Finite Group Databasebeta

← C2×#13074420 #14920114

Subgroups — C2×#13074420 #14920114

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×#66999C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3#13074420C2116yesmaximal, direct product factor
4C2×#10622290C211yesmaximal, characteristic, complemented
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622289C212yesmaximal, complemented
7C2×#10622561C212yesmaximal, complemented
8C2×#10622844C211yesmaximal, characteristic, complemented
9C2×#10622281C212yesmaximal, complemented
10C2×#10622280C211yesmaximal, characteristic, complemented
11C2×#10622568C212yesmaximal
12C2×C11×#393C211yesmaximal, characteristic, complemented
13C25×D11C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic, complemented
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C2×#66999—28no—
22C2×#66999C2218yescomplemented
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⋊Dic11C2211yescharacteristic, complemented
30C22×C4⋊Dic11C2212yescomplemented
31C22×Dic11⋊C4C2212yescomplemented
32C22×Dic11⋊C4C2212yescomplemented
33C22×Dic11⋊C4C2212yescomplemented
34C2×C22⋊C4×D11—28no—
35C2×C22⋊C4×D11C2218yes—
36C11×#393C2218yescomplemented
37C2×C11×#95C2211yescharacteristic, complemented
38C2×C11×#95C2212yescomplemented
39#10622844C2218yescomplemented
40C2×C11⋊#95C2211yescharacteristic, complemented
41C2×C11⋊#95C2212yescomplemented
42#10622568C22116yes—
43#10622562C2218yescomplemented
44#10622561C22116yescomplemented
45#10622290C2218yescomplemented
46#10622289C22116yescomplemented
47#10622281C22116yescomplemented
48#10622280C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11—24no—
51C24×D11—24no—
52C24×D11—44no—
53C24×D11—44no—
54C24×D11Q818yescomplemented
55C24×D11C2311yescharacteristic
56C24×D11C2311yescharacteristic
57C24×D11C2314yes—
58C22×Q8×C11—24no—
59C22×Q8×C11—44no—
60C22×Q8×C11C2314yescomplemented
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×C4×D11—24no—
70C22×C4×D11—44no—
71C22×C4×D11—44no—
72C22×C4×D11D418yes—
73C22×C4×D11C2314yes—
74C22×C4×D11C2314yes—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—44no—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2318yes—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—44no—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2318yes—
83#66999—232no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—44no—
98C2×C4⋊Dic11C2314yescomplemented
99C2×C4⋊Dic11C2318yescomplemented
100C2×Dic11⋊C4—28no—
101C2×Dic11⋊C4—44no—
102C2×Dic11⋊C4—44no—
103C2×Dic11⋊C4C2318yescomplemented
104C2×Dic11⋊C4C2318yescomplemented
105C2×Dic11⋊C4C2318yescomplemented
106C22⋊C4×D11—232no—
107C11×#95C2314yescomplemented
108C11×#95C2318yescomplemented
109C11⋊#95C2314yescomplemented
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—
141C2×Q8×C11—28no—
142C2×Q8×C11—48no—
143C2×Q8×C11—416no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2414yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2412yes—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11C2×D414yes—
168C22×Dic11C2414yes—
169C22×Dic11C2412yes—
170C22×Dic11C2414yes—
171C22×Dic11C2412yes—
172C2×C4×D11—28no—
173C2×C4×D11—416no—
174C2×C4×D11—48no—
175C2×C4×D11—48no—
176C2×C4×D11—416no—
177C2×C4×D11C2×D4116yes—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—48no—
180C22⋊Dic11—28no—
181C22⋊Dic11—48no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—216no—
184(C2×D11)⋊C4—216no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—48no—
187(C2×D11)⋊C4—48no—
188C4⋊Dic11—28no—
189C4⋊Dic11—48no—
190Dic11⋊C4—216no—
191Dic11⋊C4—48no—
192Dic11⋊C4—48no—
193C22×C22⋊Q8—111no—
194C23×C22⋊C4—111no—
195#2626—1116no—
196C2×#399—111no—
197C2×#399—111no—
198C2×#396—112no—
199C2×#396—112no—
200C2×#393—111no—
201C2×#393D1111yescharacteristic, complemented
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—
247Q8×C11—416no—
248C2×C4×C11—28no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—48no—
259C2×C4×C11—44no—
260C2×C4×C11—48no—
261C2×C4×C11C22×D414yes—
262C2×Dic11—28no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—44no—
273C2×Dic11—48no—
274C2×Dic11—48no—
275C2×Dic11C22×D414yes—
276C4×D11—416no—
277C4×D11—416no—
278C26—111no—
279C23×Q8C2×D1111yescharacteristic, complemented
280C24×C4—111no—
281C24×C4—111no—
282C2×C22⋊Q8—118no—
283C2×C22⋊Q8—228no—
284C22×C4⋊C4—112no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4—112no—
288C22×C4⋊C4—112no—
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#399—118no—
303#396—1116no—
304#396—1116no—
305#393—118no—
306#393C2×D1118yescomplemented
307#385—1116no—
308#380—118no—
309#379—1116no—
310C2×#95—112no—
311C2×#95—111no—
312C2×#95C2×D1112yescomplemented
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—42no—
349Dic11—44no—
350Dic11—44no—
351C25—111no—
352C25—111no—
353C25—118no—
354C25—114no—
355C25—224no—
356C25—224no—
357C25—444no—
358C25—444no—
359C25C22×D1111yescharacteristic
360C22×Q8—24no—
361C22×Q8—44no—
362C22×Q8C22×D1114yescomplemented
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—118no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—118no—
381C2×C4⋊C4—118no—
382C2×C4⋊C4—118no—
383C2×C4⋊C4—228no—
384C2×C4⋊C4—224no—
385C2×C4⋊C4—444no—
386C2×C4⋊C4—444no—
387C2×C4⋊C4—444no—
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#95C22×D1114yescomplemented
412#95C22×D1118yescomplemented
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—28no—
452C2×Q8—48no—
453C2×Q8—416no—
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—112no—
468C22×C4—114no—
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×D1114yes—
485C22×C4C23×D1114yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C4⋊C4—2216no—
489C4⋊C4—228no—
490C4⋊C4—448no—
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—224no—
522C23—224no—
523C23—228no—
524C23—2216no—
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—416no—
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—
596C22#1062312014yes—
597C22D11×C22⋊Q814yes—
598C22#1062316518yes—
599C22#1062320514yes—
600C22#1062320918yes—
601C22C22×D4×D1111yescharacteristic
602C22C2×#6703712yes—
603C22C22×Q8×D1111yescharacteristic
604C22C2×#41×D1111yescharacteristic
605C22C2×#6704212yes—
606C4—24no—
607C4—44no—
608C4—42no—
609C4—44no—
610C4—224no—
611C4—442no—
612C4—444no—
613C4—444no—
614C2—44no—
615C2—228no—
616C2—444no—
617C2#1307442018yesdirect product factor
618C2C2×D11×C22⋊Q811yescharacteristic
619C2C2×#1062312011yescharacteristic
620C2C2×#1062320511yescharacteristic
621C2C2×#1062320912yes—
622C2C2×#1062316512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#393D11
hypocenterC11C2×#2626
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#66999C2semidirect
3. #13074420C2direct (N × H)
4. C2×#10622290C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622289C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622844C2semidirect
9. C2×#10622281C2semidirect
10. C2×#10622280C2semidirect
12. C2×C11×#393C2semidirect
14. C23×Q8×C11C22semidirect
22. C2×#66999C22semidirect
29. C22×C4⋊Dic11C22semidirect
30. C22×C4⋊Dic11C22semidirect
31. C22×Dic11⋊C4C22semidirect
32. C22×Dic11⋊C4C22semidirect
33. C22×Dic11⋊C4C22semidirect
36. C11×#393C22semidirect
37. C2×C11×#95C22semidirect
38. C2×C11×#95C22semidirect
39. #10622844C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
43. #10622562C22semidirect
44. #10622561C22semidirect
45. #10622290C22semidirect
46. #10622289C22semidirect
47. #10622281C22semidirect
48. #10622280C22semidirect
54. C24×D11Q8semidirect
60. C22×Q8×C11C23semidirect
98. C2×C4⋊Dic11C23semidirect
99. C2×C4⋊Dic11C23semidirect
103. C2×Dic11⋊C4C23semidirect
104. C2×Dic11⋊C4C23semidirect
105. C2×Dic11⋊C4C23semidirect
107. C11×#95C23semidirect
108. C11×#95C23semidirect
109. C11⋊#95C23semidirect
110. C11⋊#95C23semidirect
137. C23×D11C2×Q8semidirect
201. C2×#393D11semidirect
279. C23×Q8C2×D11semidirect
306. #393C2×D11semidirect
312. C2×#95C2×D11semidirect
313. C2×#95C2×D11semidirect
362. C22×Q8C22×D11semidirect
411. #95C22×D11semidirect
412. #95C22×D11semidirect
414. C2×C11#2626semidirect
503. C11C2×#2626semidirect
617. C2#13074420direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×C22⋊C4×D112
#130744202
C2×#106222902
C2×#106225622
C2×#106222892
C2×#106225612
C2×#106228442
C2×#106222812
C2×#106222802
C2×#106225682
C2×C11×#3932
C2×#262611