Finite Group Databasebeta

← C2×#13074758 #14920503

Subgroups — C2×#13074758 #14920503

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×#66932C211yesmaximal, characteristic, complemented
2C22×#66989C211yesmaximal, characteristic, complemented
3#13074758C2116yesmaximal, direct product factor
4C2×#10622561C212yesmaximal, complemented
5C2×#10622269C211yesmaximal, characteristic, complemented
6C2×#10622835C211yesmaximal, characteristic, complemented
7C2×#10622835C212yesmaximal, complemented
8C2×#10622560C211yesmaximal, characteristic, complemented
9C2×#10622834C212yesmaximal, complemented
10C2×#10622564C212yesmaximal, complemented
11C2×#10622262C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×Dic22C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66989—28no—
26C2×#66989C2218yescomplemented
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2212yes—
33C22×C4×Dic11C2211yescharacteristic
34C2×#66932—28no—
35C2×#66932C2218yescomplemented
36C11×#392C2218yes—
37C2×C11×#95C2211yescharacteristic
38#10622835C2218yescomplemented
39#10622835C22116yescomplemented
40#10622834C22116yescomplemented
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622564C22116yescomplemented
45#10622561C22116yescomplemented
46#10622560C2218yescomplemented
47#10622269C2218yescomplemented
48#10622262C2218yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2312yes—
51C22×D4×C11—24no—
52C22×D4×C11—28no—
53C22×D4×C11—44no—
54C22×D4×C11—44no—
55C22×D4×C11—44no—
56C22×D4×C11C2314yes—
57C22×D4×C11C2318yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C22×Dic22—24no—
68C22×Dic22—44no—
69C22×Dic22C2314yes—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—28no—
72C2×C11×C22⋊C4C2314yes—
73C2×C11×C22⋊C4C2318yes—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11—44no—
79C2×C22⋊Dic11—44no—
80C2×C22⋊Dic11—44no—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2314yes—
83C2×C22⋊Dic11C2318yes—
84C2×C22⋊Dic11C2318yes—
85C2×C22⋊Dic11C2318yes—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2318yes—
88#66989—232no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11—44no—
91C2×C4⋊Dic11C2314yes—
92C2×C4⋊Dic11C2318yes—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2318yes—
99C2×C4×Dic11—44no—
100C2×C4×Dic11D418yescomplemented
101C2×C4×Dic11C2318yes—
102C2×C4×Dic11C2314yes—
103#66932—232no—
104C11×#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2662—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—24no—
121C24×C11C2412yes—
122C24×C11C2414yes—
123C24×C11C2411yescharacteristic
124C2×D4×C11—28no—
125C2×D4×C11—216no—
126C2×D4×C11—48no—
127C2×D4×C11—48no—
128C2×D4×C11—48no—
129C2×D4×C11—416no—
130C2×D4×C11—432no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11C2×D414yes—
137C22×C4×C11#4118yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2414yes—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11C2×D414yes—
156C22×Dic11C2×D414yes—
157C22×Dic11C2414yes—
158C22×Dic11C2412yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C2×Dic22—28no—
164C2×Dic22—48no—
165C2×Dic22—416no—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—216no—
168C22⋊Dic11—28no—
169C22⋊Dic11—28no—
170C22⋊Dic11—216no—
171C22⋊Dic11—216no—
172C22⋊Dic11—48no—
173C22⋊Dic11—48no—
174C22⋊Dic11—48no—
175C4⋊Dic11—28no—
176C4⋊Dic11—48no—
177Dic11⋊C4—28no—
178Dic11⋊C4—28no—
179Dic11⋊C4—216no—
180C4×Dic11—48no—
181C4×Dic11C2×D4116yescomplemented
182C22×#126—111no—
183C22×#124—111no—
184#2662—1116no—
185C2×#396—112no—
186C2×#395—111no—
187C2×#394—112no—
188C2×#394—111no—
189C2×#393—111no—
190C2×#392D1111yescharacteristic
191C2×#390—112no—
192C2×#388—112no—
193C2×C4×C4⋊C4—111no—
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—44no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11—44no—
210C23×C11—44no—
211C23×C11—48no—
212C23×C11—48no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11—48no—
218C23×C11C22×D412yes—
219C23×C11C2×#4114yes—
220C23×C11H(5,𝔽2)14yes—
221C23×C11H(5,𝔽2)12yes—
222C23×C112−1+412yes—
223C23×C11C2511yescharacteristic
224D4×C11—416no—
225D4×C11—432no—
226C2×C4×C11—28no—
227C2×C4×C11—216no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—44no—
234C2×C4×C11C22×D414yes—
235C2×C4×C11C2×#4118yes—
236C2×Dic11—28no—
237C2×Dic11—28no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—48no—
253C2×Dic11—44no—
254C2×Dic11—44no—
255C2×Dic11—48no—
256C2×Dic11C22×D414yes—
257C2×Dic11C22×D414yes—
258Dic22—416no—
259C23×Q8—111no—
260C23×D4C2×D1111yescharacteristic
261C23×D4C2×D1112yes—
262C2×#126—118no—
263C2×#126—228no—
264C2×#124—118no—
265C2×#124—228no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—112no—
271C22×C22⋊C4—111no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—111no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4C2×D1112yes—
280C22×C42—111no—
281C22×C42—112no—
282#396—1116no—
283#395—118no—
284#394—118no—
285#394—1116no—
286#393—118no—
287#392C2×D1118yes—
288#390—1116no—
289#388—1116no—
290C4×C4⋊C4—118no—
291C2×#95—111no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95C2×D1111yescharacteristic
295C22×C11—42no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—816no—
308C22×C11—88no—
309C22×C11#53214yes—
310C22×C11#53514yes—
311C22×C11#53714yes—
312C22×C11#53818yes—
313C22×C11#54218yes—
314C22×C11C23×D411yescharacteristic
315C22×C11C22×#4112yes—
316C22×C11C2×H(5,𝔽2)12yes—
317C22×C11C2×H(5,𝔽2)11yescharacteristic
318C22×C11C2×2−1+411yescharacteristic
319C4×C11—24no—
320C4×C11—28no—
321C4×C11—42no—
322Dic11—24no—
323Dic11—24no—
324Dic11—44no—
325Dic11—42no—
326Dic11—42no—
327Dic11—44no—
328C25C22×D1111yescharacteristic
329C25C22×D1112yes—
330C22×Q8—114no—
331C22×Q8—224no—
332C22×Q8—444no—
333C22×D4—24no—
334C22×D4—28no—
335C22×D4—44no—
336C22×D4—44no—
337C22×D4—44no—
338C22×D4C22×D1114yes—
339C22×D4C22×D1118yes—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—112no—
345C23×C4—112no—
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1112yes—
349#126—2232no—
350#124—2232no—
351C2×C4⋊C4—114no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—118no—
355C2×C4⋊C4—118no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—228no—
360C2×C4⋊C4—444no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—118no—
364C2×C22⋊C4—118no—
365C2×C22⋊C4—114no—
366C2×C22⋊C4—114no—
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—444no—
375C2×C22⋊C4—444no—
376C2×C22⋊C4—444no—
377C2×C22⋊C4C22×D1114yes—
378C2×C22⋊C4C22×D1118yes—
379C2×C42—118no—
380C2×C42—114no—
381C2×C42—118no—
382C2×C42—444no—
383#95—114no—
384#95—118no—
385#95—118no—
386#95C22×D1114yes—
387C2×C11—84no—
388C2×C11—82no—
389C2×C11#266218yescomplemented
390C2×C11C2×#53211yescharacteristic
391C2×C11C2×#53511yescharacteristic
392C2×C11C2×#53711yescharacteristic
393C2×C11C2×#53812yes—
394C2×C11C2×#54212yes—
395C24—22no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—22no—
405C24—24no—
406C24—22no—
407C24C23×D1112yes—
408C24C23×D1114yes—
409C24C23×D1111yescharacteristic
410C2×Q8—228no—
411C2×Q8—448no—
412C2×Q8—4416no—
413C2×D4—28no—
414C2×D4—216no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—48no—
418C2×D4—416no—
419C2×D4—432no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—114no—
426C22×C4—114no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—114no—
430C22×C4—112no—
431C22×C4—114no—
432C22×C4—112no—
433C22×C4—224no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—224no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—222no—
447C22×C4D4×D1114yes—
448C22×C4#434118yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1114yes—
452C4⋊C4—228no—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—2216no—
456C4⋊C4—448no—
457C22⋊C4—28no—
458C22⋊C4—216no—
459C22⋊C4—2216no—
460C22⋊C4—2216no—
461C22⋊C4—228no—
462C22⋊C4—228no—
463C22⋊C4—448no—
464C22⋊C4—448no—
465C22⋊C4—448no—
466C42—1116no—
467C42—448no—
468C11C2×#266211yescharacteristic, complemented, Sylow
469C23—22no—
470C23—24no—
471C23—24no—
472C23—24no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—44no—
482C23—48no—
483C23—48no—
484C23—44no—
485C23—48no—
486C23—48no—
487C23—48no—
488C23—48no—
489C23—48no—
490C23—48no—
491C23—44no—
492C23—48no—
493C23C2×D4×D1112yes—
494C23C2×#434114yes—
495C23#6703714yes—
496C23#6703712yes—
497C23#6704312yes—
498C23C24×D1111yescharacteristic
499Q8—4416no—
500D4—416no—
501D4—432no—
502C2×C4—28no—
503C2×C4—216no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—44no—
510C2×C4—114no—
511C2×C4—114no—
512C2×C4—228no—
513C2×C4—228no—
514C2×C4—224no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—222no—
528C2×C4—448no—
529C2×C4—444no—
530C2×C4—448no—
531C2×C4—444no—
532C2×C4C2×D4×D1114yes—
533C2×C4C2×#434118yes—
534C22—42no—
535C22—44no—
536C22—44no—
537C22—42no—
538C22—42no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—44no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—816no—
547C22—88no—
548C22#1062312314yes—
549C22#1062312418yes—
550C22#1062313418yes—
551C22#1062313914yes—
552C22#1062324714yes—
553C22C22×D4×D1111yescharacteristic
554C22C22×#434112yes—
555C22C2×#6703712yes—
556C22C2×#6703711yescharacteristic
557C22C2×#6704311yescharacteristic
558C4—24no—
559C4—28no—
560C4—42no—
561C4—224no—
562C4—224no—
563C4—444no—
564C4—442no—
565C4—442no—
566C4—444no—
567C2—84no—
568C2—82no—
569C2#1307475818yesdirect product factor
570C2C2×#1062324711yescharacteristic
571C2C2×#1062312311yescharacteristic
572C2C2×#1062313911yescharacteristic
573C2C2×#1062312412yes—
574C2C2×#1062313412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2662
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66932C2semidirect
2. C22×#66989C2semidirect
3. #13074758C2direct (N × H)
4. C2×#10622561C2semidirect
5. C2×#10622269C2semidirect
6. C2×#10622835C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622560C2semidirect
9. C2×#10622834C2semidirect
10. C2×#10622564C2semidirect
11. C2×#10622262C2semidirect
26. C2×#66989C22semidirect
35. C2×#66932C22semidirect
38. #10622835C22semidirect
39. #10622835C22semidirect
40. #10622834C22semidirect
44. #10622564C22semidirect
45. #10622561C22semidirect
46. #10622560C22semidirect
47. #10622269C22semidirect
48. #10622262C22semidirect
100. C2×C4×Dic11D4semidirect
181. C4×Dic11C2×D4semidirect
389. C2×C11#2662semidirect
468. C11C2×#2662semidirect
569. C2#13074758direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
C22×#669892
#130747582
C2×#106225612
C2×#106222692
C2×#106228352
C2×#106225602
C2×#106228342
C2×#106225642
C2×#106222622
C2×C11×#3922
C2×#266211