Finite Group Databasebeta

← C2×#13079581 #15624945

Subgroups — C2×#13079581 #15624945

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic, complemented
2#13079581C2116yesmaximal, direct product factor
3C2×#10622672C212yesmaximal, complemented
4C2×#10622669C212yesmaximal, complemented
5C2×#10622667C212yesmaximal, complemented
6C2×#10622670C212yesmaximal, complemented
7C2×#10622841C211yesmaximal, characteristic, complemented
8C2×#10622840C211yesmaximal, characteristic, complemented
9C2×#10622831C211yesmaximal, characteristic, complemented
10C2×#10622830C211yesmaximal, characteristic
11C2×#10622538C211yesmaximal, characteristic, complemented
12C22×C11×#124C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C2×C11×#124—21no—
16C2×C11×#124—21no—
17C2×C11×#124—24no—
18C2×C11×#124C2212yes—
19C2×C11×#124C2212yes—
20C2×C11×#124C2218yescomplemented
21C22×C11×C22⋊C4—21no—
22C22×C11×C22⋊C4—21no—
23C22×C42×C11C2211yescharacteristic
24C22×#4326C2212yescomplemented
25C22×#4325C2212yescomplemented
26C22×#4324C2212yes—
27C22×#4323C2212yes—
28C2×#66983C2211yescharacteristic
29C2×#66982—21no—
30C2×C4×C22⋊D11—21no—
31C2×#66977C2211yescharacteristic
32#10623010—24no—
33#10623010C2218yescomplemented
34C2×#66929—21no—
35C2×#66928C2211yescharacteristic, complemented
36C2×C4×D44C2211yescharacteristic, complemented
37C2×#66925—21no—
38C2×#66923C2211yescharacteristic, complemented
39C2×C4×Dic22C2211yescharacteristic, complemented
40#10622841C2218yescomplemented
41#10622840C2218yescomplemented
42C2×#66899C2212yescomplemented
43C2×#66899C2212yescomplemented
44#10622831C2218yescomplemented
45#10622830C2218yes—
46C2×#66896C2212yes—
47C2×#66896C2212yes—
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622672C22116yescomplemented
51#10622670C22116yescomplemented
52#10622669C22116yescomplemented
53#10622667C22116yescomplemented
54#10622538C2218yescomplemented
55C2×C4⋊(C11⋊C8)C2212yescomplemented
56C2×C4×C11⋊C8C2212yescomplemented
57C25×C11—21no—
58C22×Q8×C11—21no—
59C22×Q8×C11—22no—
60C22×Q8×C11—44no—
61C22×Q8×C11C2312yes—
62C22×Q8×C11C2314yes—
63C22×D4×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—44no—
66C22×D4×C11C2312yes—
67C22×D4×C11C2314yes—
68C23×C4×C11—21no—
69C23×C4×C11D411yescharacteristic
70C23×C4×C11D411yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11—21no—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×Dic22C2311yescharacteristic
76C11×#124—24no—
77C11×#124—24no—
78C11×#124—28no—
79C11×#124—28no—
80C11×#124C2318yes—
81C11×#124C2318yes—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—28no—
87C2×C11×C22⋊C4—28no—
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11D414yes—
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2314yes—
94C2×C22⋊Dic11—21no—
95C2×#4326—44no—
96C2×#4326C2318yescomplemented
97C2×#4325—44no—
98C2×#4325C2318yescomplemented
99C2×#4324—44no—
100C2×#4324C2318yes—
101C2×#4323—44no—
102C2×#4323C2318yes—
103#66983—22no—
104#66983C2314yes—
105#66982—28no—
106C4×C22⋊D11—28no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113#66977—22no—
114#66977C2314yes—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×C4×Dic11—21no—
120C22×C11⋊C8C2312yes—
121C22×C11⋊C8C2312yes—
122#66929—28no—
123#66928—22no—
124#66928C2314yescomplemented
125C4×D44—22no—
126C4×D44C2314yescomplemented
127#66925—28no—
128#66923—22no—
129#66923C2314yescomplemented
130C4×Dic22—22no—
131C4×Dic22C2314yescomplemented
132#66899C2318yescomplemented
133#66899C2318yescomplemented
134#66896C2318yes—
135#66896C2318yes—
136C22⋊(C11⋊C8)C2314yes—
137C22⋊(C11⋊C8)C2314yes—
138C4⋊(C11⋊C8)C2318yescomplemented
139C4×C11⋊C8C2318yescomplemented
140C2×#3211—111nomaximal, Sylow
141C24×C11—24no—
142C24×C11—22no—
143C24×C11—44no—
144C24×C11—44no—
145C24×C11—44no—
146C24×C11C2×D411yescharacteristic
147C23×D11—21no—
148C2×Q8×C11—24no—
149C2×Q8×C11—22no—
150C2×Q8×C11—24no—
151C2×Q8×C11—24no—
152C2×Q8×C11—48no—
153C2×Q8×C11—44no—
154C2×Q8×C11—48no—
155C2×Q8×C11C2414yes—
156C2×D4×C11—24no—
157C2×D4×C11—22no—
158C2×D4×C11—24no—
159C2×D4×C11—24no—
160C2×D4×C11—48no—
161C2×D4×C11—44no—
162C2×D4×C11—48no—
163C2×D4×C11C2414yes—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—24no—
167C22×C4×C11—22no—
168C22×C4×C11—42no—
169C22×C4×C11—44no—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D414yes—
177C22×C4×C11C2×D414yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2411yescharacteristic
180C2×C22⋊D11—24no—
181C2×C22⋊D11—44no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C2×D44—21no—
186C2×D44—24no—
187C2×D44C2412yes—
188C2×C4×D11—24no—
189C2×C4×D11—44no—
190C2×Dic22—21no—
191C2×Dic22—24no—
192C2×Dic22C2412yes—
193C11×C22⋊C4—28no—
194C11×C22⋊C4—28no—
195C11×C22⋊C4—28no—
196C11×C22⋊C4—28no—
197C42×C11C2×D412yes—
198C42×C11C2×D412yes—
199C42×C11C2×D414yes—
200C42×C11C2×D414yes—
201C42×C11C2412yes—
202C42×C11C2412yes—
203C22⋊Dic11—24no—
204#4326—48no—
205#4325—48no—
206#4324—48no—
207#4323—48no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11C2412yes—
215C4⋊Dic11C2412yes—
216Dic11⋊C4—24no—
217Dic11⋊C4—24no—
218Dic11⋊C4—24no—
219Dic11⋊C4—24no—
220C4×Dic11—24no—
221C2×C11⋊C8—24no—
222C2×C11⋊C8—24no—
223C2×C11⋊C8C2414yes—
224C2×C11⋊C8C2414yes—
225C2×#529—111no—
226C22×#124D1111yescharacteristic, complemented
227#3211—1116no—
228C2×#495—112no—
229C2×#488—112no—
230C2×#464—112no—
231C2×#463—112no—
232C2×#451—111no—
233C2×#448—111no—
234C2×#450—111no—
235C2×#447—111no—
236C2×#431—111no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—24no—
240C23×C11—48no—
241C23×C11—48no—
242C23×C11—44no—
243C23×C11—48no—
244C23×C11—44no—
245C23×C11—44no—
246C23×C11—816no—
247C23×C11#13514yes—
248C23×C11C22×D412yes—
249C23×C11C22×D411yescharacteristic
250C22×D11—22no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—42no—
254Q8×C11—24no—
255Q8×C11—24no—
256Q8×C11—48no—
257Q8×C11—44no—
258D4×C11—24no—
259D4×C11—24no—
260D4×C11—48no—
261D4×C11—44no—
262C2×C4×C11—22no—
263C2×C4×C11—28no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—44no—
272C2×C4×C11—48no—
273C2×C4×C11—44no—
274C2×C4×C11C22×D412yes—
275C2×C4×C11C22×D412yes—
276C2×C4×C11C22×D412yes—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C22×D412yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11H(5,𝔽2)14yes—
281C2×C4×C11C2511yescharacteristic
282C22⋊D11—48no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289D44—24no—
290D44—42no—
291C4×D11—48no—
292Dic22—24no—
293Dic22—42no—
294C11⋊C8—24no—
295C11⋊C8—24no—
296C23×Q8C2×D1111yescharacteristic
297C23×D4C2×D1111yescharacteristic
298C22×Q16—112no—
299C22×SD16—112no—
300C22×SD16—112no—
301C22×D8—112no—
302#529—118no—
303#529—224no—
304C2×#126—221no—
305C2×#125—111no—
306C2×#124—21no—
307C2×#124—21no—
308C2×#124—24no—
309C2×#124—111no—
310C2×#124C2×D1112yes—
311C2×#124C2×D1112yes—
312C2×#124C2×D1118yescomplemented
313C2×#123—221no—
314C2×C22⋊Q8—111no—
315C2×#121—111no—
316C2×C4×Q8—111no—
317C2×C4×D4—111no—
318C2×C4×D4—221no—
319C2×#117—221no—
320C22×C22⋊C4—21no—
321C22×C22⋊C4—21no—
322C22×C42C2×D1111yescharacteristic
323#495—1116no—
324#488—1116no—
325#464—1116no—
326#463—1116no—
327#451—118no—
328#450—118no—
329#448—118no—
330#447—118no—
331#431—118no—
332C2×C4⋊C8—112no—
333C2×#103—112no—
334C2×#103—112no—
335C2×#102—112no—
336C2×#102—112no—
337C2×C22⋊C8—111no—
338C2×C22⋊C8—111no—
339C2×C4×C8—112no—
340C22×C11—22no—
341C22×C11—28no—
342C22×C11—22no—
343C22×C11—44no—
344C22×C11—44no—
345C22×C11—44no—
346C22×C11—816no—
347C22×C11—88no—
348C22×C11#53512yes—
349C22×C11C2×#13514yes—
350C22×C11C2×#13512yes—
351C22×C11#57512yes—
352C22×C11C23×D411yescharacteristic
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—84no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—22no—
362C4×C11—44no—
363C4×C11#53512yes—
364C4×C11C2×H(5,𝔽2)12yes—
365Dic11—42no—
366Dic11—42no—
367Dic11—42no—
368C25—21no—
369C22×Q8—22no—
370C22×Q8—21no—
371C22×Q8—44no—
372C22×Q8—111no—
373C22×Q8C22×D1112yes—
374C22×Q8C22×D1114yes—
375C22×D4—22no—
376C22×D4—21no—
377C22×D4—44no—
378C22×D4—111no—
379C22×D4—221no—
380C22×D4C22×D1112yes—
381C22×D4C22×D1114yes—
382C23×C4—21no—
383C23×C4—221no—
384C23×C4C22⋊D1111yescharacteristic
385C23×C4C22⋊D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387C2×Q16—118no—
388C2×Q16—444no—
389C2×SD16—118no—
390C2×SD16—118no—
391C2×SD16—444no—
392C2×SD16—444no—
393C2×D8—118no—
394C2×D8—444no—
395C22×C8—112no—
396C22×C8—112no—
397#126—228no—
398#125—114no—
399#125—222no—
400#124—24no—
401#124—24no—
402#124—28no—
403#124—28no—
404#124—114no—
405#124—222no—
406#124C22×D1118yes—
407#124C22×D1118yes—
408#123—228no—
409C22⋊Q8—114no—
410C22⋊Q8—222no—
411#121—114no—
412#121—222no—
413C4×Q8—114no—
414C4×Q8—222no—
415C4×D4—114no—
416C4×D4—228no—
417C4×D4—222no—
418#117—228no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—28no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C42—221no—
437C2×C42C22⋊D1111yescharacteristic
438C2×C42C22⋊D1111yescharacteristic
439C2×C42C22⋊D1114yes—
440C2×C42C22×D1111yescharacteristic
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1114yes—
443C4⋊C8—118no—
444#103—118no—
445#103—118no—
446#102—118no—
447#102—118no—
448C22⋊C8—114no—
449C22⋊C8—114no—
450C4×C8—118no—
451C2×C11—24no—
452C2×C11—84no—
453C2×C11#321114yescomplemented
454C2×C11C2×#53511yescharacteristic
455C2×C11C22×#13511yescharacteristic
456C2×C11C2×#57511yescharacteristic
457D11—82no—
458C24—24no—
459C24—22no—
460C24—44no—
461C24—44no—
462C24—44no—
463C24—221no—
464C24C2×C22⋊D1111yescharacteristic
465C2×Q8—24no—
466C2×Q8—22no—
467C2×Q8—24no—
468C2×Q8—24no—
469C2×Q8—48no—
470C2×Q8—44no—
471C2×Q8—48no—
472C2×Q8—112no—
473C2×Q8—221no—
474C2×Q8—224no—
475C2×Q8C23×D1114yes—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—22no—
480C2×D4—48no—
481C2×D4—44no—
482C2×D4—48no—
483C2×D4—112no—
484C2×D4—224no—
485C2×D4—224no—
486C2×D4—221no—
487C2×D4—444no—
488C2×D4C23×D1114yes—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—42no—
494C22×C4—44no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—224no—
499C22×C4—444no—
500C22×C4C2×C22⋊D1114yes—
501C22×C4C2×C22⋊D1112yes—
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1114yes—
508C22×C4C23×D1112yes—
509C22×C4C23×D1111yescharacteristic
510Q16—448no—
511SD16—448no—
512SD16—448no—
513D8—448no—
514C2×C8—114no—
515C2×C8—114no—
516C2×C8—224no—
517C2×C8—224no—
518C4⋊C4—112no—
519C4⋊C4—112no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—224no—
523C4⋊C4—224no—
524C4⋊C4—224no—
525C4⋊C4—224no—
526C22⋊C4—28no—
527C22⋊C4—28no—
528C22⋊C4—28no—
529C22⋊C4—28no—
530C22⋊C4—224no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—224no—
534C22⋊C4—224no—
535C42—224no—
536C42C2×C22⋊D1114yes—
537C42C2×C22⋊D1112yes—
538C42C2×C22⋊D1112yes—
539C42C2×C22⋊D1114yes—
540C42C23×D1112yes—
541C42C23×D1112yes—
542C11C2×#321111yescharacteristic, complemented, Sylow
543C23—22no—
544C23—22no—
545C23—24no—
546C23—48no—
547C23—48no—
548C23—44no—
549C23—48no—
550C23—44no—
551C23—44no—
552C23—816no—
553C23—222no—
554C23—442no—
555C23—442no—
556C23—442no—
557C23#6700314yes—
558C23C22×C22⋊D1112yes—
559C23C22×C22⋊D1111yescharacteristic
560Q8—24no—
561Q8—24no—
562Q8—48no—
563Q8—44no—
564Q8—224no—
565Q8—442no—
566D4—24no—
567D4—24no—
568D4—48no—
569D4—44no—
570D4—224no—
571D4—448no—
572D4—442no—
573C2×C4—22no—
574C2×C4—28no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—44no—
583C2×C4—48no—
584C2×C4—44no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—448no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4#6703714yes—
593C2×C4C22×C22⋊D1112yes—
594C2×C4C22×C22⋊D1112yes—
595C2×C4C22×C22⋊D1112yes—
596C2×C4C22×C22⋊D1112yes—
597C2×C4C22×C22⋊D1112yes—
598C2×C4C22×C22⋊D1111yescharacteristic
599C2×C4C24×D1111yescharacteristic
600C8—224no—
601C8—224no—
602C22—28no—
603C22—22no—
604C22—22no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—816no—
609C22—88no—
610C22—442no—
611C22—442no—
612C22—442no—
613C22—884no—
614C22#1062333612yes—
615C22C2×#6700314yes—
616C22C2×#6700312yes—
617C22#1062335312yes—
618C22C23×C22⋊D1111yescharacteristic
619C4—22no—
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—44no—
625C4—442no—
626C4—442no—
627C4—442no—
628C4#1062333612yes—
629C4C2×#6703712yes—
630C2—24no—
631C2—84no—
632C2—882no—
633C2#1307958114yesdirect product factor
634C2C2×#1062333611yescharacteristic
635C2C22×#6700311yescharacteristic
636C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#124C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
hypercenterC22×#124D11
hypocenterC11C2×#3211
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. #13079581C2direct (N × H)
3. C2×#10622672C2semidirect
4. C2×#10622669C2semidirect
5. C2×#10622667C2semidirect
6. C2×#10622670C2semidirect
7. C2×#10622841C2semidirect
8. C2×#10622840C2semidirect
9. C2×#10622831C2semidirect
11. C2×#10622538C2semidirect
12. C22×C11×#124C2semidirect
20. C2×C11×#124C22semidirect
24. C22×#4326C22semidirect
25. C22×#4325C22semidirect
33. #10623010C22semidirect
35. C2×#66928C22semidirect
36. C2×C4×D44C22semidirect
38. C2×#66923C22semidirect
39. C2×C4×Dic22C22semidirect
40. #10622841C22semidirect
41. #10622840C22semidirect
42. C2×#66899C22semidirect
43. C2×#66899C22semidirect
44. #10622831C22semidirect
50. #10622672C22semidirect
51. #10622670C22semidirect
52. #10622669C22semidirect
53. #10622667C22semidirect
54. #10622538C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×C4×C11⋊C8C22semidirect
96. C2×#4326C23semidirect
98. C2×#4325C23semidirect
124. #66928C23semidirect
126. C4×D44C23semidirect
129. #66923C23semidirect
131. C4×Dic22C23semidirect
132. #66899C23semidirect
133. #66899C23semidirect
138. C4⋊(C11⋊C8)C23semidirect
139. C4×C11⋊C8C23semidirect
226. C22×#124D11semidirect
312. C2×#124C2×D11semidirect
453. C2×C11#3211semidirect
542. C11C2×#3211semidirect
633. C2#13079581direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130795812
C2×#106226722
C2×#106226692
C2×#106226672
C2×#106226702
C2×#106228412
C2×#106228402
C2×#106228312
C2×#106228302
C2×#106225382
C22×C11×#1242
C2×#321111