Finite Group Databasebeta

← C4×#10623228 #14912922

Subgroups — C4×#10623228 #14912922

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623228C211yesmaximal, characteristic
2#13071419C214yesmaximal, complemented
3#13071394C214yesmaximal
4#13071358C211yesmaximal, characteristic, complemented
5#13071333C211yesmaximal, characteristic, complemented
6#13071296C212yesmaximal
7#13071263C212yesmaximal, complemented
8#13071226C211yesmaximal, characteristic
9C4×#66922C211yesmaximal, characteristic, complemented
10C4×#66943C214yesmaximal, complemented
11C4×#66951C214yesmaximal
12C4×#66950C212yesmaximal
13C4×#66940C212yesmaximal, complemented
14C4×#66925C211yesmaximal, characteristic
15C4×C11×#125C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17#10623228C4116yesdirect product factor
18C2×#66951C2214yes—
19C2×#66950C2212yes—
20C2×#66943C2214yes—
21C2×#66940C2212yes—
22C2×#66940C2212yes—
23C2×#66925C2211yescharacteristic
24C2×#66925C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C2×C4×Dic22C2212yes—
28C11×#389C2212yes—
29C11×#387C2214yes—
30C11×#382C2211yescharacteristic
31C4×C11×C4⋊C4C2212yes—
32C4×C11×C4⋊C4C2214yes—
33C43×C11C2211yescharacteristic
34#10622603C2214yes—
35#10622600C2212yes—
36#10622598C2214yes—
37#10622598C2212yes—
38#10622594C2214yes—
39#10622591C2214yes—
40#10622590C2214yes—
41C4⋊C4×Dic11C2212yes—
42C4⋊C4×Dic11C2212yes—
43#10622587C2212yes—
44#10622586C2214yes—
45C4×(C2×D11)⋊C4C2212yes—
46C4×(C2×D11)⋊C4C2214yes—
47C4×(C2×D11)⋊C4C2212yes—
48#10622548C2211yescharacteristic
49C4×C4⋊Dic11C2214yes—
50C4×C4⋊Dic11C2214yes—
51#10622545C2211yescharacteristic
52#10622545C2211yescharacteristic
53C4×Dic11⋊C4C2212yes—
54C4×Dic11⋊C4C2214yes—
55C4×Dic11⋊C4C2212yes—
56C42×Dic11C2214yes—
57C42×Dic11C2211yescharacteristic
58#10622542C2212yes—
59#10622541C2214yes—
60#10622283C2214yes—
61#10622282C2214yes—
62#10622281C2214yes—
63#10622268C2214yes—
64#10622268C2214yes—
65#10622267C2214yes—
66#10622267C2214yes—
67#10622267C2214yes—
68#10622266C2214yes—
69#10622264C2214yes—
70#10622262C2214yes—
71#10622262C2214yes—
72C22×C4×D11C2311yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×Dic22C2312yes—
76C11×#125C2×C418yescomplemented
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2314yes—
83C2×C42×C11C2312yes—
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×(C2×D11)⋊C4C2312yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2312yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2312yes—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2312yes—
100C2×Dic11⋊C4C2314yes—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2314yes—
106C2×C4×Dic11C2312yes—
107C2×C4×Dic11C2312yes—
108C2×C4×Dic11C2314yes—
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2311yescharacteristic
113#66951C2×C4132yes—
114#66950C2×C4116yes—
115#66943C2×C4132yescomplemented
116#66940—28no—
117#66940C2×C4116yescomplemented
118#66925—24no—
119#66925C2×C418yes—
120C42×D11—24no—
121#66922C2×C418yescomplemented
122C4×Dic22—28no—
123C11×#95C2314yes—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2312yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2312yes—
135C11⋊#95C2312yes—
136C11⋊#95C2314yes—
137C11⋊#95C2312yes—
138C4×#541—111nomaximal, Sylow
139C23×D11C2411yescharacteristic
140C22×C4×C11C2412yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11C2411yescharacteristic
148C22×Dic11C2411yescharacteristic
149C22×Dic11C2414yes—
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152C22×Dic11C2411yescharacteristic
153C22×Dic11C2412yes—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—24no—
159C2×C4×D11—42no—
160C2×C4×D11C22×C414yes—
161C2×Dic22—24no—
162C2×Dic22—24no—
163C2×Dic22C22×C418yes—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—44no—
166C11×C4⋊C4C22×C418yes—
167C11×C4⋊C4C22×C4116yes—
168C42×C11—22no—
169C42×C11—28no—
170C42×C11—24no—
171C42×C11—42no—
172C42×C11C22×C414yes—
173C42×C11#4114yes—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—44no—
176(C2×D11)⋊C4C22×C418yes—
177(C2×D11)⋊C4C22×C4116yes—
178C4⋊Dic11—24no—
179C4⋊Dic11—44no—
180C4⋊Dic11—44no—
181C4⋊Dic11C22×C4116yes—
182C4⋊Dic11C22×C4116yes—
183Dic11⋊C4—24no—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186Dic11⋊C4C22×C418yes—
187Dic11⋊C4C22×C4116yes—
188C4×Dic11—28no—
189C4×Dic11—28no—
190C4×Dic11—22no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—24no—
194C4×Dic11—44no—
195C4×Dic11—42no—
196C4×Dic11—44no—
197C4×Dic11C22×C414yes—
198C4×Dic11C22×C4116yes—
199C4×Dic11#4114yes—
200C2×#541—111no—
201#2336—114no—
202#2334—114no—
203#2330—111no—
204#2327—111no—
205#2323—112no—
206#2320—112no—
207#2314—111no—
208C4×C4⋊Q8—111no—
209C4×#125—114no—
210C4×#125D1111yescharacteristic, complemented
211C4×#126—114no—
212C4×C22⋊Q8—112no—
213C42×Q8—112no—
214C4×#117—111no—
215C23×C11C2511yescharacteristic
216C22×D11—21no—
217C22×D11—21no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11C23×C412yes—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11C23×C418yes—
233C2×C4×C11C23×C414yes—
234C2×C4×C11C23×C412yes—
235C2×C4×C11C2×#4112yes—
236C2×C4×C11C2×#4112yes—
237C2×C4×C11C2×#4112yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C112−1+414yes—
240C2×Dic11—21no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—21no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11C23×C414yes—
256C2×Dic11C23×C418yes—
257C2×Dic11C23×C412yes—
258C2×Dic11C2×#4114yes—
259C4×D11—28no—
260C4×D11—44no—
261C4×D11—44no—
262Dic22—216no—
263#541—1116no—
264C2×C4⋊Q8—111no—
265C2×#126—114no—
266C2×#125—114no—
267C2×#125C2×D1111yescharacteristic
268C2×C22⋊Q8—112no—
269C2×C4×Q8—112no—
270C2×C4×Q8—112no—
271C2×C4×Q8—112no—
272C2×#117—111no—
273C2×#117—111no—
274C22×C42—111no—
275#391—112no—
276#391—112no—
277#389—114no—
278#389—114no—
279#389—112no—
280#389—114no—
281#389C2×D1112yes—
282#388—114no—
283#388—114no—
284#388—114no—
285#387—114no—
286#387—114no—
287#387—114no—
288#387—114no—
289#387—114no—
290#387—114no—
291#387—114no—
292#387—114no—
293#387C2×D1114yes—
294#385—114no—
295#384—111no—
296#383—114no—
297#382—114no—
298#382C2×D1111yescharacteristic
299#380—112no—
300C4×C4⋊C4—112no—
301C4×C4⋊C4—112no—
302C4×C4⋊C4—114no—
303C4×C4⋊C4—114no—
304C4×C4⋊C4—112no—
305C4×C4⋊C4—114no—
306C4×C4⋊C4—112no—
307C4×C4⋊C4—114no—
308C4×C4⋊C4—114no—
309C4×C4⋊C4C2×D1114yes—
310C4×C4⋊C4C2×D1112yes—
311C4×C22⋊C4—112no—
312C4×C22⋊C4—114no—
313C4×C22⋊C4—112no—
314#376—111no—
315#376—111no—
316C43—114no—
317C43—111no—
318C43C2×D1111yescharacteristic
319C22×C11C24×C411yescharacteristic
320C22×C11C22×#4111yescharacteristic
321C22×C11C22×#4111yescharacteristic
322C22×C11C2×2−1+412yes—
323C22×C11#58512yes—
324C2×D11—22no—
325C2×D11—24no—
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—42no—
329C4×C11—28no—
330C4×C11—24no—
331C4×C11—22no—
332C4×C11—44no—
333C4×C11—42no—
334C4×C11C4×#4114yes—
335C4×C11#54114yescomplemented
336Dic11—28no—
337Dic11—22no—
338Dic11—24no—
339Dic11—24no—
340Dic11—41no—
341Dic11—41no—
342Dic11—44no—
343C22×Q8—112no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C4⋊Q8—118no—
348#126—1132no—
349#125—1132no—
350#125C4×D1118yescomplemented
351C22⋊Q8—1116no—
352C4×Q8—1116no—
353C4×Q8—228no—
354C4×Q8—228no—
355#117—118no—
356#117—224no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—114no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4C22×D1112yes—
368C2×C4⋊C4C22×D1114yes—
369C2×C4⋊C4C22×D1112yes—
370C2×C4⋊C4C22×D1114yes—
371C2×C22⋊C4—112no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—112no—
374C2×C22⋊C4—114no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—114no—
378C2×C42—114no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—114no—
382C2×C42—112no—
383C2×C42—111no—
384C2×C42—112no—
385C2×C42—114no—
386C2×C42—114no—
387C2×C42—224no—
388C2×C42C22×D1111yescharacteristic
389C2×C42C22×D1114yes—
390C2×C42C22×D1112yes—
391C2×C42C22×D1112yes—
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1111yescharacteristic
394#95—112no—
395#95—112no—
396#95—112no—
397#95—112no—
398#95—114no—
399#95—114no—
400#95—114no—
401#95—114no—
402#95—114no—
403#95—114no—
404#95—114no—
405#95—114no—
406#95C22×D1114yes—
407#95C22×D1114yes—
408#95C22×D1114yes—
409C2×C11C2×C4×#4111yescharacteristic
410C2×C11C4×2−1+412yes—
411C2×C11C2×#54111yescharacteristic
412C2×C11#345511yescharacteristic
413C2×C11#346112yes—
414D11—42no—
415C24—111no—
416C2×Q8—118no—
417C2×Q8—224no—
418C2×Q8—224no—
419C22×C4—112no—
420C22×C4—112no—
421C22×C4—114no—
422C22×C4—111no—
423C22×C4—114no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—114no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—224no—
432C22×C4—442no—
433C22×C4C23×D1112yes—
434C22×C4C23×D1114yes—
435C22×C4C23×D1114yes—
436C22×C4C23×D1112yes—
437C22×C4C23×D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439C22×C4C23×D1111yescharacteristic
440C4⋊C4—24no—
441C4⋊C4—44no—
442C4⋊C4—118no—
443C4⋊C4—1116no—
444C4⋊C4—1116no—
445C4⋊C4—1116no—
446C4⋊C4—224no—
447C4⋊C4—228no—
448C4⋊C4—228no—
449C4⋊C4—224no—
450C4⋊C4—444no—
451C4⋊C4—444no—
452C4⋊C4C2×C4×D1118yes—
453C4⋊C4C2×C4×D11116yes—
454C22⋊C4—118no—
455C22⋊C4—1116no—
456C22⋊C4—224no—
457C22⋊C4—444no—
458C42—22no—
459C42—28no—
460C42—24no—
461C42—42no—
462C42—114no—
463C42—1116no—
464C42—114no—
465C42—228no—
466C42—222no—
467C42—222no—
468C42—222no—
469C42—228no—
470C42—224no—
471C42—442no—
472C42—444no—
473C42—444no—
474C42C2×C4×D1114yes—
475C42#434314yes—
476C11C4×#54111yescharacteristic, complemented, Sylow
477C23—112no—
478C23—221no—
479C23—221no—
480C23—222no—
481C23—222no—
482C23C24×D1111yescharacteristic
483Q8—2216no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—114no—
496C2×C4—118no—
497C2×C4—112no—
498C2×C4—114no—
499C2×C4—221no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—221no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—228no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—222no—
515C2×C4—444no—
516C2×C4—444no—
517C2×C4C22×C4×D1118yes—
518C2×C4C22×C4×D1114yes—
519C2×C4C22×C4×D1112yes—
520C2×C4C2×#434312yes—
521C2×C4C2×#434312yes—
522C2×C4C2×#434312yes—
523C2×C4#41×D1112yes—
524C2×C4#6704314yes—
525C22—222no—
526C22—224no—
527C22—441no—
528C22—441no—
529C22—442no—
530C22C23×C4×D1111yescharacteristic
531C22C22×#434311yescharacteristic
532C22C2×#41×D1111yescharacteristic
533C22C2×#6704312yes—
534C22#1062345312yes—
535C4—22no—
536C4—24no—
537C4—28no—
538C4—42no—
539C4—44no—
540C4—224no—
541C4—222no—
542C4—228no—
543C4—224no—
544C4—441no—
545C4—441no—
546C4—444no—
547C4C4×#434314yes—
548C4#1062322814yesdirect product factor
549C2—442no—
550C2C2×C4×#434311yescharacteristic
551C2C4×#6704312yes—
552C2C2×#1062322811yescharacteristic
553C2#1308200811yescharacteristic
554C2#1308204112yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#125C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterC4×#125D11
hypocenterC11C4×#541
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
2. #13071419C2semidirect
4. #13071358C2semidirect
5. #13071333C2semidirect
7. #13071263C2semidirect
9. C4×#66922C2semidirect
10. C4×#66943C2semidirect
13. C4×#66940C2semidirect
15. C4×C11×#125C2semidirect
17. #10623228C4direct (N × H)
76. C11×#125C2×C4semidirect
115. #66943C2×C4semidirect
117. #66940C2×C4semidirect
121. #66922C2×C4semidirect
210. C4×#125D11semidirect
335. C4×C11#541semidirect
350. #125C4×D11semidirect
476. C11C4×#541semidirect
548. C4#10623228direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232282
#130714192
#130713942
#130713582
#130713332
#130712962
#130712632
#130712262
C4×#669222
C4×#669432
C4×#669512
C4×#669502
C4×#669402
C4×#669252
C4×C11×#1252
C4×#54111