Finite Group Databasebeta

← C2×#13074749 #14920332

Subgroups — C2×#13074749 #14920332

Order 2816.

3434 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2C22×#66948C211yesmaximal, characteristic, complemented
3#13074749C2116yesmaximal, direct product factor
4C2×#10622606C211yesmaximal, characteristic, complemented
5C2×#10622604C212yesmaximal, complemented
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622284C212yesmaximal, complemented
8C2×#10622284C211yesmaximal, characteristic, complemented
9C2×#10622601C212yesmaximal, complemented
10C2×#10622282C212yesmaximal, complemented
11C2×#10622279C211yesmaximal, characteristic, complemented
12C2×C11×#398C211yesmaximal, characteristic, complemented
13C23×D44C2212yes—
14C23×D44C2211yescharacteristic
15C23×D44C2212yes—
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2212yes—
32C2×#66948—28no—
33C2×#66948C2218yescomplemented
34C2×#66947—28no—
35C2×#66947C2218yescomplemented
36C11×#398C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41#10622606C2218yescomplemented
42#10622604C2218yescomplemented
43#10622604C22116yescomplemented
44#10622601C22116yescomplemented
45#10622284C2218yescomplemented
46#10622284C22116yescomplemented
47#10622282C22116yescomplemented
48#10622279C2218yescomplemented
49C24×D11C2311yescharacteristic
50C24×D11C2312yes—
51C24×D11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×D44—24no—
61C22×D44—28no—
62C22×D44—24no—
63C22×D44—28no—
64C22×D44—44no—
65C22×D44—44no—
66C22×D44—44no—
67C22×D44—44no—
68C22×D44—44no—
69C22×D44—44no—
70C22×D44C2314yes—
71C22×D44C2318yes—
72C22×D44C2314yes—
73C22×D44C2318yes—
74C22×C4×D11—44no—
75C22×C4×D11D418yescomplemented
76C22×C4×D11C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—44no—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2318yes—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4—44no—
91C2×(C2×D11)⋊C4—44no—
92C2×(C2×D11)⋊C4C2314yes—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4C2314yes—
103C2×C4×Dic11—44no—
104C2×C4×Dic11C2318yes—
105#66948—232no—
106#66947—232no—
107C11×#95C2314yes—
108C11×#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C2×#2661—111nomaximal, Sylow
112C24×C11C2411yescharacteristic
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—22no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—22no—
129C23×D11C2×D414yes—
130C23×D11C2412yes—
131C23×D11C2414yes—
132C23×D11C2412yes—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11C2×D414yes—
145C22×C4×C11#4118yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2414yes—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11C2×D414yes—
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2412yes—
161C2×D44—28no—
162C2×D44—216no—
163C2×D44—28no—
164C2×D44—216no—
165C2×D44—48no—
166C2×D44—48no—
167C2×D44—48no—
168C2×D44—48no—
169C2×D44—48no—
170C2×D44—48no—
171C2×D44—416no—
172C2×D44—432no—
173C2×D44—416no—
174C2×D44—432no—
175C2×C4×D11—416no—
176C2×C4×D11—48no—
177C2×C4×D11C2×D4116yescomplemented
178C11×C4⋊C4—28no—
179C11×C4⋊C4—28no—
180C11×C4⋊C4—48no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—216no—
187(C2×D11)⋊C4—48no—
188(C2×D11)⋊C4—48no—
189(C2×D11)⋊C4—48no—
190Dic11⋊C4—28no—
191C4×Dic11—48no—
192C22×#123—111no—
193C22×#121—111no—
194#2661—1116no—
195C2×#398D1111yescharacteristic, complemented
196C2×#397—111no—
197C2×#394—112no—
198C2×#394—111no—
199C2×#392—112no—
200C2×#392—111no—
201C2×#390—112no—
202C2×#388—112no—
203C2×C4×C22⋊C4—111no—
204C23×C11C22×D412yes—
205C23×C11C2×#4114yes—
206C23×C11H(5,𝔽2)12yes—
207C23×C11H(5,𝔽2)14yes—
208C23×C11H(5,𝔽2)12yes—
209C23×C11C2511yescharacteristic
210C22×D11—28no—
211C22×D11—28no—
212C22×D11—28no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—22no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—22no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—48no—
230C22×D11—48no—
231C22×D11—44no—
232C22×D11—48no—
233C22×D11—48no—
234C22×D11—44no—
235C22×D11—48no—
236C22×D11—44no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11C22×D414yes—
244C2×C4×C11—28no—
245C2×C4×C11—216no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—44no—
258C2×C4×C11—48no—
259C2×C4×C11—44no—
260C2×C4×C11C22×D414yes—
261C2×C4×C11C2×#4118yes—
262C2×Dic11—28no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—44no—
270C2×Dic11—48no—
271C2×Dic11C22×D414yes—
272D44—416no—
273D44—432no—
274D44—416no—
275D44—432no—
276C4×D11—416no—
277C23×D4—111no—
278C23×D4—112no—
279C23×D4—112no—
280C23×D4—111no—
281C24×C4—111no—
282C2×#123—118no—
283C2×#123—228no—
284C2×#121—118no—
285C2×#121—228no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4C2×D1111yescharacteristic
288C22×C4⋊C4C2×D1111yescharacteristic
289C22×C4⋊C4C2×D1112yes—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—111no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C42—112no—
300#398C2×D1118yescomplemented
301#397—118no—
302#394—118no—
303#394—1116no—
304#392—118no—
305#392—1116no—
306#390—1116no—
307#388—1116no—
308C4×C22⋊C4—118no—
309C2×#95—111no—
310C2×#95—112no—
311C2×#95C2×D1111yescharacteristic
312C2×#95C2×D1112yes—
313C22×C11#53214yes—
314C22×C11#53414yes—
315C22×C11#53514yes—
316C22×C11#53818yes—
317C22×C11#54018yes—
318C22×C11C23×D411yescharacteristic
319C22×C11C22×#4112yes—
320C22×C11C2×H(5,𝔽2)11yescharacteristic
321C22×C11C2×H(5,𝔽2)12yes—
322C22×C11C2×H(5,𝔽2)11yescharacteristic
323C2×D11—24no—
324C2×D11—24no—
325C2×D11—24no—
326C2×D11—416no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—42no—
330C2×D11—44no—
331C2×D11—42no—
332C2×D11—44no—
333C2×D11—42no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—816no—
342C2×D11—88no—
343C4×C11—24no—
344C4×C11—28no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—44no—
348Dic11—24no—
349Dic11—42no—
350Dic11—44no—
351C25—111no—
352C25—111no—
353C25—112no—
354C22×D4—118no—
355C22×D4—114no—
356C22×D4—114no—
357C22×D4—118no—
358C22×D4—228no—
359C22×D4—224no—
360C22×D4—224no—
361C22×D4—228no—
362C22×D4—444no—
363C22×D4—444no—
364C22×D4—444no—
365C22×D4—444no—
366C22×D4—444no—
367C22×D4—444no—
368C23×C4—111no—
369C23×C4—118no—
370C23×C4—114no—
371C23×C4—111no—
372C23×C4—112no—
373C23×C4—444no—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1112yes—
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1112yes—
379#123—2232no—
380#121—2232no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4C22×D1114yes—
387C2×C4⋊C4C22×D1114yes—
388C2×C4⋊C4C22×D1118yes—
389C2×C22⋊C4—118no—
390C2×C22⋊C4—114no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—228no—
403C2×C22⋊C4—228no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4—444no—
407C2×C42—118no—
408C2×C42—444no—
409#95—114no—
410#95—118no—
411#95C22×D1114yes—
412#95C22×D1118yes—
413C2×C11#266118yescomplemented
414C2×C11C2×#53211yescharacteristic
415C2×C11C2×#53411yescharacteristic
416C2×C11C2×#53511yescharacteristic
417C2×C11C2×#53812yes—
418C2×C11C2×#54012yes—
419D11—44no—
420D11—82no—
421D11—84no—
422C24—114no—
423C24—112no—
424C24—112no—
425C24—114no—
426C24—222no—
427C24—224no—
428C24—224no—
429C24—222no—
430C24—222no—
431C24—224no—
432C24—224no—
433C24—222no—
434C24—224no—
435C24—224no—
436C24—224no—
437C24—222no—
438C24—224no—
439C24—224no—
440C24—224no—
441C24—224no—
442C24C23×D1111yescharacteristic
443C2×D4—2216no—
444C2×D4—228no—
445C2×D4—228no—
446C2×D4—2216no—
447C2×D4—448no—
448C2×D4—448no—
449C2×D4—448no—
450C2×D4—448no—
451C2×D4—448no—
452C2×D4—448no—
453C2×D4—4432no—
454C2×D4—4416no—
455C2×D4—4432no—
456C2×D4—4416no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—114no—
469C22×C4—112no—
470C22×C4—1116no—
471C22×C4—114no—
472C22×C4—112no—
473C22×C4—224no—
474C22×C4—222no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—4416no—
480C22×C4—448no—
481C22×C4D4×D1114yes—
482C22×C4#434318yes—
483C22×C4C23×D1114yes—
484C22×C4C23×D1112yes—
485C22×C4C23×D1112yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1114yes—
488C4⋊C4—28no—
489C4⋊C4—28no—
490C4⋊C4—48no—
491C4⋊C4—228no—
492C22⋊C4—2216no—
493C22⋊C4—228no—
494C22⋊C4—228no—
495C22⋊C4—228no—
496C22⋊C4—2216no—
497C22⋊C4—2216no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C42—448no—
502C11C2×#266111yescharacteristic, complemented, Sylow
503C23—114no—
504C23—228no—
505C23—228no—
506C23—228no—
507C23—222no—
508C23—224no—
509C23—224no—
510C23—222no—
511C23—222no—
512C23—224no—
513C23—224no—
514C23—222no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23—222no—
519C23—224no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—448no—
524C23—448no—
525C23—444no—
526C23—448no—
527C23—448no—
528C23—444no—
529C23—448no—
530C23—448no—
531C23—448no—
532C23—448no—
533C23—444no—
534C23—448no—
535C23—448no—
536C23—448no—
537C23C2×D4×D1112yes—
538C23#6703712yes—
539C23C2×#434314yes—
540C23#6704212yes—
541C23#6704214yes—
542C23C24×D1111yescharacteristic
543D4—4416no—
544D4—4432no—
545D4—4416no—
546D4—4432no—
547C2×C4—216no—
548C2×C4—28no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—44no—
561C2×C4—48no—
562C2×C4—44no—
563C2×C4—114no—
564C2×C4—228no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—4416no—
572C2×C4—444no—
573C2×C4—448no—
574C2×C4C2×D4×D1114yes—
575C2×C4C2×#434318yes—
576C22—224no—
577C22—224no—
578C22—224no—
579C22—4416no—
580C22—444no—
581C22—444no—
582C22—442no—
583C22—444no—
584C22—444no—
585C22—442no—
586C22—444no—
587C22—442no—
588C22—444no—
589C22—444no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22—8816no—
595C22—888no—
596C22#1062313814yes—
597C22#1062317518yes—
598C22#1062318414yes—
599C22#1062322918yes—
600C22#1062325614yes—
601C22C22×D4×D1111yescharacteristic
602C22C2×#6703711yescharacteristic
603C22C22×#434312yes—
604C22C2×#6704212yes—
605C22C2×#6704211yescharacteristic
606C4—24no—
607C4—28no—
608C4—42no—
609C4—44no—
610C4—42no—
611C4—224no—
612C4—442no—
613C4—444no—
614C2—444no—
615C2—884no—
616C2—882no—
617C2#1307474918yesdirect product factor
618C2C2×#1062325611yescharacteristic
619C2C2×#1062318411yescharacteristic
620C2C2×#1062313811yescharacteristic
621C2C2×#1062317512yes—
622C2C2×#1062322912yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
hypercenterC2×#398D11
hypocenterC11C2×#2661
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. C22×#66948C2semidirect
3. #13074749C2direct (N × H)
4. C2×#10622606C2semidirect
5. C2×#10622604C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622284C2semidirect
8. C2×#10622284C2semidirect
9. C2×#10622601C2semidirect
10. C2×#10622282C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#398C2semidirect
33. C2×#66948C22semidirect
35. C2×#66947C22semidirect
36. C11×#398C22semidirect
41. #10622606C22semidirect
42. #10622604C22semidirect
43. #10622604C22semidirect
44. #10622601C22semidirect
45. #10622284C22semidirect
46. #10622284C22semidirect
47. #10622282C22semidirect
48. #10622279C22semidirect
75. C22×C4×D11D4semidirect
177. C2×C4×D11C2×D4semidirect
195. C2×#398D11semidirect
300. #398C2×D11semidirect
413. C2×C11#2661semidirect
502. C11C2×#2661semidirect
617. C2#13074749direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669482
#130747492
C2×#106226062
C2×#106226042
C2×#106222842
C2×#106226012
C2×#106222822
C2×#106222792
C2×C11×#3982
C2×#266111