Finite Group Databasebeta

← C2×#13071223 #14912366

Subgroups — C2×#13071223 #14912366

Order 2816.

2678 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic
2#13071223C2116yesmaximal, direct product factor
3C2×#10622558C212yesmaximal
4C2×#10622557C212yesmaximal
5C2×#10622266C212yesmaximal, complemented
6C2×#10622267C212yesmaximal, complemented
7C2×#10622589C211yesmaximal, characteristic, complemented
8C2×#10622590C211yesmaximal, characteristic, complemented
9C2×#10622825C211yesmaximal, characteristic
10C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#380C211yesmaximal, characteristic
13C24×C4×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C2×#66979C4116yescomplemented
21C2×#66979C2218yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C11×#380C2218yes—
33C2×C11×#95C2212yes—
34#10622825C2218yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622590C2218yescomplemented
41#10622589C2218yescomplemented
42C4⋊C4×Dic11C2218yescomplemented
43C4⋊C4×Dic11C2218yescomplemented
44#10622558C22116yes—
45#10622557C22116yes—
46#10622267C22116yescomplemented
47#10622266C22116yescomplemented
48C25×C11C2311yescharacteristic
49C23×C4×C11—24no—
50C23×C4×C11—24no—
51C23×C4×C11C2×C418yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C4⋊C4C2314yes—
67C2×C11×C22⋊C4—44no—
68C2×C11×C22⋊C4C2318yes—
69C2×C22⋊Dic11—44no—
70C2×C22⋊Dic11C2×C418yes—
71C2×C22⋊Dic11C2×C418yes—
72C2×C22⋊Dic11C2318yes—
73C2×C22⋊Dic11C2314yes—
74C2×C22⋊Dic11C2314yes—
75#66979C2×C4164yescomplemented
76C2×C4⋊Dic11—24no—
77C2×C4⋊Dic11—24no—
78C2×C4⋊Dic11C2×C418yes—
79C2×C4⋊Dic11C2×C418yes—
80C2×C4⋊Dic11C2314yes—
81C2×C4⋊Dic11C2314yes—
82C2×C4⋊Dic11C2314yes—
83C2×C4⋊Dic11C2314yes—
84C2×Dic11⋊C4—44no—
85C2×Dic11⋊C4—44no—
86C2×Dic11⋊C4C2318yes—
87C2×Dic11⋊C4C2318yes—
88C2×C4×Dic11—44no—
89C2×C4×Dic11—44no—
90C2×C4×Dic11C2×C418yes—
91C2×C4×Dic11C2×C418yes—
92C2×C4×Dic11C2318yes—
93C2×C4×Dic11C2318yes—
94C2×C4×Dic11C2314yes—
95C2×C4×Dic11C2314yes—
96C11×#95C2318yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C2×#2314—111nomaximal, Sylow
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11C22×C414yes—
110C24×C11C2412yes—
111C24×C11C2411yescharacteristic
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—232no—
115C22×C4×C11—28no—
116C22×C4×C11—28no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11C22×C414yes—
124C22×C4×C11C22×C4116yes—
125C22×C4×C11C22×C414yes—
126C22×C4×C11#4114yes—
127C22×C4×C11#4114yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2414yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2412yes—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11C22×C414yes—
147C22×Dic11C22×C414yes—
148C22×Dic11C22×C414yes—
149C22×Dic11C22×C414yes—
150C22×Dic11C2414yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—28no—
158C11×C22⋊C4—48no—
159C22⋊Dic11—48no—
160C22⋊Dic11C22×C4116yes—
161C22⋊Dic11C22×C4116yes—
162C4⋊Dic11—28no—
163C4⋊Dic11—28no—
164C4⋊Dic11C22×C4116yes—
165C4⋊Dic11C22×C4116yes—
166Dic11⋊C4—48no—
167Dic11⋊C4—48no—
168C4×Dic11—48no—
169C4×Dic11—48no—
170C4×Dic11C22×C4116yes—
171C4×Dic11C22×C4116yes—
172C22×#117—111no—
173#2314—1116no—
174C2×#388—112no—
175C2×#388—112no—
176C2×#387—112no—
177C2×#387—112no—
178C2×#384—111no—
179C2×#382—111no—
180C2×#380—111no—
181C2×#380D1111yescharacteristic
182C2×C4×C4⋊C4—111no—
183C2×C4×C4⋊C4—111no—
184C23×C11—28no—
185C23×C11—28no—
186C23×C11—28no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—44no—
197C23×C11C23×C414yes—
198C23×C11C23×C412yes—
199C23×C11C2×#4112yes—
200C23×C11C2×#4112yes—
201C23×C11H(5,𝔽2)12yes—
202C23×C11H(5,𝔽2)12yes—
203C23×C112−1+412yes—
204C23×C112−1+412yes—
205C23×C11C2511yescharacteristic
206C2×C4×C11—28no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—232no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—48no—
217C2×C4×C11—48no—
218C2×C4×C11#117116yes—
219C2×C4×C11C23×C414yes—
220C2×C4×C11C23×C414yes—
221C2×C4×C11C2×#4114yes—
222C2×C4×C11C2×#4114yes—
223C2×Dic11—28no—
224C2×Dic11—28no—
225C2×Dic11—28no—
226C2×Dic11—28no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—48no—
242C2×Dic11—48no—
243C2×Dic11C23×C414yes—
244C2×Dic11C23×C414yes—
245C2×Dic11C23×C414yes—
246C2×Dic11C23×C414yes—
247C24×C4C2×D1111yescharacteristic
248C2×#117—118no—
249C2×#117—1116no—
250C22×C4⋊C4—111no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4—111no—
254C22×C4⋊C4—112no—
255C22×C4⋊C4—112no—
256C22×C4⋊C4C2×D1111yescharacteristic
257C22×C4⋊C4C2×D1111yescharacteristic
258C22×C22⋊C4—111no—
259C22×C22⋊C4—111no—
260C22×C22⋊C4—112no—
261C22×C22⋊C4C2×D1112yes—
262C22×C42—111no—
263C22×C42—111no—
264C22×C42—112no—
265C22×C42—112no—
266#388—1116no—
267#388—1116no—
268#387—1116no—
269#387—1116no—
270#384—118no—
271#382—118no—
272#380—118no—
273#380C2×D1118yes—
274C4×C4⋊C4—118no—
275C4×C4⋊C4—118no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95—112no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95C2×D1112yes—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—416no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11C2×#11714yes—
291C22×C11#52014yes—
292C22×C11#52014yes—
293C22×C11#54014yes—
294C22×C11#54114yes—
295C22×C11#54214yes—
296C22×C11#54214yes—
297C22×C11C24×C411yescharacteristic
298C22×C11C22×#4111yescharacteristic
299C22×C11C22×#4111yescharacteristic
300C22×C11C2×H(5,𝔽2)11yescharacteristic
301C22×C11C2×H(5,𝔽2)11yescharacteristic
302C22×C11C2×2−1+411yescharacteristic
303C22×C11C2×2−1+411yescharacteristic
304C4×C11—24no—
305C4×C11—44no—
306C4×C11—44no—
307C4×C11C2×#11718yes—
308Dic11—24no—
309Dic11—24no—
310Dic11—24no—
311Dic11—24no—
312Dic11—44no—
313Dic11—44no—
314C25C22×D1111yescharacteristic
315C23×C4—24no—
316C23×C4—24no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—111no—
321C23×C4—112no—
322C23×C4—112no—
323C23×C4C4×D1118yes—
324C23×C4C22×D1112yes—
325C23×C4C22×D1112yes—
326C23×C4C22×D1114yes—
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1111yescharacteristic
329#117—1164no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—118no—
333C2×C4⋊C4—118no—
334C2×C4⋊C4—114no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—114no—
337C2×C4⋊C4—114no—
338C2×C4⋊C4—118no—
339C2×C4⋊C4—118no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4—444no—
343C2×C4⋊C4—444no—
344C2×C4⋊C4C22×D1114yes—
345C2×C4⋊C4C22×D1114yes—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—118no—
348C2×C22⋊C4—118no—
349C2×C22⋊C4—114no—
350C2×C22⋊C4—114no—
351C2×C22⋊C4—118no—
352C2×C22⋊C4—444no—
353C2×C22⋊C4C22×D1118yes—
354C2×C42—118no—
355C2×C42—118no—
356C2×C42—114no—
357C2×C42—114no—
358C2×C42—118no—
359C2×C42—118no—
360C2×C42—444no—
361C2×C42—444no—
362#95—118no—
363#95—118no—
364#95—118no—
365#95—118no—
366#95—118no—
367#95C22×D1118yes—
368C2×C11—44no—
369C2×C11#231418yescomplemented
370C2×C11C22×#11711yescharacteristic
371C2×C11C2×#52011yescharacteristic
372C2×C11C2×#52011yescharacteristic
373C2×C11C2×#54011yescharacteristic
374C2×C11C2×#54111yescharacteristic
375C2×C11C2×#54211yescharacteristic
376C2×C11C2×#54211yescharacteristic
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24C2×C4×D1114yes—
384C24C23×D1112yes—
385C24C23×D1111yescharacteristic
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—232no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—114no—
398C22×C4—114no—
399C22×C4—114no—
400C22×C4—114no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—114no—
406C22×C4—114no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
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—224no—
420C22×C4—224no—
421C22×C4C2×C4×D1114yes—
422C22×C4C2×C4×D11116yes—
423C22×C4C2×C4×D1114yes—
424C22×C4#434114yes—
425C22×C4#434114yes—
426C22×C4C23×D1114yes—
427C22×C4C23×D1114yes—
428C22×C4C23×D1112yes—
429C22×C4C23×D1112yes—
430C4⋊C4—28no—
431C4⋊C4—28no—
432C4⋊C4—1116no—
433C4⋊C4—1116no—
434C4⋊C4—228no—
435C4⋊C4—228no—
436C4⋊C4—448no—
437C4⋊C4—448no—
438C22⋊C4—48no—
439C22⋊C4—1116no—
440C22⋊C4—1116no—
441C22⋊C4—448no—
442C42—1116no—
443C42—1116no—
444C42—448no—
445C42—448no—
446C11C2×#231411yescharacteristic, complemented, Sylow
447C23—28no—
448C23—28no—
449C23—28no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—44no—
457C23—44no—
458C23—44no—
459C23—44no—
460C23C22×C4×D1114yes—
461C23C22×C4×D1112yes—
462C23C2×#434112yes—
463C23C2×#434112yes—
464C23#6703712yes—
465C23#6704012yes—
466C23#6704212yes—
467C23#6704312yes—
468C23C24×D1111yescharacteristic
469C2×C4—28no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—232no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—48no—
480C2×C4—48no—
481C2×C4—114no—
482C2×C4—114no—
483C2×C4—114no—
484C2×C4—114no—
485C2×C4—228no—
486C2×C4—228no—
487C2×C4—228no—
488C2×C4—228no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—448no—
504C2×C4—448no—
505C2×C4#66930116yes—
506C2×C4C22×C4×D1114yes—
507C2×C4C22×C4×D1114yes—
508C2×C4C2×#434114yes—
509C2×C4C2×#434114yes—
510C22—24no—
511C22—24no—
512C22—24no—
513C22—42no—
514C22—416no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22C2×#6693014yes—
519C22#1062303514yes—
520C22#1062305414yes—
521C22#1062313414yes—
522C22#1062315014yes—
523C22#1062315614yes—
524C22#1062317414yes—
525C22C23×C4×D1111yescharacteristic
526C22C22×#434111yescharacteristic
527C22C22×#434111yescharacteristic
528C22C2×#6703711yescharacteristic
529C22C2×#6704011yescharacteristic
530C22C2×#6704211yescharacteristic
531C22C2×#6704311yescharacteristic
532C4—24no—
533C4—44no—
534C4—44no—
535C4—224no—
536C4—224no—
537C4—224no—
538C4—224no—
539C4—444no—
540C4—444no—
541C4C2×#6693018yes—
542C2—44no—
543C2#1307122318yesdirect product factor
544C2C22×#6693011yescharacteristic
545C2C2×#1062305411yescharacteristic
546C2C2×#1062303511yescharacteristic
547C2C2×#1062315011yescharacteristic
548C2C2×#1062315611yescharacteristic
549C2C2×#1062313411yescharacteristic
550C2C2×#1062317411yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC2×#380D11
hypocenterC11C2×#2314
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13071223C2direct (N × H)
5. C2×#10622266C2semidirect
6. C2×#10622267C2semidirect
7. C2×#10622589C2semidirect
8. C2×#10622590C2semidirect
10. C2×C4⋊C4×Dic11C2semidirect
11. C2×C4⋊C4×Dic11C2semidirect
20. C2×#66979C4semidirect
40. #10622590C22semidirect
41. #10622589C22semidirect
42. C4⋊C4×Dic11C22semidirect
43. C4⋊C4×Dic11C22semidirect
46. #10622267C22semidirect
47. #10622266C22semidirect
75. #66979C2×C4semidirect
369. C2×C11#2314semidirect
446. C11C2×#2314semidirect
543. C2#13071223direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669792
#130712232
C2×#106225582
C2×#106225572
C2×#106222662
C2×#106222672
C2×#106225892
C2×#106225902
C2×#106228252
C2×C4⋊C4×Dic112
C2×C11×#3802
C2×#231411