Finite Group Databasebeta

← #14721537

Subgroups — #14721537

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082412C211yesmaximal, characteristic
2#13077643C211yesmaximal, characteristic
3#13071559C211yesmaximal, characteristic
4#13067186C212yesmaximal, complemented
5#13067165C212yesmaximal, complemented
6#13067150C211yesmaximal, characteristic, complemented
7#13067149C211yesmaximal, characteristic, complemented
8#13067135C211yesmaximal, characteristic, complemented
9#13067126C212yesmaximal, complemented
10D11×#328C212yesmaximal, complemented
11C11×#1508C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2211yescharacteristic
13Q8×C22⋊D11C412yescomplemented
14C2×C4×C22⋊D11C2211yescharacteristic
15C2×#66977C2211yescharacteristic
16#10623167—22no—
17#10623166C412yescomplemented
18#10623165—21no—
19#10623163C412yescomplemented
20D11×C22⋊Q8C2212yes—
21#10623154—21no—
22#10623153C2212yes—
23#10623042—22no—
24#10623042C412yescomplemented
25#10623017—21no—
26#10623014—21no—
27C11×#407C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29#10622824C2211yescharacteristic
30#10622820C2211yescharacteristic
31#10622740—22no—
32#10622569—21no—
33#10622557—21no—
34C4×(C2×D11)⋊C4—21no—
35#10622546—21no—
36#10622341—22no—
37D11×C22⋊C8C2212yes—
38#10622332C2212yes—
39#10622280C2211yescharacteristic
40D11×#95C2211yescharacteristic
41#10622264C2211yescharacteristic
42#10622261C2211yescharacteristic
43C11×#328C2212yes—
44C11×#328C2212yes—
45#10622176C2212yes—
46#10622176C2212yes—
47#10622105C2212yes—
48#10622105C2212yes—
49#10622090C2212yes—
50#10622090C2212yes—
51C22×Q8×C11C2×C411yescharacteristic, complemented
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11D411yescharacteristic
54C2×Q8×D11C2×C412yes—
55C22×C4×D11—21no—
56C22×C4×D11C2311yescharacteristic
57C22×Dic22C2×C411yescharacteristic, complemented
58C2×C11×M16—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8C2×C412yescomplemented
62C11×C22⋊Q8C2312yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C42×C11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11D411yescharacteristic
71#66999—22no—
72#66999C2×C412yes—
73Q8×Dic11C2×C412yescomplemented
74#66997—22no—
75#66997C2×C412yescomplemented
76C4×C22⋊D11—22no—
77C4×C22⋊D11—22no—
78C4×C22⋊D11C2×C412yes—
79C4×C22⋊D11C2×C412yes—
80C4×C22⋊D11D412yes—
81C4×C22⋊D11D412yes—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×C4⋊Dic11C2×C411yescharacteristic, complemented
85#66977—21no—
86#66977—21no—
87#66977—22no—
88#66977—22no—
89#66977C2×C412yescomplemented
90#66977C2312yes—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4D411yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C2×#4318—21no—
97C2×C8×D11—22no—
98#66950—22no—
99#66950C2×C412yes—
100#66949—22no—
101#66949—22no—
102#66949—22no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11C2×C412yes—
105#66942—22no—
106#66942—22no—
107#66942—22no—
108#66941—22no—
109#66941C2×C412yescomplemented
110#66940—22no—
111#66940C2×C412yescomplemented
112(C22⋊D11)⋊C4—22no—
113(C22⋊D11)⋊C4—22no—
114C22⋊C4×D11—22no—
115#66931—22no—
116#66931—22no—
117#66931—22no—
118#66931—22no—
119#66930—22no—
120C11×C22⋊C8—21no—
121C11×C22⋊C8C2312yes—
122C11×#95C2311yescharacteristic
123C11×#95C2311yescharacteristic
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95C2311yescharacteristic
130C11⋊#95C2311yescharacteristic
131C22⋊(C11⋊C8)—21no—
132C22⋊(C11⋊C8)C2312yes—
133(C2×D11)⋊C8—22no—
134#66879—22no—
135Dic11⋊C8—22no—
136#17621—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—81no—
141C2×Q8×C11C22×C412yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—81no—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11C22⋊C412yes—
156C2×C22⋊D11C22⋊C412yes—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164Q8×D11—82no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×C4×D11C22×C412yes—
172C2×C4×D11C2×D412yes—
173C2×Dic22—22no—
174C2×Dic22—22no—
175C2×Dic22—21no—
176C2×Dic22—81no—
177C2×Dic22C22×C412yes—
178C11×M16—81no—
179C2×C8×C11—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4C22×C412yes—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—42no—
187C42×C11—81no—
188C22⋊Dic11—22no—
189C22⋊Dic11—22no—
190C22⋊Dic11—81no—
191C22⋊Dic11C22⋊C412yes—
192C22⋊Dic11C22⋊C412yes—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4C22⋊C412yes—
197(C2×D11)⋊C4C22⋊C412yes—
198C4⋊Dic11—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11—21no—
201C4⋊Dic11C22×C412yes—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—81no—
211Dic11⋊C4C22⋊C412yes—
212Dic11⋊C4C22⋊C412yes—
213C4×Dic11—22no—
214C4×Dic11—22no—
215C4×Dic11—42no—
216C4×Dic11C22×C412yes—
217C4×Dic11C2×D412yes—
218#4318—81no—
219C2×C11⋊C8—22no—
220C8×D11—82no—
221#3501—111no—
222#2973—111no—
223#2353—111no—
224#1520—112no—
225#1515—112no—
226#1511—111no—
227#1511—111no—
228#1508—111no—
229#1508D1111yescharacteristic, complemented
230#1506—112no—
231C2×#328—112no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11C2×C22⋊C411yescharacteristic
237C23×C11C2×C22⋊C411yescharacteristic
238C23×C11C22×D411yescharacteristic
239C22×D11—41no—
240C22×D11—41no—
241C22×D11C2×C22⋊C412yes—
242C22×D11#13712yes—
243C22×D11#13712yes—
244Q8×C11—42no—
245Q8×C11—81no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—81no—
261C2×C4×C11—81no—
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C22⋊D11—24no—
267C22⋊D11—24no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—22no—
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—81no—
281C2×Dic11—81no—
282C2×Dic11C2×C22⋊C412yes—
283C2×Dic11C2×C22⋊C412yes—
284C2×Dic11C2×C22⋊C412yes—
285C4×D11—42no—
286C4×D11—42no—
287C4×D11—82no—
288C4×D11—82no—
289C4×D11—84no—
290Dic22—42no—
291Dic22—82no—
292Dic22—82no—
293Dic22—81no—
294C8×C11—42no—
295C11⋊C8—42no—
296#554—112no—
297#554—112no—
298#554—222no—
299#554—222no—
300D4×Q8—112no—
301D4×Q8—112no—
302#544—221no—
303#543—221no—
304#543—221no—
305#533—112no—
306C2×C22⋊Q8—111no—
307C2×C22⋊Q8—112no—
308C2×C22⋊Q8C2×D1111yescharacteristic
309#518—221no—
310C2×C4×D4—111no—
311#435—222no—
312#435—222no—
313#432—112no—
314#407—111no—
315#407C2×D1111yescharacteristic
316C2×C22⋊C8—112no—
317#388—221no—
318#387—221no—
319#386—221no—
320#383—111no—
321#381—111no—
322#380—111no—
323C4×C22⋊C4—221no—
324C4×C22⋊C4C2×D1111yescharacteristic
325#376—111no—
326C2×#95—111no—
327#328—112no—
328#328—112no—
329#328—112no—
330#328—112no—
331#328—112no—
332#328—112no—
333#328C2×D1112yes—
334#328C2×D1112yes—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11C22×C22⋊C411yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C22×C11C2×#13711yescharacteristic
348C2×D11—22no—
349C2×D11—22no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11#41914yes—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—42no—
358C4×C11—42no—
359C4×C11—42no—
360C4×C11—81no—
361Dic11—22no—
362Dic11—22no—
363Dic11—22no—
364Dic11—42no—
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368C22×Q8—112no—
369C22×Q8—111no—
370C22×Q8C4×D1111yescharacteristic, complemented
371C22×D4—111no—
372C23×C4—111no—
373C23×C4—221no—
374C23×C4C22×D1111yescharacteristic
375C2×M16—21no—
376C2×M16—221no—
377C22×C8—222no—
378C4⋊Q8—112no—
379C4⋊Q8—112no—
380C4⋊Q8—222no—
381C4⋊Q8—222no—
382#125—222no—
383#125—222no—
384#125—222no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—112no—
388C22⋊Q8—112no—
389C22⋊Q8—112no—
390C22⋊Q8—112no—
391C22⋊Q8—222no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395C22⋊Q8—222no—
396C22⋊Q8—222no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399C22⋊Q8—222no—
400C22⋊Q8—222no—
401C22⋊Q8—222no—
402C22⋊Q8—221no—
403C22⋊Q8—221no—
404C22⋊Q8C4×D1112yescomplemented
405C22⋊Q8C22×D1112yes—
406C4×Q8—112no—
407C4×Q8—112no—
408C4×Q8—222no—
409C4×D4—112no—
410C4×D4—112no—
411C4×D4—112no—
412C4×D4—112no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—222no—
416C4×D4—222no—
417#117—222no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—222no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4C4×D1111yescharacteristic, complemented
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—111no—
429C2×C22⋊C4—111no—
430C2×C22⋊C4—222no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C42—21no—
435C2×C42—111no—
436C2×C42—221no—
437C4⋊C8—222no—
438C22⋊C8—21no—
439C22⋊C8—112no—
440C22⋊C8—222no—
441C22⋊C8—221no—
442C22⋊C8C22×D1112yes—
443#97—222no—
444#95—111no—
445#95—111no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95C22×D1111yescharacteristic
452#95C22×D1111yescharacteristic
453C2×C11—21no—
454C2×C11—21no—
455C2×C11—41no—
456C2×C11—41no—
457C2×C11#288311yescharacteristic
458C2×C11C2×#41911yescharacteristic
459C2×C11#290111yescharacteristic
460D11—24no—
461C24—111no—
462C24D4×D1111yescharacteristic
463C2×Q8—21no—
464C2×Q8—81no—
465C2×Q8—112no—
466C2×Q8—222no—
467C2×Q8—222no—
468C2×Q8—221no—
469C2×Q8—881no—
470C2×Q8—882no—
471C2×Q8C2×C4×D1112yes—
472C2×D4—112no—
473C2×D4—112no—
474C2×D4—222no—
475C2×D4—222no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—81no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—881no—
495C22×C4—881no—
496C22×C4C2×C4×D1111yescharacteristic
497C22×C4C2×C4×D1111yescharacteristic
498C22×C4D4×D1111yescharacteristic
499C22×C4D4×D1111yescharacteristic
500C22×C4D4×D1111yescharacteristic
501C22×C4C23×D1111yescharacteristic
502M16—81no—
503M16—881no—
504C2×C8—22no—
505C2×C8—222no—
506C2×C8—882no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—112no—
511C4⋊C4—112no—
512C4⋊C4—112no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C4⋊C4—222no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—221no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—881no—
525C4⋊C4C2×C4×D1112yes—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—42no—
529C22⋊C4—112no—
530C22⋊C4—112no—
531C22⋊C4—112no—
532C22⋊C4—112no—
533C22⋊C4—222no—
534C22⋊C4—222no—
535C22⋊C4—222no—
536C22⋊C4—222no—
537C22⋊C4—442no—
538C22⋊C4—881no—
539C42—81no—
540C42—112no—
541C42—112no—
542C42—222no—
543C42—222no—
544C42—442no—
545C11#1762111yescharacteristic, complemented, Sylow
546C23—21no—
547C23—21no—
548C23—41no—
549C23—41no—
550C23—112no—
551C23—112no—
552C23—112no—
553C23—441no—
554C23—441no—
555C23C22⋊C4×D1111yescharacteristic
556C23C22⋊C4×D1111yescharacteristic
557C23C2×D4×D1111yescharacteristic
558Q8—42no—
559Q8—81no—
560Q8—442no—
561Q8—881no—
562Q8—882no—
563Q8—882no—
564D4—224no—
565D4—224no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—112no—
583C2×C4—112no—
584C2×C4—112no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—882no—
600C2×C4—882no—
601C2×C4—884no—
602C2×C4—881no—
603C2×C4—881no—
604C2×C4C22⋊C4×D1111yescharacteristic
605C2×C4C22⋊C4×D1111yescharacteristic
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×D4×D1111yescharacteristic
608C8—42no—
609C8—442no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—81no—
619C22—81no—
620C22—114no—
621C22—222no—
622C22—222no—
623C22—442no—
624C22—442no—
625C22C2×C22⋊C4×D1111yescharacteristic
626C22D11×#13711yescharacteristic
627C22D11×#13711yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—81no—
636C4—222no—
637C4—222no—
638C4—222no—
639C4—442no—
640C4—442no—
641C4—881no—
642C4—881no—
643C2—21no—
644C2—21no—
645C2—41no—
646C2—41no—
647C2—224no—
648C2#1307707411yescharacteristic
649C2D11×#41911yescharacteristic
650C2#1307716011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1508C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenter#1508D11
hypocenterC11#17621
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
4. #13067186C2semidirect
5. #13067165C2semidirect
6. #13067150C2semidirect
7. #13067149C2semidirect
8. #13067135C2semidirect
9. #13067126C2semidirect
10. D11×#328C2semidirect
11. C11×#1508C2semidirect
13. Q8×C22⋊D11C4semidirect
17. #10623166C4semidirect
19. #10623163C4semidirect
24. #10623042C4semidirect
51. C22×Q8×C11C2×C4semidirect
57. C22×Dic22C2×C4semidirect
61. C11×C22⋊Q8C2×C4semidirect
64. C2×C11×C4⋊C4C2×C4semidirect
73. Q8×Dic11C2×C4semidirect
75. #66997C2×C4semidirect
84. C2×C4⋊Dic11C2×C4semidirect
89. #66977C2×C4semidirect
109. #66941C2×C4semidirect
111. #66940C2×C4semidirect
229. #1508D11semidirect
370. C22×Q8C4×D11semidirect
404. C22⋊Q8C4×D11semidirect
425. C2×C4⋊C4C4×D11semidirect
545. C11#17621semidirect

Maximal subgroups

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

subgroupindex
#130824122
#130776432
#130715592
#130671862
#130671652
#130671502
#130671492
#130671352
#130671262
D11×#3282
C11×#15082
#1762111