Finite Group Databasebeta

← #14775643

Subgroups — #14775643

Order 2816.

914 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×#10622503C211yesmaximal, characteristic
2#13071669C211yesmaximal, characteristic, complemented
3#13071517C211yesmaximal, characteristic
4#13069575C211yesmaximal, characteristic, complemented
5#13069376C211yesmaximal, characteristic, complemented
6#13069353C211yesmaximal, characteristic, complemented
7#13069210C211yesmaximal, characteristic, complemented
8#13069205C211yesmaximal, characteristic, complemented
9#13068876C211yesmaximal, characteristic
10#13068874C211yesmaximal, characteristic
11#13068484C211yesmaximal, characteristic, complemented
12#13068442C211yesmaximal, characteristic
13#13068440C211yesmaximal, characteristic
14#13068430C211yesmaximal, characteristic
15C11×#1943C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×C4⋊C4×D11—21no—
19C2×#66941C2211yescharacteristic
20C2×#66940—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622602—21no—
33#10622598C2211yescharacteristic
34#10622591—21no—
35#10622589C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C4×Dic11⋊C4C2211yescharacteristic
45#10622503C418yescomplemented
46#10622281—21no—
47#10622280—21no—
48#10622265—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×Dic22—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4D411yescharacteristic
86C2×Dic11⋊C4D411yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66946—22no—
95#66946—22no—
96#66946—41no—
97#66946C2×C414yes—
98C4⋊C4×D11—44no—
99#66941—22no—
100#66941C2×C414yescomplemented
101#66940—44no—
102C4×D44—22no—
103C4×D44—41no—
104C11×#107C2×C414yescomplemented
105C11×#106—41no—
106C11×#97—41no—
107C11×#95—21no—
108C11×#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116#66885C2×C414yes—
117#66885Q814yescomplemented
118#66879—41no—
119Dic11⋊C8C2×C414yescomplemented
120C8×Dic11—22no—
121#66873—22no—
122#66873C2×C414yes—
123#66872—41no—
124#66871C2×C414yescomplemented
125#22968—111nomaximal, Sylow
126C23×D11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44C22×C412yes—
145C2×D44C2×Q812yes—
146C2×D44#4112yes—
147C2×C4×D11—24no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—81no—
155C2×C4×D11—81no—
156C2×Dic22—24no—
157C2×Dic22—42no—
158C2×Dic22—42no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C22×C412yes—
164C2×C8×C11C2×Q812yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4C22×C412yes—
174C11×C4⋊C4C22×C412yes—
175C42×C11—21no—
176C42×C11—21no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—42no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—42no—
185C4⋊Dic11C22×C412yes—
186C4⋊Dic11C2×Q812yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—81no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—42no—
196C4×Dic11—42no—
197C4×Dic11—42no—
198C4×Dic11C22×C412yes—
199C4×Dic11#4112yes—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C22×C412yes—
206C2×#474—111no—
207#2365—111no—
208D4×C4⋊C4—111no—
209#1990—111no—
210#1948—111no—
211#1943—111no—
212#1943D1111yescharacteristic, complemented
213#1921—111no—
214#1921—111no—
215#1864—111no—
216#1864—111no—
217#1770—111no—
218#1762—111no—
219#1762—111no—
220C4×#102—111no—
221C23×C11C22×D411yescharacteristic
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
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—41no—
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×C11C23×C411yescharacteristic
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11C4×D412yes—
271C2×Dic11C4×D412yes—
272C2×Dic11AGL(1,ℤ/8)12yes—
273C2×Dic11AGL(1,ℤ/8)12yes—
274D44—22no—
275D44—22no—
276D44—22no—
277D44C4×Q814yescomplemented
278C4×D11—48no—
279C4×D11—84no—
280C4×D11—84no—
281Dic22—48no—
282C8×C11—22no—
283C8×C11—22no—
284C11⋊C8—22no—
285C11⋊C8—41no—
286C2×C4⋊Q8—111no—
287C2×C4×Q8—221no—
288C2×C4×D4—111no—
289C2×C4×D4—111no—
290C2×C4×D4—111no—
291C22×C4⋊C4—221no—
292#474—118no—
293C2×#107—111no—
294C2×#107C2×D1111yescharacteristic
295C2×#106—111no—
296C2×#106C2×D1111yescharacteristic
297C2×C4⋊C8—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×#97—111no—
303C2×#97C2×D1111yescharacteristic
304C2×C4×C8—111no—
305#391—221no—
306#389—111no—
307#389—111no—
308#389C2×D1111yescharacteristic
309#389C2×D1111yescharacteristic
310#387—221no—
311#387—221no—
312#385—221no—
313#385—221no—
314#384—111no—
315#380—221no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—111no—
319C4×C4⋊C4—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340C2×D1111yescharacteristic
327#340C2×D1111yescharacteristic
328#336—111no—
329#336—111no—
330C22×C11C2×C4×D411yescharacteristic
331C22×C11#54611yescharacteristic
332C22×C11D4×Q811yescharacteristic
333C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C11#57711yescharacteristic
336C22×C11#57811yescharacteristic
337C2×D11—24no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—42no—
344C4×C11—41no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11C2×C4×Q811yescharacteristic
351C4×C11#52011yescharacteristic
352C4×C11#55211yescharacteristic
353C4×C11#55411yescharacteristic
354Dic11—22no—
355Dic11—41no—
356Dic11—42no—
357Dic11—42no—
358Dic11—41no—
359Dic11—81no—
360Dic11#44214yes—
361C22×Q8—221no—
362C22×D4—111no—
363C23×C4—221no—
364C23×C4—221no—
365C23×C4—221no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C4⋊Q8—114no—
371C4⋊Q8—222no—
372C4×Q8—444no—
373C4×D4—114no—
374C4×D4—222no—
375C4×D4—222no—
376C4×D4—222no—
377C4×D4—441no—
378C4×D4—441no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—111no—
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—444no—
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42C22×D1111yescharacteristic
405#107—114no—
406#107C4×D1114yescomplemented
407#106—41no—
408#106—441no—
409C4⋊C8—114no—
410#102—114no—
411#102—114no—
412#102—114no—
413#102—222no—
414#97—41no—
415#97—441no—
416C4×C8—222no—
417#95—21no—
418#95—21no—
419#95—111no—
420#95—111no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426C2×C11#236011yescharacteristic
427C2×C11C2×#44211yescharacteristic
428C2×C11#294711yescharacteristic
429C2×C11#332411yescharacteristic
430C2×C11#333011yescharacteristic
431C2×C11#338411yescharacteristic
432C2×C11#338611yescharacteristic
433D11—44no—
434C24—221no—
435C2×Q8—224no—
436C2×Q8—442no—
437C2×Q8—442no—
438C2×D4—112no—
439C2×D4—112no—
440C2×D4—112no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—224no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—881no—
463C22×C4—881no—
464C22×C4D4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4C23×D1111yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—112no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8C2×C4×D1112yes—
478C2×C8Q8×D1112yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—112no—
488C4⋊C4—112no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—224no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—442no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—881no—
500C4⋊C4C2×C4×D1112yes—
501C4⋊C4C2×C4×D1112yes—
502C22⋊C4—224no—
503C22⋊C4—442no—
504C22⋊C4—442no—
505C42—21no—
506C42—21no—
507C42—112no—
508C42—112no—
509C42—221no—
510C42—221no—
511C42—442no—
512C42—442no—
513C42—442no—
514C11#2296811yescharacteristic, complemented, Sylow
515C23—222no—
516C23—222no—
517C23—222no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23—441no—
522C23C2×D4×D1111yescharacteristic
523Q8—448no—
524D4—114no—
525D4—222no—
526D4—222no—
527D4—222no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
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—41no—
545C2×C4—41no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—112no—
549C2×C4—112no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—222no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—222no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—448no—
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—884no—
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4#6703711yescharacteristic
572C2×C4C2×Q8×D1111yescharacteristic
573C2×C4#6704011yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C8—22no—
577C8—22no—
578C8—222no—
579C8—441no—
580C22—224no—
581C22—442no—
582C22—442no—
583C22—442no—
584C22—442no—
585C22—442no—
586C22—442no—
587C22C4×D4×D1111yescharacteristic
588C22#1062314111yescharacteristic
589C22#1062325811yescharacteristic
590C22D11×AGL(1,ℤ/8)11yescharacteristic
591C22D11×AGL(1,ℤ/8)11yescharacteristic
592C22#1062330911yescharacteristic
593C22#1062331011yescharacteristic
594C4—41no—
595C4—41no—
596C4—42no—
597C4—42no—
598C4—81no—
599C4—81no—
600C4—114no—
601C4—222no—
602C4—441no—
603C4—441no—
604C4—442no—
605C4—442no—
606C4—881no—
607C4#1062303511yescharacteristic
608C4C4×Q8×D1111yescharacteristic
609C4#1062316711yescharacteristic
610C4#1062322411yescharacteristic
611C2—444no—
612C2#1307161811yescharacteristic
613C2D11×#44211yescharacteristic
614C2#1307745811yescharacteristic
615C2#1308084211yescharacteristic
616C2#1308091611yescharacteristic
617C2#1308151211yescharacteristic
618C2#1308153411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1943C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1943D11
hypocenterC11#22968
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
2. #13071669C2semidirect
4. #13069575C2semidirect
5. #13069376C2semidirect
6. #13069353C2semidirect
7. #13069210C2semidirect
8. #13069205C2semidirect
11. #13068484C2semidirect
15. C11×#1943C2semidirect
45. #10622503C4semidirect
100. #66941C2×C4semidirect
104. C11×#107C2×C4semidirect
117. #66885Q8semidirect
119. Dic11⋊C8C2×C4semidirect
124. #66871C2×C4semidirect
212. #1943D11semidirect
277. D44C4×Q8semidirect
406. #107C4×D11semidirect
514. C11#22968semidirect

Maximal subgroups

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

subgroupindex
C2×#106225032
#130716692
#130715172
#130695752
#130693762
#130693532
#130692102
#130692052
#130688762
#130688742
#130684842
#130684422
#130684402
#130684302
C11×#19432
#2296811