Finite Group Databasebeta

← C2×#13072932 #14922945

Subgroups — C2×#13072932 #14922945

Order 2816.

3374 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×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
3#13072932C2116yesmaximal, direct product factor
4C2×#10622271C212yesmaximal, complemented
5C2×#10622605C212yesmaximal, complemented
6C2×#10622585C212yesmaximal, complemented
7C2×#10622826C211yesmaximal, characteristic
8C2×#10622571C211yesmaximal, characteristic
9C2×#10622559C211yesmaximal, characteristic, complemented
10C2×#10622280C212yesmaximal, complemented
11C2×#10622555C211yesmaximal, characteristic, complemented
12C2×C11×#385C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×Dic11⋊C4—28no—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2218yescomplemented
32C22×C4×Dic11C2211yescharacteristic
33C2×(C22⋊D11)⋊C4—28no—
34C2×(C22⋊D11)⋊C4C2218yes—
35C11×#385C2218yescomplemented
36C2×C11×#95C2212yes—
37#10622826C2218yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622605C22116yescomplemented
43#10622585C22116yescomplemented
44#10622571C2218yes—
45#10622559C2218yescomplemented
46#10622555C2218yescomplemented
47#10622280C22116yescomplemented
48#10622271C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11—24no—
52C23×C4×C11—44no—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2314yes—
58C22×C22⋊D11—24no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11Q818yes—
61C22×C22⋊D11C2314yes—
62C23×Dic11—28no—
63C23×Dic11—24no—
64C23×Dic11—44no—
65C23×Dic11D418yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C23×Dic11C2314yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2314yes—
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—24no—
74C22×C4×D11—28no—
75C22×C4×D11C2314yes—
76C2×C11×C4⋊C4—44no—
77C2×C11×C4⋊C4C2318yes—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11C2314yes—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—232no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4—44no—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2318yes—
98C2×Dic11⋊C4C2318yes—
99C2×Dic11⋊C4C2318yes—
100C2×Dic11⋊C4C2318yes—
101C2×C4×Dic11—24no—
102C2×C4×Dic11C2314yes—
103(C22⋊D11)⋊C4—232no—
104C11×#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C2×#2487—111nomaximal, Sylow
110C24×C11—24no—
111C24×C11—24no—
112C24×C11C2×D414yes—
113C24×C11C2×Q814yes—
114C24×C11#4114yes—
115C24×C11C2412yes—
116C24×C11C2411yescharacteristic
117C23×D11—22no—
118C23×D11—24no—
119C23×D11—22no—
120C23×D11—24no—
121C23×D11C2×Q814yes—
122C23×D11C2412yes—
123C22×C4×C11—22no—
124C22×C4×C11—28no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—48no—
135C22×C4×C11—416no—
136C22×C4×C11C2412yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2412yes—
140C2×C22⋊D11—232no—
141C2×C22⋊D11—28no—
142C2×C22⋊D11—28no—
143C2×C22⋊D11C2×Q8116yes—
144C22×Dic11—232no—
145C22×Dic11—216no—
146C22×Dic11—22no—
147C22×Dic11—28no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—48no—
157C22×Dic11—416no—
158C22×Dic11C2×D4116yes—
159C22×Dic11C2×D414yes—
160C22×Dic11C2×D414yes—
161C22×Dic11C2×Q814yes—
162C22×Dic11#4118yes—
163C22×Dic11C2414yes—
164C22×Dic11C2414yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2412yes—
168C2×C4×D11—28no—
169C2×C4×D11—216no—
170C2×C4×D11—416no—
171C11×C4⋊C4—48no—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—28no—
174C22⋊Dic11—28no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178Dic11⋊C4—28no—
179Dic11⋊C4—216no—
180Dic11⋊C4—216no—
181Dic11⋊C4—216no—
182Dic11⋊C4—48no—
183C4×Dic11—28no—
184C22×C4×D4—111no—
185C23×C4⋊C4—111no—
186#2487—1116no—
187C2×#400—112no—
188C2×#399—112no—
189C2×#389—112no—
190C2×#386—111no—
191C2×#386—111no—
192C2×#385—111no—
193C2×#385D1111yescharacteristic, complemented
194C2×#380—112no—
195C2×#380—111no—
196C23×C11—28no—
197C23×C11—28no—
198C23×C11—216no—
199C23×C11—216no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11C22⋊Q8116yes—
203C23×C11C22×D414yes—
204C23×C11C22×D412yes—
205C23×C11C22×Q814yes—
206C23×C11C22×Q812yes—
207C23×C11C2×#4114yes—
208C23×C11C2×#4112yes—
209C23×C11C2×#4114yes—
210C23×C11H(5,𝔽2)14yes—
211C23×C11C2511yescharacteristic
212C22×D11—28no—
213C22×D11—216no—
214C22×D11—22no—
215C22×D11—24no—
216C22×D11—22no—
217C22×D11—24no—
218C22×D11—44no—
219C22×D11—44no—
220C22×D11—48no—
221C22×D11C22×Q814yes—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
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—416no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11—48no—
236C2×C4×C11—48no—
237C22⋊D11—232no—
238C2×Dic11—28no—
239C2×Dic11—28no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—232no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—416no—
251C2×Dic11—48no—
252C2×Dic11—48no—
253C2×Dic11#123116yes—
254C2×Dic11C22×D414yes—
255C2×Dic11C22×D414yes—
256C2×Dic11C22×Q814yes—
257C2×Dic11C2×#4118yes—
258C4×D11—416no—
259C23×D4—111no—
260C24×C4—111no—
261C24×C4—111no—
262C24×C4—111no—
263C24×C4C2×D1111yescharacteristic
264C2×C4×D4—118no—
265C2×C4×D4—228no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4—112no—
270C22×C4⋊C4—118no—
271C22×C4⋊C4—112no—
272C22×C4⋊C4—228no—
273C22×C4⋊C4C2×D1112yes—
274C22×C22⋊C4—111no—
275C22×C22⋊C4—111no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4C2×D1111yescharacteristic
280C22×C42—111no—
281#400—1116no—
282#399—1116no—
283#389—1116no—
284#386—118no—
285#386—118no—
286#385—118no—
287#385C2×D1118yescomplemented
288#380—118no—
289#380—1116no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95C2×D1112yes—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—28no—
298C22×C11—28no—
299C22×C11—232no—
300C22×C11C2×C22⋊Q818yes—
301C22×C11C2×C22⋊Q814yes—
302C22×C11C2×#12314yes—
303C22×C11#53514yes—
304C22×C11#55318yes—
305C22×C11#55418yes—
306C22×C11C23×D411yescharacteristic
307C22×C11C23×Q811yescharacteristic
308C22×C11C22×#4111yescharacteristic
309C22×C11C22×#4112yes—
310C22×C11C2×H(5,𝔽2)12yes—
311C2×D11—24no—
312C2×D11—28no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—44no—
316C2×D11—416no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—44no—
320C4×C11—44no—
321Dic11—24no—
322Dic11—24no—
323Dic11—44no—
324Dic11—44no—
325Dic11C2×#12318yes—
326C25—111no—
327C25C22×D1111yescharacteristic
328C22×D4—118no—
329C22×D4—114no—
330C22×D4—224no—
331C22×D4—224no—
332C23×C4—24no—
333C23×C4—44no—
334C23×C4—111no—
335C23×C4—118no—
336C23×C4—114no—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—112no—
340C23×C4—112no—
341C23×C4—114no—
342C23×C4—114no—
343C23×C4—224no—
344C23×C4—228no—
345C23×C4—228no—
346C23×C4—224no—
347C23×C4—444no—
348C23×C4C22×D1111yescharacteristic
349C23×C4C22×D1112yes—
350C23×C4C22×D1112yes—
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1114yes—
353C4×D4—2232no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—118no—
356C2×C4⋊C4—118no—
357C2×C4⋊C4—114no—
358C2×C4⋊C4—118no—
359C2×C4⋊C4—118no—
360C2×C4⋊C4—228no—
361C2×C4⋊C4—228no—
362C2×C4⋊C4—2232no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—228no—
365C2×C4⋊C4—444no—
366C2×C4⋊C4C22×D1118yes—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—114no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—444no—
376C2×C22⋊C4—444no—
377C2×C22⋊C4C22×D1114yes—
378C2×C22⋊C4C22×D1114yes—
379C2×C42—114no—
380C2×C42—224no—
381#95—118no—
382#95—118no—
383#95—118no—
384#95—118no—
385#95C22×D1118yes—
386C2×C11—28no—
387C2×C11#248718yescomplemented
388C2×C11C22×C22⋊Q811yescharacteristic
389C2×C11C22×#12311yescharacteristic
390C2×C11C2×#53511yescharacteristic
391C2×C11C2×#55312yes—
392C2×C11C2×#55412yes—
393D11—44no—
394C24—24no—
395C24—24no—
396C24—114no—
397C24—112no—
398C24—222no—
399C24—222no—
400C24—224no—
401C24—224no—
402C24#433914yes—
403C24D4×D1114yes—
404C24Q8×D1114yes—
405C24C23×D1112yes—
406C24C23×D1111yescharacteristic
407C2×D4—1116no—
408C2×D4—2232no—
409C2×D4—228no—
410C2×D4—228no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—28no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—48no—
423C22×C4—416no—
424C22×C4—114no—
425C22×C4—118no—
426C22×C4—112no—
427C22×C4—114no—
428C22×C4—1116no—
429C22×C4—114no—
430C22×C4—112no—
431C22×C4—112no—
432C22×C4—114no—
433C22×C4—114no—
434C22×C4—228no—
435C22×C4—2216no—
436C22×C4—2232no—
437C22×C4—2216no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—228no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—4416no—
449C22×C4—448no—
450C22×C4—4416no—
451C22×C4C23×D1112yes—
452C22×C4C23×D1114yes—
453C22×C4C23×D1114yes—
454C22×C4C23×D1112yes—
455C4⋊C4—48no—
456C4⋊C4—2216no—
457C4⋊C4—2216no—
458C4⋊C4—228no—
459C4⋊C4—2216no—
460C4⋊C4—448no—
461C22⋊C4—28no—
462C22⋊C4—28no—
463C22⋊C4—228no—
464C22⋊C4—228no—
465C22⋊C4—448no—
466C22⋊C4—448no—
467C42—228no—
468C11C2×#248711yescharacteristic, complemented, Sylow
469C23—216no—
470C23—28no—
471C23—216no—
472C23—28no—
473C23—24no—
474C23—24no—
475C23—114no—
476C23—228no—
477C23—2216no—
478C23—222no—
479C23—222no—
480C23—224no—
481C23—224no—
482C23—448no—
483C23—444no—
484C23—444no—
485C23#66949116yes—
486C23C2×#433914yes—
487C23C2×#433912yes—
488C23C2×D4×D1114yes—
489C23C2×D4×D1112yes—
490C23#6703714yes—
491C23C2×Q8×D1114yes—
492C23C2×Q8×D1112yes—
493C23#41×D1114yes—
494C23C24×D1111yescharacteristic
495D4—2232no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—416no—
507C2×C4—48no—
508C2×C4—44no—
509C2×C4—48no—
510C2×C4—44no—
511C2×C4—1116no—
512C2×C4—114no—
513C2×C4—118no—
514C2×C4—114no—
515C2×C4—114no—
516C2×C4—2232no—
517C2×C4—228no—
518C2×C4—228no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—4416no—
529C2×C4—4416no—
530C2×C4—448no—
531C2×C4—448no—
532C22—28no—
533C22—28no—
534C22—232no—
535C22—24no—
536C22—24no—
537C22—228no—
538C22—224no—
539C22—444no—
540C22—4416no—
541C22—442no—
542C22—442no—
543C22C2×#6694918yes—
544C22C2×#6694914yes—
545C22#1062307118yes—
546C22#1062312314yes—
547C22#1062316718yes—
548C22D11×#12314yes—
549C22C22×#433911yescharacteristic
550C22C22×D4×D1111yescharacteristic
551C22C2×#6703712yes—
552C22C22×Q8×D1111yescharacteristic
553C22C2×#41×D1112yes—
554C4—44no—
555C4—44no—
556C4—42no—
557C4—42no—
558C4—118no—
559C4—224no—
560C4—224no—
561C4—444no—
562C4—444no—
563C2—28no—
564C2—444no—
565C2#1307293218yesdirect product factor
566C2C22×#6694911yescharacteristic
567C2C2×D11×#12311yescharacteristic
568C2C2×#1062312311yescharacteristic
569C2C2×#1062307112yes—
570C2C2×#1062316712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11C2×#2487
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C23×Dic11⋊C4C2semidirect
3. #13072932C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622605C2semidirect
6. C2×#10622585C2semidirect
9. C2×#10622559C2semidirect
10. C2×#10622280C2semidirect
11. C2×#10622555C2semidirect
12. C2×C11×#385C2semidirect
31. C22×Dic11⋊C4C22semidirect
35. C11×#385C22semidirect
42. #10622605C22semidirect
43. #10622585C22semidirect
45. #10622559C22semidirect
46. #10622555C22semidirect
47. #10622280C22semidirect
48. #10622271C22semidirect
193. C2×#385D11semidirect
287. #385C2×D11semidirect
387. C2×C11#2487semidirect
468. C11C2×#2487semidirect
565. C2#13072932direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C23×Dic11⋊C42
#130729322
C2×#106222712
C2×#106226052
C2×#106225852
C2×#106228262
C2×#106225712
C2×#106225592
C2×#106222802
C2×#106225552
C2×C11×#3852
C2×#248711