Finite Group Databasebeta

← C2×#13076616 #14959920

Subgroups — C2×#13076616 #14959920

Order 2816.

3322 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×#66982C211yesmaximal, characteristic, complemented
2#13076616C2116yesmaximal, direct product factor
3C2×#10622595C211yesmaximal, characteristic, complemented
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622561C212yesmaximal, complemented
6C2×#10622574C212yesmaximal, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622835C212yesmaximal, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622836C212yesmaximal, complemented
11C2×#10622825C211yesmaximal, characteristic, complemented
12C22×C11×#121C211yesmaximal, characteristic, complemented
13C23×D4×C11C2212yes—
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2212yes—
18C2×C11×#121—28no—
19C2×C11×#121C2218yescomplemented
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C2×#66982—28no—
28C2×#66982C2218yescomplemented
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2212yes—
32C22×C4⋊Dic11C2212yes—
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2212yes—
36#10622836C22116yescomplemented
37#10622836C2218yescomplemented
38#10622835C2218yescomplemented
39#10622835C22116yescomplemented
40#10622825C2218yescomplemented
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622605C2218yescomplemented
46#10622595C2218yescomplemented
47#10622574C22116yescomplemented
48#10622561C22116yescomplemented
49C25×C11C2312yes—
50C25×C11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C22×D4×C11—28no—
53C22×D4×C11—24no—
54C22×D4×C11—44no—
55C22×D4×C11—44no—
56C22×D4×C11—44no—
57C22×D4×C11C2318yes—
58C22×D4×C11C2314yes—
59C23×C4×C11—44no—
60C23×C4×C11D418yescomplemented
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2314yes—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11—44no—
68C22×C22⋊D11—44no—
69C22×C22⋊D11—44no—
70C22×C22⋊D11C2314yes—
71C22×C22⋊D11C2318yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2312yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2312yes—
77C11×#121—232no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C22⋊C4—28no—
81C2×C11×C22⋊C4C2318yes—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—44no—
84C2×C22⋊Dic11—44no—
85C2×C22⋊Dic11—44no—
86C2×C22⋊Dic11—44no—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2318yes—
89C2×C22⋊Dic11C2318yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2318yes—
92#66982—232no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—44no—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×C4⋊Dic11—44no—
100C2×C4⋊Dic11C2318yes—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—44no—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C2×#2813—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—22no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11C2×D414yes—
124C24×C11C2414yes—
125C24×C11C2412yes—
126C24×C11C2411yescharacteristic
127C23×D11—22no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11C2412yes—
133C2×D4×C11—216no—
134C2×D4×C11—28no—
135C2×D4×C11—48no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—416no—
139C2×D4×C11—432no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—416no—
146C22×C4×C11—48no—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D4116yescomplemented
150C22×C4×C11C2414yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2412yes—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—48no—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—416no—
159C2×C22⋊D11—432no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—22no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11—22no—
173C22×Dic11C2414yes—
174C22×Dic11C2412yes—
175C22×Dic11C2412yes—
176C22×Dic11C2414yes—
177C22×Dic11C2412yes—
178C11×C4⋊C4—28no—
179C11×C22⋊C4—216no—
180C22⋊Dic11—28no—
181C22⋊Dic11—48no—
182C22⋊Dic11—48no—
183C22⋊Dic11—48no—
184C22⋊Dic11—48no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—48no—
188C4⋊Dic11—48no—
189Dic11⋊C4—28no—
190Dic11⋊C4—28no—
191Dic11⋊C4—48no—
192C22×#123—111no—
193C22×#121D1111yescharacteristic, complemented
194#2813—1116no—
195C2×#400—111no—
196C2×#399—111no—
197C2×#396—112no—
198C2×#394—112no—
199C2×#394—111no—
200C2×#394—112no—
201C2×#392—111no—
202C2×#392—112no—
203C2×#380—111no—
204C23×C11—28no—
205C23×C11—28no—
206C23×C11—28no—
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—22no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—48no—
219C23×C11—48no—
220C23×C11—48no—
221C23×C11—48no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11C22×D414yes—
228C23×C11C22×D412yes—
229C23×C11H(5,𝔽2)14yes—
230C23×C11H(5,𝔽2)14yes—
231C23×C11H(5,𝔽2)12yes—
232C23×C112−1+412yes—
233C23×C11C2511yescharacteristic
234C22×D11—22no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—48no—
243C22×D11—48no—
244D4×C11—416no—
245D4×C11—432no—
246C2×C4×C11—28no—
247C2×C4×C11—28no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—416no—
254C2×C4×C11—48no—
255C2×C4×C11C22×D414yes—
256C2×C4×C11C22×D414yes—
257C22⋊D11—416no—
258C22⋊D11—432no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—44no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11—48no—
276C2×Dic11—48no—
277C23×D4—111no—
278C23×D4—112no—
279C23×D4C2×D1112yes—
280C23×D4C2×D1111yescharacteristic
281C24×C4C2×D1111yescharacteristic
282C2×#123—118no—
283C2×#123—228no—
284C2×#121—28no—
285C2×#121C2×D1118yescomplemented
286C22×C4⋊C4—111no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—112no—
289C22×C4⋊C4—112no—
290C22×C4⋊C4C2×D1111yescharacteristic
291C22×C22⋊C4—111no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4C2×D1112yes—
300#400—118no—
301#399—118no—
302#396—1116no—
303#394—118no—
304#394—1116no—
305#394—1116no—
306#392—118no—
307#392—1116no—
308#380—118no—
309C2×#95—112no—
310C2×#95—111no—
311C2×#95—112no—
312C2×#95—111no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—416no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—816no—
327C22×C11#53414yes—
328C22×C11#53514yes—
329C22×C11#53714yes—
330C22×C11#56018yes—
331C22×C11#56218yes—
332C22×C11C23×D411yescharacteristic
333C22×C11C2×H(5,𝔽2)12yes—
334C22×C11C2×H(5,𝔽2)12yes—
335C22×C11C2×H(5,𝔽2)11yescharacteristic
336C22×C11C2×2−1+411yescharacteristic
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—88no—
343C4×C11—24no—
344C4×C11—24no—
345C4×C11—44no—
346Dic11—42no—
347Dic11—42no—
348Dic11—42no—
349Dic11—44no—
350Dic11—44no—
351C25—111no—
352C25C22×D1112yes—
353C25C22×D1111yescharacteristic
354C22×D4—28no—
355C22×D4—24no—
356C22×D4—44no—
357C22×D4—44no—
358C22×D4—44no—
359C22×D4—114no—
360C22×D4—118no—
361C22×D4—224no—
362C22×D4—444no—
363C22×D4—444no—
364C22×D4—444no—
365C22×D4—444no—
366C22×D4C22×D1118yes—
367C22×D4C22×D1114yes—
368C23×C4—44no—
369C23×C4—111no—
370C23×C4—112no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—112no—
374C23×C4C22⋊D1118yescomplemented
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1114yes—
379#123—2232no—
380#121—232no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—118no—
385C2×C4⋊C4—118no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—444no—
389C2×C4⋊C4—444no—
390C2×C4⋊C4C22×D1114yes—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—444no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4C22×D1118yes—
409#95—114no—
410#95—114no—
411#95—118no—
412#95—118no—
413C2×C11—44no—
414C2×C11—84no—
415C2×C11#281318yescomplemented
416C2×C11C2×#53411yescharacteristic
417C2×C11C2×#53511yescharacteristic
418C2×C11C2×#53711yescharacteristic
419C2×C11C2×#56012yes—
420C2×C11C2×#56212yes—
421D11—82no—
422C24—24no—
423C24—24no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—112no—
434C24—224no—
435C24—224no—
436C24—222no—
437C24—222no—
438C24—222no—
439C24C2×C22⋊D1114yes—
440C24C23×D1114yes—
441C24C23×D1112yes—
442C24C23×D1111yescharacteristic
443C2×D4—216no—
444C2×D4—28no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—416no—
449C2×D4—432no—
450C2×D4—228no—
451C2×D4—448no—
452C2×D4—448no—
453C2×D4—448no—
454C2×D4—448no—
455C2×D4—4416no—
456C2×D4—4432no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—48no—
463C22×C4—416no—
464C22×C4—114no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—114no—
468C22×C4—112no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—222no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4C2×C22⋊D1114yes—
483C22×C4C2×C22⋊D1114yes—
484C22×C4C2×C22⋊D11116yescomplemented
485C22×C4C23×D1114yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C4⋊C4—28no—
489C4⋊C4—228no—
490C4⋊C4—228no—
491C4⋊C4—448no—
492C4⋊C4—448no—
493C22⋊C4—216no—
494C22⋊C4—228no—
495C22⋊C4—228no—
496C22⋊C4—228no—
497C22⋊C4—448no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C22⋊C4—448no—
502C11C2×#281311yescharacteristic, complemented, Sylow
503C23—28no—
504C23—28no—
505C23—28no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—48no—
518C23—48no—
519C23—48no—
520C23—48no—
521C23—48no—
522C23—48no—
523C23—48no—
524C23—48no—
525C23—48no—
526C23—224no—
527C23—224no—
528C23—222no—
529C23—222no—
530C23—222no—
531C23—444no—
532C23—444no—
533C23—444no—
534C23—448no—
535C23—448no—
536C23#6703714yes—
537C23#6703714yes—
538C23#6704212yes—
539C23#6704312yes—
540C23C22×C22⋊D1114yes—
541C23C22×C22⋊D1112yes—
542C23C24×D1111yescharacteristic
543D4—416no—
544D4—432no—
545D4—4416no—
546D4—4432no—
547C2×C4—28no—
548C2×C4—28no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—416no—
555C2×C4—48no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—444no—
570C2×C4—444no—
571C2×C4—444no—
572C2×C4—448no—
573C2×C4—448no—
574C2×C4C22×C22⋊D1114yes—
575C2×C4C22×C22⋊D1114yes—
576C22—24no—
577C22—24no—
578C22—24no—
579C22—44no—
580C22—44no—
581C22—416no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—816no—
590C22—442no—
591C22—442no—
592C22—442no—
593C22—444no—
594C22—444no—
595C22—888no—
596C22#1062315118yes—
597C22#1062315218yes—
598C22#1062333514yes—
599C22#1062333614yes—
600C22#1062336414yes—
601C22C2×#6703712yes—
602C22C2×#6703712yes—
603C22C2×#6704211yescharacteristic
604C22C2×#6704311yescharacteristic
605C22C23×C22⋊D1111yescharacteristic
606C4—24no—
607C4—24no—
608C4—44no—
609C4—442no—
610C4—442no—
611C4—442no—
612C4—444no—
613C4—444no—
614C2—44no—
615C2—84no—
616C2—882no—
617C2#1307661618yesdirect product factor
618C2C2×#1062333511yescharacteristic
619C2C2×#1062333611yescharacteristic
620C2C2×#1062336411yescharacteristic
621C2C2×#1062315112yes—
622C2C2×#1062315212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2813
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
2. #13076616C2direct (N × H)
3. C2×#10622595C2semidirect
4. C2×#10622605C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622825C2semidirect
12. C22×C11×#121C2semidirect
19. C2×C11×#121C22semidirect
28. C2×#66982C22semidirect
36. #10622836C22semidirect
37. #10622836C22semidirect
38. #10622835C22semidirect
39. #10622835C22semidirect
40. #10622825C22semidirect
45. #10622605C22semidirect
46. #10622595C22semidirect
47. #10622574C22semidirect
48. #10622561C22semidirect
60. C23×C4×C11D4semidirect
149. C22×C4×C11C2×D4semidirect
193. C22×#121D11semidirect
285. C2×#121C2×D11semidirect
374. C23×C4C22⋊D11semidirect
415. C2×C11#2813semidirect
484. C22×C4C2×C22⋊D11semidirect
502. C11C2×#2813semidirect
617. C2#13076616direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
#130766162
C2×#106225952
C2×#106226052
C2×#106225612
C2×#106225742
C2×#106228352
C2×#106228362
C2×#106228252
C22×C11×#1212
C2×#281311