Finite Group Databasebeta

← C2×#13072282 #14921200

Subgroups — C2×#13072282 #14921200

Order 2816.

4926 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C212yesmaximal, complemented
2C23×C22⋊Dic11C212yesmaximal
3#13072282C2116yesmaximal, direct product factor
4C2×#10622562C211yesmaximal, characteristic, complemented
5C2×#10622561C212yesmaximal, complemented
6C2×#10622560C211yesmaximal, characteristic, complemented
7C2×#10622563C212yesmaximal, complemented
8C2×#10622559C212yesmaximal, complemented
9C2×#10622555C212yesmaximal, complemented
10C2×C11×#379C211yesmaximal, characteristic
11C26×C11C2211yescharacteristic
12C24×Dic11C2212yes—
13C24×Dic11C2212yes—
14C23×Dic22C2211yescharacteristic, complemented
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11—216no—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C22116yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C4⋊Dic11C2212yescomplemented
26C22×C4⋊Dic11C2211yescharacteristic, complemented
27C22×Dic11⋊C4C2212yescomplemented
28C22×Dic11⋊C4C2212yescomplemented
29C22×Dic11⋊C4C2212yescomplemented
30C2×#66931—216no—
31C2×#66931C22116yescomplemented
32C11×#379C2218yes—
33C2×C11⋊#95C2211yescharacteristic, complemented
34C2×C11⋊#95C2212yescomplemented
35C2×C11⋊#95C2211yescharacteristic, complemented
36C2×C11⋊#95C2212yescomplemented
37#10622563C22116yescomplemented
38#10622562C2218yescomplemented
39#10622561C22116yescomplemented
40#10622560C2218yescomplemented
41#10622559C22116yescomplemented
42#10622555C22116yescomplemented
43C25×C11—28no—
44C25×C11—28no—
45C25×C11—42no—
46C25×C11—42no—
47C25×C11Q818yescomplemented
48C25×C11C2311yescharacteristic
49C25×C11C2314yes—
50C25×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—28no—
55C23×Dic11—28no—
56C23×Dic11—28no—
57C23×Dic11—28no—
58C23×Dic11—44no—
59C23×Dic11—44no—
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2318yes—
63C23×Dic11C2318yes—
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C22×Dic22—28no—
67C22×Dic22—42no—
68C22×Dic22C2314yescomplemented
69C2×C11×C22⋊C4—28no—
70C2×C11×C22⋊C4—28no—
71C2×C11×C22⋊C4—42no—
72C2×C11×C22⋊C4—42no—
73C2×C11×C22⋊C4C2318yes—
74C2×C11×C22⋊C4C2318yes—
75C2×C11×C22⋊C4C2314yes—
76C2×C11×C22⋊C4C2314yes—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11—28no—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11—264no—
81C2×C22⋊Dic11D4116yes—
82C2×C22⋊Dic11C2318yes—
83C2×C22⋊Dic11C2318yes—
84C2×C22⋊Dic11C2318yes—
85C2×C22⋊Dic11C2318yes—
86C2×C4⋊Dic11—28no—
87C2×C4⋊Dic11—42no—
88C2×C4⋊Dic11C2318yescomplemented
89C2×C4⋊Dic11C2314yescomplemented
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4C2318yescomplemented
94C2×Dic11⋊C4C2318yescomplemented
95C2×Dic11⋊C4C2318yescomplemented
96#66931—264no—
97C11⋊#95C2314yescomplemented
98C11⋊#95C2318yescomplemented
99C11⋊#95C2314yescomplemented
100C11⋊#95C2318yescomplemented
101C2×#2437—111nomaximal, Sylow
102C24×C11—24no—
103C24×C11—24no—
104C24×C11—24no—
105C24×C11—24no—
106C24×C11—264no—
107C24×C11—216no—
108C24×C11—24no—
109C24×C11—216no—
110C24×C11—24no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—416no—
114C24×C11—44no—
115C24×C11—44no—
116C24×C11—416no—
117C24×C11—432no—
118C24×C11—416no—
119C24×C11C2×D418yes—
120C24×C11C2×Q814yes—
121C24×C11C2×Q818yes—
122C24×C11C2×Q8116yescomplemented
123C24×C11#4118yes—
124C24×C11C2412yes—
125C24×C11C2414yes—
126C24×C11C2411yescharacteristic
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11C2412yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2412yes—
137C22×Dic11—216no—
138C22×Dic11—216no—
139C22×Dic11—24no—
140C22×Dic11—216no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—216no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—48no—
152C22×Dic11—48no—
153C22×Dic11—432no—
154C22×Dic11—432no—
155C22×Dic11C2×D418yes—
156C22×Dic11C2×D418yes—
157C22×Dic11C2414yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C2×Dic22—216no—
162C2×Dic22—44no—
163C2×Dic22—416no—
164C11×C22⋊C4—216no—
165C11×C22⋊C4—216no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4—44no—
168C22⋊Dic11—216no—
169C22⋊Dic11—216no—
170C22⋊Dic11—216no—
171C22⋊Dic11C2×D4132yes—
172C4⋊Dic11—216no—
173C4⋊Dic11—44no—
174Dic11⋊C4—216no—
175Dic11⋊C4—216no—
176Dic11⋊C4—48no—
177C22×C22⋊Q8—112no—
178C23×C22⋊C4—112no—
179#2437—1116no—
180C2×#399—111no—
181C2×#396—112no—
182C2×#393—111no—
183C2×#385—112no—
184C2×#385—112no—
185C2×#380—112no—
186C2×#379D1111yescharacteristic
187C23×C11—216no—
188C23×C11—216no—
189C23×C11—216no—
190C23×C11—216no—
191C23×C11—216no—
192C23×C11—216no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—216no—
198C23×C11—264no—
199C23×C11—28no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—416no—
205C23×C11—4128no—
206C23×C11—416no—
207C23×C11—432no—
208C23×C11—416no—
209C23×C11—44no—
210C23×C11—48no—
211C23×C11—44no—
212C23×C11C22⋊Q8132yescomplemented
213C23×C11C22×D418yes—
214C23×C11C22×D414yes—
215C23×C11C22×Q814yes—
216C23×C11C22×Q818yes—
217C23×C11C22×Q812yes—
218C23×C11C2×#4118yes—
219C23×C11C2×#4114yes—
220C23×C11H(5,𝔽2)12yes—
221C23×C11H(5,𝔽2)12yes—
222C23×C11C2511yescharacteristic
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—44no—
231C2×C4×C11—48no—
232C2×C4×C11—44no—
233C2×Dic11—216no—
234C2×Dic11—216no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—432no—
246C2×Dic11—432no—
247C2×Dic11—48no—
248C2×Dic11—48no—
249C2×Dic11C22×D418yes—
250C2×Dic11C22×D418yes—
251Dic22—416no—
252C26C2×D1111yescharacteristic
253C23×Q8—111no—
254C24×C4—112no—
255C24×C4—112no—
256C2×C22⋊Q8—1116no—
257C2×C22⋊Q8—2216no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4—112no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4—112no—
262C22×C4⋊C4—111no—
263C22×C22⋊C4—112no—
264C22×C22⋊C4—112no—
265C22×C22⋊C4—112no—
266C22×C22⋊C4—1116no—
267C22×C22⋊C4—112no—
268C22×C22⋊C4—2216no—
269C22×C22⋊C4C2×D1112yes—
270C22×C22⋊C4C2×D1112yes—
271C22×C22⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4C2×D1111yescharacteristic
273#399—118no—
274#396—1116no—
275#393—118no—
276#385—1116no—
277#385—1116no—
278#380—1116no—
279#379C2×D1118yes—
280C2×#95—111no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—111no—
284C22×C11—28no—
285C22×C11—28no—
286C22×C11—264no—
287C22×C11—28no—
288C22×C11—28no—
289C22×C11—28no—
290C22×C11—28no—
291C22×C11—28no—
292C22×C11—24no—
293C22×C11—464no—
294C22×C11—416no—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11—42no—
298C22×C11C2×C22⋊Q818yes—
299C22×C11C2×C22⋊Q8116yescomplemented
300C22×C11#54314yes—
301C22×C11D4214yes—
302C22×C11#54618yes—
303C22×C11#55114yes—
304C22×C11C23×D412yes—
305C22×C11C23×Q811yescharacteristic
306C22×C11C22×#4112yes—
307C22×C11C2×H(5,𝔽2)11yescharacteristic
308C22×C11C2×H(5,𝔽2)11yescharacteristic
309C4×C11—42no—
310C4×C11—44no—
311C4×C11—42no—
312Dic11—28no—
313Dic11—28no—
314Dic11—44no—
315Dic11—44no—
316C25—28no—
317C25—28no—
318C25—42no—
319C25—42no—
320C25Dic2218yescomplemented
321C25C22×D1111yescharacteristic
322C25C22×D1114yes—
323C25C22×D1112yes—
324C22×Q8—114no—
325C22×Q8—228no—
326C22×Q8—442no—
327C23×C4—112no—
328C23×C4—112no—
329C23×C4—112no—
330C23×C4—112no—
331C23×C4—118no—
332C23×C4—118no—
333C23×C4—228no—
334C23×C4—228no—
335C23×C4—228no—
336C23×C4—228no—
337C23×C4—444no—
338C23×C4—444no—
339C23×C4C22×D1112yes—
340C23×C4C22×D1111yescharacteristic
341C23×C4C22×D1111yescharacteristic
342C22⋊Q8—2264no—
343C2×C4⋊C4—118no—
344C2×C4⋊C4—118no—
345C2×C4⋊C4—118no—
346C2×C4⋊C4—118no—
347C2×C4⋊C4—114no—
348C2×C4⋊C4—228no—
349C2×C4⋊C4—228no—
350C2×C4⋊C4—228no—
351C2×C4⋊C4—444no—
352C2×C4⋊C4—442no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—1116no—
358C2×C22⋊C4—118no—
359C2×C22⋊C4—118no—
360C2×C22⋊C4—118no—
361C2×C22⋊C4—118no—
362C2×C22⋊C4—2264no—
363C2×C22⋊C4—228no—
364C2×C22⋊C4—228no—
365C2×C22⋊C4—228no—
366C2×C22⋊C4C22×D1118yes—
367C2×C22⋊C4C22×D1118yes—
368C2×C22⋊C4C22×D1114yes—
369C2×C22⋊C4C22×D1114yes—
370#95—114no—
371#95—118no—
372#95—118no—
373#95—114no—
374C2×C11—216no—
375C2×C11—44no—
376C2×C11#243718yescomplemented
377C2×C11C22×C22⋊Q812yes—
378C2×C11C2×#54311yescharacteristic
379C2×C11C2×D4211yescharacteristic
380C2×C11C2×#54612yes—
381C2×C11C2×#55111yescharacteristic
382C24—24no—
383C24—24no—
384C24—24no—
385C24—24no—
386C24—264no—
387C24—216no—
388C24—24no—
389C24—216no—
390C24—24no—
391C24—22no—
392C24—22no—
393C24—44no—
394C24—44no—
395C24—416no—
396C24—416no—
397C24—416no—
398C24—432no—
399C24C2×Dic2214yes—
400C24C2×Dic2218yes—
401C24C2×Dic22116yescomplemented
402C24D4×D1118yes—
403C24#434118yes—
404C24C23×D1112yes—
405C24C23×D1114yes—
406C24C23×D1111yescharacteristic
407C2×Q8—2216no—
408C2×Q8—444no—
409C2×Q8—4416no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—118no—
418C22×C4—118no—
419C22×C4—114no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—114no—
423C22×C4—2216no—
424C22×C4—2216no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—2216no—
433C22×C4—2216no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—448no—
438C22×C4—448no—
439C22×C4—4432no—
440C22×C4—4432no—
441C22×C4C23×D1112yes—
442C22×C4C23×D1114yes—
443C22×C4C23×D1112yes—
444C4⋊C4—2216no—
445C4⋊C4—2216no—
446C4⋊C4—2216no—
447C4⋊C4—448no—
448C4⋊C4—444no—
449C22⋊C4—216no—
450C22⋊C4—216no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—1132no—
454C22⋊C4—2216no—
455C22⋊C4—2216no—
456C22⋊C4—2216no—
457C11C2×#243711yescharacteristic, complemented, Sylow
458C23—216no—
459C23—216no—
460C23—216no—
461C23—216no—
462C23—216no—
463C23—216no—
464C23—24no—
465C23—24no—
466C23—24no—
467C23—24no—
468C23—216no—
469C23—264no—
470C23—28no—
471C23—24no—
472C23—24no—
473C23—22no—
474C23—22no—
475C23—416no—
476C23—416no—
477C23—4128no—
478C23—416no—
479C23—432no—
480C23—44no—
481C23—44no—
482C23—48no—
483C23#66931132yescomplemented
484C23C22×Dic2214yes—
485C23C22×Dic2218yes—
486C23C22×Dic2212yes—
487C23C2×D4×D1118yes—
488C23C2×D4×D1114yes—
489C23C2×#434118yes—
490C23C2×#434114yes—
491C23#6703712yes—
492C23#6703712yes—
493C23C24×D1111yescharacteristic
494Q8—4416no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—48no—
505C2×C4—118no—
506C2×C4—118no—
507C2×C4—2216no—
508C2×C4—2216no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—4432no—
520C2×C4—4432no—
521C2×C4—448no—
522C2×C4—448no—
523C22—28no—
524C22—264no—
525C22—28no—
526C22—28no—
527C22—28no—
528C22—28no—
529C22—28no—
530C22—24no—
531C22—28no—
532C22—464no—
533C22—42no—
534C22—416no—
535C22—42no—
536C22—44no—
537C22C2×#6693118yes—
538C22C2×#66931116yescomplemented
539C22#1062301414yes—
540C22#1062311814yes—
541C22#1062312114yes—
542C22#1062312218yes—
543C22C23×Dic2211yescharacteristic
544C22C22×D4×D1112yes—
545C22C22×#434112yes—
546C22C2×#6703711yescharacteristic
547C22C2×#6703711yescharacteristic
548C4—42no—
549C4—42no—
550C4—44no—
551C4—228no—
552C4—228no—
553C4—444no—
554C4—444no—
555C2—216no—
556C2—44no—
557C2#1307228218yesdirect product factor
558C2C22×#6693112yes—
559C2C2×#1062301411yescharacteristic
560C2C2×#1062312111yescharacteristic
561C2C2×#1062312212yes—
562C2C2×#1062311811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#379C2
socleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11C2×#2437
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#66931C2semidirect
3. #13072282C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622560C2semidirect
7. C2×#10622563C2semidirect
8. C2×#10622559C2semidirect
9. C2×#10622555C2semidirect
14. C23×Dic22C22semidirect
25. C22×C4⋊Dic11C22semidirect
26. C22×C4⋊Dic11C22semidirect
27. C22×Dic11⋊C4C22semidirect
28. C22×Dic11⋊C4C22semidirect
29. C22×Dic11⋊C4C22semidirect
31. C2×#66931C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. #10622563C22semidirect
38. #10622562C22semidirect
39. #10622561C22semidirect
40. #10622560C22semidirect
41. #10622559C22semidirect
42. #10622555C22semidirect
47. C25×C11Q8semidirect
68. C22×Dic22C23semidirect
88. C2×C4⋊Dic11C23semidirect
89. C2×C4⋊Dic11C23semidirect
93. C2×Dic11⋊C4C23semidirect
94. C2×Dic11⋊C4C23semidirect
95. C2×Dic11⋊C4C23semidirect
97. C11⋊#95C23semidirect
98. C11⋊#95C23semidirect
99. C11⋊#95C23semidirect
100. C11⋊#95C23semidirect
122. C24×C11C2×Q8semidirect
212. C23×C11C22⋊Q8semidirect
299. C22×C11C2×C22⋊Q8semidirect
320. C25Dic22semidirect
376. C2×C11#2437semidirect
401. C24C2×Dic22semidirect
457. C11C2×#2437semidirect
483. C23#66931semidirect
538. C22C2×#66931semidirect
557. C2#13072282direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C23×C22⋊Dic112
#130722822
C2×#106225622
C2×#106225612
C2×#106225602
C2×#106225632
C2×#106225592
C2×#106225552
C2×C11×#3792
C2×#243711