Finite Group Databasebeta

← C2×#13079314 #15623684

Subgroups — C2×#13079314 #15623684

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
2C2×#10623010C211yesmaximal, characteristic, complemented
3#13079314C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622325C211yesmaximal, characteristic, complemented
6C2×#10622326C211yesmaximal, characteristic, complemented
7C2×#10622327C211yesmaximal, characteristic, complemented
8C2×#10622728C212yesmaximal, complemented
9C2×#10622727C212yesmaximal, complemented
10C2×#10622324C212yesmaximal, complemented
11C2×#10622323C212yesmaximal, complemented
12C22×C11×#97C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C23×C8×C11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C2×#66983—21no—
17C2×#66983C2211yescharacteristic
18C2×#66983C2212yes—
19C2×#66982—21no—
20C2×C4×C22⋊D11—21no—
21C2×#66977C2211yescharacteristic
22C22×D88C2212yes—
23C22×#4314C2212yes—
24#10623010—24no—
25#10623010C2218yescomplemented
26C2×#66929—21no—
27#10623008—24no—
28#10623008C2218yescomplemented
29C2×#66928—21no—
30C2×#66928C2211yescharacteristic
31C2×#66927C2211yescharacteristic
32C2×C4×D44—21no—
33C2×C4×D44C2211yescharacteristic
34C2×C4×D44C2212yes—
35C2×#66925—21no—
36C2×#66923C2211yescharacteristic
37C2×#66922C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C11×#97C2212yes—
41C2×C11×#97C2211yescharacteristic
42C2×C11×#97C2218yescomplemented
43#10622728C22116yescomplemented
44#10622727C22116yescomplemented
45C2×#66885C2212yes—
46C2×#66885C2212yes—
47C2×#66885C2212yes—
48C2×#66882C2212yes—
49C2×#66881C2212yes—
50C2×#66880C2212yes—
51#10622327C2218yescomplemented
52#10622326C2218yescomplemented
53#10622325C2218yescomplemented
54#10622324C22116yescomplemented
55#10622323C22116yescomplemented
56#10622315C2218yescomplemented
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11—22no—
62C2×#4339—28no—
63C2×#4339—48no—
64C22×D44—21no—
65C22×D44—21no—
66C22×D44C2312yes—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×C4×D11—22no—
70C22×Dic22—21no—
71C22×Dic22C2311yescharacteristic
72C22×C8×C11—28no—
73C22×C8×C11C2312yes—
74C22×C8×C11C2318yes—
75C22×C8×C11C2312yes—
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11D414yes—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2314yes—
82C2×C22⋊Dic11—21no—
83#66983—24no—
84#66983—28no—
85#66983—22no—
86#66983C2318yes—
87#66983C2314yes—
88#66982—28no—
89C4×C22⋊D11—28no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100#66977—22no—
101#66977C2314yes—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×D88—28no—
108C2×D88C2318yes—
109C2×#4314—28no—
110C2×#4314C2318yes—
111#66929—28no—
112#66928—28no—
113#66928—22no—
114#66928C2314yes—
115#66927—22no—
116#66927C2314yes—
117C4×D44—28no—
118C4×D44—24no—
119C4×D44—22no—
120C4×D44C2318yes—
121C4×D44C2314yes—
122#66925—28no—
123#66923—22no—
124#66923C2314yes—
125#66922—22no—
126#66922C2314yes—
127C4×Dic22—22no—
128C4×Dic22C2314yes—
129C11×#97C2314yes—
130C11×#97C2318yes—
131C11×#97C2314yes—
132#66885C2318yes—
133#66885C2318yes—
134#66885C2318yes—
135#66882C2318yes—
136#66881C2318yes—
137#66880C2318yes—
138C2×#3180—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C23×D11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—42no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—24no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—44no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163#4339—432no—
164C2×D44—22no—
165C2×D44—24no—
166C2×D44—21no—
167C2×D44—24no—
168C2×D44—24no—
169C2×D44—24no—
170C2×D44—24no—
171C2×D44—44no—
172C2×D44—44no—
173C2×D44C2414yes—
174C2×D44C2412yes—
175C2×C4×D11—24no—
176C2×C4×D11—28no—
177C2×C4×D11—44no—
178C2×C4×D11—48no—
179C2×Dic22—21no—
180C2×Dic22—24no—
181C2×Dic22—24no—
182C2×Dic22—44no—
183C2×Dic22C2412yes—
184C2×C8×C11—216no—
185C2×C8×C11—24no—
186C2×C8×C11#4118yescomplemented
187C2×C8×C11C2414yes—
188C2×C8×C11C2414yes—
189C42×C11C2×D412yes—
190C42×C11C2×D412yes—
191C42×C11C2×D414yes—
192C42×C11C2×D414yes—
193C42×C11C2412yes—
194C42×C11C2412yes—
195C22⋊Dic11—24no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202C4⋊Dic11—21no—
203C4⋊Dic11—22no—
204C4⋊Dic11—24no—
205C4⋊Dic11—21no—
206C4⋊Dic11C2414yes—
207C4⋊Dic11C2412yes—
208C4⋊Dic11C2412yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213C4×Dic11—24no—
214D88—216no—
215#4314—216no—
216C2×#532—111no—
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×#97D1111yescharacteristic, complemented
228C23×C11—22no—
229C23×C11—22no—
230C23×C11AGL(1,ℤ/8)14yes—
231C23×C11C22×D412yes—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—24no—
235C22×D11—44no—
236C22×D11—42no—
237C22×D11—44no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—44no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—28no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—44no—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4114yes—
257C2×C4×C11C2511yescharacteristic
258C22⋊D11—416no—
259C22⋊D11—48no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—42no—
265C2×Dic11—44no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268D44—24no—
269D44—24no—
270D44—24no—
271D44—48no—
272D44—48no—
273D44—44no—
274D44—42no—
275C4×D11—48no—
276C4×D11—416no—
277Dic22—24no—
278Dic22—48no—
279Dic22—42no—
280C8×C11—24no—
281C8×C11C2×#4118yescomplemented
282C22×#41—221no—
283C22×SD16—112no—
284C22×D8—112no—
285C23×C8C2×D1112yes—
286#532—118no—
287#532—224no—
288C2×C4⋊Q8—111no—
289C2×#127—111no—
290#529—118no—
291#529—224no—
292C2×#126—221no—
293C2×#125—111no—
294C2×#124—111no—
295C2×#124—221no—
296C2×#123—221no—
297C2×C22⋊Q8—111no—
298C2×#121—111no—
299C2×#121—112no—
300C2×#121—221no—
301C2×C4×Q8—111no—
302C2×C4×D4—111no—
303C2×C4×D4—112no—
304C2×C4×D4—221no—
305C2×C4×D4—221no—
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×#97C2×D1111yescharacteristic
323C2×#97C2×D1111yescharacteristic
324C2×#97C2×D1112yes—
325C2×#97C2×D1118yescomplemented
326C22×C11—28no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11#53212yes—
330C22×C11C2×AGL(1,ℤ/8)14yes—
331C22×C11C2×AGL(1,ℤ/8)12yes—
332C22×C11#57512yes—
333C22×C11C23×D411yescharacteristic
334C2×D11—42no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—44no—
340C2×D11—88no—
341C2×D11—84no—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11#53212yes—
348C4×C11C22×#4112yes—
349Dic11—42no—
350Dic11—44no—
351Dic11—42no—
352Dic11—42no—
353C2×#41—228no—
354C2×#41—448no—
355C22×Q8—111no—
356C22×Q8—221no—
357C22×D4—111no—
358C22×D4—112no—
359C22×D4—221no—
360C22×D4—222no—
361C22×D4—221no—
362C22×D4—221no—
363C23×C4—221no—
364C23×C4—222no—
365C23×C4D4411yescharacteristic
366C23×C4D4411yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C2×SD16—118no—
369C2×SD16—228no—
370C2×D8—118no—
371C2×D8—228no—
372C22×C8—28no—
373C22×C8C22×D1112yes—
374C22×C8C22×D1118yes—
375C22×C8C22×D1112yes—
376C4⋊Q8—114no—
377C4⋊Q8—222no—
378#127—114no—
379#127—222no—
380#126—228no—
381#125—114no—
382#125—222no—
383#124—114no—
384#124—222no—
385#124—228no—
386#123—228no—
387C22⋊Q8—114no—
388C22⋊Q8—222no—
389#121—114no—
390#121—118no—
391#121—222no—
392#121—224no—
393#121—228no—
394C4×Q8—114no—
395C4×Q8—222no—
396C4×D4—114no—
397C4×D4—118no—
398C4×D4—228no—
399C4×D4—222no—
400C4×D4—224no—
401C4×D4—228no—
402#117—228no—
403C2×C4⋊C4—112no—
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⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—221no—
418C2×C42—221no—
419C2×C42D4411yescharacteristic
420C2×C42D4411yescharacteristic
421C2×C42D4414yes—
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#97C22×D1118yes—
432#97C22×D1114yes—
433#97C22×D1114yes—
434C2×C11—24no—
435C2×C11#318014yescomplemented
436C2×C11C2×#53211yescharacteristic
437C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
438C2×C11C2×#57511yescharacteristic
439D11—84no—
440D11—82no—
441C24—221no—
442C24—222no—
443C24C2×D4411yescharacteristic
444#41—4432no—
445C2×Q8—112no—
446C2×Q8—221no—
447C2×Q8—224no—
448C2×Q8—224no—
449C2×Q8—444no—
450C2×D4—112no—
451C2×D4—114no—
452C2×D4—224no—
453C2×D4—228no—
454C2×D4—221no—
455C2×D4—224no—
456C2×D4—222no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—224no—
460C2×D4—224no—
461C2×D4—444no—
462C2×D4—444no—
463C2×D4—448no—
464C2×D4—444no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—42no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—222no—
472C22×C4—224no—
473C22×C4—228no—
474C22×C4—448no—
475C22×C4—444no—
476C22×C4C2×D4414yes—
477C22×C4C2×D4412yes—
478C22×C4C2×D4411yescharacteristic
479C22×C4C2×D4411yescharacteristic
480C22×C4C2×D4411yescharacteristic
481C22×C4C2×D4411yescharacteristic
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×D4414yes—
484C22×C4C23×D1112yes—
485C22×C4C23×D1111yescharacteristic
486SD16—2216no—
487D8—2216no—
488C2×C8—24no—
489C2×C8—216no—
490C2×C8#433918yescomplemented
491C2×C8C23×D1114yes—
492C2×C8C23×D1114yes—
493C4⋊C4—112no—
494C4⋊C4—112no—
495C4⋊C4—114no—
496C4⋊C4—222no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C22⋊C4—224no—
505C22⋊C4—224no—
506C22⋊C4—224no—
507C22⋊C4—228no—
508C22⋊C4—224no—
509C22⋊C4—228no—
510C22⋊C4—224no—
511C42—224no—
512C42C2×D4414yes—
513C42C2×D4412yes—
514C42C2×D4414yes—
515C42C2×D4412yes—
516C42C23×D1112yes—
517C42C23×D1112yes—
518C11C2×#318011yescharacteristic, complemented, Sylow
519C23—22no—
520C23—22no—
521C23—222no—
522C23—224no—
523C23—442no—
524C23—444no—
525C23—444no—
526C23—442no—
527C23—442no—
528C23—444no—
529C23#6696114yes—
530C23C22×D4412yes—
531C23C22×D4411yescharacteristic
532Q8—224no—
533Q8—448no—
534Q8—442no—
535D4—224no—
536D4—224no—
537D4—224no—
538D4—448no—
539D4—448no—
540D4—4416no—
541D4—448no—
542D4—442no—
543D4—444no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—28no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—44no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—224no—
557C2×C4—4416no—
558C2×C4—448no—
559C2×C4—442no—
560C2×C4—444no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4C22×D4412yes—
564C2×C4C22×D4412yes—
565C2×C4C22×D4412yes—
566C2×C4C22×D4412yes—
567C2×C4C22×D4412yes—
568C2×C4C22×D4411yescharacteristic
569C2×C4C2×#433914yes—
570C2×C4C24×D1111yescharacteristic
571C8—24no—
572C8C2×#433918yescomplemented
573C22—28no—
574C22—22no—
575C22—22no—
576C22—442no—
577C22—444no—
578C22—444no—
579C22—442no—
580C22—442no—
581C22—444no—
582C22—888no—
583C22—884no—
584C22#1062300812yes—
585C22C2×#6696114yes—
586C22C2×#6696112yes—
587C22#1062327912yes—
588C22C23×D4411yescharacteristic
589C4—22no—
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—442no—
595C4—444no—
596C4—442no—
597C4—442no—
598C4#1062300812yes—
599C4C22×#433912yes—
600C2—24no—
601C2—884no—
602C2—882no—
603C2#1307931414yesdirect product factor
604C2C2×#1062300811yescharacteristic
605C2C22×#6696111yescharacteristic
606C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#97C2
socleC23×C11C22×D4
hypercenterC22×#97D11
hypocenterC11C2×#3180
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. C2×#10623010C2semidirect
3. #13079314C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622325C2semidirect
6. C2×#10622326C2semidirect
7. C2×#10622327C2semidirect
8. C2×#10622728C2semidirect
9. C2×#10622727C2semidirect
10. C2×#10622324C2semidirect
11. C2×#10622323C2semidirect
12. C22×C11×#97C2semidirect
25. #10623010C22semidirect
28. #10623008C22semidirect
42. C2×C11×#97C22semidirect
43. #10622728C22semidirect
44. #10622727C22semidirect
51. #10622327C22semidirect
52. #10622326C22semidirect
53. #10622325C22semidirect
54. #10622324C22semidirect
55. #10622323C22semidirect
56. #10622315C22semidirect
186. C2×C8×C11#41semidirect
227. C22×#97D11semidirect
281. C8×C11C2×#41semidirect
325. C2×#97C2×D11semidirect
435. C2×C11#3180semidirect
490. C2×C8#4339semidirect
518. C11C2×#3180semidirect
572. C8C2×#4339semidirect
603. C2#13079314direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106230102
#130793142
C2×#106223152
C2×#106223252
C2×#106223262
C2×#106223272
C2×#106227282
C2×#106227272
C2×#106223242
C2×#106223232
C22×C11×#972
C2×#318011