Finite Group Databasebeta

← C2×#13082335 #15661838

Subgroups — C2×#13082335 #15661838

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#13082335C2132yesmaximal, direct product factor
2C2×#10623172C214yesmaximal, complemented
3C2×#10623147C214yesmaximal, complemented
4C2×#10623149C214yesmaximal, complemented
5C2×#10623173C214yesmaximal, complemented
6C2×#10623031C211yesmaximal, characteristic, complemented
7C2×#10623148C214yesmaximal, complemented
8C2×#10623131C214yesmaximal, complemented
9C2×#10623359C212yesmaximal, complemented
10C2×#10623358C212yesmaximal, complemented
11C22×#66945C211yesmaximal, characteristic, complemented
12C2×C11×#537C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C23×C4×D11C2211yescharacteristic
15C11×#537C22116yescomplemented
16C2×C11×C22⋊Q8C2214yescomplemented
17C2×C11×#121C2214yes—
18C2×C11×#121C2214yescomplemented
19C22×C11×C4⋊C4C2211yescharacteristic
20#10623359C22132yescomplemented
21#10623358C22132yescomplemented
22C2×#66999C2212yes—
23C2×#66999C2212yes—
24C2×Q8×Dic11C2214yescomplemented
25C2×#66992C2218yes—
26C2×#66991C2212yes—
27C2×#66991C2212yes—
28C2×#66990C2214yes—
29C2×#66989C2214yescomplemented
30C2×#66988C2214yes—
31C2×D4×Dic11C2218yes—
32C2×D4×Dic11C2214yescomplemented
33C2×D4×Dic11C2214yescomplemented
34C2×C4×C22⋊D11C2214yes—
35C2×C4×C22⋊D11C2214yes—
36C22×(C2×D11)⋊C4C2212yes—
37C2×#66979C2212yes—
38C2×#66979C2214yescomplemented
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2214yescomplemented
41C2×#66977C2214yes—
42C22×C4×Dic11C2212yes—
43#10623173C22164yescomplemented
44#10623172C22164yescomplemented
45#10623149C22164yescomplemented
46#10623148C22164yescomplemented
47#10623147C22164yescomplemented
48#10623131C22164yescomplemented
49C2×#66951C2218yes—
50C2×#66945C2214yes—
51C2×#66945C2214yes—
52C2×#66945C22116yescomplemented
53#10623031C22116yescomplemented
54C2×#66943C2214yescomplemented
55C2×#66943C2214yescomplemented
56C2×#66941C2214yescomplemented
57C2×#66940C2214yescomplemented
58C2×#66939C2218yes—
59C2×#66938C2218yes—
60C2×#66932C2218yescomplemented
61C2×#66930C2218yescomplemented
62C24×D11C2311yescharacteristic
63C2×C11×#41—216no—
64C2×C11×#41C23116yes—
65C22×Q8×C11C2312yes—
66C22×D4×C11C2314yes—
67C22×D4×C11C2312yes—
68C22×D4×C11C2314yes—
69C23×C4×C11C2314yes—
70C23×C4×C11C2312yes—
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11C2314yes—
73C22×C22⋊D11C2314yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2318yes—
76C23×Dic11C2312yes—
77C22×C4×D11—28no—
78C22×C4×D11C2312yes—
79C22×C4×D11C2312yes—
80C22×C4×D11C2318yes—
81C22×Dic22C2314yes—
82C11×C22⋊Q8C23132yescomplemented
83C11×#121C23132yes—
84C11×#121C23132yescomplemented
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2318yes—
88C2×C11×C22⋊C4C2318yes—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2314yes—
93#66999C23116yes—
94#66999C23116yes—
95Q8×Dic11C23132yescomplemented
96#66992C23164yes—
97#66991C23116yes—
98#66991C23116yes—
99#66990C23132yes—
100#66989C23132yescomplemented
101#66988C23132yes—
102D4×Dic11C23164yes—
103D4×Dic11C23132yescomplemented
104D4×Dic11C23132yescomplemented
105C4×C22⋊D11C23132yes—
106C4×C22⋊D11C23132yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2318yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C23116yes—
111#66979C23116yes—
112#66979C23132yescomplemented
113C2×C4⋊Dic11C2318yes—
114C2×C4⋊Dic11C2314yes—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2318yes—
119C2×C4⋊Dic11C23132yescomplemented
120#66977C23132yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2318yes—
123C2×Dic11⋊C4C2314yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2318yes—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C23116yes—
129#66951C23164yes—
130#66945C23132yes—
131#66945C23132yes—
132#66943C23132yescomplemented
133#66943C23132yescomplemented
134#66941C23132yescomplemented
135#66940C23132yescomplemented
136#66939C23164yes—
137#66938C23164yes—
138#66932C23164yescomplemented
139#66930C23164yescomplemented
140C2×#3493—111nomaximal, Sylow
141C24×C11C2414yes—
142C24×C11C2411yescharacteristic
143C23×D11—24no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11C2412yes—
147C23×D11C2414yes—
148C11×#41—264no—
149C2×Q8×C11—28no—
150C2×Q8×C11C2418yes—
151C2×D4×C11—216no—
152C2×D4×C11—28no—
153C2×D4×C11—48no—
154C2×D4×C11C24116yes—
155C2×D4×C11C2418yes—
156C2×D4×C11C24116yes—
157C22×C4×C11—216no—
158C22×C4×C11—44no—
159C22×C4×C11#4118yes—
160C22×C4×C11C2414yes—
161C22×C4×C11C2414yes—
162C22×C4×C11C24116yes—
163C22×C4×C11C2418yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2414yes—
166C2×C22⋊D11—48no—
167C2×C22⋊D11—48no—
168C2×C22⋊D11C24116yes—
169C2×C22⋊D11C24116yes—
170C22×Dic11—24no—
171C22×Dic11—44no—
172C22×Dic11—416no—
173C22×Dic11C2411yescharacteristic
174C22×Dic11C2411yescharacteristic
175C22×Dic11C2414yes—
176C22×Dic11C2414yes—
177C22×Dic11C2414yes—
178C22×Dic11C2414yes—
179C22×Dic11C24132yes—
180C22×Dic11C2418yes—
181C2×C4×D11—28no—
182C2×C4×D11—28no—
183C2×C4×D11—232no—
184C2×C4×D11C2418yes—
185C2×C4×D11C2418yes—
186C2×Dic22—48no—
187C2×Dic22C24116yes—
188C11×C4⋊C4C24116yes—
189C11×C4⋊C4C24116yes—
190C11×C22⋊C4C24132yes—
191C22⋊Dic11C24116yes—
192C22⋊Dic11C24116yes—
193C22⋊Dic11C24132yes—
194C22⋊Dic11C24116yes—
195(C2×D11)⋊C4C24116yes—
196(C2×D11)⋊C4C24132yes—
197(C2×D11)⋊C4C24116yes—
198C4⋊Dic11C24132yes—
199C4⋊Dic11C24116yes—
200C4⋊Dic11C2418yes—
201C4⋊Dic11C2418yes—
202C4⋊Dic11C24116yes—
203Dic11⋊C4C24116yes—
204Dic11⋊C4C24132yes—
205Dic11⋊C4C24116yes—
206C4×Dic11C24116yes—
207C4×Dic11C24132yes—
208C4×Dic11C24116yes—
209C4×Dic11C24116yes—
210#3493—1132no—
211C2×#556—114no—
212C2×#555—114no—
213C2×#553—114no—
214C2×#552—114no—
215C2×#544—111no—
216C2×#538—114no—
217C2×#537D1111yescharacteristic, complemented
218C2×#529—114no—
219C2×#525—112no—
220C2×#520—112no—
221C22×#117—111no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—28no—
225C23×C11—28no—
226C23×C11—28no—
227C23×C11C2×#4114yes—
228C23×C11C2518yes—
229C23×C11C2512yes—
230C23×C11C2511yescharacteristic
231C22×D11—28no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—44no—
236C22×D11—44no—
237C22×D11—416no—
238C22×D11C2514yes—
239Q8×C11—216no—
240D4×C11—232no—
241D4×C11—216no—
242D4×C11—416no—
243C2×C4×C11—28no—
244C2×C4×C11—28no—
245C2×C4×C11—232no—
246C2×C4×C11—48no—
247C2×C4×C11C2×#4118yes—
248C2×C4×C11C2×#41116yes—
249C2×C4×C11C2518yes—
250C2×C4×C11C2518yes—
251C2×C4×C11C2514yes—
252C22⋊D11—416no—
253C22⋊D11—416no—
254C2×Dic11—28no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—28no—
258C2×Dic11—28no—
259C2×Dic11—28no—
260C2×Dic11—48no—
261C2×Dic11—432no—
262C2×Dic11C2512yes—
263C2×Dic11C2512yes—
264C2×Dic11C2518yes—
265C2×Dic11C2518yes—
266C2×Dic11C2518yes—
267C4×D11—216no—
268C4×D11—216no—
269Dic22—416no—
270C22×#41C2×D1112yes—
271C24×C4—111no—
272#556—1164no—
273#555—1164no—
274#553—1164no—
275#552—1164no—
276#544—1116no—
277#538—1164no—
278#537C2×D11116yescomplemented
279C2×C4⋊Q8—114no—
280#529—1164no—
281C2×#126—118no—
282C2×#126—118no—
283C2×#125—114no—
284C2×#125—114no—
285C2×#124—114no—
286C2×#124—118no—
287#525—1132no—
288C2×#123—114no—
289C2×#123—118no—
290C2×C22⋊Q8—112no—
291C2×C22⋊Q8—112no—
292C2×C22⋊Q8—114no—
293C2×C22⋊Q8C2×D1114yescomplemented
294C2×#121—112no—
295C2×#121—112no—
296C2×#121—118no—
297C2×#121C2×D1114yes—
298C2×#121C2×D1114yescomplemented
299C2×#120—114no—
300#520—1132no—
301C2×C4×Q8—114no—
302C2×C4×Q8—114no—
303C2×C4×D4—118no—
304C2×C4×D4—114no—
305C2×C4×D4—114no—
306C2×C4×D4—114no—
307C2×C4×D4—114no—
308C2×#117—112no—
309C2×#117—114no—
310C2×#117—114no—
311C2×#117—114no—
312C2×#117—1116no—
313C2×#117—118no—
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×C11—28no—
323C22×C11—28no—
324C22×C11—28no—
325C22×C11—416no—
326C22×C11C22×#4114yes—
327C22×C11C22×#4112yes—
328C22×C11#58512yes—
329C22×C11#58512yes—
330C22×C11C2611yescharacteristic
331C2×D11—24no—
332C2×D11—24no—
333C2×D11—24no—
334C2×D11—416no—
335C2×D11—48no—
336C4×C11—28no—
337C4×C11—28no—
338C4×C11C22×#4118yes—
339Dic11—22no—
340Dic11—22no—
341Dic11—28no—
342Dic11—28no—
343Dic11—28no—
344C25—111no—
345C2×#41—216no—
346C2×#41C22×D11116yes—
347C22×Q8—114no—
348C22×Q8C22×D1112yes—
349C22×D4—114no—
350C22×D4—114no—
351C22×D4C22×D1114yes—
352C22×D4C22×D1112yes—
353C22×D4C22×D1114yes—
354C23×C4—111no—
355C23×C4—112no—
356C23×C4—118no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—118no—
360C23×C4—228no—
361C23×C4C22×D1114yes—
362C23×C4C22×D1112yes—
363C23×C4C22×D1111yescharacteristic
364C4⋊Q8—1132no—
365#126—1164no—
366#126—1164no—
367#125—1132no—
368#125—1132no—
369#124—1132no—
370#124—1164no—
371#123—1132no—
372#123—1164no—
373C22⋊Q8—1116no—
374C22⋊Q8—1116no—
375C22⋊Q8—1132no—
376C22⋊Q8C22×D11132yescomplemented
377#121—1116no—
378#121—1116no—
379#121—1164no—
380#121C22×D11132yes—
381#121C22×D11132yescomplemented
382#120—1132no—
383C4×Q8—1132no—
384C4×Q8—1132no—
385C4×D4—1164no—
386C4×D4—1132no—
387C4×D4—1132no—
388C4×D4—1132no—
389C4×D4—1132no—
390#117—1116no—
391#117—1132no—
392#117—1132no—
393#117—1132no—
394#117—1164no—
395C2×C4⋊C4—114no—
396C2×C4⋊C4—112no—
397C2×C4⋊C4—118no—
398C2×C4⋊C4—118no—
399C2×C4⋊C4—1132no—
400C2×C4⋊C4—112no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—118no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4C22×D1114yes—
406C2×C4⋊C4C22×D1118yes—
407C2×C4⋊C4C22×D1114yes—
408C2×C22⋊C4—114no—
409C2×C22⋊C4—114no—
410C2×C22⋊C4—118no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—1116no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—114no—
416C2×C22⋊C4C22×D1118yes—
417C2×C42—114no—
418C2×C42—118no—
419C2×C42—114no—
420C2×C42—1116no—
421C2×C42—114no—
422C2×C11—24no—
423C2×C11—48no—
424C2×C11#349314yescomplemented
425C2×C11C23×#4111yescharacteristic
426C2×C11C2×#58511yescharacteristic
427C2×C11C2×#58511yescharacteristic
428D11—44no—
429C24—112no—
430C24—114no—
431C24—224no—
432C24—442no—
433C24—442no—
434C24C23×D1114yes—
435C24C23×D1111yescharacteristic
436#41—264no—
437C2×Q8—28no—
438C2×Q8—1116no—
439C2×Q8—448no—
440C2×Q8C23×D1118yes—
441C2×D4—216no—
442C2×D4—28no—
443C2×D4—48no—
444C2×D4—1116no—
445C2×D4—1116no—
446C2×D4—448no—
447C2×D4—448no—
448C2×D4C23×D11116yes—
449C2×D4C23×D1118yes—
450C2×D4C23×D11116yes—
451C22×C4—216no—
452C22×C4—44no—
453C22×C4—114no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—118no—
460C22×C4—1132no—
461C22×C4—118no—
462C22×C4—118no—
463C22×C4—224no—
464C22×C4—228no—
465C22×C4—228no—
466C22×C4—2232no—
467C22×C4—444no—
468C22×C4—4416no—
469C22×C4#434118yes—
470C22×C4C23×D11116yes—
471C22×C4C23×D1114yes—
472C22×C4C23×D1114yes—
473C22×C4C23×D1118yes—
474C22×C4C23×D1114yes—
475C22×C4C23×D1112yes—
476C4⋊C4—1116no—
477C4⋊C4—118no—
478C4⋊C4—1132no—
479C4⋊C4—118no—
480C4⋊C4—1116no—
481C4⋊C4—1132no—
482C4⋊C4—1116no—
483C4⋊C4—1116no—
484C4⋊C4C23×D11116yes—
485C4⋊C4C23×D11116yes—
486C22⋊C4—1116no—
487C22⋊C4—1116no—
488C22⋊C4—1132no—
489C22⋊C4—1116no—
490C22⋊C4—1132no—
491C22⋊C4—1116no—
492C22⋊C4—1116no—
493C22⋊C4C23×D11132yes—
494C42—1116no—
495C42—1116no—
496C42—1132no—
497C42—1116no—
498C11C2×#349311yescharacteristic, complemented, Sylow
499C23—22no—
500C23—22no—
501C23—28no—
502C23—28no—
503C23—28no—
504C23—114no—
505C23—228no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—444no—
510C23—444no—
511C23—4416no—
512C23C2×#434114yes—
513C23C24×D1118yes—
514C23C24×D1112yes—
515C23C24×D1111yescharacteristic
516Q8—216no—
517Q8—4416no—
518D4—232no—
519D4—216no—
520D4—416no—
521D4—4416no—
522D4—4416no—
523C2×C4—28no—
524C2×C4—28no—
525C2×C4—232no—
526C2×C4—48no—
527C2×C4—112no—
528C2×C4—112no—
529C2×C4—118no—
530C2×C4—118no—
531C2×C4—118no—
532C2×C4—228no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—228no—
536C2×C4—228no—
537C2×C4—228no—
538C2×C4—2216no—
539C2×C4—2216no—
540C2×C4—448no—
541C2×C4—4432no—
542C2×C4C2×#434118yes—
543C2×C4C2×#4341116yes—
544C2×C4C24×D1118yes—
545C2×C4C24×D1118yes—
546C2×C4C24×D1114yes—
547C22—22no—
548C22—22no—
549C22—28no—
550C22—28no—
551C22—28no—
552C22—28no—
553C22—416no—
554C22—224no—
555C22—224no—
556C22—224no—
557C22—4416no—
558C22—448no—
559C22C22×#434114yes—
560C22C22×#434112yes—
561C22#1062345512yes—
562C22#1062345712yes—
563C22C25×D1111yescharacteristic
564C4—28no—
565C4—28no—
566C4—222no—
567C4—222no—
568C4—228no—
569C4—228no—
570C4—228no—
571C4C22×#434118yes—
572C2—24no—
573C2—48no—
574C2—444no—
575C2#1308233514yesdirect product factor
576C2C23×#434111yescharacteristic
577C2C2×#1062345511yescharacteristic
578C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#537C2
socleC23×C11C25
hypercenterC2×#537D11
hypocenterC11C2×#3493
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13082335C2direct (N × H)
2. C2×#10623172C2semidirect
3. C2×#10623147C2semidirect
4. C2×#10623149C2semidirect
5. C2×#10623173C2semidirect
6. C2×#10623031C2semidirect
7. C2×#10623148C2semidirect
8. C2×#10623131C2semidirect
9. C2×#10623359C2semidirect
10. C2×#10623358C2semidirect
11. C22×#66945C2semidirect
12. C2×C11×#537C2semidirect
15. C11×#537C22semidirect
16. C2×C11×C22⋊Q8C22semidirect
18. C2×C11×#121C22semidirect
20. #10623359C22semidirect
21. #10623358C22semidirect
24. C2×Q8×Dic11C22semidirect
29. C2×#66989C22semidirect
32. C2×D4×Dic11C22semidirect
33. C2×D4×Dic11C22semidirect
38. C2×#66979C22semidirect
40. C22×C4⋊Dic11C22semidirect
43. #10623173C22semidirect
44. #10623172C22semidirect
45. #10623149C22semidirect
46. #10623148C22semidirect
47. #10623147C22semidirect
48. #10623131C22semidirect
52. C2×#66945C22semidirect
53. #10623031C22semidirect
54. C2×#66943C22semidirect
55. C2×#66943C22semidirect
56. C2×#66941C22semidirect
57. C2×#66940C22semidirect
60. C2×#66932C22semidirect
61. C2×#66930C22semidirect
82. C11×C22⋊Q8C23semidirect
84. C11×#121C23semidirect
95. Q8×Dic11C23semidirect
100. #66989C23semidirect
103. D4×Dic11C23semidirect
104. D4×Dic11C23semidirect
112. #66979C23semidirect
119. C2×C4⋊Dic11C23semidirect
132. #66943C23semidirect
133. #66943C23semidirect
134. #66941C23semidirect
135. #66940C23semidirect
138. #66932C23semidirect
139. #66930C23semidirect
217. C2×#537D11semidirect
278. #537C2×D11semidirect
293. C2×C22⋊Q8C2×D11semidirect
298. C2×#121C2×D11semidirect
376. C22⋊Q8C22×D11semidirect
381. #121C22×D11semidirect
424. C2×C11#3493semidirect
498. C11C2×#3493semidirect
575. C2#13082335direct (N × H)

Maximal subgroups

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

subgroupindex
#130823352
C2×#106231722
C2×#106231472
C2×#106231492
C2×#106231732
C2×#106230312
C2×#106231482
C2×#106231312
C2×#106233592
C2×#106233582
C22×#669452
C2×C11×#5372
C2×#349311