Finite Group Databasebeta

← C2×#13079214 #15623541

Subgroups — C2×#13079214 #15623541

Order 2816.

2266 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×#10623256C211yesmaximal, characteristic, complemented
2C2×#10623211C211yesmaximal, characteristic, complemented
3#13079214C2116yesmaximal, direct product factor
4C2×#10622693C211yesmaximal, characteristic, complemented
5C2×#10622671C211yesmaximal, characteristic, complemented
6C2×#10622326C211yesmaximal, characteristic, complemented
7C2×#10622395C212yesmaximal, complemented
8C2×#10622425C212yesmaximal, complemented
9C2×#10622401C212yesmaximal, complemented
10C2×#10622369C212yesmaximal, complemented
11C2×#10622320C211yesmaximal, characteristic, complemented
12C2×C11×#489C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×#67000—21no—
17C2×#66999C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2212yes—
20C2×#66991C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C22×#4323C2212yes—
23C22×#4313C2212yes—
24#10623256—24no—
25#10623256C2218yescomplemented
26#10623211—24no—
27#10623211C2218yescomplemented
28C2×#66948—21no—
29C2×#66948C2212yes—
30C2×#66946—21no—
31C2×#66946C2212yes—
32C2×#66936—21no—
33C2×(C22⋊D11)⋊C4—21no—
34C2×#66932—21no—
35C2×#66930—21no—
36C2×#66927C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×#66923C2211yescharacteristic
39C11×#489C2218yescomplemented
40C2×C11×#103C2212yes—
41C2×C11×#102C2212yes—
42C2×C11×#97C2211yescharacteristic
43C2×#66885C2212yes—
44C2×#66885C2212yes—
45C2×C8×Dic11C2212yes—
46#10622693C2218yescomplemented
47#10622671C2218yescomplemented
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×#66867C2211yescharacteristic
51#10622425C22116yescomplemented
52#10622401C22116yescomplemented
53#10622395C22116yescomplemented
54#10622369C22116yescomplemented
55#10622326C2218yescomplemented
56#10622320C2218yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C2×#4343—28no—
63C2×#4343—48no—
64C22×D44—22no—
65C22×D44—21no—
66C22×D44—21no—
67C22×D44C2312yes—
68C22×C4×D11—22no—
69C22×C4×D11D411yescharacteristic
70C22×C4×D11D411yescharacteristic
71C22×C4×D11C2311yescharacteristic
72C22×C8×C11C2312yes—
73C11×C4⋊Q8—22no—
74C11×C4⋊Q8C2314yes—
75C11×#124—22no—
76C11×#124C2314yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84#67000—28no—
85#66999—22no—
86#66999C2314yes—
87Q8×Dic11—22no—
88Q8×Dic11C2314yes—
89C2×#4325—28no—
90C2×#4325C2318yes—
91#66991—22no—
92#66991C2314yes—
93D4×Dic11—22no—
94D4×Dic11C2314yes—
95C2×#4323—28no—
96C2×#4323C2318yes—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11D411yescharacteristic
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2312yes—
111C2×#4313—28no—
112C2×#4313C2318yes—
113#66948—24no—
114#66948—28no—
115#66948C2318yes—
116#66946—24no—
117#66946—28no—
118#66946C2318yes—
119#66936—28no—
120(C22⋊D11)⋊C4—28no—
121#66932—28no—
122#66930—28no—
123#66927—22no—
124#66927C2314yes—
125C42×D11D414yes—
126C42×D11C2314yes—
127#66923—22no—
128#66923C2314yes—
129C11×#103C2318yes—
130C11×#102C2318yes—
131C11×#97C2314yes—
132#66885C2318yes—
133#66885C2318yes—
134C8×Dic11C2318yes—
135#66872C2318yes—
136#66871C2318yes—
137#66867C2314yes—
138C2×#3171—111nomaximal, Sylow
139C24×C11—21no—
140C23×D11—22no—
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—24no—
144C2×Q8×C11—24no—
145C2×Q8×C11—44no—
146C2×Q8×C11C2412yes—
147C2×D4×C11—21no—
148C2×D4×C11—24no—
149C2×D4×C11C2412yes—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—24no—
156C2×C22⋊D11—44no—
157C22×Dic11—24no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—44no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164#4343—432no—
165C2×D44—28no—
166C2×D44—22no—
167C2×D44—24no—
168C2×D44—24no—
169C2×D44—24no—
170C2×D44—24no—
171C2×D44—44no—
172C2×D44—44no—
173C2×D44—48no—
174C2×D44C2414yes—
175C2×C4×D11—24no—
176C2×C4×D11—28no—
177C2×C4×D11—24no—
178C2×C4×D11—42no—
179C2×C4×D11—48no—
180C2×C4×D11C2×D412yes—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2×D414yes—
183C2×C4×D11C2412yes—
184C2×C8×C11—24no—
185C2×C8×C11C2414yes—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4C2414yes—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—24no—
191C42×C11C2×D412yes—
192C42×C11C2412yes—
193C22⋊Dic11—24no—
194C22⋊Dic11—24no—
195#4325—216no—
196#4323—216no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—24no—
200C4⋊Dic11—24no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11C2412yes—
204C4⋊Dic11C2412yes—
205Dic11⋊C4—24no—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208C4×Dic11—24no—
209C4×Dic11C2×D412yes—
210C4×Dic11C2×D414yes—
211C4×Dic11C2×D414yes—
212C4×Dic11C2412yes—
213C2×C11⋊C8#4118yescomplemented
214C2×C11⋊C8C2414yes—
215#4313—216no—
216C2×#532—111no—
217C2×#529—111no—
218#3171—1116no—
219C2×#501—111no—
220C2×#496—111no—
221C2×#490—111no—
222C2×#489D1111yescharacteristic, complemented
223C2×#469—112no—
224C2×#468—112no—
225C2×C4×SD16—112no—
226C2×C4×D8—112no—
227C2×C4×M16—111no—
228C23×C11—22no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—24no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11C22×D412yes—
241Q8×C11—24no—
242Q8×C11—48no—
243Q8×C11—42no—
244D4×C11—24no—
245D4×C11—42no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—42no—
251C2×C4×C11—44no—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4114yes—
256C2×C4×C11C2511yescharacteristic
257C22⋊D11—48no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—48no—
265C2×Dic11AGL(1,ℤ/8)14yes—
266C2×Dic11C22×D412yes—
267C2×Dic11C22×D412yes—
268C2×Dic11C22×D412yes—
269D44—24no—
270D44—24no—
271D44—48no—
272D44—48no—
273D44—416no—
274D44—44no—
275C4×D11—24no—
276C4×D11—24no—
277C4×D11—28no—
278C4×D11—44no—
279C4×D11—416no—
280C8×C11—24no—
281C11⋊C8C2×#4118yescomplemented
282C22×#41—221no—
283C22×SD16—112no—
284C22×D8—112no—
285C22×M16—112no—
286#532—118no—
287#532—224no—
288C2×C4⋊Q8C2×D1111yescharacteristic
289C2×#127—111no—
290#529—118no—
291#529—224no—
292C2×#126—221no—
293C2×#125—111no—
294C2×#124—221no—
295C2×#124C2×D1111yescharacteristic
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×C42—111no—
308#501—118no—
309#496—118no—
310#490—118no—
311#489C2×D1118yescomplemented
312#469—1116no—
313#468—1116no—
314C4×SD16—1116no—
315C4×D8—1116no—
316C2×#107—112no—
317C2×#106—112no—
318C2×#103C2×D1112yes—
319C2×#102—112no—
320C2×#102—112no—
321C2×#102C2×D1112yes—
322C4×M16—118no—
323C2×#97—111no—
324C2×#97C2×D1111yescharacteristic
325C2×C4×C8—112no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—84no—
330C22×C11#53212yes—
331C22×C11C2×AGL(1,ℤ/8)12yes—
332C22×C11#57512yes—
333C22×C11C23×D411yescharacteristic
334C2×D11—22no—
335C2×D11—22no—
336C2×D11—22no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—88no—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—42no—
345C4×C11—44no—
346C4×C11#53212yes—
347C4×C11C22×#4112yes—
348Dic11—22no—
349Dic11—22no—
350Dic11—42no—
351Dic11—42no—
352Dic11C2×AGL(1,ℤ/8)14yes—
353C2×#41—228no—
354C2×#41—448no—
355C22×Q8—21no—
356C22×Q8C22×D1111yescharacteristic
357C22×D4—112no—
358C22×D4—222no—
359C22×D4—221no—
360C22×D4—221no—
361C22×D4—221no—
362C22×D4C22×D1111yescharacteristic
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—222no—
367C23×C4—221no—
368C2×SD16—118no—
369C2×SD16—228no—
370C2×D8—118no—
371C2×D8—228no—
372C2×M16—118no—
373C2×M16—228no—
374C22×C8—112no—
375C22×C8C22×D1112yes—
376C4⋊Q8—22no—
377C4⋊Q8C22×D1114yes—
378#127—114no—
379#127—222no—
380#126—228no—
381#125—114no—
382#125—222no—
383#124—22no—
384#124—228no—
385#124C22×D1114yes—
386#123—228no—
387C22⋊Q8—114no—
388C22⋊Q8—222no—
389#121—114no—
390#121—118no—
391#121—224no—
392#121—228no—
393#121—222no—
394C4×Q8—114no—
395C4×Q8—222no—
396C4×D4—114no—
397C4×D4—118no—
398C4×D4—224no—
399C4×D4—228no—
400C4×D4—222no—
401C4×D4—228no—
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—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—114no—
422C2×C42—114no—
423C2×C42—221no—
424C2×C42C22×D1111yescharacteristic
425#107—118no—
426#106—118no—
427#103C22×D1118yes—
428#102—118no—
429#102—118no—
430#102C22×D1118yes—
431#97—114no—
432#97C22×D1114yes—
433C4×C8—118no—
434C2×C11—82no—
435C2×C11#317114yescomplemented
436C2×C11C2×#53211yescharacteristic
437C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
438C2×C11C2×#57511yescharacteristic
439D11—42no—
440D11—84no—
441C24—21no—
442C24—111no—
443C24—222no—
444#41—4432no—
445C2×Q8—21no—
446C2×Q8—24no—
447C2×Q8—24no—
448C2×Q8—44no—
449C2×Q8C23×D1112yes—
450C2×D4—21no—
451C2×D4—24no—
452C2×D4—114no—
453C2×D4—228no—
454C2×D4—224no—
455C2×D4—224no—
456C2×D4—222no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—224no—
460C2×D4—444no—
461C2×D4—444no—
462C2×D4—448no—
463C2×D4—444no—
464C2×D4C23×D1112yes—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—114no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—114no—
474C22×C4—224no—
475C22×C4—228no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—442no—
481C22×C4—448no—
482C22×C4—444no—
483C22×C4D4×D1111yescharacteristic
484C22×C4D4×D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486SD16—2216no—
487D8—2216no—
488M16—2216no—
489C2×C8—24no—
490C2×C8—118no—
491C2×C8—114no—
492C2×C8C23×D1114yes—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—112no—
496C4⋊C4—112no—
497C4⋊C4—224no—
498C4⋊C4—224no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4C23×D1114yes—
504C22⋊C4—24no—
505C22⋊C4—24no—
506C22⋊C4—228no—
507C22⋊C4—228no—
508C22⋊C4—224no—
509C22⋊C4—224no—
510C22⋊C4—224no—
511C42—114no—
512C42—112no—
513C42—114no—
514C42—112no—
515C42—224no—
516C42D4×D1112yes—
517C42C23×D1112yes—
518C11C2×#317111yescharacteristic, complemented, Sylow
519C23—22no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—112no—
524C23—222no—
525C23—222no—
526C23—222no—
527C23—224no—
528C23—444no—
529C23—444no—
530C23—444no—
531C23C2×D4×D1111yescharacteristic
532Q8—24no—
533Q8—48no—
534Q8—42no—
535D4—24no—
536D4—42no—
537D4—224no—
538D4—224no—
539D4—448no—
540D4—448no—
541D4—4416no—
542D4—448no—
543D4—444no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—114no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—228no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—444no—
562C2×C4—4416no—
563C2×C4—448no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4C2×D4×D1112yes—
567C2×C4C2×D4×D1112yes—
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4#41×D1114yes—
570C2×C4C24×D1111yescharacteristic
571C8—24no—
572C8—118no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—84no—
577C22—222no—
578C22—222no—
579C22—222no—
580C22—444no—
581C22—444no—
582C22—444no—
583C22—444no—
584C22—888no—
585C22#1062319912yes—
586C22D11×AGL(1,ℤ/8)12yes—
587C22#1062330812yes—
588C22C22×D4×D1111yescharacteristic
589C4—22no—
590C4—22no—
591C4—42no—
592C4—44no—
593C4—114no—
594C4—222no—
595C4—222no—
596C4—442no—
597C4—442no—
598C4#1062319912yes—
599C4C2×#41×D1112yes—
600C2—82no—
601C2—442no—
602C2—884no—
603C2#1307921414yesdirect product factor
604C2C2×#1062319911yescharacteristic
605C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
606C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
hypercenterC2×#489D11
hypocenterC11C2×#3171
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10623256C2semidirect
2. C2×#10623211C2semidirect
3. #13079214C2direct (N × H)
4. C2×#10622693C2semidirect
5. C2×#10622671C2semidirect
6. C2×#10622326C2semidirect
7. C2×#10622395C2semidirect
8. C2×#10622425C2semidirect
9. C2×#10622401C2semidirect
10. C2×#10622369C2semidirect
11. C2×#10622320C2semidirect
12. C2×C11×#489C2semidirect
25. #10623256C22semidirect
27. #10623211C22semidirect
39. C11×#489C22semidirect
46. #10622693C22semidirect
47. #10622671C22semidirect
51. #10622425C22semidirect
52. #10622401C22semidirect
53. #10622395C22semidirect
54. #10622369C22semidirect
55. #10622326C22semidirect
56. #10622320C22semidirect
213. C2×C11⋊C8#41semidirect
222. C2×#489D11semidirect
281. C11⋊C8C2×#41semidirect
311. #489C2×D11semidirect
435. C2×C11#3171semidirect
518. C11C2×#3171semidirect
603. C2#13079214direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106232112
#130792142
C2×#106226932
C2×#106226712
C2×#106223262
C2×#106223952
C2×#106224252
C2×#106224012
C2×#106223692
C2×#106223202
C2×C11×#4892
C2×#317111