Finite Group Databasebeta

← C2×#13074744 #14920324

Subgroups — C2×#13074744 #14920324

Order 2816.

3434 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×#66983C211yesmaximal, characteristic, complemented
2#13074744C2116yesmaximal, direct product factor
3C2×#10622596C211yesmaximal, characteristic, complemented
4C2×#10622566C211yesmaximal, characteristic, complemented
5C2×#10622604C211yesmaximal, characteristic, complemented
6C2×#10622572C212yesmaximal, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622836C212yesmaximal, complemented
9C2×#10622570C212yesmaximal, complemented
10C2×#10622603C212yesmaximal, complemented
11C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
12C22×C11×#123C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2212yes—
16C23×C22⋊D11C2212yes—
17C23×D44C2211yescharacteristic
18C2×C11×#123—28no—
19C2×C11×#123C2218yescomplemented
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C2×#66983—28no—
28C2×#66983C2218yescomplemented
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×(C2×D11)⋊C4C2212yes—
32C22×(C2×D11)⋊C4C2212yes—
33C22×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2212yes—
35C22×C4×Dic11C2212yes—
36#10622836C22116yescomplemented
37C4×C22⋊Dic11C2218yescomplemented
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622604C2218yescomplemented
43#10622603C22116yescomplemented
44#10622596C2218yescomplemented
45#10622573C2218yescomplemented
46#10622572C22116yescomplemented
47#10622570C22116yescomplemented
48#10622566C2218yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2311yescharacteristic
51C24×D11C2312yes—
52C22×D4×C11—24no—
53C22×D4×C11—44no—
54C22×D4×C11C2314yes—
55C23×C4×C11—44no—
56C23×C4×C11D418yescomplemented
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2314yes—
63C22×C22⋊D11—28no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11—44no—
68C22×C22⋊D11—44no—
69C22×C22⋊D11C2318yes—
70C22×C22⋊D11C2318yes—
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C23×Dic11C2312yes—
74C22×D44—24no—
75C22×D44—44no—
76C22×D44C2314yes—
77C11×#123—232no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C22⋊Dic11—28no—
89C2×C22⋊Dic11—44no—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2318yes—
92#66983—232no—
93C2×(C2×D11)⋊C4—28no—
94C2×(C2×D11)⋊C4—28no—
95C2×(C2×D11)⋊C4—44no—
96C2×(C2×D11)⋊C4—44no—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×C4⋊Dic11—24no—
102C2×C4⋊Dic11C2314yes—
103C2×Dic11⋊C4—44no—
104C2×Dic11⋊C4C2318yes—
105C2×C4×Dic11—44no—
106C2×C4×Dic11C2318yes—
107C11⋊#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C2×#2661—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—22no—
117C24×C11—24no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—24no—
121C24×C11C2×D414yes—
122C24×C11C2412yes—
123C24×C11C2412yes—
124C24×C11C2411yescharacteristic
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11C2414yes—
133C2×D4×C11—28no—
134C2×D4×C11—48no—
135C2×D4×C11—416no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
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×C11C2412yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C2×C22⋊D11—216no—
156C2×C22⋊D11—216no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—432no—
162C2×C22⋊D11—432no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11#4118yes—
172C22×Dic11C2414yes—
173C22×Dic11C2414yes—
174C22×Dic11C2414yes—
175C2×D44—28no—
176C2×D44—48no—
177C2×D44—416no—
178C11×C4⋊C4—28no—
179C11×C4⋊C4—28no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—28no—
182C11×C22⋊C4—28no—
183C22⋊Dic11—216no—
184C22⋊Dic11—48no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—216no—
187(C2×D11)⋊C4—48no—
188(C2×D11)⋊C4—48no—
189C4⋊Dic11—28no—
190Dic11⋊C4—48no—
191C4×Dic11—48no—
192C22×#123D1111yescharacteristic, complemented
193C22×#121—111no—
194#2661—1116no—
195C2×#398—111no—
196C2×#397—111no—
197C2×#394—111no—
198C2×#394—112no—
199C2×#392—112no—
200C2×#392—111no—
201C2×#390—112no—
202C2×#388—112no—
203C2×C4×C22⋊C4—111no—
204C23×C11—28no—
205C23×C11—28no—
206C23×C11—28no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—48no—
217C23×C11—48no—
218C23×C11—44no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—48no—
222C23×C11—48no—
223C23×C11C22×D414yes—
224C23×C11C22×D412yes—
225C23×C11C2×#4114yes—
226C23×C11H(5,𝔽2)14yes—
227C23×C11H(5,𝔽2)12yes—
228C23×C11H(5,𝔽2)12yes—
229C23×C11C2511yescharacteristic
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—48no—
244D4×C11—416no—
245C2×C4×C11—28no—
246C2×C4×C11—28no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—416no—
257C2×C4×C11—44no—
258C2×C4×C11—44no—
259C2×C4×C11—44no—
260C2×C4×C11C22×D414yes—
261C2×C4×C11C22×D414yes—
262C22⋊D11—432no—
263C22⋊D11—432no—
264C2×Dic11—216no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—48no—
274C2×Dic11—48no—
275C2×Dic11C2×#4118yes—
276D44—416no—
277C23×D4—112no—
278C23×D4—112no—
279C23×D4—111no—
280C23×D4C2×D1111yescharacteristic
281C24×C4C2×D1111yescharacteristic
282C2×#123—28no—
283C2×#123C2×D1118yescomplemented
284C2×#121—118no—
285C2×#121—228no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—112no—
288C22×C4⋊C4C2×D1111yescharacteristic
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4C2×D1111yescharacteristic
297C22×C22⋊C4C2×D1111yescharacteristic
298C22×C22⋊C4C2×D1111yescharacteristic
299C22×C42—112no—
300#398—118no—
301#397—118no—
302#394—118no—
303#394—1116no—
304#392—1116no—
305#392—118no—
306#390—1116no—
307#388—1116no—
308C4×C22⋊C4—118no—
309C2×#95—111no—
310C2×#95—112no—
311C2×#95—111no—
312C2×#95—112no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—416no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—88no—
325C22×C11#53214yes—
326C22×C11#53414yes—
327C22×C11#53514yes—
328C22×C11#53818yes—
329C22×C11#54018yes—
330C22×C11C23×D411yescharacteristic
331C22×C11C22×#4112yes—
332C22×C11C2×H(5,𝔽2)12yes—
333C22×C11C2×H(5,𝔽2)11yescharacteristic
334C22×C11C2×H(5,𝔽2)11yescharacteristic
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—816no—
343C4×C11—24no—
344C4×C11—24no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—42no—
348Dic11—28no—
349Dic11—44no—
350Dic11—44no—
351C25—112no—
352C25C22×D1111yescharacteristic
353C25C22×D1111yescharacteristic
354C22×D4—24no—
355C22×D4—44no—
356C22×D4—118no—
357C22×D4—118no—
358C22×D4—114no—
359C22×D4—228no—
360C22×D4—228no—
361C22×D4—224no—
362C22×D4—444no—
363C22×D4—444no—
364C22×D4—444no—
365C22×D4—444no—
366C22×D4—444no—
367C22×D4C22×D1114yes—
368C23×C4—44no—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4—112no—
372C23×C4C22⋊D1118yescomplemented
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1114yes—
379#123—232no—
380#121—2232no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—118no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—444no—
387C2×C4⋊C4C22×D1114yes—
388C2×C4⋊C4C22×D1114yes—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4—228no—
400C2×C22⋊C4—228no—
401C2×C22⋊C4—444no—
402C2×C22⋊C4—444no—
403C2×C22⋊C4—444no—
404C2×C22⋊C4C22×D1114yes—
405C2×C22⋊C4C22×D1114yes—
406C2×C22⋊C4C22×D1114yes—
407C2×C42—118no—
408C2×C42—444no—
409#95—114no—
410#95—114no—
411#95—118no—
412#95—118no—
413C2×C11—44no—
414C2×C11—82no—
415C2×C11#266118yescomplemented
416C2×C11C2×#53211yescharacteristic
417C2×C11C2×#53411yescharacteristic
418C2×C11C2×#53511yescharacteristic
419C2×C11C2×#53812yes—
420C2×C11C2×#54012yes—
421D11—84no—
422C24—24no—
423C24—24no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—24no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—114no—
432C24—224no—
433C24—224no—
434C24—224no—
435C24—224no—
436C24—224no—
437C24—224no—
438C24—224no—
439C24C2×C22⋊D1114yes—
440C24C23×D1112yes—
441C24C23×D1112yes—
442C24C23×D1111yescharacteristic
443C2×D4—28no—
444C2×D4—48no—
445C2×D4—416no—
446C2×D4—2216no—
447C2×D4—2216no—
448C2×D4—228no—
449C2×D4—448no—
450C2×D4—4416no—
451C2×D4—448no—
452C2×D4—448no—
453C2×D4—448no—
454C2×D4—448no—
455C2×D4—4432no—
456C2×D4—4432no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—48no—
467C22×C4—416no—
468C22×C4—118no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4C2×C22⋊D1114yes—
481C22×C4C2×C22⋊D1114yes—
482C22×C4C2×C22⋊D11116yescomplemented
483C22×C4C23×D1112yes—
484C22×C4C23×D1112yes—
485C22×C4C23×D1112yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C4⋊C4—28no—
489C4⋊C4—28no—
490C4⋊C4—228no—
491C4⋊C4—448no—
492C22⋊C4—28no—
493C22⋊C4—28no—
494C22⋊C4—28no—
495C22⋊C4—2216no—
496C22⋊C4—2216no—
497C22⋊C4—2216no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C42—448no—
502C11C2×#266111yescharacteristic, complemented, Sylow
503C23—28no—
504C23—28no—
505C23—28no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—48no—
516C23—48no—
517C23—44no—
518C23—44no—
519C23—44no—
520C23—48no—
521C23—48no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—448no—
530C23—448no—
531C23—448no—
532C23—448no—
533C23—448no—
534C23—448no—
535C23—448no—
536C23#6703714yes—
537C23#41×D1114yes—
538C23#6704212yes—
539C23#6704212yes—
540C23C22×C22⋊D1114yes—
541C23C22×C22⋊D1112yes—
542C23C24×D1111yescharacteristic
543D4—416no—
544D4—4416no—
545D4—4432no—
546D4—4432no—
547C2×C4—28no—
548C2×C4—28no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—416no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—118no—
563C2×C4—2216no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—448no—
573C2×C4—448no—
574C2×C4C22×C22⋊D1114yes—
575C2×C4C22×C22⋊D1114yes—
576C22—24no—
577C22—24no—
578C22—24no—
579C22—416no—
580C22—44no—
581C22—44no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—44no—
586C22—44no—
587C22—88no—
588C22—444no—
589C22—444no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22—444no—
595C22—8816no—
596C22#1062318818yes—
597C22#1062319418yes—
598C22#1062333514yes—
599C22#1062336114yes—
600C22#1062336314yes—
601C22C2×#6703712yes—
602C22C2×#41×D1112yes—
603C22C2×#6704211yescharacteristic
604C22C2×#6704211yescharacteristic
605C22C23×C22⋊D1111yescharacteristic
606C4—24no—
607C4—24no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—228no—
612C4—444no—
613C4—444no—
614C2—44no—
615C2—82no—
616C2—884no—
617C2#1307474418yesdirect product factor
618C2C2×#1062336311yescharacteristic
619C2C2×#1062333511yescharacteristic
620C2C2×#1062336111yescharacteristic
621C2C2×#1062318812yes—
622C2C2×#1062319412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
hypercenterC22×#123D11
hypocenterC11C2×#2661
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#66983C2semidirect
2. #13074744C2direct (N × H)
3. C2×#10622596C2semidirect
4. C2×#10622566C2semidirect
5. C2×#10622604C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622603C2semidirect
11. C2×C4×C22⋊Dic11C2semidirect
12. C22×C11×#123C2semidirect
19. C2×C11×#123C22semidirect
28. C2×#66983C22semidirect
36. #10622836C22semidirect
37. C4×C22⋊Dic11C22semidirect
42. #10622604C22semidirect
43. #10622603C22semidirect
44. #10622596C22semidirect
45. #10622573C22semidirect
46. #10622572C22semidirect
47. #10622570C22semidirect
48. #10622566C22semidirect
56. C23×C4×C11D4semidirect
149. C22×C4×C11C2×D4semidirect
192. C22×#123D11semidirect
283. C2×#123C2×D11semidirect
372. C23×C4C22⋊D11semidirect
415. C2×C11#2661semidirect
482. C22×C4C2×C22⋊D11semidirect
502. C11C2×#2661semidirect
617. C2#13074744direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669832
#130747442
C2×#106225962
C2×#106225662
C2×#106226042
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106225702
C2×#106226032
C2×C4×C22⋊Dic112
C22×C11×#1232
C2×#266111