Finite Group Databasebeta

← C2×#13072124 #14921644

Subgroups — C2×#13072124 #14921644

Order 2816.

3830 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C212yesmaximal, complemented
2C22×#66991C211yesmaximal, characteristic
3#13072124C2116yesmaximal, direct product factor
4C2×#10622565C212yesmaximal, complemented
5C2×#10622572C212yesmaximal, complemented
6C2×#10622834C211yesmaximal, characteristic, complemented
7C2×#10622541C211yesmaximal, characteristic, complemented
8C2×#10622823C212yesmaximal, complemented
9C2×#10622589C211yesmaximal, characteristic, complemented
10C2×#10622600C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12C22×C4×D4×C11C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C2×C4×D4×C11—28no—
18C2×C4×D4×C11C2218yescomplemented
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66991—28no—
26C2×#66991C2218yes—
27C2×#66982—216no—
28C2×#66982C22116yescomplemented
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2212yes—
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2212yes—
35C22×Dic11⋊C4C2212yes—
36C22×Dic11⋊C4C2212yes—
37C22×C4×Dic11C2211yescharacteristic
38#10622834C2218yescomplemented
39#10622823C22116yescomplemented
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622600C2218yescomplemented
45#10622589C2218yescomplemented
46#10622572C22116yescomplemented
47#10622565C22116yescomplemented
48C4×(C2×D11)⋊C4C2218yescomplemented
49#10622541C2218yescomplemented
50C25×C11C2312yes—
51C24×D11C2311yescharacteristic
52C22×D4×C11—24no—
53C22×D4×C11—24no—
54C22×D4×C11D418yes—
55C22×D4×C11C2314yes—
56C23×C4×C11—28no—
57C23×C4×C11—28no—
58C23×C4×C11—44no—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2318yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—28no—
65C22×C22⋊D11—28no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11C2318yes—
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—24no—
74C22×C4×D11—24no—
75C22×C4×D11—24no—
76C22×C4×D11C2314yes—
77C4×D4×C11—232no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C22⋊C4—28no—
81C2×C11×C22⋊C4C2318yes—
82C2×C42×C11—24no—
83C2×C42×C11C2314yes—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11—28no—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11C2318yes—
88C2×C22⋊Dic11C2318yes—
89C2×C22⋊Dic11C2318yes—
90#66991—232no—
91#66982—264no—
92C2×(C2×D11)⋊C4—28no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4D418yescomplemented
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×C4⋊Dic11—24no—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11C2314yes—
101C2×C4⋊Dic11C2314yes—
102C2×Dic11⋊C4—28no—
103C2×Dic11⋊C4—28no—
104C2×Dic11⋊C4—44no—
105C2×Dic11⋊C4C2318yes—
106C2×Dic11⋊C4C2318yes—
107C2×Dic11⋊C4C2318yes—
108C2×C4×Dic11—24no—
109C2×C4×Dic11C2314yes—
110C11⋊#95C2318yes—
111C11⋊#95C2314yes—
112C11⋊#95C2314yes—
113C11⋊#95C2318yes—
114C2×#2422—111nomaximal, Sylow
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11C2×D418yes—
122C24×C11C2414yes—
123C24×C11C2411yescharacteristic
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11C2×D414yes—
131C23×D11C2412yes—
132C2×D4×C11—232no—
133C2×D4×C11—28no—
134C2×D4×C11—28no—
135C2×D4×C11C2×D4116yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—216no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—216no—
146C22×C4×C11—48no—
147C22×C4×C11—432no—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11#4114yes—
151C22×C4×C11#4114yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C2×C22⋊D11—216no—
157C2×C22⋊D11—216no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—432no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—24no—
172C22×Dic11—22no—
173C22×Dic11C2×D414yes—
174C22×Dic11#4114yes—
175C22×Dic11C2412yes—
176C22×Dic11C2414yes—
177C22×Dic11C2414yes—
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C2×C4×D11—28no—
181C2×C4×D11—28no—
182C2×C4×D11—28no—
183C2×C4×D11—416no—
184C11×C4⋊C4—28no—
185C11×C22⋊C4—216no—
186C42×C11—28no—
187C22⋊Dic11—216no—
188C22⋊Dic11—216no—
189C22⋊Dic11—216no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—216no—
192(C2×D11)⋊C4C2×D4116yescomplemented
193C4⋊Dic11—28no—
194C4⋊Dic11—28no—
195Dic11⋊C4—216no—
196Dic11⋊C4—216no—
197Dic11⋊C4—48no—
198C4×Dic11—28no—
199C22×#123—112no—
200C22×#121—111no—
201C22×C4×D4D1111yescharacteristic, complemented
202#2422—1116no—
203C2×#397—112no—
204C2×#394—112no—
205C2×#390—111no—
206C2×#389—111no—
207C2×#385—112no—
208C2×#384—111no—
209C2×#380—111no—
210C2×C4×C22⋊C4—111no—
211C23×C11—216no—
212C23×C11—216no—
213C23×C11—216no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—48no—
221C23×C11—48no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11C22×D412yes—
225C23×C11C22×D418yes—
226C23×C11C22×D412yes—
227C23×C11C2×#4112yes—
228C23×C11C2×#4112yes—
229C23×C11C2×#4112yes—
230C23×C11H(5,𝔽2)12yes—
231C23×C112−1+412yes—
232C23×C11C2511yescharacteristic
233C22×D11—28no—
234C22×D11—28no—
235C22×D11—28no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—44no—
243C22×D11—44no—
244C22×D11—44no—
245C22×D11—44no—
246C22×D11C22×D414yes—
247D4×C11—232no—
248C2×C4×C11—28no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—432no—
258C2×C4×C11—48no—
259C2×C4×C11—44no—
260C2×C4×C11#123116yescomplemented
261C2×C4×C11C22×D414yes—
262C2×C4×C11C22×D414yes—
263C2×C4×C11C2×#4114yes—
264C2×C4×C11C2×#4114yes—
265C22⋊D11—432no—
266C2×Dic11—28no—
267C2×Dic11—28no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—24no—
281C2×Dic11—44no—
282C2×Dic11—48no—
283C2×Dic11—48no—
284C2×Dic11C22×D414yes—
285C2×Dic11C2×#4114yes—
286C4×D11—416no—
287C23×D4—112no—
288C23×D4C2×D1111yescharacteristic
289C24×C4—111no—
290C24×C4C2×D1112yes—
291C2×#123—1116no—
292C2×#123—2216no—
293C2×#121—118no—
294C2×#121—228no—
295C2×C4×D4—28no—
296C2×C4×D4C2×D1118yescomplemented
297C22×C4⋊C4—112no—
298C22×C4⋊C4—112no—
299C22×C4⋊C4—111no—
300C22×C4⋊C4—111no—
301C22×C4⋊C4—112no—
302C22×C4⋊C4C2×D1111yescharacteristic
303C22×C22⋊C4—111no—
304C22×C22⋊C4—112no—
305C22×C22⋊C4—112no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—111no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4C2×D1112yes—
310C22×C42—111no—
311C22×C42C2×D1111yescharacteristic
312#397—1116no—
313#394—1116no—
314#390—118no—
315#389—118no—
316#385—1116no—
317#384—118no—
318#380—118no—
319C4×C22⋊C4—118no—
320C2×#95—112no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—111no—
324C22×C11—28no—
325C22×C11—28no—
326C22×C11—28no—
327C22×C11—44no—
328C22×C11—432no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11C2×#12314yes—
333C22×C11#53214yes—
334C22×C11#54214yes—
335C22×C11D4214yes—
336C22×C11#54714yes—
337C22×C11#54714yes—
338C22×C11#55314yes—
339C22×C11C23×D411yescharacteristic
340C22×C11C23×D411yescharacteristic
341C22×C11C22×#4111yescharacteristic
342C22×C11C22×#4111yescharacteristic
343C22×C11C22×#4111yescharacteristic
344C22×C11C2×H(5,𝔽2)11yescharacteristic
345C22×C11C2×2−1+411yescharacteristic
346C2×D11—24no—
347C2×D11—24no—
348C2×D11—24no—
349C2×D11—42no—
350C2×D11—416no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C4×C11—24no—
355C4×C11—44no—
356C4×C11—42no—
357C4×C11C2×#12318yescomplemented
358Dic11—24no—
359Dic11—24no—
360Dic11—42no—
361Dic11—44no—
362Dic11—44no—
363C25—111no—
364C25C22×D1112yes—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—118no—
368C22×D4—228no—
369C22×D4—228no—
370C22×D4—444no—
371C22×D4C22⋊D1118yes—
372C22×D4C22×D1114yes—
373C23×C4—28no—
374C23×C4—28no—
375C23×C4—44no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—112no—
379C23×C4—111no—
380C23×C4—112no—
381C23×C4—114no—
382C23×C4—224no—
383C23×C4—224no—
384C23×C4—224no—
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1112yes—
387C23×C4C22×D1118yes—
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1111yescharacteristic
390#123—2264no—
391#121—2232no—
392C4×D4—232no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—118no—
396C2×C4⋊C4—118no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—118no—
399C2×C4⋊C4—228no—
400C2×C4⋊C4—224no—
401C2×C4⋊C4—228no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—444no—
404C2×C4⋊C4C22×D1114yes—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—114no—
408C2×C22⋊C4—118no—
409C2×C22⋊C4—118no—
410C2×C22⋊C4—118no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4—224no—
414C2×C22⋊C4—228no—
415C2×C22⋊C4—228no—
416C2×C22⋊C4—228no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4C22×D1118yes—
419C2×C42—24no—
420C2×C42—114no—
421C2×C42—224no—
422C2×C42C22×D1114yes—
423#95—114no—
424#95—114no—
425#95—118no—
426#95—118no—
427C2×C11—48no—
428C2×C11#242218yescomplemented
429C2×C11C22×#12311yescharacteristic
430C2×C11C2×#53211yescharacteristic
431C2×C11C2×#54211yescharacteristic
432C2×C11C2×D4211yescharacteristic
433C2×C11C2×#54711yescharacteristic
434C2×C11C2×#54711yescharacteristic
435C2×C11C2×#55311yescharacteristic
436D11—44no—
437C24—24no—
438C24—24no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—114no—
444C24—112no—
445C24—222no—
446C24—222no—
447C24—222no—
448C24—222no—
449C24—222no—
450C24—222no—
451C24C2×C22⋊D1118yes—
452C24C23×D1114yes—
453C24C23×D1111yescharacteristic
454C2×D4—232no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—2216no—
458C2×D4—2216no—
459C2×D4—448no—
460C2×D4—4432no—
461C2×D4C2×C22⋊D11116yes—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—48no—
473C22×C4—432no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—112no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—114no—
480C22×C4—114no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—224no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—224no—
492C22×C4—222no—
493C22×C4—224no—
494C22×C4—228no—
495C22×C4—228no—
496C22×C4—228no—
497C22×C4—4416no—
498C22×C4#433914yes—
499C22×C4#433914yes—
500C22×C4D4×D1114yes—
501C22×C4C2×C22⋊D1114yes—
502C22×C4C23×D1112yes—
503C22×C4C23×D1114yes—
504C22×C4C23×D1112yes—
505C22×C4C23×D1112yes—
506C4⋊C4—28no—
507C4⋊C4—2216no—
508C4⋊C4—228no—
509C4⋊C4—2216no—
510C4⋊C4—228no—
511C4⋊C4—448no—
512C22⋊C4—216no—
513C22⋊C4—1116no—
514C22⋊C4—228no—
515C22⋊C4—2216no—
516C22⋊C4—2216no—
517C22⋊C4—2216no—
518C22⋊C4—2216no—
519C42—28no—
520C42—228no—
521C11C2×#242211yescharacteristic, complemented, Sylow
522C23—216no—
523C23—216no—
524C23—216no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—48no—
532C23—48no—
533C23—48no—
534C23—48no—
535C23—114no—
536C23—228no—
537C23—228no—
538C23—228no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23—222no—
543C23—222no—
544C23—222no—
545C23—444no—
546C23—444no—
547C23—444no—
548C23—444no—
549C23C2×#433912yes—
550C23C2×#433912yes—
551C23C2×D4×D1112yes—
552C23#6703712yes—
553C23#41×D1112yes—
554C23#6704312yes—
555C23C22×C22⋊D1118yes—
556C23C22×C22⋊D1112yes—
557C23C24×D1111yescharacteristic
558D4—232no—
559D4—4432no—
560C2×C4—28no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—432no—
570C2×C4—48no—
571C2×C4—44no—
572C2×C4—114no—
573C2×C4—114no—
574C2×C4—228no—
575C2×C4—228no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—224no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—222no—
588C2×C4—224no—
589C2×C4—444no—
590C2×C4—448no—
591C2×C4—448no—
592C2×C4—4416no—
593C2×C4#66982116yescomplemented
594C2×C4C2×#433914yes—
595C2×C4C2×#433914yes—
596C2×C4C2×D4×D1114yes—
597C2×C4C22×C22⋊D1114yes—
598C22—28no—
599C22—28no—
600C22—28no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—432no—
606C22—224no—
607C22—224no—
608C22—224no—
609C22—442no—
610C22—442no—
611C22—442no—
612C22—442no—
613C22—4416no—
614C22#1062307914yes—
615C22#1062308214yes—
616C22#1062308914yes—
617C22#1062309214yes—
618C22C2×#6698214yes—
619C22D4×C22⋊D1114yes—
620C22#1062335514yes—
621C22C22×#433911yescharacteristic
622C22C22×#433911yescharacteristic
623C22C22×D4×D1111yescharacteristic
624C22C2×#6703711yescharacteristic
625C22C2×#41×D1111yescharacteristic
626C22C2×#6704311yescharacteristic
627C22C23×C22⋊D1111yescharacteristic
628C4—24no—
629C4—44no—
630C4—42no—
631C4—224no—
632C4—224no—
633C4—444no—
634C4—444no—
635C4—442no—
636C4C2×#6698218yescomplemented
637C2—48no—
638C2—444no—
639C2#1307212418yesdirect product factor
640C2C22×#6698211yescharacteristic
641C2C2×#1062307911yescharacteristic
642C2C2×#1062309211yescharacteristic
643C2C2×D4×C22⋊D1111yescharacteristic
644C2C2×#1062335511yescharacteristic
645C2C2×#1062308211yescharacteristic
646C2C2×#1062308911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC22×#66991C2
hypercenterC22×C4×D4D11
hypocenterC11C2×#2422
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
3. #13072124C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622572C2semidirect
6. C2×#10622834C2semidirect
7. C2×#10622541C2semidirect
8. C2×#10622823C2semidirect
9. C2×#10622589C2semidirect
10. C2×#10622600C2semidirect
11. C2×C4×(C2×D11)⋊C4C2semidirect
12. C22×C4×D4×C11C2semidirect
18. C2×C4×D4×C11C22semidirect
28. C2×#66982C22semidirect
38. #10622834C22semidirect
39. #10622823C22semidirect
44. #10622600C22semidirect
45. #10622589C22semidirect
46. #10622572C22semidirect
47. #10622565C22semidirect
48. C4×(C2×D11)⋊C4C22semidirect
49. #10622541C22semidirect
94. C2×(C2×D11)⋊C4D4semidirect
192. (C2×D11)⋊C4C2×D4semidirect
201. C22×C4×D4D11semidirect
260. C2×C4×C11#123semidirect
296. C2×C4×D4C2×D11semidirect
357. C4×C11C2×#123semidirect
428. C2×C11#2422semidirect
521. C11C2×#2422semidirect
593. C2×C4#66982semidirect
636. C4C2×#66982semidirect
639. C2#13072124direct (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×#669912
#130721242
C2×#106225652
C2×#106225722
C2×#106228342
C2×#106225412
C2×#106228232
C2×#106225892
C2×#106226002
C2×C4×(C2×D11)⋊C42
C22×C4×D4×C112
C2×#242211