Finite Group Databasebeta

← C2×#13073576 #14923793

Subgroups — C2×#13073576 #14923793

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×#66983C212yesmaximal, complemented
2C22×#66983C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13073576C2116yesmaximal, direct product factor
5C2×#10622274C211yesmaximal, characteristic, complemented
6C2×#10622287C211yesmaximal, characteristic, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622284C211yesmaximal, characteristic, complemented
9C2×#10622283C212yesmaximal, complemented
10C2×#10622826C212yesmaximal, complemented
11C2×#10622278C212yesmaximal, complemented
12C22×C11×#95C211yesmaximal, characteristic, complemented
13C24×C4×C11C2212yes—
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2212yes—
16C23×C22⋊D11C2211yescharacteristic
17C23×D44C2212yes—
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C2×#66983—28no—
22C2×#66983—216no—
23C2×#66983C22116yescomplemented
24C2×#66983C2218yescomplemented
25C2×C4×C22⋊D11—28no—
26C2×C4×C22⋊D11C2218yescomplemented
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2212yes—
31C22×(C2×D11)⋊C4C2212yes—
32C22×(C2×D11)⋊C4C2212yes—
33C22×C4⋊Dic11C2212yes—
34C22×C4⋊Dic11C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C11×#95C2212yes—
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2218yescomplemented
41#10622826C22116yescomplemented
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622287C2218yescomplemented
45#10622285C2218yescomplemented
46#10622284C2218yescomplemented
47#10622283C22116yescomplemented
48#10622278C22116yescomplemented
49#10622274C2218yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11C2312yes—
52C24×D11C2311yescharacteristic
53C23×C4×C11—28no—
54C23×C4×C11—28no—
55C23×C4×C11—44no—
56C23×C4×C11—44no—
57C23×C4×C11D418yescomplemented
58C23×C4×C11C2312yes—
59C23×C4×C11C2318yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C23×C4×C11C2314yes—
64C22×C22⋊D11—24no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—28no—
67C22×C22⋊D11—28no—
68C22×C22⋊D11—28no—
69C22×C22⋊D11D418yescomplemented
70C22×C22⋊D11C2318yes—
71C22×C22⋊D11C2314yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2312yes—
75C23×Dic11C2311yescharacteristic
76C22×D44—28no—
77C22×D44—24no—
78C22×D44—28no—
79C22×D44—44no—
80C22×D44—44no—
81C22×D44C2318yes—
82C22×D44C2314yes—
83C22×C4×D11—24no—
84C22×C4×D11—44no—
85C22×C4×D11C2314yes—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11C2314yes—
88#66983—232no—
89#66983—264no—
90C4×C22⋊D11—232no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—28no—
94C2×(C2×D11)⋊C4—28no—
95C2×(C2×D11)⋊C4—28no—
96C2×(C2×D11)⋊C4—44no—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2318yes—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11—28no—
105C2×C4⋊Dic11C2318yes—
106C2×C4⋊Dic11C2314yes—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4C2314yes—
109C2×C4×Dic11—24no—
110C2×C4×Dic11C2314yes—
111C11×#95C2314yes—
112C11×#95C2318yes—
113C11×#95C2314yes—
114C11⋊#95C2318yes—
115C11⋊#95C2318yes—
116C2×#2543—111nomaximal, Sylow
117C24×C11—24no—
118C24×C11—24no—
119C24×C11C2×D414yes—
120C24×C11C2×D414yes—
121C24×C11#4114yes—
122C24×C11C2412yes—
123C24×C11C2411yescharacteristic
124C23×D11—22no—
125C23×D11—24no—
126C23×D11—22no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11—24no—
134C23×D11—24no—
135C23×D11C2×D414yes—
136C23×D11C2414yes—
137C23×D11C2412yes—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—216no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—216no—
147C22×C4×C11—416no—
148C22×C4×C11—48no—
149C22×C4×C11—48no—
150C22×C4×C11—432no—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D4116yescomplemented
154C22×C4×C11#4118yes—
155C22×C4×C11C2414yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2414yes—
159C2×C22⋊D11—232no—
160C2×C22⋊D11—28no—
161C2×C22⋊D11—216no—
162C2×C22⋊D11—216no—
163C2×C22⋊D11—28no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11—432no—
166C2×C22⋊D11C2×D4116yescomplemented
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11—22no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11C2×D414yes—
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C22×Dic11C2414yes—
180C22×Dic11C2412yes—
181C2×D44—216no—
182C2×D44—28no—
183C2×D44—216no—
184C2×D44—48no—
185C2×D44—48no—
186C2×D44—432no—
187C2×D44—416no—
188C2×C4×D11—28no—
189C2×C4×D11—48no—
190C2×C4×D11—416no—
191C22⋊Dic11—28no—
192(C2×D11)⋊C4—216no—
193(C2×D11)⋊C4—216no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—216no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—48no—
198C4⋊Dic11—216no—
199C4⋊Dic11—28no—
200Dic11⋊C4—28no—
201C4×Dic11—28no—
202C22×#121—112no—
203C22×#121—111no—
204C22×C4×D4—111no—
205#2543—1116no—
206C2×#398—111no—
207C2×#397—111no—
208C2×#394—111no—
209C2×#392—111no—
210C2×#388—112no—
211C2×#386—112no—
212C2×#386—112no—
213C22×#95D1111yescharacteristic, complemented
214C23×C11—28no—
215C23×C11—28no—
216C23×C11—216no—
217C23×C11—216no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11#121116yes—
221C23×C11C22×D414yes—
222C23×C11C22×D412yes—
223C23×C11C22×D414yes—
224C23×C11C22×D412yes—
225C23×C11C2×#4114yes—
226C23×C11C2×#4114yes—
227C23×C11C2×#4112yes—
228C23×C11H(5,𝔽2)14yes—
229C23×C11C2511yescharacteristic
230C22×D11—28no—
231C22×D11—216no—
232C22×D11—22no—
233C22×D11—24no—
234C22×D11—22no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—44no—
244C22×D11—44no—
245C22×D11—48no—
246C22×D11—48no—
247C22×D11—48no—
248C22×D11—48no—
249C22×D11—48no—
250C22×D11—48no—
251C22×D11—48no—
252C22×D11—48no—
253C22×D11C22×D414yes—
254C2×C4×C11—28no—
255C2×C4×C11—28no—
256C2×C4×C11—216no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—416no—
265C2×C4×C11—432no—
266C2×C4×C11—48no—
267C2×C4×C11C22×D414yes—
268C2×C4×C11C22×D414yes—
269C2×C4×C11C2×#4118yes—
270C22⋊D11—232no—
271C22⋊D11—432no—
272C2×Dic11—28no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—48no—
283C2×Dic11—44no—
284C2×Dic11—44no—
285C2×Dic11C22×D414yes—
286D44—432no—
287D44—416no—
288C4×D11—416no—
289C23×D4—111no—
290C23×D4—112no—
291C23×D4—112no—
292C23×D4—111no—
293C24×C4—111no—
294C24×C4C2×D1112yes—
295C24×C4C2×D1111yescharacteristic
296C2×#121—118no—
297C2×#121—1116no—
298C2×#121—2216no—
299C2×#121—228no—
300C2×C4×D4—118no—
301C2×C4×D4—228no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—112no—
305C22×C22⋊C4—111no—
306C22×C22⋊C4—111no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C42—111no—
313#398—118no—
314#397—118no—
315#394—118no—
316#392—118no—
317#388—1116no—
318#386—1116no—
319#386—1116no—
320C2×#95—112no—
321C2×#95—112no—
322C2×#95C2×D1111yescharacteristic
323C2×#95C2×D1111yescharacteristic
324C2×#95C2×D1112yes—
325C2×#95C2×D1118yescomplemented
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—28no—
329C22×C11—28no—
330C22×C11—232no—
331C22×C11C2×#12118yes—
332C22×C11C2×#12114yes—
333C22×C11#53214yes—
334C22×C11#53414yes—
335C22×C11#54618yes—
336C22×C11#55318yes—
337C22×C11C23×D411yescharacteristic
338C22×C11C23×D411yescharacteristic
339C22×C11C22×#4112yes—
340C22×C11C22×#4111yescharacteristic
341C22×C11C2×H(5,𝔽2)12yes—
342C2×D11—24no—
343C2×D11—28no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—44no—
347C2×D11—416no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—44no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—816no—
356C4×C11—24no—
357C4×C11—24no—
358C4×C11—28no—
359C4×C11—44no—
360Dic11—24no—
361Dic11—44no—
362Dic11—42no—
363Dic11—42no—
364C25—111no—
365C25—112no—
366C25C22×D1111yescharacteristic
367C22×D4—118no—
368C22×D4—114no—
369C22×D4—118no—
370C22×D4—118no—
371C22×D4—114no—
372C22×D4—228no—
373C22×D4—224no—
374C22×D4—224no—
375C22×D4—228no—
376C22×D4—228no—
377C22×D4—228no—
378C22×D4—224no—
379C22×D4—228no—
380C22×D4—444no—
381C22×D4—444no—
382C23×C4—28no—
383C23×C4—28no—
384C23×C4—44no—
385C23×C4—44no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—112no—
390C23×C4—114no—
391C23×C4—224no—
392C23×C4—444no—
393C23×C4D4418yescomplemented
394C23×C4C22×D1112yes—
395C23×C4C22×D1118yes—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1112yes—
399C23×C4C22×D1114yes—
400#121—2264no—
401#121—2232no—
402C4×D4—2232no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—118no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—228no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4—224no—
409C2×C22⋊C4—114no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—118no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—228no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4—224no—
419C2×C22⋊C4—224no—
420C2×C22⋊C4—228no—
421C2×C22⋊C4—228no—
422C2×C22⋊C4—444no—
423C2×C42—114no—
424C2×C42—224no—
425#95—118no—
426#95—118no—
427#95C22×D1118yes—
428#95C22×D1114yes—
429#95C22×D1114yes—
430C2×C11—28no—
431C2×C11#254318yescomplemented
432C2×C11C22×#12111yescharacteristic
433C2×C11C2×#53211yescharacteristic
434C2×C11C2×#53411yescharacteristic
435C2×C11C2×#54612yes—
436C2×C11C2×#55312yes—
437D11—44no—
438D11—84no—
439C24—24no—
440C24—24no—
441C24—114no—
442C24—112no—
443C24—114no—
444C24—222no—
445C24—224no—
446C24—224no—
447C24—222no—
448C24—224no—
449C24—224no—
450C24—224no—
451C24—224no—
452C24—224no—
453C24—224no—
454C24—224no—
455C24C2×D4414yes—
456C24D4×D1114yes—
457C24#434314yes—
458C24C23×D1112yes—
459C24C23×D1111yescharacteristic
460C2×D4—1116no—
461C2×D4—2216no—
462C2×D4—2232no—
463C2×D4—228no—
464C2×D4—228no—
465C2×D4—2216no—
466C2×D4—2216no—
467C2×D4—2216no—
468C2×D4—228no—
469C2×D4—2216no—
470C2×D4—448no—
471C2×D4—448no—
472C2×D4—4432no—
473C2×D4—4416no—
474C2×D4—4432no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—216no—
482C22×C4—24no—
483C22×C4—216no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—416no—
487C22×C4—432no—
488C22×C4—114no—
489C22×C4—112no—
490C22×C4—112no—
491C22×C4—112no—
492C22×C4—114no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—224no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—224no—
502C22×C4—228no—
503C22×C4—448no—
504C22×C4—4416no—
505C22×C4C2×D4414yes—
506C22×C4C2×D4414yes—
507C22×C4C2×D44116yescomplemented
508C22×C4#433918yes—
509C22×C4C23×D1114yes—
510C22×C4C23×D1112yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1114yes—
513C4⋊C4—2216no—
514C4⋊C4—228no—
515C4⋊C4—228no—
516C22⋊C4—2216no—
517C22⋊C4—2216no—
518C22⋊C4—228no—
519C22⋊C4—228no—
520C22⋊C4—2216no—
521C22⋊C4—2216no—
522C22⋊C4—448no—
523C42—228no—
524C11C2×#254311yescharacteristic, complemented, Sylow
525C23—28no—
526C23—216no—
527C23—28no—
528C23—216no—
529C23—24no—
530C23—24no—
531C23—114no—
532C23—2216no—
533C23—228no—
534C23—222no—
535C23—224no—
536C23—224no—
537C23—222no—
538C23—224no—
539C23—224no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—224no—
544C23—224no—
545C23—444no—
546C23—444no—
547C23—448no—
548C23—448no—
549C23—448no—
550C23—448no—
551C23—448no—
552C23—448no—
553C23—448no—
554C23—448no—
555C23#66948116yes—
556C23C22×D4414yes—
557C23C22×D4412yes—
558C23C2×#433914yes—
559C23C2×D4×D1114yes—
560C23C2×D4×D1112yes—
561C23#6703714yes—
562C23C2×#434314yes—
563C23C2×#434312yes—
564C23C24×D1111yescharacteristic
565D4—2232no—
566D4—4432no—
567D4—4416no—
568D4—4432no—
569C2×C4—216no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—416no—
580C2×C4—432no—
581C2×C4—48no—
582C2×C4—114no—
583C2×C4—228no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—4416no—
594C2×C4—444no—
595C2×C4—444no—
596C2×C4—448no—
597C2×C4C22×D4414yes—
598C2×C4C22×D4414yes—
599C2×C4C2×#433918yes—
600C22—28no—
601C22—24no—
602C22—24no—
603C22—232no—
604C22—28no—
605C22—228no—
606C22—224no—
607C22—444no—
608C22—442no—
609C22—442no—
610C22—4416no—
611C22—444no—
612C22—444no—
613C22—444no—
614C22—444no—
615C22—444no—
616C22—444no—
617C22—444no—
618C22—8816no—
619C22#1062300814yes—
620C22#1062302118yes—
621C22#1062302414yes—
622C22C2×#6694818yes—
623C22C2×#6694814yes—
624C22#1062304518yes—
625C22C23×D4411yescharacteristic
626C22C22×#433912yes—
627C22C22×D4×D1111yescharacteristic
628C22C2×#6703712yes—
629C22C22×#434311yescharacteristic
630C4—24no—
631C4—24no—
632C4—28no—
633C4—44no—
634C4—224no—
635C4—442no—
636C4—442no—
637C4—444no—
638C2—28no—
639C2—444no—
640C2—884no—
641C2#1307357618yesdirect product factor
642C2C22×#6694811yescharacteristic
643C2C2×#1062300811yescharacteristic
644C2C2×#1062302411yescharacteristic
645C2C2×#1062302112yes—
646C2C2×#1062304512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#95C2
socleC24×C11C24
hypercenterC22×#95D11
hypocenterC11C2×#2543
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C22×#66983C2semidirect
2. C22×#66983C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13073576C2direct (N × H)
5. C2×#10622274C2semidirect
6. C2×#10622287C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622284C2semidirect
9. C2×#10622283C2semidirect
10. C2×#10622826C2semidirect
11. C2×#10622278C2semidirect
12. C22×C11×#95C2semidirect
23. C2×#66983C22semidirect
24. C2×#66983C22semidirect
26. C2×C4×C22⋊D11C22semidirect
40. C2×C11×#95C22semidirect
41. #10622826C22semidirect
44. #10622287C22semidirect
45. #10622285C22semidirect
46. #10622284C22semidirect
47. #10622283C22semidirect
48. #10622278C22semidirect
49. #10622274C22semidirect
57. C23×C4×C11D4semidirect
69. C22×C22⋊D11D4semidirect
153. C22×C4×C11C2×D4semidirect
166. C2×C22⋊D11C2×D4semidirect
213. C22×#95D11semidirect
325. C2×#95C2×D11semidirect
393. C23×C4D44semidirect
431. C2×C11#2543semidirect
507. C22×C4C2×D44semidirect
524. C11C2×#2543semidirect
641. C2#13073576direct (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
#130735762
C2×#106222742
C2×#106222872
C2×#106222852
C2×#106222842
C2×#106222832
C2×#106228262
C2×#106222782
C22×C11×#952
C2×#254311