Finite Group Databasebeta

← C2×#13074753 #14920508

Subgroups — C2×#13074753 #14920508

Order 2816.

3002 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×#66929C211yesmaximal, characteristic, complemented
2C22×#66928C211yesmaximal, characteristic, complemented
3#13074753C2116yesmaximal, direct product factor
4C2×#10622607C212yesmaximal, complemented
5C2×#10622269C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622604C212yesmaximal, complemented
8C2×#10622286C211yesmaximal, characteristic, complemented
9C2×#10622284C211yesmaximal, characteristic
10C2×#10622552C212yesmaximal, complemented
11C2×#10622553C212yesmaximal, complemented
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×D44C2212yes—
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C42×C11C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C2×#66929—28no—
33C2×#66929C2218yescomplemented
34C2×#66928—28no—
35C2×#66928C2218yescomplemented
36C4×C11×C4⋊C4C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622607C22116yescomplemented
42#10622604C22116yescomplemented
43#10622553C22116yescomplemented
44#10622552C22116yescomplemented
45#10622286C2218yescomplemented
46#10622285C2218yescomplemented
47#10622284C2218yes—
48#10622269C2218yescomplemented
49C24×D11C2311yescharacteristic
50C24×D11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C22×D44—24no—
61C22×D44—28no—
62C22×D44—44no—
63C22×D44—44no—
64C22×D44—44no—
65C22×D44C2314yes—
66C22×D44C2318yes—
67C22×Dic22—24no—
68C22×Dic22—44no—
69C22×Dic22C2314yes—
70C2×C11×C4⋊C4—28no—
71C2×C11×C4⋊C4C2318yes—
72C2×C42×C11—44no—
73C2×C42×C11D418yescomplemented
74C2×C42×C11C2318yes—
75C2×C42×C11C2314yes—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4—44no—
83C2×(C2×D11)⋊C4—44no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4C2318yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×C4⋊Dic11—44no—
95C2×C4⋊Dic11C2318yes—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2314yes—
102#66929—232no—
103#66928—232no—
104C11×#95C2314yes—
105C11×#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2662—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C23×D11—22no—
111C23×D11—24no—
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—24no—
122C23×D11C2412yes—
123C23×D11C2414yes—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×D414yes—
136C22×C4×C11#4118yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2414yes—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C22×Dic11C2414yes—
155C22×Dic11C2412yes—
156C2×D44—28no—
157C2×D44—216no—
158C2×D44—48no—
159C2×D44—48no—
160C2×D44—48no—
161C2×D44—416no—
162C2×D44—432no—
163C2×Dic22—28no—
164C2×Dic22—48no—
165C2×Dic22—416no—
166C11×C4⋊C4—216no—
167C42×C11—48no—
168C42×C11C2×D4116yescomplemented
169(C2×D11)⋊C4—216no—
170(C2×D11)⋊C4—216no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—216no—
175(C2×D11)⋊C4—48no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178C4⋊Dic11—48no—
179Dic11⋊C4—28no—
180Dic11⋊C4—28no—
181Dic11⋊C4—28no—
182C22×#126—111no—
183C22×#124—111no—
184#2662—1116no—
185C2×#396—112no—
186C2×#395—111no—
187C2×#394—111no—
188C2×#394—112no—
189C2×#393—111no—
190C2×#392—111no—
191C2×#390—112no—
192C2×#388—112no—
193C2×C4×C4⋊C4D1111yescharacteristic, complemented
194C23×C11C22×D412yes—
195C23×C11C2×#4114yes—
196C23×C11H(5,𝔽2)12yes—
197C23×C11H(5,𝔽2)14yes—
198C23×C112−1+412yes—
199C23×C11C2511yescharacteristic
200C22×D11—22no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—22no—
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—24no—
212C22×D11—44no—
213C22×D11—48no—
214C22×D11—48no—
215C22×D11—44no—
216C22×D11—44no—
217C22×D11—48no—
218C22×D11—48no—
219C22×D11—48no—
220C22×D11—48no—
221C22×D11—48no—
222C22×D11—48no—
223C22×D11—48no—
224C2×C4×C11—28no—
225C2×C4×C11—28no—
226C2×C4×C11—28no—
227C2×C4×C11—216no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—48no—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D414yes—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C2×#4118yes—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—44no—
253C2×Dic11—48no—
254C2×Dic11—44no—
255C2×Dic11—44no—
256D44—416no—
257D44—432no—
258Dic22—416no—
259C23×Q8—111no—
260C23×D4—111no—
261C23×D4—112no—
262C2×#126—118no—
263C2×#126—228no—
264C2×#124—118no—
265C2×#124—228no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—112no—
270C22×C4⋊C4C2×D1112yes—
271C22×C22⋊C4—111no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—111no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C22×C42C2×D1112yes—
281C22×C42C2×D1111yescharacteristic
282#396—1116no—
283#395—118no—
284#394—1116no—
285#394—118no—
286#393—118no—
287#392—118no—
288#390—1116no—
289#388—1116no—
290C4×C4⋊C4C2×D1118yescomplemented
291C2×#95—112no—
292C2×#95—112no—
293C2×#95C2×D1111yescharacteristic
294C2×#95C2×D1111yescharacteristic
295C22×C11#53214yes—
296C22×C11#53514yes—
297C22×C11#53714yes—
298C22×C11#53818yes—
299C22×C11#54218yes—
300C22×C11C23×D411yescharacteristic
301C22×C11C22×#4112yes—
302C22×C11C2×H(5,𝔽2)11yescharacteristic
303C22×C11C2×H(5,𝔽2)12yes—
304C22×C11C2×2−1+411yescharacteristic
305C2×D11—42no—
306C2×D11—44no—
307C2×D11—42no—
308C2×D11—44no—
309C2×D11—42no—
310C2×D11—44no—
311C2×D11—44no—
312C2×D11—44no—
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—816no—
318C2×D11—88no—
319C4×C11—24no—
320C4×C11—24no—
321C4×C11—24no—
322C4×C11—28no—
323C4×C11—44no—
324Dic11—42no—
325Dic11—44no—
326Dic11—42no—
327Dic11—42no—
328C25—111no—
329C25—112no—
330C22×Q8—114no—
331C22×Q8—224no—
332C22×Q8—444no—
333C22×D4—114no—
334C22×D4—118no—
335C22×D4—224no—
336C22×D4—228no—
337C22×D4—444no—
338C22×D4—444no—
339C22×D4—444no—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—112no—
344C23×C4C22×D1112yes—
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1112yes—
349#126—2232no—
350#124—2232no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—118no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—444no—
360C2×C4⋊C4C22×D1118yes—
361C2×C22⋊C4—118no—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—114no—
364C2×C22⋊C4—114no—
365C2×C22⋊C4—114no—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—228no—
371C2×C22⋊C4—228no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—444no—
377C2×C22⋊C4—444no—
378C2×C22⋊C4—444no—
379C2×C42—44no—
380C2×C42D4418yescomplemented
381C2×C42C22×D1118yes—
382C2×C42C22×D1114yes—
383#95—118no—
384#95—118no—
385#95C22×D1114yes—
386#95C22×D1114yes—
387C2×C11#266218yescomplemented
388C2×C11C2×#53211yescharacteristic
389C2×C11C2×#53511yescharacteristic
390C2×C11C2×#53711yescharacteristic
391C2×C11C2×#53812yes—
392C2×C11C2×#54212yes—
393D11—82no—
394D11—84no—
395C24—112no—
396C24—114no—
397C24—222no—
398C24—224no—
399C24—224no—
400C24—224no—
401C24—224no—
402C24—224no—
403C24—222no—
404C24—222no—
405C24—224no—
406C24—224no—
407C24—224no—
408C24—224no—
409C24C23×D1111yescharacteristic
410C2×Q8—228no—
411C2×Q8—448no—
412C2×Q8—4416no—
413C2×D4—228no—
414C2×D4—2216no—
415C2×D4—448no—
416C2×D4—448no—
417C2×D4—448no—
418C2×D4—4416no—
419C2×D4—4432no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—112no—
430C22×C4—112no—
431C22×C4—114no—
432C22×C4—112no—
433C22×C4—224no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4C2×D4414yes—
444C22×C4C2×D4414yes—
445C22×C4C2×D4414yes—
446C22×C4#433918yes—
447C22×C4C23×D1114yes—
448C22×C4C23×D1112yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1114yes—
452C4⋊C4—216no—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—228no—
456C4⋊C4—448no—
457C22⋊C4—2216no—
458C22⋊C4—2216no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C22⋊C4—2216no—
463C22⋊C4—448no—
464C22⋊C4—448no—
465C22⋊C4—448no—
466C42—48no—
467C42C2×D44116yescomplemented
468C11C2×#266211yescharacteristic, complemented, Sylow
469C23—222no—
470C23—224no—
471C23—224no—
472C23—224no—
473C23—224no—
474C23—224no—
475C23—222no—
476C23—222no—
477C23—224no—
478C23—224no—
479C23—224no—
480C23—224no—
481C23—444no—
482C23—448no—
483C23—444no—
484C23—448no—
485C23—448no—
486C23—444no—
487C23—448no—
488C23—448no—
489C23—448no—
490C23—448no—
491C23—448no—
492C23—448no—
493C23C22×D4412yes—
494C23C2×#433914yes—
495C23#6703712yes—
496C23#6704012yes—
497C23#6704214yes—
498C23C24×D1111yescharacteristic
499Q8—4416no—
500D4—4416no—
501D4—4432no—
502C2×C4—28no—
503C2×C4—28no—
504C2×C4—28no—
505C2×C4—216no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—48no—
516C2×C4—224no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—444no—
527C2×C4—444no—
528C2×C4—448no—
529C2×C4—444no—
530C2×C4C22×D4414yes—
531C2×C4C22×D4414yes—
532C2×C4C22×D4414yes—
533C2×C4C2×#433918yes—
534C22—442no—
535C22—444no—
536C22—444no—
537C22—442no—
538C22—442no—
539C22—444no—
540C22—444no—
541C22—444no—
542C22—444no—
543C22—444no—
544C22—444no—
545C22—444no—
546C22—8816no—
547C22—888no—
548C22#1062300814yes—
549C22#1062304114yes—
550C22#1062305614yes—
551C22#1062309118yes—
552C22#1062311318yes—
553C22C23×D4411yescharacteristic
554C22C22×#433912yes—
555C22C2×#6703711yescharacteristic
556C22C2×#6704011yescharacteristic
557C22C2×#6704212yes—
558C4—24no—
559C4—24no—
560C4—24no—
561C4—28no—
562C4—44no—
563C4—442no—
564C4—444no—
565C4—442no—
566C4—442no—
567C2—884no—
568C2—882no—
569C2#1307475318yesdirect product factor
570C2C2×#1062300811yescharacteristic
571C2C2×#1062305611yescharacteristic
572C2C2×#1062304111yescharacteristic
573C2C2×#1062309112yes—
574C2C2×#1062311312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socleC24×C11C24
prime radicalC2×#10622284C2
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2662
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66929C2semidirect
2. C22×#66928C2semidirect
3. #13074753C2direct (N × H)
4. C2×#10622607C2semidirect
5. C2×#10622269C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622286C2semidirect
10. C2×#10622552C2semidirect
11. C2×#10622553C2semidirect
12. C2×C4×C11×C4⋊C4C2semidirect
33. C2×#66929C22semidirect
35. C2×#66928C22semidirect
36. C4×C11×C4⋊C4C22semidirect
41. #10622607C22semidirect
42. #10622604C22semidirect
43. #10622553C22semidirect
44. #10622552C22semidirect
45. #10622286C22semidirect
46. #10622285C22semidirect
48. #10622269C22semidirect
73. C2×C42×C11D4semidirect
168. C42×C11C2×D4semidirect
193. C2×C4×C4⋊C4D11semidirect
290. C4×C4⋊C4C2×D11semidirect
380. C2×C42D44semidirect
387. C2×C11#2662semidirect
467. C42C2×D44semidirect
468. C11C2×#2662semidirect
569. C2#13074753direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669292
C22×#669282
#130747532
C2×#106226072
C2×#106222692
C2×#106222852
C2×#106226042
C2×#106222862
C2×#106222842
C2×#106225522
C2×#106225532
C2×C4×C11×C4⋊C42
C2×#266211