Finite Group Databasebeta

← C2×#13076658 #14960329

Subgroups — C2×#13076658 #14960329

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×#66951C211yesmaximal, characteristic, complemented
3#13076658C2116yesmaximal, direct product factor
4C2×#10622604C211yesmaximal, characteristic, complemented
5C2×#10622574C212yesmaximal, complemented
6C2×#10622572C212yesmaximal, complemented
7C2×#10622284C211yesmaximal, characteristic, complemented
8C2×#10622573C212yesmaximal, complemented
9C2×#10622573C212yesmaximal, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622264C211yesmaximal, characteristic, complemented
12C2×C11×#394C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×C22⋊D11C2212yes—
17C23×D44C2211yescharacteristic
18C23×D44C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2212yes—
23C2×#66993—28no—
24C2×#66993C2218yescomplemented
25C22×(C2×D11)⋊C4C2211yescharacteristic
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⋊C4C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×#66951—28no—
35C2×#66951C2218yescomplemented
36C11×#394C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38#10622836C2218yescomplemented
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622604C2218yescomplemented
43#10622574C22116yescomplemented
44#10622573C22116yescomplemented
45#10622573C22116yescomplemented
46#10622572C22116yescomplemented
47#10622284C2218yescomplemented
48#10622264C2218yescomplemented
49C25×C11C2312yes—
50C24×D11C2311yescharacteristic
51C24×D11C2312yes—
52C22×D4×C11—24no—
53C22×D4×C11—44no—
54C22×D4×C11C2314yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—28no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11—44no—
68C22×C22⋊D11C2318yes—
69C22×C22⋊D11C2318yes—
70C22×C22⋊D11C2318yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×D44—24no—
76C22×D44—44no—
77C22×D44—44no—
78C22×D44—44no—
79C22×D44—44no—
80C22×D44C2314yes—
81C22×D44C2318yes—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C22⋊C4—44no—
85C2×C11×C22⋊C4—44no—
86C2×C11×C22⋊C4C2318yes—
87C2×C11×C22⋊C4C2318yes—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11C2318yes—
90#66993—232no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—44no—
95C2×(C2×D11)⋊C4—44no—
96C2×(C2×D11)⋊C4—44no—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2318yes—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11C2314yes—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4C2314yes—
107C2×C4×Dic11D418yescomplemented
108C2×C4×Dic11C2314yes—
109#66951—232no—
110C11×#95C2314yes—
111C11⋊#95C2318yes—
112C11⋊#95C2318yes—
113C11⋊#95C2314yes—
114C2×#2818—111nomaximal, Sylow
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11C2414yes—
123C24×C11C2411yescharacteristic
124C23×D11—22no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—22no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11—24no—
134C23×D11—24no—
135C23×D11—22no—
136C23×D11C2412yes—
137C23×D11C2414yes—
138C2×D4×C11—28no—
139C2×D4×C11—48no—
140C2×D4×C11—416no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2412yes—
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—22no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11C2×D414yes—
176C22×Dic11C2×D414yes—
177C22×Dic11C2414yes—
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C22×Dic11C2412yes—
181C2×D44—28no—
182C2×D44—48no—
183C2×D44—48no—
184C2×D44—48no—
185C2×D44—48no—
186C2×D44—416no—
187C2×D44—432no—
188C11×C4⋊C4—28no—
189C11×C22⋊C4—48no—
190C11×C22⋊C4—48no—
191C22⋊Dic11—48no—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—48no—
196(C2×D11)⋊C4—48no—
197(C2×D11)⋊C4—48no—
198C4⋊Dic11—28no—
199Dic11⋊C4—28no—
200C4×Dic11C2×D4116yescomplemented
201C22×#127—111no—
202C22×#126—111no—
203#2818—1116no—
204C2×#394—111no—
205C2×#394—112no—
206C2×#394—112no—
207C2×#394D1111yescharacteristic, complemented
208C2×#392—111no—
209C2×#392—111no—
210C2×#392—112no—
211C2×#392—112no—
212C2×#383—111no—
213C23×C11—24no—
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×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11C22×D412yes—
228C23×C11H(5,𝔽2)14yes—
229C23×C11H(5,𝔽2)12yes—
230C23×C11H(5,𝔽2)12yes—
231C23×C11H(5,𝔽2)14yes—
232C23×C11C2511yescharacteristic
233C22×D11—22no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—22no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—22no—
245C22×D11—48no—
246C22×D11—48no—
247C22×D11—48no—
248C22×D11—44no—
249C22×D11—44no—
250C22×D11—44no—
251C22×D11—48no—
252C22×D11—48no—
253C22×D11—48no—
254C22×D11—48no—
255C22×D11—48no—
256C22×D11—48no—
257D4×C11—416no—
258C2×C4×C11—28no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—22no—
266C2×C4×C11—24no—
267C2×C4×C11—24no—
268C2×C4×C11—44no—
269C2×C4×C11—44no—
270C2×C4×C11—48no—
271C2×C4×C11C22×D414yes—
272C22⋊D11—432no—
273C22⋊D11—432no—
274C22⋊D11—432no—
275C2×Dic11—28no—
276C2×Dic11—28no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—44no—
286C2×Dic11—48no—
287C2×Dic11C22×D414yes—
288C2×Dic11C22×D414yes—
289D44—416no—
290D44—432no—
291C23×D4—112no—
292C23×D4—112no—
293C23×D4—112no—
294C23×D4—111no—
295C23×D4—112no—
296C23×D4C2×D1111yescharacteristic
297C2×#127—118no—
298C2×#127—228no—
299C2×#126—118no—
300C2×#126—228no—
301C22×C4⋊C4—111no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4C2×D1111yescharacteristic
304C22×C22⋊C4—111no—
305C22×C22⋊C4—111no—
306C22×C22⋊C4—111no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4C2×D1112yes—
312C22×C22⋊C4C2×D1112yes—
313C22×C42—111no—
314#394—118no—
315#394—1116no—
316#394—1116no—
317#394C2×D1118yescomplemented
318#392—118no—
319#392—1116no—
320#392—1116no—
321#392—118no—
322#383—118no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—111no—
326C2×#95C2×D1111yescharacteristic
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—816no—
335C22×C11#53514yes—
336C22×C11#53514yes—
337C22×C11#53514yes—
338C22×C11#56018yes—
339C22×C11#56018yes—
340C22×C11C23×D411yescharacteristic
341C22×C11C2×H(5,𝔽2)12yes—
342C22×C11C2×H(5,𝔽2)11yescharacteristic
343C22×C11C2×H(5,𝔽2)11yescharacteristic
344C22×C11C2×H(5,𝔽2)12yes—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—44no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—816no—
358C2×D11—88no—
359C4×C11—24no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—44no—
363Dic11—24no—
364Dic11—24no—
365Dic11—42no—
366Dic11—44no—
367C25—111no—
368C25—112no—
369C25C22×D1112yes—
370C22×D4—24no—
371C22×D4—44no—
372C22×D4—118no—
373C22×D4—118no—
374C22×D4—118no—
375C22×D4—114no—
376C22×D4—118no—
377C22×D4—228no—
378C22×D4—228no—
379C22×D4—224no—
380C22×D4—444no—
381C22×D4—444no—
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×D4—444no—
391C22×D4C22×D1114yes—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—112no—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1112yes—
399C23×C4C22×D1111yescharacteristic
400#127—2232no—
401#126—2232no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—224no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4C22×D1114yes—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—114no—
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—224no—
420C2×C22⋊C4—444no—
421C2×C22⋊C4—444no—
422C2×C22⋊C4—444no—
423C2×C22⋊C4—444no—
424C2×C22⋊C4C22×D1118yes—
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#281818yescomplemented
434C2×C11C2×#53511yescharacteristic
435C2×C11C2×#53511yescharacteristic
436C2×C11C2×#53511yescharacteristic
437C2×C11C2×#56012yes—
438C2×C11C2×#56012yes—
439D11—82no—
440D11—84no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—112no—
449C24—114no—
450C24—222no—
451C24—224no—
452C24—224no—
453C24—224no—
454C24—224no—
455C24—224no—
456C24—222no—
457C24—224no—
458C24—224no—
459C24—222no—
460C24—224no—
461C24—224no—
462C24C23×D1114yes—
463C24C23×D1111yescharacteristic
464C2×D4—28no—
465C2×D4—48no—
466C2×D4—416no—
467C2×D4—2216no—
468C2×D4—2216no—
469C2×D4—228no—
470C2×D4—448no—
471C2×D4—448no—
472C2×D4—448no—
473C2×D4—448no—
474C2×D4—4416no—
475C2×D4—4432no—
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—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—114no—
496C22×C4—114no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—114no—
500C22×C4—112no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—224no—
504C22×C4—222no—
505C22×C4—224no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—224no—
509C22×C4D4×D1114yes—
510C22×C4C23×D1114yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C22×C4C23×D1112yes—
514C4⋊C4—28no—
515C4⋊C4—228no—
516C4⋊C4—228no—
517C22⋊C4—48no—
518C22⋊C4—48no—
519C22⋊C4—228no—
520C22⋊C4—228no—
521C22⋊C4—228no—
522C22⋊C4—448no—
523C22⋊C4—448no—
524C22⋊C4—448no—
525C22⋊C4—448no—
526C42—1116no—
527C11C2×#281811yescharacteristic, complemented, Sylow
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—48no—
536C23—48no—
537C23—48no—
538C23—48no—
539C23—48no—
540C23—48no—
541C23—48no—
542C23—222no—
543C23—224no—
544C23—224no—
545C23—224no—
546C23—224no—
547C23—224no—
548C23—222no—
549C23—224no—
550C23—224no—
551C23—222no—
552C23—224no—
553C23—224no—
554C23—448no—
555C23—444no—
556C23—448no—
557C23—444no—
558C23—448no—
559C23—448no—
560C23—448no—
561C23—448no—
562C23—448no—
563C23—448no—
564C23—448no—
565C23—444no—
566C23C2×D4×D1112yes—
567C23#6703714yes—
568C23#6703712yes—
569C23#6704212yes—
570C23#6704214yes—
571C23C24×D1111yescharacteristic
572D4—416no—
573D4—4416no—
574D4—4432no—
575D4—4432no—
576D4—4432no—
577D4—4432no—
578C2×C4—28no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—48no—
591C2×C4—114no—
592C2×C4—114no—
593C2×C4—228no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—228no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—448no—
604C2×C4—444no—
605C2×C4C2×D4×D1114yes—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—816no—
614C22—444no—
615C22—442no—
616C22—444no—
617C22—442no—
618C22—444no—
619C22—442no—
620C22—444no—
621C22—444no—
622C22—444no—
623C22—444no—
624C22—444no—
625C22—444no—
626C22—8816no—
627C22—888no—
628C22#1062312314yes—
629C22#1062313814yes—
630C22#1062315118yes—
631C22#1062319718yes—
632C22#1062320514yes—
633C22C22×D4×D1111yescharacteristic
634C22C2×#6703712yes—
635C22C2×#6703711yescharacteristic
636C22C2×#6704211yescharacteristic
637C22C2×#6704212yes—
638C4—24no—
639C4—42no—
640C4—42no—
641C4—44no—
642C4—224no—
643C4—224no—
644C4—442no—
645C4—444no—
646C2—84no—
647C2—884no—
648C2—882no—
649C2#1307665818yesdirect product factor
650C2C2×#1062312311yescharacteristic
651C2C2×#1062313811yescharacteristic
652C2C2×#1062320511yescharacteristic
653C2C2×#1062315112yes—
654C2C2×#1062319712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2818
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×#66951C2semidirect
3. #13076658C2direct (N × H)
4. C2×#10622604C2semidirect
5. C2×#10622574C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622284C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622264C2semidirect
12. C2×C11×#394C2semidirect
24. C2×#66993C22semidirect
35. C2×#66951C22semidirect
36. C11×#394C22semidirect
38. #10622836C22semidirect
42. #10622604C22semidirect
43. #10622574C22semidirect
44. #10622573C22semidirect
45. #10622573C22semidirect
46. #10622572C22semidirect
47. #10622284C22semidirect
48. #10622264C22semidirect
107. C2×C4×Dic11D4semidirect
200. C4×Dic11C2×D4semidirect
207. C2×#394D11semidirect
317. #394C2×D11semidirect
433. C2×C11#2818semidirect
527. C11C2×#2818semidirect
649. C2#13076658direct (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×#669512
#130766582
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106222842
C2×#106225732
C2×#106228362
C2×#106222642
C2×C11×#3942
C2×#281811