Finite Group Databasebeta

← C2×#13072920 #14922821

Subgroups — C2×#13072920 #14922821

Order 2816.

3678 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C212yesmaximal
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4#13072920C2116yesmaximal, direct product factor
5C2×#10622270C212yesmaximal, complemented
6C2×#10622565C212yesmaximal, complemented
7C2×#10622598C211yesmaximal, characteristic, complemented
8C2×#10622586C211yesmaximal, characteristic, complemented
9C2×#10622277C212yesmaximal, complemented
10C2×#10622825C211yesmaximal, characteristic, complemented
11C2×#10622600C211yesmaximal, characteristic, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C2×C4×C22⋊D11—28no—
23C2×C4×C22⋊D11C2218yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×C4⋊C4×D11—28no—
34C2×C4⋊C4×D11C2218yescomplemented
35C2×#66936—216no—
36C2×#66936C22116yes—
37C11×#380C2218yescomplemented
38C2×C11×#95C2212yes—
39#10622825C2218yescomplemented
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622600C2218yescomplemented
45#10622598C2218yescomplemented
46#10622586C2218yescomplemented
47#10622565C22116yescomplemented
48#10622277C22116yescomplemented
49#10622270C22116yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11—24no—
53C23×C4×C11—24no—
54C23×C4×C11—24no—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×C4×C11C2314yes—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—24no—
61C22×C22⋊D11—24no—
62C22×C22⋊D11D418yes—
63C22×C22⋊D11C2314yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×C4×D11—24no—
70C22×C4×D11—24no—
71C22×C4×D11—28no—
72C22×C4×D11—28no—
73C22×C4×D11—28no—
74C22×C4×D11D418yes—
75C22×C4×D11C2318yes—
76C22×C4×D11C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4—28no—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11—28no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11C2318yes—
86C2×C22⋊Dic11C2314yes—
87C4×C22⋊D11—232no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11—28no—
95C2×C4⋊Dic11C2318yes—
96C2×C4⋊Dic11C2314yes—
97C2×C4⋊Dic11C2314yes—
98C2×Dic11⋊C4—28no—
99C2×Dic11⋊C4—28no—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4C2318yes—
102C2×Dic11⋊C4C2318yes—
103C2×Dic11⋊C4C2314yes—
104C2×C4×Dic11—24no—
105C2×C4×Dic11C2314yes—
106C4⋊C4×D11—232no—
107#66936—264no—
108C11×#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C11⋊#95C2318yes—
113C2×#2486—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11C2×D414yes—
121C24×C11C2412yes—
122C24×C11C2411yescharacteristic
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11C2×D414yes—
128C23×D11C2×D414yes—
129C23×D11#4114yes—
130C23×D11C2412yes—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—28no—
141C22×C4×C11—28no—
142C22×C4×C11—28no—
143C22×C4×C11—416no—
144C22×C4×C11C2×D414yes—
145C22×C4×C11#4114yes—
146C22×C4×C11#4114yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2412yes—
151C2×C22⋊D11—232no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11C2×D4116yes—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—22no—
168C22×Dic11C2×D414yes—
169C22×Dic11C2×D414yes—
170C22×Dic11C2412yes—
171C22×Dic11C2414yes—
172C22×Dic11C2414yes—
173C22×Dic11C2412yes—
174C22×Dic11C2412yes—
175C2×C4×D11—216no—
176C2×C4×D11—216no—
177C2×C4×D11—216no—
178C2×C4×D11—232no—
179C2×C4×D11—28no—
180C2×C4×D11—28no—
181C2×C4×D11—432no—
182C2×C4×D11C2×D4116yes—
183C11×C4⋊C4—28no—
184C11×C4⋊C4—28no—
185C11×C22⋊C4—216no—
186C22⋊Dic11—28no—
187C22⋊Dic11—216no—
188(C2×D11)⋊C4—216no—
189(C2×D11)⋊C4—28no—
190C4⋊Dic11—216no—
191C4⋊Dic11—28no—
192C4⋊Dic11—28no—
193Dic11⋊C4—216no—
194Dic11⋊C4—216no—
195Dic11⋊C4—28no—
196C4×Dic11—28no—
197C22×#123—112no—
198C22×C4×D4—111no—
199C23×C4⋊C4—111no—
200#2486—1116no—
201C2×#398—112no—
202C2×#397—112no—
203C2×#389—111no—
204C2×#389—111no—
205C2×#381—112no—
206C2×#380—111no—
207C2×#380—111no—
208C2×#380D1111yescharacteristic, complemented
209C23×C11—28no—
210C23×C11—28no—
211C23×C11—28no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—44no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11C22×D414yes—
223C23×C11C22×D412yes—
224C23×C11C22×D412yes—
225C23×C11C2×#4112yes—
226C23×C11C2×#4112yes—
227C23×C11C2×#4112yes—
228C23×C112−1+412yes—
229C23×C112−1+412yes—
230C23×C11C2511yescharacteristic
231C22×D11—28no—
232C22×D11—28no—
233C22×D11—28no—
234C22×D11—28no—
235C22×D11—28no—
236C22×D11—28no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11#121116yes—
242C22×D11C22×D414yes—
243C22×D11C22×D414yes—
244C22×D11C2×#4114yes—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—48no—
255C2×C4×C11—44no—
256C2×C4×C11—48no—
257C2×C4×C11—416no—
258C2×C4×C11#123116yescomplemented
259C2×C4×C11C22×D414yes—
260C2×C4×C11C2×#4114yes—
261C2×C4×C11C2×#4114yes—
262C22⋊D11—232no—
263C2×Dic11—28no—
264C2×Dic11—28no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—48no—
279C2×Dic11—44no—
280C2×Dic11—48no—
281C2×Dic11C22×D414yes—
282C2×Dic11C22×D414yes—
283C4×D11—232no—
284C4×D11—432no—
285C23×D4—111no—
286C24×C4—111no—
287C24×C4—112no—
288C24×C4C2×D1111yescharacteristic
289C2×#123—1116no—
290C2×#123—2216no—
291C2×C4×D4—118no—
292C2×C4×D4—228no—
293C22×C4⋊C4—112no—
294C22×C4⋊C4—111no—
295C22×C4⋊C4—112no—
296C22×C4⋊C4—112no—
297C22×C4⋊C4—111no—
298C22×C4⋊C4—111no—
299C22×C4⋊C4—118no—
300C22×C4⋊C4—228no—
301C22×C4⋊C4C2×D1111yescharacteristic
302C22×C4⋊C4C2×D1111yescharacteristic
303C22×C22⋊C4—111no—
304C22×C22⋊C4—112no—
305C22×C22⋊C4—111no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4C2×D1112yes—
308C22×C42—111no—
309#398—1116no—
310#397—1116no—
311#389—118no—
312#389—118no—
313#381—1116no—
314#380—118no—
315#380—118no—
316#380C2×D1118yescomplemented
317C2×#95—112no—
318C2×#95—112no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95C2×D1112yes—
322C22×C11—24no—
323C22×C11—24no—
324C22×C11—24no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—416no—
330C22×C11C2×#12114yes—
331C22×C11C2×#12314yes—
332C22×C11#53614yes—
333C22×C11#54714yes—
334C22×C11#54714yes—
335C22×C11#55214yes—
336C22×C11#55214yes—
337C22×C11C23×D411yescharacteristic
338C22×C11C23×D411yescharacteristic
339C22×C11C22×#4111yescharacteristic
340C22×C11C22×#4111yescharacteristic
341C22×C11C22×#4111yescharacteristic
342C22×C11C2×2−1+411yescharacteristic
343C22×C11C2×2−1+411yescharacteristic
344C2×D11—24no—
345C2×D11—24no—
346C2×D11—24no—
347C2×D11—24no—
348C2×D11—24no—
349C2×D11—24no—
350C2×D11—232no—
351C2×D11C2×#12118yes—
352C4×C11—44no—
353C4×C11—42no—
354C4×C11—44no—
355C4×C11C2×#12318yescomplemented
356Dic11—24no—
357Dic11—24no—
358Dic11—44no—
359Dic11—42no—
360Dic11—44no—
361C25—111no—
362C25C22×D1111yescharacteristic
363C22×D4—118no—
364C22×D4—114no—
365C22×D4—224no—
366C22×D4—224no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—118no—
373C23×C4—114no—
374C23×C4—112no—
375C23×C4—111no—
376C23×C4—112no—
377C23×C4—118no—
378C23×C4—228no—
379C23×C4—228no—
380C23×C4—228no—
381C23×C4—224no—
382C23×C4—224no—
383C23×C4C22×D1114yes—
384C23×C4C22×D1112yes—
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1112yes—
387C23×C4C22×D1111yescharacteristic
388#123—2264no—
389C4×D4—2232no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—118no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—118no—
396C2×C4⋊C4—118no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—2232no—
399C2×C4⋊C4—228no—
400C2×C4⋊C4—224no—
401C2×C4⋊C4—228no—
402C2×C4⋊C4—228no—
403C2×C4⋊C4—224no—
404C2×C4⋊C4—224no—
405C2×C4⋊C4C22×D1114yes—
406C2×C4⋊C4C22×D1114yes—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—114no—
409C2×C22⋊C4—118no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—224no—
413C2×C22⋊C4—228no—
414C2×C22⋊C4—224no—
415C2×C22⋊C4—228no—
416C2×C22⋊C4C22×D1118yes—
417C2×C42—114no—
418C2×C42—224no—
419#95—118no—
420#95—118no—
421#95—118no—
422#95—118no—
423#95C22×D1118yes—
424C2×C11—44no—
425C2×C11#248618yescomplemented
426C2×C11C22×#12111yescharacteristic
427C2×C11C22×#12311yescharacteristic
428C2×C11C2×#53611yescharacteristic
429C2×C11C2×#54711yescharacteristic
430C2×C11C2×#54711yescharacteristic
431C2×C11C2×#55211yescharacteristic
432C2×C11C2×#55211yescharacteristic
433D11—28no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—114no—
441C24—114no—
442C24—114no—
443C24—112no—
444C24—222no—
445C24—222no—
446C24—222no—
447C24—222no—
448C24D4×D1114yes—
449C24C23×D1112yes—
450C24C23×D1111yescharacteristic
451C2×D4—1116no—
452C2×D4—228no—
453C2×D4—2232no—
454C2×D4—228no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—416no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—1116no—
473C22×C4—112no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—2216no—
477C22×C4—2216no—
478C22×C4—2216no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—2232no—
484C22×C4—228no—
485C22×C4—228no—
486C22×C4—224no—
487C22×C4—222no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—224no—
492C22×C4—222no—
493C22×C4—224no—
494C22×C4—222no—
495C22×C4—4432no—
496C22×C4#433914yes—
497C22×C4D4×D1114yes—
498C22×C4#434114yes—
499C22×C4C23×D1112yes—
500C22×C4C23×D1114yes—
501C22×C4C23×D1114yes—
502C22×C4C23×D1112yes—
503C4⋊C4—28no—
504C4⋊C4—28no—
505C4⋊C4—2216no—
506C4⋊C4—228no—
507C4⋊C4—2216no—
508C4⋊C4—2216no—
509C4⋊C4—228no—
510C4⋊C4—228no—
511C22⋊C4—216no—
512C22⋊C4—228no—
513C22⋊C4—2216no—
514C22⋊C4—228no—
515C22⋊C4—2216no—
516C42—228no—
517C11C2×#248611yescharacteristic, complemented, Sylow
518C23—28no—
519C23—28no—
520C23—28no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23—1116no—
532C23—114no—
533C23—114no—
534C23—114no—
535C23—228no—
536C23—228no—
537C23—228no—
538C23—228no—
539C23—228no—
540C23—228no—
541C23—222no—
542C23—222no—
543C23—222no—
544C23—222no—
545C23C2×#433912yes—
546C23C2×D4×D1114yes—
547C23C2×D4×D1112yes—
548C23C2×D4×D1112yes—
549C23C2×#434112yes—
550C23#6704012yes—
551C23#41×D1112yes—
552C23#6704312yes—
553C23C24×D1111yescharacteristic
554D4—2232no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—44no—
565C2×C4—48no—
566C2×C4—48no—
567C2×C4—416no—
568C2×C4—114no—
569C2×C4—114no—
570C2×C4—228no—
571C2×C4—228no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—2232no—
577C2×C4—224no—
578C2×C4—222no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—222no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—222no—
586C2×C4—4432no—
587C2×C4—448no—
588C2×C4—448no—
589C2×C4—444no—
590C2×C4#66936116yescomplemented
591C2×C4C2×#433914yes—
592C2×C4C2×D4×D1114yes—
593C2×C4C2×#434114yes—
594C22—24no—
595C22—24no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—416no—
600C22—42no—
601C22—42no—
602C22—118no—
603C22—224no—
604C22—224no—
605C22—2232no—
606C22—224no—
607C22—224no—
608C22—224no—
609C22—224no—
610C22C2×#6693614yes—
611C22#1062303814yes—
612C22#1062306014yes—
613C22D11×#12114yes—
614C22#1062314214yes—
615C22#1062315914yes—
616C22#1062317014yes—
617C22C22×#433911yescharacteristic
618C22C22×D4×D1111yescharacteristic
619C22C22×D4×D1111yescharacteristic
620C22C22×#434111yescharacteristic
621C22C2×#6704011yescharacteristic
622C22C2×#41×D1111yescharacteristic
623C22C2×#6704311yescharacteristic
624C4—44no—
625C4—44no—
626C4—42no—
627C4—224no—
628C4—224no—
629C4—442no—
630C4—444no—
631C4—444no—
632C4C2×#6693618yescomplemented
633C2—44no—
634C2—228no—
635C2#1307292018yesdirect product factor
636C2C2×D11×#12111yescharacteristic
637C2C22×#6693611yescharacteristic
638C2C2×#1062315911yescharacteristic
639C2C2×#1062314211yescharacteristic
640C2C2×#1062303811yescharacteristic
641C2C2×#1062317011yescharacteristic
642C2C2×#1062306011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#380D11
hypocenterC11C2×#2486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D11C2semidirect
4. #13072920C2direct (N × H)
5. C2×#10622270C2semidirect
6. C2×#10622565C2semidirect
7. C2×#10622598C2semidirect
8. C2×#10622586C2semidirect
9. C2×#10622277C2semidirect
10. C2×#10622825C2semidirect
11. C2×#10622600C2semidirect
12. C2×C11×#380C2semidirect
34. C2×C4⋊C4×D11C22semidirect
37. C11×#380C22semidirect
39. #10622825C22semidirect
44. #10622600C22semidirect
45. #10622598C22semidirect
46. #10622586C22semidirect
47. #10622565C22semidirect
48. #10622277C22semidirect
49. #10622270C22semidirect
208. C2×#380D11semidirect
258. C2×C4×C11#123semidirect
316. #380C2×D11semidirect
355. C4×C11C2×#123semidirect
425. C2×C11#2486semidirect
517. C11C2×#2486semidirect
590. C2×C4#66936semidirect
632. C4C2×#66936semidirect
635. C2#13072920direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×C4×C22⋊D112
C22×C4⋊C4×D112
#130729202
C2×#106222702
C2×#106225652
C2×#106225982
C2×#106225862
C2×#106222772
C2×#106228252
C2×#106226002
C2×C11×#3802
C2×#248611