Finite Group Databasebeta

← C2×#13074503 #14920174

Subgroups — C2×#13074503 #14920174

Order 2816.

3606 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13074503C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622290C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622574C212yesmaximal, complemented
8C2×#10622284C211yesmaximal, characteristic, complemented
9C2×#10622573C212yesmaximal, complemented
10C2×#10622283C212yesmaximal, complemented
11C2×#10622278C212yesmaximal, complemented
12C2×C11×#381C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2212yes—
16C23×D44C2212yes—
17C23×D44C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C2×#66983—28no—
22C2×#66983C2218yescomplemented
23C2×C4×C22⋊D11—28no—
24C2×C4×C22⋊D11C2218yescomplemented
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2212yes—
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C11×#381C2218yescomplemented
36C2×C11×#95C2212yes—
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622574C22116yescomplemented
42#10622573C22116yescomplemented
43#10622290C2218yescomplemented
44#10622285C2218yescomplemented
45#10622284C2218yescomplemented
46#10622283C22116yescomplemented
47#10622278C22116yescomplemented
48#10622272C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2312yes—
51C24×D11C2311yescharacteristic
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—24no—
61C22×C22⋊D11—28no—
62C22×C22⋊D11—24no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11C2314yes—
66C22×C22⋊D11C2318yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C22×D44—28no—
72C22×D44—24no—
73C22×D44—44no—
74C22×D44—44no—
75C22×D44—44no—
76C22×D44C2318yes—
77C22×D44C2314yes—
78C22×C4×D11—24no—
79C22×C4×D11—44no—
80C22×C4×D11C2314yes—
81C2×C11×C22⋊C4—44no—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11C2314yes—
85#66983—232no—
86C4×C22⋊D11—232no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—28no—
90C2×(C2×D11)⋊C4—44no—
91C2×(C2×D11)⋊C4—44no—
92C2×(C2×D11)⋊C4—44no—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2314yes—
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⋊C4C2314yes—
105C2×C4×Dic11—24no—
106C2×C4×Dic11C2314yes—
107C11×#95C2314yes—
108C11×#95C2318yes—
109C11×#95C2314yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C2×#2635—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11C2×D414yes—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11#4114yes—
132C23×D11C2414yes—
133C23×D11C2412yes—
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—24no—
142C22×C4×C11—416no—
143C22×C4×C11—48no—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D4116yescomplemented
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C2×C22⋊D11—232no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—216no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—432no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11#4114yes—
169C22×Dic11C2412yes—
170C22×Dic11C2414yes—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C2×D44—216no—
174C2×D44—28no—
175C2×D44—48no—
176C2×D44—48no—
177C2×D44—48no—
178C2×D44—416no—
179C2×D44—432no—
180C2×C4×D11—28no—
181C2×C4×D11—48no—
182C2×C4×D11—416no—
183C11×C22⋊C4—48no—
184C22⋊Dic11—28no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4—48no—
189(C2×D11)⋊C4—48no—
190(C2×D11)⋊C4—48no—
191C4⋊Dic11—28no—
192C4⋊Dic11—48no—
193Dic11⋊C4—28no—
194C4×Dic11—28no—
195C22×#121—111no—
196C22×C4×D4—111no—
197#2635—1116no—
198C2×#400—111no—
199C2×#399—111no—
200C2×#394—111no—
201C2×#394—112no—
202C2×#392—111no—
203C2×#392—112no—
204C2×#388—112no—
205C2×#386—112no—
206C2×#381D1111yescharacteristic, complemented
207C23×C11—28no—
208C23×C11—28no—
209C23×C11—28no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11C22×D414yes—
217C23×C11C22×D412yes—
218C23×C11C2×#4112yes—
219C23×C11C2×#4112yes—
220C23×C11H(5,𝔽2)14yes—
221C23×C11H(5,𝔽2)14yes—
222C23×C11C2511yescharacteristic
223C22×D11—28no—
224C22×D11—216no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—44no—
237C22×D11—44no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11C2×#4114yes—
247C2×C4×C11—28no—
248C2×C4×C11—28no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—416no—
258C2×C4×C11—48no—
259C2×C4×C11—48no—
260C2×C4×C11C22×D414yes—
261C2×C4×C11C22×D414yes—
262C22⋊D11—232no—
263C22⋊D11—432no—
264C2×Dic11—28no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276C2×Dic11—48no—
277C2×Dic11C2×#4114yes—
278D44—416no—
279D44—432no—
280C4×D11—416no—
281C23×D4—111no—
282C23×D4—112no—
283C23×D4—112no—
284C23×D4—111no—
285C24×C4—111no—
286C24×C4C2×D1111yescharacteristic
287C2×#121—118no—
288C2×#121—228no—
289C2×C4×D4—118no—
290C2×C4×D4—228no—
291C22×C4⋊C4—111no—
292C22×C4⋊C4—111no—
293C22×C4⋊C4—112no—
294C22×C22⋊C4—111no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C22⋊C4C2×D1112yes—
302C22×C42—111no—
303#400—118no—
304#399—118no—
305#394—1116no—
306#394—118no—
307#392—1116no—
308#392—118no—
309#388—1116no—
310#386—1116no—
311#381C2×D1118yescomplemented
312C2×#95—112no—
313C2×#95—112no—
314C2×#95C2×D1111yescharacteristic
315C2×#95C2×D1111yescharacteristic
316C2×#95C2×D1112yes—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—416no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11#52514yes—
324C22×C11#53414yes—
325C22×C11#53514yes—
326C22×C11#53818yes—
327C22×C11#54018yes—
328C22×C11C23×D411yescharacteristic
329C22×C11C22×#4111yescharacteristic
330C22×C11C22×#4111yescharacteristic
331C22×C11C2×H(5,𝔽2)12yes—
332C22×C11C2×H(5,𝔽2)12yes—
333C2×D11—24no—
334C2×D11—28no—
335C2×D11—416no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—816no—
347C4×C11—24no—
348C4×C11—24no—
349C4×C11—44no—
350C4×C11—44no—
351Dic11—24no—
352Dic11—42no—
353Dic11—42no—
354Dic11—44no—
355C25—111no—
356C25—112no—
357C25C22×D1111yescharacteristic
358C22×D4—114no—
359C22×D4—118no—
360C22×D4—114no—
361C22×D4—118no—
362C22×D4—228no—
363C22×D4—224no—
364C22×D4—224no—
365C22×D4—224no—
366C22×D4—228no—
367C22×D4—224no—
368C22×D4—444no—
369C22×D4—444no—
370C22×D4—444no—
371C22×D4—444no—
372C22×D4—444no—
373C23×C4—44no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—112no—
378C23×C4—114no—
379C23×C4—224no—
380C23×C4—444no—
381C23×C4D4418yescomplemented
382C23×C4C22×D1112yes—
383C23×C4C22×D1112yes—
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1114yes—
387#121—2232no—
388C4×D4—2232no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—114no—
391C2×C4⋊C4—118no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4—224no—
394C2×C4⋊C4—444no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—114no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—118no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—228no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—228no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4—444no—
410C2×C22⋊C4C22×D1118yes—
411C2×C42—114no—
412C2×C42—224no—
413#95—118no—
414#95—118no—
415#95C22×D1118yes—
416#95C22×D1114yes—
417#95C22×D1114yes—
418C2×C11—44no—
419C2×C11#263518yescomplemented
420C2×C11C2×#52511yescharacteristic
421C2×C11C2×#53411yescharacteristic
422C2×C11C2×#53511yescharacteristic
423C2×C11C2×#53812yes—
424C2×C11C2×#54012yes—
425D11—44no—
426D11—84no—
427C24—24no—
428C24—22no—
429C24—22no—
430C24—24no—
431C24—114no—
432C24—112no—
433C24—114no—
434C24—222no—
435C24—224no—
436C24—222no—
437C24—224no—
438C24—224no—
439C24—224no—
440C24—224no—
441C24—224no—
442C24—224no—
443C24—224no—
444C24—224no—
445C24C2×D4414yes—
446C24C23×D1112yes—
447C24C23×D1111yescharacteristic
448C2×D4—2216no—
449C2×D4—228no—
450C2×D4—228no—
451C2×D4—2232no—
452C2×D4—228no—
453C2×D4—2216no—
454C2×D4—228no—
455C2×D4—448no—
456C2×D4—448no—
457C2×D4—448no—
458C2×D4—4416no—
459C2×D4—4432no—
460C2×D4—448no—
461C2×D4—448no—
462C2×D4—4432no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—48no—
472C22×C4—416no—
473C22×C4—114no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—112no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—228no—
488C22×C4—448no—
489C22×C4—4416no—
490C22×C4C2×D4414yes—
491C22×C4C2×D4414yes—
492C22×C4C2×D44116yescomplemented
493C22×C4C23×D1114yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1112yes—
497C4⋊C4—228no—
498C4⋊C4—228no—
499C4⋊C4—448no—
500C22⋊C4—48no—
501C22⋊C4—2216no—
502C22⋊C4—228no—
503C22⋊C4—228no—
504C22⋊C4—2216no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C42—228no—
509C11C2×#263511yescharacteristic, complemented, Sylow
510C23—28no—
511C23—28no—
512C23—28no—
513C23—24no—
514C23—22no—
515C23—22no—
516C23—24no—
517C23—48no—
518C23—48no—
519C23—114no—
520C23—228no—
521C23—222no—
522C23—2216no—
523C23—224no—
524C23—222no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—444no—
534C23—444no—
535C23—448no—
536C23—448no—
537C23—448no—
538C23—448no—
539C23—448no—
540C23—448no—
541C23—448no—
542C23—448no—
543C23C22×D4414yes—
544C23C22×D4412yes—
545C23#6703714yes—
546C23#41×D1112yes—
547C23#41×D1112yes—
548C23#6704214yes—
549C23C24×D1111yescharacteristic
550D4—2232no—
551D4—4416no—
552D4—4432no—
553D4—4432no—
554C2×C4—28no—
555C2×C4—28no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—416no—
565C2×C4—48no—
566C2×C4—48no—
567C2×C4—114no—
568C2×C4—228no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—4416no—
579C2×C4—444no—
580C2×C4—448no—
581C2×C4—444no—
582C2×C4C22×D4414yes—
583C2×C4C22×D4414yes—
584C22—24no—
585C22—24no—
586C22—24no—
587C22—416no—
588C22—44no—
589C22—44no—
590C22—224no—
591C22—228no—
592C22—442no—
593C22—4416no—
594C22—442no—
595C22—444no—
596C22—444no—
597C22—444no—
598C22—444no—
599C22—444no—
600C22—444no—
601C22—444no—
602C22—444no—
603C22—8816no—
604C22#1062302414yes—
605C22#1062305514yes—
606C22#1062305614yes—
607C22#1062318818yes—
608C22#1062319418yes—
609C22C23×D4411yescharacteristic
610C22C2×#6703712yes—
611C22C2×#41×D1111yescharacteristic
612C22C2×#41×D1111yescharacteristic
613C22C2×#6704212yes—
614C4—24no—
615C4—24no—
616C4—44no—
617C4—44no—
618C4—224no—
619C4—442no—
620C4—444no—
621C4—442no—
622C2—44no—
623C2—444no—
624C2—884no—
625C2#1307450318yesdirect product factor
626C2C2×#1062305511yescharacteristic
627C2C2×#1062302411yescharacteristic
628C2C2×#1062305611yescharacteristic
629C2C2×#1062318812yes—
630C2C2×#1062319412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#381C2
socleC24×C11C24
hypercenterC2×#381D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
1. C22×#66983C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13074503C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622290C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622284C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622283C2semidirect
11. C2×#10622278C2semidirect
12. C2×C11×#381C2semidirect
22. C2×#66983C22semidirect
24. C2×C4×C22⋊D11C22semidirect
35. C11×#381C22semidirect
41. #10622574C22semidirect
42. #10622573C22semidirect
43. #10622290C22semidirect
44. #10622285C22semidirect
45. #10622284C22semidirect
46. #10622283C22semidirect
47. #10622278C22semidirect
48. #10622272C22semidirect
53. C23×C4×C11D4semidirect
146. C22×C4×C11C2×D4semidirect
206. C2×#381D11semidirect
311. #381C2×D11semidirect
381. C23×C4D44semidirect
419. C2×C11#2635semidirect
492. C22×C4C2×D44semidirect
509. C11C2×#2635semidirect
625. C2#13074503direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669832
C22×C4×C22⋊D112
#130745032
C2×#106222722
C2×#106222902
C2×#106222852
C2×#106225742
C2×#106222842
C2×#106225732
C2×#106222832
C2×#106222782
C2×C11×#3812
C2×#263511