Finite Group Databasebeta

← C4×#10623250 #14912880

Subgroups — C4×#10623250 #14912880

Order 2816.

2518 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623250C211yesmaximal, characteristic
2#13071403C214yesmaximal, complemented
3#13071375C214yesmaximal, complemented
4#13071355C211yesmaximal, characteristic, complemented
5#13071342C211yesmaximal, characteristic, complemented
6#13071312C212yesmaximal, complemented
7#13071253C212yesmaximal, complemented
8#13071224C211yesmaximal, characteristic, complemented
9C4×#66923C211yesmaximal, characteristic, complemented
10C4×#66988C214yesmaximal, complemented
11C4×#66992C214yesmaximal, complemented
12C4×#66991C212yesmaximal, complemented
13C4×D4×Dic11C212yesmaximal, complemented
14C4×#66925C211yesmaximal, characteristic, complemented
15C4×C11×#127C211yesmaximal, characteristic, complemented
16C2×C11×#127C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2214yes—
19C2×#66992C2214yes—
20C2×#66991C2212yes—
21C2×#66988C2214yes—
22C2×D4×Dic11C2212yes—
23C2×D4×Dic11C2212yes—
24C2×C4×C22⋊D11C2214yes—
25C22×C4×Dic11C2214yes—
26#10623250C4116yesdirect product factor
27C2×#66925C2211yescharacteristic
28C2×#66925C2211yescharacteristic
29C2×C42×D11C2211yescharacteristic
30C2×#66923C2211yescharacteristic
31C11×#390C2214yes—
32C11×#390C2212yes—
33C11×#384C2211yescharacteristic
34C43×C11C2211yescharacteristic
35#10622834C2212yes—
36#10622833C2214yes—
37#10622833C2214yes—
38C4×C22⋊Dic11C2214yes—
39C4×C22⋊Dic11C2214yes—
40#10622603C2214yes—
41#10622600C2212yes—
42#10622591C2214yes—
43#10622591C2214yes—
44C4⋊C4×Dic11C2212yes—
45C4⋊C4×Dic11C2212yes—
46#10622586C2212yes—
47#10622585C2214yes—
48#10622571C2214yes—
49#10622570C2214yes—
50#10622569C2214yes—
51#10622559C2214yes—
52#10622558C2214yes—
53#10622557C2214yes—
54#10622557C2214yes—
55#10622557C2214yes—
56#10622556C2214yes—
57#10622555C2214yes—
58C22⋊C4×Dic11C2214yes—
59C22⋊C4×Dic11C2214yes—
60C4×(C2×D11)⋊C4C2212yes—
61C4×(C2×D11)⋊C4C2212yes—
62#10622549C2211yescharacteristic
63C4×C4⋊Dic11C2212yes—
64#10622546C2214yes—
65#10622545C2211yescharacteristic
66#10622545C2211yescharacteristic
67C4×Dic11⋊C4C2214yes—
68C4×Dic11⋊C4C2212yes—
69C4×Dic11⋊C4C2212yes—
70C42×Dic11C2211yescharacteristic
71#10622541C2212yes—
72C22×D4×C11C2312yes—
73C22×D4×C11C2314yes—
74C23×C4×C11C2314yes—
75C22×C22⋊D11C2314yes—
76C23×Dic11C2314yes—
77C23×Dic11C2314yes—
78C22×C4×D11C2311yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C11×#127C2×C418yescomplemented
82C4×D4×C11—28no—
83C4×D4×C11—48no—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11C2314yes—
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2314yes—
97C2×C22⋊Dic11C2314yes—
98C2×C22⋊Dic11C2314yes—
99#66992C2×C4132yescomplemented
100#66991C2×C4116yescomplemented
101#66988C2×C4132yescomplemented
102D4×Dic11—28no—
103D4×Dic11C2×C4116yescomplemented
104C4×C22⋊D11—48no—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2312yes—
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2312yes—
110C2×Dic11⋊C4C2312yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2312yes—
115C2×C4×Dic11—48no—
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2311yescharacteristic
119C2×C4×Dic11C2312yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2311yescharacteristic
125C2×C4×Dic11C2311yescharacteristic
126#66925—24no—
127#66925C2×C418yescomplemented
128C42×D11—24no—
129#66923C2×C418yescomplemented
130C11⋊#95C2314yes—
131C11⋊#95C2312yes—
132C11⋊#95C2312yes—
133C11⋊#95C2312yes—
134C11⋊#95C2312yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C4×#540—111nomaximal, Sylow
142C24×C11C2414yes—
143C23×D11C2411yescharacteristic
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11C22×C418yes—
149C2×D4×C11C22×C4116yes—
150C22×C4×C11—28no—
151C22×C4×C11—28no—
152C22×C4×C11—28no—
153C22×C4×C11C2414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—44no—
160C2×C22⋊D11—44no—
161C2×C22⋊D11C22×C4116yes—
162C22×Dic11—28no—
163C22×Dic11—44no—
164C22×Dic11—44no—
165C22×Dic11—44no—
166C22×Dic11—44no—
167C22×Dic11C22×C4116yes—
168C22×Dic11C2411yescharacteristic
169C22×Dic11C2414yes—
170C22×Dic11C2411yescharacteristic
171C22×Dic11C2412yes—
172C22×Dic11C2414yes—
173C22×Dic11C2411yescharacteristic
174C22×Dic11C2412yes—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—24no—
180C2×C4×D11—42no—
181C2×C4×D11C22×C414yes—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—44no—
184C11×C22⋊C4—28no—
185C11×C22⋊C4—44no—
186C11×C22⋊C4—44no—
187C42×C11—22no—
188C42×C11—24no—
189C42×C11—42no—
190C42×C11C22×C414yes—
191C42×C11#4114yes—
192C22⋊Dic11—28no—
193C22⋊Dic11—44no—
194C22⋊Dic11—44no—
195C22⋊Dic11C22×C4116yes—
196C22⋊Dic11C22×C4116yes—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—44no—
199(C2×D11)⋊C4C22×C418yes—
200C4⋊Dic11—24no—
201C4⋊Dic11C22×C418yes—
202Dic11⋊C4—24no—
203Dic11⋊C4—44no—
204Dic11⋊C4—44no—
205Dic11⋊C4C22×C4116yes—
206Dic11⋊C4C22×C418yes—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—22no—
210C4×Dic11—24no—
211C4×Dic11—28no—
212C4×Dic11—44no—
213C4×Dic11—44no—
214C4×Dic11—42no—
215C4×Dic11C22×C414yes—
216C4×Dic11#4114yes—
217C2×#540—111no—
218#2335—114no—
219#2333—114no—
220#2330—111no—
221#2328—111no—
222#2324—112no—
223#2319—112no—
224#2314—111no—
225C4×#127D1111yescharacteristic, complemented
226C4×#125—111no—
227C4×#123—114no—
228C4×#121—112no—
229C4×#121—114no—
230C42×D4—112no—
231C4×#117—111no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11C23×C418yes—
239C23×C11C2511yescharacteristic
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11C23×C412yes—
245D4×C11—216no—
246D4×C11—416no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—416no—
257C2×C4×C11C23×C414yes—
258C2×C4×C11C23×C412yes—
259C2×C4×C11C2×#4112yes—
260C2×C4×C11C2×#4112yes—
261C2×C4×C11C2×#4112yes—
262C2×C4×C11C2×#4112yes—
263C2×C4×C11H(5,𝔽2)14yes—
264C22⋊D11—416no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—416no—
281C2×Dic11—416no—
282C2×Dic11C23×C414yes—
283C2×Dic11C23×C418yes—
284C2×Dic11C23×C412yes—
285C2×Dic11C2×#4114yes—
286C4×D11—28no—
287C4×D11—44no—
288C4×D11—44no—
289#540—1116no—
290C2×#127C2×D1111yescharacteristic
291C2×#125—111no—
292C2×#123—114no—
293C2×#121—112no—
294C2×#121—114no—
295C2×C4×D4—112no—
296C2×C4×D4—112no—
297C2×C4×D4—114no—
298C2×C4×D4C2×D1112yes—
299C2×C4×D4C2×D1114yes—
300C2×#117—111no—
301C2×#117—111no—
302C22×C42—114no—
303C22×C42—111no—
304#390—112no—
305#390—114no—
306#390C2×D1112yes—
307#390C2×D1114yes—
308#389—112no—
309#389—114no—
310#389—112no—
311#388—114no—
312#388—114no—
313#388—114no—
314#388—114no—
315#388—114no—
316#387—114no—
317#387—114no—
318#387—114no—
319#386—114no—
320#386—114no—
321#386—114no—
322#386—114no—
323#385—114no—
324#384C2×D1111yescharacteristic
325#382—111no—
326#381—114no—
327#380—112no—
328#380—114no—
329C4×C4⋊C4—112no—
330C4×C4⋊C4—112no—
331C4×C4⋊C4—114no—
332C4×C4⋊C4—112no—
333C4×C4⋊C4—112no—
334C4×C4⋊C4—112no—
335C4×C22⋊C4—114no—
336C4×C22⋊C4—114no—
337C4×C22⋊C4—114no—
338C4×C22⋊C4—114no—
339C4×C22⋊C4—112no—
340C4×C22⋊C4—112no—
341#376—111no—
342#376—111no—
343C43—111no—
344C43C2×D1111yescharacteristic
345C22×C11—28no—
346C22×C11—28no—
347C22×C11—28no—
348C22×C11—44no—
349C22×C11—44no—
350C22×C11—44no—
351C22×C11—44no—
352C22×C11C24×C411yescharacteristic
353C22×C11C22×#4111yescharacteristic
354C22×C11C22×#4111yescharacteristic
355C22×C11C2×H(5,𝔽2)12yes—
356C22×C11#58512yes—
357C2×D11—22no—
358C2×D11—24no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—42no—
362C4×C11—24no—
363C4×C11—22no—
364C4×C11—44no—
365C4×C11—42no—
366C4×C11C4×#4114yes—
367C4×C11#54014yescomplemented
368Dic11—22no—
369Dic11—24no—
370Dic11—28no—
371Dic11—24no—
372Dic11—41no—
373Dic11—41no—
374Dic11—44no—
375C22×D4—114no—
376C22×D4C22×D1112yes—
377C22×D4C22×D1114yes—
378C23×C4—114no—
379C23×C4—111no—
380C23×C4—114no—
381C23×C4—111no—
382C23×C4—111no—
383C23×C4C22×D1114yes—
384#127C4×D1118yescomplemented
385#125—118no—
386#123—1132no—
387#121—1116no—
388#121—1132no—
389C4×D4—28no—
390C4×D4—48no—
391C4×D4—1116no—
392C4×D4—228no—
393C4×D4—448no—
394#117—118no—
395#117—224no—
396C2×C4⋊C4—112no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—112no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—114no—
403C2×C4⋊C4C22×D1112yes—
404C2×C4⋊C4C22×D1114yes—
405C2×C22⋊C4—114no—
406C2×C22⋊C4—114no—
407C2×C22⋊C4—112no—
408C2×C22⋊C4—114no—
409C2×C22⋊C4—112no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4C22×D1114yes—
414C2×C22⋊C4C22×D1114yes—
415C2×C22⋊C4C22×D1114yes—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—114no—
421C2×C42—112no—
422C2×C42—111no—
423C2×C42—112no—
424C2×C42—114no—
425C2×C42—114no—
426C2×C42—224no—
427C2×C42—448no—
428C2×C42C22×D1111yescharacteristic
429C2×C42C22×D1112yes—
430C2×C42C22×D1112yes—
431C2×C42C22×D1111yescharacteristic
432C2×C42C22×D1111yescharacteristic
433#95—112no—
434#95—112no—
435#95—112no—
436#95—112no—
437#95—114no—
438#95—114no—
439#95—114no—
440#95—114no—
441#95—114no—
442#95—114no—
443#95—114no—
444C2×C11—48no—
445C2×C11C2×C4×#4111yescharacteristic
446C2×C11C4×H(5,𝔽2)12yes—
447C2×C11C2×#54011yescharacteristic
448C2×C11#345511yescharacteristic
449C2×C11#346012yes—
450D11—42no—
451C24—111no—
452C24C23×D1114yes—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—1116no—
458C2×D4—444no—
459C2×D4—444no—
460C2×D4C2×C4×D1118yes—
461C2×D4C2×C4×D11116yes—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—111no—
468C22×C4—114no—
469C22×C4—1116no—
470C22×C4—114no—
471C22×C4—111no—
472C22×C4—114no—
473C22×C4—111no—
474C22×C4—228no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—442no—
481C22×C4—444no—
482C22×C4—444no—
483C22×C4—444no—
484C22×C4—444no—
485C22×C4C23×D1114yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C22×C4C23×D1111yescharacteristic
489C22×C4C23×D1111yescharacteristic
490C22×C4C23×D1111yescharacteristic
491C4⋊C4—24no—
492C4⋊C4—44no—
493C4⋊C4—118no—
494C4⋊C4—118no—
495C4⋊C4—1116no—
496C4⋊C4—224no—
497C4⋊C4—224no—
498C4⋊C4—444no—
499C4⋊C4—444no—
500C22⋊C4—28no—
501C22⋊C4—44no—
502C22⋊C4—44no—
503C22⋊C4—1116no—
504C22⋊C4—1116no—
505C22⋊C4—118no—
506C22⋊C4—224no—
507C22⋊C4—228no—
508C22⋊C4—444no—
509C22⋊C4—444no—
510C22⋊C4—444no—
511C42—24no—
512C42—22no—
513C42—42no—
514C42—114no—
515C42—114no—
516C42—222no—
517C42—222no—
518C42—222no—
519C42—224no—
520C42—228no—
521C42—444no—
522C42—444no—
523C42—442no—
524C42C2×C4×D1114yes—
525C42#434114yes—
526C11C4×#54011yescharacteristic, complemented, Sylow
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—112no—
534C23—221no—
535C23—222no—
536C23—221no—
537C23—222no—
538C23C22×C4×D1118yes—
539C23C24×D1111yescharacteristic
540D4—216no—
541D4—416no—
542D4—4416no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—416no—
553C2×C4—114no—
554C2×C4—112no—
555C2×C4—118no—
556C2×C4—114no—
557C2×C4—221no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—221no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—224no—
565C2×C4—228no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—444no—
574C2×C4—4416no—
575C2×C4—4416no—
576C2×C4—444no—
577C2×C4C22×C4×D1114yes—
578C2×C4C22×C4×D1112yes—
579C2×C4C2×#434112yes—
580C2×C4C2×#434112yes—
581C2×C4C2×#434112yes—
582C2×C4#6703714yes—
583C2×C4#41×D1112yes—
584C22—28no—
585C22—28no—
586C22—28no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—222no—
592C22—224no—
593C22—441no—
594C22—441no—
595C22—442no—
596C22C23×C4×D1111yescharacteristic
597C22C22×#434111yescharacteristic
598C22C2×#6703712yes—
599C22C2×#41×D1111yescharacteristic
600C22#1062345312yes—
601C4—22no—
602C4—24no—
603C4—44no—
604C4—42no—
605C4—224no—
606C4—222no—
607C4—224no—
608C4—228no—
609C4—441no—
610C4—441no—
611C4—444no—
612C4C4×#434114yes—
613C4#1062325014yesdirect product factor
614C2—48no—
615C2—442no—
616C2C2×C4×#434111yescharacteristic
617C2C4×#6703712yes—
618C2C2×#1062325011yescharacteristic
619C2#1308200511yescharacteristic
620C2#1308203012yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#127C2
socle, cosocleC23×C11C25
prime radicalC2×#10623250C2
hypercenterC4×#127D11
hypocenterC11C4×#540
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
2. #13071403C2semidirect
3. #13071375C2semidirect
4. #13071355C2semidirect
5. #13071342C2semidirect
6. #13071312C2semidirect
7. #13071253C2semidirect
8. #13071224C2semidirect
9. C4×#66923C2semidirect
10. C4×#66988C2semidirect
11. C4×#66992C2semidirect
12. C4×#66991C2semidirect
13. C4×D4×Dic11C2semidirect
14. C4×#66925C2semidirect
15. C4×C11×#127C2semidirect
26. #10623250C4direct (N × H)
81. C11×#127C2×C4semidirect
99. #66992C2×C4semidirect
100. #66991C2×C4semidirect
101. #66988C2×C4semidirect
103. D4×Dic11C2×C4semidirect
127. #66925C2×C4semidirect
129. #66923C2×C4semidirect
225. C4×#127D11semidirect
367. C4×C11#540semidirect
384. #127C4×D11semidirect
526. C11C4×#540semidirect
613. C4#10623250direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232502
#130714032
#130713752
#130713552
#130713422
#130713122
#130712532
#130712242
C4×#669232
C4×#669882
C4×#669922
C4×#669912
C4×D4×Dic112
C4×#669252
C4×C11×#1272
C4×#54011