Finite Group Databasebeta

← #14770477

Subgroups — #14770477

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic22C211yesmaximal, characteristic
2M16×Dic22C211yesmaximal, characteristic, complemented
3#13071093C211yesmaximal, characteristic, complemented
4#13069595C212yesmaximal, complemented
5#13069593C211yesmaximal, characteristic, complemented
6#13069560C211yesmaximal, characteristic, complemented
7#13069558C212yesmaximal, complemented
8#13068636C211yesmaximal, characteristic
9#13068634C212yesmaximal
10#13068428C212yesmaximal
11C4×C11×#104C211yesmaximal, characteristic
12C4×C11×#41C2211yescharacteristic
13#41×Dic11C2212yes—
14#10623101C411yescharacteristic, complemented
15#10623100C412yescomplemented
16Q8×Dic22C411yescharacteristic, complemented
17#10623074—21no—
18#10623074C411yescharacteristic, complemented
19#10623070—22no—
20#10623070C412yescomplemented
21D4×Dic22—21no—
22D4×Dic22C411yescharacteristic, complemented
23#10623048—22no—
24#10623048C2212yes—
25#10623001—21no—
26#10623001C2211yescharacteristic
27C2×C4×Dic22—21no—
28C2×C4×Dic22C2211yescharacteristic
29C2×C11×#104C2211yescharacteristic
30C2×C11×#104C2211yescharacteristic
31C4×C11×M16C2211yescharacteristic
32C43×C11C2211yescharacteristic
33C2×#66901C2212yes—
34#10622731C2212yes—
35M16×Dic11C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622546—22no—
38#10622545C2212yes—
39C4×Dic11⋊C4C2212yes—
40#10622542—21no—
41#10622541—21no—
42#10622537C2211yescharacteristic
43#10622314—22no—
44#10622292—21no—
45C8×Dic22—21no—
46C11×#339C2211yescharacteristic
47C11×#339C2211yescharacteristic
48#10622193C2212yes—
49#10622193C2212yes—
50#10622170C2212yes—
51#10622161C2212yes—
52#10622161C2212yes—
53C2×C11×#41C2311yescharacteristic
54C22×Dic22—21no—
55C22×Dic22D411yescharacteristic
56C2×C11×M16C2311yescharacteristic
57C2×C11×M16C2311yescharacteristic
58C4×Q8×C11C2×C411yescharacteristic
59C4×Q8×C11C2×C411yescharacteristic
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11C2×C411yescharacteristic
63C4×D4×C11C2×C411yescharacteristic
64C11×#117—21no—
65C11×#117C2311yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72Q8×Dic11C2×C412yes—
73Q8×Dic11C2×C412yes—
74D4×Dic11—22no—
75D4×Dic11—22no—
76D4×Dic11C2×C412yes—
77D4×Dic11C2×C412yes—
78#66979—22no—
79#66979C2312yes—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D411yescharacteristic
83#66977—21no—
84#66977—21no—
85#66977—21no—
86#66977—21no—
87#66977—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4D412yes—
91C2×C4×Dic11—22no—
92C2×C4×Dic11C2312yes—
93C2×C4×Dic11C2312yes—
94C2×#4318C2312yes—
95#66943—22no—
96#66943—22no—
97#66943C2×C412yes—
98#66943C2×C412yes—
99#66941—22no—
100#66941—22no—
101#66941C2×C412yes—
102#66941C2×C412yes—
103#66931—22no—
104#66931—22no—
105#66931—22no—
106#66931—22no—
107#66931—22no—
108#66931—22no—
109#66923—22no—
110#66923C2×C412yes—
111#66922—21no—
112#66922—21no—
113#66922C2×C411yescharacteristic
114#66922C2×C411yescharacteristic
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—21no—
118C4×Dic22—21no—
119C4×Dic22—22no—
120C4×Dic22—22no—
121C4×Dic22—22no—
122C4×Dic22C2×C411yescharacteristic
123C4×Dic22C2×C412yes—
124C4×Dic22C2×C411yescharacteristic
125C4×Dic22D411yescharacteristic
126C4×Dic22D411yescharacteristic
127C4×Dic22D412yes—
128C11×#104—22no—
129C11×#104Q814yescomplemented
130C11×#97—21no—
131C4×C8×C11—21no—
132#66901—24no—
133C11⋊#95—21no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137#66879—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140C8×Dic11—22no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)—21no—
143#22529—111nomaximal, Sylow
144C11×#41—21no—
145C11×#41—21no—
146C11×#41C2×Q812yes—
147C11×#41#4112yes—
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11C2×D412yes—
163C22×Dic11C2×D412yes—
164C2×Dic22—22no—
165C2×Dic22—22no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—42no—
169C2×Dic22—44no—
170C2×Dic22C22⋊C411yescharacteristic
171C2×Dic22C22⋊C411yescharacteristic
172C2×Dic22C22⋊C412yes—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16—21no—
176C11×M16C2×Q812yescomplemented
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—42no—
193C42×C11—42no—
194C42×C11C22×C411yescharacteristic
195C42×C11C22×C411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2×Q812yescomplemented
199C22⋊Dic11—22no—
200C22⋊Dic11—22no—
201C22⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—42no—
209C4⋊Dic11C22⋊C411yescharacteristic
210C4⋊Dic11C22⋊C411yescharacteristic
211C4⋊Dic11C22⋊C412yes—
212C4⋊Dic11C22×C412yes—
213C4⋊Dic11C22×C412yes—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4—44no—
221Dic11⋊C4C22⋊C412yes—
222Dic11⋊C4C22⋊C412yes—
223Dic11⋊C4C22⋊C412yes—
224Dic11⋊C4C22⋊C412yes—
225C4×Dic11—22no—
226C4×Dic11—22no—
227C4×Dic11—22no—
228C4×Dic11—22no—
229C4×Dic11—22no—
230C4×Dic11C22×C412yes—
231C4×Dic11C22×C412yes—
232C4×Dic11C2×D412yes—
233C4×Dic11C2×D412yes—
234#4318—22no—
235#4318—22no—
236C2×C11⋊C8—22no—
237Q8×#41—111no—
238Q8×M16—111no—
239#2295—111no—
240#1995—112no—
241#1994—111no—
242#1986—111no—
243#1986—112no—
244#1806—112no—
245#1806—111no—
246#1759—112no—
247C4×#104D1111yescharacteristic
248C23×C11—21no—
249C23×C11C22×D411yescharacteristic
250Q8×C11—21no—
251Q8×C11C4×Q812yes—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11—21no—
255D4×C11C4×Q812yes—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—81no—
271C2×C4×C11C2×C22⋊C411yescharacteristic
272C2×C4×C11C2×C22⋊C411yescharacteristic
273C2×C4×C11C2×C22⋊C411yescharacteristic
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×Q811yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×C4×C112−1+411yescharacteristic
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—44no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—82no—
290C2×Dic11C2×C22⋊C412yes—
291C2×Dic11C2×C22⋊C412yes—
292C2×Dic11C2×C22⋊C412yes—
293C2×Dic11C2×C22⋊C412yes—
294Dic22—22no—
295Dic22—22no—
296Dic22—42no—
297Dic22—44no—
298Dic22—42no—
299Dic22—82no—
300Dic22—81no—
301C8×C11—22no—
302C8×C11—41no—
303C11⋊C8—42no—
304Q82—111no—
305#557—112no—
306#557—111no—
307#554—112no—
308#554—111no—
309#554—222no—
310#554—221no—
311D4×Q8—111no—
312D4×Q8—221no—
313#533—112no—
314#533—111no—
315#533—221no—
316#533—222no—
317C4×#41—112no—
318C4×#41C2×D1111yescharacteristic
319C2×C4×Q8—111no—
320C2×C4×Q8—221no—
321#446—221no—
322#446—222no—
323C8×Q8—221no—
324#423—112no—
325#423—111no—
326C2×#104—112no—
327C2×#104C2×D1111yescharacteristic
328C2×#104C2×D1111yescharacteristic
329C4×M16—112no—
330C4×M16C2×D1111yescharacteristic
331#391—221no—
332#389—221no—
333#387—222no—
334C4×C4⋊C4—112no—
335C4×C4⋊C4—111no—
336#376—112no—
337C43C2×D1111yescharacteristic
338#339—112no—
339#339—112no—
340#339—112no—
341#339—112no—
342#339—112no—
343#339C2×D1111yescharacteristic
344#339C2×D1111yescharacteristic
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—22no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11C22×C22⋊C411yescharacteristic
351C22×C11#54811yescharacteristic
352C22×C11D4×Q811yescharacteristic
353C4×C11—22no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—42no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11#42112yes—
362C4×C11C2×C4×Q811yescharacteristic
363C4×C11#51911yescharacteristic
364C4×C11#54811yescharacteristic
365C4×C11D4×Q811yescharacteristic
366Dic11—22no—
367Dic11—22no—
368Dic11—22no—
369Dic11—22no—
370Dic11—42no—
371Dic11—42no—
372Dic11—82no—
373C2×#41C22×D1111yescharacteristic
374C22×Q8—111no—
375C22×Q8—221no—
376C2×M16—112no—
377C2×M16C22×D1111yescharacteristic
378C2×M16C22×D1111yescharacteristic
379C4⋊Q8—112no—
380C4⋊Q8—112no—
381C4⋊Q8—111no—
382C4⋊Q8—111no—
383C4⋊Q8—221no—
384C4⋊Q8—221no—
385C4⋊Q8—222no—
386C4⋊Q8—222no—
387#125—112no—
388#125—112no—
389#125—112no—
390#125—222no—
391#125—222no—
392#125—222no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395C22⋊Q8—222no—
396C22⋊Q8—222no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399C22⋊Q8—221no—
400C22⋊Q8—222no—
401C22⋊Q8—221no—
402C22⋊Q8—221no—
403C22⋊Q8—221no—
404C4×Q8—111no—
405C4×Q8—111no—
406C4×Q8—112no—
407C4×Q8—111no—
408C4×Q8—111no—
409C4×Q8—112no—
410C4×Q8—112no—
411C4×Q8—112no—
412C4×Q8—222no—
413C4×Q8—222no—
414C4×Q8—222no—
415C4×Q8—221no—
416C4×Q8—221no—
417C4×Q8—221no—
418C4×Q8—221no—
419C4×Q8C4×D1111yescharacteristic
420C4×Q8C4×D1111yescharacteristic
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—112no—
424C4×D4—112no—
425C4×D4—222no—
426C4×D4—222no—
427C4×D4C4×D1111yescharacteristic
428C4×D4C4×D1111yescharacteristic
429#117—21no—
430#117—112no—
431#117—222no—
432#117C22×D1111yescharacteristic
433C2×C4⋊C4—112no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—222no—
438C2×C4⋊C4—221no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—112no—
443C2×C42—112no—
444C2×C42—222no—
445C2×C42C22×D1111yescharacteristic
446C2×C42C22×D1111yescharacteristic
447C2×C42C22×D1111yescharacteristic
448C4⋊C8—222no—
449C4⋊C8—222no—
450C4⋊C8—221no—
451C4⋊C8—221no—
452#104—22no—
453#104—224no—
454#104Dic2214yescomplemented
455#97—21no—
456#97—222no—
457C4×C8—21no—
458C4×C8—222no—
459#95—222no—
460#95—222no—
461#95—222no—
462#95—221no—
463C2×C11—21no—
464C2×C11—21no—
465C2×C11—42no—
466C2×C11Q8×C22⋊C411yescharacteristic
467C2×C11C2×#42111yescharacteristic
468C2×C11#290111yescharacteristic
469#41—21no—
470#41—21no—
471#41C2×Dic2212yes—
472#41#433912yes—
473C2×Q8—111no—
474C2×Q8—111no—
475C2×Q8—112no—
476C2×Q8—222no—
477C2×Q8—222no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—442no—
481C2×Q8—444no—
482C2×Q8C2×C4×D1111yescharacteristic
483C2×D4—21no—
484C2×D4C2×C4×D1111yescharacteristic
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—112no—
491C22×C4—112no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4D4×D1111yescharacteristic
496C22×C4D4×D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498M16—21no—
499M16—21no—
500M16—21no—
501M16—222no—
502M16—222no—
503M16C2×Dic2212yescomplemented
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—222no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—112no—
510C4⋊C4—111no—
511C4⋊C4—112no—
512C4⋊C4—112no—
513C4⋊C4—112no—
514C4⋊C4—112no—
515C4⋊C4—111no—
516C4⋊C4—112no—
517C4⋊C4—112no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—221no—
528C4⋊C4—222no—
529C4⋊C4—221no—
530C4⋊C4—444no—
531C4⋊C4—442no—
532C4⋊C4C2×C4×D1111yescharacteristic
533C4⋊C4C2×C4×D1111yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—222no—
538C22⋊C4—222no—
539C22⋊C4—222no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—42no—
547C42—42no—
548C42—112no—
549C42—112no—
550C42—112no—
551C42—112no—
552C42—222no—
553C42—222no—
554C42—222no—
555C42—222no—
556C42—222no—
557C42C2×Dic2212yescomplemented
558C42C2×C4×D1111yescharacteristic
559C42C2×C4×D1111yescharacteristic
560C42D4×D1111yescharacteristic
561C42D4×D1111yescharacteristic
562C11#2252911yescharacteristic, complemented, Sylow
563C23—21no—
564C23C2×D4×D1111yescharacteristic
565Q8—21no—
566Q8—222no—
567Q8—222no—
568Q8—442no—
569Q8—444no—
570Q8—442no—
571Q8—881no—
572Q8—882no—
573Q8C4×Dic2212yes—
574D4—22no—
575D4—22no—
576D4—21no—
577D4C4×Dic2212yes—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—81no—
593C2×C4—112no—
594C2×C4—112no—
595C2×C4—112no—
596C2×C4—112no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—444no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—882no—
606C2×C4C22⋊C4×D1111yescharacteristic
607C2×C4C22⋊C4×D1111yescharacteristic
608C2×C4C22⋊C4×D1111yescharacteristic
609C2×C4C22⋊C4×D1111yescharacteristic
610C2×C4C22×Dic2211yescharacteristic
611C2×C4C22×C4×D1111yescharacteristic
612C2×C4C2×#433911yescharacteristic
613C2×C4C2×D4×D1111yescharacteristic
614C2×C4#6704311yescharacteristic
615C2×C4#6704311yescharacteristic
616C8—22no—
617C8—41no—
618C8—442no—
619C22—21no—
620C22—21no—
621C22—22no—
622C22—41no—
623C22—41no—
624C22C2×C22⋊C4×D1111yescharacteristic
625C22D4×Dic2211yescharacteristic
626C22#1062308311yescharacteristic
627C4—22no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—42no—
632C4—42no—
633C4—41no—
634C4—41no—
635C4—222no—
636C4—222no—
637C4—222no—
638C4—222no—
639C4—442no—
640C4—442no—
641C4—882no—
642C4#1062243412yes—
643C4C2×C4×Dic2211yescharacteristic
644C4#1062304711yescharacteristic
645C4D4×Dic2211yescharacteristic
646C4#1062308311yescharacteristic
647C2—21no—
648C2—21no—
649C2—42no—
650C2C22⋊C4×Dic2211yescharacteristic
651C2C2×#1062243411yescharacteristic
652C2#1307716011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#104C2
socleC22×C11C22×C22⋊C4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenterC4×#104D11
hypocenterC11#22529
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. M16×Dic22C2semidirect
3. #13071093C2semidirect
4. #13069595C2semidirect
5. #13069593C2semidirect
6. #13069560C2semidirect
7. #13069558C2semidirect
14. #10623101C4semidirect
15. #10623100C4semidirect
16. Q8×Dic22C4semidirect
18. #10623074C4semidirect
20. #10623070C4semidirect
22. D4×Dic22C4semidirect
129. C11×#104Q8semidirect
176. C11×M16C2×Q8semidirect
198. C42×C11C2×Q8semidirect
454. #104Dic22semidirect
503. M16C2×Dic22semidirect
557. C42C2×Dic22semidirect
562. C11#22529semidirect

Maximal subgroups

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

subgroupindex
#41×Dic222
M16×Dic222
#130710932
#130695952
#130695932
#130695602
#130695582
#130686362
#130686342
#130684282
C4×C11×#1042
#2252911