Finite Group Databasebeta

← C2×#13072919 #14922823

Subgroups — C2×#13072919 #14922823

Order 2816.

3678 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C212yesmaximal
2C22×#66946C211yesmaximal, characteristic
3C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4#13072919C2116yesmaximal, direct product factor
5C2×#10622596C211yesmaximal, characteristic, complemented
6C2×#10622287C211yesmaximal, characteristic, complemented
7C2×#10622606C211yesmaximal, characteristic, complemented
8C2×#10622585C212yesmaximal, complemented
9C2×#10622277C212yesmaximal, complemented
10C2×#10622280C211yesmaximal, characteristic, complemented
11C2×#10622280C212yesmaximal, complemented
12C2×C11×#398C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66947—216no—
31C2×#66947C22116yes—
32C2×#66946—28no—
33C2×#66946C2218yes—
34C2×C4⋊C4×D11—28no—
35C2×C4⋊C4×D11C2218yescomplemented
36C11×#398C2218yescomplemented
37C2×C11×#95C2212yes—
38C2×C11×#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622606C2218yescomplemented
44#10622596C2218yescomplemented
45#10622585C22116yescomplemented
46#10622287C2218yescomplemented
47#10622280C22116yescomplemented
48#10622280C2218yescomplemented
49#10622277C22116yescomplemented
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C22×D44—24no—
62C22×D44—24no—
63C22×D44D418yes—
64C22×D44C2314yes—
65C22×C4×D11—28no—
66C22×C4×D11—28no—
67C22×C4×D11—28no—
68C22×C4×D11—28no—
69C22×C4×D11—24no—
70C22×C4×D11—28no—
71C22×C4×D11D418yes—
72C22×C4×D11C2318yes—
73C22×C4×D11C2314yes—
74C22×C4×D11C2314yes—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—28no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2318yes—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×C4⋊Dic11—24no—
92C2×C4⋊Dic11C2314yes—
93C2×Dic11⋊C4—28no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4—28no—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2318yes—
98C2×Dic11⋊C4C2318yes—
99C2×C4×Dic11—24no—
100C2×C4×Dic11C2314yes—
101#66947—264no—
102#66946—232no—
103C4⋊C4×D11—232no—
104C11×#95C2318yes—
105C11×#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C2×#2486—111nomaximal, Sylow
111C24×C11C2411yescharacteristic
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—22no—
115C23×D11—24no—
116C23×D11—22no—
117C23×D11—24no—
118C23×D11C2×D414yes—
119C23×D11C2×D414yes—
120C23×D11C2×D414yes—
121C23×D11#4114yes—
122C23×D11C2412yes—
123C23×D11C2412yes—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11C2×D414yes—
151C22×Dic11#4118yes—
152C22×Dic11C2412yes—
153C22×Dic11C2414yes—
154C22×Dic11C2414yes—
155C22×Dic11C2412yes—
156C2×D44—232no—
157C2×D44—28no—
158C2×D44—28no—
159C2×D44C2×D4116yes—
160C2×C4×D11—232no—
161C2×C4×D11—216no—
162C2×C4×D11—28no—
163C2×C4×D11—216no—
164C2×C4×D11—216no—
165C2×C4×D11—216no—
166C2×C4×D11—216no—
167C2×C4×D11—416no—
168C2×C4×D11—432no—
169C2×C4×D11C2×D4116yes—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—216no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—216no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—28no—
178C4⋊Dic11—28no—
179Dic11⋊C4—216no—
180Dic11⋊C4—216no—
181Dic11⋊C4—216no—
182C4×Dic11—28no—
183C22×#123—112no—
184C22×C4×D4—111no—
185C23×C4⋊C4—111no—
186#2486—1116no—
187C2×#398—111no—
188C2×#398D1111yescharacteristic, complemented
189C2×#397—111no—
190C2×#397—111no—
191C2×#389—112no—
192C2×#381—112no—
193C2×#380—112no—
194C2×#380—111no—
195C23×C11C22×D412yes—
196C23×C11C22×D412yes—
197C23×C11C2×#4112yes—
198C23×C11C2×#4114yes—
199C23×C112−1+414yes—
200C23×C11C2511yescharacteristic
201C22×D11—28no—
202C22×D11—28no—
203C22×D11—216no—
204C22×D11—216no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—28no—
208C22×D11—216no—
209C22×D11—22no—
210C22×D11—24no—
211C22×D11—22no—
212C22×D11—24no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—48no—
216C22×D11#121116yes—
217C22×D11C22×D414yes—
218C22×D11C22×D414yes—
219C22×D11C22×D414yes—
220C22×D11C2×#4114yes—
221C2×C4×C11—28no—
222C2×C4×C11—28no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—48no—
235C2×C4×C11—44no—
236C2×C4×C11—48no—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C22×D414yes—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—48no—
248C2×Dic11—44no—
249C2×Dic11—48no—
250C2×Dic11#123116yescomplemented
251C2×Dic11C22×D414yes—
252C2×Dic11C2×#4118yes—
253D44—232no—
254C4×D11—232no—
255C4×D11—432no—
256C4×D11—416no—
257C23×D4—111no—
258C24×C4—111no—
259C24×C4—112no—
260C24×C4—111no—
261C2×#123—1116no—
262C2×#123—2216no—
263C2×C4×D4—118no—
264C2×C4×D4—228no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—118no—
270C22×C4⋊C4—228no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C4⋊C4C2×D1111yescharacteristic
273C22×C4⋊C4C2×D1112yes—
274C22×C22⋊C4—111no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—112no—
279C22×C42—111no—
280#398—118no—
281#398C2×D1118yescomplemented
282#397—118no—
283#397—118no—
284#389—1116no—
285#381—1116no—
286#380—1116no—
287#380—118no—
288C2×#95—111no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95C2×D1111yescharacteristic
293C2×#95C2×D1112yes—
294C22×C11C2×#12114yes—
295C22×C11C2×#12314yes—
296C22×C11#53614yes—
297C22×C11#54718yes—
298C22×C11#55218yes—
299C22×C11C23×D411yescharacteristic
300C22×C11C23×D411yescharacteristic
301C22×C11C22×#4111yescharacteristic
302C22×C11C22×#4112yes—
303C22×C11C2×2−1+412yes—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—28no—
307C2×D11—28no—
308C2×D11—232no—
309C2×D11—24no—
310C2×D11—28no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—44no—
314C2×D11—416no—
315C2×D11C2×#12118yes—
316C4×C11—24no—
317C4×C11—24no—
318C4×C11—44no—
319C4×C11—42no—
320C4×C11—44no—
321Dic11—44no—
322Dic11—42no—
323Dic11—44no—
324Dic11C2×#12318yescomplemented
325C25—111no—
326C25—111no—
327C22×D4—118no—
328C22×D4—114no—
329C22×D4—224no—
330C22×D4—224no—
331C23×C4—111no—
332C23×C4—118no—
333C23×C4—114no—
334C23×C4—112no—
335C23×C4—111no—
336C23×C4—112no—
337C23×C4—118no—
338C23×C4—114no—
339C23×C4—228no—
340C23×C4—224no—
341C23×C4—228no—
342C23×C4—228no—
343C23×C4—228no—
344C23×C4—228no—
345C23×C4C22×D1112yes—
346C23×C4C22×D1112yes—
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C23×C4C22×D1111yescharacteristic
350#123—2264no—
351C4×D4—2232no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—118no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—118no—
359C2×C4⋊C4—2232no—
360C2×C4⋊C4—228no—
361C2×C4⋊C4—228no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—228no—
364C2×C4⋊C4C22×D1114yes—
365C2×C4⋊C4C22×D1114yes—
366C2×C4⋊C4C22×D1118yes—
367C2×C22⋊C4—114no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—224no—
377C2×C42—114no—
378C2×C42—224no—
379#95—118no—
380#95—114no—
381#95—118no—
382#95—118no—
383#95C22×D1118yes—
384#95C22×D1114yes—
385C2×C11#248618yescomplemented
386C2×C11C22×#12111yescharacteristic
387C2×C11C22×#12311yescharacteristic
388C2×C11C2×#53611yescharacteristic
389C2×C11C2×#54712yes—
390C2×C11C2×#55212yes—
391D11—28no—
392D11—44no—
393C24—114no—
394C24—114no—
395C24—114no—
396C24—112no—
397C24—114no—
398C24—112no—
399C24—224no—
400C24—224no—
401C24—222no—
402C24—224no—
403C24—224no—
404C24—222no—
405C24C23×D1111yescharacteristic
406C2×D4—1116no—
407C2×D4—228no—
408C2×D4—2232no—
409C2×D4—228no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—114no—
422C22×C4—118no—
423C22×C4—112no—
424C22×C4—1116no—
425C22×C4—112no—
426C22×C4—114no—
427C22×C4—114no—
428C22×C4—2232no—
429C22×C4—2216no—
430C22×C4—228no—
431C22×C4—2216no—
432C22×C4—2216no—
433C22×C4—2216no—
434C22×C4—2216no—
435C22×C4—222no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—4416no—
444C22×C4—4432no—
445C22×C4D4×D1114yes—
446C22×C4D4×D1114yes—
447C22×C4C23×D1112yes—
448C22×C4C23×D1114yes—
449C22×C4C23×D1114yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1112yes—
452C4⋊C4—28no—
453C4⋊C4—28no—
454C4⋊C4—216no—
455C4⋊C4—2216no—
456C4⋊C4—2216no—
457C4⋊C4—228no—
458C4⋊C4—2216no—
459C22⋊C4—228no—
460C22⋊C4—2216no—
461C22⋊C4—2216no—
462C22⋊C4—2216no—
463C22⋊C4—228no—
464C42—228no—
465C11C2×#248611yescharacteristic, complemented, Sylow
466C23—1116no—
467C23—114no—
468C23—114no—
469C23—114no—
470C23—114no—
471C23—228no—
472C23—2216no—
473C23—228no—
474C23—224no—
475C23—224no—
476C23—2216no—
477C23—228no—
478C23—2216no—
479C23—222no—
480C23—224no—
481C23—224no—
482C23—222no—
483C23—444no—
484C23—444no—
485C23—448no—
486C23C2×D4×D1112yes—
487C23C2×D4×D1112yes—
488C23#6704014yes—
489C23#41×D1112yes—
490C23#41×D1114yes—
491C23C24×D1111yescharacteristic
492D4—2232no—
493C2×C4—28no—
494C2×C4—28no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—48no—
507C2×C4—48no—
508C2×C4—44no—
509C2×C4—1116no—
510C2×C4—114no—
511C2×C4—118no—
512C2×C4—2232no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—4416no—
522C2×C4—4432no—
523C2×C4—444no—
524C2×C4—448no—
525C2×C4—448no—
526C2×C4C2×D4×D1114yes—
527C2×C4C2×D4×D1114yes—
528C22—118no—
529C22—228no—
530C22—2232no—
531C22—224no—
532C22—228no—
533C22—224no—
534C22—228no—
535C22—224no—
536C22—444no—
537C22—4416no—
538C22—442no—
539C22—442no—
540C22D11×#12114yes—
541C22#1062316218yes—
542C22D11×#12314yes—
543C22#1062322418yes—
544C22#1062325514yes—
545C22C22×D4×D1111yescharacteristic
546C22C22×D4×D1111yescharacteristic
547C22C2×#6704012yes—
548C22C2×#41×D1111yescharacteristic
549C22C2×#41×D1112yes—
550C4—24no—
551C4—24no—
552C4—44no—
553C4—44no—
554C4—42no—
555C4—118no—
556C4—442no—
557C4—444no—
558C4—444no—
559C2—228no—
560C2—444no—
561C2#1307291918yesdirect product factor
562C2C2×D11×#12111yescharacteristic
563C2C2×D11×#12311yescharacteristic
564C2C2×#1062325511yescharacteristic
565C2C2×#1062316212yes—
566C2C2×#1062322412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#398D11
hypocenterC11C2×#2486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D11C2semidirect
4. #13072919C2direct (N × H)
5. C2×#10622596C2semidirect
6. C2×#10622287C2semidirect
7. C2×#10622606C2semidirect
8. C2×#10622585C2semidirect
9. C2×#10622277C2semidirect
10. C2×#10622280C2semidirect
11. C2×#10622280C2semidirect
12. C2×C11×#398C2semidirect
35. C2×C4⋊C4×D11C22semidirect
36. C11×#398C22semidirect
43. #10622606C22semidirect
44. #10622596C22semidirect
45. #10622585C22semidirect
46. #10622287C22semidirect
47. #10622280C22semidirect
48. #10622280C22semidirect
49. #10622277C22semidirect
188. C2×#398D11semidirect
250. C2×Dic11#123semidirect
281. #398C2×D11semidirect
324. Dic11C2×#123semidirect
385. C2×C11#2486semidirect
465. C11C2×#2486semidirect
561. C2#13072919direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669462
C22×C4⋊C4×D112
#130729192
C2×#106225962
C2×#106222872
C2×#106226062
C2×#106225852
C2×#106222772
C2×#106222802
C2×C11×#3982
C2×#248611