Finite Group Databasebeta

← #14775166

Subgroups — #14775166

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622584C211yesmaximal, characteristic
2#13071621C211yesmaximal, characteristic
3#13071485C211yesmaximal, characteristic
4#13069358C211yesmaximal, characteristic, complemented
5#13069307C211yesmaximal, characteristic, complemented
6#13069255C211yesmaximal, characteristic, complemented
7#13069204C211yesmaximal, characteristic, complemented
8#13069192C211yesmaximal, characteristic, complemented
9#13069039C211yesmaximal, characteristic
10#13068871C211yesmaximal, characteristic, complemented
11#13068804C211yesmaximal, characteristic
12#13068512C211yesmaximal, characteristic, complemented
13#13068445C211yesmaximal, characteristic, complemented
14#13068392C211yesmaximal, characteristic
15C2×C11×#340C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66979—21no—
20C2×#66977C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22#10622825C2211yescharacteristic
23#10622824—21no—
24#10622823—21no—
25C4×C22⋊Dic11—21no—
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622594—21no—
35#10622594—21no—
36#10622591—21no—
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622586C2211yescharacteristic
42#10622585—21no—
43#10622584C418yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2×C414yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83#66979—44no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89#66977—22no—
90#66977C2×C414yes—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66940—22no—
103#66940—41no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115C22⋊(C11⋊C8)C2×C414yes—
116#66880—22no—
117#66880—41no—
118#66879—22no—
119#66879—41no—
120#66874C2×C414yescomplemented
121#66874C2×C414yescomplemented
122#66872C2×C414yescomplemented
123#66872C2×C414yescomplemented
124#66871—22no—
125#66871—41no—
126#22934—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—24no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—81no—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11#4112yes—
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—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22C22×C412yes—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—44no—
166C2×C8×C11#4112yes—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4C22×C412yes—
175C11×C4⋊C4C22×C412yes—
176C11×C4⋊C4#4112yes—
177C22⋊Dic11—24no—
178C22⋊Dic11—22no—
179C22⋊Dic11—22no—
180C22⋊Dic11—42no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—42no—
187C4⋊Dic11—42no—
188C4⋊Dic11C22×C412yes—
189Dic11⋊C4—24no—
190Dic11⋊C4—42no—
191Dic11⋊C4—81no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—42no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C4×Dic11—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C412yes—
205C2×C11⋊C8C22×C412yes—
206C2×#483—111no—
207#2360—111no—
208#2344—111no—
209#1944—111no—
210#1935—111no—
211#1928—111no—
212#1920—111no—
213#1919—111no—
214#1892—111no—
215#1863—111no—
216#1852—111no—
217#1776—111no—
218#1763—111no—
219#1752—111no—
220C2×#340D1111yescharacteristic
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11C4×D412yes—
226C23×C11AGL(1,ℤ/8)12yes—
227C23×C11#13712yes—
228C23×C11C22×D411yescharacteristic
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
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—48no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—84no—
249C2×C4×C11C4×D412yes—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
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—
280Dic22—22no—
281Dic22—22no—
282Dic22—41no—
283Dic22—41no—
284C8×C11—22no—
285C8×C11—41no—
286C11⋊C8—22no—
287C11⋊C8—22no—
288C23×C8C2×D1111yescharacteristic
289C2×C22⋊Q8—111no—
290C2×C4×Q8—111no—
291C2×#117—221no—
292C22×C4⋊C4C2×D1111yescharacteristic
293C22×C4⋊C4C2×D1111yescharacteristic
294#483—118no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#106—111no—
298C2×#106—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×C22⋊C8—111no—
304C2×#97—111no—
305C2×#97—111no—
306#391—111no—
307#389—111no—
308#389—111no—
309#389—111no—
310#389—221no—
311#387—221no—
312#387—221no—
313#387—221no—
314#385—221no—
315#381—221no—
316#380—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—111no—
319C4×C4⋊C4—111no—
320C4×C22⋊C4—111no—
321C4×C22⋊C4—221no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340C2×D1111yescharacteristic
327#340C2×D1111yescharacteristic
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#336—111no—
331#336—111no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11#44014yes—
339C22×C11C2×C4×D411yescharacteristic
340C22×C11#54611yescharacteristic
341C22×C11#54711yescharacteristic
342C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C11C2×#13711yescharacteristic
344C22×C11#57711yescharacteristic
345C22×C11#57811yescharacteristic
346C4×C11—22no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—81no—
351C4×C11C4×#4111yescharacteristic
352C4×C11#52011yescharacteristic
353C4×C11#55111yescharacteristic
354C4×C11#55211yescharacteristic
355Dic11—41no—
356Dic11—41no—
357Dic11—42no—
358Dic11—42no—
359Dic11—41no—
360Dic11—41no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—111no—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4C22×D1111yescharacteristic
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—41no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C22⋊Q8—114no—
375C22⋊Q8—222no—
376C4×Q8—222no—
377C4×Q8—441no—
378#117—444no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4C4×D1114yes—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C22⋊C4—111no—
398C2×C22⋊C4—111no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42—221no—
407#107—222no—
408#107—441no—
409#106—114no—
410#106—114no—
411#103—114no—
412#103—114no—
413#103—222no—
414#103—441no—
415C22⋊C8—114no—
416#97—222no—
417#97—441no—
418#95—111no—
419#95—111no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429C2×C11—24no—
430C2×C11#235911yescharacteristic
431C2×C11C2×#44011yescharacteristic
432C2×C11#294711yescharacteristic
433C2×C11#330611yescharacteristic
434C2×C11#331211yescharacteristic
435C2×C11#334311yescharacteristic
436C2×C11#334411yescharacteristic
437C24D4×D1111yescharacteristic
438C2×Q8—112no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—221no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—81no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4C2×C4×D1112yes—
467C22×C4D4×D1111yescharacteristic
468C22×C4#434112yes—
469C22×C4C23×D1111yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—44no—
476C2×C8—112no—
477C2×C8—112no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8#433912yes—
483C4⋊C4—24no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—112no—
491C4⋊C4—224no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—881no—
501C4⋊C4C2×C4×D1112yes—
502C4⋊C4C2×C4×D1112yes—
503C4⋊C4#433912yes—
504C22⋊C4—224no—
505C22⋊C4—222no—
506C22⋊C4—222no—
507C22⋊C4—442no—
508C42—221no—
509C42—221no—
510C42—221no—
511C42—221no—
512C42—442no—
513C42—442no—
514C42—442no—
515C42—881no—
516C11#2293411yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23(C22⋊D11)⋊C412yes—
522C23#6696412yes—
523C23#6696812yes—
524C23C2×D4×D1111yescharacteristic
525Q8—222no—
526Q8—222no—
527Q8—441no—
528Q8—441no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—48no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—84no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4(C22⋊D11)⋊C412yes—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4C2×#433911yescharacteristic
576C2×C4C2×#433911yescharacteristic
577C2×C4C2×#434111yescharacteristic
578C2×C4#6703711yescharacteristic
579C2×C4#6704011yescharacteristic
580C8—22no—
581C8—41no—
582C8—222no—
583C8—222no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22#1062237014yes—
591C22C2×(C22⋊D11)⋊C411yescharacteristic
592C22#1062302111yescharacteristic
593C22#1062303811yescharacteristic
594C22C2×#6696411yescharacteristic
595C22C2×#6696811yescharacteristic
596C22#1062329311yescharacteristic
597C22#1062329711yescharacteristic
598C4—22no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—81no—
603C4—441no—
604C4—442no—
605C4—441no—
606C4—441no—
607C4—442no—
608C4—441no—
609C4—881no—
610C4—881no—
611C4C4×#433911yescharacteristic
612C4#1062302611yescharacteristic
613C4#1062303511yescharacteristic
614C4#1062304411yescharacteristic
615C2—24no—
616C2#1307160411yescharacteristic
617C2C2×#1062237011yescharacteristic
618C2#1307745311yescharacteristic
619C2#1308057311yescharacteristic
620C2#1308066311yescharacteristic
621C2#1308105211yescharacteristic
622C2#1308106711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#340D11
hypocenterC11#22934
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #13069358C2semidirect
5. #13069307C2semidirect
6. #13069255C2semidirect
7. #13069204C2semidirect
8. #13069192C2semidirect
10. #13068871C2semidirect
12. #13068512C2semidirect
13. #13068445C2semidirect
43. #10622584C4semidirect
120. #66874C2×C4semidirect
121. #66874C2×C4semidirect
122. #66872C2×C4semidirect
123. #66872C2×C4semidirect
516. C11#22934semidirect

Maximal subgroups

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

subgroupindex
C2×#106225842
#130716212
#130714852
#130693582
#130693072
#130692552
#130692042
#130691922
#130690392
#130688712
#130688042
#130685122
#130684452
#130683922
C2×C11×#3402
#2293411