Finite Group Databasebeta

← C2×#13071791 #14916401

Subgroups — C2×#13071791 #14916401

Order 2816.

3798 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2#13071791C2116yesmaximal, direct product factor
3C2×#10622833C211yesmaximal, characteristic, complemented
4C2×#10622826C212yesmaximal, complemented
5C2×#10622278C212yesmaximal, complemented
6C2×#10622571C212yesmaximal, complemented
7C2×#10622569C212yesmaximal, complemented
8C2×#10622569C212yesmaximal, complemented
9C2×#10622264C212yesmaximal, complemented
10C2×C11×#386C211yesmaximal, characteristic, complemented
11C23×D4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C23×C22⋊D11C2212yes—
15C24×Dic11C2211yescharacteristic
16C23×D44C2211yescharacteristic
17C23×C4×D11C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C2×#66993C4116yescomplemented
23C2×#66993C2218yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C11×#386C2218yescomplemented
29C2×C11×#95C2212yes—
30#10622833C2218yescomplemented
31#10622826C22116yescomplemented
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622571C22116yescomplemented
38#10622569C22116yescomplemented
39#10622569C22116yescomplemented
40#10622278C22116yescomplemented
41#10622264C22116yescomplemented
42C25×C11C2311yescharacteristic
43C25×C11C2311yescharacteristic
44C24×D11C2312yes—
45C22×D4×C11—42no—
46C22×D4×C11—42no—
47C22×D4×C11C2×C418yescomplemented
48C22×D4×C11C2314yes—
49C23×C4×C11—42no—
50C23×C4×C11—44no—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2314yes—
55C22×C22⋊D11—44no—
56C22×C22⋊D11—44no—
57C22×C22⋊D11—44no—
58C22×C22⋊D11—44no—
59C22×C22⋊D11C2×C4116yescomplemented
60C22×C22⋊D11C2×C4116yescomplemented
61C22×C22⋊D11C2318yes—
62C22×C22⋊D11C2318yes—
63C23×Dic11—42no—
64C23×Dic11—44no—
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C23×Dic11C2314yes—
69C22×D44—42no—
70C22×D44—42no—
71C22×D44C2×C418yescomplemented
72C22×D44C2314yes—
73C22×C4×D11—44no—
74C22×C4×D11—44no—
75C22×C4×D11—44no—
76C22×C4×D11C2318yes—
77C2×C11×C22⋊C4—42no—
78C2×C11×C22⋊C4—44no—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—42no—
82C2×C22⋊Dic11—44no—
83C2×C22⋊Dic11C2314yes—
84C2×C22⋊Dic11C2318yes—
85#66993C2×C4164yescomplemented
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4×Dic11C2×C418yescomplemented
93C2×C4×Dic11C2314yes—
94C11×#95C2318yes—
95C11⋊#95C2318yes—
96C11⋊#95C2318yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C2×#2380—111nomaximal, Sylow
101C24×C11—24no—
102C24×C11—22no—
103C24×C11—24no—
104C24×C11—22no—
105C24×C11—24no—
106C24×C11—22no—
107C24×C11—24no—
108C24×C11—22no—
109C24×C11C22×C414yes—
110C24×C11C22×C414yes—
111C24×C11C2412yes—
112C24×C11C2412yes—
113C24×C11C2411yescharacteristic
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11C22×C418yes—
121C23×D11C2414yes—
122C2×D4×C11—416no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11C22×C4116yescomplemented
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—44no—
135C22×C4×C11—48no—
136C22×C4×C11—416no—
137C22×C4×C11C22×C414yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C2×C22⋊D11—432no—
142C2×C22⋊D11—432no—
143C2×C22⋊D11—48no—
144C2×C22⋊D11—48no—
145C2×C22⋊D11—48no—
146C2×C22⋊D11—48no—
147C2×C22⋊D11C22×C4132yescomplemented
148C2×C22⋊D11C22×C4132yescomplemented
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—48no—
158C22×Dic11—44no—
159C22×Dic11—416no—
160C22×Dic11C22×C418yes—
161C22×Dic11C2414yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C2×D44—416no—
165C2×D44—44no—
166C2×D44—44no—
167C2×D44C22×C4116yescomplemented
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—48no—
171C2×C4×D11—432no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—48no—
174C22⋊Dic11—48no—
175C22⋊Dic11—44no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179C4×Dic11C22×C4116yescomplemented
180C22×#127—111no—
181#2380—1116no—
182C2×#386—112no—
183C2×#386—111no—
184C2×#386—112no—
185C2×#386—112no—
186C2×#386—112no—
187C2×#386—112no—
188C2×#386D1111yescharacteristic, complemented
189C2×#383—112no—
190C23×C11—216no—
191C23×C11—216no—
192C23×C11—28no—
193C23×C11—28no—
194C23×C11—24no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—44no—
208C23×C11C23×C414yes—
209C23×C11C23×C414yes—
210C23×C11C23×C412yes—
211C23×C11H(5,𝔽2)12yes—
212C23×C11H(5,𝔽2)12yes—
213C23×C11H(5,𝔽2)14yes—
214C23×C11H(5,𝔽2)14yes—
215C23×C11C2511yescharacteristic
216C22×D11—216no—
217C22×D11—216no—
218C22×D11—216no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—48no—
226C22×D11—48no—
227C22×D11—48no—
228C22×D11—48no—
229C22×D11C23×C418yes—
230D4×C11—416no—
231C2×C4×C11—28no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—416no—
241C2×C4×C11—48no—
242C2×C4×C11—48no—
243C2×C4×C11C23×C414yes—
244C22⋊D11—432no—
245C22⋊D11—432no—
246C2×Dic11—216no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—416no—
256C2×Dic11—48no—
257C2×Dic11—48no—
258C2×Dic11C23×C418yes—
259D44—416no—
260C4×D11—432no—
261C23×D4—112no—
262C23×D4—112no—
263C23×D4—111no—
264C23×D4C2×D1111yescharacteristic
265C24×C4—111no—
266C24×C4—112no—
267C24×C4C2×D1111yescharacteristic
268C2×#127—118no—
269C2×#127—1116no—
270C22×C22⋊C4—112no—
271C22×C22⋊C4—111no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4C2×D1112yes—
276C22×C22⋊C4C2×D1111yescharacteristic
277C22×C42—111no—
278#386—118no—
279#386—1116no—
280#386—1116no—
281#386—1116no—
282#386—1116no—
283#386—1116no—
284#386C2×D1118yescomplemented
285#383—1116no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95C2×D1112yes—
292C22×C11—24no—
293C22×C11—24no—
294C22×C11—28no—
295C22×C11—28no—
296C22×C11—416no—
297C22×C11—416no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11#51814yes—
305C22×C11#51818yes—
306C22×C11#56014yes—
307C22×C11#56018yes—
308C22×C11#56014yes—
309C22×C11C24×C411yescharacteristic
310C22×C11C2×H(5,𝔽2)11yescharacteristic
311C22×C11C2×H(5,𝔽2)12yes—
312C22×C11C2×H(5,𝔽2)11yescharacteristic
313C22×C11C2×H(5,𝔽2)12yes—
314C2×D11—28no—
315C2×D11—28no—
316C2×D11—28no—
317C2×D11—432no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—44no—
322C4×C11—24no—
323C4×C11—44no—
324C4×C11—44no—
325Dic11—28no—
326Dic11—44no—
327Dic11—44no—
328C25—112no—
329C25C22×D1111yescharacteristic
330C25C22×D1111yescharacteristic
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—1116no—
334C22×D4—1116no—
335C22×D4—118no—
336C22×D4—118no—
337C22×D4—118no—
338C22×D4—114no—
339C22×D4—442no—
340C22×D4—442no—
341C22×D4—444no—
342C22×D4—444no—
343C22×D4—444no—
344C22×D4—444no—
345C22×D4C4×D1118yescomplemented
346C22×D4C22×D1114yes—
347C23×C4—44no—
348C23×C4—42no—
349C23×C4—112no—
350C23×C4—112no—
351C23×C4—112no—
352C23×C4—114no—
353C23×C4—118no—
354C23×C4—444no—
355C23×C4—444no—
356C23×C4—444no—
357C23×C4—442no—
358C23×C4—444no—
359C23×C4C22×D1112yes—
360C23×C4C22×D1112yes—
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1114yes—
363#127—1164no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—114no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—444no—
372C2×C22⋊C4—444no—
373C2×C22⋊C4—444no—
374C2×C22⋊C4—442no—
375C2×C22⋊C4—444no—
376C2×C22⋊C4C22×D1118yes—
377C2×C22⋊C4C22×D1114yes—
378C2×C42—118no—
379C2×C42—114no—
380#95—118no—
381#95—118no—
382#95—118no—
383#95—118no—
384#95—118no—
385#95C22×D1118yes—
386C2×C11—44no—
387C2×C11—44no—
388C2×C11#238018yescomplemented
389C2×C11C2×#51812yes—
390C2×C11C2×#51811yescharacteristic
391C2×C11C2×#56012yes—
392C2×C11C2×#56011yescharacteristic
393C2×C11C2×#56011yescharacteristic
394D11—48no—
395C24—22no—
396C24—24no—
397C24—22no—
398C24—22no—
399C24—24no—
400C24—22no—
401C24—24no—
402C24—24no—
403C24—118no—
404C24—114no—
405C24—224no—
406C24—224no—
407C24—224no—
408C24—224no—
409C24—224no—
410C24—224no—
411C24C2×C4×D1114yes—
412C24C2×C4×D1114yes—
413C24C23×D1112yes—
414C24C23×D1112yes—
415C24C23×D1111yescharacteristic
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—416no—
419C2×D4—1132no—
420C2×D4—1132no—
421C2×D4—1116no—
422C2×D4—4416no—
423C2×D4—444no—
424C2×D4—444no—
425C2×D4—4432no—
426C2×D4—4432no—
427C2×D4—448no—
428C2×D4—448no—
429C2×D4—448no—
430C2×D4—448no—
431C2×D4C2×C4×D11116yescomplemented
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—48no—
441C22×C4—44no—
442C22×C4—416no—
443C22×C4—118no—
444C22×C4—114no—
445C22×C4—114no—
446C22×C4—114no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—448no—
456C22×C4—448no—
457C22×C4—448no—
458C22×C4—4432no—
459C22×C4—444no—
460C22×C4—448no—
461C22×C4—4416no—
462C22×C4C2×C4×D1114yes—
463C22×C4C23×D1114yes—
464C22×C4C23×D1114yes—
465C22×C4C23×D1112yes—
466C22⋊C4—48no—
467C22⋊C4—44no—
468C22⋊C4—448no—
469C22⋊C4—448no—
470C22⋊C4—448no—
471C22⋊C4—444no—
472C22⋊C4—448no—
473C42—1116no—
474C11C2×#238011yescharacteristic, complemented, Sylow
475C23—28no—
476C23—28no—
477C23—216no—
478C23—216no—
479C23—22no—
480C23—24no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—22no—
485C23—24no—
486C23—24no—
487C23—44no—
488C23—44no—
489C23—48no—
490C23—48no—
491C23—44no—
492C23—44no—
493C23—118no—
494C23—2216no—
495C23—2216no—
496C23—2216no—
497C23—224no—
498C23—224no—
499C23—224no—
500C23—224no—
501C23—224no—
502C23—224no—
503C23—448no—
504C23—448no—
505C23—448no—
506C23—448no—
507C23C22×C4×D1114yes—
508C23C22×C4×D1114yes—
509C23C22×C4×D1112yes—
510C23#6703712yes—
511C23#6703712yes—
512C23#6703714yes—
513C23#6704214yes—
514C23C24×D1111yescharacteristic
515D4—416no—
516D4—4416no—
517D4—4432no—
518D4—4432no—
519C2×C4—28no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—416no—
529C2×C4—48no—
530C2×C4—48no—
531C2×C4—118no—
532C2×C4—2216no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—4432no—
542C2×C4—4416no—
543C2×C4—448no—
544C2×C4—448no—
545C2×C4C22×C4×D1114yes—
546C22—28no—
547C22—28no—
548C22—24no—
549C22—24no—
550C22—44no—
551C22—44no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—416no—
557C22—416no—
558C22—228no—
559C22—228no—
560C22—228no—
561C22—444no—
562C22—444no—
563C22—444no—
564C22—444no—
565C22—4432no—
566C22#1062301714yes—
567C22#1062307618yes—
568C22#1062312614yes—
569C22#1062315118yes—
570C22#1062319714yes—
571C22C23×C4×D1111yescharacteristic
572C22C2×#6703711yescharacteristic
573C22C2×#6703712yes—
574C22C2×#6703711yescharacteristic
575C22C2×#6704212yes—
576C4—24no—
577C4—44no—
578C4—44no—
579C4—228no—
580C4—444no—
581C4—444no—
582C2—44no—
583C2—44no—
584C2—448no—
585C2#1307179118yesdirect product factor
586C2C2×#1062307612yes—
587C2C2×#1062301711yescharacteristic
588C2C2×#1062315112yes—
589C2C2×#1062312611yescharacteristic
590C2C2×#1062319711yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66993C2
cosocleC23×C11C25
hypercenterC2×#386D11
hypocenterC11C2×#2380
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. #13071791C2direct (N × H)
3. C2×#10622833C2semidirect
4. C2×#10622826C2semidirect
5. C2×#10622278C2semidirect
6. C2×#10622571C2semidirect
7. C2×#10622569C2semidirect
8. C2×#10622569C2semidirect
9. C2×#10622264C2semidirect
10. C2×C11×#386C2semidirect
22. C2×#66993C4semidirect
28. C11×#386C22semidirect
30. #10622833C22semidirect
31. #10622826C22semidirect
37. #10622571C22semidirect
38. #10622569C22semidirect
39. #10622569C22semidirect
40. #10622278C22semidirect
41. #10622264C22semidirect
47. C22×D4×C11C2×C4semidirect
59. C22×C22⋊D11C2×C4semidirect
60. C22×C22⋊D11C2×C4semidirect
71. C22×D44C2×C4semidirect
85. #66993C2×C4semidirect
92. C2×C4×Dic11C2×C4semidirect
125. C2×D4×C11C22×C4semidirect
147. C2×C22⋊D11C22×C4semidirect
148. C2×C22⋊D11C22×C4semidirect
167. C2×D44C22×C4semidirect
179. C4×Dic11C22×C4semidirect
188. C2×#386D11semidirect
284. #386C2×D11semidirect
345. C22×D4C4×D11semidirect
388. C2×C11#2380semidirect
431. C2×D4C2×C4×D11semidirect
474. C11C2×#2380semidirect
585. C2#13071791direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669932
#130717912
C2×#106228332
C2×#106228262
C2×#106222782
C2×#106225712
C2×#106225692
C2×#106222642
C2×C11×#3862
C2×#238011