Finite Group Databasebeta

← C2×#13074505 #14920165

Subgroups — C2×#13074505 #14920165

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×#66991C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13074505C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622572C212yesmaximal, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622836C212yesmaximal, complemented
9C2×#10622558C212yesmaximal, complemented
10C2×#10622833C212yesmaximal, complemented
11C2×#10622277C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic, complemented
13C23×D4×C11C2212yes—
14C23×D4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66991—28no—
26C2×#66991C2218yescomplemented
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×(C22⋊D11)⋊C4—28no—
34C2×(C22⋊D11)⋊C4C2218yescomplemented
35C11×#392C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37#10622836C22116yescomplemented
38#10622835C2218yescomplemented
39#10622833C22116yescomplemented
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622572C22116yescomplemented
45#10622562C2218yescomplemented
46#10622558C22116yescomplemented
47#10622277C2218yescomplemented
48#10622272C2218yescomplemented
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×C11C2314yes—
58C22×D4×C11C2318yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—24no—
63C22×C22⋊D11—24no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11—44no—
68C22×C22⋊D11C2314yes—
69C22×C22⋊D11C2318yes—
70C23×Dic11—24no—
71C23×Dic11—44no—
72C23×Dic11C2312yes—
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2314yes—
78C22×C4×D11—44no—
79C22×C4×D11D418yescomplemented
80C22×C4×D11C2314yes—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—44no—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2318yes—
85C2×C22⋊Dic11—28no—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11—44no—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11C2318yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2318yes—
93#66991—232no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—44no—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×C4⋊Dic11—24no—
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4—44no—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2318yes—
104C2×C4×Dic11—24no—
105C2×C4×Dic11C2314yes—
106(C22⋊D11)⋊C4—232no—
107C11×#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2314yes—
112C2×#2635—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11#4114yes—
125C24×C11C2414yes—
126C24×C11C2412yes—
127C24×C11C2411yescharacteristic
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11C2×D414yes—
133C23×D11C2412yes—
134C2×D4×C11—216no—
135C2×D4×C11—28no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—416no—
140C2×D4×C11—432no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C2×C22⋊D11—232no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—28no—
155C2×C22⋊D11—216no—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—432no—
159C22×Dic11—28no—
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—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—48no—
172C22×Dic11—416no—
173C22×Dic11C2×D414yes—
174C22×Dic11#4114yes—
175C22×Dic11C2414yes—
176C22×Dic11C2414yes—
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C2×C4×D11—416no—
181C2×C4×D11—48no—
182C2×C4×D11C2×D4116yescomplemented
183C11×C22⋊C4—28no—
184C11×C22⋊C4—48no—
185C22⋊Dic11—216no—
186C22⋊Dic11—216no—
187C22⋊Dic11—48no—
188C22⋊Dic11—48no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—48no—
191C4⋊Dic11—28no—
192Dic11⋊C4—28no—
193Dic11⋊C4—48no—
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—112no—
203C2×#392D1111yescharacteristic, complemented
204C2×#388—112no—
205C2×#386—112no—
206C2×#381—111no—
207C23×C11—28no—
208C23×C11—216no—
209C23×C11—22no—
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—24no—
219C23×C11—24no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11C22×D412yes—
231C23×C11C2×#4114yes—
232C23×C11C2×#4112yes—
233C23×C11C2×#4112yes—
234C23×C11H(5,𝔽2)14yes—
235C23×C11H(5,𝔽2)14yes—
236C23×C11C2511yescharacteristic
237C22×D11—28no—
238C22×D11—28no—
239C22×D11—28no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11C22×D414yes—
247D4×C11—416no—
248D4×C11—432no—
249C2×C4×C11—28no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—44no—
257C2×C4×C11—48no—
258C2×C4×C11C22×D414yes—
259C22⋊D11—232no—
260C22⋊D11—432no—
261C2×Dic11—28no—
262C2×Dic11—28no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—416no—
275C2×Dic11—44no—
276C2×Dic11—48no—
277C2×Dic11—48no—
278C2×Dic11C22×D414yes—
279C2×Dic11C2×#4114yes—
280C4×D11—416no—
281C23×D4—111no—
282C23×D4—112no—
283C23×D4C2×D1112yes—
284C23×D4C2×D1111yescharacteristic
285C24×C4—111no—
286C24×C4—111no—
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—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4C2×D1111yescharacteristic
301C22×C22⋊C4C2×D1112yes—
302C22×C42—111no—
303#400—118no—
304#399—118no—
305#394—118no—
306#394—1116no—
307#392—1116no—
308#392C2×D1118yescomplemented
309#388—1116no—
310#386—1116no—
311#381—118no—
312C2×#95—112no—
313C2×#95—111no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95C2×D1111yescharacteristic
317C22×C11—24no—
318C22×C11—28no—
319C22×C11—416no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—816no—
331C22×C11#52514yes—
332C22×C11#53414yes—
333C22×C11#53514yes—
334C22×C11#53818yes—
335C22×C11#54018yes—
336C22×C11C23×D411yescharacteristic
337C22×C11C22×#4111yescharacteristic
338C22×C11C22×#4111yescharacteristic
339C22×C11C2×H(5,𝔽2)12yes—
340C22×C11C2×H(5,𝔽2)12yes—
341C2×D11—24no—
342C2×D11—24no—
343C2×D11—24no—
344C2×D11—416no—
345C2×D11—44no—
346C2×D11—44no—
347C4×C11—24no—
348C4×C11—42no—
349C4×C11—44no—
350Dic11—24no—
351Dic11—24no—
352Dic11—42no—
353Dic11—44no—
354Dic11—44no—
355C25—111no—
356C25C22×D1112yes—
357C25C22×D1111yescharacteristic
358C22×D4—28no—
359C22×D4—24no—
360C22×D4—44no—
361C22×D4—44no—
362C22×D4—44no—
363C22×D4—114no—
364C22×D4—118no—
365C22×D4—224no—
366C22×D4—224no—
367C22×D4—224no—
368C22×D4—228no—
369C22×D4—444no—
370C22×D4—444no—
371C22×D4C22×D1114yes—
372C22×D4C22×D1118yes—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—118no—
376C23×C4—114no—
377C23×C4—112no—
378C23×C4—111no—
379C23×C4—112no—
380C23×C4—114no—
381C23×C4—224no—
382C23×C4—444no—
383C23×C4—444no—
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1112yes—
386C23×C4C22×D1111yescharacteristic
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—24no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—114no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—118no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—228no—
405C2×C22⋊C4—228no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4C22×D1114yes—
410C2×C22⋊C4C22×D1118yes—
411C2×C42—114no—
412C2×C42—224no—
413#95—118no—
414#95—114no—
415#95—118no—
416#95—118no—
417#95C22×D1114yes—
418C2×C11—44no—
419C2×C11—84no—
420C2×C11#263518yescomplemented
421C2×C11C2×#52511yescharacteristic
422C2×C11C2×#53411yescharacteristic
423C2×C11C2×#53511yescharacteristic
424C2×C11C2×#53812yes—
425C2×C11C2×#54012yes—
426D11—44no—
427C24—22no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—24no—
438C24—114no—
439C24—112no—
440C24—222no—
441C24—224no—
442C24—224no—
443C24—222no—
444C24#434114yes—
445C24C23×D1114yes—
446C24C23×D1112yes—
447C24C23×D1111yescharacteristic
448C2×D4—216no—
449C2×D4—28no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—416no—
454C2×D4—432no—
455C2×D4—228no—
456C2×D4—228no—
457C2×D4—2232no—
458C2×D4—228no—
459C2×D4—2216no—
460C2×D4—448no—
461C2×D4—448no—
462C2×D4—4432no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—1116no—
474C22×C4—114no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—228no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—224no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—224no—
489C22×C4—4416no—
490C22×C4—448no—
491C22×C4—448no—
492C22×C4—4416no—
493C22×C4D4×D1114yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1112yes—
497C4⋊C4—228no—
498C4⋊C4—228no—
499C4⋊C4—448no—
500C22⋊C4—28no—
501C22⋊C4—48no—
502C22⋊C4—228no—
503C22⋊C4—2216no—
504C22⋊C4—2216no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C42—228no—
509C11C2×#263511yescharacteristic, complemented, Sylow
510C23—216no—
511C23—28no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—22no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—44no—
524C23—44no—
525C23—48no—
526C23—48no—
527C23—48no—
528C23—48no—
529C23—48no—
530C23—48no—
531C23—48no—
532C23—48no—
533C23—114no—
534C23—228no—
535C23—228no—
536C23—228no—
537C23—222no—
538C23—224no—
539C23—224no—
540C23—222no—
541C23—448no—
542C23—448no—
543C23C2×D4×D1112yes—
544C23C2×#434114yes—
545C23C2×#434112yes—
546C23#6703714yes—
547C23#6703714yes—
548C23#41×D1112yes—
549C23C24×D1111yescharacteristic
550D4—416no—
551D4—432no—
552D4—2232no—
553D4—4432no—
554C2×C4—28no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—44no—
562C2×C4—48no—
563C2×C4—114no—
564C2×C4—114no—
565C2×C4—228no—
566C2×C4—228no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—222no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—4416no—
579C2×C4—4416no—
580C2×C4—448no—
581C2×C4—444no—
582C2×C4—448no—
583C2×C4C2×D4×D1114yes—
584C22—24no—
585C22—28no—
586C22—42no—
587C22—42no—
588C22—416no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—816no—
598C22—224no—
599C22—224no—
600C22—224no—
601C22—4416no—
602C22—444no—
603C22—444no—
604C22#1062312014yes—
605C22#1062312418yes—
606C22#1062313714yes—
607C22#1062314618yes—
608C22#1062324614yes—
609C22C22×D4×D1111yescharacteristic
610C22C22×#434111yescharacteristic
611C22C2×#6703712yes—
612C22C2×#6703712yes—
613C22C2×#41×D1111yescharacteristic
614C4—24no—
615C4—42no—
616C4—44no—
617C4—224no—
618C4—224no—
619C4—442no—
620C4—444no—
621C4—444no—
622C2—44no—
623C2—84no—
624C2—444no—
625C2#1307450518yesdirect product factor
626C2C2×#1062313711yescharacteristic
627C2C2×#1062312011yescharacteristic
628C2C2×#1062324611yescharacteristic
629C2C2×#1062312412yes—
630C2C2×#1062314612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66991C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13074505C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622558C2semidirect
10. C2×#10622833C2semidirect
11. C2×#10622277C2semidirect
12. C2×C11×#392C2semidirect
26. C2×#66991C22semidirect
34. C2×(C22⋊D11)⋊C4C22semidirect
35. C11×#392C22semidirect
37. #10622836C22semidirect
38. #10622835C22semidirect
39. #10622833C22semidirect
44. #10622572C22semidirect
45. #10622562C22semidirect
46. #10622558C22semidirect
47. #10622277C22semidirect
48. #10622272C22semidirect
79. C22×C4×D11D4semidirect
182. C2×C4×D11C2×D4semidirect
203. C2×#392D11semidirect
308. #392C2×D11semidirect
420. C2×C11#2635semidirect
509. C11C2×#2635semidirect
625. C2#13074505direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
C22×(C22⋊D11)⋊C42
#130745052
C2×#106222722
C2×#106225622
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106225582
C2×#106228332
C2×#106222772
C2×C11×#3922
C2×#263511