Finite Group Databasebeta

← C2×#13076655 #14960327

Subgroups — C2×#13076655 #14960327

Order 2816.

3666 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic, complemented
2C22×#66932C211yesmaximal, characteristic, complemented
3#13076655C2116yesmaximal, direct product factor
4C2×#10622285C211yesmaximal, characteristic, complemented
5C2×#10622574C212yesmaximal, complemented
6C2×#10622572C212yesmaximal, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622836C212yesmaximal, complemented
10C2×#10622836C212yesmaximal, complemented
11C2×#10622264C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×C22⋊D11C2212yes—
17C23×C22⋊D11C2212yes—
18C23×D44C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66993—28no—
26C2×#66993C2218yescomplemented
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×#66932—28no—
35C2×#66932C2218yescomplemented
36C11×#392C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38#10622836C22116yescomplemented
39#10622836C22116yescomplemented
40#10622835C2218yescomplemented
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2211yescharacteristic
44#10622574C22116yescomplemented
45#10622573C2218yescomplemented
46#10622572C22116yescomplemented
47#10622285C2218yescomplemented
48#10622264C2218yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2312yes—
51C24×D11C2312yes—
52C22×D4×C11—24no—
53C22×D4×C11—44no—
54C22×D4×C11—44no—
55C22×D4×C11—44no—
56C22×D4×C11—44no—
57C22×D4×C11C2314yes—
58C22×D4×C11C2318yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—28no—
63C22×C22⋊D11—28no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11—44no—
68C22×C22⋊D11—44no—
69C22×C22⋊D11—44no—
70C22×C22⋊D11—44no—
71C22×C22⋊D11C2318yes—
72C22×C22⋊D11C2318yes—
73C22×C22⋊D11C2318yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2312yes—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C22×D44—24no—
80C22×D44—44no—
81C22×D44C2314yes—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—44no—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2318yes—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11—44no—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2318yes—
94#66993—232no—
95C2×(C2×D11)⋊C4—44no—
96C2×(C2×D11)⋊C4—44no—
97C2×(C2×D11)⋊C4—44no—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×C4⋊Dic11—24no—
102C2×C4⋊Dic11C2314yes—
103C2×Dic11⋊C4—24no—
104C2×Dic11⋊C4—24no—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×C4×Dic11D418yescomplemented
108C2×C4×Dic11C2314yes—
109#66932—232no—
110C11×#95C2314yes—
111C11⋊#95C2318yes—
112C11⋊#95C2314yes—
113C11⋊#95C2318yes—
114C2×#2818—111nomaximal, Sylow
115C24×C11—22no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—22no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11—24no—
125C24×C11—24no—
126C24×C11—22no—
127C24×C11C2412yes—
128C24×C11C2414yes—
129C24×C11C2411yescharacteristic
130C23×D11—24no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11—24no—
134C23×D11—24no—
135C23×D11—24no—
136C23×D11—24no—
137C23×D11C2414yes—
138C2×D4×C11—28no—
139C2×D4×C11—48no—
140C2×D4×C11—48no—
141C2×D4×C11—48no—
142C2×D4×C11—48no—
143C2×D4×C11—416no—
144C2×D4×C11—432no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C2×C22⋊D11—216no—
156C2×C22⋊D11—216no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—48no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11—432no—
165C2×C22⋊D11—432no—
166C2×C22⋊D11—432no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—24no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—22no—
176C22×Dic11—24no—
177C22×Dic11—24no—
178C22×Dic11C2×D414yes—
179C22×Dic11C2×D414yes—
180C22×Dic11C2414yes—
181C22×Dic11C2412yes—
182C22×Dic11C2412yes—
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C2×D44—28no—
186C2×D44—48no—
187C2×D44—416no—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—48no—
190C22⋊Dic11—28no—
191C22⋊Dic11—28no—
192C22⋊Dic11—48no—
193C22⋊Dic11—48no—
194(C2×D11)⋊C4—48no—
195(C2×D11)⋊C4—48no—
196(C2×D11)⋊C4—48no—
197C4⋊Dic11—28no—
198Dic11⋊C4—28no—
199Dic11⋊C4—28no—
200C4×Dic11C2×D4116yescomplemented
201C22×#127—111no—
202C22×#126—111no—
203#2818—1116no—
204C2×#394—111no—
205C2×#394—111no—
206C2×#394—112no—
207C2×#394—112no—
208C2×#392—112no—
209C2×#392—112no—
210C2×#392—111no—
211C2×#392D1111yescharacteristic, complemented
212C2×#383—111no—
213C23×C11—22no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—22no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11—44no—
229C23×C11—44no—
230C23×C11—44no—
231C23×C11—48no—
232C23×C11—48no—
233C23×C11—48no—
234C23×C11—48no—
235C23×C11—48no—
236C23×C11—48no—
237C23×C11C22×D412yes—
238C23×C11H(5,𝔽2)14yes—
239C23×C11H(5,𝔽2)14yes—
240C23×C11H(5,𝔽2)12yes—
241C23×C11H(5,𝔽2)12yes—
242C23×C11C2511yescharacteristic
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—48no—
251C22×D11—48no—
252C22×D11—48no—
253C22×D11—48no—
254C22×D11—48no—
255C22×D11—48no—
256C22×D11—48no—
257D4×C11—416no—
258D4×C11—432no—
259C2×C4×C11—28no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—44no—
267C2×C4×C11—48no—
268C2×C4×C11C22×D414yes—
269C22⋊D11—432no—
270C22⋊D11—432no—
271C22⋊D11—432no—
272C2×Dic11—28no—
273C2×Dic11—28no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—44no—
286C2×Dic11—44no—
287C2×Dic11—48no—
288C2×Dic11C22×D414yes—
289C2×Dic11C22×D414yes—
290D44—416no—
291C23×D4—112no—
292C23×D4—112no—
293C23×D4—112no—
294C23×D4—111no—
295C23×D4C2×D1111yescharacteristic
296C23×D4C2×D1112yes—
297C2×#127—118no—
298C2×#127—228no—
299C2×#126—118no—
300C2×#126—228no—
301C22×C4⋊C4—111no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—111no—
304C22×C22⋊C4—111no—
305C22×C22⋊C4—111no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4C2×D1111yescharacteristic
312C22×C22⋊C4C2×D1112yes—
313C22×C42—111no—
314#394—118no—
315#394—1116no—
316#394—1116no—
317#394—118no—
318#392—1116no—
319#392—1116no—
320#392—118no—
321#392C2×D1118yescomplemented
322#383—118no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—111no—
326C2×#95C2×D1111yescharacteristic
327C22×C11—44no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—44no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—44no—
339C22×C11—816no—
340C22×C11—88no—
341C22×C11#53514yes—
342C22×C11#53514yes—
343C22×C11#53514yes—
344C22×C11#56018yes—
345C22×C11#56018yes—
346C22×C11C23×D411yescharacteristic
347C22×C11C2×H(5,𝔽2)12yes—
348C22×C11C2×H(5,𝔽2)12yes—
349C22×C11C2×H(5,𝔽2)11yescharacteristic
350C22×C11C2×H(5,𝔽2)11yescharacteristic
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—816no—
359C4×C11—24no—
360C4×C11—42no—
361C4×C11—44no—
362Dic11—24no—
363Dic11—24no—
364Dic11—42no—
365Dic11—42no—
366Dic11—44no—
367C25—112no—
368C25C22×D1111yescharacteristic
369C25C22×D1112yes—
370C22×D4—24no—
371C22×D4—44no—
372C22×D4—44no—
373C22×D4—44no—
374C22×D4—44no—
375C22×D4—118no—
376C22×D4—118no—
377C22×D4—118no—
378C22×D4—114no—
379C22×D4—228no—
380C22×D4—228no—
381C22×D4—224no—
382C22×D4—444no—
383C22×D4—444no—
384C22×D4—444no—
385C22×D4—444no—
386C22×D4—444no—
387C22×D4—444no—
388C22×D4—444no—
389C22×D4—444no—
390C22×D4C22×D1114yes—
391C22×D4C22×D1118yes—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—111no—
396C23×C4—112no—
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1112yes—
399C23×C4C22×D1111yescharacteristic
400#127—2232no—
401#126—2232no—
402C2×C4⋊C4—114no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—224no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4—224no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—118no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—224no—
418C2×C22⋊C4—224no—
419C2×C22⋊C4—444no—
420C2×C22⋊C4—444no—
421C2×C22⋊C4—444no—
422C2×C22⋊C4—444no—
423C2×C22⋊C4—444no—
424C2×C22⋊C4C22×D1114yes—
425C2×C22⋊C4C22×D1118yes—
426C2×C42—118no—
427C2×C42—114no—
428#95—118no—
429#95—118no—
430#95—114no—
431#95C22×D1114yes—
432C2×C11—84no—
433C2×C11—82no—
434C2×C11#281818yescomplemented
435C2×C11C2×#53511yescharacteristic
436C2×C11C2×#53511yescharacteristic
437C2×C11C2×#53511yescharacteristic
438C2×C11C2×#56012yes—
439C2×C11C2×#56012yes—
440D11—84no—
441C24—22no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—22no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—22no—
453C24—114no—
454C24—224no—
455C24—224no—
456C24—224no—
457C24—224no—
458C24—224no—
459C24—224no—
460C24—224no—
461C24C23×D1112yes—
462C24C23×D1114yes—
463C24C23×D1111yescharacteristic
464C2×D4—28no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—416no—
470C2×D4—432no—
471C2×D4—2216no—
472C2×D4—2216no—
473C2×D4—228no—
474C2×D4—448no—
475C2×D4—4416no—
476C2×D4—448no—
477C2×D4—448no—
478C2×D4—448no—
479C2×D4—448no—
480C2×D4—448no—
481C2×D4—448no—
482C2×D4—448no—
483C2×D4—4432no—
484C2×D4—4432no—
485C2×D4—4432no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—114no—
493C22×C4—114no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—114no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—224no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—224no—
505C22×C4—222no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—222no—
509C22×C4—224no—
510C22×C4D4×D1114yes—
511C22×C4C23×D1114yes—
512C22×C4C23×D1112yes—
513C22×C4C23×D1112yes—
514C4⋊C4—228no—
515C4⋊C4—228no—
516C4⋊C4—228no—
517C22⋊C4—28no—
518C22⋊C4—48no—
519C22⋊C4—228no—
520C22⋊C4—228no—
521C22⋊C4—448no—
522C22⋊C4—448no—
523C22⋊C4—448no—
524C22⋊C4—448no—
525C22⋊C4—448no—
526C42—1116no—
527C11C2×#281811yescharacteristic, complemented, Sylow
528C23—22no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—22no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—22no—
540C23—48no—
541C23—44no—
542C23—48no—
543C23—44no—
544C23—48no—
545C23—48no—
546C23—48no—
547C23—48no—
548C23—44no—
549C23—48no—
550C23—48no—
551C23—48no—
552C23—224no—
553C23—224no—
554C23—224no—
555C23—224no—
556C23—224no—
557C23—224no—
558C23—224no—
559C23—448no—
560C23—448no—
561C23—448no—
562C23—448no—
563C23—448no—
564C23—448no—
565C23—448no—
566C23C2×D4×D1112yes—
567C23#6703714yes—
568C23#6703714yes—
569C23#6703712yes—
570C23#6704212yes—
571C23C24×D1111yescharacteristic
572D4—416no—
573D4—432no—
574D4—4416no—
575D4—4432no—
576D4—4432no—
577D4—4432no—
578C2×C4—28no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—44no—
586C2×C4—48no—
587C2×C4—114no—
588C2×C4—114no—
589C2×C4—228no—
590C2×C4—228no—
591C2×C4—224no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—222no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—444no—
603C2×C4—444no—
604C2×C4—448no—
605C2×C4C2×D4×D1114yes—
606C22—44no—
607C22—42no—
608C22—44no—
609C22—42no—
610C22—44no—
611C22—42no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—816no—
619C22—88no—
620C22—444no—
621C22—444no—
622C22—444no—
623C22—444no—
624C22—444no—
625C22—444no—
626C22—444no—
627C22—8816no—
628C22#1062312314yes—
629C22#1062312618yes—
630C22#1062313814yes—
631C22#1062315118yes—
632C22#1062324614yes—
633C22C22×D4×D1111yescharacteristic
634C22C2×#6703712yes—
635C22C2×#6703712yes—
636C22C2×#6703711yescharacteristic
637C22C2×#6704211yescharacteristic
638C4—24no—
639C4—42no—
640C4—44no—
641C4—224no—
642C4—224no—
643C4—442no—
644C4—442no—
645C4—444no—
646C2—84no—
647C2—82no—
648C2—884no—
649C2#1307665518yesdirect product factor
650C2C2×#1062324611yescharacteristic
651C2C2×#1062312311yescharacteristic
652C2C2×#1062313811yescharacteristic
653C2C2×#1062315112yes—
654C2C2×#1062312612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2818
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66993C2semidirect
2. C22×#66932C2semidirect
3. #13076655C2direct (N × H)
4. C2×#10622285C2semidirect
5. C2×#10622574C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622264C2semidirect
12. C2×C11×#392C2semidirect
26. C2×#66993C22semidirect
35. C2×#66932C22semidirect
36. C11×#392C22semidirect
38. #10622836C22semidirect
39. #10622836C22semidirect
40. #10622835C22semidirect
44. #10622574C22semidirect
45. #10622573C22semidirect
46. #10622572C22semidirect
47. #10622285C22semidirect
48. #10622264C22semidirect
107. C2×C4×Dic11D4semidirect
200. C4×Dic11C2×D4semidirect
211. C2×#392D11semidirect
321. #392C2×D11semidirect
434. C2×C11#2818semidirect
527. C11C2×#2818semidirect
649. C2#13076655direct (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×#669322
#130766552
C2×#106222852
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106225732
C2×#106228362
C2×#106222642
C2×C11×#3922
C2×#281811