Finite Group Databasebeta

← #15620293

Subgroups — #15620293

Order 2816.

4810 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
1C2×#10623453C211yesmaximal, characteristic, complemented
2C2×#10623353C212yesmaximal, complemented
3#13077928C218yesmaximal, complemented
4#13077917C218yesmaximal, complemented
5#13077874C214yesmaximal, complemented
6#13077866C214yesmaximal, complemented
7C2×#10622579C212yesmaximal, complemented
8#13077061C211yesmaximal, characteristic, complemented
9C2×C11×#537C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic, complemented
12#10623453—216no—
13C2×#67043C2214yescomplemented
14C2×#67042C2214yescomplemented
15C2×#41×D11—24no—
16C2×#67040—21no—
17C2×#67037—22no—
18C2×#67037—21no—
19C22×#4339C2214yes—
20C22×#4339C2212yes—
21C11×#537—24no—
22C11×#537C2218yescomplemented
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8C2212yescomplemented
25C2×C11×#121—21no—
26C2×C11×#121—22no—
27C2×C11×#121C2212yescomplemented
28C22×C11×C4⋊C4C2211yescharacteristic, complemented
29C2×#67004C2214yescomplemented
30#10623353—216no—
31C2×#67003C2218yescomplemented
32C2×#67002C2214yescomplemented
33C2×#66995C2214yescomplemented
34C2×#66985C2214yescomplemented
35C22×#4318C2212yescomplemented
36#10622847C2218yescomplemented
37#10622820C2214yescomplemented
38#10622663C2218yescomplemented
39#10622660C22116yescomplemented
40#10622659C2218yescomplemented
41#10622653C2218yescomplemented
42#10622650C22116yescomplemented
43#10622649C2218yescomplemented
44C2×#66874C2214yescomplemented
45#10622579C2218yescomplemented
46#10622579C2218yescomplemented
47C2×#66873C2214yescomplemented
48C2×C11×#41—28no—
49C2×C11×#41—22no—
50C2×C11×#41—28no—
51C2×C11×#41D414yes—
52C2×C11×#41C2314yes—
53C2×C11×#41C2314yes—
54C22×Q8×C11D411yescharacteristic
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11D412yes—
59C22×D4×C11D411yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—24no—
66C22×C22⋊D11—22no—
67#67043—216no—
68#67043—216no—
69#67042—216no—
70#67042—216no—
71#41×D11—264no—
72#67040—216no—
73C2×#4343—24no—
74C2×Q8×D11—24no—
75#67037—232no—
76#67037—216no—
77C2×#4341—28no—
78C2×#4341—24no—
79C2×D4×D11—28no—
80C2×D4×D11—24no—
81C2×#4339—24no—
82C2×#4339—22no—
83C2×#4339—24no—
84C2×#4339—22no—
85C2×#4339—28no—
86C2×#4339—232no—
87C2×#4339D4116yescomplemented
88C2×#4339C2318yes—
89C2×#4339C2314yes—
90C2×#4339C2314yes—
91C22×D44C2314yes—
92C22×D44C2312yes—
93C22×C4×D11—24no—
94C22×C4×D11—22no—
95C22×Dic22C2314yes—
96C22×Dic22C2312yes—
97C11×C22⋊Q8—28no—
98C11×C22⋊Q8—24no—
99C11×C22⋊Q8C2318yes—
100C11×#121—28no—
101C11×#121—216no—
102C11×#121—24no—
103C11×#121C2318yes—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111#67004—216no—
112#67003—232no—
113#67002—216no—
114C2×#4326C2318yes—
115#66995—216no—
116C2×#4325C2318yes—
117C2×#4324C2318yes—
118#66985—216no—
119C2×#4323C2318yes—
120C2×#4318—28no—
121C2×#4318C2314yes—
122C2×#4318C2314yes—
123C22×C11⋊C8C2314yes—
124C22⋊(C11⋊C8)C2318yes—
125C22⋊(C11⋊C8)C2318yes—
126#66874C23116yes—
127#66873C23116yes—
128#60371—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11C2×D412yes—
131C24×C11C2×D411yescharacteristic
132C23×D11—24no—
133C23×D11—22no—
134C11×#41—216no—
135C11×#41—28no—
136C11×#41—28no—
137C11×#41—28no—
138C11×#41—28no—
139C11×#41—48no—
140C2×Q8×C11—24no—
141C2×Q8×C11—21no—
142C2×Q8×C11—24no—
143C2×Q8×C11C2×D414yes—
144C2×Q8×C11C2412yes—
145C2×D4×C11—28no—
146C2×D4×C11—24no—
147C2×D4×C11—28no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—44no—
152C2×D4×C11—84no—
153C2×D4×C11C2×D418yes—
154C2×D4×C11C2×D414yes—
155C2×D4×C11C2412yes—
156C22×C4×C11—28no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—44no—
162C22×C4×C11—82no—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D418yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C2×C22⋊D11—232no—
172C2×C22⋊D11—216no—
173C2×C22⋊D11—24no—
174C2×C22⋊D11—28no—
175C2×C22⋊D11—24no—
176C22×Dic11—24no—
177C22×Dic11—22no—
178#4343—232no—
179Q8×D11—232no—
180#4341—264no—
181#4341—232no—
182D4×D11—264no—
183D4×D11—232no—
184#4339—232no—
185#4339—232no—
186#4339—216no—
187#4339—216no—
188#4339—216no—
189#4339—216no—
190#4339—28no—
191#4339—28no—
192#4339C2×D4116yes—
193#4339C2×D4116yescomplemented
194C2×D44—216no—
195C2×D44—24no—
196C2×D44—22no—
197C2×D44—24no—
198C2×D44C2×D418yescomplemented
199C2×D44C2414yes—
200C2×C4×D11—232no—
201C2×C4×D11—216no—
202C2×C4×D11—24no—
203C2×C4×D11—28no—
204C2×C4×D11—24no—
205C2×Dic22—216no—
206C2×Dic22—24no—
207C2×Dic22—22no—
208C2×Dic22—24no—
209C2×Dic22C2×D418yescomplemented
210C2×Dic22C2414yes—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—28no—
214C11×C4⋊C4C2414yes—
215C11×C22⋊C4—28no—
216C11×C22⋊C4—28no—
217#4326—216no—
218#4325—216no—
219#4324—216no—
220#4323—216no—
221#4318—28no—
222#4318—28no—
223C2×C11⋊C8—28no—
224C2×C11⋊C8C2418yes—
225C2×#585—111no—
226C2×#575—112no—
227C2×#537D1111yescharacteristic, complemented
228#3013—118no—
229#3012—118no—
230#3007—114no—
231#3006—114no—
232C2×#417—112no—
233#2879—111no—
234C23×C11—24no—
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11#12014yes—
244C23×C11C22×D414yes—
245C23×C11C22×D412yes—
246C23×C11C22×D411yescharacteristic
247C22×D11—24no—
248C22×D11—216no—
249C22×D11—28no—
250C22×D11—82no—
251C22×D11—84no—
252C22×D11—82no—
253C22×D11—84no—
254Q8×C11—28no—
255Q8×C11—24no—
256Q8×C11—42no—
257D4×C11—216no—
258D4×C11—28no—
259D4×C11—24no—
260D4×C11—48no—
261D4×C11—42no—
262D4×C11—88no—
263C2×C4×C11—24no—
264C2×C4×C11—28no—
265C2×C4×C11—28no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—44no—
269C2×C4×C11—42no—
270C2×C4×C11—48no—
271C2×C4×C11—84no—
272C2×C4×C11#12018yes—
273C2×C4×C11#12014yes—
274C2×C4×C11C22×D414yes—
275C2×C4×C11C22×D414yes—
276C2×C4×C11C22×D414yes—
277C2×C4×C11C22×D414yes—
278C2×C4×C11C22×D412yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2511yescharacteristic
281C22⋊D11—232no—
282C22⋊D11—216no—
283C22⋊D11—216no—
284C2×Dic11—216no—
285C2×Dic11—28no—
286C2×Dic11—24no—
287D44—216no—
288D44—28no—
289D44—24no—
290D44C22×D418yes—
291C4×D11—232no—
292C4×D11—216no—
293C4×D11—216no—
294Dic22—216no—
295Dic22—28no—
296Dic22—24no—
297Dic22C22×D418yes—
298C11⋊C8—28no—
299#585—2216no—
300C2×2−1+4—114no—
301C2×2−1+4—221no—
302C2×H(5,𝔽2)—114no—
303C2×H(5,𝔽2)—221no—
304C2×H(5,𝔽2)—222no—
305C22×#41—112no—
306C22×#41—114no—
307C22×#41—224no—
308C22×#41C2×D1111yescharacteristic
309C22×#41C2×D1111yescharacteristic, complemented
310#575—2216no—
311C2×#137—114no—
312C2×#137—114no—
313C2×AGL(1,ℤ/8)—114no—
314C2×AGL(1,ℤ/8)—114no—
315C2×#135—118no—
316C22×M16—112no—
317#537—24no—
318#537C2×D1118yescomplemented
319C2×C22⋊Q8—21no—
320C2×C22⋊Q8C2×D1112yescomplemented
321C2×#121—21no—
322C2×#121—22no—
323C2×#121C2×D1112yescomplemented
324C22×C4⋊C4C2×D1111yescharacteristic, complemented
325#452—1116no—
326#451—118no—
327#450—118no—
328#449—1116no—
329#448—118no—
330#447—118no—
331#417—118no—
332#417—118no—
333C2×#103—114no—
334C2×#102—114no—
335#408—118no—
336#407—114no—
337C22×C11—21no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—21no—
341C22×C11—24no—
342C22×C11—24no—
343C22×C11—24no—
344C22×C11—44no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—84no—
349C22×C11—84no—
350C22×C11C2×#12012yes—
351C22×C11C2×#12014yes—
352C22×C11C23×D411yescharacteristic
353C2×D11—28no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—88no—
357C2×D11—816no—
358C4×C11—24no—
359C4×C11—44no—
360C4×C11—42no—
361C4×C11C2×#12012yes—
362C4×C11C2×#12014yes—
363C4×C11C23×D412yes—
364Dic11—28no—
3652−1+4—2216no—
3662−1+4—2216no—
3672−1+4—2216no—
368H(5,𝔽2)—2232no—
369H(5,𝔽2)—2216no—
370H(5,𝔽2)—2216no—
371H(5,𝔽2)—2216no—
372C2×#41—28no—
373C2×#41—22no—
374C2×#41—28no—
375C2×#41—1116no—
376C2×#41—114no—
377C2×#41—114no—
378C2×#41—118no—
379C2×#41—2232no—
380C2×#41—2264no—
381C2×#41—224no—
382C2×#41—224no—
383C2×#41—228no—
384C2×#41—228no—
385C2×#41—224no—
386C2×#41—222no—
387C2×#41—224no—
388C2×#41—222no—
389C2×#41C22⋊D1114yes—
390C2×#41C22×D1114yes—
391C2×#41C22×D1114yes—
392C22×Q8—112no—
393C22×Q8—114no—
394C22×Q8—224no—
395C22×Q8C22⋊D1111yescharacteristic
396C22×Q8C22×D1111yescharacteristic
397C22×D4—21no—
398C22×D4—22no—
399C22×D4—112no—
400C22×D4—114no—
401C22×D4—224no—
402C22×D4—222no—
403C22×D4—228no—
404C22×D4—224no—
405C22×D4C22⋊D1112yes—
406C22×D4C22⋊D1111yescharacteristic
407C22×D4C22×D1111yescharacteristic
408C23×C4—21no—
409C23×C4—21no—
410C23×C4—224no—
411C23×C4—222no—
412C23×C4C22×D1112yes—
413C23×C4C22×D1111yescharacteristic
414#137—2216no—
415#137—2216no—
416AGL(1,ℤ/8)—2216no—
417AGL(1,ℤ/8)—2216no—
418#135—2232no—
419C2×Q16—118no—
420C2×SD16—118no—
421C2×SD16—118no—
422C2×D8—118no—
423C2×M16—114no—
424C2×M16—114no—
425C2×M16—228no—
426C22×C8—114no—
427C22⋊Q8—28no—
428C22⋊Q8—24no—
429C22⋊Q8C22×D1118yes—
430#121—28no—
431#121—216no—
432#121—24no—
433#121C22×D1118yes—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4C22×D1112yes—
438C2×C4⋊C4C22×D1114yes—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441#103—1116no—
442#102—1116no—
443C22⋊C8—118no—
444C22⋊C8—118no—
445C2×C11—24no—
446C2×C11—22no—
447C2×C11—44no—
448C2×C11—82no—
449C2×C11C22×#12011yescharacteristic
450C2×C11#358511yescharacteristic
451C2×C11#358611yescharacteristic
452D11—48no—
453C24—21no—
454C24—224no—
455C24—222no—
456C24C2×C22⋊D1112yes—
457C24C2×C22⋊D1111yescharacteristic
458#41—216no—
459#41—28no—
460#41—28no—
461#41—28no—
462#41—28no—
463#41—48no—
464#41—1116no—
465#41—1116no—
466#41—2216no—
467#41—2216no—
468#41—2232no—
469#41—2232no—
470#41—2264no—
471#41—2232no—
472#41—2232no—
473#41—2216no—
474#41—2216no—
475#41—228no—
476#41—228no—
477C2×Q8—24no—
478C2×Q8—21no—
479C2×Q8—24no—
480C2×Q8—118no—
481C2×Q8—114no—
482C2×Q8—2216no—
483C2×Q8—2232no—
484C2×Q8—224no—
485C2×Q8—224no—
486C2×Q8—222no—
487C2×Q8C2×C22⋊D1114yes—
488C2×Q8C23×D1112yes—
489C2×D4—28no—
490C2×D4—24no—
491C2×D4—28no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—21no—
495C2×D4—44no—
496C2×D4—84no—
497C2×D4—118no—
498C2×D4—114no—
499C2×D4—2216no—
500C2×D4—2264no—
501C2×D4—2232no—
502C2×D4—2232no—
503C2×D4—2216no—
504C2×D4—228no—
505C2×D4—224no—
506C2×D4—224no—
507C2×D4—224no—
508C2×D4—224no—
509C2×D4—222no—
510C2×D4C2×C22⋊D1118yes—
511C2×D4C2×C22⋊D1114yes—
512C2×D4C23×D1112yes—
513C22×C4—28no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—44no—
519C22×C4—82no—
520C22×C4—2232no—
521C22×C4—224no—
522C22×C4—222no—
523C22×C4—2216no—
524C22×C4—224no—
525C22×C4—228no—
526C22×C4—224no—
527C22×C4D4×D1118yes—
528C22×C4C2×C22⋊D1112yes—
529C22×C4C2×C22⋊D1114yes—
530C22×C4C2×C22⋊D1111yescharacteristic
531C22×C4C2×C22⋊D1112yes—
532C22×C4C23×D1114yes—
533C22×C4C23×D1112yes—
534C22×C4C23×D1111yescharacteristic
535Q16—2216no—
536SD16—2216no—
537SD16—2216no—
538D8—2216no—
539M16—228no—
540M16—228no—
541C2×C8—118no—
542C2×C8—228no—
543C4⋊C4—24no—
544C4⋊C4—22no—
545C4⋊C4—28no—
546C4⋊C4C23×D1114yes—
547C22⋊C4—28no—
548C22⋊C4—28no—
549C11#6037111yescharacteristic, complemented, Sylow
550C23—24no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—2216no—
560C23—224no—
561C23—228no—
562C23—882no—
563C23—882no—
564C23—884no—
565C23—884no—
566C23#6699014yes—
567C23C22×C22⋊D1114yes—
568C23C22×C22⋊D1111yescharacteristic
569C23C22×C22⋊D1112yes—
570Q8—28no—
571Q8—24no—
572Q8—42no—
573Q8—118no—
574Q8—2216no—
575Q8—228no—
576Q8—224no—
577D4—216no—
578D4—28no—
579D4—24no—
580D4—48no—
581D4—42no—
582D4—88no—
583D4—118no—
584D4—2216no—
585D4—2232no—
586D4—2216no—
587D4—2216no—
588D4—228no—
589D4—224no—
590C2×C4—24no—
591C2×C4—28no—
592C2×C4—28no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—44no—
596C2×C4—42no—
597C2×C4—48no—
598C2×C4—84no—
599C2×C4—2232no—
600C2×C4—2216no—
601C2×C4—228no—
602C2×C4—224no—
603C2×C4—2216no—
604C2×C4—2216no—
605C2×C4#6699014yes—
606C2×C4#6699018yes—
607C2×C4C2×D4×D1114yes—
608C2×C4C2×D4×D1114yes—
609C2×C4C2×D4×D1114yes—
610C2×C4C22×C22⋊D1114yes—
611C2×C4C22×C22⋊D1112yes—
612C2×C4C22×C22⋊D1111yescharacteristic
613C2×C4C24×D1111yescharacteristic
614C8—228no—
615C22—21no—
616C22—22no—
617C22—21no—
618C22—22no—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—44no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—84no—
627C22—84no—
628C22—228no—
629C22—444no—
630C22—444no—
631C22—888no—
632C22—8816no—
633C22C2×#6699012yes—
634C22C2×#6699014yes—
635C22C23×C22⋊D1111yescharacteristic
636C4—24no—
637C4—44no—
638C4—42no—
639C4—228no—
640C4C2×#6699012yes—
641C4C2×#6699014yes—
642C4C22×D4×D1112yes—
643C2—22no—
644C2—24no—
645C2—44no—
646C2—82no—
647C2—448no—
648C2C22×#6699011yescharacteristic
649C2#1308339611yescharacteristic
650C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#537C2
socleC22×C11C23×D4
hypercenterC2×#537D11
hypocenterC11#60371
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#10623453C2semidirect
2. C2×#10623353C2semidirect
3. #13077928C2semidirect
4. #13077917C2semidirect
5. #13077874C2semidirect
6. #13077866C2semidirect
7. C2×#10622579C2semidirect
8. #13077061C2semidirect
9. C2×C11×#537C2semidirect
11. C22×C11×#41C22semidirect
13. C2×#67043C22semidirect
14. C2×#67042C22semidirect
22. C11×#537C22semidirect
24. C2×C11×C22⋊Q8C22semidirect
27. C2×C11×#121C22semidirect
28. C22×C11×C4⋊C4C22semidirect
29. C2×#67004C22semidirect
31. C2×#67003C22semidirect
32. C2×#67002C22semidirect
33. C2×#66995C22semidirect
34. C2×#66985C22semidirect
35. C22×#4318C22semidirect
36. #10622847C22semidirect
37. #10622820C22semidirect
38. #10622663C22semidirect
39. #10622660C22semidirect
40. #10622659C22semidirect
41. #10622653C22semidirect
42. #10622650C22semidirect
43. #10622649C22semidirect
44. C2×#66874C22semidirect
45. #10622579C22semidirect
46. #10622579C22semidirect
47. C2×#66873C22semidirect
87. C2×#4339D4semidirect
193. #4339C2×D4semidirect
198. C2×D44C2×D4semidirect
209. C2×Dic22C2×D4semidirect
227. C2×#537D11semidirect
309. C22×#41C2×D11semidirect
318. #537C2×D11semidirect
320. C2×C22⋊Q8C2×D11semidirect
323. C2×#121C2×D11semidirect
324. C22×C4⋊C4C2×D11semidirect
549. C11#60371semidirect

Maximal subgroups

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

subgroupindex
C2×#106234532
C2×#106233532
#130779282
#130779172
#130778742
#130778662
C2×#106225792
#130770612
C2×C11×#5372
#6037111