Finite Group Databasebeta

← C2×#13073204 #14922913

Subgroups — C2×#13073204 #14922913

Order 2816.

2726 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66932C212yesmaximal, complemented
2#13073204C2116yesmaximal, direct product factor
3C2×#10622566C212yesmaximal, complemented
4C2×#10622561C212yesmaximal, complemented
5C2×#10622834C211yesmaximal, characteristic
6C2×#10622834C211yesmaximal, characteristic
7C2×#10622586C211yesmaximal, characteristic, complemented
8C2×#10622564C212yesmaximal, complemented
9C2×#10622548C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
11C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
12C2×C11×#390C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C2×#66932—216no—
33C2×#66932C22116yescomplemented
34C11×#390C2218yes—
35#10622834C2218yes—
36#10622834C2218yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C4⋊C4×Dic11C2218yescomplemented
42#10622586C2218yescomplemented
43#10622566C22116yescomplemented
44#10622564C22116yescomplemented
45#10622561C22116yescomplemented
46#10622548C2218yescomplemented
47C4×Dic11⋊C4C2218yescomplemented
48C25×C11C2312yes—
49C22×D4×C11—24no—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11C2314yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C22⋊C4—28no—
66C2×C11×C22⋊C4—28no—
67C2×C11×C22⋊C4C2318yes—
68C2×C11×C22⋊C4C2318yes—
69C2×C42×C11—24no—
70C2×C42×C11C2314yes—
71C2×C22⋊Dic11—28no—
72C2×C22⋊Dic11—28no—
73C2×C22⋊Dic11—44no—
74C2×C22⋊Dic11—44no—
75C2×C22⋊Dic11C2318yes—
76C2×C22⋊Dic11C2318yes—
77C2×C22⋊Dic11C2318yes—
78C2×C22⋊Dic11C2318yes—
79C2×C4⋊Dic11—28no—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—44no—
83C2×C4⋊Dic11C2318yes—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2314yes—
86C2×C4⋊Dic11C2318yes—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—28no—
89C2×Dic11⋊C4D418yescomplemented
90C2×Dic11⋊C4C2318yes—
91C2×Dic11⋊C4C2314yes—
92C2×Dic11⋊C4C2314yes—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—28no—
96C2×C4×Dic11C2318yes—
97C2×C4×Dic11C2314yes—
98C2×C4×Dic11C2314yes—
99#66932—264no—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C2×#2512—111nomaximal, Sylow
105C24×C11—24no—
106C24×C11—24no—
107C24×C11—24no—
108C24×C11—24no—
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11C2414yes—
113C24×C11C2411yescharacteristic
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—28no—
117C2×D4×C11—416no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11C2×D414yes—
126C22×C4×C11#4114yes—
127C22×C4×C11#4114yes—
128C22×C4×C11#4114yes—
129C22×C4×C11#4114yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2412yes—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11C2×D414yes—
151C22×Dic11C2×D414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C22×Dic11C2414yes—
155C22×Dic11C2414yes—
156C22×Dic11C2412yes—
157C22×Dic11C2412yes—
158C11×C4⋊C4—28no—
159C11×C22⋊C4—216no—
160C11×C22⋊C4—216no—
161C42×C11—28no—
162C22⋊Dic11—216no—
163C22⋊Dic11—216no—
164C22⋊Dic11—48no—
165C22⋊Dic11—48no—
166C4⋊Dic11—216no—
167C4⋊Dic11—28no—
168C4⋊Dic11—28no—
169C4⋊Dic11—48no—
170Dic11⋊C4—216no—
171Dic11⋊C4—28no—
172Dic11⋊C4C2×D4116yescomplemented
173C4×Dic11—216no—
174C4×Dic11—28no—
175C4×Dic11—28no—
176C22×#126—112no—
177#2512—1116no—
178C2×#397—112no—
179C2×#396—112no—
180C2×#390—111no—
181C2×#390—111no—
182C2×#390D1111yescharacteristic
183C2×#389—111no—
184C2×#388—112no—
185C2×#384—111no—
186C2×C4×C4⋊C4—111no—
187C2×C4×C4⋊C4—111no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—48no—
196C23×C11—48no—
197C23×C11—48no—
198C23×C11—48no—
199C23×C11—48no—
200C23×C11—48no—
201C23×C11—48no—
202C23×C11C22×D412yes—
203C23×C11C2×#4112yes—
204C23×C11C2×#4112yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4112yes—
207C23×C11H(5,𝔽2)12yes—
208C23×C112−1+412yes—
209C23×C11C2511yescharacteristic
210D4×C11—416no—
211C2×C4×C11—28no—
212C2×C4×C11—28no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—48no—
221C2×C4×C11#126116yescomplemented
222C2×C4×C11C22×D414yes—
223C2×C4×C11C2×#4114yes—
224C2×C4×C11C2×#4114yes—
225C2×C4×C11C2×#4114yes—
226C2×C4×C11C2×#4114yes—
227C2×Dic11—28no—
228C2×Dic11—28no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—44no—
246C2×Dic11—48no—
247C2×Dic11—48no—
248C2×Dic11—44no—
249C2×Dic11C22×D414yes—
250C2×Dic11C22×D414yes—
251C23×D4C2×D1111yescharacteristic
252C2×#126—1116no—
253C2×#126—2216no—
254C22×C4⋊C4—111no—
255C22×C4⋊C4—111no—
256C22×C4⋊C4—112no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4—111no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C22⋊C4—112no—
263C22×C22⋊C4—112no—
264C22×C22⋊C4—112no—
265C22×C22⋊C4—112no—
266C22×C22⋊C4C2×D1112yes—
267C22×C22⋊C4C2×D1112yes—
268C22×C42—112no—
269C22×C42—111no—
270C22×C42—111no—
271C22×C42C2×D1111yescharacteristic
272#397—1116no—
273#396—1116no—
274#390—118no—
275#390—118no—
276#390C2×D1118yes—
277#389—118no—
278#388—1116no—
279#384—118no—
280C4×C4⋊C4—118no—
281C4×C4⋊C4—118no—
282C2×#95—112no—
283C2×#95—111no—
284C2×#95—112no—
285C2×#95—111no—
286C22×C11—44no—
287C22×C11—44no—
288C22×C11—44no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—816no—
294C22×C11C2×#12614yes—
295C22×C11#53214yes—
296C22×C11#54214yes—
297C22×C11#54714yes—
298C22×C11#55014yes—
299C22×C11#55314yes—
300C22×C11#55614yes—
301C22×C11C23×D411yescharacteristic
302C22×C11C22×#4111yescharacteristic
303C22×C11C22×#4111yescharacteristic
304C22×C11C22×#4111yescharacteristic
305C22×C11C22×#4111yescharacteristic
306C22×C11C2×H(5,𝔽2)11yescharacteristic
307C22×C11C2×2−1+411yescharacteristic
308C4×C11—24no—
309C4×C11—24no—
310C4×C11—44no—
311C4×C11C2×#12618yescomplemented
312Dic11—24no—
313Dic11—24no—
314Dic11—42no—
315Dic11—44no—
316Dic11—44no—
317Dic11—42no—
318C25C22×D1112yes—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—24no—
322C22×D4C22×D1114yes—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—112no—
326C23×C4—112no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4C22×D1112yes—
330C23×C4C22×D1111yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C23×C4C22×D1111yescharacteristic
333#126—2264no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—118no—
336C2×C4⋊C4—114no—
337C2×C4⋊C4—118no—
338C2×C4⋊C4—118no—
339C2×C4⋊C4—114no—
340C2×C4⋊C4—114no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—118no—
343C2×C4⋊C4—228no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—228no—
347C2×C4⋊C4—224no—
348C2×C4⋊C4—444no—
349C2×C4⋊C4C22×D1114yes—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—118no—
353C2×C22⋊C4—118no—
354C2×C22⋊C4—118no—
355C2×C22⋊C4—118no—
356C2×C22⋊C4—228no—
357C2×C22⋊C4—228no—
358C2×C22⋊C4—444no—
359C2×C22⋊C4—444no—
360C2×C22⋊C4C22×D1118yes—
361C2×C22⋊C4C22×D1118yes—
362C2×C42—24no—
363C2×C42—118no—
364C2×C42—114no—
365C2×C42—114no—
366C2×C42—228no—
367C2×C42—224no—
368C2×C42—224no—
369C2×C42C22×D1114yes—
370#95—114no—
371#95—118no—
372#95—114no—
373#95—118no—
374C2×C11—84no—
375C2×C11#251218yescomplemented
376C2×C11C22×#12611yescharacteristic
377C2×C11C2×#53211yescharacteristic
378C2×C11C2×#54211yescharacteristic
379C2×C11C2×#54711yescharacteristic
380C2×C11C2×#55011yescharacteristic
381C2×C11C2×#55311yescharacteristic
382C2×C11C2×#55611yescharacteristic
383C24—24no—
384C24—24no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24—24no—
389C24—24no—
390C24C23×D1114yes—
391C24C23×D1111yescharacteristic
392C2×D4—28no—
393C2×D4—28no—
394C2×D4—28no—
395C2×D4—416no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—114no—
404C22×C4—114no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—112no—
409C22×C4—114no—
410C22×C4—114no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—222no—
427C22×C4#433914yes—
428C22×C4D4×D1114yes—
429C22×C4#434114yes—
430C22×C4#434114yes—
431C22×C4#434114yes—
432C22×C4C23×D1114yes—
433C22×C4C23×D1112yes—
434C22×C4C23×D1112yes—
435C22×C4C23×D1112yes—
436C4⋊C4—28no—
437C4⋊C4—1116no—
438C4⋊C4—2216no—
439C4⋊C4—228no—
440C4⋊C4—228no—
441C4⋊C4—2216no—
442C4⋊C4—228no—
443C4⋊C4—448no—
444C22⋊C4—216no—
445C22⋊C4—216no—
446C22⋊C4—2216no—
447C22⋊C4—2216no—
448C22⋊C4—448no—
449C22⋊C4—448no—
450C42—28no—
451C42—2216no—
452C42—228no—
453C42—228no—
454C11C2×#251211yescharacteristic, complemented, Sylow
455C23—24no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—48no—
463C23—48no—
464C23—48no—
465C23—48no—
466C23—48no—
467C23—48no—
468C23—48no—
469C23C2×#433912yes—
470C23C2×D4×D1112yes—
471C23C2×#434112yes—
472C23C2×#434112yes—
473C23C2×#434112yes—
474C23#6704212yes—
475C23#6704312yes—
476C23C24×D1111yescharacteristic
477D4—416no—
478C2×C4—28no—
479C2×C4—28no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—48no—
488C2×C4—114no—
489C2×C4—114no—
490C2×C4—228no—
491C2×C4—228no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—448no—
509C2×C4—448no—
510C2×C4—444no—
511C2×C4—444no—
512C2×C4#66932116yescomplemented
513C2×C4C2×#433914yes—
514C2×C4C2×D4×D1114yes—
515C2×C4C2×#434114yes—
516C2×C4C2×#434114yes—
517C2×C4C2×#434114yes—
518C22—44no—
519C22—44no—
520C22—44no—
521C22—44no—
522C22—44no—
523C22—44no—
524C22—44no—
525C22—816no—
526C22C2×#6693214yes—
527C22#1062307314yes—
528C22#1062308414yes—
529C22#1062314214yes—
530C22#1062314914yes—
531C22#1062321314yes—
532C22#1062324714yes—
533C22C22×#433911yescharacteristic
534C22C22×D4×D1111yescharacteristic
535C22C22×#434111yescharacteristic
536C22C22×#434111yescharacteristic
537C22C22×#434111yescharacteristic
538C22C2×#6704211yescharacteristic
539C22C2×#6704311yescharacteristic
540C4—24no—
541C4—24no—
542C4—44no—
543C4—224no—
544C4—224no—
545C4—442no—
546C4—442no—
547C4—444no—
548C4—444no—
549C4C2×#6693218yescomplemented
550C2—84no—
551C2#1307320418yesdirect product factor
552C2C22×#6693211yescharacteristic
553C2C2×#1062324711yescharacteristic
554C2C2×#1062321311yescharacteristic
555C2C2×#1062314211yescharacteristic
556C2C2×#1062308411yescharacteristic
557C2C2×#1062314911yescharacteristic
558C2C2×#1062307311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11C2×#2512
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66932C2semidirect
2. #13073204C2direct (N × H)
3. C2×#10622566C2semidirect
4. C2×#10622561C2semidirect
7. C2×#10622586C2semidirect
8. C2×#10622564C2semidirect
9. C2×#10622548C2semidirect
10. C2×C4⋊C4×Dic11C2semidirect
11. C2×C4×Dic11⋊C4C2semidirect
33. C2×#66932C22semidirect
41. C4⋊C4×Dic11C22semidirect
42. #10622586C22semidirect
43. #10622566C22semidirect
44. #10622564C22semidirect
45. #10622561C22semidirect
46. #10622548C22semidirect
47. C4×Dic11⋊C4C22semidirect
89. C2×Dic11⋊C4D4semidirect
172. Dic11⋊C4C2×D4semidirect
221. C2×C4×C11#126semidirect
311. C4×C11C2×#126semidirect
375. C2×C11#2512semidirect
454. C11C2×#2512semidirect
512. C2×C4#66932semidirect
549. C4C2×#66932semidirect
551. C2#13073204direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
#130732042
C2×#106225662
C2×#106225612
C2×#106228342
C2×#106225862
C2×#106225642
C2×#106225482
C2×C4⋊C4×Dic112
C2×C4×Dic11⋊C42
C2×C11×#3902
C2×#251211