Finite Group Databasebeta

← C2×#13079423 #15624365

Subgroups — C2×#13079423 #15624365

Order 2816.

2666 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic
3#13079423C2116yesmaximal, direct product factor
4C2×#10622335C212yesmaximal, complemented
5C2×#10622349C212yesmaximal, complemented
6C2×#10622747C214yesmaximal, complemented
7C2×#10622351C212yesmaximal, complemented
8C2×#10622344C212yesmaximal, complemented
9C2×C11×#407C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11—21no—
12C23×D44C2211yescharacteristic
13C23×Dic22C2211yescharacteristic, complemented
14C22×C11×M16C2212yescomplemented
15C22×C22⋊Dic11—21no—
16C2×#66983—21no—
17C2×#66983—21no—
18C2×#66983—24no—
19C2×#66983C2212yes—
20C2×#66983C2218yes—
21C2×#66983C2212yes—
22C22×(C2×D11)⋊C4—21no—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic, complemented
25C2×#66977—21no—
26C2×#66977—24no—
27C2×#66977—21no—
28C2×#66977C2212yes—
29C2×#66977C2218yescomplemented
30C2×#66977C2212yescomplemented
31C22×Dic11⋊C4—21no—
32C22×#4314C2214yescomplemented
33C11×#407C2218yescomplemented
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yescomplemented
36#10622747C22132yescomplemented
37C2×#66885C2214yescomplemented
38C2×#66882C2214yescomplemented
39C2×#66880C2214yescomplemented
40#10622351C22116yescomplemented
41#10622349C22116yescomplemented
42#10622344C22116yescomplemented
43#10622335C22116yescomplemented
44C25×C11D411yescharacteristic
45C24×D11—21no—
46C23×C4×C11—44no—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D414yes—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2314yes—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—28no—
57C22×C22⋊D11—22no—
58C22×C22⋊D11—48no—
59C23×Dic11—21no—
60C23×Dic11—21no—
61C23×Dic11—21no—
62C22×D44—21no—
63C22×D44—22no—
64C22×D44—44no—
65C22×D44C2312yes—
66C22×D44C2314yes—
67C22×Dic22—22no—
68C22×Dic22—21no—
69C22×Dic22—44no—
70C22×Dic22C2312yes—
71C22×Dic22C2314yescomplemented
72C2×C11×M16—44no—
73C2×C11×M16C2318yescomplemented
74C22×C8×C11C2314yes—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—22no—
78#66983—24no—
79#66983—24no—
80#66983—28no—
81#66983—28no—
82#66983C2318yes—
83#66983C2318yes—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—28no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2314yescomplemented
95#66977—24no—
96#66977—28no—
97#66977—24no—
98#66977—28no—
99#66977C2318yes—
100#66977C2318yescomplemented
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—28no—
103C2×Dic11⋊C4—22no—
104C2×#4314—48no—
105C2×#4314C23116yescomplemented
106C11×C22⋊C8C2318yes—
107C11×C22⋊C8C2318yescomplemented
108#66885C23116yescomplemented
109#66882C23116yescomplemented
110#66880C23116yescomplemented
111C2×#3193—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—42no—
115C24×C11C2×D411yescharacteristic
116C24×C11C2×D414yes—
117C24×C11C2×D411yescharacteristic
118C24×C11C2×D411yescharacteristic
119C23×D11—24no—
120C23×D11—22no—
121C23×D11—44no—
122C23×D11—44no—
123C23×D11—44no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—48no—
128C22×C4×C11—48no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—28no—
146C2×C22⋊D11—28no—
147C2×C22⋊D11—432no—
148C2×C22⋊D11—48no—
149C2×C22⋊D11—48no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11—44no—
157C22×Dic11—44no—
158C22×Dic11—44no—
159C2×D44—24no—
160C2×D44—22no—
161C2×D44—28no—
162C2×D44—48no—
163C2×D44—44no—
164C2×D44—48no—
165C2×D44C2414yes—
166C2×Dic22—22no—
167C2×Dic22—24no—
168C2×Dic22—28no—
169C2×Dic22—48no—
170C2×Dic22—44no—
171C2×Dic22—48no—
172C2×Dic22C2414yes—
173C11×M16—48no—
174C2×C8×C11—28no—
175C2×C8×C11C2418yes—
176C22⋊Dic11—28no—
177C22⋊Dic11—28no—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—28no—
180C4⋊Dic11—22no—
181C4⋊Dic11—24no—
182C4⋊Dic11—24no—
183C4⋊Dic11—22no—
184C4⋊Dic11C2414yes—
185C4⋊Dic11C2414yes—
186Dic11⋊C4—28no—
187Dic11⋊C4—28no—
188#4314—416no—
189C22×C22⋊Q8—111no—
190C22×#121—111no—
191#3193—1116no—
192C2×#484—112no—
193C2×#480—112no—
194C2×#468—114no—
195C2×#448—112no—
196C2×#450—112no—
197C2×#407D1111yescharacteristic, complemented
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—28no—
204C23×C11—22no—
205C23×C11—28no—
206C23×C11—22no—
207C23×C11—44no—
208C23×C11—416no—
209C23×C11AGL(1,ℤ/8)14yes—
210C23×C11#13714yes—
211C23×C11C22×D412yes—
212C23×C11C22×D412yes—
213C23×C11C22×D412yes—
214C23×C11C22×D411yescharacteristic
215C22×D11—24no—
216C22×D11—48no—
217C22×D11—48no—
218C22×D11—44no—
219C22×D11—44no—
220C22×D11—48no—
221C22×D11—44no—
222C22×D11—816no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11H(5,𝔽2)14yes—
240C2×C4×C11C2511yescharacteristic
241C22⋊D11—416no—
242C22⋊D11—416no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—48no—
247C2×Dic11—48no—
248C2×Dic11—44no—
249C2×Dic11—48no—
250C2×Dic11—44no—
251C2×Dic11—44no—
252D44—28no—
253D44—48no—
254D44—44no—
255Dic22—28no—
256Dic22—48no—
257Dic22—44no—
258C8×C11—28no—
259C23×Q8—111no—
260C23×D4—111no—
261C23×D4—221no—
262C24×C4C2×D1111yescharacteristic
263C22×SD16—114no—
264C22×M16C2×D1112yescomplemented
265C2×C22⋊Q8—112no—
266C2×C22⋊Q8—118no—
267C2×C22⋊Q8—112no—
268C2×C22⋊Q8—221no—
269C2×C22⋊Q8—224no—
270C2×C22⋊Q8—221no—
271C2×#121—112no—
272C2×#121—118no—
273C2×#121—112no—
274C2×#121—221no—
275C2×#121—224no—
276C2×#121—221no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4—221no—
280C22×C22⋊C4—221no—
281C22×C22⋊C4—221no—
282#484—1116no—
283#480—1116no—
284#468—1132no—
285#450—1116no—
286#448—1116no—
287C2×#107—114no—
288C2×#103—114no—
289C2×#102—114no—
290#407C2×D1118yescomplemented
291C2×C22⋊C8C2×D1112yes—
292C2×C22⋊C8C2×D1112yescomplemented
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—28no—
296C22×C11—28no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—416no—
303C22×C11—44no—
304C22×C11#53412yes—
305C22×C11C2×AGL(1,ℤ/8)14yes—
306C22×C11C2×AGL(1,ℤ/8)12yes—
307C22×C11C2×#13714yes—
308C22×C11C2×#13712yes—
309C22×C11C23×D411yescharacteristic
310C2×D11—44no—
311C2×D11—44no—
312C2×D11—44no—
313C2×D11—816no—
314C2×D11—88no—
315C4×C11—22no—
316C4×C11—22no—
317C4×C11—22no—
318C4×C11#53412yes—
319C4×C11C2×H(5,𝔽2)12yes—
320Dic11—44no—
321Dic11—44no—
322Dic11—44no—
323C25—221no—
324C25D4411yescharacteristic
325C22×Q8—112no—
326C22×Q8—114no—
327C22×Q8—222no—
328C22×Q8—221no—
329C22×Q8—444no—
330C22×D4—112no—
331C22×D4—114no—
332C22×D4—228no—
333C22×D4—222no—
334C22×D4—222no—
335C22×D4—222no—
336C22×D4—221no—
337C22×D4—444no—
338C22×D4—448no—
339C23×C4—44no—
340C23×C4—221no—
341C23×C4—221no—
342C23×C4—221no—
343C23×C4D4411yescharacteristic
344C23×C4D4411yescharacteristic
345C23×C4D4414yes—
346C23×C4D4411yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1114yes—
351C2×SD16—1116no—
352C2×SD16—448no—
353C2×M16—44no—
354C2×M16C22×D1118yescomplemented
355C22×C8C22×D1114yes—
356C22⋊Q8—118no—
357C22⋊Q8—118no—
358C22⋊Q8—224no—
359C22⋊Q8—224no—
360C22⋊Q8—228no—
361C22⋊Q8—228no—
362#121—118no—
363#121—118no—
364#121—224no—
365#121—224no—
366#121—228no—
367#121—228no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—228no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C22⋊C4—228no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—228no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385#107—1116no—
386#103—1116no—
387#102—1116no—
388C22⋊C8C22×D1118yes—
389C22⋊C8C22×D1118yescomplemented
390C2×C11—24no—
391C2×C11—24no—
392C2×C11—42no—
393C2×C11#319314yescomplemented
394C2×C11C2×#53411yescharacteristic
395C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
396C2×C11C22×#13711yescharacteristic
397D11—84no—
398C24—24no—
399C24—24no—
400C24—42no—
401C24—224no—
402C24—222no—
403C24—444no—
404C24—444no—
405C24—444no—
406C24C2×D4411yescharacteristic
407C24C2×D4414yes—
408C24C2×D4411yescharacteristic
409C24C2×D4411yescharacteristic
410C2×Q8—114no—
411C2×Q8—224no—
412C2×Q8—222no—
413C2×Q8—228no—
414C2×Q8—448no—
415C2×Q8—444no—
416C2×Q8—448no—
417C2×D4—114no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—224no—
421C2×D4—222no—
422C2×D4—228no—
423C2×D4—448no—
424C2×D4—444no—
425C2×D4—448no—
426C2×D4—4432no—
427C2×D4—448no—
428C2×D4—448no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—48no—
433C22×C4—48no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—444no—
444C22×C4—444no—
445C22×C4—444no—
446C22×C4C2×D4412yes—
447C22×C4C2×D4412yes—
448C22×C4C2×D4412yes—
449C22×C4C2×D4411yescharacteristic
450C22×C4C2×D4411yescharacteristic
451C22×C4C2×D4411yescharacteristic
452C22×C4C2×D4414yes—
453C22×C4C2×D4414yes—
454C22×C4C2×D4414yes—
455C22×C4C23×D1112yes—
456C22×C4C23×D1112yes—
457C22×C4C23×D1112yes—
458C22×C4C23×D1111yescharacteristic
459SD16—4416no—
460M16—48no—
461C2×C8—28no—
462C2×C8C23×D1118yes—
463C4⋊C4—114no—
464C4⋊C4—114no—
465C4⋊C4—224no—
466C4⋊C4—222no—
467C4⋊C4—224no—
468C4⋊C4—222no—
469C4⋊C4—228no—
470C4⋊C4—228no—
471C22⋊C4—228no—
472C22⋊C4—228no—
473C22⋊C4—228no—
474C22⋊C4—228no—
475C11C2×#319311yescharacteristic, complemented, Sylow
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—28no—
481C23—22no—
482C23—28no—
483C23—22no—
484C23—22no—
485C23—44no—
486C23—416no—
487C23—224no—
488C23—448no—
489C23—448no—
490C23—444no—
491C23—448no—
492C23—444no—
493C23—444no—
494C23—8816no—
495C23#6696114yes—
496C23#6696214yes—
497C23C22×D4412yes—
498C23C22×D4412yes—
499C23C22×D4412yes—
500C23C22×D4411yescharacteristic
501Q8—228no—
502Q8—448no—
503Q8—444no—
504D4—228no—
505D4—448no—
506D4—4416no—
507D4—4416no—
508D4—444no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—448no—
525C2×C4—448no—
526C2×C4—444no—
527C2×C4—448no—
528C2×C4—444no—
529C2×C4—444no—
530C2×C4C22×D4412yes—
531C2×C4C22×D4412yes—
532C2×C4C22×D4412yes—
533C2×C4C22×D4411yescharacteristic
534C2×C4#6703714yes—
535C2×C4C24×D1111yescharacteristic
536C8—28no—
537C22—22no—
538C22—22no—
539C22—28no—
540C22—28no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—416no—
547C22—44no—
548C22—444no—
549C22—444no—
550C22—444no—
551C22—8816no—
552C22—888no—
553C22#1062302412yes—
554C22C2×#6696114yes—
555C22C2×#6696112yes—
556C22C2×#6696214yes—
557C22C2×#6696212yes—
558C22C23×D4411yescharacteristic
559C4—22no—
560C4—22no—
561C4—22no—
562C4—444no—
563C4—444no—
564C4—444no—
565C4#1062302412yes—
566C4C2×#6703712yes—
567C2—24no—
568C2—24no—
569C2—42no—
570C2—884no—
571C2#1307942314yesdirect product factor
572C2C2×#1062302411yescharacteristic
573C2C22×#6696111yescharacteristic
574C2C22×#6696211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#407C2
socleC23×C11C22×D4
prime radicalC22×#66983C2
hypercenterC2×#407D11
hypocenterC11C2×#3193
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C22×#66977C2semidirect
3. #13079423C2direct (N × H)
4. C2×#10622335C2semidirect
5. C2×#10622349C2semidirect
6. C2×#10622747C2semidirect
7. C2×#10622351C2semidirect
8. C2×#10622344C2semidirect
9. C2×C11×#407C2semidirect
13. C23×Dic22C22semidirect
14. C22×C11×M16C22semidirect
24. C22×C4⋊Dic11C22semidirect
29. C2×#66977C22semidirect
30. C2×#66977C22semidirect
32. C22×#4314C22semidirect
33. C11×#407C22semidirect
35. C2×C11×C22⋊C8C22semidirect
36. #10622747C22semidirect
37. C2×#66885C22semidirect
38. C2×#66882C22semidirect
39. C2×#66880C22semidirect
40. #10622351C22semidirect
41. #10622349C22semidirect
42. #10622344C22semidirect
43. #10622335C22semidirect
71. C22×Dic22C23semidirect
73. C2×C11×M16C23semidirect
94. C2×C4⋊Dic11C23semidirect
100. #66977C23semidirect
105. C2×#4314C23semidirect
107. C11×C22⋊C8C23semidirect
108. #66885C23semidirect
109. #66882C23semidirect
110. #66880C23semidirect
197. C2×#407D11semidirect
264. C22×M16C2×D11semidirect
290. #407C2×D11semidirect
292. C2×C22⋊C8C2×D11semidirect
354. C2×M16C22×D11semidirect
389. C22⋊C8C22×D11semidirect
393. C2×C11#3193semidirect
475. C11C2×#3193semidirect
571. C2#13079423direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
C22×#669832
#130794232
C2×#106223352
C2×#106223492
C2×#106227472
C2×#106223512
C2×#106223442
C2×C11×#4072
C2×#319311