Finite Group Databasebeta

← C2×#13073579 #14923800

Subgroups — C2×#13073579 #14923800

Order 2816.

4326 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C212yesmaximal, complemented
2C22×#66991C211yesmaximal, characteristic, complemented
3C22×#66946C211yesmaximal, characteristic, complemented
4#13073579C2116yesmaximal, direct product factor
5C2×#10622596C211yesmaximal, characteristic, complemented
6C2×#10622287C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622558C212yesmaximal, complemented
9C2×#10622569C212yesmaximal, complemented
10C2×#10622569C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#394C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×D44C2211yescharacteristic
17C23×C4×D11C2212yes—
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C11×C22⋊C4C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66991—28no—
26C2×#66991C2218yescomplemented
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×#66946—28no—
34C2×#66946C2218yescomplemented
35C2×#66937—216no—
36C2×#66937C22116yescomplemented
37C11×#394C2218yescomplemented
38C2×C11×#95C2211yescharacteristic
39#10622836C2218yescomplemented
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622596C2218yescomplemented
45#10622569C22116yescomplemented
46#10622569C22116yescomplemented
47#10622558C22116yescomplemented
48#10622287C2218yescomplemented
49D11×#95C2218yescomplemented
50C25×C11C2312yes—
51C24×D11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C22×D4×C11—24no—
54C22×D4×C11—44no—
55C22×D4×C11C2314yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—28no—
61C22×C22⋊D11—28no—
62C22×C22⋊D11—28no—
63C22×C22⋊D11—28no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11C2318yes—
67C22×C22⋊D11C2318yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C22×D44—24no—
73C22×D44—24no—
74C22×D44D418yescomplemented
75C22×D44C2314yes—
76C22×C4×D11—28no—
77C22×C4×D11—24no—
78C22×C4×D11—28no—
79C22×C4×D11—44no—
80C22×C4×D11—44no—
81C22×C4×D11—44no—
82C22×C4×D11D418yescomplemented
83C22×C4×D11C2318yes—
84C22×C4×D11C2314yes—
85C22×C4×D11C2314yes—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C22⋊C4—28no—
89C2×C11×C22⋊C4—44no—
90C2×C11×C22⋊C4C2318yes—
91C2×C11×C22⋊C4C2318yes—
92C2×C22⋊Dic11—28no—
93C2×C22⋊Dic11—28no—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2318yes—
96#66991—232no—
97C2×(C2×D11)⋊C4—28no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11C2314yes—
105C2×Dic11⋊C4—28no—
106C2×Dic11⋊C4C2318yes—
107C2×C4×Dic11—24no—
108C2×C4×Dic11C2314yes—
109#66946—232no—
110#66937—264no—
111C11×#95C2314yes—
112C11⋊#95C2318yes—
113C11⋊#95C2314yes—
114C11⋊#95C2318yes—
115C11⋊#95C2318yes—
116C2×#2543—111nomaximal, Sylow
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11C2414yes—
125C24×C11C2411yescharacteristic
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11C2×D414yes—
133C23×D11C2×D414yes—
134C23×D11C2×D414yes—
135C23×D11#4114yes—
136C23×D11C2412yes—
137C23×D11C2412yes—
138C2×D4×C11—28no—
139C2×D4×C11—48no—
140C2×D4×C11—416no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—22no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C2×C22⋊D11—216no—
156C2×C22⋊D11—216no—
157C2×C22⋊D11—216no—
158C2×C22⋊D11—216no—
159C2×C22⋊D11—216no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—432no—
162C2×C22⋊D11—432no—
163C22×Dic11—24no—
164C22×Dic11—22no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11C2×D414yes—
172C22×Dic11#4118yes—
173C22×Dic11C2412yes—
174C22×Dic11C2414yes—
175C22×Dic11C2412yes—
176C22×Dic11C2414yes—
177C2×D44—232no—
178C2×D44—28no—
179C2×D44—28no—
180C2×D44C2×D4116yescomplemented
181C2×C4×D11—28no—
182C2×C4×D11—216no—
183C2×C4×D11—216no—
184C2×C4×D11—416no—
185C2×C4×D11—48no—
186C2×C4×D11—48no—
187C2×C4×D11—48no—
188C2×C4×D11—432no—
189C2×C4×D11—416no—
190C2×C4×D11C2×D4116yescomplemented
191C11×C4⋊C4—28no—
192C11×C22⋊C4—216no—
193C11×C22⋊C4—48no—
194C22⋊Dic11—216no—
195C22⋊Dic11—216no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—28no—
199C4⋊Dic11—28no—
200Dic11⋊C4—216no—
201C4×Dic11—28no—
202C22×#121—111no—
203C22×#121—112no—
204C22×C4×D4—111no—
205#2543—1116no—
206C2×#398—111no—
207C2×#397—111no—
208C2×#394D1111yescharacteristic, complemented
209C2×#392—111no—
210C2×#388—112no—
211C2×#386—112no—
212C2×#386—112no—
213C22×#95—111no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—48no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11C22×D412yes—
229C23×C11C22×D412yes—
230C23×C11C2×#4112yes—
231C23×C11C2×#4114yes—
232C23×C11H(5,𝔽2)14yes—
233C23×C11C2511yescharacteristic
234C22×D11—28no—
235C22×D11—28no—
236C22×D11—216no—
237C22×D11—216no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—28no—
241C22×D11—216no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—48no—
249C22×D11#121116yes—
250C22×D11C22×D414yes—
251C22×D11C22×D414yes—
252C22×D11C22×D414yes—
253C22×D11C2×#4114yes—
254D4×C11—416no—
255C2×C4×C11—28no—
256C2×C4×C11—28no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—44no—
266C2×C4×C11—48no—
267C2×C4×C11C22×D414yes—
268C2×C4×C11C22×D414yes—
269C22⋊D11—432no—
270C22⋊D11—432no—
271C2×Dic11—28no—
272C2×Dic11—216no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—48no—
282C2×Dic11—44no—
283C2×Dic11C22×D414yes—
284C2×Dic11C2×#4118yes—
285D44—232no—
286C4×D11—416no—
287C4×D11—432no—
288C4×D11—416no—
289C23×D4—112no—
290C23×D4—112no—
291C23×D4—111no—
292C23×D4C2×D1111yescharacteristic
293C24×C4—111no—
294C24×C4—112no—
295C24×C4—111no—
296C2×#121—118no—
297C2×#121—1116no—
298C2×#121—2216no—
299C2×#121—228no—
300C2×C4×D4—118no—
301C2×C4×D4—228no—
302C22×C4⋊C4—112no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4C2×D1111yescharacteristic
305C22×C22⋊C4—112no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—111no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—111no—
310C22×C22⋊C4C2×D1112yes—
311C22×C22⋊C4C2×D1112yes—
312C22×C42—111no—
313#398—118no—
314#397—118no—
315#394C2×D1118yescomplemented
316#392—118no—
317#388—1116no—
318#386—1116no—
319#386—1116no—
320C2×#95—111no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—118no—
325C2×#95C2×D1111yescharacteristic
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—816no—
334C22×C11C2×#12114yes—
335C22×C11#53214yes—
336C22×C11#53414yes—
337C22×C11#54618yes—
338C22×C11#55318yes—
339C22×C11C23×D411yescharacteristic
340C22×C11C23×D411yescharacteristic
341C22×C11C22×#4111yescharacteristic
342C22×C11C22×#4112yes—
343C22×C11C2×H(5,𝔽2)12yes—
344C2×D11—24no—
345C2×D11—24no—
346C2×D11—28no—
347C2×D11—28no—
348C2×D11—232no—
349C2×D11—24no—
350C2×D11—28no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—44no—
354C2×D11—416no—
355C2×D11C2×#12118yes—
356C4×C11—24no—
357C4×C11—24no—
358C4×C11—42no—
359C4×C11—44no—
360Dic11—24no—
361Dic11—28no—
362Dic11—44no—
363Dic11—42no—
364C25—111no—
365C25—111no—
366C25C22×D1112yes—
367C22×D4—24no—
368C22×D4—44no—
369C22×D4—118no—
370C22×D4—118no—
371C22×D4—118no—
372C22×D4—114no—
373C22×D4—224no—
374C22×D4—224no—
375C22×D4—228no—
376C22×D4—228no—
377C22×D4—228no—
378C22×D4—228no—
379C22×D4—228no—
380C22×D4—444no—
381C22×D4C22×D1114yes—
382C23×C4—111no—
383C23×C4—112no—
384C23×C4—118no—
385C23×C4—114no—
386C23×C4—111no—
387C23×C4—112no—
388C23×C4—118no—
389C23×C4—114no—
390C23×C4—224no—
391C23×C4—228no—
392C23×C4—228no—
393C23×C4—444no—
394C23×C4—444no—
395C23×C4—444no—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1112yes—
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400#121—2264no—
401#121—2232no—
402C4×D4—2232no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—118no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—228no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4C22×D1114yes—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—224no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4—228no—
419C2×C22⋊C4—228no—
420C2×C22⋊C4—224no—
421C2×C22⋊C4C22×D1118yes—
422C2×C22⋊C4C22×D1118yes—
423C2×C42—114no—
424C2×C42—224no—
425#95—118no—
426#95—114no—
427#95—118no—
428#95—118no—
429#95C22×D1114yes—
430C2×C11—84no—
431C2×C11#254318yescomplemented
432C2×C11C22×#12111yescharacteristic
433C2×C11C2×#53211yescharacteristic
434C2×C11C2×#53411yescharacteristic
435C2×C11C2×#54612yes—
436C2×C11C2×#55312yes—
437D11—28no—
438D11—44no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—114no—
447C24—114no—
448C24—114no—
449C24—112no—
450C24—114no—
451C24—112no—
452C24—224no—
453C24—224no—
454C24—222no—
455C24—224no—
456C24—222no—
457C24—224no—
458C24C23×D1114yes—
459C24C23×D1111yescharacteristic
460C2×D4—28no—
461C2×D4—48no—
462C2×D4—416no—
463C2×D4—1116no—
464C2×D4—228no—
465C2×D4—2232no—
466C2×D4—228no—
467C2×D4—2216no—
468C2×D4—2216no—
469C2×D4—2216no—
470C2×D4—2216no—
471C2×D4—2216no—
472C2×D4—448no—
473C2×D4—4432no—
474C2×D4—4432no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—114no—
484C22×C4—118no—
485C22×C4—114no—
486C22×C4—112no—
487C22×C4—1116no—
488C22×C4—112no—
489C22×C4—114no—
490C22×C4—228no—
491C22×C4—2216no—
492C22×C4—2216no—
493C22×C4—224no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—222no—
497C22×C4—224no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—4416no—
502C22×C4—448no—
503C22×C4—448no—
504C22×C4—448no—
505C22×C4—4432no—
506C22×C4—4416no—
507C22×C4D4×D1114yes—
508C22×C4D4×D1114yes—
509C22×C4C23×D1114yes—
510C22×C4C23×D1112yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C4⋊C4—28no—
514C4⋊C4—2216no—
515C4⋊C4—228no—
516C22⋊C4—216no—
517C22⋊C4—48no—
518C22⋊C4—228no—
519C22⋊C4—2216no—
520C22⋊C4—2216no—
521C22⋊C4—2216no—
522C22⋊C4—228no—
523C42—228no—
524C11C2×#254311yescharacteristic, complemented, Sylow
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—48no—
533C23—48no—
534C23—48no—
535C23—48no—
536C23—48no—
537C23—48no—
538C23—48no—
539C23—1116no—
540C23—114no—
541C23—114no—
542C23—114no—
543C23—114no—
544C23—228no—
545C23—2216no—
546C23—224no—
547C23—2216no—
548C23—224no—
549C23—228no—
550C23—228no—
551C23—2216no—
552C23—222no—
553C23—224no—
554C23—224no—
555C23—222no—
556C23—444no—
557C23—448no—
558C23—444no—
559C23C2×D4×D1112yes—
560C23C2×D4×D1112yes—
561C23#6703714yes—
562C23#41×D1112yes—
563C23#41×D1114yes—
564C23C24×D1111yescharacteristic
565D4—416no—
566D4—2232no—
567D4—4432no—
568D4—4432no—
569C2×C4—28no—
570C2×C4—28no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—44no—
580C2×C4—48no—
581C2×C4—114no—
582C2×C4—118no—
583C2×C4—228no—
584C2×C4—2216no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—4416no—
594C2×C4—4432no—
595C2×C4—4416no—
596C2×C4—448no—
597C2×C4—444no—
598C2×C4C2×D4×D1114yes—
599C2×C4C2×D4×D1114yes—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—816no—
608C22—118no—
609C22—228no—
610C22—224no—
611C22—224no—
612C22—2232no—
613C22—228no—
614C22—228no—
615C22—224no—
616C22—444no—
617C22—442no—
618C22—442no—
619C22—4416no—
620C22#1062312014yes—
621C22D11×#12114yes—
622C22#1062314318yes—
623C22#1062319218yes—
624C22#1062319914yes—
625C22C22×D4×D1111yescharacteristic
626C22C22×D4×D1111yescharacteristic
627C22C2×#6703712yes—
628C22C2×#41×D1111yescharacteristic
629C22C2×#41×D1112yes—
630C4—24no—
631C4—24no—
632C4—42no—
633C4—44no—
634C4—224no—
635C4—228no—
636C4—442no—
637C4—444no—
638C2—84no—
639C2—228no—
640C2—444no—
641C2#1307357918yesdirect product factor
642C2C2×D11×#12111yescharacteristic
643C2C2×#1062319911yescharacteristic
644C2C2×#1062312011yescharacteristic
645C2C2×#1062314312yes—
646C2C2×#1062319212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2543
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66937C2semidirect
2. C22×#66991C2semidirect
3. C22×#66946C2semidirect
4. #13073579C2direct (N × H)
5. C2×#10622596C2semidirect
6. C2×#10622287C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622558C2semidirect
9. C2×#10622569C2semidirect
10. C2×#10622569C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#394C2semidirect
26. C2×#66991C22semidirect
34. C2×#66946C22semidirect
36. C2×#66937C22semidirect
37. C11×#394C22semidirect
39. #10622836C22semidirect
44. #10622596C22semidirect
45. #10622569C22semidirect
46. #10622569C22semidirect
47. #10622558C22semidirect
48. #10622287C22semidirect
49. D11×#95C22semidirect
74. C22×D44D4semidirect
82. C22×C4×D11D4semidirect
180. C2×D44C2×D4semidirect
190. C2×C4×D11C2×D4semidirect
208. C2×#394D11semidirect
315. #394C2×D11semidirect
431. C2×C11#2543semidirect
524. C11C2×#2543semidirect
641. C2#13073579direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×#669912
C22×#669462
#130735792
C2×#106225962
C2×#106222872
C2×#106228362
C2×#106225582
C2×#106225692
C2×D11×#952
C2×C11×#3942
C2×#254311