Finite Group Databasebeta

← C2×#13072047 #14922188

Subgroups — C2×#13072047 #14922188

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic, complemented
2C22×#66977C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic
4C22×#66945C211yesmaximal, characteristic, complemented
5#13072047C2116yesmaximal, direct product factor
6C2×#10622288C212yesmaximal, complemented
7C2×#10622572C212yesmaximal
8C2×#10622587C211yesmaximal, characteristic, complemented
9C2×#10622260C212yesmaximal, complemented
10C2×#10622586C211yesmaximal, characteristic, complemented
11C2×#10622564C212yesmaximal, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×Dic22C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C2×C4×C22⋊D11—28no—
23C2×C4×C22⋊D11C2218yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C2×#66977—28no—
30C2×#66977C2218yescomplemented
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2212yes—
33C22×Dic11⋊C4C2212yes—
34C22×C4×Dic11C2212yes—
35C22×C4×Dic11C2211yescharacteristic
36C2×#66950—28no—
37C2×#66950C2218yescomplemented
38C2×#66945—28no—
39C2×#66945C2218yescomplemented
40C11×#380C2218yescomplemented
41C2×C11×#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622587C2218yescomplemented
46#10622586C2218yescomplemented
47#10622572C22116yes—
48#10622564C22116yescomplemented
49#10622288C22116yescomplemented
50#10622260C22116yescomplemented
51C25×C11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C23×C4×C11—24no—
54C23×C4×C11—24no—
55C23×C4×C11—24no—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2314yes—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—24no—
62C22×C22⋊D11—24no—
63C22×C22⋊D11—24no—
64C22×C22⋊D11C2314yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C22×C4×D11—24no—
71C22×C4×D11—24no—
72C22×C4×D11D418yes—
73C22×C4×D11C2314yes—
74C22×Dic22—24no—
75C22×Dic22—24no—
76C22×Dic22—24no—
77C22×Dic22C2314yes—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C22⋊C4—28no—
83C2×C11×C22⋊C4C2318yes—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2314yes—
88C4×C22⋊D11—232no—
89C2×(C2×D11)⋊C4—28no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×C4⋊Dic11—28no—
96C2×C4⋊Dic11D418yescomplemented
97C2×C4⋊Dic11C2318yes—
98C2×C4⋊Dic11C2314yes—
99#66977—232no—
100C2×Dic11⋊C4—28no—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—28no—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2318yes—
105C2×Dic11⋊C4C2318yes—
106C2×C4×Dic11—24no—
107C2×C4×Dic11—28no—
108C2×C4×Dic11C2318yes—
109C2×C4×Dic11C2314yes—
110#66950—232no—
111#66945—232no—
112C11×#95C2318yes—
113C11⋊#95C2318yes—
114C11⋊#95C2318yes—
115C11⋊#95C2318yes—
116C2×#2415—111nomaximal, Sylow
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11#4114yes—
124C24×C11C2412yes—
125C24×C11C2411yescharacteristic
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11C2×D414yes—
133C23×D11C2412yes—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—28no—
144C22×C4×C11—28no—
145C22×C4×C11—28no—
146C22×C4×C11—416no—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11#4114yes—
150C22×C4×C11C2414yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C2×C22⋊D11—232no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—28no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11C2×D418yes—
171C22×Dic11C2×D414yes—
172C22×Dic11#4114yes—
173C22×Dic11C2412yes—
174C22×Dic11C2414yes—
175C22×Dic11C2414yes—
176C22×Dic11C2412yes—
177C22×Dic11C2412yes—
178C2×C4×D11—232no—
179C2×C4×D11—28no—
180C2×C4×D11—28no—
181C2×C4×D11C2×D4116yes—
182C2×Dic22—28no—
183C2×Dic22—28no—
184C2×Dic22—28no—
185C2×Dic22—416no—
186C11×C4⋊C4—28no—
187C11×C4⋊C4—28no—
188C11×C22⋊C4—216no—
189C22⋊Dic11—216no—
190C22⋊Dic11—28no—
191(C2×D11)⋊C4—216no—
192(C2×D11)⋊C4—216no—
193(C2×D11)⋊C4—28no—
194C4⋊Dic11—216no—
195C4⋊Dic11C2×D4116yescomplemented
196Dic11⋊C4—216no—
197Dic11⋊C4—28no—
198Dic11⋊C4—216no—
199C4×Dic11—216no—
200C4×Dic11—28no—
201C22×C22⋊Q8—111no—
202C22×C22⋊Q8—111no—
203C22×C4×D4—111no—
204C22×#117—111no—
205#2415—1116no—
206C2×#397—112no—
207C2×#394—112no—
208C2×#391—111no—
209C2×#389—112no—
210C2×#389—111no—
211C2×#388—112no—
212C2×#380D1111yescharacteristic, complemented
213C23×C11—28no—
214C23×C11—28no—
215C23×C11—28no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—44no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11C22×D412yes—
227C23×C11C22×D412yes—
228C23×C11C2×#4112yes—
229C23×C11C2×#4114yes—
230C23×C11C2×#4112yes—
231C23×C11C2×#4112yes—
232C23×C112−1+412yes—
233C23×C112−1+412yes—
234C23×C11C2511yescharacteristic
235C22×D11—28no—
236C22×D11—28no—
237C22×D11—28no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—44no—
245C22×D11—44no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11C22×D414yes—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—44no—
259C2×C4×C11—48no—
260C2×C4×C11—48no—
261C2×C4×C11—416no—
262C2×C4×C11#121116yes—
263C2×C4×C11C22×D414yes—
264C2×C4×C11C22×D414yes—
265C2×C4×C11C2×#4114yes—
266C22⋊D11—232no—
267C2×Dic11—28no—
268C2×Dic11—28no—
269C2×Dic11—216no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—48no—
283C2×Dic11—44no—
284C2×Dic11C22×D418yes—
285C2×Dic11C22×D414yes—
286C2×Dic11C2×#4114yes—
287C4×D11—232no—
288Dic22—416no—
289C23×Q8—111no—
290C23×D4—111no—
291C24×C4—111no—
292C24×C4C2×D1111yescharacteristic
293C2×C22⋊Q8—118no—
294C2×C22⋊Q8—118no—
295C2×C22⋊Q8—228no—
296C2×C22⋊Q8—228no—
297C2×C4×D4—118no—
298C2×C4×D4—228no—
299C2×#117—118no—
300C2×#117—228no—
301C22×C4⋊C4—111no—
302C22×C4⋊C4—112no—
303C22×C4⋊C4—112no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4—112no—
306C22×C4⋊C4C2×D1111yescharacteristic
307C22×C4⋊C4C2×D1111yescharacteristic
308C22×C22⋊C4—112no—
309C22×C22⋊C4—111no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C22⋊C4—111no—
313C22×C22⋊C4C2×D1112yes—
314C22×C42—112no—
315C22×C42—111no—
316#397—1116no—
317#394—1116no—
318#391—118no—
319#389—118no—
320#389—1116no—
321#388—1116no—
322#380C2×D1118yescomplemented
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95C2×D1112yes—
327C22×C11—24no—
328C22×C11—24no—
329C22×C11—24no—
330C22×C11—42no—
331C22×C11—416no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11C2×#12114yes—
336C22×C11#52514yes—
337C22×C11#53614yes—
338C22×C11#54714yes—
339C22×C11#54814yes—
340C22×C11#55214yes—
341C22×C11#55614yes—
342C22×C11C23×D411yescharacteristic
343C22×C11C23×D411yescharacteristic
344C22×C11C22×#4111yescharacteristic
345C22×C11C22×#4111yescharacteristic
346C22×C11C22×#4111yescharacteristic
347C22×C11C2×2−1+411yescharacteristic
348C22×C11C2×2−1+411yescharacteristic
349C2×D11—24no—
350C2×D11—24no—
351C2×D11—24no—
352C2×D11—416no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C4×C11—42no—
358C4×C11—44no—
359C4×C11—44no—
360C4×C11C2×#12118yes—
361Dic11—24no—
362Dic11—24no—
363Dic11—28no—
364Dic11—44no—
365Dic11—42no—
366C25—111no—
367C25C22×D1111yescharacteristic
368C22×Q8—114no—
369C22×Q8—224no—
370C22×Q8—224no—
371C22×Q8—224no—
372C22×D4—114no—
373C22×D4—224no—
374C22×D4—224no—
375C22×D4—224no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—112no—
380C23×C4—111no—
381C23×C4—111no—
382C23×C4—118no—
383C23×C4—114no—
384C23×C4—112no—
385C23×C4—111no—
386C23×C4—224no—
387C23×C4—224no—
388C23×C4C22×D1114yes—
389C23×C4C22×D1112yes—
390C23×C4C22×D1112yes—
391C23×C4C22×D1111yescharacteristic
392C23×C4C22×D1111yescharacteristic
393C22⋊Q8—2232no—
394C22⋊Q8—2232no—
395C4×D4—2232no—
396#117—2232no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—118no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—118no—
403C2×C4⋊C4—118no—
404C2×C4⋊C4—118no—
405C2×C4⋊C4—224no—
406C2×C4⋊C4—228no—
407C2×C4⋊C4—228no—
408C2×C4⋊C4—228no—
409C2×C4⋊C4C22×D1114yes—
410C2×C4⋊C4C22×D1114yes—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4—118no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—114no—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4—224no—
419C2×C22⋊C4—228no—
420C2×C22⋊C4—224no—
421C2×C22⋊C4—228no—
422C2×C22⋊C4C22×D1118yes—
423C2×C42—118no—
424C2×C42—114no—
425C2×C42—228no—
426C2×C42—224no—
427#95—118no—
428#95—118no—
429#95—118no—
430#95C22×D1118yes—
431C2×C11—44no—
432C2×C11#241518yescomplemented
433C2×C11C22×#12111yescharacteristic
434C2×C11C2×#52511yescharacteristic
435C2×C11C2×#53611yescharacteristic
436C2×C11C2×#54711yescharacteristic
437C2×C11C2×#54811yescharacteristic
438C2×C11C2×#55211yescharacteristic
439C2×C11C2×#55611yescharacteristic
440D11—44no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—114no—
448C24—112no—
449C24—222no—
450C24—222no—
451C24—222no—
452C24—222no—
453C24—222no—
454C24—222no—
455C24#434114yes—
456C24C23×D1112yes—
457C24C23×D1111yescharacteristic
458C2×Q8—228no—
459C2×Q8—228no—
460C2×Q8—228no—
461C2×Q8—4416no—
462C2×D4—228no—
463C2×D4—228no—
464C2×D4—2232no—
465C2×D4—228no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—416no—
479C22×C4—118no—
480C22×C4—114no—
481C22×C4—114no—
482C22×C4—112no—
483C22×C4—114no—
484C22×C4—112no—
485C22×C4—1116no—
486C22×C4—112no—
487C22×C4—114no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—224no—
493C22×C4—224no—
494C22×C4—2232no—
495C22×C4—228no—
496C22×C4—228no—
497C22×C4—224no—
498C22×C4—222no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4#433914yes—
504C22×C4D4×D1114yes—
505C22×C4D4×D1114yes—
506C22×C4C23×D1114yes—
507C22×C4C23×D1114yes—
508C22×C4C23×D1112yes—
509C22×C4C23×D1112yes—
510C4⋊C4—28no—
511C4⋊C4—28no—
512C4⋊C4—1116no—
513C4⋊C4—228no—
514C4⋊C4—2216no—
515C4⋊C4—2216no—
516C4⋊C4—2216no—
517C22⋊C4—216no—
518C22⋊C4—2216no—
519C22⋊C4—228no—
520C22⋊C4—2216no—
521C22⋊C4—228no—
522C22⋊C4—2216no—
523C42—2216no—
524C42—228no—
525C11C2×#241511yescharacteristic, complemented, Sylow
526C23—28no—
527C23—28no—
528C23—28no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—44no—
536C23—44no—
537C23—44no—
538C23—44no—
539C23—114no—
540C23—228no—
541C23—228no—
542C23—228no—
543C23—222no—
544C23—222no—
545C23—222no—
546C23—222no—
547C23—222no—
548C23—222no—
549C23—444no—
550C23—444no—
551C23—444no—
552C23—444no—
553C23C2×#433912yes—
554C23C2×D4×D1112yes—
555C23C2×D4×D1112yes—
556C23C2×#434114yes—
557C23C2×#434112yes—
558C23#6704012yes—
559C23#41×D1112yes—
560C23#6704312yes—
561C23C24×D1111yescharacteristic
562Q8—4416no—
563D4—2232no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—44no—
574C2×C4—48no—
575C2×C4—48no—
576C2×C4—416no—
577C2×C4—118no—
578C2×C4—114no—
579C2×C4—114no—
580C2×C4—228no—
581C2×C4—228no—
582C2×C4—2216no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—2232no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—448no—
597C2×C4—444no—
598C2×C4#66937116yes—
599C2×C4C2×#433914yes—
600C2×C4C2×D4×D1114yes—
601C2×C4C2×D4×D1114yes—
602C22—24no—
603C22—24no—
604C22—24no—
605C22—42no—
606C22—42no—
607C22—416no—
608C22—42no—
609C22—42no—
610C22—224no—
611C22—224no—
612C22—224no—
613C22—442no—
614C22—442no—
615C22—4416no—
616C22—442no—
617C22—442no—
618C22C2×#6693714yes—
619C22#1062304414yes—
620C22#1062306414yes—
621C22#1062312914yes—
622C22#1062313714yes—
623C22#1062315914yes—
624C22#1062316214yes—
625C22C22×#433911yescharacteristic
626C22C22×D4×D1111yescharacteristic
627C22C22×D4×D1111yescharacteristic
628C22C22×#434111yescharacteristic
629C22C2×#6704011yescharacteristic
630C22C2×#41×D1111yescharacteristic
631C22C2×#6704311yescharacteristic
632C4—44no—
633C4—44no—
634C4—42no—
635C4—224no—
636C4—228no—
637C4—224no—
638C4—442no—
639C4—444no—
640C4C2×#6693718yes—
641C2—44no—
642C2—444no—
643C2#1307204718yesdirect product factor
644C2C22×#6693711yescharacteristic
645C2C2×#1062313711yescharacteristic
646C2C2×#1062315911yescharacteristic
647C2C2×#1062316211yescharacteristic
648C2C2×#1062312911yescharacteristic
649C2C2×#1062304411yescharacteristic
650C2C2×#1062306411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#380D11
hypocenterC11C2×#2415
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#66950C2semidirect
2. C22×#66977C2semidirect
4. C22×#66945C2semidirect
5. #13072047C2direct (N × H)
6. C2×#10622288C2semidirect
8. C2×#10622587C2semidirect
9. C2×#10622260C2semidirect
10. C2×#10622586C2semidirect
11. C2×#10622564C2semidirect
12. C2×C11×#380C2semidirect
30. C2×#66977C22semidirect
37. C2×#66950C22semidirect
39. C2×#66945C22semidirect
40. C11×#380C22semidirect
45. #10622587C22semidirect
46. #10622586C22semidirect
48. #10622564C22semidirect
49. #10622288C22semidirect
50. #10622260C22semidirect
96. C2×C4⋊Dic11D4semidirect
195. C4⋊Dic11C2×D4semidirect
212. C2×#380D11semidirect
322. #380C2×D11semidirect
432. C2×C11#2415semidirect
525. C11C2×#2415semidirect
643. C2#13072047direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
C22×#669772
C22×C4×C22⋊D112
C22×#669452
#130720472
C2×#106222882
C2×#106225722
C2×#106225872
C2×#106222602
C2×#106225862
C2×#106225642
C2×C11×#3802
C2×#241511