Finite Group Databasebeta

← C2×#13079413 #15624354

Subgroups — C2×#13079413 #15624354

Order 2816.

3010 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic, complemented
2#13079413C2116yesmaximal, direct product factor
3C2×#10622581C212yesmaximal, complemented
4C2×#10622647C212yesmaximal, complemented
5C2×#10622652C214yesmaximal, complemented
6C2×#10622830C212yesmaximal, complemented
7C2×#10622649C212yesmaximal, complemented
8C2×#10622820C211yesmaximal, characteristic, complemented
9C22×C11×#121C211yesmaximal, characteristic, complemented
10C23×D4×C11—21no—
11C23×D4×C11C2211yescharacteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11—21no—
14C23×D44C2211yescharacteristic, complemented
15C2×C11×#121—21no—
16C2×C11×#121—24no—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C11×#121C2212yescomplemented
20C2×C11×#121C2218yescomplemented
21C22×C11×C4⋊C4C2211yescharacteristic, complemented
22C22×C11×C22⋊C4—21no—
23C22×#4323C2214yescomplemented
24C2×#66983—21no—
25C2×#66983—24no—
26C2×#66983—21no—
27C2×#66983C2212yes—
28C2×#66983C2212yescomplemented
29C2×#66983C2218yescomplemented
30C22×(C2×D11)⋊C4—21no—
31C22×C4⋊Dic11C2211yescharacteristic, complemented
32C22×#4318C2212yescomplemented
33#10622830C22116yescomplemented
34C2×#66896C2214yescomplemented
35#10622820C2218yescomplemented
36C2×C22⋊(C11⋊C8)C2212yescomplemented
37C2×C22⋊(C11⋊C8)C2212yescomplemented
38#10622652C22132yescomplemented
39#10622649C22116yescomplemented
40#10622647C22116yescomplemented
41#10622581C22116yescomplemented
42C2×#66873C2214yescomplemented
43C2×#66872C2214yescomplemented
44C25×C11—21no—
45C25×C11D411yescharacteristic
46C24×D11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—28no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—44no—
53C22×D4×C11—48no—
54C22×D4×C11C2312yes—
55C22×D4×C11C2314yescomplemented
56C23×C4×C11—21no—
57C23×C4×C11—44no—
58C23×C4×C11D411yescharacteristic
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D414yes—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2314yes—
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—28no—
69C22×C22⋊D11—48no—
70C23×Dic11—21no—
71C22×D44—22no—
72C22×D44—21no—
73C22×D44—44no—
74C22×D44C2312yes—
75C22×D44C2314yescomplemented
76C11×#121—24no—
77C11×#121—28no—
78C11×#121—24no—
79C11×#121—28no—
80C11×#121C2318yes—
81C11×#121C2318yescomplemented
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2314yescomplemented
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—28no—
88C2×C11×C22⋊C4—22no—
89C2×#4323—48no—
90C2×#4323C23116yescomplemented
91#66983—24no—
92#66983—24no—
93#66983—28no—
94#66983—28no—
95#66983C2318yes—
96#66983C2318yescomplemented
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—28no—
99C2×(C2×D11)⋊C4—22no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2314yescomplemented
104C2×#4318—44no—
105C2×#4318C2318yescomplemented
106C22×C11⋊C8C2314yes—
107#66896C23116yescomplemented
108C22⋊(C11⋊C8)C2318yescomplemented
109C22⋊(C11⋊C8)C2318yescomplemented
110#66873C23116yescomplemented
111#66872C23116yescomplemented
112C2×#3192—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—22no—
116C24×C11—24no—
117C24×C11—42no—
118C24×C11—44no—
119C24×C11—44no—
120C24×C11—44no—
121C24×C11C2×D411yescharacteristic
122C24×C11C2×D414yes—
123C24×C11C2×D411yescharacteristic
124C24×C11C2×D411yescharacteristic
125C23×D11—22no—
126C23×D11—24no—
127C23×D11—44no—
128C23×D11—44no—
129C23×D11—44no—
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C2×D4×C11—22no—
133C2×D4×C11—24no—
134C2×D4×C11—28no—
135C2×D4×C11—48no—
136C2×D4×C11—44no—
137C2×D4×C11—48no—
138C2×D4×C11—432no—
139C2×D4×C11—48no—
140C2×D4×C11—48no—
141C2×D4×C11C2414yes—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—22no—
146C22×C4×C11—24no—
147C22×C4×C11—48no—
148C22×C4×C11—48no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—44no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11—28no—
167C2×C22⋊D11—28no—
168C2×C22⋊D11—432no—
169C2×C22⋊D11—48no—
170C2×C22⋊D11—48no—
171C22×Dic11—22no—
172C22×Dic11—24no—
173C22×Dic11—44no—
174C2×D44—22no—
175C2×D44—24no—
176C2×D44—28no—
177C2×D44—48no—
178C2×D44—44no—
179C2×D44—48no—
180C2×D44C2414yes—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4C2414yes—
184C11×C22⋊C4—28no—
185C11×C22⋊C4—28no—
186#4323—416no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189C4⋊Dic11—22no—
190C4⋊Dic11—24no—
191C4⋊Dic11C2414yes—
192#4318—48no—
193C2×C11⋊C8—28no—
194C2×C11⋊C8C2418yes—
195C22×#121—111no—
196C22×#121D1111yescharacteristic, complemented
197#3192—1116no—
198C2×#481—112no—
199C2×#481—112no—
200C2×#469—114no—
201C2×#447—112no—
202C2×#447—112no—
203C2×#407—111no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—28no—
210C23×C11—22no—
211C23×C11—28no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—44no—
215C23×C11—416no—
216C23×C11—48no—
217C23×C11—48no—
218C23×C11—44no—
219C23×C11—44no—
220C23×C11—48no—
221C23×C11—44no—
222C23×C11—816no—
223C23×C11AGL(1,ℤ/8)14yes—
224C23×C11AGL(1,ℤ/8)14yes—
225C23×C11C22×D412yes—
226C23×C11C22×D412yes—
227C23×C11C22×D412yes—
228C23×C11C22×D411yescharacteristic
229C22×D11—24no—
230C22×D11—48no—
231C22×D11—48no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—48no—
235C22×D11—44no—
236C22×D11—816no—
237D4×C11—28no—
238D4×C11—48no—
239D4×C11—416no—
240D4×C11—416no—
241D4×C11—44no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11—44no—
255C2×C4×C11—48no—
256C2×C4×C11—44no—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11H(5,𝔽2)14yes—
262C2×C4×C11C2511yescharacteristic
263C22⋊D11—416no—
264C22⋊D11—416no—
265C2×Dic11—24no—
266C2×Dic11—48no—
267C2×Dic11—44no—
268D44—28no—
269D44—48no—
270D44—44no—
271C11⋊C8—28no—
272C23×D4—21no—
273C23×D4—111no—
274C23×D4—221no—
275C23×D4C2×D1111yescharacteristic, complemented
276C24×C4C2×D1111yescharacteristic
277C22×D8—114no—
278C22×M16—112no—
279C2×#121—21no—
280C2×#121—24no—
281C2×#121—21no—
282C2×#121—112no—
283C2×#121—118no—
284C2×#121—112no—
285C2×#121—221no—
286C2×#121—224no—
287C2×#121—221no—
288C2×#121C2×D1112yes—
289C2×#121C2×D1112yescomplemented
290C2×#121C2×D1118yescomplemented
291C22×C4⋊C4—111no—
292C22×C4⋊C4C2×D1111yescharacteristic, complemented
293C22×C22⋊C4—21no—
294C22×C22⋊C4—221no—
295#481—1116no—
296#481—1116no—
297#469—1132no—
298#447—1116no—
299#447—1116no—
300C2×#106—114no—
301C2×#102—114no—
302C2×#102—114no—
303#407—118no—
304C2×C22⋊C8—112no—
305C2×C22⋊C8—112no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—28no—
309C22×C11—28no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—416no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—816no—
321C22×C11—88no—
322C22×C11#53412yes—
323C22×C11C2×AGL(1,ℤ/8)14yes—
324C22×C11C2×AGL(1,ℤ/8)12yes—
325C22×C11C2×AGL(1,ℤ/8)14yes—
326C22×C11C2×AGL(1,ℤ/8)12yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—816no—
332C2×D11—88no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—44no—
337C4×C11#53412yes—
338C4×C11C2×H(5,𝔽2)12yes—
339Dic11—44no—
340C25—21no—
341C25—221no—
342C25C22⋊D1111yescharacteristic
343C22×D4—22no—
344C22×D4—28no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—21no—
348C22×D4—44no—
349C22×D4—48no—
350C22×D4—112no—
351C22×D4—114no—
352C22×D4—228no—
353C22×D4—222no—
354C22×D4—222no—
355C22×D4—222no—
356C22×D4—221no—
357C22×D4—444no—
358C22×D4—448no—
359C22×D4C22×D1112yes—
360C22×D4C22×D1114yescomplemented
361C23×C4—21no—
362C23×C4—44no—
363C23×C4—221no—
364C23×C4C22⋊D1111yescharacteristic
365C23×C4C22⋊D1111yescharacteristic
366C23×C4C22⋊D1114yes—
367C23×C4C22⋊D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1111yescharacteristic
370C23×C4C22×D1111yescharacteristic
371C23×C4C22×D1114yes—
372C2×D8—1116no—
373C2×D8—448no—
374C2×M16—118no—
375C2×M16—444no—
376C22×C8—114no—
377#121—24no—
378#121—28no—
379#121—24no—
380#121—28no—
381#121—118no—
382#121—118no—
383#121—224no—
384#121—224no—
385#121—228no—
386#121—228no—
387#121C22×D1118yes—
388#121C22×D1118yescomplemented
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—112no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4C22×D1112yes—
396C2×C4⋊C4C22×D1114yescomplemented
397C2×C22⋊C4—22no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—228no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—222no—
403#106—1116no—
404#102—1116no—
405#102—1116no—
406C22⋊C8—118no—
407C22⋊C8—118no—
408C2×C11—24no—
409C2×C11—24no—
410C2×C11—42no—
411C2×C11—84no—
412C2×C11#319214yescomplemented
413C2×C11C2×#53411yescharacteristic
414C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
415C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
416D11—84no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—22no—
421C24—42no—
422C24—44no—
423C24—44no—
424C24—44no—
425C24—224no—
426C24—222no—
427C24—444no—
428C24—444no—
429C24—444no—
430C24C2×C22⋊D1111yescharacteristic
431C24C2×C22⋊D1114yes—
432C24C2×C22⋊D1111yescharacteristic
433C24C2×C22⋊D1111yescharacteristic
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—28no—
437C2×D4—22no—
438C2×D4—24no—
439C2×D4—48no—
440C2×D4—44no—
441C2×D4—48no—
442C2×D4—432no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—114no—
446C2×D4—228no—
447C2×D4—228no—
448C2×D4—228no—
449C2×D4—224no—
450C2×D4—222no—
451C2×D4—448no—
452C2×D4—444no—
453C2×D4—448no—
454C2×D4—4432no—
455C2×D4—448no—
456C2×D4—448no—
457C2×D4C23×D1114yes—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—48no—
464C22×C4—48no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—44no—
469C22×C4—224no—
470C22×C4—222no—
471C22×C4—444no—
472C22×C4C2×C22⋊D1112yes—
473C22×C4C2×C22⋊D1112yes—
474C22×C4C2×C22⋊D1112yes—
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1114yes—
479C22×C4C2×C22⋊D1114yes—
480C22×C4C2×C22⋊D1114yes—
481C22×C4C23×D1112yes—
482C22×C4C23×D1112yes—
483C22×C4C23×D1112yes—
484C22×C4C23×D1111yescharacteristic
485D8—4416no—
486M16—448no—
487C2×C8—118no—
488C2×C8—228no—
489C4⋊C4—22no—
490C4⋊C4—24no—
491C4⋊C4—114no—
492C4⋊C4—224no—
493C4⋊C4—222no—
494C4⋊C4C23×D1114yes—
495C22⋊C4—28no—
496C22⋊C4—28no—
497C22⋊C4—228no—
498C22⋊C4—228no—
499C11C2×#319211yescharacteristic, complemented, Sylow
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—28no—
505C23—22no—
506C23—22no—
507C23—28no—
508C23—22no—
509C23—24no—
510C23—44no—
511C23—416no—
512C23—48no—
513C23—48no—
514C23—44no—
515C23—44no—
516C23—48no—
517C23—44no—
518C23—816no—
519C23—224no—
520C23—448no—
521C23—448no—
522C23—448no—
523C23—444no—
524C23—444no—
525C23—444no—
526C23—8816no—
527C23#6698514yes—
528C23#6700214yes—
529C23C22×C22⋊D1112yes—
530C23C22×C22⋊D1112yes—
531C23C22×C22⋊D1112yes—
532C23C22×C22⋊D1111yescharacteristic
533D4—28no—
534D4—48no—
535D4—416no—
536D4—416no—
537D4—44no—
538D4—228no—
539D4—448no—
540D4—4416no—
541D4—4416no—
542D4—444no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—48no—
557C2×C4—44no—
558C2×C4—224no—
559C2×C4—448no—
560C2×C4—444no—
561C2×C4#6703714yes—
562C2×C4C22×C22⋊D1112yes—
563C2×C4C22×C22⋊D1112yes—
564C2×C4C22×C22⋊D1112yes—
565C2×C4C22×C22⋊D1111yescharacteristic
566C2×C4C24×D1111yescharacteristic
567C8—228no—
568C22—22no—
569C22—22no—
570C22—28no—
571C22—28no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—416no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—816no—
583C22—88no—
584C22—444no—
585C22—444no—
586C22—444no—
587C22—8816no—
588C22—888no—
589C22C2×#6698514yes—
590C22C2×#6698512yes—
591C22#1062333512yes—
592C22C2×#6700214yes—
593C22C2×#6700212yes—
594C22C23×C22⋊D1111yescharacteristic
595C4—22no—
596C4—22no—
597C4—22no—
598C4—44no—
599C4—444no—
600C4#1062333512yes—
601C4C2×#6703712yes—
602C2—24no—
603C2—24no—
604C2—42no—
605C2—84no—
606C2—884no—
607C2#1307941314yesdirect product factor
608C2C2×#1062333511yescharacteristic
609C2C22×#6700211yescharacteristic
610C2C22×#6698511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#121C2
socleC23×C11C22×D4
hypercenterC22×#121D11
hypocenterC11C2×#3192
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66983C2semidirect
2. #13079413C2direct (N × H)
3. C2×#10622581C2semidirect
4. C2×#10622647C2semidirect
5. C2×#10622652C2semidirect
6. C2×#10622830C2semidirect
7. C2×#10622649C2semidirect
8. C2×#10622820C2semidirect
9. C22×C11×#121C2semidirect
11. C23×D4×C11C22semidirect
14. C23×D44C22semidirect
19. C2×C11×#121C22semidirect
20. C2×C11×#121C22semidirect
21. C22×C11×C4⋊C4C22semidirect
23. C22×#4323C22semidirect
28. C2×#66983C22semidirect
29. C2×#66983C22semidirect
31. C22×C4⋊Dic11C22semidirect
32. C22×#4318C22semidirect
33. #10622830C22semidirect
34. C2×#66896C22semidirect
35. #10622820C22semidirect
36. C2×C22⋊(C11⋊C8)C22semidirect
37. C2×C22⋊(C11⋊C8)C22semidirect
38. #10622652C22semidirect
39. #10622649C22semidirect
40. #10622647C22semidirect
41. #10622581C22semidirect
42. C2×#66873C22semidirect
43. C2×#66872C22semidirect
55. C22×D4×C11C23semidirect
75. C22×D44C23semidirect
81. C11×#121C23semidirect
85. C2×C11×C4⋊C4C23semidirect
90. C2×#4323C23semidirect
96. #66983C23semidirect
103. C2×C4⋊Dic11C23semidirect
105. C2×#4318C23semidirect
107. #66896C23semidirect
108. C22⋊(C11⋊C8)C23semidirect
109. C22⋊(C11⋊C8)C23semidirect
110. #66873C23semidirect
111. #66872C23semidirect
196. C22×#121D11semidirect
275. C23×D4C2×D11semidirect
289. C2×#121C2×D11semidirect
290. C2×#121C2×D11semidirect
292. C22×C4⋊C4C2×D11semidirect
360. C22×D4C22×D11semidirect
388. #121C22×D11semidirect
396. C2×C4⋊C4C22×D11semidirect
412. C2×C11#3192semidirect
499. C11C2×#3192semidirect
607. C2#13079413direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669832
#130794132
C2×#106225812
C2×#106226472
C2×#106226522
C2×#106228302
C2×#106226492
C2×#106228202
C22×C11×#1212
C2×#319211