Finite Group Databasebeta

← C2×#13072896 #14922697

Subgroups — C2×#13072896 #14922697

Order 2816.

4382 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D11)⋊C4C211yesmaximal, characteristic
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3#13072896C2116yesmaximal, direct product factor
4C2×#10622288C212yesmaximal, complemented
5C2×#10622606C212yesmaximal, complemented
6C2×#10622823C211yesmaximal, characteristic, complemented
7C2×#10622602C212yesmaximal, complemented
8C2×#10622277C212yesmaximal, complemented
9C2×#10622556C211yesmaximal, characteristic, complemented
10C2×#10622556C211yesmaximal, characteristic, complemented
11C2×#10622568C211yesmaximal, characteristic
12C2×C11×#385C211yesmaximal, characteristic, complemented
13C25×D11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2212yescomplemented
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×(C2×D11)⋊C4—28no—
24C22×(C2×D11)⋊C4C2218yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×Dic11⋊C4C2212yescomplemented
32C2×C22⋊C4×D11—28no—
33C2×C22⋊C4×D11C2218yes—
34C11×#385C2218yescomplemented
35C2×C11×#95C2212yescomplemented
36#10622823C2218yescomplemented
37C2×C11⋊#95C2212yescomplemented
38C2×C11⋊#95C2212yescomplemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41C2×C11⋊#95C2212yescomplemented
42#10622606C22116yescomplemented
43#10622602C22116yescomplemented
44#10622568C2218yes—
45#10622556C2218yescomplemented
46#10622556C2218yescomplemented
47#10622288C22116yescomplemented
48#10622277C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11—24no—
51C24×D11—24no—
52C24×D11—28no—
53C24×D11—44no—
54C24×D11D418yes—
55C24×D11C2311yescharacteristic
56C24×D11C2314yes—
57C24×D11C2311yescharacteristic
58C23×C4×C11—24no—
59C23×C4×C11—44no—
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2314yes—
65C23×Dic11—24no—
66C23×Dic11—24no—
67C23×Dic11—24no—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C23×Dic11C2314yes—
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—24no—
74C22×C4×D11—24no—
75C22×C4×D11—28no—
76C22×C4×D11—44no—
77C22×C4×D11C2314yes—
78C22×C4×D11C2314yes—
79C2×C11×C4⋊C4—44no—
80C2×C11×C4⋊C4C2318yescomplemented
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2314yes—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—232no—
93C2×(C2×D11)⋊C4—28no—
94C2×(C2×D11)⋊C4—28no—
95C2×(C2×D11)⋊C4—44no—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×Dic11⋊C4—44no—
103C2×Dic11⋊C4C2318yescomplemented
104C22⋊C4×D11—232no—
105C11×#95C2318yescomplemented
106C11⋊#95C2318yescomplemented
107C11⋊#95C2318yescomplemented
108C11⋊#95C2318yescomplemented
109C11⋊#95C2318yescomplemented
110C11⋊#95C2318yescomplemented
111C2×#2483—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—24no—
114C24×C11C2×D414yes—
115C24×C11#4114yes—
116C24×C11#4114yes—
117C24×C11C2412yes—
118C24×C11C2411yescharacteristic
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—232no—
123C23×D11—28no—
124C23×D11—28no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—232no—
130C23×D11—216no—
131C23×D11—416no—
132C23×D11—48no—
133C23×D11—432no—
134C23×D11—432no—
135C23×D11C2×D414yes—
136C23×D11C2×D4116yes—
137C23×D11C2×D414yes—
138C23×D11#4118yes—
139C23×D11C2412yes—
140C23×D11C2412yes—
141C22×C4×C11—28no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—48no—
153C22×C4×C11—416no—
154C22×C4×C11C2412yes—
155C22×C4×C11C2414yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2414yes—
158C22×Dic11—28no—
159C22×Dic11—24no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—28no—
166C22×Dic11—24no—
167C22×Dic11—28no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—416no—
172C22×Dic11C2414yes—
173C22×Dic11C2412yes—
174C22×Dic11C2414yes—
175C22×Dic11C2412yes—
176C2×C4×D11—28no—
177C2×C4×D11—28no—
178C2×C4×D11—216no—
179C2×C4×D11—48no—
180C2×C4×D11—416no—
181C2×C4×D11—416no—
182C11×C4⋊C4—48no—
183C11×C22⋊C4—28no—
184C11×C22⋊C4—28no—
185C22⋊Dic11—28no—
186C22⋊Dic11—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—216no—
190(C2×D11)⋊C4—216no—
191(C2×D11)⋊C4—216no—
192(C2×D11)⋊C4—48no—
193Dic11⋊C4—48no—
194C23×C22⋊C4—111no—
195C23×C22⋊C4—111no—
196#2483—1116no—
197C2×#397—112no—
198C2×#397—112no—
199C2×#385—111no—
200C2×#385—112no—
201C2×#385D1111yescharacteristic, complemented
202C2×#381—112no—
203C2×#381—111no—
204C2×#381—111no—
205C2×#379—111no—
206C23×C11—28no—
207C23×C11—28no—
208C23×C11—216no—
209C23×C11—216no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11#123116yes—
213C23×C11C22×D414yes—
214C23×C11C22×D412yes—
215C23×C11C2×#4114yes—
216C23×C11C2×#4112yes—
217C23×C11C2×#4114yes—
218C23×C11C2×#4112yes—
219C23×C11C2×#4114yes—
220C23×C11H(5,𝔽2)14yes—
221C23×C11C2511yescharacteristic
222C22×D11—28no—
223C22×D11—28no—
224C22×D11—216no—
225C22×D11—216no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—24no—
229C22×D11—232no—
230C22×D11—28no—
231C22×D11—28no—
232C22×D11—28no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—232no—
238C22×D11—416no—
239C22×D11—432no—
240C22×D11—432no—
241C22×D11—4128no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11#123116yes—
245C22×D11C22×D414yes—
246C22×D11C22×D414yes—
247C22×D11C2×#4118yes—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
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—24no—
258C2×C4×C11—416no—
259C2×C4×C11—44no—
260C2×C4×C11—44no—
261C2×C4×C11—48no—
262C2×C4×C11—48no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—44no—
274C2×Dic11—416no—
275C2×Dic11—48no—
276C2×Dic11—44no—
277C2×Dic11—48no—
278C4×D11—416no—
279C4×D11—416no—
280C26—111no—
281C24×C4—111no—
282C24×C4—111no—
283C24×C4—111no—
284C24×C4C2×D1111yescharacteristic
285C22×C4⋊C4—112no—
286C22×C4⋊C4C2×D1112yescomplemented
287C22×C22⋊C4—111no—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—118no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—118no—
297C22×C22⋊C4—228no—
298C22×C22⋊C4—228no—
299C22×C22⋊C4C2×D1111yescharacteristic
300C22×C22⋊C4C2×D1111yescharacteristic
301#397—1116no—
302#397—1116no—
303#385—118no—
304#385—1116no—
305#385C2×D1118yescomplemented
306#381—118no—
307#381—118no—
308#381—1116no—
309#379—118no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95C2×D1112yescomplemented
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—28no—
319C22×C11—28no—
320C22×C11—232no—
321C22×C11C2×#12318yes—
322C22×C11C2×#12314yes—
323C22×C11C2×#12314yes—
324C22×C11#53414yes—
325C22×C11#55118yes—
326C22×C11#55118yes—
327C22×C11C23×D411yescharacteristic
328C22×C11C22×#4111yescharacteristic
329C22×C11C22×#4111yescharacteristic
330C22×C11C22×#4112yes—
331C22×C11C2×H(5,𝔽2)12yes—
332C2×D11—24no—
333C2×D11—24no—
334C2×D11—28no—
335C2×D11—28no—
336C2×D11—232no—
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—464no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—416no—
344C2×D11C2×#12318yes—
345C4×C11—42no—
346C4×C11—44no—
347C4×C11—42no—
348C4×C11—44no—
349Dic11—42no—
350Dic11—44no—
351Dic11—42no—
352Dic11—44no—
353C25—111no—
354C25—111no—
355C25—118no—
356C25—114no—
357C25—228no—
358C25—224no—
359C25—224no—
360C25—444no—
361C25C22×D1111yescharacteristic
362C23×C4—24no—
363C23×C4—44no—
364C23×C4—114no—
365C23×C4—112no—
366C23×C4—111no—
367C23×C4—112no—
368C23×C4—111no—
369C23×C4—114no—
370C23×C4—114no—
371C23×C4—224no—
372C23×C4—224no—
373C23×C4—228no—
374C23×C4—224no—
375C23×C4—224no—
376C23×C4—224no—
377C23×C4—444no—
378C23×C4C22×D1112yes—
379C23×C4C22×D1112yes—
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1114yes—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—118no—
385C2×C4⋊C4—444no—
386C2×C4⋊C4C22×D1118yescomplemented
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—114no—
390C2×C22⋊C4—114no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—2232no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—228no—
401C2×C22⋊C4—228no—
402C2×C22⋊C4—2232no—
403C2×C22⋊C4—228no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4C22×D1114yes—
408C2×C22⋊C4C22×D1114yes—
409#95—118no—
410#95—118no—
411#95—118no—
412#95—118no—
413#95—118no—
414#95C22×D1118yescomplemented
415C2×C11—28no—
416C2×C11#248318yescomplemented
417C2×C11C22×#12311yescharacteristic
418C2×C11C22×#12311yescharacteristic
419C2×C11C2×#53411yescharacteristic
420C2×C11C2×#55112yes—
421C2×C11C2×#55112yes—
422D11—28no—
423D11—44no—
424C24—24no—
425C24—24no—
426C24—114no—
427C24—118no—
428C24—112no—
429C24—114no—
430C24—112no—
431C24—1116no—
432C24—2232no—
433C24—2216no—
434C24—222no—
435C24—224no—
436C24—222no—
437C24—2232no—
438C24—228no—
439C24—222no—
440C24—224no—
441C24—228no—
442C24—222no—
443C24—224no—
444C24—4416no—
445C24—448no—
446C24—4432no—
447C24—4432no—
448C24#433914yes—
449C24D4×D1114yes—
450C24#434314yes—
451C24C23×D1112yes—
452C24C23×D1111yescharacteristic
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—28no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—48no—
465C22×C4—416no—
466C22×C4—114no—
467C22×C4—112no—
468C22×C4—114no—
469C22×C4—112no—
470C22×C4—228no—
471C22×C4—228no—
472C22×C4—2216no—
473C22×C4—228no—
474C22×C4—224no—
475C22×C4—228no—
476C22×C4—224no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—228no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—448no—
487C22×C4—4416no—
488C22×C4—4416no—
489C22×C4—4416no—
490C22×C4C23×D1112yes—
491C22×C4C23×D1114yes—
492C22×C4C23×D1112yes—
493C22×C4C23×D1114yes—
494C4⋊C4—48no—
495C4⋊C4—448no—
496C22⋊C4—28no—
497C22⋊C4—28no—
498C22⋊C4—228no—
499C22⋊C4—228no—
500C22⋊C4—2216no—
501C22⋊C4—2216no—
502C22⋊C4—2216no—
503C22⋊C4—228no—
504C22⋊C4—228no—
505C22⋊C4—448no—
506C11C2×#248311yescharacteristic, complemented, Sylow
507C23—216no—
508C23—28no—
509C23—216no—
510C23—28no—
511C23—24no—
512C23—24no—
513C23—1116no—
514C23—114no—
515C23—118no—
516C23—114no—
517C23—2232no—
518C23—228no—
519C23—2216no—
520C23—228no—
521C23—2216no—
522C23—222no—
523C23—224no—
524C23—222no—
525C23—2232no—
526C23—228no—
527C23—228no—
528C23—228no—
529C23—222no—
530C23—224no—
531C23—222no—
532C23—224no—
533C23—4416no—
534C23—44128no—
535C23—4432no—
536C23—4432no—
537C23—448no—
538C23—448no—
539C23#66947116yes—
540C23C2×#433914yes—
541C23C2×#433912yes—
542C23C2×D4×D1114yes—
543C23C2×D4×D1112yes—
544C23#6703714yes—
545C23C2×#434314yes—
546C23C2×#434312yes—
547C23#41×D1114yes—
548C23C24×D1111yescharacteristic
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—416no—
560C2×C4—48no—
561C2×C4—48no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—224no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—4416no—
575C2×C4—4416no—
576C2×C4—4416no—
577C2×C4—448no—
578C2×C4—444no—
579C2×C4—448no—
580C2×C4—444no—
581C22—232no—
582C22—28no—
583C22—28no—
584C22—24no—
585C22—24no—
586C22—118no—
587C22—2232no—
588C22—228no—
589C22—228no—
590C22—224no—
591C22—224no—
592C22—224no—
593C22—224no—
594C22—224no—
595C22—4464no—
596C22—4416no—
597C22—444no—
598C22—444no—
599C22C2×#6694718yes—
600C22C2×#6694714yes—
601C22#1062308718yes—
602C22#1062312014yes—
603C22#1062316818yes—
604C22D11×#12314yes—
605C22C22×#433911yescharacteristic
606C22C22×D4×D1111yescharacteristic
607C22C2×#6703712yes—
608C22C22×#434311yescharacteristic
609C22C2×#41×D1112yes—
610C4—44no—
611C4—44no—
612C4—42no—
613C4—42no—
614C4—444no—
615C4—442no—
616C4—442no—
617C4—444no—
618C2—28no—
619C2—228no—
620C2—444no—
621C2#1307289618yesdirect product factor
622C2C2×D11×#12311yescharacteristic
623C2C22×#6694711yescharacteristic
624C2C2×#1062312011yescharacteristic
625C2C2×#1062316812yes—
626C2C2×#1062308712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#385D11
hypocenterC11C2×#2483
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. #13072896C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622606C2semidirect
6. C2×#10622823C2semidirect
7. C2×#10622602C2semidirect
8. C2×#10622277C2semidirect
9. C2×#10622556C2semidirect
10. C2×#10622556C2semidirect
12. C2×C11×#385C2semidirect
18. C22×C11×C4⋊C4C22semidirect
31. C22×Dic11⋊C4C22semidirect
34. C11×#385C22semidirect
35. C2×C11×#95C22semidirect
36. #10622823C22semidirect
37. C2×C11⋊#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
42. #10622606C22semidirect
43. #10622602C22semidirect
45. #10622556C22semidirect
46. #10622556C22semidirect
47. #10622288C22semidirect
48. #10622277C22semidirect
80. C2×C11×C4⋊C4C23semidirect
103. C2×Dic11⋊C4C23semidirect
105. C11×#95C23semidirect
106. C11⋊#95C23semidirect
107. C11⋊#95C23semidirect
108. C11⋊#95C23semidirect
109. C11⋊#95C23semidirect
110. C11⋊#95C23semidirect
201. C2×#385D11semidirect
286. C22×C4⋊C4C2×D11semidirect
305. #385C2×D11semidirect
315. C2×#95C2×D11semidirect
386. C2×C4⋊C4C22×D11semidirect
414. #95C22×D11semidirect
416. C2×C11#2483semidirect
506. C11C2×#2483semidirect
621. C2#13072896direct (N × H)

Maximal subgroups

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

subgroupindex
C23×(C2×D11)⋊C42
C22×C22⋊C4×D112
#130728962
C2×#106222882
C2×#106226062
C2×#106228232
C2×#106226022
C2×#106222772
C2×#106225562
C2×#106225682
C2×C11×#3852
C2×#248311