Finite Group Databasebeta

← C2×#13074368 #14920780

Subgroups — C2×#13074368 #14920780

Order 2816.

4342 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic, complemented
2C22×#66937C212yesmaximal, complemented
3C22×#66945C211yesmaximal, characteristic, complemented
4#13074368C2116yesmaximal, direct product factor
5C2×#10622604C211yesmaximal, characteristic, complemented
6C2×#10622574C212yesmaximal, complemented
7C2×#10622284C211yesmaximal, characteristic, complemented
8C2×#10622573C212yesmaximal, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622570C212yesmaximal, complemented
11C2×#10622263C211yesmaximal, characteristic, complemented
12C2×C11×#394C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×C22⋊D11C2212yes—
17C23×D44C2211yescharacteristic
18C23×D44C2212yes—
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C11×C22⋊C4C2212yes—
23C22×C22⋊Dic11C2212yes—
24C2×#66993—28no—
25C2×#66993C2218yescomplemented
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2212yes—
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66945—28no—
36C2×#66945C2218yescomplemented
37C2×#66937—216no—
38C2×#66937C22116yescomplemented
39C11×#394C2218yescomplemented
40C2×C11×#95C2211yescharacteristic
41#10622836C2218yescomplemented
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2212yes—
44#10622604C2218yescomplemented
45#10622574C22116yescomplemented
46#10622573C22116yescomplemented
47#10622570C22116yescomplemented
48#10622284C2218yescomplemented
49#10622263C2218yescomplemented
50C25×C11C2312yes—
51C24×D11C2312yes—
52C24×D11C2311yescharacteristic
53C22×D4×C11—24no—
54C22×D4×C11—44no—
55C22×D4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—28no—
61C22×C22⋊D11—28no—
62C22×C22⋊D11—28no—
63C22×C22⋊D11—28no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11—44no—
68C22×C22⋊D11—44no—
69C22×C22⋊D11C2318yes—
70C22×C22⋊D11C2318yes—
71C22×C22⋊D11C2318yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C22×D44—28no—
77C22×D44—24no—
78C22×D44—44no—
79C22×D44—44no—
80C22×D44—44no—
81C22×D44C2318yes—
82C22×D44C2314yes—
83C22×C4×D11—24no—
84C22×C4×D11—24no—
85C22×C4×D11D418yescomplemented
86C22×C4×D11C2314yes—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C22⋊C4—28no—
90C2×C11×C22⋊C4—44no—
91C2×C11×C22⋊C4C2318yes—
92C2×C11×C22⋊C4C2318yes—
93C2×C22⋊Dic11—44no—
94C2×C22⋊Dic11C2318yes—
95#66993—232no—
96C2×(C2×D11)⋊C4—28no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—44no—
100C2×(C2×D11)⋊C4—44no—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×(C2×D11)⋊C4C2318yes—
106C2×C4⋊Dic11—24no—
107C2×C4⋊Dic11C2314yes—
108C2×Dic11⋊C4—28no—
109C2×Dic11⋊C4C2318yes—
110C2×C4×Dic11—24no—
111C2×C4×Dic11D418yescomplemented
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2314yes—
114#66945—232no—
115#66937—264no—
116C11×#95C2314yes—
117C11⋊#95C2318yes—
118C11⋊#95C2314yes—
119C2×#2619—111nomaximal, Sylow
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11—24no—
125C24×C11—24no—
126C24×C11—24no—
127C24×C11C2414yes—
128C24×C11C2411yescharacteristic
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11—24no—
134C23×D11—24no—
135C23×D11—24no—
136C23×D11—24no—
137C23×D11—24no—
138C23×D11—24no—
139C23×D11—24no—
140C23×D11C2×D414yes—
141C23×D11C2414yes—
142C23×D11C2412yes—
143C2×D4×C11—28no—
144C2×D4×C11—48no—
145C2×D4×C11—416no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2412yes—
160C2×C22⋊D11—216no—
161C2×C22⋊D11—216no—
162C2×C22⋊D11—216no—
163C2×C22⋊D11—216no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11—48no—
166C2×C22⋊D11—48no—
167C2×C22⋊D11—48no—
168C2×C22⋊D11—48no—
169C2×C22⋊D11—432no—
170C2×C22⋊D11—432no—
171C2×C22⋊D11—432no—
172C22×Dic11—22no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—24no—
177C22×Dic11—24no—
178C22×Dic11C2×D414yes—
179C22×Dic11C2×D414yes—
180C22×Dic11C2×D414yes—
181C22×Dic11#4114yes—
182C22×Dic11C2414yes—
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C2×D44—216no—
187C2×D44—28no—
188C2×D44—48no—
189C2×D44—48no—
190C2×D44—48no—
191C2×D44—416no—
192C2×D44—432no—
193C2×C4×D11—232no—
194C2×C4×D11—28no—
195C2×C4×D11—28no—
196C2×C4×D11C2×D4116yescomplemented
197C11×C4⋊C4—28no—
198C11×C22⋊C4—216no—
199C11×C22⋊C4—48no—
200C22⋊Dic11—48no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—216no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—48no—
205(C2×D11)⋊C4—48no—
206C4⋊Dic11—28no—
207Dic11⋊C4—216no—
208C4×Dic11—28no—
209C4×Dic11C2×D4116yescomplemented
210C22×#127—111no—
211C22×#121—112no—
212C22×#117—111no—
213#2619—1116no—
214C2×#394—111no—
215C2×#394—112no—
216C2×#394D1111yescharacteristic, complemented
217C2×#392—111no—
218C2×#392—111no—
219C2×#392—112no—
220C2×#390—112no—
221C2×#382—111no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—48no—
230C23×C11—48no—
231C23×C11—48no—
232C23×C11—48no—
233C23×C11—48no—
234C23×C11—48no—
235C23×C11—48no—
236C23×C11C22×D412yes—
237C23×C11C22×D412yes—
238C23×C11C2×#4112yes—
239C23×C11H(5,𝔽2)14yes—
240C23×C11H(5,𝔽2)14yes—
241C23×C11C2511yescharacteristic
242C22×D11—28no—
243C22×D11—216no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—44no—
256C22×D11—44no—
257C22×D11—48no—
258C22×D11—48no—
259C22×D11—48no—
260C22×D11—48no—
261C22×D11—48no—
262C22×D11—48no—
263C22×D11—48no—
264C22×D11—48no—
265C22×D11C22×D414yes—
266D4×C11—416no—
267C2×C4×C11—28no—
268C2×C4×C11—28no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—22no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—48no—
278C2×C4×C11—44no—
279C2×C4×C11C22×D414yes—
280C2×C4×C11C22×D414yes—
281C22⋊D11—432no—
282C22⋊D11—432no—
283C22⋊D11—432no—
284C2×Dic11—28no—
285C2×Dic11—24no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—44no—
292C2×Dic11—48no—
293C2×Dic11#121116yes—
294C2×Dic11C22×D414yes—
295C2×Dic11C22×D414yes—
296C2×Dic11C22×D414yes—
297C2×Dic11C2×#4114yes—
298D44—416no—
299D44—432no—
300C4×D11—232no—
301C23×D4—112no—
302C23×D4—112no—
303C23×D4—112no—
304C23×D4—112no—
305C23×D4—111no—
306C23×D4C2×D1111yescharacteristic
307C24×C4—111no—
308C2×#127—118no—
309C2×#127—228no—
310C2×#121—1116no—
311C2×#121—2216no—
312C2×#117—118no—
313C2×#117—228no—
314C22×C4⋊C4—111no—
315C22×C4⋊C4—112no—
316C22×C4⋊C4C2×D1111yescharacteristic
317C22×C22⋊C4—111no—
318C22×C22⋊C4—111no—
319C22×C22⋊C4—112no—
320C22×C22⋊C4—112no—
321C22×C22⋊C4—112no—
322C22×C22⋊C4—112no—
323C22×C22⋊C4C2×D1112yes—
324C22×C22⋊C4C2×D1112yes—
325C22×C42—111no—
326C22×C42—111no—
327#394—118no—
328#394—1116no—
329#394C2×D1118yescomplemented
330#392—118no—
331#392—1116no—
332#392—118no—
333#390—1116no—
334#382—118no—
335C2×#95—112no—
336C2×#95—111no—
337C2×#95C2×D1111yescharacteristic
338C22×C11—44no—
339C22×C11—44no—
340C22×C11—44no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—44no—
344C22×C11—44no—
345C22×C11—816no—
346C22×C11C2×#12114yes—
347C22×C11#53514yes—
348C22×C11#53518yes—
349C22×C11#53514yes—
350C22×C11#54018yes—
351C22×C11C23×D411yescharacteristic
352C22×C11C23×D411yescharacteristic
353C22×C11C22×#4111yescharacteristic
354C22×C11C2×H(5,𝔽2)12yes—
355C22×C11C2×H(5,𝔽2)12yes—
356C2×D11—24no—
357C2×D11—28no—
358C2×D11—416no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—44no—
362C2×D11—44no—
363C2×D11—44no—
364C2×D11—44no—
365C2×D11—44no—
366C2×D11—44no—
367C2×D11—44no—
368C2×D11—44no—
369C2×D11—816no—
370C4×C11—24no—
371C4×C11—24no—
372C4×C11—42no—
373C4×C11—44no—
374Dic11—24no—
375Dic11—42no—
376Dic11—44no—
377Dic11C2×#12118yes—
378C25—111no—
379C25—112no—
380C25C22×D1112yes—
381C22×D4—24no—
382C22×D4—44no—
383C22×D4—118no—
384C22×D4—118no—
385C22×D4—118no—
386C22×D4—118no—
387C22×D4—114no—
388C22×D4—228no—
389C22×D4—228no—
390C22×D4—228no—
391C22×D4—228no—
392C22×D4—228no—
393C22×D4—228no—
394C22×D4—224no—
395C22×D4—444no—
396C22×D4—444no—
397C22×D4—444no—
398C22×D4—444no—
399C22×D4—444no—
400C22×D4—444no—
401C22×D4—444no—
402C22×D4C22×D1114yes—
403C23×C4—111no—
404C23×C4—111no—
405C23×C4—118no—
406C23×C4—114no—
407C23×C4—111no—
408C23×C4—112no—
409C23×C4—224no—
410C23×C4—224no—
411C23×C4C22×D1111yescharacteristic
412C23×C4C22×D1112yes—
413C23×C4C22×D1111yescharacteristic
414C23×C4C22×D1111yescharacteristic
415#127—2232no—
416#121—2264no—
417#117—2232no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—118no—
421C2×C4⋊C4—224no—
422C2×C4⋊C4—228no—
423C2×C4⋊C4C22×D1114yes—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—118no—
429C2×C22⋊C4—118no—
430C2×C22⋊C4—118no—
431C2×C22⋊C4—118no—
432C2×C22⋊C4—224no—
433C2×C22⋊C4—224no—
434C2×C22⋊C4—228no—
435C2×C22⋊C4—444no—
436C2×C22⋊C4—444no—
437C2×C22⋊C4—444no—
438C2×C22⋊C4C22×D1118yes—
439C2×C22⋊C4C22×D1118yes—
440C2×C42—118no—
441C2×C42—114no—
442C2×C42—114no—
443C2×C42—224no—
444#95—118no—
445#95—114no—
446#95C22×D1114yes—
447C2×C11—84no—
448C2×C11#261918yescomplemented
449C2×C11C22×#12111yescharacteristic
450C2×C11C2×#53511yescharacteristic
451C2×C11C2×#53512yes—
452C2×C11C2×#53511yescharacteristic
453C2×C11C2×#54012yes—
454D11—44no—
455D11—84no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24—24no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—114no—
464C24—112no—
465C24—114no—
466C24—222no—
467C24—224no—
468C24—222no—
469C24—224no—
470C24—224no—
471C24—224no—
472C24—224no—
473C24—224no—
474C24—224no—
475C24—224no—
476C24—224no—
477C24C23×D1114yes—
478C24C23×D1111yescharacteristic
479C2×D4—28no—
480C2×D4—48no—
481C2×D4—416no—
482C2×D4—2216no—
483C2×D4—2216no—
484C2×D4—2216no—
485C2×D4—2216no—
486C2×D4—2216no—
487C2×D4—2216no—
488C2×D4—228no—
489C2×D4—448no—
490C2×D4—448no—
491C2×D4—448no—
492C2×D4—4416no—
493C2×D4—4432no—
494C2×D4—4432no—
495C2×D4—448no—
496C2×D4—448no—
497C2×D4—448no—
498C2×D4—448no—
499C2×D4—4432no—
500C2×D4—4432no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—114no—
510C22×C4—114no—
511C22×C4—114no—
512C22×C4—112no—
513C22×C4—114no—
514C22×C4—112no—
515C22×C4—1116no—
516C22×C4—114no—
517C22×C4—112no—
518C22×C4—228no—
519C22×C4—2232no—
520C22×C4—228no—
521C22×C4—224no—
522C22×C4—222no—
523C22×C4—224no—
524C22×C4—224no—
525C22×C4—224no—
526C22×C4—224no—
527C22×C4D4×D1114yes—
528C22×C4D4×D1114yes—
529C22×C4C23×D1114yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1112yes—
532C22×C4C23×D1112yes—
533C4⋊C4—28no—
534C4⋊C4—228no—
535C4⋊C4—2216no—
536C22⋊C4—216no—
537C22⋊C4—48no—
538C22⋊C4—228no—
539C22⋊C4—228no—
540C22⋊C4—2216no—
541C22⋊C4—448no—
542C22⋊C4—448no—
543C22⋊C4—448no—
544C42—1116no—
545C42—228no—
546C11C2×#261911yescharacteristic, complemented, Sylow
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—48no—
555C23—48no—
556C23—48no—
557C23—48no—
558C23—48no—
559C23—48no—
560C23—48no—
561C23—114no—
562C23—228no—
563C23—2216no—
564C23—222no—
565C23—224no—
566C23—222no—
567C23—224no—
568C23—224no—
569C23—224no—
570C23—224no—
571C23—224no—
572C23—224no—
573C23—224no—
574C23—224no—
575C23—444no—
576C23—448no—
577C23—444no—
578C23—448no—
579C23—448no—
580C23—448no—
581C23—448no—
582C23—448no—
583C23—448no—
584C23—448no—
585C23C2×D4×D1112yes—
586C23C2×D4×D1112yes—
587C23#6703714yes—
588C23#41×D1112yes—
589C23#6704214yes—
590C23C24×D1111yescharacteristic
591D4—416no—
592D4—4416no—
593D4—4432no—
594D4—4432no—
595D4—4432no—
596D4—4432no—
597C2×C4—28no—
598C2×C4—28no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—44no—
608C2×C4—48no—
609C2×C4—1116no—
610C2×C4—114no—
611C2×C4—114no—
612C2×C4—114no—
613C2×C4—114no—
614C2×C4—2232no—
615C2×C4—224no—
616C2×C4—228no—
617C2×C4—222no—
618C2×C4—224no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—448no—
623C2×C4—444no—
624C2×C4C2×D4×D1114yes—
625C2×C4C2×D4×D1114yes—
626C22—44no—
627C22—44no—
628C22—44no—
629C22—44no—
630C22—44no—
631C22—44no—
632C22—44no—
633C22—816no—
634C22—228no—
635C22—224no—
636C22—442no—
637C22—442no—
638C22—444no—
639C22—4416no—
640C22—444no—
641C22—444no—
642C22—444no—
643C22—444no—
644C22—444no—
645C22—444no—
646C22—444no—
647C22—8816no—
648C22#1062312314yes—
649C22D11×#12114yes—
650C22#1062313818yes—
651C22#1062319418yes—
652C22#1062320514yes—
653C22C22×D4×D1111yescharacteristic
654C22C22×D4×D1111yescharacteristic
655C22C2×#6703712yes—
656C22C2×#41×D1111yescharacteristic
657C22C2×#6704212yes—
658C4—24no—
659C4—24no—
660C4—42no—
661C4—44no—
662C4—118no—
663C4—224no—
664C4—444no—
665C4—442no—
666C2—84no—
667C2—444no—
668C2—884no—
669C2#1307436818yesdirect product factor
670C2C2×D11×#12111yescharacteristic
671C2C2×#1062312311yescharacteristic
672C2C2×#1062313812yes—
673C2C2×#1062320511yescharacteristic
674C2C2×#1062319412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2619
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66993C2semidirect
2. C22×#66937C2semidirect
3. C22×#66945C2semidirect
4. #13074368C2direct (N × H)
5. C2×#10622604C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622284C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622263C2semidirect
12. C2×C11×#394C2semidirect
25. C2×#66993C22semidirect
36. C2×#66945C22semidirect
38. C2×#66937C22semidirect
39. C11×#394C22semidirect
41. #10622836C22semidirect
44. #10622604C22semidirect
45. #10622574C22semidirect
46. #10622573C22semidirect
47. #10622570C22semidirect
48. #10622284C22semidirect
49. #10622263C22semidirect
85. C22×C4×D11D4semidirect
111. C2×C4×Dic11D4semidirect
196. C2×C4×D11C2×D4semidirect
209. C4×Dic11C2×D4semidirect
216. C2×#394D11semidirect
329. #394C2×D11semidirect
448. C2×C11#2619semidirect
546. C11C2×#2619semidirect
669. C2#13074368direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669932
C22×#669372
C22×#669452
#130743682
C2×#106226042
C2×#106225742
C2×#106222842
C2×#106225732
C2×#106228362
C2×#106225702
C2×#106222632
C2×C11×#3942
C2×#261911