57711yescharacteristic
344C22×C11#57711yescharacteristic
345C4×C11—22no—
346C4×C11—42no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11C2×C22⋊Q811yescharacteristic
351C4×C11#54411yescharacteristic
352C4×C11D4×Q811yescharacteristic
353C4×C11#55411yescharacteristic
354Dic11—22no—
355Dic11—22no—
356Dic11—41no—
357Dic11—42no—
358Dic11—41no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8—221no—
363C23×C4—21no—
364C23×C4C22×D1111yescharacteristic
365C2×M16—114no—
366C2×M16—222no—
367C2×M16—222no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C4⋊Q8—222no—
373C4⋊Q8—441no—
374#125—222no—
375#125—441no—
376C22⋊Q8—444no—
377#117—222no—
378#117—441no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
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⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—111no—
403C2×C22⋊C4—111no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—221no—
409#107—114no—
410#107—222no—
411#107—222no—
412#107—222no—
413#106—22no—
414#106—41no—
415#106—222no—
416#106—222no—
417#106—222no—
418#106—441no—
419C22⋊C8Dic2214yescomplemented
420#97—222no—
421C4×C8—222no—
422#95—21no—
423#95—111no—
424#95—111no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430C2×C11—42no—
431C2×C11#244011yescharacteristic
432C2×C11#316311yescharacteristic
433C2×C11#316511yescharacteristic
434C2×C11#327211yescharacteristic
435C2×C11#327811yescharacteristic
436C2×C11#334411yescharacteristic
437C2×C11#334511yescharacteristic
438C24D4×D1111yescharacteristic
439C2×Q8—442no—
440C2×Q8—442no—
441C2×Q8—881no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—81no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4C2×Dic2212yes—
462C22×C4D4×D1111yescharacteristic
463C22×C4Q8×D1112yes—
464C22×C4C23×D1111yescharacteristic
465M16—228no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—112no—
471C2×C8—112no—
472C2×C8—112no—
473C2×C8—112no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8C2×Dic2212yes—
477C2×C8C2×Dic2212yes—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—112no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4—442no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—881no—
503C4⋊C4—881no—
504C4⋊C4—881no—
505C4⋊C4D4×D1112yes—
506C22⋊C4—81no—
507C22⋊C4—222no—
508C22⋊C4—222no—
509C22⋊C4—442no—
510C22⋊C4—442no—
511C42—221no—
512C42—221no—
513C42—221no—
514C42—221no—
515C42—442no—
516C11#2607811yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#6694112yes—
524C23C2×D4×D1111yescharacteristic
525Q8—884no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—84no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—222no—
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—441no—
569C2×C4#6694112yes—
570C2×C4C22×Dic2211yescharacteristic
571C2×C4C2×D4×D1111yescharacteristic
572C2×C4#6703711yescharacteristic
573C2×C4C2×Q8×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#6704311yescharacteristic
576C8—22no—
577C8—22no—
578C8—114no—
579C8—222no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×#6694111yescharacteristic
588C22#1062312111yescharacteristic
589C22#1062318611yescharacteristic
590C22#1062329311yescharacteristic
591C22#1062329311yescharacteristic
592C22D11×AGL(1,ℤ/8)11yescharacteristic
593C22D11×#13711yescharacteristic
594C4—22no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—222no—
600C4—222no—
601C4—441no—
602C4—442no—
603C4—441no—
604C4—881no—
605C4—881no—
606C4—881no—
607C4D4×Dic2211yescharacteristic
608C4#1062307011yescharacteristic
609C4#1062315411yescharacteristic
610C4D11×C22⋊Q811yescharacteristic
611C2—42no—
612C2#1307231711yescharacteristic
613C2#1307914411yescharacteristic
614C2#1307916011yescharacteristic
615C2#1308021411yescharacteristic
616C2#1308028011yescharacteristic
617C2#1308107411yescharacteristic
618C2#1308107911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1853C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1853D11
hypocenterC11#26078
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
1. C2×#10622469C2semidirect
5. #13070095C2semidirect
6. #13070091C2semidirect
7. #13069956C2semidirect
8. #13069948C2semidirect
9. #13069353C2semidirect
10. #13069348C2semidirect
12. #13068771C2semidirect
101. C2×#4318Q8semidirect
110. C11×C22⋊C8Q8semidirect
285. C11⋊C8C22⋊Q8semidirect
419. C22⋊C8Dic22semidirect
516. C11#26078semidirect

Maximal subgroups

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

subgroupindex
C2×#106224692
C2×#106225772
#130723302
#130723122
#130700952
#130700912
#130699562
#130699482
#130693532
#130693482
#130688172
#130687712
#130686472
#130684022
C11×#18532
#2607811