Finite Group Databasebeta

← #14775165

Subgroups — #14775165

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×#10622475C211yesmaximal, characteristic
2#13071620C211yesmaximal, characteristic
3#13071484C211yesmaximal, characteristic
4#13069307C211yesmaximal, characteristic, complemented
5#13069256C211yesmaximal, characteristic, complemented
6#13069203C211yesmaximal, characteristic, complemented
7#13069191C211yesmaximal, characteristic, complemented
8#13069038C211yesmaximal, characteristic
9#13068869C211yesmaximal, characteristic, complemented
10#13068802C211yesmaximal, characteristic
11#13068512C211yesmaximal, characteristic, complemented
12#13068447C211yesmaximal, characteristic, complemented
13#13068393C211yesmaximal, characteristic
14D11×#340C211yesmaximal, characteristic
15C11×#1944C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×#66950C2211yescharacteristic
18C2×#66945—21no—
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31#10622602—21no—
32#10622600C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622591—21no—
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622586—21no—
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622475C418yescomplemented
46#10622279—21no—
47#10622277—21no—
48#10622268—21no—
49#10622267—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×(C2×D11)⋊C4D411yescharacteristic
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C2×C8×D11—22no—
93C2×C8×D11—22no—
94C2×C8×D11—41no—
95#66950—22no—
96#66950C2×C414yes—
97#66945—44no—
98C4⋊C4×D11—22no—
99C4⋊C4×D11—22no—
100C4⋊C4×D11—41no—
101C4⋊C4×D11C2×C414yes—
102C4×Dic22—22no—
103C4×Dic22—41no—
104C11×#107—41no—
105C11×#106C2×C414yescomplemented
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⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118(C2×D11)⋊C8C2×C414yes—
119#66880—22no—
120#66880C2×C414yescomplemented
121#66879—22no—
122#66874—41no—
123#66874C2×C414yescomplemented
124#66872C2×C414yescomplemented
125#66871—22no—
126#22934—111nomaximal, Sylow
127C23×D11C2×D411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×C4×D11—24no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11—81no—
152C2×C4×D11C22×C412yes—
153C2×C4×D11#4112yes—
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×C11C22×C412yes—
165C2×C8×C11#4112yes—
166C11×C4⋊C4—21no—
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⋊C4C22×C412yes—
175C11×C4⋊C4C22×C412yes—
176C42×C11—21no—
177C42×C11—21no—
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—22no—
181(C2×D11)⋊C4—42no—
182C4⋊Dic11—24no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—42no—
188C4⋊Dic11C22×C412yes—
189C4⋊Dic11#4112yes—
190Dic11⋊C4—24no—
191Dic11⋊C4—42no—
192Dic11⋊C4—42no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—42no—
196C4×Dic11—42no—
197C4×Dic11—42no—
198C4×Dic11—81no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C412yes—
205C8×D11—44no—
206C2×#483—111no—
207#2360—111no—
208#2344—111no—
209#1944D1111yescharacteristic, complemented
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×#340—111no—
221C23×C11C22×D411yescharacteristic
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11C4×D412yes—
227C22×D11AGL(1,ℤ/8)12yes—
228C22×D11#13712yes—
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×C11C2×#4111yescharacteristic
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—22no—
257C2×Dic11—22no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
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×Dic11C4×D412yes—
274C4×D11—22no—
275C4×D11—22no—
276C4×D11—22no—
277C4×D11—22no—
278C4×D11—48no—
279C4×D11—84no—
280Dic22—22no—
281Dic22—22no—
282Dic22—41no—
283Dic22—41no—
284C8×C11—22no—
285C8×C11—22no—
286C11⋊C8—22no—
287C11⋊C8—41no—
288C23×C8—111no—
289C2×C22⋊Q8—111no—
290C2×C4×Q8—111no—
291C2×#117—221no—
292C22×C4⋊C4—111no—
293C22×C4⋊C4—111no—
294#483—118no—
295C2×#107—111no—
296C2×#107C2×D1111yescharacteristic
297C2×#106—111no—
298C2×#106C2×D1111yescharacteristic
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×C22⋊C8—111no—
304C2×#97—111no—
305C2×#97C2×D1111yescharacteristic
306#391—111no—
307#389—111no—
308#389—221no—
309#389C2×D1111yescharacteristic
310#389C2×D1111yescharacteristic
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#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#336—111no—
331#336—111no—
332C22×C11C2×C4×D411yescharacteristic
333C22×C11#54611yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C11C2×#13711yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57811yescharacteristic
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—22no—
345C2×D11#44014yes—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11C4×#4111yescharacteristic
353C4×C11#52011yescharacteristic
354C4×C11#55111yescharacteristic
355C4×C11#55211yescharacteristic
356Dic11—22no—
357Dic11—41no—
358Dic11—41no—
359Dic11—42no—
360Dic11—42no—
361Dic11—42no—
362Dic11—81no—
363C22×Q8—111no—
364C23×C4—111no—
365C23×C4—221no—
366C23×C4—221no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—222no—
370C22×C8—222no—
371C22×C8—441no—
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—21no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—441no—
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—221no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407#107—41no—
408#107—222no—
409#106—114no—
410#106C4×D1114yescomplemented
411#103—114no—
412#103—114no—
413#103—222no—
414#103—441no—
415C22⋊C8—114no—
416#97—41no—
417#97—222no—
418#95—21no—
419#95—21no—
420#95—111no—
421#95—111no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429C2×C11#235911yescharacteristic
430C2×C11C2×#44011yescharacteristic
431C2×C11#294711yescharacteristic
432C2×C11#330611yescharacteristic
433C2×C11#331211yescharacteristic
434C2×C11#334311yescharacteristic
435C2×C11#334411yescharacteristic
436D11—24no—
437C24—111no—
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—111no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—224no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—442no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—881no—
467C22×C4D4×D1111yescharacteristic
468C22×C4D4×D1111yescharacteristic
469C22×C4C23×D1111yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—112no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—444no—
481C2×C8C2×C4×D1112yes—
482C2×C8#434312yes—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—81no—
491C4⋊C4—112no—
492C4⋊C4—112no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4C2×C4×D1112yes—
503C4⋊C4C2×C4×D1112yes—
504C22⋊C4—222no—
505C22⋊C4—222no—
506C22⋊C4—224no—
507C22⋊C4—442no—
508C42—21no—
509C42—21no—
510C42—221no—
511C42—221no—
512C42—442no—
513C42—442no—
514C42—442no—
515C42—881no—
516C11#2293411yescharacteristic, complemented, Sylow
517C23—112no—
518C23—112no—
519C23—112no—
520C23—221no—
521C23—221no—
522C23—221no—
523C23—221no—
524C23C2×D4×D1111yescharacteristic
525Q8—222no—
526Q8—222no—
527Q8—441no—
528Q8—441no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
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—41no—
547C2×C4—112no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—448no—
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—884no—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4#6703711yescharacteristic
576C2×C4C2×#434311yescharacteristic
577C2×C4#6704011yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C8—22no—
581C8—22no—
582C8—222no—
583C8—441no—
584C22—114no—
585C22—222no—
586C22—222no—
587C22—222no—
588C22—222no—
589C22—222no—
590C22—222no—
591C22C4×D4×D1111yescharacteristic
592C22#1062314111yescharacteristic
593C22#1062325711yescharacteristic
594C22D11×AGL(1,ℤ/8)11yescharacteristic
595C22#1062330611yescharacteristic
596C22D11×#13711yescharacteristic
597C22#1062331011yescharacteristic
598C4—41no—
599C4—42no—
600C4—42no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4—222no—
605C4—442no—
606C4—441no—
607C4—441no—
608C4—442no—
609C4—442no—
610C4—881no—
611C4#1062303511yescharacteristic
612C4C4×#434311yescharacteristic
613C4#1062316811yescharacteristic
614C4#1062322411yescharacteristic
615C2—224no—
616C2#1307160311yescharacteristic
617C2D11×#44011yescharacteristic
618C2#1307745611yescharacteristic
619C2#1308057211yescharacteristic
620C2#1308066211yescharacteristic
621C2#1308105511yescharacteristic
622C2#1308107011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1944C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1944D11
hypocenterC11#22934
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
4. #13069307C2semidirect
5. #13069256C2semidirect
6. #13069203C2semidirect
7. #13069191C2semidirect
9. #13068869C2semidirect
11. #13068512C2semidirect
12. #13068447C2semidirect
15. C11×#1944C2semidirect
45. #10622475C4semidirect
105. C11×#106C2×C4semidirect
120. #66880C2×C4semidirect
123. #66874C2×C4semidirect
124. #66872C2×C4semidirect
209. #1944D11semidirect
410. #106C4×D11semidirect
516. C11#22934semidirect

Maximal subgroups

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

subgroupindex
C2×#106224752
#130716202
#130714842
#130693072
#130692562
#130692032
#130691912
#130690382
#130688692
#130688022
#130685122
#130684472
#130683932
D11×#3402
C11×#19442
#2293411