Finite Group Databasebeta

← C2×#13074090 #14924284

Subgroups — C2×#13074090 #14924284

Order 2816.

3438 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3#13074090C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622599C211yesmaximal, characteristic, complemented
6C2×#10622835C211yesmaximal, characteristic, complemented
7C2×#10622564C212yesmaximal, complemented
8C2×#10622557C212yesmaximal, complemented
9C2×#10622569C212yesmaximal, complemented
10C2×#10622569C212yesmaximal, complemented
11C2×#10622279C211yesmaximal, characteristic, complemented
12C2×C11×#394C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C2×#66991—28no—
25C2×#66991C2218yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2212yes—
32C2×C4⋊C4×D11—28no—
33C2×C4⋊C4×D11C2218yescomplemented
34C11×#394C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36#10622835C2218yescomplemented
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622599C2218yescomplemented
43#10622569C22116yescomplemented
44#10622569C22116yescomplemented
45#10622564C22116yescomplemented
46#10622557C22116yescomplemented
47#10622279C2218yescomplemented
48#10622272C2218yescomplemented
49C25×C11C2312yes—
50C24×D11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—44no—
53C22×D4×C11C2314yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—28no—
59C22×C22⋊D11—28no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11C2318yes—
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C22×C4×D11—24no—
68C22×C4×D11—24no—
69C22×C4×D11—24no—
70C22×C4×D11—24no—
71C22×C4×D11—44no—
72C22×C4×D11—44no—
73C22×C4×D11D418yes—
74C22×C4×D11C2314yes—
75C22×C4×D11C2314yes—
76C22×C4×D11C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4—28no—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4C2318yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11—28no—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11—44no—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2318yes—
88C2×C22⋊Dic11C2318yes—
89#66991—232no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2314yes—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×C4×Dic11—44no—
101C2×C4×Dic11C2318yes—
102C4⋊C4×D11—232no—
103C11×#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2314yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C2×#2591—111nomaximal, Sylow
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11C2414yes—
118C24×C11C2411yescharacteristic
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—24no—
122C23×D11C2×D414yes—
123C23×D11#4118yes—
124C23×D11C2412yes—
125C2×D4×C11—28no—
126C2×D4×C11—48no—
127C2×D4×C11—416no—
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—216no—
145C2×C22⋊D11—432no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11C2×D414yes—
158C22×Dic11#4114yes—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164C2×C4×D11—232no—
165C2×C4×D11—28no—
166C2×C4×D11—28no—
167C2×C4×D11—28no—
168C2×C4×D11—28no—
169C2×C4×D11—416no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—416no—
173C2×C4×D11C2×D4116yes—
174C11×C4⋊C4—28no—
175C11×C22⋊C4—216no—
176C11×C22⋊C4—48no—
177C22⋊Dic11—216no—
178C22⋊Dic11—216no—
179C22⋊Dic11—48no—
180(C2×D11)⋊C4—216no—
181C4⋊Dic11—28no—
182C4⋊Dic11—28no—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185C4×Dic11—48no—
186C22×#121—111no—
187C23×C4⋊C4—111no—
188#2591—1116no—
189C2×#400—111no—
190C2×#400—111no—
191C2×#394—111no—
192C2×#394D1111yescharacteristic, complemented
193C2×#388—112no—
194C2×#388—112no—
195C2×#386—112no—
196C2×#386—112no—
197C2×C4×C22⋊C4—111no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11—48no—
212C23×C11C22×D412yes—
213C23×C11C2×#4112yes—
214C23×C11C2×#4112yes—
215C23×C11C2×#4114yes—
216C23×C11H(5,𝔽2)14yes—
217C23×C11C2511yescharacteristic
218C22×D11—28no—
219C22×D11—28no—
220C22×D11—216no—
221C22×D11—216no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—24no—
225C22×D11#124116yes—
226C22×D11C22×D414yes—
227C22×D11C2×#4118yes—
228D4×C11—416no—
229C2×C4×C11—28no—
230C2×C4×C11—28no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—44no—
240C2×C4×C11—48no—
241C2×C4×C11C22×D414yes—
242C2×C4×C11C2×#4114yes—
243C22⋊D11—432no—
244C2×Dic11—28no—
245C2×Dic11—28no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—48no—
258C2×Dic11—44no—
259C2×Dic11—48no—
260C2×Dic11C22×D414yes—
261C2×Dic11C2×#4114yes—
262C4×D11—232no—
263C4×D11—416no—
264C4×D11—416no—
265C23×D4—112no—
266C23×D4C2×D1111yescharacteristic
267C24×C4—111no—
268C24×C4—111no—
269C24×C4—111no—
270C2×#121—118no—
271C2×#121—228no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—118no—
277C22×C4⋊C4—228no—
278C22×C4⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4C2×D1112yes—
284C22×C22⋊C4C2×D1112yes—
285C22×C42—112no—
286#400—118no—
287#400—118no—
288#394—118no—
289#394C2×D1118yescomplemented
290#388—1116no—
291#388—1116no—
292#386—1116no—
293#386—1116no—
294C4×C22⋊C4—118no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95C2×D1111yescharacteristic
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—816no—
309C22×C11#52514yes—
310C22×C11C2×#12414yes—
311C22×C11#53414yes—
312C22×C11#55318yes—
313C22×C11#55318yes—
314C22×C11C23×D411yescharacteristic
315C22×C11C22×#4111yescharacteristic
316C22×C11C22×#4111yescharacteristic
317C22×C11C22×#4112yes—
318C22×C11C2×H(5,𝔽2)12yes—
319C2×D11—232no—
320C2×D11—24no—
321C2×D11—24no—
322C2×D11—28no—
323C2×D11—28no—
324C2×D11C2×#12418yes—
325C4×C11—24no—
326C4×C11—24no—
327C4×C11—42no—
328C4×C11—44no—
329Dic11—24no—
330Dic11—24no—
331Dic11—44no—
332Dic11—42no—
333Dic11—44no—
334C25—111no—
335C25C22×D1112yes—
336C22×D4—24no—
337C22×D4—44no—
338C22×D4—118no—
339C22×D4—228no—
340C22×D4—228no—
341C22×D4—228no—
342C22×D4C22×D1114yes—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—118no—
346C23×C4—114no—
347C23×C4—112no—
348C23×C4—111no—
349C23×C4—112no—
350C23×C4—114no—
351C23×C4—114no—
352C23×C4—224no—
353C23×C4—224no—
354C23×C4—224no—
355C23×C4—224no—
356C23×C4—444no—
357C23×C4—444no—
358C23×C4C22×D1112yes—
359C23×C4C22×D1111yescharacteristic
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1111yescharacteristic
362#121—2232no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—2232no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—224no—
372C2×C4⋊C4—224no—
373C2×C4⋊C4C22×D1114yes—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—228no—
381C2×C22⋊C4—228no—
382C2×C22⋊C4—228no—
383C2×C22⋊C4—444no—
384C2×C22⋊C4C22×D1118yes—
385C2×C22⋊C4C22×D1118yes—
386C2×C42—118no—
387C2×C42—444no—
388#95—114no—
389#95—118no—
390#95—118no—
391#95—118no—
392#95—118no—
393#95C22×D1114yes—
394C2×C11—84no—
395C2×C11#259118yescomplemented
396C2×C11C2×#52511yescharacteristic
397C2×C11C22×#12411yescharacteristic
398C2×C11C2×#53411yescharacteristic
399C2×C11C2×#55312yes—
400C2×C11C2×#55312yes—
401D11—28no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—24no—
407C24—24no—
408C24—24no—
409C24—114no—
410C24—118no—
411C24—112no—
412C24—222no—
413C24—224no—
414C24—222no—
415C24C23×D1114yes—
416C24C23×D1111yescharacteristic
417C2×D4—28no—
418C2×D4—48no—
419C2×D4—416no—
420C2×D4—2216no—
421C2×D4—2216no—
422C2×D4—2216no—
423C2×D4—4432no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—114no—
433C22×C4—114no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—1116no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—228no—
441C22×C4—228no—
442C22×C4—2232no—
443C22×C4—228no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—224no—
447C22×C4—228no—
448C22×C4—224no—
449C22×C4—222no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—4416no—
457C22×C4—448no—
458C22×C4—448no—
459C22×C4—4416no—
460C22×C4D4×D1114yes—
461C22×C4#434114yes—
462C22×C4C23×D1114yes—
463C22×C4C23×D1112yes—
464C22×C4C23×D1112yes—
465C22×C4C23×D1112yes—
466C4⋊C4—28no—
467C4⋊C4—228no—
468C4⋊C4—228no—
469C4⋊C4—228no—
470C4⋊C4—228no—
471C22⋊C4—216no—
472C22⋊C4—48no—
473C22⋊C4—2216no—
474C22⋊C4—2216no—
475C22⋊C4—2216no—
476C22⋊C4—448no—
477C42—448no—
478C11C2×#259111yescharacteristic, complemented, Sylow
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—24no—
485C23—24no—
486C23—48no—
487C23—48no—
488C23—48no—
489C23—48no—
490C23—48no—
491C23—48no—
492C23—48no—
493C23—114no—
494C23—118no—
495C23—1116no—
496C23—228no—
497C23—228no—
498C23—2216no—
499C23—222no—
500C23—224no—
501C23—2216no—
502C23—222no—
503C23C2×D4×D1112yes—
504C23C2×#434112yes—
505C23#6703714yes—
506C23#41×D1112yes—
507C23#41×D1114yes—
508C23C24×D1111yescharacteristic
509D4—416no—
510D4—4432no—
511C2×C4—28no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—44no—
522C2×C4—48no—
523C2×C4—114no—
524C2×C4—114no—
525C2×C4—2232no—
526C2×C4—228no—
527C2×C4—228no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—4416no—
540C2×C4—4416no—
541C2×C4—444no—
542C2×C4—448no—
543C2×C4—448no—
544C2×C4C2×D4×D1114yes—
545C2×C4C2×#434114yes—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—816no—
554C22—118no—
555C22—224no—
556C22—228no—
557C22—228no—
558C22—224no—
559C22—2232no—
560C22#1062312014yes—
561C22#1062313714yes—
562C22#1062314518yes—
563C22#1062319218yes—
564C22D11×#12414yes—
565C22C22×D4×D1111yescharacteristic
566C22C22×#434111yescharacteristic
567C22C2×#6703712yes—
568C22C2×#41×D1111yescharacteristic
569C22C2×#41×D1112yes—
570C4—24no—
571C4—24no—
572C4—44no—
573C4—42no—
574C4—224no—
575C4—224no—
576C4—444no—
577C4—444no—
578C4—442no—
579C2—84no—
580C2—228no—
581C2#1307409018yesdirect product factor
582C2C2×#1062313711yescharacteristic
583C2C2×D11×#12411yescharacteristic
584C2C2×#1062312011yescharacteristic
585C2C2×#1062319212yes—
586C2C2×#1062314512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66991C2
hypercenterC2×#394D11
hypocenterC11C2×#2591
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
3. #13074090C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622599C2semidirect
6. C2×#10622835C2semidirect
7. C2×#10622564C2semidirect
8. C2×#10622557C2semidirect
9. C2×#10622569C2semidirect
10. C2×#10622569C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#394C2semidirect
33. C2×C4⋊C4×D11C22semidirect
34. C11×#394C22semidirect
36. #10622835C22semidirect
42. #10622599C22semidirect
43. #10622569C22semidirect
44. #10622569C22semidirect
45. #10622564C22semidirect
46. #10622557C22semidirect
47. #10622279C22semidirect
48. #10622272C22semidirect
192. C2×#394D11semidirect
289. #394C2×D11semidirect
395. C2×C11#2591semidirect
478. C11C2×#2591semidirect
581. C2#13074090direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
C22×C4⋊C4×D112
#130740902
C2×#106222722
C2×#106225992
C2×#106228352
C2×#106225642
C2×#106225572
C2×#106225692
C2×#106222792
C2×C11×#3942
C2×#259111