Finite Group Databasebeta

← C2×#13074400 #14920388

Subgroups — C2×#13074400 #14920388

Order 2816.

3002 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic
2C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
3#13074400C2116yesmaximal, direct product factor
4C2×#10622271C212yesmaximal, complemented
5C2×#10622562C212yesmaximal, complemented
6C2×#10622270C212yesmaximal, complemented
7C2×#10622565C212yesmaximal, complemented
8C2×#10622833C211yesmaximal, characteristic
9C2×#10622563C211yesmaximal, characteristic, complemented
10C2×#10622823C211yesmaximal, characteristic, complemented
11C2×#10622556C211yesmaximal, characteristic, complemented
12C2×C11×#386C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C2×#66988—28no—
25C2×#66988C2218yes—
26C22×C4⋊Dic11C2212yes—
27C22×Dic11⋊C4—28no—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2212yes—
33C22×Dic11⋊C4C2218yescomplemented
34C11×#386C2218yes—
35C2×C11×#95C2212yes—
36#10622833C2218yes—
37#10622823C2218yescomplemented
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622565C22116yescomplemented
44#10622563C2218yescomplemented
45#10622562C22116yescomplemented
46#10622556C2218yescomplemented
47#10622271C22116yescomplemented
48#10622270C22116yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11—24no—
54C22×D4×C11C2314yes—
55C23×C4×C11—24no—
56C23×C4×C11—44no—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C23×C4×C11C2314yes—
61C23×Dic11—24no—
62C23×Dic11—24no—
63C23×Dic11—24no—
64C23×Dic11—44no—
65C23×Dic11D418yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2314yes—
73C23×Dic11C2314yes—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—44no—
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2318yes—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—44no—
83C2×C22⋊Dic11C2314yes—
84C2×C22⋊Dic11C2314yes—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2314yes—
87C2×C22⋊Dic11C2318yes—
88#66988—232no—
89C2×C4⋊Dic11—44no—
90C2×C4⋊Dic11C2318yes—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—232no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—44no—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2318yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2318yes—
101C2×Dic11⋊C4C2318yes—
102C11×#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2623—111nomaximal, Sylow
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11C2×D414yes—
117C24×C11#4114yes—
118C24×C11#4114yes—
119C24×C11C2412yes—
120C24×C11C2412yes—
121C24×C11C2411yescharacteristic
122C2×D4×C11—28no—
123C2×D4×C11—28no—
124C2×D4×C11—28no—
125C2×D4×C11—416no—
126C22×C4×C11—28no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—48no—
137C22×C4×C11—416no—
138C22×C4×C11C2414yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2414yes—
141C22×Dic11—232no—
142C22×Dic11—28no—
143C22×Dic11—24no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—28no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—28no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—48no—
160C22×Dic11—416no—
161C22×Dic11C2×D414yes—
162C22×Dic11C2×D414yes—
163C22×Dic11C2×D4116yes—
164C22×Dic11C2412yes—
165C22×Dic11C2414yes—
166C22×Dic11C2414yes—
167C22×Dic11C2412yes—
168C22×Dic11C2412yes—
169C22×Dic11C2412yes—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—48no—
172C22⋊Dic11—28no—
173C22⋊Dic11—28no—
174C22⋊Dic11—28no—
175C22⋊Dic11—28no—
176C22⋊Dic11—48no—
177C4⋊Dic11—48no—
178Dic11⋊C4—216no—
179Dic11⋊C4—216no—
180Dic11⋊C4—28no—
181Dic11⋊C4—28no—
182Dic11⋊C4—48no—
183C22×#123—111no—
184C23×C4⋊C4—111no—
185#2623—1116no—
186C2×#400—112no—
187C2×#399—112no—
188C2×#398—112no—
189C2×#397—112no—
190C2×#386—111no—
191C2×#386D1111yescharacteristic
192C2×#385—111no—
193C2×#385—111no—
194C2×#381—111no—
195C23×C11—28no—
196C23×C11—28no—
197C23×C11—216no—
198C23×C11—216no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—44no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11#123116yes—
212C23×C11C22×D414yes—
213C23×C11C22×D412yes—
214C23×C11C2×#4114yes—
215C23×C11C2×#4112yes—
216C23×C11C2×#4114yes—
217C23×C11C2×#4112yes—
218C23×C11H(5,𝔽2)14yes—
219C23×C112−1+414yes—
220C23×C11C2511yescharacteristic
221D4×C11—416no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—416no—
232C2×C4×C11—44no—
233C2×C4×C11—48no—
234C2×C4×C11—48no—
235C2×Dic11—232no—
236C2×Dic11—28no—
237C2×Dic11—28no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—416no—
253C2×Dic11—44no—
254C2×Dic11—48no—
255C2×Dic11—44no—
256C2×Dic11—48no—
257C2×Dic11C22×D414yes—
258C2×Dic11C22×D414yes—
259C23×D4C2×D1111yescharacteristic
260C24×C4—111no—
261C24×C4—111no—
262C24×C4C2×D1111yescharacteristic
263C2×#123—118no—
264C2×#123—228no—
265C22×C4⋊C4—118no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—112no—
271C22×C4⋊C4—112no—
272C22×C4⋊C4—228no—
273C22×C22⋊C4—111no—
274C22×C22⋊C4—111no—
275C22×C22⋊C4—111no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4C2×D1112yes—
280#400—1116no—
281#399—1116no—
282#398—1116no—
283#397—1116no—
284#386—118no—
285#386C2×D1118yes—
286#385—118no—
287#385—118no—
288#381—118no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95C2×D1112yes—
295C22×C11—232no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—28no—
299C22×C11—28no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—88no—
306C22×C11C2×#12318yes—
307C22×C11C2×#12314yes—
308C22×C11#53514yes—
309C22×C11#53614yes—
310C22×C11#53918yes—
311C22×C11#53918yes—
312C22×C11C23×D411yescharacteristic
313C22×C11C22×#4111yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C2×H(5,𝔽2)12yes—
316C22×C11C2×2−1+412yes—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11—44no—
320Dic11—24no—
321Dic11—24no—
322Dic11—42no—
323Dic11—44no—
324Dic11—42no—
325Dic11—44no—
326C25C22×D1111yescharacteristic
327C25C22×D1111yescharacteristic
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4C22×D1114yes—
332C23×C4—24no—
333C23×C4—44no—
334C23×C4—118no—
335C23×C4—114no—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—112no—
340C23×C4—111no—
341C23×C4—112no—
342C23×C4—114no—
343C23×C4—224no—
344C23×C4—224no—
345C23×C4—224no—
346C23×C4—444no—
347C23×C4C22×D1112yes—
348C23×C4C22×D1112yes—
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1114yes—
351#123—2232no—
352C2×C4⋊C4—118no—
353C2×C4⋊C4—118no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—118no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—228no—
359C2×C4⋊C4—228no—
360C2×C4⋊C4—2232no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—444no—
364C2×C4⋊C4—444no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—114no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—114no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—444no—
377C2×C22⋊C4C22×D1114yes—
378C2×C22⋊C4C22×D1118yes—
379#95—118no—
380#95—118no—
381#95—118no—
382#95—118no—
383#95—118no—
384#95C22×D1118yes—
385C2×C11—28no—
386C2×C11—82no—
387C2×C11#262318yescomplemented
388C2×C11C22×#12311yescharacteristic
389C2×C11C2×#53511yescharacteristic
390C2×C11C2×#53611yescharacteristic
391C2×C11C2×#53912yes—
392C2×C11C2×#53912yes—
393C24—24no—
394C24—24no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—24no—
400C24#433914yes—
401C24D4×D1114yes—
402C24#434114yes—
403C24C23×D1112yes—
404C24C23×D1112yes—
405C24C23×D1111yescharacteristic
406C2×D4—28no—
407C2×D4—28no—
408C2×D4—28no—
409C2×D4—416no—
410C22×C4—22no—
411C22×C4—28no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—48no—
421C22×C4—416no—
422C22×C4—114no—
423C22×C4—114no—
424C22×C4—1116no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—114no—
428C22×C4—112no—
429C22×C4—114no—
430C22×C4—112no—
431C22×C4—2232no—
432C22×C4—228no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—228no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—228no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—448no—
450C22×C4—4416no—
451C22×C4C23×D1114yes—
452C22×C4C23×D1112yes—
453C22×C4C23×D1114yes—
454C4⋊C4—2216no—
455C4⋊C4—2216no—
456C4⋊C4—228no—
457C4⋊C4—228no—
458C4⋊C4—448no—
459C4⋊C4—448no—
460C22⋊C4—28no—
461C22⋊C4—48no—
462C22⋊C4—228no—
463C22⋊C4—228no—
464C22⋊C4—228no—
465C22⋊C4—228no—
466C22⋊C4—448no—
467C11C2×#262311yescharacteristic, complemented, Sylow
468C23—216no—
469C23—28no—
470C23—216no—
471C23—28no—
472C23—24no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—24no—
478C23—24no—
479C23—44no—
480C23—48no—
481C23—44no—
482C23—48no—
483C23—44no—
484C23#66936116yes—
485C23C2×#433914yes—
486C23C2×#433912yes—
487C23C2×D4×D1114yes—
488C23C2×D4×D1112yes—
489C23C2×#434114yes—
490C23C2×#434112yes—
491C23#6703714yes—
492C23#6704314yes—
493C23C24×D1111yescharacteristic
494D4—416no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—416no—
505C2×C4—44no—
506C2×C4—48no—
507C2×C4—48no—
508C2×C4—114no—
509C2×C4—114no—
510C2×C4—2232no—
511C2×C4—228no—
512C2×C4—228no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—4416no—
528C2×C4—448no—
529C2×C4—448no—
530C2×C4—444no—
531C2×C4—444no—
532C22—24no—
533C22—24no—
534C22—28no—
535C22—28no—
536C22—232no—
537C22—42no—
538C22—42no—
539C22—44no—
540C22—44no—
541C22—42no—
542C22—88no—
543C22C2×#6693618yes—
544C22C2×#6693614yes—
545C22#1062309518yes—
546C22#1062312314yes—
547C22#1062313318yes—
548C22#1062317914yes—
549C22C22×#433911yescharacteristic
550C22C22×D4×D1111yescharacteristic
551C22C22×#434111yescharacteristic
552C22C2×#6703712yes—
553C22C2×#6704312yes—
554C4—44no—
555C4—44no—
556C4—42no—
557C4—224no—
558C4—224no—
559C4—444no—
560C4—442no—
561C4—442no—
562C4—444no—
563C2—28no—
564C2—82no—
565C2#1307440018yesdirect product factor
566C2C22×#6693611yescharacteristic
567C2C2×#1062312311yescharacteristic
568C2C2×#1062317911yescharacteristic
569C2C2×#1062309512yes—
570C2C2×#1062313312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11C2×#2623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×Dic11⋊C4C2semidirect
3. #13074400C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622270C2semidirect
7. C2×#10622565C2semidirect
9. C2×#10622563C2semidirect
10. C2×#10622823C2semidirect
11. C2×#10622556C2semidirect
33. C22×Dic11⋊C4C22semidirect
37. #10622823C22semidirect
43. #10622565C22semidirect
44. #10622563C22semidirect
45. #10622562C22semidirect
46. #10622556C22semidirect
47. #10622271C22semidirect
48. #10622270C22semidirect
387. C2×C11#2623semidirect
467. C11C2×#2623semidirect
565. C2#13074400direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669882
C23×Dic11⋊C42
#130744002
C2×#106222712
C2×#106225622
C2×#106222702
C2×#106225652
C2×#106228332
C2×#106225632
C2×#106228232
C2×#106225562
C2×C11×#3862
C2×#262311