Finite Group Databasebeta

← C2×#13082337 #15661840

Subgroups — C2×#13082337 #15661840

Order 2816.

7302 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082337C2132yesmaximal, direct product factor
2C2×#10623263C214yesmaximal, complemented
3C2×#10623265C214yesmaximal, complemented
4C2×#10623226C214yesmaximal, complemented
5C2×#10623225C214yesmaximal, complemented
6C2×#10623175C214yesmaximal, complemented
7C2×#10623041C211yesmaximal, characteristic, complemented
8C2×#10623155C214yesmaximal, complemented
9C2×#10623055C212yesmaximal, complemented
10C2×#10623054C212yesmaximal, complemented
11C22×#66945C211yesmaximal, characteristic, complemented
12C2×C11×#544C211yesmaximal, characteristic, complemented
13C22×#4339C2212yes—
14C23×C4×D11C2211yescharacteristic
15C11×#544C22116yescomplemented
16C2×C11×C4⋊Q8C2214yescomplemented
17C2×C11×#125C2214yescomplemented
18C2×C11×C22⋊Q8C2214yes—
19C2×C11×#117C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#67000C2218yes—
22C2×#67000C2214yescomplemented
23C2×Q8×Dic11C2214yescomplemented
24C2×#66983C2214yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28#10623265C22164yescomplemented
29#10623263C22164yescomplemented
30#10623226C22164yescomplemented
31#10623225C22164yescomplemented
32#10623175C22164yescomplemented
33#10623155C22164yescomplemented
34#10623055C22132yescomplemented
35#10623054C22132yescomplemented
36C2×#66951C2218yes—
37C2×#66951C2218yescomplemented
38#10623041C22116yescomplemented
39C2×#66950C2212yes—
40C2×#66950C2212yes—
41C2×#66950C2214yescomplemented
42C2×#66948C2212yes—
43C2×#66948C2212yes—
44C2×#66948C2218yes—
45C2×#66948C2214yescomplemented
46C2×#66947C2218yes—
47C2×#66946C2214yescomplemented
48C2×#66945C2214yes—
49C2×#66945C2214yes—
50C2×#66945C22116yescomplemented
51C2×#66945C2218yescomplemented
52C2×#66945C2214yescomplemented
53C2×C4⋊C4×D11C2214yescomplemented
54C2×#66943C2214yescomplemented
55C2×#66939C2214yes—
56C2×#66935C2214yes—
57C2×(C22⋊D11)⋊C4C2218yes—
58C2×C4×D44C2214yes—
59C2×C4×D44C2214yes—
60C2×C4×D44C2214yescomplemented
61C2×C4×Dic22C2214yescomplemented
62C24×D11C2311yescharacteristic
63C22×Q8×C11C2314yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2314yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C2×#4339—216no—
70C2×#4339C23116yes—
71C22×D44C2312yes—
72C22×D44C2314yes—
73C22×D44C2314yes—
74C22×D44C2314yes—
75C22×C4×D11—28no—
76C22×C4×D11C2314yes—
77C22×C4×D11C2312yes—
78C22×C4×D11C2312yes—
79C22×C4×D11C2318yes—
80C22×C4×D11C2318yes—
81C22×Dic22C2312yes—
82C11×C4⋊Q8C23132yescomplemented
83C11×#125C23132yescomplemented
84C11×C22⋊Q8C23132yes—
85C11×#117C23116yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2318yes—
91C2×C11×C4⋊C4C2318yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C42×C11C2314yes—
94#67000C23164yes—
95#67000C23132yescomplemented
96Q8×Dic11C23132yescomplemented
97#66983C23132yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2318yes—
103C2×(C2×D11)⋊C4C2318yes—
104C2×(C2×D11)⋊C4C23116yes—
105C2×(C2×D11)⋊C4C2318yes—
106C2×C4⋊Dic11C2314yes—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2314yes—
110C2×C4⋊Dic11C2318yes—
111C2×Dic11⋊C4C2318yes—
112C2×C4×Dic11C2318yes—
113C2×C4×Dic11C2314yes—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C23116yes—
116#66951C23164yes—
117#66951C23164yescomplemented
118#66950C23116yes—
119#66950C23116yes—
120#66950C23132yescomplemented
121#66948C23116yes—
122#66948C23164yes—
123#66948C23116yes—
124#66948C23132yescomplemented
125#66947C23164yes—
126#66946C23132yescomplemented
127#66945C23132yes—
128#66945C23132yes—
129#66945C23132yescomplemented
130#66945C23164yescomplemented
131C4⋊C4×D11C23132yescomplemented
132#66943C23132yescomplemented
133#66939C23132yes—
134#66935C23132yes—
135(C22⋊D11)⋊C4C23164yes—
136C4×D44C23132yes—
137C4×D44C23132yes—
138C4×D44C23132yescomplemented
139C4×Dic22C23132yescomplemented
140C2×#3493—111nomaximal, Sylow
141C24×C11C2411yescharacteristic
142C23×D11—24no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11C2412yes—
146C23×D11C2414yes—
147C23×D11C2414yes—
148C2×Q8×C11—48no—
149C2×Q8×C11C24116yes—
150C22×C4×C11—44no—
151C22×C4×C11#4118yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2414yes—
155C22×C4×C11C2418yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2414yes—
158C2×C22⋊D11—216no—
159C2×C22⋊D11C24116yes—
160C22×Dic11—24no—
161C22×Dic11—44no—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2411yescharacteristic
165C22×Dic11C2411yescharacteristic
166C22×Dic11C2414yes—
167C22×Dic11C2418yes—
168#4339—264no—
169C2×D44—28no—
170C2×D44—48no—
171C2×D44—48no—
172C2×D44—48no—
173C2×D44C2418yes—
174C2×D44C24116yes—
175C2×D44C24116yes—
176C2×D44C24116yes—
177C2×C4×D11—28no—
178C2×C4×D11—28no—
179C2×C4×D11—232no—
180C2×C4×D11—216no—
181C2×C4×D11—416no—
182C2×C4×D11C24116yes—
183C2×C4×D11C2418yes—
184C2×C4×D11C2418yes—
185C2×C4×D11C24132yes—
186C2×Dic22—28no—
187C2×Dic22C2418yes—
188C11×C4⋊C4C24116yes—
189C11×C4⋊C4C2418yes—
190C11×C4⋊C4C24116yes—
191C11×C4⋊C4C2418yes—
192C11×C4⋊C4C24132yes—
193C11×C22⋊C4C24116yes—
194C42×C11C24116yes—
195(C2×D11)⋊C4C24116yes—
196(C2×D11)⋊C4C24116yes—
197(C2×D11)⋊C4C24116yes—
198(C2×D11)⋊C4C24116yes—
199(C2×D11)⋊C4C24132yes—
200(C2×D11)⋊C4C24132yes—
201(C2×D11)⋊C4C24132yes—
202C4⋊Dic11C24116yes—
203C4⋊Dic11C24116yes—
204C4⋊Dic11C24116yes—
205C4⋊Dic11C24116yes—
206Dic11⋊C4C24132yes—
207C4×Dic11C24132yes—
208C4×Dic11C24116yes—
209C4×Dic11C24116yes—
210#3493—1132no—
211C2×#556—114no—
212C2×#555—114no—
213C2×#553—114no—
214C2×#552—114no—
215C2×#544D1111yescharacteristic, complemented
216C2×#538—114no—
217C2×#537—111no—
218C2×#529—114no—
219C2×#525—112no—
220C2×#520—112no—
221C22×#117—111no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11C2×#4114yes—
225C23×C11C2512yes—
226C23×C11C2511yescharacteristic
227C22×D11—28no—
228C22×D11—24no—
229C22×D11—28no—
230C22×D11—28no—
231C22×D11—28no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11—416no—
237C22×D11C2514yes—
238C22×D11C2518yes—
239Q8×C11—416no—
240C2×C4×C11—28no—
241C2×C4×C11—28no—
242C2×C4×C11—28no—
243C2×C4×C11—48no—
244C2×C4×C11C2×#4118yes—
245C2×C4×C11C2×#41116yes—
246C2×C4×C11C2518yes—
247C2×C4×C11C2518yes—
248C2×C4×C11C2518yes—
249C2×C4×C11C2514yes—
250C22⋊D11—232no—
251C2×Dic11—28no—
252C2×Dic11—28no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—28no—
256C2×Dic11—48no—
257C2×Dic11C2518yes—
258C2×Dic11C2512yes—
259C2×Dic11C2512yes—
260C2×Dic11C2518yes—
261D44—216no—
262D44—416no—
263D44—416no—
264D44—416no—
265C4×D11—216no—
266C4×D11—216no—
267C4×D11—232no—
268C4×D11—432no—
269Dic22—216no—
270C22×#41—112no—
271C24×C4—111no—
272#556—1164no—
273#555—1164no—
274#553—1164no—
275#552—1164no—
276#544C2×D11116yescomplemented
277#538—1164no—
278#537—1116no—
279C2×C4⋊Q8C2×D1114yescomplemented
280#529—1164no—
281C2×#126—118no—
282C2×#126—118no—
283C2×#125—114no—
284C2×#125C2×D1114yescomplemented
285C2×#124—114no—
286C2×#124—118no—
287#525—1132no—
288C2×#123—118no—
289C2×#123—114no—
290C2×C22⋊Q8—112no—
291C2×C22⋊Q8—112no—
292C2×C22⋊Q8—114no—
293C2×C22⋊Q8C2×D1114yes—
294C2×#121—114no—
295C2×#121—112no—
296C2×#121—112no—
297C2×#121—118no—
298C2×#121—114no—
299C2×#120—114no—
300#520—1132no—
301C2×C4×Q8—114no—
302C2×C4×Q8—114no—
303C2×C4×D4—114no—
304C2×C4×D4—118no—
305C2×C4×D4—114no—
306C2×C4×D4—114no—
307C2×C4×D4—114no—
308C2×#117—114no—
309C2×#117—114no—
310C2×#117—1116no—
311C2×#117—114no—
312C2×#117—118no—
313C2×#117C2×D1112yes—
314C22×C4⋊C4—111no—
315C22×C4⋊C4—114no—
316C22×C4⋊C4C2×D1111yescharacteristic
317C22×C22⋊C4—112no—
318C22×C42—112no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—28no—
322C22×C11C22×#4114yes—
323C22×C11C22×#4112yes—
324C22×C11#58512yes—
325C22×C11#58512yes—
326C22×C11C2611yescharacteristic
327C2×D11—24no—
328C2×D11—28no—
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—28no—
332C2×D11—28no—
333C2×D11—416no—
334C2×D11—416no—
335C2×D11—48no—
336C4×C11—28no—
337C4×C11—28no—
338C4×C11—28no—
339C4×C11C22×#4118yes—
340Dic11—28no—
341Dic11—22no—
342Dic11—22no—
343Dic11—28no—
344C25—111no—
345C2×#41—1116no—
346C2×#41—2216no—
347C22×Q8—112no—
348C22×Q8C22×D1114yes—
349C22×D4—114no—
350C22×D4—112no—
351C22×D4—114no—
352C22×D4—114no—
353C22×D4—114no—
354C23×C4—111no—
355C23×C4—112no—
356C23×C4—114no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—118no—
360C23×C4—118no—
361C23×C4—228no—
362C23×C4C22×D1112yes—
363C23×C4C22×D1111yescharacteristic
364C4⋊Q8C22×D11132yescomplemented
365#126—1164no—
366#126—1164no—
367#125—1132no—
368#125C22×D11132yescomplemented
369#124—1132no—
370#124—1164no—
371#123—1164no—
372#123—1132no—
373C22⋊Q8—1116no—
374C22⋊Q8—1116no—
375C22⋊Q8—1132no—
376C22⋊Q8C22×D11132yes—
377#121—1132no—
378#121—1116no—
379#121—1116no—
380#121—1132no—
381#121—1164no—
382#120—1132no—
383C4×Q8—1132no—
384C4×Q8—1132no—
385C4×D4—1132no—
386C4×D4—1164no—
387C4×D4—1132no—
388C4×D4—1132no—
389C4×D4—1132no—
390#117—1132no—
391#117—1132no—
392#117—1132no—
393#117—1164no—
394#117C22×D11116yes—
395C2×C4⋊C4—114no—
396C2×C4⋊C4—118no—
397C2×C4⋊C4—118no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—1132no—
402C2×C4⋊C4C22×D1112yes—
403C2×C4⋊C4C22×D1114yes—
404C2×C4⋊C4C22×D1118yes—
405C2×C4⋊C4C22×D1112yes—
406C2×C4⋊C4C22×D1118yes—
407C2×C4⋊C4C22×D1114yes—
408C2×C22⋊C4—118no—
409C2×C22⋊C4—1116no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—114no—
416C2×C22⋊C4C22×D1114yes—
417C2×C42—114no—
418C2×C42—118no—
419C2×C42—114no—
420C2×C42—1116no—
421C2×C42C22×D1114yes—
422C2×C11—24no—
423C2×C11#349314yescomplemented
424C2×C11C23×#4111yescharacteristic
425C2×C11C2×#58511yescharacteristic
426C2×C11C2×#58511yescharacteristic
427D11—48no—
428D11—44no—
429C24—112no—
430C24—114no—
431C24—114no—
432C24—224no—
433C24—442no—
434C24—442no—
435C24C23×D1111yescharacteristic
436#41—2264no—
437C2×Q8—48no—
438C2×Q8—118no—
439C2×Q8—228no—
440C2×Q8C23×D11116yes—
441C2×D4—1116no—
442C2×D4—118no—
443C2×D4—1116no—
444C2×D4—1116no—
445C2×D4—1116no—
446C2×D4—2216no—
447C2×D4—228no—
448C2×D4—448no—
449C2×D4—448no—
450C2×D4—448no—
451C22×C4—44no—
452C22×C4—114no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—114no—
456C22×C4—114no—
457C22×C4—118no—
458C22×C4—1116no—
459C22×C4—118no—
460C22×C4—118no—
461C22×C4—1132no—
462C22×C4—224no—
463C22×C4—228no—
464C22×C4—228no—
465C22×C4—2232no—
466C22×C4—2216no—
467C22×C4—4416no—
468C22×C4—444no—
469C22×C4#434318yes—
470C22×C4C23×D1114yes—
471C22×C4C23×D1114yes—
472C22×C4C23×D1114yes—
473C22×C4C23×D1118yes—
474C22×C4C23×D1114yes—
475C22×C4C23×D1112yes—
476C4⋊C4—1116no—
477C4⋊C4—1132no—
478C4⋊C4—1116no—
479C4⋊C4—1116no—
480C4⋊C4—1116no—
481C4⋊C4C23×D1118yes—
482C4⋊C4C23×D11116yes—
483C4⋊C4C23×D1118yes—
484C4⋊C4C23×D11132yes—
485C4⋊C4C23×D11116yes—
486C22⋊C4—1132no—
487C22⋊C4—1116no—
488C22⋊C4—1132no—
489C22⋊C4—1132no—
490C22⋊C4—1116no—
491C22⋊C4—1116no—
492C22⋊C4—1116no—
493C22⋊C4C23×D11116yes—
494C42—1116no—
495C42—1116no—
496C42—1132no—
497C42C23×D11116yes—
498C11C2×#349311yescharacteristic, complemented, Sylow
499C23—22no—
500C23—22no—
501C23—114no—
502C23—118no—
503C23—228no—
504C23—224no—
505C23—228no—
506C23—228no—
507C23—224no—
508C23—228no—
509C23—224no—
510C23—444no—
511C23—444no—
512C23—4416no—
513C23C2×#434314yes—
514C23C24×D1112yes—
515C23C24×D1111yescharacteristic
516Q8—416no—
517Q8—2216no—
518D4—2232no—
519D4—2216no—
520D4—4416no—
521D4—4416no—
522D4—4416no—
523C2×C4—28no—
524C2×C4—28no—
525C2×C4—28no—
526C2×C4—48no—
527C2×C4—112no—
528C2×C4—112no—
529C2×C4—118no—
530C2×C4—118no—
531C2×C4—228no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—228no—
535C2×C4—228no—
536C2×C4—2216no—
537C2×C4—2216no—
538C2×C4—2232no—
539C2×C4—4432no—
540C2×C4—448no—
541C2×C4C2×#434318yes—
542C2×C4C2×#4343116yes—
543C2×C4C24×D1118yes—
544C2×C4C24×D1118yes—
545C2×C4C24×D1118yes—
546C2×C4C24×D1114yes—
547C22—22no—
548C22—22no—
549C22—28no—
550C22—224no—
551C22—228no—
552C22—228no—
553C22—224no—
554C22—228no—
555C22—224no—
556C22—4416no—
557C22—448no—
558C22—4416no—
559C22C22×#434314yes—
560C22C22×#434312yes—
561C22#1062345512yes—
562C22#1062345712yes—
563C22C25×D1111yescharacteristic
564C4—28no—
565C4—28no—
566C4—28no—
567C4—222no—
568C4—222no—
569C4—228no—
570C4—228no—
571C4C22×#434318yes—
572C2—24no—
573C2—444no—
574C2—448no—
575C2#1308233714yesdirect product factor
576C2C23×#434311yescharacteristic
577C2C2×#1062345511yescharacteristic
578C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#544C2
socleC23×C11C25
hypercenterC2×#544D11
hypocenterC11C2×#3493
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13082337C2direct (N × H)
2. C2×#10623263C2semidirect
3. C2×#10623265C2semidirect
4. C2×#10623226C2semidirect
5. C2×#10623225C2semidirect
6. C2×#10623175C2semidirect
7. C2×#10623041C2semidirect
8. C2×#10623155C2semidirect
9. C2×#10623055C2semidirect
10. C2×#10623054C2semidirect
11. C22×#66945C2semidirect
12. C2×C11×#544C2semidirect
15. C11×#544C22semidirect
16. C2×C11×C4⋊Q8C22semidirect
17. C2×C11×#125C22semidirect
22. C2×#67000C22semidirect
23. C2×Q8×Dic11C22semidirect
28. #10623265C22semidirect
29. #10623263C22semidirect
30. #10623226C22semidirect
31. #10623225C22semidirect
32. #10623175C22semidirect
33. #10623155C22semidirect
34. #10623055C22semidirect
35. #10623054C22semidirect
37. C2×#66951C22semidirect
38. #10623041C22semidirect
41. C2×#66950C22semidirect
45. C2×#66948C22semidirect
47. C2×#66946C22semidirect
50. C2×#66945C22semidirect
51. C2×#66945C22semidirect
52. C2×#66945C22semidirect
53. C2×C4⋊C4×D11C22semidirect
54. C2×#66943C22semidirect
60. C2×C4×D44C22semidirect
61. C2×C4×Dic22C22semidirect
82. C11×C4⋊Q8C23semidirect
83. C11×#125C23semidirect
95. #67000C23semidirect
96. Q8×Dic11C23semidirect
117. #66951C23semidirect
120. #66950C23semidirect
124. #66948C23semidirect
126. #66946C23semidirect
129. #66945C23semidirect
130. #66945C23semidirect
131. C4⋊C4×D11C23semidirect
132. #66943C23semidirect
138. C4×D44C23semidirect
139. C4×Dic22C23semidirect
215. C2×#544D11semidirect
276. #544C2×D11semidirect
279. C2×C4⋊Q8C2×D11semidirect
284. C2×#125C2×D11semidirect
364. C4⋊Q8C22×D11semidirect
368. #125C22×D11semidirect
423. C2×C11#3493semidirect
498. C11C2×#3493semidirect
575. C2#13082337direct (N × H)

Maximal subgroups

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

subgroupindex
#130823372
C2×#106232632
C2×#106232652
C2×#106232262
C2×#106232252
C2×#106231752
C2×#106230412
C2×#106231552
C2×#106230552
C2×#106230542
C22×#669452
C2×C11×#5442
C2×#349311