Finite Group Databasebeta

← C2×#13079308 #15623678

Subgroups — C2×#13079308 #15623678

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic, complemented
2#13079308C2116yesmaximal, direct product factor
3C2×#10622693C211yesmaximal, characteristic, complemented
4C2×#10622687C211yesmaximal, characteristic, complemented
5C2×#10622684C211yesmaximal, characteristic, complemented
6C2×#10622702C211yesmaximal, characteristic, complemented
7C2×#10622651C212yesmaximal, complemented
8C2×#10622654C212yesmaximal, complemented
9C2×#10622627C212yesmaximal, complemented
10C2×#10622631C212yesmaximal, complemented
11C22×#66867C211yesmaximal, characteristic, complemented
12C2×C11×#532C211yesmaximal, characteristic, complemented
13C22×C11×#41—21no—
14C11×#532—24no—
15C11×#532C2218yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#127C2211yescharacteristic
18C2×C11×#124—21no—
19C2×C11×#121—21no—
20C2×C11×#121C2212yes—
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2212yes—
23C22×C42×C11C2211yescharacteristic
24C22×#4324C2212yes—
25C22×#4323C2212yes—
26C2×#66983C2211yescharacteristic
27C2×#66982—21no—
28C2×C4×C22⋊D11—21no—
29C2×#66977C2211yescharacteristic
30C23×C11⋊C8C2212yes—
31#10623010—24no—
32#10623010C2218yescomplemented
33C2×#66929—21no—
34C2×#66928C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×#66925—21no—
37C2×#66923C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C2×#66896C2212yes—
40C2×#66896C2212yes—
41#10622702C2218yescomplemented
42#10622693C2218yescomplemented
43#10622687C2218yescomplemented
44#10622684C2218yescomplemented
45#10622654C22116yescomplemented
46#10622651C22116yescomplemented
47#10622631C22116yescomplemented
48#10622627C22116yescomplemented
49C2×#66874C2212yes—
50C2×#66873C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53C2×#66867C2211yescharacteristic
54C2×#66867C2212yes—
55C2×#66867C2211yescharacteristic
56C2×#66867C2218yescomplemented
57C2×C11×#41—28no—
58C2×C11×#41—48no—
59C22×Q8×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11C2312yes—
64C23×C4×C11—22no—
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D411yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×Dic22C2311yescharacteristic
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8C2314yes—
74C11×#127—22no—
75C11×#127C2314yes—
76C11×#124—28no—
77C11×#121—28no—
78C11×#121—24no—
79C11×#121C2318yes—
80C4×D4×C11—28no—
81C4×D4×C11—24no—
82C4×D4×C11C2318yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C42×C11D411yescharacteristic
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D414yes—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2314yes—
93C2×C22⋊Dic11—21no—
94C2×#4324—28no—
95C2×#4324C2318yes—
96C2×#4323—28no—
97C2×#4323C2318yes—
98#66983—22no—
99#66983C2314yes—
100#66982—28no—
101C4×C22⋊D11—28no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108#66977—22no—
109#66977C2314yes—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×C4×Dic11—21no—
115C22×C11⋊C8—28no—
116C22×C11⋊C8C2312yes—
117C22×C11⋊C8C2318yes—
118C22×C11⋊C8C2312yes—
119#66929—28no—
120#66928—22no—
121#66928C2314yes—
122C4×D44—22no—
123C4×D44C2314yes—
124#66925—28no—
125#66923—22no—
126#66923C2314yes—
127C4×Dic22—22no—
128C4×Dic22C2314yes—
129#66896C2318yes—
130#66896C2318yes—
131#66874C2318yes—
132#66873C2318yes—
133#66872C2318yes—
134#66871C2318yes—
135#66867C2318yes—
136#66867C2314yes—
137#66867C2314yes—
138C2×#3180—111nomaximal, Sylow
139C24×C11—22no—
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C11×#41—432no—
143C2×Q8×C11—24no—
144C2×Q8×C11—44no—
145C2×D4×C11—28no—
146C2×D4×C11—22no—
147C2×D4×C11—24no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—44no—
152C2×D4×C11—44no—
153C2×D4×C11—48no—
154C2×D4×C11C2414yes—
155C22×C4×C11—24no—
156C22×C4×C11—24no—
157C22×C4×C11—22no—
158C22×C4×C11—28no—
159C22×C4×C11—42no—
160C22×C4×C11—48no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C2×C22⋊D11—24no—
172C2×C22⋊D11—44no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C2×D44—21no—
177C2×D44—24no—
178C2×D44C2412yes—
179C2×C4×D11—24no—
180C2×C4×D11—44no—
181C2×Dic22—21no—
182C2×Dic22—24no—
183C2×Dic22C2412yes—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4C2414yes—
187C11×C22⋊C4—28no—
188C11×C22⋊C4—28no—
189C42×C11C2×D412yes—
190C42×C11C2×D412yes—
191C42×C11C2×D414yes—
192C42×C11C2×D414yes—
193C42×C11C2412yes—
194C42×C11C2412yes—
195C22⋊Dic11—24no—
196#4324—216no—
197#4323—216no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C2412yes—
205C4⋊Dic11C2412yes—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210C4×Dic11—24no—
211C2×C11⋊C8—216no—
212C2×C11⋊C8—24no—
213C2×C11⋊C8#4118yescomplemented
214C2×C11⋊C8C2414yes—
215C2×C11⋊C8C2414yes—
216C2×#532D1111yescharacteristic, complemented
217C2×#529—111no—
218#3180—1116no—
219C2×#501—111no—
220C2×#496—111no—
221C2×#490—111no—
222C2×#489—111no—
223C2×#466—112no—
224C2×#465—112no—
225C2×#442—112no—
226C2×#440—112no—
227C22×#97—111no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—24no—
231C23×C11—44no—
232C23×C11—44no—
233C23×C11—44no—
234C23×C11AGL(1,ℤ/8)14yes—
235C23×C11C22×D412yes—
236C23×C11C22×D411yescharacteristic
237C22×D11—22no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—42no—
241Q8×C11—48no—
242D4×C11—24no—
243D4×C11—24no—
244D4×C11—48no—
245D4×C11—48no—
246D4×C11—416no—
247D4×C11—44no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—28no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—44no—
258C2×C4×C11—416no—
259C2×C4×C11—44no—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4114yes—
267C2×C4×C11C2511yescharacteristic
268C22⋊D11—48no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275D44—24no—
276D44—42no—
277C4×D11—48no—
278Dic22—24no—
279Dic22—42no—
280C11⋊C8—24no—
281C11⋊C8C2×#4118yescomplemented
282C22×#41—21no—
283C22×SD16—112no—
284C22×D8—112no—
285C23×C8—112no—
286#532—24no—
287#532C2×D1118yescomplemented
288C2×C4⋊Q8C2×D1111yescharacteristic
289C2×#127C2×D1111yescharacteristic
290#529—118no—
291#529—224no—
292C2×#126—221no—
293C2×#125—111no—
294C2×#124—21no—
295C2×#124—111no—
296C2×#123—221no—
297C2×C22⋊Q8—111no—
298C2×#121—21no—
299C2×#121—111no—
300C2×#121C2×D1112yes—
301C2×C4×Q8—111no—
302C2×C4×D4—21no—
303C2×C4×D4—111no—
304C2×C4×D4—221no—
305C2×C4×D4C2×D1112yes—
306C2×#117—221no—
307C22×C42C2×D1111yescharacteristic
308#501—118no—
309#496—118no—
310#490—118no—
311#489—118no—
312#466—1116no—
313#465—1116no—
314#442—1116no—
315#440—1116no—
316C2×#107—112no—
317C2×#106—112no—
318C2×#103—112no—
319C2×#102—112no—
320C2×#102—112no—
321C2×#102—112no—
322C2×#97—111no—
323C2×#97—111no—
324C2×#97—112no—
325C2×#97—118no—
326C22×C11—28no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11—88no—
333C22×C11#53212yes—
334C22×C11C2×AGL(1,ℤ/8)14yes—
335C22×C11C2×AGL(1,ℤ/8)12yes—
336C22×C11#57512yes—
337C22×C11C23×D411yescharacteristic
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—84no—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—44no—
348C4×C11#53212yes—
349C4×C11C22×#4112yes—
350Dic11—42no—
351Dic11—42no—
352Dic11—42no—
353C2×#41—28no—
354C2×#41—48no—
355C22×Q8—21no—
356C22×Q8—111no—
357C22×D4—22no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—111no—
361C22×D4—221no—
362C22×D4C22×D1112yes—
363C23×C4—22no—
364C23×C4—221no—
365C23×C4C22⋊D1111yescharacteristic
366C23×C4C22⋊D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C2×SD16—118no—
369C2×SD16—228no—
370C2×D8—118no—
371C2×D8—228no—
372C22×C8—112no—
373C22×C8—112no—
374C22×C8—118no—
375C22×C8—228no—
376C4⋊Q8—22no—
377C4⋊Q8C22×D1114yes—
378#127—22no—
379#127C22×D1114yes—
380#126—228no—
381#125—114no—
382#125—222no—
383#124—28no—
384#124—114no—
385#124—222no—
386#123—228no—
387C22⋊Q8—114no—
388C22⋊Q8—222no—
389#121—28no—
390#121—24no—
391#121—114no—
392#121—222no—
393#121C22×D1118yes—
394C4×Q8—114no—
395C4×Q8—222no—
396C4×D4—28no—
397C4×D4—24no—
398C4×D4—114no—
399C4×D4—228no—
400C4×D4—222no—
401C4×D4C22×D1118yes—
402#117—228no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4C22×D1112yes—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—221no—
419C2×C42C22⋊D1111yescharacteristic
420C2×C42C22⋊D1111yescharacteristic
421C2×C42C22⋊D1114yes—
422C2×C42C22×D1111yescharacteristic
423C2×C42C22×D1111yescharacteristic
424C2×C42C22×D1114yes—
425#107—118no—
426#106—118no—
427#103—118no—
428#102—118no—
429#102—118no—
430#102—118no—
431#97—118no—
432#97—114no—
433#97—114no—
434C2×C11—24no—
435C2×C11—84no—
436C2×C11#318014yescomplemented
437C2×C11C2×#53211yescharacteristic
438C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
439C2×C11C2×#57511yescharacteristic
440D11—82no—
441C24—22no—
442C24—221no—
443C24C2×C22⋊D1111yescharacteristic
444#41—432no—
445C2×Q8—24no—
446C2×Q8—44no—
447C2×Q8—112no—
448C2×Q8—221no—
449C2×Q8—224no—
450C2×D4—28no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—22no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—48no—
459C2×D4—112no—
460C2×D4—224no—
461C2×D4—224no—
462C2×D4—221no—
463C2×D4—444no—
464C2×D4C23×D1114yes—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—28no—
469C22×C4—42no—
470C22×C4—48no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—224no—
475C22×C4—444no—
476C22×C4C2×C22⋊D1114yes—
477C22×C4C2×C22⋊D1112yes—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1114yes—
484C22×C4C23×D1112yes—
485C22×C4C23×D1111yescharacteristic
486SD16—2216no—
487D8—2216no—
488C2×C8—118no—
489C2×C8—114no—
490C2×C8—114no—
491C2×C8—2216no—
492C2×C8—224no—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—112no—
496C4⋊C4—112no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4C23×D1114yes—
504C22⋊C4—28no—
505C22⋊C4—28no—
506C22⋊C4—224no—
507C22⋊C4—224no—
508C22⋊C4—224no—
509C22⋊C4—224no—
510C22⋊C4—224no—
511C42—224no—
512C42C2×C22⋊D1114yes—
513C42C2×C22⋊D1112yes—
514C42C2×C22⋊D1114yes—
515C42C2×C22⋊D1112yes—
516C42C23×D1112yes—
517C42C23×D1112yes—
518C11C2×#318011yescharacteristic, complemented, Sylow
519C23—22no—
520C23—22no—
521C23—24no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—222no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23#6698514yes—
530C23C22×C22⋊D1112yes—
531C23C22×C22⋊D1111yescharacteristic
532Q8—48no—
533Q8—224no—
534Q8—442no—
535D4—24no—
536D4—24no—
537D4—48no—
538D4—48no—
539D4—416no—
540D4—44no—
541D4—224no—
542D4—448no—
543D4—442no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—28no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—44no—
554C2×C4—416no—
555C2×C4—44no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—448no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4#41×D1114yes—
564C2×C4C22×C22⋊D1112yes—
565C2×C4C22×C22⋊D1112yes—
566C2×C4C22×C22⋊D1112yes—
567C2×C4C22×C22⋊D1112yes—
568C2×C4C22×C22⋊D1112yes—
569C2×C4C22×C22⋊D1111yescharacteristic
570C2×C4C24×D1111yescharacteristic
571C8—118no—
572C8—224no—
573C22—28no—
574C22—22no—
575C22—22no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—88no—
580C22—442no—
581C22—442no—
582C22—442no—
583C22—884no—
584C22C2×#6698514yes—
585C22C2×#6698512yes—
586C22#1062335312yes—
587C22#1062336312yes—
588C22C23×C22⋊D1111yescharacteristic
589C4—22no—
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—44no—
595C4—442no—
596C4—442no—
597C4—442no—
598C4#1062336312yes—
599C4C2×#41×D1112yes—
600C2—24no—
601C2—84no—
602C2—882no—
603C2#1307930814yesdirect product factor
604C2C2×#1062336311yescharacteristic
605C2C22×#6698511yescharacteristic
606C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#532C2
socleC23×C11C22×D4
hypercenterC2×#532D11
hypocenterC11C2×#3180
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. #13079308C2direct (N × H)
3. C2×#10622693C2semidirect
4. C2×#10622687C2semidirect
5. C2×#10622684C2semidirect
6. C2×#10622702C2semidirect
7. C2×#10622651C2semidirect
8. C2×#10622654C2semidirect
9. C2×#10622627C2semidirect
10. C2×#10622631C2semidirect
11. C22×#66867C2semidirect
12. C2×C11×#532C2semidirect
15. C11×#532C22semidirect
32. #10623010C22semidirect
41. #10622702C22semidirect
42. #10622693C22semidirect
43. #10622687C22semidirect
44. #10622684C22semidirect
45. #10622654C22semidirect
46. #10622651C22semidirect
47. #10622631C22semidirect
48. #10622627C22semidirect
56. C2×#66867C22semidirect
213. C2×C11⋊C8#41semidirect
216. C2×#532D11semidirect
281. C11⋊C8C2×#41semidirect
287. #532C2×D11semidirect
436. C2×C11#3180semidirect
518. C11C2×#3180semidirect
603. C2#13079308direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130793082
C2×#106226932
C2×#106226872
C2×#106226842
C2×#106227022
C2×#106226512
C2×#106226542
C2×#106226272
C2×#106226312
C22×#668672
C2×C11×#5322
C2×#318011