Finite Group Databasebeta

← C4×D11×#125 #14912258

Subgroups — C4×D11×#125 #14912258

Order 2816.

2622 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2#125×Dic11C211yesmaximal, characteristic, complemented
3C4×#66923C211yesmaximal, characteristic, complemented
4#13071175C212yesmaximal, complemented
5C4×#66943C212yesmaximal, complemented
6#13071173C214yesmaximal, complemented
7C4×#66942C214yesmaximal, complemented
8#13071171C211yesmaximal, characteristic, complemented
9D11×#389C212yesmaximal
10D11×#387C214yesmaximal
11D11×#382C211yesmaximal, characteristic
12C4×C4⋊C4×D11C214yesmaximal
13C4×C4⋊C4×D11C212yesmaximal
14C43×D11C211yesmaximal, characteristic
15C4×C11×#125C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17D11×#125C4116yesdirect product factor
18C2×C4⋊C4×D11C2212yes—
19C2×C4⋊C4×D11C2214yes—
20C2×C4⋊C4×D11C2214yes—
21C2×C4⋊C4×D11C2212yes—
22C2×#66943C2212yes—
23C2×#66942C2214yes—
24C2×C42×D11C2212yes—
25C2×C42×D11C2212yes—
26C2×C42×D11C2211yescharacteristic
27C2×C42×D11C2214yes—
28C2×C42×D11C2211yescharacteristic
29C2×C42×D11C2211yescharacteristic
30C2×#66923C2211yescharacteristic
31C11×#389C2212yes—
32C11×#387C2214yes—
33C11×#382C2211yescharacteristic
34C4×C11×C4⋊C4C2214yes—
35C4×C11×C4⋊C4C2212yes—
36C43×C11C2211yescharacteristic
37#10622598C2212yes—
38#10622594C2214yes—
39#10622591C2214yes—
40#10622590C2212yes—
41C4⋊C4×Dic11C2212yes—
42C4⋊C4×Dic11C2214yes—
43C4⋊C4×Dic11C2214yes—
44C4⋊C4×Dic11C2212yes—
45#10622586C2212yes—
46#10622585C2214yes—
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2214yes—
49C4×C4⋊Dic11C2212yes—
50#10622546C2214yes—
51C4×Dic11⋊C4C2214yes—
52C4×Dic11⋊C4C2214yes—
53C4×Dic11⋊C4C2214yes—
54C42×Dic11C2211yescharacteristic
55C42×Dic11C2212yes—
56C42×Dic11C2212yes—
57C42×Dic11C2211yescharacteristic
58C42×Dic11C2211yescharacteristic
59#10622541C2212yes—
60D11×#95C2214yes—
61D11×#95C2214yes—
62D11×#95C2214yes—
63#10622268C2214yes—
64#10622267C2214yes—
65#10622266C2214yes—
66#10622265C2214yes—
67#10622263C2214yes—
68#10622262C2214yes—
69#10622262C2214yes—
70#10622262C2214yes—
71#10622260C2214yes—
72C22×C4×D11C2314yes—
73C22×C4×D11C2312yes—
74C22×C4×D11C2314yes—
75C22×C4×D11C2311yescharacteristic
76C22×C4×D11C2312yes—
77C22×C4×D11C2311yescharacteristic
78C22×C4×D11C2311yescharacteristic
79C11×#125C2×C418yescomplemented
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2312yes—
86C2×C42×C11C2312yes—
87C2×C42×C11C2314yes—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C4⋊Dic11C2314yes—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2314yes—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×C4×Dic11C2312yes—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2312yes—
103C2×C4×Dic11C2312yes—
104C2×C4×Dic11C2314yes—
105C2×C4×Dic11C2312yes—
106C2×C4×Dic11C2312yes—
107C2×C4×Dic11C2312yes—
108C2×C4×Dic11C2312yes—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C4⋊C4×D11—28no—
117C4⋊C4×D11—216no—
118C4⋊C4×D11C2×C4132yes—
119C4⋊C4×D11C2×C4116yes—
120#66943C2×C4116yescomplemented
121#66942C2×C4132yescomplemented
122C42×D11—28no—
123C42×D11—24no—
124C42×D11—28no—
125C42×D11—216no—
126C42×D11C2×C418yes—
127C42×D11Q818yes—
128#66923C2×C418yescomplemented
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C2×C4×#125—111nomaximal, Sylow
142C23×D11C2411yescharacteristic
143C22×C4×C11C2414yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2414yes—
146C22×C4×C11C2411yescharacteristic
147C22×C4×C11C2412yes—
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11C2414yes—
151C22×Dic11C2412yes—
152C22×Dic11C2414yes—
153C22×Dic11C2411yescharacteristic
154C22×Dic11C2412yes—
155C22×Dic11C2411yescharacteristic
156C22×Dic11C2411yescharacteristic
157C2×C4×D11—24no—
158C2×C4×D11—24no—
159C2×C4×D11—28no—
160C2×C4×D11—24no—
161C2×C4×D11—24no—
162C2×C4×D11—24no—
163C2×C4×D11—28no—
164C2×C4×D11—28no—
165C2×C4×D11—28no—
166C2×C4×D11—28no—
167C2×C4×D11C22×C418yes—
168C2×C4×D11C22×C4116yes—
169C2×C4×D11C22×C414yes—
170C2×C4×D11C2×Q814yes—
171C2×C4×D11C2×Q814yes—
172C2×C4×D11C2×Q814yes—
173C2×C4×D11#4118yes—
174C2×C4×D11#4114yes—
175C2×C4×D11#4118yes—
176C11×C4⋊C4—28no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4C22×C4116yes—
179C11×C4⋊C4C22×C418yes—
180C42×C11—24no—
181C42×C11—22no—
182C42×C11—24no—
183C42×C11—28no—
184C42×C11C22×C414yes—
185C42×C11C2×Q814yes—
186C4⋊Dic11—28no—
187C4⋊Dic11—24no—
188C4⋊Dic11C22×C418yes—
189C4⋊Dic11C22×C4116yes—
190Dic11⋊C4—28no—
191Dic11⋊C4—28no—
192Dic11⋊C4—28no—
193Dic11⋊C4C22×C4116yes—
194Dic11⋊C4C22×C4116yes—
195Dic11⋊C4C22×C4116yes—
196C4×Dic11—24no—
197C4×Dic11—24no—
198C4×Dic11—24no—
199C4×Dic11—24no—
200C4×Dic11—24no—
201C4×Dic11—28no—
202C4×Dic11—28no—
203C4×Dic11—24no—
204C4×Dic11—22no—
205C4×Dic11—24no—
206C4×Dic11—28no—
207C4×Dic11C22×C418yes—
208C4×Dic11C22×C414yes—
209C4×Dic11C2×Q814yes—
210C4×Dic11C2×Q814yes—
211C4×Dic11C2×Q814yes—
212C22×#125—111no—
213C4×#125—112no—
214C4×#125—114no—
215C4×#125—111no—
216C4×#125—114no—
217C4×#125—112no—
218C4×#125—111no—
219C4×#125—111no—
220C4×#125D1111yescharacteristic, direct product factor
221C2×#389—112no—
222C2×#387—114no—
223C2×#382—111no—
224C2×C4×C4⋊C4—114no—
225C2×C4×C4⋊C4—112no—
226C2×C43—111no—
227C23×C11C2511yescharacteristic
228C22×D11C23×C412yes—
229C22×D11C22×Q812yes—
230C22×D11C2×#4112yes—
231C22×D11C2×#4114yes—
232C22×D11C2×#4114yes—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11C23×C414yes—
244C2×C4×C11C23×C418yes—
245C2×C4×C11C23×C412yes—
246C2×C4×C11C22×Q812yes—
247C2×C4×C11C22×Q812yes—
248C2×C4×C11C22×Q812yes—
249C2×C4×C11C2×#4114yes—
250C2×C4×C11C2×#4112yes—
251C2×C4×C11C2×#4114yes—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11C23×C414yes—
263C2×Dic11C23×C418yes—
264C2×Dic11C23×C412yes—
265C2×Dic11C22×Q812yes—
266C2×Dic11C22×Q812yes—
267C2×Dic11C22×Q812yes—
268C2×Dic11C2×#4114yes—
269C2×Dic11C2×#4112yes—
270C2×Dic11C2×#4114yes—
271C4×D11—216no—
272C4×D11—232no—
273C4×D11—216no—
274C4×D11—28no—
275C4×D11—416no—
276C4×D11C4×Q8116yes—
277C4×D11#125116yesdirect product factor
278C2×#125—1116no—
279C2×#125—114no—
280C2×#125—112no—
281C2×#125—111no—
282C2×#125C2×D1111yescharacteristic
283C22×C4⋊C4—114no—
284C22×C4⋊C4—112no—
285C22×C4⋊C4—112no—
286C22×C4⋊C4—114no—
287C22×C42—111no—
288C22×C42—111no—
289C22×C42—112no—
290C22×C42—112no—
291C22×C42—111no—
292C22×C42—114no—
293#389—114no—
294#389—112no—
295#389—112no—
296#389—112no—
297#389—114no—
298#389C2×D1112yes—
299#387—114no—
300#387—114no—
301#387—114no—
302#387—114no—
303#387—114no—
304#387—114no—
305#387—114no—
306#387C2×D1114yes—
307#382—112no—
308#382—111no—
309#382—114no—
310#382C2×D1111yescharacteristic
311C4×C4⋊C4—114no—
312C4×C4⋊C4—114no—
313C4×C4⋊C4—112no—
314C4×C4⋊C4—112no—
315C4×C4⋊C4—114no—
316C4×C4⋊C4—114no—
317C4×C4⋊C4—114no—
318C4×C4⋊C4—114no—
319C4×C4⋊C4—112no—
320C4×C4⋊C4—114no—
321C4×C4⋊C4—114no—
322C4×C4⋊C4—114no—
323C4×C4⋊C4C2×D1114yes—
324C4×C4⋊C4C2×D1112yes—
325C2×#95—114no—
326C2×#95—114no—
327C2×#95—114no—
328C43—111no—
329C43—112no—
330C43—112no—
331C43—111no—
332C43—111no—
333C43C2×D1111yescharacteristic
334C22×C11C24×C411yescharacteristic
335C22×C11C23×Q811yescharacteristic
336C22×C11C22×#4111yescharacteristic
337C22×C11C22×#4112yes—
338C22×C11C22×#4112yes—
339C2×D11C2×C4×Q814yes—
340C2×D11C4×#4118yes—
341C2×D11C2×#12514yes—
342C2×D11#52918yes—
343C2×D11#53314yes—
344C4×C11—24no—
345C4×C11—28no—
346C4×C11—24no—
347C4×C11—22no—
348C4×C11—44no—
349C4×C11C2×C4×Q814yes—
350C4×C11C2×#12514yescomplemented
351Dic11—24no—
352Dic11—28no—
353Dic11—24no—
354Dic11—22no—
355Dic11—44no—
356Dic11C2×C4×Q814yes—
357Dic11C2×#12514yescomplemented
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—114no—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4—111no—
364C23×C4—114no—
365#125—1132no—
366#125—1116no—
367#125—118no—
368#125C4×D1118yesdirect product factor
369C2×C4⋊C4—114no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—1116no—
375C2×C4⋊C4—1132no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—228no—
382C2×C4⋊C4—2216no—
383C2×C4⋊C4C22×D1112yes—
384C2×C4⋊C4C22×D1114yes—
385C2×C4⋊C4C22×D1114yes—
386C2×C4⋊C4C22×D1112yes—
387C2×C42—112no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—118no—
393C2×C42—118no—
394C2×C42—112no—
395C2×C42—112no—
396C2×C42—112no—
397C2×C42—112no—
398C2×C42—112no—
399C2×C42—112no—
400C2×C42—111no—
401C2×C42—114no—
402C2×C42—114no—
403C2×C42—112no—
404C2×C42—114no—
405C2×C42—228no—
406C2×C42—2216no—
407C2×C42—224no—
408C2×C42—228no—
409C2×C42C22×D1112yes—
410C2×C42C22×D1111yescharacteristic
411C2×C42C22×D1112yes—
412C2×C42C22×D1114yes—
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415#95—114no—
416#95—114no—
417#95—114no—
418#95—114no—
419#95—114no—
420#95—114no—
421#95—114no—
422#95—114no—
423#95—114no—
424#95C22×D1114yes—
425#95C22×D1114yes—
426#95C22×D1114yes—
427C2×C11C22×C4×Q811yescharacteristic
428C2×C11C2×C4×#4112yes—
429C2×C11C22×#12511yescharacteristic
430C2×C11C2×#52912yes—
431C2×C11C2×#53311yescharacteristic
432D11C4×#12518yesdirect product factor
433C24—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—118no—
440C22×C4—114no—
441C22×C4—111no—
442C22×C4—112no—
443C22×C4—112no—
444C22×C4—114no—
445C22×C4—118no—
446C22×C4—1116no—
447C22×C4—114no—
448C22×C4—118no—
449C22×C4—114no—
450C22×C4—228no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—228no—
457C22×C4—228no—
458C22×C4—228no—
459C22×C4—228no—
460C22×C4C23×D1114yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1114yes—
463C22×C4C23×D1111yescharacteristic
464C22×C4C23×D1112yes—
465C22×C4C23×D1111yescharacteristic
466C22×C4C23×D1111yescharacteristic
467C4⋊C4—28no—
468C4⋊C4—24no—
469C4⋊C4—1116no—
470C4⋊C4—1116no—
471C4⋊C4—1116no—
472C4⋊C4—1116no—
473C4⋊C4—118no—
474C4⋊C4—228no—
475C4⋊C4—228no—
476C4⋊C4—228no—
477C4⋊C4—228no—
478C4⋊C4—224no—
479C4⋊C4C2×C4×D11116yes—
480C4⋊C4C2×C4×D1118yes—
481C42—24no—
482C42—22no—
483C42—24no—
484C42—28no—
485C42—118no—
486C42—114no—
487C42—114no—
488C42—114no—
489C42—114no—
490C42—224no—
491C42—224no—
492C42—228no—
493C42—224no—
494C42—224no—
495C42—224no—
496C42—228no—
497C42—224no—
498C42—222no—
499C42—224no—
500C42—228no—
501C42C2×C4×D1114yes—
502C42Q8×D1114yes—
503C11C2×C4×#12511yescharacteristic, complemented, Sylow
504C23—112no—
505C23—112no—
506C23—114no—
507C23—112no—
508C23—114no—
509C23C24×D1111yescharacteristic
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—112no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—114no—
524C2×C4—112no—
525C2×C4—1116no—
526C2×C4—1116no—
527C2×C4—114no—
528C2×C4—118no—
529C2×C4—112no—
530C2×C4—114no—
531C2×C4—2216no—
532C2×C4—228no—
533C2×C4—2216no—
534C2×C4—2232no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—4416no—
546C2×C4C22×C4×D1114yes—
547C2×C4C22×C4×D1118yes—
548C2×C4C22×C4×D1112yes—
549C2×C4C2×Q8×D1112yes—
550C2×C4C2×Q8×D1112yes—
551C2×C4C2×Q8×D1112yes—
552C2×C4#41×D1114yes—
553C2×C4#41×D1112yes—
554C2×C4#41×D1114yes—
555C22—114no—
556C22—118no—
557C22—114no—
558C22—114no—
559C22—118no—
560C22C23×C4×D1111yescharacteristic
561C22C22×Q8×D1111yescharacteristic
562C22C2×#41×D1112yes—
563C22C2×#41×D1111yescharacteristic
564C22C2×#41×D1112yes—
565C4—24no—
566C4—22no—
567C4—24no—
568C4—28no—
569C4—44no—
570C4—114no—
571C4—114no—
572C4—224no—
573C4—222no—
574C4—224no—
575C4—228no—
576C4—444no—
577C4C4×Q8×D1114yes—
578C4D11×#12514yesdirect product factor
579C2—118no—
580C2C2×C4×Q8×D1111yescharacteristic
581C2C4×#41×D1112yes—
582C2C2×D11×#12511yescharacteristic
583C2D11×#52912yes—
584C2D11×#53311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#125C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterC4×#125D11
hypocenterC11C2×C4×#125
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
2. #125×Dic11C2semidirect
3. C4×#66923C2semidirect
4. #13071175C2semidirect
5. C4×#66943C2semidirect
6. #13071173C2semidirect
7. C4×#66942C2semidirect
8. #13071171C2semidirect
15. C4×C11×#125C2semidirect
17. D11×#125C4direct (N × H)
79. C11×#125C2×C4semidirect
120. #66943C2×C4semidirect
121. #66942C2×C4semidirect
128. #66923C2×C4semidirect
220. C4×#125D11direct (N × H)
277. C4×D11#125direct (N × H)
350. C4×C11C2×#125semidirect
357. Dic11C2×#125semidirect
368. #125C4×D11direct (N × H)
432. D11C4×#125direct (N × H)
503. C11C2×C4×#125semidirect
578. C4D11×#125direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D11×#1252
#125×Dic112
C4×#669232
#130711752
C4×#669432
#130711732
C4×#669422
#130711712
D11×#3892
D11×#3872
D11×#3822
C4×C4⋊C4×D112
C43×D112
C4×C11×#1252
C2×C4×#12511