Finite Group Databasebeta

← C2×#13074177 #14924404

Subgroups — C2×#13074177 #14924404

Order 2816.

3502 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic, complemented
2C22×#66945C211yesmaximal, characteristic, complemented
3#13074177C2116yesmaximal, direct product factor
4C2×#10622599C211yesmaximal, characteristic, complemented
5C2×#10622290C211yesmaximal, characteristic, complemented
6C2×#10622836C211yesmaximal, characteristic
7C2×#10622564C212yesmaximal, complemented
8C2×#10622571C212yesmaximal, complemented
9C2×#10622569C212yesmaximal, complemented
10C2×#10622563C212yesmaximal, complemented
11C2×#10622264C211yesmaximal, characteristic, complemented
12C2×C11×#394C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C24×Dic11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C2×D4×Dic11—28no—
23C2×D4×Dic11C2218yescomplemented
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C2×#66945—28no—
33C2×#66945C2218yescomplemented
34C11×#394C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36#10622836C2218yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622599C2218yescomplemented
43#10622571C22116yescomplemented
44#10622569C22116yescomplemented
45#10622564C22116yescomplemented
46#10622563C22116yescomplemented
47#10622290C2218yescomplemented
48#10622264C2218yescomplemented
49C25×C11C2312yes—
50C24×D11C2311yescharacteristic
51C22×D4×C11—28no—
52C22×D4×C11—24no—
53C22×D4×C11C2314yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—28no—
59C22×C22⋊D11—28no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11C2318yes—
62C23×Dic11—28no—
63C23×Dic11—44no—
64C23×Dic11—44no—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2318yes—
71C22×C4×D11—24no—
72C22×C4×D11—24no—
73C22×C4×D11—24no—
74C22×C4×D11C2314yes—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C22⋊C4—28no—
78C2×C11×C22⋊C4—28no—
79C2×C11×C22⋊C4C2318yes—
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—44no—
83C2×C22⋊Dic11C2318yes—
84C2×C22⋊Dic11C2318yes—
85D4×Dic11—232no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11—44no—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2314yes—
97C2×C4⋊Dic11C2318yes—
98C2×C4×Dic11—24no—
99C2×C4×Dic11D418yescomplemented
100C2×C4×Dic11C2314yes—
101C2×C4×Dic11C2314yes—
102#66945—232no—
103C11×#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2314yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C2×#2598—111nomaximal, Sylow
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11#4118yes—
117C24×C11C2414yes—
118C24×C11C2411yescharacteristic
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11#4114yes—
124C23×D11C2412yes—
125C2×D4×C11—232no—
126C2×D4×C11—216no—
127C2×D4×C11—28no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11C2×D414yes—
137C22×C4×C11#4114yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C2×C22⋊D11—216no—
143C2×C22⋊D11—216no—
144C2×C22⋊D11—48no—
145C2×C22⋊D11—432no—
146C22×Dic11—216no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—48no—
159C22×Dic11—48no—
160C22×Dic11—432no—
161C22×Dic11C2×D414yes—
162C22×Dic11C2×D414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2414yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2412yes—
168C2×C4×D11—232no—
169C2×C4×D11—28no—
170C2×C4×D11—28no—
171C2×C4×D11—28no—
172C11×C4⋊C4—28no—
173C11×C22⋊C4—216no—
174C11×C22⋊C4—216no—
175C22⋊Dic11—216no—
176C22⋊Dic11—48no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—48no—
180C4⋊Dic11—28no—
181C4⋊Dic11—28no—
182C4⋊Dic11—48no—
183C4×Dic11—28no—
184C4×Dic11C2×D4116yescomplemented
185C22×C4×D4—111no—
186C22×#117—111no—
187#2598—1116no—
188C2×#400—111no—
189C2×#399—111no—
190C2×#394D1111yescharacteristic, complemented
191C2×#392—111no—
192C2×#388—112no—
193C2×#386—112no—
194C2×#386—112no—
195C2×#385—112no—
196C2×#383—111no—
197C23×C11—216no—
198C23×C11—216no—
199C23×C11—216no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11C22×D412yes—
211C23×C11C2×#4118yes—
212C23×C11C2×#4114yes—
213C23×C11C2×#4112yes—
214C23×C11C2×#4112yes—
215C23×C11H(5,𝔽2)14yes—
216C23×C11C2511yescharacteristic
217C22×D11—28no—
218C22×D11—216no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—44no—
224C22×D11—44no—
225C22×D11—48no—
226C22×D11C2×#4114yes—
227D4×C11—232no—
228C2×C4×C11—28no—
229C2×C4×C11—28no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—44no—
239C2×C4×C11—48no—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C2×#4114yes—
242C22⋊D11—432no—
243C2×Dic11—28no—
244C2×Dic11—28no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—432no—
257C2×Dic11—44no—
258C2×Dic11—48no—
259C2×Dic11—48no—
260C2×Dic11C22×D414yes—
261C2×Dic11C22×D414yes—
262C4×D11—232no—
263C23×D4—112no—
264C23×D4C2×D1111yescharacteristic
265C24×C4—112no—
266C24×C4—111no—
267C2×C4×D4—118no—
268C2×C4×D4—228no—
269C2×#117—118no—
270C2×#117—228no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—112no—
274C22×C4⋊C4C2×D1111yescharacteristic
275C22×C22⋊C4—112no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4C2×D1112yes—
281C22×C22⋊C4C2×D1112yes—
282C22×C42—111no—
283C22×C42—111no—
284#400—118no—
285#399—118no—
286#394C2×D1118yescomplemented
287#392—118no—
288#388—1116no—
289#386—1116no—
290#386—1116no—
291#385—1116no—
292#383—118no—
293C2×#95—111no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95C2×D1111yescharacteristic
299C22×C11—28no—
300C22×C11—28no—
301C22×C11—28no—
302C22×C11—432no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11#52514yes—
308C22×C11#52514yes—
309C22×C11#53514yes—
310C22×C11#55118yes—
311C22×C11#55318yes—
312C22×C11C23×D411yescharacteristic
313C22×C11C22×#4112yes—
314C22×C11C22×#4111yescharacteristic
315C22×C11C22×#4111yescharacteristic
316C22×C11C2×H(5,𝔽2)12yes—
317C2×D11—24no—
318C2×D11—28no—
319C2×D11—416no—
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—44no—
323C4×C11—24no—
324C4×C11—24no—
325C4×C11—42no—
326C4×C11—44no—
327Dic11—24no—
328Dic11—24no—
329Dic11—42no—
330Dic11—44no—
331Dic11—44no—
332C25—111no—
333C25C22×D1112yes—
334C22×D4—28no—
335C22×D4—24no—
336C22×D4—118no—
337C22×D4—228no—
338C22×D4—228no—
339C22×D4—444no—
340C22×D4C22×D1114yes—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—112no—
345C23×C4—112no—
346C23×C4—118no—
347C23×C4—114no—
348C23×C4—224no—
349C23×C4—224no—
350C23×C4—228no—
351C23×C4—224no—
352C23×C4—444no—
353C23×C4—444no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1111yescharacteristic
358C4×D4—2232no—
359#117—2232no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—444no—
367C2×C4⋊C4C22×D1114yes—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—228no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—444no—
379C2×C22⋊C4—444no—
380C2×C22⋊C4C22×D1118yes—
381C2×C22⋊C4C22×D1118yes—
382C2×C42—118no—
383C2×C42—114no—
384C2×C42—114no—
385C2×C42—224no—
386#95—118no—
387#95—118no—
388#95—114no—
389#95—118no—
390#95—118no—
391#95C22×D1114yes—
392C2×C11—48no—
393C2×C11#259818yescomplemented
394C2×C11C2×#52511yescharacteristic
395C2×C11C2×#52511yescharacteristic
396C2×C11C2×#53511yescharacteristic
397C2×C11C2×#55112yes—
398C2×C11C2×#55312yes—
399D11—44no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—114no—
407C24—112no—
408C24—222no—
409C24—222no—
410C24—224no—
411C24—224no—
412C24#434118yes—
413C24C23×D1114yes—
414C24C23×D1111yescharacteristic
415C2×D4—232no—
416C2×D4—216no—
417C2×D4—28no—
418C2×D4—2216no—
419C2×D4—2216no—
420C2×D4—448no—
421C2×D4—4432no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—112no—
437C22×C4—228no—
438C22×C4—228no—
439C22×C4—2232no—
440C22×C4—2216no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—224no—
444C22×C4—228no—
445C22×C4—222no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—448no—
454C22×C4—448no—
455C22×C4—4432no—
456C22×C4D4×D1114yes—
457C22×C4#434114yes—
458C22×C4C23×D1114yes—
459C22×C4C23×D1112yes—
460C22×C4C23×D1112yes—
461C22×C4C23×D1112yes—
462C4⋊C4—28no—
463C4⋊C4—228no—
464C4⋊C4—228no—
465C4⋊C4—448no—
466C22⋊C4—216no—
467C22⋊C4—216no—
468C22⋊C4—228no—
469C22⋊C4—2216no—
470C22⋊C4—228no—
471C22⋊C4—448no—
472C22⋊C4—448no—
473C42—1116no—
474C42—228no—
475C11C2×#259811yescharacteristic, complemented, Sylow
476C23—216no—
477C23—216no—
478C23—24no—
479C23—216no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—24no—
485C23—48no—
486C23—48no—
487C23—48no—
488C23—48no—
489C23—114no—
490C23—228no—
491C23—222no—
492C23—2216no—
493C23—222no—
494C23—224no—
495C23—224no—
496C23—444no—
497C23—448no—
498C23—444no—
499C23C2×D4×D1112yes—
500C23C2×#434118yes—
501C23C2×#434114yes—
502C23C2×#434112yes—
503C23#41×D1112yes—
504C23#6704214yes—
505C23C24×D1111yescharacteristic
506D4—232no—
507D4—4432no—
508C2×C4—28no—
509C2×C4—28no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—44no—
519C2×C4—48no—
520C2×C4—114no—
521C2×C4—114no—
522C2×C4—2232no—
523C2×C4—228no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—224no—
527C2×C4—228no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—4432no—
537C2×C4—448no—
538C2×C4—448no—
539C2×C4—444no—
540C2×C4C2×D4×D1114yes—
541C2×C4C2×#434114yes—
542C22—28no—
543C22—28no—
544C22—28no—
545C22—432no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—224no—
551C22—228no—
552C22—4416no—
553C22—444no—
554C22—442no—
555C22—442no—
556C22#1062311714yes—
557C22#1062313714yes—
558C22#1062314918yes—
559C22#1062318918yes—
560C22#1062320514yes—
561C22C22×D4×D1111yescharacteristic
562C22C22×#434111yescharacteristic
563C22C22×#434112yes—
564C22C2×#41×D1111yescharacteristic
565C22C2×#6704212yes—
566C4—24no—
567C4—24no—
568C4—44no—
569C4—42no—
570C4—224no—
571C4—224no—
572C4—444no—
573C4—442no—
574C4—444no—
575C2—48no—
576C2—444no—
577C2#1307417718yesdirect product factor
578C2C2×#1062311711yescharacteristic
579C2C2×#1062313711yescharacteristic
580C2C2×#1062320511yescharacteristic
581C2C2×#1062318912yes—
582C2C2×#1062314912yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#394D11
hypocenterC11C2×#2598
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic11C2semidirect
2. C22×#66945C2semidirect
3. #13074177C2direct (N × H)
4. C2×#10622599C2semidirect
5. C2×#10622290C2semidirect
7. C2×#10622564C2semidirect
8. C2×#10622571C2semidirect
9. C2×#10622569C2semidirect
10. C2×#10622563C2semidirect
11. C2×#10622264C2semidirect
12. C2×C11×#394C2semidirect
23. C2×D4×Dic11C22semidirect
33. C2×#66945C22semidirect
34. C11×#394C22semidirect
42. #10622599C22semidirect
43. #10622571C22semidirect
44. #10622569C22semidirect
45. #10622564C22semidirect
46. #10622563C22semidirect
47. #10622290C22semidirect
48. #10622264C22semidirect
99. C2×C4×Dic11D4semidirect
184. C4×Dic11C2×D4semidirect
190. C2×#394D11semidirect
286. #394C2×D11semidirect
393. C2×C11#2598semidirect
475. C11C2×#2598semidirect
577. C2#13074177direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C22×#669452
#130741772
C2×#106225992
C2×#106222902
C2×#106228362
C2×#106225642
C2×#106225712
C2×#106225692
C2×#106225632
C2×#106222642
C2×C11×#3942
C2×#259811