Finite Group Databasebeta

← C2×#13079315 #15623685

Subgroups — C2×#13079315 #15623685

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×#10623008C211yesmaximal, characteristic, complemented
2#13079315C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622671C211yesmaximal, characteristic, complemented
5C2×#10622680C211yesmaximal, characteristic, complemented
6C2×#10622668C211yesmaximal, characteristic, complemented
7C2×#10622651C212yesmaximal, complemented
8C2×#10622661C212yesmaximal, complemented
9C2×#10622627C212yesmaximal, complemented
10C2×#10622639C212yesmaximal, complemented
11C22×#66867C211yesmaximal, characteristic, complemented
12C2×C11×#529C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C11×#529—24no—
15C11×#529C2218yescomplemented
16C2×C11×#126—21no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117—21no—
26C22×C42×C11C2211yescharacteristic
27C22×#4325C2212yes—
28C22×#4323C2212yes—
29C2×#66983—21no—
30C2×#66983C2212yes—
31C23×C11⋊C8C2212yes—
32#10623008—24no—
33#10623008C2218yescomplemented
34C2×#66928—21no—
35C2×#66927C2211yescharacteristic
36C2×C4×D44—21no—
37C2×C4×D44C2212yes—
38C2×#66922C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66896C2212yes—
41#10622680C2218yescomplemented
42#10622678C2218yescomplemented
43#10622671C2218yescomplemented
44#10622668C2218yescomplemented
45#10622661C22116yescomplemented
46#10622651C22116yescomplemented
47#10622639C22116yescomplemented
48#10622627C22116yescomplemented
49C2×#66873C2212yes—
50C2×#66873C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53C2×#66867C2211yescharacteristic
54C2×#66867C2212yes—
55C2×#66867C2211yescharacteristic
56C2×#66867C2218yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—22no—
65C2×#4339—28no—
66C2×#4339—48no—
67C22×D44—21no—
68C22×D44—21no—
69C22×D44C2312yes—
70C22×C4×D11—22no—
71C22×Dic22—21no—
72C11×#126—28no—
73C11×#125—22no—
74C11×#125C2314yes—
75C11×#124—22no—
76C11×#124C2314yes—
77C11×#123—28no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8C2314yes—
80C11×#121—22no—
81C11×#121C2314yes—
82C4×Q8×C11—22no—
83C4×Q8×C11C2314yes—
84C4×D4×C11—28no—
85C4×D4×C11—22no—
86C4×D4×C11C2314yes—
87C11×#117—28no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C42×C11—21no—
100C2×C42×C11D411yescharacteristic
101C2×C42×C11D411yescharacteristic
102C2×C42×C11D414yes—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2314yes—
106C2×#4325—28no—
107C2×#4325C2318yes—
108C2×#4323—28no—
109C2×#4323C2318yes—
110#66983—24no—
111#66983—28no—
112#66983C2318yes—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11C2312yes—
117C22×C11⋊C8—28no—
118C22×C11⋊C8C2312yes—
119C22×C11⋊C8C2318yes—
120C22×C11⋊C8C2312yes—
121#66928—28no—
122#66927—22no—
123#66927C2314yes—
124C4×D44—28no—
125C4×D44—24no—
126C4×D44C2318yes—
127#66922—22no—
128#66922C2314yes—
129#66899C2318yes—
130#66896C2318yes—
131#66873C2318yes—
132#66873C2318yes—
133#66872C2318yes—
134#66871C2318yes—
135#66867C2318yes—
136#66867C2314yes—
137#66867C2314yes—
138C2×#3180—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C23×D11—22no—
142C2×Q8×C11—21no—
143C2×Q8×C11—24no—
144C2×Q8×C11C2412yes—
145C2×D4×C11—24no—
146C2×D4×C11—21no—
147C2×D4×C11—24no—
148C2×D4×C11—44no—
149C2×D4×C11C2412yes—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—24no—
156C22×C4×C11—42no—
157C22×C4×C11—44no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D414yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—28no—
169C2×C22⋊D11—48no—
170C22×Dic11—22no—
171#4339—432no—
172C2×D44—22no—
173C2×D44—24no—
174C2×D44—24no—
175C2×D44—24no—
176C2×D44—24no—
177C2×D44—44no—
178C2×D44—44no—
179C2×D44C2414yes—
180C2×C4×D11—28no—
181C2×C4×D11—48no—
182C2×Dic22—24no—
183C2×Dic22—44no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C2412yes—
191C11×C4⋊C4C2412yes—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C42×C11—24no—
198C42×C11C2×D412yes—
199C42×C11C2×D412yes—
200C42×C11C2×D414yes—
201C42×C11C2×D414yes—
202C42×C11C2412yes—
203C42×C11C2412yes—
204#4325—216no—
205#4323—216no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—28no—
208C4⋊Dic11—22no—
209C4⋊Dic11—24no—
210C4⋊Dic11C2414yes—
211C2×C11⋊C8—216no—
212C2×C11⋊C8—24no—
213C2×C11⋊C8#4118yescomplemented
214C2×C11⋊C8C2414yes—
215C2×C11⋊C8C2414yes—
216C2×#532—111no—
217C2×#529D1111yescharacteristic, complemented
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—22no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11AGL(1,ℤ/8)14yes—
235C23×C11C22×D412yes—
236C23×C11C22×D411yescharacteristic
237C22×D11—24no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11—44no—
241Q8×C11—24no—
242Q8×C11—42no—
243D4×C11—24no—
244D4×C11—48no—
245D4×C11—42no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—28no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—44no—
258C2×C4×C11—48no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D412yes—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4114yes—
269C2×C4×C11C2511yescharacteristic
270C22⋊D11—416no—
271C2×Dic11—24no—
272C2×Dic11—44no—
273D44—24no—
274D44—24no—
275D44—48no—
276D44—48no—
277D44—44no—
278C4×D11—416no—
279Dic22—48no—
280C11⋊C8—24no—
281C11⋊C8C2×#4118yescomplemented
282C22×#41—221no—
283C22×SD16—112no—
284C22×D8—112no—
285C23×C8—112no—
286#532—118no—
287#532—224no—
288C2×C4⋊Q8—111no—
289C2×#127—111no—
290#529—24no—
291#529C2×D1118yescomplemented
292C2×#126—21no—
293C2×#125C2×D1111yescharacteristic
294C2×#124—221no—
295C2×#124C2×D1111yescharacteristic
296C2×#123—21no—
297C2×C22⋊Q8C2×D1111yescharacteristic
298C2×#121—112no—
299C2×#121—221no—
300C2×#121C2×D1111yescharacteristic
301C2×C4×Q8C2×D1111yescharacteristic
302C2×C4×D4—21no—
303C2×C4×D4—112no—
304C2×C4×D4—221no—
305C2×C4×D4C2×D1111yescharacteristic
306C2×#117—21no—
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—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—84no—
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—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—88no—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11#53212yes—
351C4×C11C22×#4112yes—
352Dic11—44no—
353C2×#41—228no—
354C2×#41—448no—
355C22×Q8—221no—
356C22×Q8C22×D1111yescharacteristic
357C22×D4—21no—
358C22×D4—112no—
359C22×D4—222no—
360C22×D4—221no—
361C22×D4—221no—
362C22×D4C22×D1111yescharacteristic
363C23×C4—21no—
364C23×C4—222no—
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—114no—
377C4⋊Q8—222no—
378#127—114no—
379#127—222no—
380#126—28no—
381#125—22no—
382#125C22×D1114yes—
383#124—22no—
384#124—228no—
385#124C22×D1114yes—
386#123—28no—
387C22⋊Q8—22no—
388C22⋊Q8C22×D1114yes—
389#121—22no—
390#121—118no—
391#121—224no—
392#121—228no—
393#121C22×D1114yes—
394C4×Q8—22no—
395C4×Q8C22×D1114yes—
396C4×D4—28no—
397C4×D4—22no—
398C4×D4—118no—
399C4×D4—224no—
400C4×D4—228no—
401C4×D4C22×D1114yes—
402#117—28no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—222no—
418C2×C42—21no—
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—82no—
436C2×C11#318014yescomplemented
437C2×C11C2×#53211yescharacteristic
438C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
439C2×C11C2×#57511yescharacteristic
440D11—84no—
441C24—21no—
442C24—222no—
443C24C2×C22⋊D1111yescharacteristic
444#41—4432no—
445C2×Q8—21no—
446C2×Q8—24no—
447C2×Q8—224no—
448C2×Q8—444no—
449C2×Q8C23×D1112yes—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—21no—
453C2×D4—44no—
454C2×D4—114no—
455C2×D4—228no—
456C2×D4—224no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—222no—
460C2×D4—224no—
461C2×D4—444no—
462C2×D4—444no—
463C2×D4—448no—
464C2×D4C23×D1112yes—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—42no—
472C22×C4—44no—
473C22×C4—222no—
474C22×C4—228no—
475C22×C4—448no—
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—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—114no—
500C4⋊C4—222no—
501C4⋊C4—224no—
502C4⋊C4C23×D1112yes—
503C4⋊C4C23×D1112yes—
504C22⋊C4—24no—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C22⋊C4—24no—
508C22⋊C4—24no—
509C22⋊C4—228no—
510C22⋊C4—228no—
511C42—24no—
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—22no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—224no—
526C23—444no—
527C23—444no—
528C23—444no—
529C23#6700214yes—
530C23C22×C22⋊D1112yes—
531C23C22×C22⋊D1111yescharacteristic
532Q8—24no—
533Q8—42no—
534Q8—448no—
535D4—24no—
536D4—48no—
537D4—42no—
538D4—224no—
539D4—224no—
540D4—448no—
541D4—448no—
542D4—4416no—
543D4—444no—
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—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—44no—
556C2×C4—48no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—224no—
561C2×C4—4416no—
562C2×C4—444no—
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—42no—
577C22—42no—
578C22—42no—
579C22—84no—
580C22—444no—
581C22—444no—
582C22—444no—
583C22—888no—
584C22C2×#6700214yes—
585C22C2×#6700212yes—
586C22#1062335312yes—
587C22#1062336312yes—
588C22C23×C22⋊D1111yescharacteristic
589C4—22no—
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—444no—
598C4#1062336312yes—
599C4C2×#41×D1112yes—
600C2—24no—
601C2—82no—
602C2—884no—
603C2#1307931514yesdirect product factor
604C2C2×#1062336311yescharacteristic
605C2C22×#6700211yescharacteristic
606C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
hypercenterC2×#529D11
hypocenterC11C2×#3180
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. #13079315C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622671C2semidirect
5. C2×#10622680C2semidirect
6. C2×#10622668C2semidirect
7. C2×#10622651C2semidirect
8. C2×#10622661C2semidirect
9. C2×#10622627C2semidirect
10. C2×#10622639C2semidirect
11. C22×#66867C2semidirect
12. C2×C11×#529C2semidirect
15. C11×#529C22semidirect
33. #10623008C22semidirect
41. #10622680C22semidirect
42. #10622678C22semidirect
43. #10622671C22semidirect
44. #10622668C22semidirect
45. #10622661C22semidirect
46. #10622651C22semidirect
47. #10622639C22semidirect
48. #10622627C22semidirect
56. C2×#66867C22semidirect
213. C2×C11⋊C8#41semidirect
217. C2×#529D11semidirect
281. C11⋊C8C2×#41semidirect
291. #529C2×D11semidirect
436. C2×C11#3180semidirect
518. C11C2×#3180semidirect
603. C2#13079315direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
#130793152
C2×#106226782
C2×#106226712
C2×#106226802
C2×#106226682
C2×#106226512
C2×#106226612
C2×#106226272
C2×#106226392
C22×#668672
C2×C11×#5292
C2×#318011