Finite Group Databasebeta

← C2×#13074422 #14920120

Subgroups — C2×#13074422 #14920120

Order 2816.

4142 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×#66950C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3#13074422C2116yesmaximal, direct product factor
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622561C212yesmaximal, complemented
6C2×#10622607C212yesmaximal, complemented
7C2×#10622286C211yesmaximal, characteristic, complemented
8C2×#10622560C211yesmaximal, characteristic, complemented
9C2×#10622602C212yesmaximal, complemented
10C2×#10622280C211yesmaximal, characteristic, complemented
11C2×#10622568C212yesmaximal
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C25×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×Dic22C2211yescharacteristic, complemented
17C22×C11×C4⋊C4C2211yescharacteristic, complemented
18C22×C11×C4⋊C4C2212yescomplemented
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×C4⋊Dic11C2212yescomplemented
30C22×Dic11⋊C4C2212yescomplemented
31C22×Dic11⋊C4C2212yescomplemented
32C2×#66950—28no—
33C2×#66950C2218yescomplemented
34C2×C22⋊C4×D11—28no—
35C2×C22⋊C4×D11C2218yes—
36C11×#399C2218yescomplemented
37C2×C11×#95C2211yescharacteristic, complemented
38C2×C11⋊#95C2211yescharacteristic, complemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41#10622607C22116yescomplemented
42#10622605C2218yescomplemented
43#10622602C22116yescomplemented
44#10622568C22116yes—
45#10622561C22116yescomplemented
46#10622560C2218yescomplemented
47#10622286C2218yescomplemented
48#10622280C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11—24no—
51C24×D11—24no—
52C24×D11—44no—
53C24×D11—44no—
54C24×D11Q818yescomplemented
55C24×D11C2311yescharacteristic
56C24×D11C2311yescharacteristic
57C24×D11C2314yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C22×C4×D11—24no—
67C22×C4×D11—44no—
68C22×C4×D11—44no—
69C22×C4×D11D418yes—
70C22×C4×D11C2314yes—
71C22×C4×D11C2314yes—
72C22×Dic22—24no—
73C22×Dic22—44no—
74C22×Dic22C2314yescomplemented
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—44no—
77C2×C11×C4⋊C4C2314yescomplemented
78C2×C11×C4⋊C4C2318yescomplemented
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—44no—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2318yes—
87C2×(C2×D11)⋊C4—28no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—44no—
92C2×(C2×D11)⋊C4—44no—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×C4⋊Dic11—28no—
100C2×C4⋊Dic11C2318yescomplemented
101C2×Dic11⋊C4—44no—
102C2×Dic11⋊C4—44no—
103C2×Dic11⋊C4C2318yescomplemented
104C2×Dic11⋊C4C2318yescomplemented
105#66950—232no—
106C22⋊C4×D11—232no—
107C11×#95C2314yescomplemented
108C11⋊#95C2314yescomplemented
109C11⋊#95C2318yescomplemented
110C11⋊#95C2318yescomplemented
111C2×#2626—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11C2×Q814yes—
117C24×C11C2412yes—
118C24×C11C2411yescharacteristic
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—232no—
126C23×D11—28no—
127C23×D11—28no—
128C23×D11—432no—
129C23×D11—48no—
130C23×D11—48no—
131C23×D11—416no—
132C23×D11—416no—
133C23×D11—432no—
134C23×D11C2×D414yes—
135C23×D11C2×Q814yes—
136C23×D11C2×Q814yes—
137C23×D11C2×Q8116yescomplemented
138C23×D11#4114yes—
139C23×D11C2412yes—
140C23×D11C2412yes—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2412yes—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11C2×D414yes—
165C22×Dic11C2414yes—
166C22×Dic11C2412yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C2×C4×D11—28no—
170C2×C4×D11—416no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C2×C4×D11—416no—
174C2×C4×D11C2×D4116yes—
175C2×Dic22—28no—
176C2×Dic22—48no—
177C2×Dic22—416no—
178C11×C4⋊C4—28no—
179C11×C4⋊C4—48no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—48no—
182C22⋊Dic11—28no—
183C22⋊Dic11—48no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—216no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—48no—
189(C2×D11)⋊C4—48no—
190C4⋊Dic11—216no—
191Dic11⋊C4—48no—
192Dic11⋊C4—48no—
193C22×C22⋊Q8—111no—
194C23×C22⋊C4—111no—
195#2626—1116no—
196C2×#399—111no—
197C2×#399D1111yescharacteristic, complemented
198C2×#396—112no—
199C2×#396—112no—
200C2×#393—111no—
201C2×#393—111no—
202C2×#385—112no—
203C2×#380—111no—
204C2×#379—112no—
205C23×C11—28no—
206C23×C11—216no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—48no—
214C23×C11C22×D412yes—
215C23×C11C22×Q814yes—
216C23×C11C22×Q812yes—
217C23×C11C2×#4112yes—
218C23×C11H(5,𝔽2)14yes—
219C23×C11H(5,𝔽2)14yes—
220C23×C11C2511yescharacteristic
221C22×D11—28no—
222C22×D11—28no—
223C22×D11—216no—
224C22×D11—216no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—28no—
228C22×D11—216no—
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—232no—
234C22×D11—432no—
235C22×D11—4128no—
236C22×D11—416no—
237C22×D11—416no—
238C22×D11—432no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—48no—
242C22×D11C22⋊Q8116yes—
243C22×D11C22×D414yes—
244C22×D11C22×Q814yes—
245C22×D11C22×Q814yes—
246C22×D11C2×#4114yes—
247C2×C4×C11—28no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—44no—
258C2×C4×C11—48no—
259C2×C4×C11—48no—
260C2×C4×C11C22×D414yes—
261C2×Dic11—28no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—48no—
272C2×Dic11—44no—
273C2×Dic11—48no—
274C2×Dic11C22×D414yes—
275C4×D11—416no—
276C4×D11—416no—
277Dic22—416no—
278C26—111no—
279C23×Q8—111no—
280C24×C4—111no—
281C24×C4—111no—
282C2×C22⋊Q8—118no—
283C2×C22⋊Q8—228no—
284C22×C4⋊C4—112no—
285C22×C4⋊C4—112no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4C2×D1111yescharacteristic, complemented
288C22×C4⋊C4C2×D1112yescomplemented
289C22×C22⋊C4—111no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—118no—
298C22×C22⋊C4—228no—
299C22×C22⋊C4C2×D1111yescharacteristic
300C22×C22⋊C4C2×D1112yes—
301#399—118no—
302#399C2×D1118yescomplemented
303#396—1116no—
304#396—1116no—
305#393—118no—
306#393—118no—
307#385—1116no—
308#380—118no—
309#379—1116no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—111no—
313C2×#95C2×D1111yescharacteristic, complemented
314C22×C11—24no—
315C22×C11—28no—
316C22×C11—416no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11C2×C22⋊Q814yes—
321C22×C11#53414yes—
322C22×C11#53514yes—
323C22×C11#53818yes—
324C22×C11#54318yes—
325C22×C11C23×D411yescharacteristic
326C22×C11C23×Q811yescharacteristic
327C22×C11C22×#4111yescharacteristic
328C22×C11C2×H(5,𝔽2)12yes—
329C22×C11C2×H(5,𝔽2)12yes—
330C2×D11—232no—
331C2×D11—24no—
332C2×D11—24no—
333C2×D11—28no—
334C2×D11—28no—
335C2×D11—24no—
336C2×D11—28no—
337C2×D11—464no—
338C2×D11—416no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—44no—
342C2×D11C2×C22⋊Q818yes—
343C4×C11—24no—
344C4×C11—44no—
345C4×C11—42no—
346C4×C11—44no—
347Dic11—24no—
348Dic11—44no—
349Dic11—42no—
350Dic11—44no—
351C25—111no—
352C25—111no—
353C25—118no—
354C25—114no—
355C25—224no—
356C25—224no—
357C25—444no—
358C25—444no—
359C25C22×D1111yescharacteristic
360C22×Q8—114no—
361C22×Q8—224no—
362C22×Q8—444no—
363C23×C4—111no—
364C23×C4—118no—
365C23×C4—114no—
366C23×C4—112no—
367C23×C4—112no—
368C23×C4—111no—
369C23×C4—114no—
370C23×C4—224no—
371C23×C4—444no—
372C23×C4—444no—
373C23×C4C22×D1112yes—
374C23×C4C22×D1112yes—
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1111yescharacteristic
377C22⋊Q8—2232no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—118no—
381C2×C4⋊C4—118no—
382C2×C4⋊C4—118no—
383C2×C4⋊C4—228no—
384C2×C4⋊C4—444no—
385C2×C4⋊C4—444no—
386C2×C4⋊C4C22×D1114yescomplemented
387C2×C4⋊C4C22×D1118yescomplemented
388C2×C22⋊C4—24no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—114no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—2232no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—228no—
401C2×C22⋊C4—228no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4C22×D1114yes—
408C2×C22⋊C4C22×D1118yes—
409#95—114no—
410#95—118no—
411#95—118no—
412#95C22×D1114yescomplemented
413C2×C11—44no—
414C2×C11#262618yescomplemented
415C2×C11C22×C22⋊Q811yescharacteristic
416C2×C11C2×#53411yescharacteristic
417C2×C11C2×#53511yescharacteristic
418C2×C11C2×#53812yes—
419C2×C11C2×#54312yes—
420D11—28no—
421D11—44no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—24no—
426C24—114no—
427C24—114no—
428C24—114no—
429C24—112no—
430C24—114no—
431C24—112no—
432C24—1116no—
433C24—228no—
434C24—2232no—
435C24—228no—
436C24—224no—
437C24—224no—
438C24—222no—
439C24—224no—
440C24—222no—
441C24—224no—
442C24—4432no—
443C24—448no—
444C24—448no—
445C24—4416no—
446C24—4416no—
447C24—4432no—
448C24Q8×D1114yes—
449C24C23×D1112yes—
450C24C23×D1111yescharacteristic
451C2×Q8—228no—
452C2×Q8—448no—
453C2×Q8—4416no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—114no—
464C22×C4—112no—
465C22×C4—1116no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—112no—
469C22×C4—228no—
470C22×C4—224no—
471C22×C4—222no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—4416no—
480C22×C4—448no—
481C22×C4—448no—
482C22×C4—4416no—
483C22×C4D4×D1114yes—
484C22×C4C23×D1112yes—
485C22×C4C23×D1114yes—
486C22×C4C23×D1114yes—
487C22×C4C23×D1112yes—
488C4⋊C4—28no—
489C4⋊C4—48no—
490C4⋊C4—2216no—
491C4⋊C4—448no—
492C4⋊C4—448no—
493C22⋊C4—28no—
494C22⋊C4—48no—
495C22⋊C4—228no—
496C22⋊C4—2216no—
497C22⋊C4—2216no—
498C22⋊C4—228no—
499C22⋊C4—228no—
500C22⋊C4—448no—
501C22⋊C4—448no—
502C22⋊C4—448no—
503C11C2×#262611yescharacteristic, complemented, Sylow
504C23—28no—
505C23—216no—
506C23—22no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—44no—
511C23—44no—
512C23—48no—
513C23—1116no—
514C23—114no—
515C23—114no—
516C23—114no—
517C23—114no—
518C23—2232no—
519C23—228no—
520C23—2216no—
521C23—228no—
522C23—2216no—
523C23—224no—
524C23—224no—
525C23—228no—
526C23—2216no—
527C23—222no—
528C23—224no—
529C23—222no—
530C23—224no—
531C23—4432no—
532C23—4416no—
533C23—4416no—
534C23—4432no—
535C23—44128no—
536C23—444no—
537C23—444no—
538C23—448no—
539C23C2×D4×D1112yes—
540C23#6703714yes—
541C23C2×Q8×D1114yes—
542C23C2×Q8×D1112yes—
543C23#41×D1112yes—
544C23#6704214yes—
545C23C24×D1111yescharacteristic
546Q8—4416no—
547C2×C4—28no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—48no—
558C2×C4—44no—
559C2×C4—48no—
560C2×C4—114no—
561C2×C4—228no—
562C2×C4—224no—
563C2×C4—222no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—4416no—
572C2×C4—4416no—
573C2×C4—444no—
574C2×C4—448no—
575C2×C4—448no—
576C2×C4C2×D4×D1114yes—
577C22—28no—
578C22—24no—
579C22—42no—
580C22—42no—
581C22—44no—
582C22—416no—
583C22—118no—
584C22—224no—
585C22—224no—
586C22—228no—
587C22—228no—
588C22—2232no—
589C22—228no—
590C22—224no—
591C22—4464no—
592C22—442no—
593C22—442no—
594C22—444no—
595C22—4416no—
596C22D11×C22⋊Q814yes—
597C22#1062316518yes—
598C22#1062318414yes—
599C22#1062318818yes—
600C22#1062324614yes—
601C22C22×D4×D1111yescharacteristic
602C22C2×#6703712yes—
603C22C22×Q8×D1111yescharacteristic
604C22C2×#41×D1111yescharacteristic
605C22C2×#6704212yes—
606C4—24no—
607C4—42no—
608C4—44no—
609C4—44no—
610C4—224no—
611C4—444no—
612C4—442no—
613C4—444no—
614C2—44no—
615C2—228no—
616C2—444no—
617C2#1307442218yesdirect product factor
618C2C2×D11×C22⋊Q811yescharacteristic
619C2C2×#1062318411yescharacteristic
620C2C2×#1062324611yescharacteristic
621C2C2×#1062318812yes—
622C2C2×#1062316512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#399D11
hypocenterC11C2×#2626
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#66950C2semidirect
3. #13074422C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622607C2semidirect
7. C2×#10622286C2semidirect
8. C2×#10622560C2semidirect
9. C2×#10622602C2semidirect
10. C2×#10622280C2semidirect
12. C2×C11×#399C2semidirect
16. C23×Dic22C22semidirect
17. C22×C11×C4⋊C4C22semidirect
18. C22×C11×C4⋊C4C22semidirect
29. C22×C4⋊Dic11C22semidirect
30. C22×Dic11⋊C4C22semidirect
31. C22×Dic11⋊C4C22semidirect
33. C2×#66950C22semidirect
36. C11×#399C22semidirect
37. C2×C11×#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. #10622607C22semidirect
42. #10622605C22semidirect
43. #10622602C22semidirect
45. #10622561C22semidirect
46. #10622560C22semidirect
47. #10622286C22semidirect
48. #10622280C22semidirect
54. C24×D11Q8semidirect
74. C22×Dic22C23semidirect
77. C2×C11×C4⋊C4C23semidirect
78. C2×C11×C4⋊C4C23semidirect
100. C2×C4⋊Dic11C23semidirect
103. C2×Dic11⋊C4C23semidirect
104. C2×Dic11⋊C4C23semidirect
107. C11×#95C23semidirect
108. C11⋊#95C23semidirect
109. C11⋊#95C23semidirect
110. C11⋊#95C23semidirect
137. C23×D11C2×Q8semidirect
197. C2×#399D11semidirect
287. C22×C4⋊C4C2×D11semidirect
288. C22×C4⋊C4C2×D11semidirect
302. #399C2×D11semidirect
313. C2×#95C2×D11semidirect
386. C2×C4⋊C4C22×D11semidirect
387. C2×C4⋊C4C22×D11semidirect
412. #95C22×D11semidirect
414. C2×C11#2626semidirect
503. C11C2×#2626semidirect
617. C2#13074422direct (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×C22⋊C4×D112
#130744222
C2×#106226052
C2×#106225612
C2×#106226072
C2×#106222862
C2×#106225602
C2×#106226022
C2×#106222802
C2×#106225682
C2×C11×#3992
C2×#262611