Finite Group Databasebeta

← #14785938

Subgroups — #14785938

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic
2C2×#10622840C211yesmaximal, characteristic, complemented
3C22×#66899C211yesmaximal, characteristic, complemented
4#13069757C212yesmaximal, complemented
5#13069617C212yesmaximal, complemented
6#13069042C211yesmaximal, characteristic, complemented
7#13068953C212yesmaximal, complemented
8#13068924C212yesmaximal, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068700C211yesmaximal, characteristic, complemented
11C11×#2409C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×#4341—21no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4325C2212yes—
17C2×#66983C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22#10623086—24no—
23#10623086—24no—
24C2×#66950—21no—
25C2×#66939—21no—
26C2×#66939—21no—
27C2×C4×D44C2211yescharacteristic
28C2×#66922C2211yescharacteristic
29C11×#395—21no—
30C11×#393—21no—
31C11×#391C2212yes—
32C11×#386—21no—
33C11×#385—21no—
34C11×#380C2211yescharacteristic
35#10622840—24no—
36C2×#66899—24no—
37C2×#66899C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2212yes—
42C2×#66873C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11—24no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—42no—
52C22×Q8×C11C2312yes—
53C22×D4×C11D411yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C22×C22⋊D11—21no—
59C23×Dic11—21no—
60C23×Dic11—21no—
61C2×#4341—28no—
62C2×#4341—44no—
63C2×#4341—44no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22—21no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—42no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×#4325—24no—
80C2×#4325—24no—
81C2×#4325—42no—
82#66983—22no—
83#66983—22no—
84#66983—22no—
85#66983D414yes—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11D414yes—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C22×C11⋊C8—22no—
100C22×C11⋊C8—42no—
101C22×C11⋊C8C2312yes—
102C22×C11⋊C8C2312yes—
103#66950—28no—
104#66939—28no—
105#66939—28no—
106C4×D44—22no—
107C4×D44—22no—
108#66922—22no—
109#66922—22no—
110C11×#95—21no—
111C11×#95—22no—
112C11×#95—22no—
113#66899—24no—
114#66899—24no—
115#66899—24no—
116C22⋊(C11⋊C8)—22no—
117C22⋊(C11⋊C8)—42no—
118#66873—42no—
119#23961—111nomaximal, Sylow
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D411yescharacteristic
122C23×D11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—28no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—44no—
130C2×Q8×C11—48no—
131C2×Q8×C11—44no—
132C2×Q8×C11—42no—
133C2×Q8×C11#4114yescomplemented
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11SD1614yescomplemented
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—44no—
146C22×C4×C11—42no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—24no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—42no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—42no—
166C22×Dic11—42no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169#4341—432no—
170C2×D44—21no—
171C2×D44—22no—
172C2×D44—22no—
173C2×D44C2×D412yes—
174C2×C4×D11—24no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×Dic22—24no—
178C2×Dic22—42no—
179C2×Dic22—42no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—44no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—44no—
187C11×C22⋊C4—42no—
188C42×C11—21no—
189C42×C11—21no—
190#4325—48no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194C4⋊Dic11—24no—
195C4⋊Dic11—24no—
196C4⋊Dic11—24no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C2×D412yes—
201C4⋊Dic11C2×D412yes—
202C4⋊Dic11C2×D412yes—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—44no—
210C2×#547—111no—
211C2×#448—111no—
212C22×#103—111no—
213#2409D1111yescharacteristic, complemented
214#2024—112no—
215#2000—112no—
216#1893—111no—
217#1877—112no—
218#1872—112no—
219#1869—111no—
220#1823—111no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—21no—
224C23×C11—22no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11#12012yes—
228C23×C11C2×SD1612yes—
229C23×C11C2×SD1612yes—
230C23×C11AGL(1,ℤ/8)12yes—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—42no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—42no—
237Q8×C11—24no—
238Q8×C11—24no—
239Q8×C11—48no—
240Q8×C11—42no—
241Q8×C11—42no—
242D4×C11—28no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—48no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11#12012yes—
264C2×C4×C11C2×SD1612yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4112yes—
268C2×C4×C11H(5,𝔽2)12yes—
269C22⋊D11—48no—
270C22⋊D11—48no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—48no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—48no—
282D44—24no—
283D44—41no—
284D44—41no—
285C4×D11—48no—
286Dic22—48no—
287C11⋊C8—42no—
288C11⋊C8—42no—
289C22×#41—221no—
290C23×Q8C2×D1111yescharacteristic
291C22×SD16—112no—
292C23×C8—111no—
293#547—224no—
294#547—224no—
295C2×C4⋊Q8—111no—
296C2×#123—221no—
297C2×#123—221no—
298C2×C22⋊Q8—221no—
299C2×C22⋊Q8C2×D1112yes—
300C2×#121—111no—
301C2×#121—111no—
302C2×C4×D4—111no—
303C2×C4×D4C2×D1111yescharacteristic
304C22×C4⋊C4—111no—
305C22×C4⋊C4—111no—
306#448—224no—
307C2×#103—112no—
308C2×#103—112no—
309C2×#103—112no—
310C2×#103—224no—
311C2×#102—112no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—112no—
314#395—21no—
315#393—21no—
316#391C2×D1112yes—
317#386—21no—
318#385—21no—
319#380C2×D1111yescharacteristic
320#340—112no—
321#340—112no—
322#340—112no—
323#336—112no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—22no—
329C22×C11—24no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—42no—
333C22×C11#45014yes—
334C22×C11C2×#12011yescharacteristic
335C22×C11#54612yes—
336C22×C11C22×SD1611yescharacteristic
337C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C11#57812yes—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—82no—
343C2×D11—82no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—41no—
347C4×C11—44no—
348C4×C11—41no—
349C4×C11—82no—
350C4×C11#52511yescharacteristic
351C4×C11#53511yescharacteristic
352C4×C11#54612yes—
353Dic11—42no—
354Dic11—42no—
355Dic11—42no—
356C2×#41—228no—
357C2×#41—444no—
358C2×#41—444no—
359C22×Q8—21no—
360C22×Q8—24no—
361C22×Q8—22no—
362C22×Q8—22no—
363C22×Q8—42no—
364C22×Q8—221no—
365C22×Q8C22×D1112yes—
366C22×D4—111no—
367C22×D4—221no—
368C22×D4—221no—
369C22×D4C22⋊D1111yescharacteristic
370C23×C4—21no—
371C23×C4—221no—
372C23×C4—221no—
373C23×C4—221no—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C2×SD16—224no—
377C2×SD16—224no—
378C2×SD16—442no—
379C22×C8—112no—
380C22×C8—112no—
381C22×C8—222no—
382C22×C8—442no—
383C4⋊Q8—222no—
384C4⋊Q8—222no—
385#123—228no—
386#123—228no—
387C22⋊Q8—24no—
388C22⋊Q8—42no—
389C22⋊Q8—228no—
390#121—114no—
391#121—222no—
392#121—222no—
393#121—222no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—222no—
397C4×D4—222no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4C22⋊D1111yescharacteristic
410C2×C4⋊C4C22×D1112yes—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4C22⋊D1111yescharacteristic
417C2×C22⋊C4C22⋊D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419#103—224no—
420#103—224no—
421#103—224no—
422#102—442no—
423C22⋊C8—222no—
424C22⋊C8—442no—
425#95—21no—
426#95—22no—
427#95—22no—
428C2×C11—24no—
429C2×C11—42no—
430C2×C11#240411yescharacteristic
431C2×C11C2×#45011yescharacteristic
432C2×C11#301111yescharacteristic
433C2×C11#329812yes—
434C2×C11#330812yes—
435D11—82no—
436C24—221no—
437C24C2×C22⋊D1111yescharacteristic
438C24C2×C22⋊D1111yescharacteristic
439#41—4432no—
440C2×Q8—22no—
441C2×Q8—28no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—44no—
447C2×Q8—48no—
448C2×Q8—44no—
449C2×Q8—42no—
450C2×Q8—224no—
451C2×Q8—442no—
452C2×Q8—442no—
453C2×Q8#434114yescomplemented
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—112no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—221no—
460C2×D4—222no—
461C2×D4—222no—
462C2×D4—442no—
463C2×D4—442no—
464C2×D4—442no—
465C2×D4—442no—
466C2×D4#432514yescomplemented
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—44no—
476C22×C4—42no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—442no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4D4×D1112yes—
490C22×C4D4×D1112yes—
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496SD16—448no—
497C2×C8—222no—
498C2×C8—222no—
499C2×C8—222no—
500C2×C8—222no—
501C2×C8—222no—
502C2×C8—222no—
503C2×C8—444no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—44no—
508C4⋊C4—112no—
509C4⋊C4—112no—
510C4⋊C4—112no—
511C4⋊C4—224no—
512C4⋊C4—224no—
513C4⋊C4—224no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—44no—
520C22⋊C4—42no—
521C22⋊C4—224no—
522C22⋊C4—224no—
523C22⋊C4—224no—
524C42—21no—
525C42—21no—
526C11#2396111yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—21no—
530C23—22no—
531C23—21no—
532C23—22no—
533C23—222no—
534C23—442no—
535C23—441no—
536C23—441no—
537C23—442no—
538C23#6699012yes—
539C23C2×#432512yes—
540C23C2×#432512yes—
541C23#6700212yes—
542C23C22×C22⋊D1111yescharacteristic
543Q8—24no—
544Q8—24no—
545Q8—48no—
546Q8—42no—
547Q8—42no—
548Q8—448no—
549D4—28no—
550D4—224no—
551D4—448no—
552D4—448no—
553D4—441no—
554D4—441no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—48no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—448no—
579C2×C4—448no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—448no—
587C2×C4#6699012yes—
588C2×C4C2×#432512yes—
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4C2×D4×D1111yescharacteristic
591C2×C4C2×#434112yes—
592C2×C4#6703712yes—
593C8—442no—
594C8—442no—
595C22—24no—
596C22—22no—
597C22—22no—
598C22—24no—
599C22—22no—
600C22—24no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—882no—
608C22—882no—
609C22#1062265914yes—
610C22C2×#6699011yescharacteristic
611C22#1062333712yes—
612C22C22×#432511yescharacteristic
613C22C2×#6700211yescharacteristic
614C22#1062336912yes—
615C4—22no—
616C4—22no—
617C4—41no—
618C4—44no—
619C4—41no—
620C4—82no—
621C4—442no—
622C4—442no—
623C4—442no—
624C4#1062311711yescharacteristic
625C4#1062312212yes—
626C4#1062312311yescharacteristic
627C2—24no—
628C2—42no—
629C2—882no—
630C2#1307193211yescharacteristic
631C2C2×#1062265911yescharacteristic
632C2#1307790911yescharacteristic
633C2#1308048112yes—
634C2#1308060712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2409C2
socleC23×C11C22×D4
prime radicalC2×#10623086C2
hypercenter#2409D11
hypocenterC11#23961
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
2. C2×#10622840C2semidirect
3. C22×#66899C2semidirect
4. #13069757C2semidirect
5. #13069617C2semidirect
6. #13069042C2semidirect
7. #13068953C2semidirect
8. #13068924C2semidirect
9. #13068909C2semidirect
10. #13068700C2semidirect
11. C11×#2409C2semidirect
133. C2×Q8×C11#41semidirect
136. C2×D4×C11SD16semidirect
213. #2409D11semidirect
453. C2×Q8#4341semidirect
466. C2×D4#4325semidirect
526. C11#23961semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106228402
C22×#668992
#130697572
#130696172
#130690422
#130689532
#130689242
#130689092
#130687002
C11×#24092
#2396111