Finite Group Databasebeta

← C2×C4×#66982 #14912209

Subgroups — C2×C4×#66982 #14912209

Order 2816.

4070 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3C4×#66982C2116yesmaximal, direct product factor
4C2×#10622553C212yesmaximal, complemented
5C2×#10622546C212yesmaximal, complemented
6C2×#10622826C211yesmaximal, characteristic
7C2×#10622823C211yesmaximal, characteristic, complemented
8C2×#10622824C211yesmaximal, characteristic, complemented
9C2×C4×Dic11⋊C4C212yesmaximal, complemented
10C2×C4×(C2×D11)⋊C4C212yesmaximal, complemented
11C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
12C23×C42×C11C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C42×C11—28no—
19C22×C42×C11C2212yes—
20C22×C42×C11C2212yes—
21C22×C42×C11C2218yescomplemented
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C2×#66982C4116yesdirect product factor
26C2×#66982C2218yes—
27C2×C4×C22⋊D11—28no—
28C2×C4×C22⋊D11C2218yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2212yes—
32C22×Dic11⋊C4C2212yes—
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2212yes—
35C22×C4×Dic11C2212yes—
36C22×C4×Dic11C2211yescharacteristic
37#10622826C2218yes—
38#10622824C2218yescomplemented
39#10622823C2218yescomplemented
40C4×C22⋊Dic11C2218yescomplemented
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45C2×C11⋊#95C2212yes—
46#10622553C22116yescomplemented
47C4×(C2×D11)⋊C4C22116yescomplemented
48#10622546C22116yescomplemented
49C4×Dic11⋊C4C22116yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11—24no—
53C23×C4×C11—24no—
54C23×C4×C11—24no—
55C23×C4×C11—28no—
56C23×C4×C11—28no—
57C23×C4×C11C2×C418yescomplemented
58C23×C4×C11D418yes—
59C23×C4×C11C2314yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2314yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2314yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—24no—
67C22×C22⋊D11—24no—
68C22×C22⋊D11C2×C418yes—
69C22×C22⋊D11C2314yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2312yes—
75C22×C4×D11—24no—
76C22×C4×D11—28no—
77C22×C4×D11C2314yes—
78C2×C42×C11—28no—
79C2×C42×C11—28no—
80C2×C42×C11—232no—
81C2×C42×C11C2318yes—
82C2×C42×C11C2318yes—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11C2×C418yescomplemented
86C2×C22⋊Dic11C2314yes—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2314yes—
89#66982C2×C4164yesdirect product factor
90C4×C22⋊D11—232no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—28no—
93C2×(C2×D11)⋊C4C2×C4116yescomplemented
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—28no—
99C2×Dic11⋊C4C2×C4116yescomplemented
100C2×Dic11⋊C4C2318yes—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2318yes—
103C2×C4×Dic11—24no—
104C2×C4×Dic11—28no—
105C2×C4×Dic11C2314yes—
106C2×C4×Dic11C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C2×C4×#123—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—24no—
115C24×C11C22×C414yes—
116C24×C11C2×D414yes—
117C24×C11#4114yes—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—22no—
124C23×D11C22×C414yes—
125C23×D11C2412yes—
126C22×C4×C11—232no—
127C22×C4×C11—232no—
128C22×C4×C11—28no—
129C22×C4×C11—24no—
130C22×C4×C11—28no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—28no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—232no—
137C22×C4×C11—216no—
138C22×C4×C11—216no—
139C22×C4×C11C22×C418yes—
140C22×C4×C11C22×C4116yescomplemented
141C22×C4×C11C2×D414yes—
142C22×C4×C11C2×D4116yes—
143C22×C4×C11C2×D414yes—
144C22×C4×C11#4118yes—
145C22×C4×C11#4118yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C2×C22⋊D11—232no—
151C2×C22⋊D11—28no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11C22×C4116yes—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11C22×C414yes—
166C22×Dic11C22×C418yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C22×Dic11C2412yes—
170C22×Dic11C2412yes—
171C22×Dic11C2414yes—
172C2×C4×D11—28no—
173C2×C4×D11—216no—
174C2×C4×D11—416no—
175C42×C11—216no—
176C42×C11—216no—
177C22⋊Dic11—28no—
178C22⋊Dic11—28no—
179C22⋊Dic11C22×C4116yescomplemented
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4C22×C4132yescomplemented
183Dic11⋊C4—28no—
184Dic11⋊C4—216no—
185Dic11⋊C4C22×C4132yescomplemented
186C4×Dic11—28no—
187C4×Dic11—216no—
188C22×#123—111no—
189C22×C4×D4—111no—
190C23×C42D1111yescharacteristic, complemented
191C4×#123—1116no—
192C2×#388—112no—
193C2×#387—112no—
194C2×#386—111no—
195C2×#385—111no—
196C2×#381—111no—
197C2×C4×C4⋊C4—112no—
198C2×C4×C22⋊C4—112no—
199C2×C4×C22⋊C4—111no—
200C23×C11—216no—
201C23×C11—28no—
202C23×C11—28no—
203C23×C11—216no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11C4×D4116yes—
207C23×C11C23×C414yes—
208C23×C11C23×C412yes—
209C23×C11C22×D414yes—
210C23×C11C22×D412yes—
211C23×C11C2×#4114yes—
212C23×C11C2×#4112yes—
213C23×C11C2×#4114yes—
214C23×C11C2×#4114yes—
215C23×C11C2511yescharacteristic
216C22×D11—28no—
217C22×D11—216no—
218C22×D11—22no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—22no—
222C22×D11—44no—
223C22×D11—44no—
224C22×D11—48no—
225C22×D11C23×C414yes—
226C2×C4×C11—232no—
227C2×C4×C11—216no—
228C2×C4×C11—232no—
229C2×C4×C11—28no—
230C2×C4×C11—216no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—232no—
237C2×C4×C11#123116yescomplemented
238C2×C4×C11C23×C418yes—
239C2×C4×C11C22×D414yes—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C2×#4118yes—
242C2×C4×C11C2×#4118yes—
243C22⋊D11—232no—
244C2×Dic11—28no—
245C2×Dic11—216no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—44no—
258C2×Dic11—44no—
259C2×Dic11—48no—
260C2×Dic11C23×C414yes—
261C2×Dic11C23×C418yes—
262C4×D11—416no—
263C23×D4—111no—
264C24×C4—111no—
265C24×C4C2×D1111yescharacteristic
266C24×C4C2×D1111yescharacteristic
267C24×C4C2×D1111yescharacteristic
268C2×#123—118no—
269C2×#123—1116no—
270C2×C4×D4—118no—
271C2×C4×D4—228no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4—112no—
275C22×C22⋊C4—111no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—111no—
279C22×C22⋊C4—111no—
280C22×C22⋊C4—112no—
281C22×C42—28no—
282C22×C42—111no—
283C22×C42—112no—
284C22×C42C2×D1112yes—
285C22×C42C2×D1112yes—
286C22×C42C2×D1118yescomplemented
287#388—1116no—
288#387—1116no—
289#386—118no—
290#385—118no—
291#381—118no—
292C4×C4⋊C4—1116no—
293C4×C22⋊C4—118no—
294C4×C22⋊C4—1116no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C22×C11—28no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—28no—
304C22×C11—232no—
305C22×C11C2×C4×D418yes—
306C22×C11C2×C4×D414yes—
307C22×C11C4×#4118yes—
308C22×C11C2×#12314yes—
309C22×C11#52514yes—
310C22×C11#52918yes—
311C22×C11C24×C411yescharacteristic
312C22×C11C23×D411yescharacteristic
313C22×C11C22×#4111yescharacteristic
314C22×C11C22×#4112yes—
315C22×C11C22×#4112yes—
316C2×D11—24no—
317C2×D11—28no—
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—44no—
321C2×D11—416no—
322C4×C11—28no—
323C4×C11—24no—
324C4×C11—28no—
325C4×C11C2×#12318yescomplemented
326Dic11—24no—
327Dic11—28no—
328Dic11—42no—
329Dic11—42no—
330Dic11—44no—
331C25—111no—
332C25C22×D1111yescharacteristic
333C22×D4—118no—
334C22×D4—114no—
335C22×D4—224no—
336C22×D4—224no—
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—24no—
340C23×C4—28no—
341C23×C4—28no—
342C23×C4—112no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—112no—
346C23×C4—111no—
347C23×C4—114no—
348C23×C4—228no—
349C23×C4—224no—
350C23×C4C4×D1118yescomplemented
351C23×C4C22⋊D1118yes—
352C23×C4C22×D1114yes—
353C23×C4C22×D1112yes—
354C23×C4C22×D1114yes—
355C23×C4C22×D1112yes—
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1114yes—
358C23×C4C22×D1111yescharacteristic
359#123—1164no—
360C4×D4—2232no—
361C2×C4⋊C4—1116no—
362C2×C4⋊C4—118no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—118no—
365C2×C4⋊C4—228no—
366C2×C4⋊C4—224no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—1116no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—114no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—228no—
378C2×C22⋊C4—224no—
379C2×C42—28no—
380C2×C42—28no—
381C2×C42—232no—
382C2×C42—114no—
383C2×C42—118no—
384C2×C42—228no—
385C2×C42—224no—
386C2×C42C22×D1118yes—
387C2×C42C22×D1118yes—
388#95—118no—
389#95—118no—
390#95—118no—
391#95—118no—
392#95—118no—
393C2×C11—28no—
394C2×C11C4×#12318yescomplemented
395C2×C11C22×C4×D411yescharacteristic
396C2×C11C2×C4×#4112yes—
397C2×C11C22×#12311yescharacteristic
398C2×C11C2×#52511yescharacteristic
399C2×C11C2×#52912yes—
400D11—44no—
401C24—24no—
402C24—24no—
403C24—114no—
404C24—112no—
405C24—224no—
406C24—224no—
407C24—222no—
408C24—222no—
409C24C2×C4×D1114yes—
410C24#433914yes—
411C24C2×C22⋊D1114yes—
412C24C23×D1112yes—
413C24C23×D1111yescharacteristic
414C2×D4—1116no—
415C2×D4—2232no—
416C2×D4—228no—
417C2×D4—228no—
418C22×C4—232no—
419C22×C4—232no—
420C22×C4—24no—
421C22×C4—28no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—28no—
425C22×C4—24no—
426C22×C4—28no—
427C22×C4—24no—
428C22×C4—232no—
429C22×C4—216no—
430C22×C4—216no—
431C22×C4—118no—
432C22×C4—114no—
433C22×C4—114no—
434C22×C4—112no—
435C22×C4—114no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—2216no—
450C22×C4—228no—
451C22×C4—4416no—
452C22×C4C2×C4×D1118yes—
453C22×C4C2×C4×D11116yescomplemented
454C22×C4#433918yes—
455C22×C4#433918yes—
456C22×C4C2×C22⋊D1114yes—
457C22×C4C2×C22⋊D11116yes—
458C22×C4C2×C22⋊D1114yes—
459C22×C4C23×D1114yes—
460C22×C4C23×D1114yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1112yes—
463C4⋊C4—1132no—
464C4⋊C4—2216no—
465C4⋊C4—228no—
466C22⋊C4—1116no—
467C22⋊C4—1132no—
468C22⋊C4—228no—
469C22⋊C4—228no—
470C22⋊C4—2216no—
471C22⋊C4—228no—
472C42—216no—
473C42—216no—
474C42—2216no—
475C42—228no—
476C11C2×C4×#12311yescharacteristic, complemented, Sylow
477C23—216no—
478C23—216no—
479C23—28no—
480C23—28no—
481C23—24no—
482C23—24no—
483C23—114no—
484C23—2216no—
485C23—228no—
486C23—224no—
487C23—224no—
488C23—222no—
489C23—222no—
490C23—448no—
491C23—444no—
492C23—444no—
493C23C4×C22⋊D11116yes—
494C23C22×C4×D1114yes—
495C23C22×C4×D1112yes—
496C23C2×#433914yes—
497C23C2×#433914yes—
498C23C2×#433914yes—
499C23C2×#433912yes—
500C23C22×C22⋊D1114yes—
501C23C22×C22⋊D1112yes—
502C23C24×D1111yescharacteristic
503D4—2232no—
504C2×C4—232no—
505C2×C4—216no—
506C2×C4—232no—
507C2×C4—28no—
508C2×C4—216no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—232no—
515C2×C4—118no—
516C2×C4—114no—
517C2×C4—2216no—
518C2×C4—228no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—448no—
531C2×C4—444no—
532C2×C4—444no—
533C2×C4—4416no—
534C2×C4#66982116yesdirect product factor
535C2×C4C22×C4×D1118yes—
536C2×C4C2×#433918yes—
537C2×C4C2×#433918yes—
538C2×C4C22×C22⋊D1114yes—
539C2×C4C22×C22⋊D1114yes—
540C22—24no—
541C22—28no—
542C22—232no—
543C22—28no—
544C22—24no—
545C22—224no—
546C22—228no—
547C22—442no—
548C22—444no—
549C22—4416no—
550C22—442no—
551C22C4×#433918yes—
552C22#1062301018yes—
553C22C2×C4×C22⋊D1118yes—
554C22C2×C4×C22⋊D1114yes—
555C22C2×#6698214yes—
556C22#1062332214yes—
557C22C23×C4×D1111yescharacteristic
558C22C22×#433912yes—
559C22C22×#433911yescharacteristic
560C22C22×#433912yes—
561C22C23×C22⋊D1111yescharacteristic
562C4—28no—
563C4—28no—
564C4—24no—
565C4—224no—
566C4—228no—
567C4—442no—
568C4—444no—
569C4—442no—
570C4C2×#6698218yesdirect product factor
571C2—28no—
572C2—444no—
573C2C4×#6698218yesdirect product factor
574C2C22×C4×C22⋊D1111yescharacteristic
575C2C2×C4×#433912yes—
576C2C22×#6698211yescharacteristic
577C2C2×#1062332211yescharacteristic
578C2C2×#1062301012yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC23×C42×C11C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
cosocleC23×C11C25
hypercenterC23×C42D11
hypocenterC11C2×C4×#123
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C23×C42

Complements

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

NH ≅ G/Ntype
3. C4×#66982C2direct (N × H)
4. C2×#10622553C2semidirect
5. C2×#10622546C2semidirect
7. C2×#10622823C2semidirect
8. C2×#10622824C2semidirect
9. C2×C4×Dic11⋊C4C2semidirect
10. C2×C4×(C2×D11)⋊C4C2semidirect
11. C2×C4×C22⋊Dic11C2semidirect
12. C23×C42×C11C2semidirect
21. C22×C42×C11C22semidirect
25. C2×#66982C4direct (N × H)
38. #10622824C22semidirect
39. #10622823C22semidirect
40. C4×C22⋊Dic11C22semidirect
46. #10622553C22semidirect
47. C4×(C2×D11)⋊C4C22semidirect
48. #10622546C22semidirect
49. C4×Dic11⋊C4C22semidirect
57. C23×C4×C11C2×C4semidirect
85. C2×C22⋊Dic11C2×C4semidirect
89. #66982C2×C4direct (N × H)
93. C2×(C2×D11)⋊C4C2×C4semidirect
99. C2×Dic11⋊C4C2×C4semidirect
140. C22×C4×C11C22×C4semidirect
179. C22⋊Dic11C22×C4semidirect
182. (C2×D11)⋊C4C22×C4semidirect
185. Dic11⋊C4C22×C4semidirect
190. C23×C42D11semidirect
237. C2×C4×C11#123semidirect
286. C22×C42C2×D11semidirect
325. C4×C11C2×#123semidirect
350. C23×C4C4×D11semidirect
394. C2×C11C4×#123semidirect
453. C22×C4C2×C4×D11semidirect
476. C11C2×C4×#123semidirect
534. C2×C4#66982direct (N × H)
570. C4C2×#66982direct (N × H)
573. C2C4×#66982direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
C22×C4×C22⋊D112
C4×#669822
C2×#106225532
C2×#106225462
C2×#106228262
C2×#106228232
C2×#106228242
C2×C4×Dic11⋊C42
C2×C4×(C2×D11)⋊C42
C2×C4×C22⋊Dic112
C23×C42×C112
C2×C4×#12311