Finite Group Databasebeta

← C2×#13072405 #14921929

Subgroups — C2×#13072405 #14921929

Order 2816.

3070 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×#66928C211yesmaximal, characteristic
2C22×#66946C211yesmaximal, characteristic
3#13072405C2116yesmaximal, direct product factor
4C2×#10622288C212yesmaximal, complemented
5C2×#10622606C212yesmaximal, complemented
6C2×#10622587C211yesmaximal, characteristic, complemented
7C2×#10622587C211yesmaximal, characteristic, complemented
8C2×#10622601C211yesmaximal, characteristic
9C2×#10622602C212yesmaximal, complemented
10C2×#10622277C212yesmaximal, complemented
11C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C2×#66946—28no—
30C2×#66946C2218yes—
31C2×#66928—28no—
32C2×#66928C2218yes—
33C11×#389C2218yescomplemented
34C2×C11×#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622606C22116yescomplemented
42#10622602C22116yescomplemented
43#10622601C2218yes—
44#10622587C2218yescomplemented
45#10622587C2218yescomplemented
46C4×Dic11⋊C4C2218yescomplemented
47#10622288C22116yescomplemented
48#10622277C22116yescomplemented
49C24×D11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×D44—24no—
61C22×D44—24no—
62C22×D44D418yes—
63C22×D44C2314yes—
64C22×C4×D11—28no—
65C22×C4×D11—28no—
66C22×C4×D11—44no—
67C22×C4×D11C2318yes—
68C22×Dic22—24no—
69C22×Dic22—24no—
70C22×Dic22—24no—
71C22×Dic22C2314yes—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—44no—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2318yes—
78C2×C42×C11—24no—
79C2×C42×C11C2314yes—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4C2318yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4C2314yes—
93C2×Dic11⋊C4C2314yes—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—24no—
96C2×C4×Dic11C2314yes—
97C2×C4×Dic11C2314yes—
98#66946—232no—
99#66928—232no—
100C11×#95C2318yes—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2314yes—
107C2×#2447—111nomaximal, Sylow
108C24×C11C2411yescharacteristic
109C23×D11—24no—
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—24no—
115C23×D11C2×D418yes—
116C23×D11C2414yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11C2×D414yes—
130C22×C4×C11#4114yes—
131C22×C4×C11#4114yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2412yes—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11#4114yes—
151C22×Dic11#4114yes—
152C22×Dic11C2412yes—
153C22×Dic11C2414yes—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C22×Dic11C2412yes—
157C2×D44—232no—
158C2×D44—28no—
159C2×D44—28no—
160C2×D44C2×D4116yes—
161C2×C4×D11—216no—
162C2×C4×D11—216no—
163C2×C4×D11—48no—
164C2×C4×D11—432no—
165C2×Dic22—28no—
166C2×Dic22—28no—
167C2×Dic22—28no—
168C2×Dic22—416no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—48no—
172C42×C11—28no—
173(C2×D11)⋊C4—216no—
174(C2×D11)⋊C4—216no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—48no—
178Dic11⋊C4—28no—
179Dic11⋊C4—28no—
180C4×Dic11—28no—
181C4×Dic11—28no—
182C22×#124—111no—
183C22×C4×D4—111no—
184#2447—1116no—
185C2×#397—112no—
186C2×#397—112no—
187C2×#391—111no—
188C2×#391—111no—
189C2×#390—111no—
190C2×#389D1111yescharacteristic, complemented
191C2×#385—112no—
192C2×#381—112no—
193C2×C4×C4⋊C4—111no—
194C23×C11C22×D412yes—
195C23×C11C2×#4112yes—
196C23×C11C2×#4112yes—
197C23×C11C2×#4112yes—
198C23×C11C2×#4112yes—
199C23×C11H(5,𝔽2)12yes—
200C23×C112−1+412yes—
201C23×C11C2511yescharacteristic
202C22×D11—216no—
203C22×D11—216no—
204C22×D11—216no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—48no—
212C22×D11—48no—
213C22×D11—48no—
214C22×D11—48no—
215C22×D11C22×D418yes—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—48no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11—48no—
232C2×C4×C11#123116yes—
233C2×C4×C11C22×D414yes—
234C2×C4×C11C2×#4114yes—
235C2×C4×C11C2×#4114yes—
236C2×Dic11—28no—
237C2×Dic11—28no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—48no—
252C2×Dic11—44no—
253C2×Dic11—44no—
254C2×Dic11C2×#4114yes—
255C2×Dic11C2×#4114yes—
256D44—232no—
257C4×D11—432no—
258Dic22—416no—
259C23×Q8—111no—
260C23×D4—111no—
261C24×C4—112no—
262C2×#124—118no—
263C2×#124—228no—
264C2×C4×D4—118no—
265C2×C4×D4—228no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4C2×D1111yescharacteristic
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C4⋊C4C2×D1112yes—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C42—111no—
277C22×C42—111no—
278C22×C42C2×D1111yescharacteristic
279#397—1116no—
280#397—1116no—
281#391—118no—
282#391—118no—
283#390—118no—
284#389C2×D1118yescomplemented
285#385—1116no—
286#381—1116no—
287C4×C4⋊C4—118no—
288C2×#95—111no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—111no—
293C2×#95—112no—
294C2×#95C2×D1112yes—
295C22×C11C2×#12314yes—
296C22×C11#52914yes—
297C22×C11#54214yes—
298C22×C11#54614yes—
299C22×C11#54714yes—
300C22×C11#55614yes—
301C22×C11#55914yes—
302C22×C11C23×D411yescharacteristic
303C22×C11C22×#4111yescharacteristic
304C22×C11C22×#4111yescharacteristic
305C22×C11C22×#4111yescharacteristic
306C22×C11C22×#4111yescharacteristic
307C22×C11C2×H(5,𝔽2)11yescharacteristic
308C22×C11C2×2−1+411yescharacteristic
309C2×D11—28no—
310C2×D11—28no—
311C2×D11—28no—
312C2×D11—44no—
313C2×D11—44no—
314C2×D11—432no—
315C2×D11—44no—
316C2×D11—44no—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11—42no—
320C4×C11—44no—
321C4×C11C2×#12318yes—
322Dic11—24no—
323Dic11—24no—
324Dic11—44no—
325Dic11—42no—
326Dic11—42no—
327C25—112no—
328C22×Q8—114no—
329C22×Q8—224no—
330C22×Q8—224no—
331C22×Q8—224no—
332C22×D4—118no—
333C22×D4—114no—
334C22×D4—224no—
335C22×D4—224no—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—112no—
340C23×C4—111no—
341C23×C4—118no—
342C23×C4—228no—
343C23×C4—228no—
344C23×C4—444no—
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1112yes—
348C23×C4C22×D1112yes—
349C23×C4C22×D1111yescharacteristic
350#124—2232no—
351C4×D4—2232no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4C22×D1114yes—
360C2×C4⋊C4C22×D1114yes—
361C2×C4⋊C4C22×D1118yes—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—118no—
364C2×C22⋊C4—118no—
365C2×C22⋊C4—118no—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—228no—
368C2×C22⋊C4—228no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4—228no—
371C2×C22⋊C4—444no—
372C2×C42—24no—
373C2×C42—114no—
374C2×C42—114no—
375C2×C42—224no—
376C2×C42—224no—
377C2×C42C22×D1114yes—
378#95—114no—
379#95—114no—
380#95—118no—
381#95—118no—
382#95—118no—
383#95—118no—
384#95C22×D1118yes—
385C2×C11#244718yescomplemented
386C2×C11C22×#12311yescharacteristic
387C2×C11C2×#52911yescharacteristic
388C2×C11C2×#54211yescharacteristic
389C2×C11C2×#54611yescharacteristic
390C2×C11C2×#54711yescharacteristic
391C2×C11C2×#55611yescharacteristic
392C2×C11C2×#55911yescharacteristic
393D11—48no—
394C24—118no—
395C24—114no—
396C24—224no—
397C24—224no—
398C24—224no—
399C24—224no—
400C24—224no—
401C24—224no—
402C24C23×D1111yescharacteristic
403C2×Q8—228no—
404C2×Q8—228no—
405C2×Q8—228no—
406C2×Q8—4416no—
407C2×D4—1116no—
408C2×D4—2232no—
409C2×D4—228no—
410C2×D4—228no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—114no—
424C22×C4—114no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—114no—
429C22×C4—112no—
430C22×C4—2216no—
431C22×C4—2216no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—224no—
437C22×C4—222no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—448no—
446C22×C4—4432no—
447C22×C4#433914yes—
448C22×C4D4×D1114yes—
449C22×C4#434314yes—
450C22×C4C23×D1114yes—
451C22×C4C23×D1114yes—
452C22×C4C23×D1112yes—
453C22×C4C23×D1112yes—
454C22×C4C23×D1112yes—
455C4⋊C4—28no—
456C4⋊C4—28no—
457C4⋊C4—48no—
458C4⋊C4—228no—
459C4⋊C4—228no—
460C22⋊C4—2216no—
461C22⋊C4—2216no—
462C22⋊C4—2216no—
463C22⋊C4—2216no—
464C22⋊C4—448no—
465C42—28no—
466C42—228no—
467C42—228no—
468C11C2×#244711yescharacteristic, complemented, Sylow
469C23—118no—
470C23—2216no—
471C23—2216no—
472C23—2216no—
473C23—224no—
474C23—224no—
475C23—224no—
476C23—224no—
477C23—224no—
478C23—224no—
479C23—448no—
480C23—448no—
481C23—448no—
482C23—448no—
483C23C2×#433912yes—
484C23C2×D4×D1112yes—
485C23#6703712yes—
486C23C2×#434312yes—
487C23#6704012yes—
488C23#41×D1112yes—
489C23#41×D1112yes—
490C23C24×D1111yescharacteristic
491Q8—4416no—
492D4—2232no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—48no—
506C2×C4—44no—
507C2×C4—48no—
508C2×C4—44no—
509C2×C4—114no—
510C2×C4—114no—
511C2×C4—228no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—228no—
517C2×C4—224no—
518C2×C4—222no—
519C2×C4—224no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—4432no—
527C2×C4—444no—
528C2×C4—448no—
529C2×C4—444no—
530C2×C4#66947116yes—
531C2×C4C2×#433914yes—
532C2×C4C2×D4×D1114yes—
533C2×C4C2×#434314yes—
534C22—228no—
535C22—228no—
536C22—228no—
537C22—4432no—
538C22—444no—
539C22—444no—
540C22—444no—
541C22—444no—
542C22C2×#6694714yes—
543C22#1062309014yes—
544C22#1062309914yes—
545C22#1062314314yes—
546C22#1062316214yes—
547C22#1062322214yes—
548C22#1062326414yes—
549C22C22×#433911yescharacteristic
550C22C22×D4×D1111yescharacteristic
551C22C2×#6703711yescharacteristic
552C22C22×#434311yescharacteristic
553C22C2×#6704011yescharacteristic
554C22C2×#41×D1111yescharacteristic
555C22C2×#41×D1111yescharacteristic
556C4—44no—
557C4—44no—
558C4—42no—
559C4—42no—
560C4—224no—
561C4—224no—
562C4—442no—
563C4—442no—
564C4—444no—
565C4C2×#6694718yes—
566C2—448no—
567C2#1307240518yesdirect product factor
568C2C22×#6694711yescharacteristic
569C2C2×#1062322211yescharacteristic
570C2C2×#1062326411yescharacteristic
571C2C2×#1062314311yescharacteristic
572C2C2×#1062316211yescharacteristic
573C2C2×#1062309911yescharacteristic
574C2C2×#1062309011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#389D11
hypocenterC11C2×#2447
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #13072405C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622606C2semidirect
6. C2×#10622587C2semidirect
7. C2×#10622587C2semidirect
9. C2×#10622602C2semidirect
10. C2×#10622277C2semidirect
11. C2×C4×Dic11⋊C4C2semidirect
12. C2×C11×#389C2semidirect
33. C11×#389C22semidirect
41. #10622606C22semidirect
42. #10622602C22semidirect
44. #10622587C22semidirect
45. #10622587C22semidirect
46. C4×Dic11⋊C4C22semidirect
47. #10622288C22semidirect
48. #10622277C22semidirect
190. C2×#389D11semidirect
284. #389C2×D11semidirect
385. C2×C11#2447semidirect
468. C11C2×#2447semidirect
567. C2#13072405direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669282
C22×#669462
#130724052
C2×#106222882
C2×#106226062
C2×#106225872
C2×#106226012
C2×#106226022
C2×#106222772
C2×C4×Dic11⋊C42
C2×C11×#3892
C2×#244711