Finite Group Databasebeta

← C2×#13076620 #14959922

Subgroups — C2×#13076620 #14959922

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
2C22×#66983C211yesmaximal, characteristic, complemented
3#13076620C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622290C211yesmaximal, characteristic, complemented
6C2×#10622607C212yesmaximal, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622604C212yesmaximal, complemented
9C2×#10622574C212yesmaximal, complemented
10C2×#10622284C211yesmaximal, characteristic, complemented
11C2×#10622573C212yesmaximal, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2212yes—
16C23×D44C2211yescharacteristic
17C23×D44C2212yes—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C2×#66983—28no—
22C2×#66983C2218yescomplemented
23C2×#66982—28no—
24C2×#66982C2218yescomplemented
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×(C2×D11)⋊C4C2212yes—
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2212yes—
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C11×#380C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622607C22116yescomplemented
42#10622604C22116yescomplemented
43#10622574C22116yescomplemented
44#10622573C22116yescomplemented
45#10622290C2218yescomplemented
46#10622285C2218yescomplemented
47#10622284C2218yescomplemented
48#10622272C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C24×D11C2312yes—
52C23×C4×C11—44no—
53C23×C4×C11D418yescomplemented
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2314yes—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11C2314yes—
65C22×C22⋊D11C2318yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C22×D44—24no—
71C22×D44—44no—
72C22×D44—44no—
73C22×D44—44no—
74C22×D44—44no—
75C22×D44C2314yes—
76C22×D44C2318yes—
77C2×C11×C4⋊C4—44no—
78C2×C11×C4⋊C4C2318yes—
79C2×C11×C22⋊C4—44no—
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11C2314yes—
83#66983—232no—
84#66982—232no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—28no—
88C2×(C2×D11)⋊C4—44no—
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)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11—44no—
101C2×C4⋊Dic11C2314yes—
102C2×C4⋊Dic11C2318yes—
103C2×Dic11⋊C4—24no—
104C2×Dic11⋊C4—24no—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C11×#95C2314yes—
108C11×#95C2314yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C2×#2813—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—22no—
116C24×C11C2×D414yes—
117C24×C11C2412yes—
118C24×C11C2411yescharacteristic
119C23×D11—22no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—22no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—22no—
130C23×D11—24no—
131C23×D11C2412yes—
132C23×D11C2414yes—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—416no—
142C22×C4×C11—48no—
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D4116yescomplemented
146C22×C4×C11C2414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2412yes—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—216no—
152C2×C22⋊D11—48no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—416no—
156C2×C22⋊D11—432no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—22no—
167C22×Dic11C2412yes—
168C22×Dic11C2412yes—
169C22×Dic11C2414yes—
170C22×Dic11C2412yes—
171C2×D44—28no—
172C2×D44—48no—
173C2×D44—48no—
174C2×D44—48no—
175C2×D44—48no—
176C2×D44—416no—
177C2×D44—432no—
178C11×C4⋊C4—48no—
179C11×C22⋊C4—48no—
180C22⋊Dic11—28no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—216no—
184(C2×D11)⋊C4—48no—
185(C2×D11)⋊C4—48no—
186(C2×D11)⋊C4—48no—
187(C2×D11)⋊C4—48no—
188C4⋊Dic11—28no—
189C4⋊Dic11—48no—
190Dic11⋊C4—28no—
191Dic11⋊C4—28no—
192C22×#123—111no—
193C22×#121—111no—
194#2813—1116no—
195C2×#400—111no—
196C2×#399—111no—
197C2×#396—112no—
198C2×#394—111no—
199C2×#394—112no—
200C2×#394—112no—
201C2×#392—111no—
202C2×#392—112no—
203C2×#380D1111yescharacteristic, complemented
204C23×C11—28no—
205C23×C11—28no—
206C23×C11—28no—
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—22no—
211C23×C11—48no—
212C23×C11—48no—
213C23×C11C22×D414yes—
214C23×C11C22×D412yes—
215C23×C11H(5,𝔽2)14yes—
216C23×C11H(5,𝔽2)12yes—
217C23×C11H(5,𝔽2)14yes—
218C23×C112−1+412yes—
219C23×C11C2511yescharacteristic
220C22×D11—22no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—22no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—22no—
231C22×D11—24no—
232C22×D11—48no—
233C22×D11—44no—
234C22×D11—48no—
235C22×D11—44no—
236C22×D11—44no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—48no—
244C2×C4×C11—28no—
245C2×C4×C11—28no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—416no—
255C2×C4×C11—48no—
256C2×C4×C11—48no—
257C2×C4×C11C22×D414yes—
258C2×C4×C11C22×D414yes—
259C22⋊D11—416no—
260C22⋊D11—432no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—44no—
272C2×Dic11—44no—
273C2×Dic11—48no—
274C2×Dic11—44no—
275D44—416no—
276D44—432no—
277C23×D4—111no—
278C23×D4—112no—
279C23×D4—111no—
280C23×D4—112no—
281C24×C4C2×D1111yescharacteristic
282C2×#123—118no—
283C2×#123—228no—
284C2×#121—118no—
285C2×#121—228no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—111no—
289C22×C4⋊C4—112no—
290C22×C4⋊C4C2×D1112yes—
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—1116no—
304#394—1116no—
305#394—118no—
306#392—1116no—
307#392—118no—
308#380C2×D1118yescomplemented
309C2×#95—112no—
310C2×#95—112no—
311C2×#95C2×D1111yescharacteristic
312C2×#95C2×D1111yescharacteristic
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—416no—
319C22×C11#53414yes—
320C22×C11#53514yes—
321C22×C11#53714yes—
322C22×C11#56018yes—
323C22×C11#56218yes—
324C22×C11C23×D411yescharacteristic
325C22×C11C2×H(5,𝔽2)12yes—
326C22×C11C2×H(5,𝔽2)11yescharacteristic
327C22×C11C2×H(5,𝔽2)12yes—
328C22×C11C2×2−1+411yescharacteristic
329C2×D11—44no—
330C2×D11—42no—
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—24no—
345C4×C11—44no—
346C4×C11—44no—
347Dic11—42no—
348Dic11—42no—
349Dic11—44no—
350Dic11—42no—
351C25—111no—
352C25—112no—
353C25C22×D1111yescharacteristic
354C22×D4—118no—
355C22×D4—114no—
356C22×D4—114no—
357C22×D4—118no—
358C22×D4—228no—
359C22×D4—224no—
360C22×D4—224no—
361C22×D4—444no—
362C22×D4—444no—
363C22×D4—444no—
364C22×D4—444no—
365C22×D4—444no—
366C22×D4—444no—
367C22×D4—444no—
368C23×C4—44no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—112no—
372C23×C4—111no—
373C23×C4D4418yescomplemented
374C23×C4C22×D1112yes—
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1114yes—
379#123—2232no—
380#121—2232no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—118no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4—444no—
390C2×C4⋊C4C22×D1118yes—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—228no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4C22×D1118yes—
409#95—118no—
410#95—118no—
411#95C22×D1114yes—
412#95C22×D1114yes—
413C2×C11—44no—
414C2×C11#281318yescomplemented
415C2×C11C2×#53411yescharacteristic
416C2×C11C2×#53511yescharacteristic
417C2×C11C2×#53711yescharacteristic
418C2×C11C2×#56012yes—
419C2×C11C2×#56212yes—
420D11—84no—
421D11—82no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—24no—
426C24—112no—
427C24—114no—
428C24—222no—
429C24—224no—
430C24—224no—
431C24—224no—
432C24—224no—
433C24—224no—
434C24—222no—
435C24—222no—
436C24—224no—
437C24—224no—
438C24—224no—
439C24—224no—
440C24C2×D4414yes—
441C24C23×D1112yes—
442C24C23×D1111yescharacteristic
443C2×D4—2216no—
444C2×D4—228no—
445C2×D4—228no—
446C2×D4—448no—
447C2×D4—448no—
448C2×D4—448no—
449C2×D4—448no—
450C2×D4—4416no—
451C2×D4—4432no—
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—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—48no—
466C22×C4—416no—
467C22×C4—112no—
468C22×C4—114no—
469C22×C4—112no—
470C22×C4—112no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—224no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—224no—
477C22×C4—222no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4C2×D4414yes—
482C22×C4C2×D4414yes—
483C22×C4C2×D44116yescomplemented
484C22×C4C23×D1114yes—
485C22×C4C23×D1114yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C4⋊C4—48no—
489C4⋊C4—228no—
490C4⋊C4—228no—
491C4⋊C4—228no—
492C4⋊C4—448no—
493C22⋊C4—48no—
494C22⋊C4—228no—
495C22⋊C4—2216no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C22⋊C4—448no—
502C11C2×#281311yescharacteristic, complemented, Sylow
503C23—28no—
504C23—28no—
505C23—28no—
506C23—22no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—48no—
511C23—48no—
512C23—222no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23—222no—
519C23—222no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—448no—
525C23—444no—
526C23—444no—
527C23—448no—
528C23—448no—
529C23—444no—
530C23—448no—
531C23—448no—
532C23—448no—
533C23—448no—
534C23—448no—
535C23—448no—
536C23C22×D4414yes—
537C23C22×D4412yes—
538C23#6703714yes—
539C23#6703712yes—
540C23#6704012yes—
541C23#6704214yes—
542C23C24×D1111yescharacteristic
543D4—4416no—
544D4—4432no—
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—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—416no—
558C2×C4—48no—
559C2×C4—48no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—444no—
571C2×C4—444no—
572C2×C4—448no—
573C2×C4—444no—
574C2×C4C22×D4414yes—
575C2×C4C22×D4414yes—
576C22—24no—
577C22—24no—
578C22—24no—
579C22—44no—
580C22—44no—
581C22—416no—
582C22—444no—
583C22—442no—
584C22—444no—
585C22—442no—
586C22—442no—
587C22—444no—
588C22—444no—
589C22—444no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22—8816no—
595C22—888no—
596C22#1062302414yes—
597C22#1062304114yes—
598C22#1062305614yes—
599C22#1062315118yes—
600C22#1062317818yes—
601C22C23×D4411yescharacteristic
602C22C2×#6703712yes—
603C22C2×#6703711yescharacteristic
604C22C2×#6704011yescharacteristic
605C22C2×#6704212yes—
606C4—24no—
607C4—24no—
608C4—44no—
609C4—44no—
610C4—442no—
611C4—444no—
612C4—442no—
613C4—442no—
614C2—44no—
615C2—884no—
616C2—882no—
617C2#1307662018yesdirect product factor
618C2C2×#1062302411yescharacteristic
619C2C2×#1062305611yescharacteristic
620C2C2×#1062304111yescharacteristic
621C2C2×#1062315112yes—
622C2C2×#1062317812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
hypercenterC2×#380D11
hypocenterC11C2×#2813
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
2. C22×#66983C2semidirect
3. #13076620C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622290C2semidirect
6. C2×#10622607C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622604C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622284C2semidirect
11. C2×#10622573C2semidirect
12. C2×C11×#380C2semidirect
22. C2×#66983C22semidirect
24. C2×#66982C22semidirect
36. C11×#380C22semidirect
41. #10622607C22semidirect
42. #10622604C22semidirect
43. #10622574C22semidirect
44. #10622573C22semidirect
45. #10622290C22semidirect
46. #10622285C22semidirect
47. #10622284C22semidirect
48. #10622272C22semidirect
53. C23×C4×C11D4semidirect
145. C22×C4×C11C2×D4semidirect
203. C2×#380D11semidirect
308. #380C2×D11semidirect
373. C23×C4D44semidirect
414. C2×C11#2813semidirect
483. C22×C4C2×D44semidirect
502. C11C2×#2813semidirect
617. C2#13076620direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
C22×#669832
#130766202
C2×#106222722
C2×#106222902
C2×#106226072
C2×#106222852
C2×#106226042
C2×#106225742
C2×#106222842
C2×#106225732
C2×C11×#3802
C2×#281311