Finite Group Databasebeta

← C2×#13072889 #14923539

Subgroups — C2×#13072889 #14923539

Order 2816.

4166 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66930C211yesmaximal, characteristic, complemented
2C23×(C2×D11)⋊C4C211yesmaximal, characteristic
3#13072889C2116yesmaximal, direct product factor
4C2×#10622605C212yesmaximal, complemented
5C2×#10622288C212yesmaximal, complemented
6C2×#10622603C212yesmaximal, complemented
7C2×#10622282C212yesmaximal, complemented
8C2×#10622823C211yesmaximal, characteristic, complemented
9C2×#10622556C211yesmaximal, characteristic, complemented
10C2×#10622568C211yesmaximal, characteristic
11C2×#10622568C211yesmaximal, characteristic
12C2×C11×#385C211yesmaximal, characteristic, complemented
13C25×D11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C4⋊C4C2212yescomplemented
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×(C2×D11)⋊C4—28no—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2218yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic, complemented
30C22×Dic11⋊C4C2211yescharacteristic, complemented
31C22×Dic11⋊C4C2212yescomplemented
32C22×C4×Dic11C2211yescharacteristic, complemented
33C22×C4×Dic11C2211yescharacteristic, complemented
34C2×#66930—28no—
35C2×#66930C2218yescomplemented
36C11×#385C2218yescomplemented
37C2×C11×#95C2212yescomplemented
38#10622823C2218yescomplemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41C2×C11⋊#95C2212yescomplemented
42#10622605C22116yescomplemented
43#10622603C22116yescomplemented
44#10622568C2218yes—
45#10622568C2218yes—
46#10622556C2218yescomplemented
47#10622288C22116yescomplemented
48#10622282C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11—24no—
51C24×D11—28no—
52C24×D11—24no—
53C24×D11—24no—
54C24×D11—44no—
55C24×D11C2312yes—
56C24×D11C2314yes—
57C23×C4×C11—24no—
58C23×C4×C11—44no—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2314yes—
64C23×Dic11—24no—
65C23×Dic11—24no—
66C23×Dic11D418yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C23×Dic11C2314yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C2×C11×C4⋊C4—44no—
74C2×C11×C4⋊C4C2318yescomplemented
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2314yes—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2314yes—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—232no—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—28no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—44no—
99C2×Dic11⋊C4C2314yescomplemented
100C2×Dic11⋊C4C2314yescomplemented
101C2×Dic11⋊C4C2318yescomplemented
102C2×C4×Dic11—24no—
103C2×C4×Dic11—24no—
104C2×C4×Dic11C2314yescomplemented
105C2×C4×Dic11C2314yescomplemented
106#66930—232no—
107C11×#95C2318yescomplemented
108C11⋊#95C2318yescomplemented
109C11⋊#95C2318yescomplemented
110C11⋊#95C2318yescomplemented
111C2×#2482—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—24no—
114C24×C11C2×D414yes—
115C24×C11#4114yes—
116C24×C11#4114yes—
117C24×C11C2412yes—
118C24×C11C2411yescharacteristic
119C23×D11—232no—
120C23×D11—28no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—216no—
128C23×D11—28no—
129C23×D11—28no—
130C23×D11—48no—
131C23×D11—432no—
132C23×D11—432no—
133C23×D11—416no—
134C23×D11—416no—
135C23×D11#4118yes—
136C23×D11C2414yes—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—28no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—48no—
149C22×C4×C11—416no—
150C22×C4×C11C2414yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C22×Dic11—232no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—28no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—28no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11C2×D4116yes—
169C22×Dic11C2×D414yes—
170C22×Dic11C2×D414yes—
171C22×Dic11C2414yes—
172C22×Dic11C2412yes—
173C22×Dic11C2412yes—
174C22×Dic11C2412yes—
175C22×Dic11C2412yes—
176C11×C4⋊C4—48no—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—28no—
179C22⋊Dic11—28no—
180C22⋊Dic11—28no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—216no—
184(C2×D11)⋊C4—216no—
185(C2×D11)⋊C4—48no—
186(C2×D11)⋊C4—48no—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189Dic11⋊C4—48no—
190C4×Dic11—28no—
191C4×Dic11—28no—
192C22×#117—111no—
193C23×C22⋊C4—111no—
194#2482—1116no—
195C2×#399—112no—
196C2×#397—112no—
197C2×#388—112no—
198C2×#388—112no—
199C2×#385—111no—
200C2×#385D1111yescharacteristic, complemented
201C2×#381—111no—
202C2×#379—111no—
203C2×#379—111no—
204C23×C11—28no—
205C23×C11—28no—
206C23×C11—216no—
207C23×C11—216no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11#123116yes—
211C23×C11C22×D414yes—
212C23×C11C22×D412yes—
213C23×C11C2×#4114yes—
214C23×C11C2×#4112yes—
215C23×C11C2×#4114yes—
216C23×C11C2×#4112yes—
217C23×C11C2×#4114yes—
218C23×C11H(5,𝔽2)14yes—
219C23×C11C2511yescharacteristic
220C22×D11—232no—
221C22×D11—216no—
222C22×D11—216no—
223C22×D11—216no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—432no—
231C22×D11—432no—
232C22×D11—416no—
233C22×D11—4128no—
234C22×D11—416no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11C2×#4118yes—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—416no—
251C2×C4×C11—44no—
252C2×C4×C11—44no—
253C2×C4×C11—48no—
254C2×C4×C11—48no—
255C2×Dic11—232no—
256C2×Dic11—28no—
257C2×Dic11—28no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271C2×Dic11—48no—
272C2×Dic11C22×D414yes—
273C2×Dic11C22×D414yes—
274C26—111no—
275C24×C4—111no—
276C24×C4C2×D1111yescharacteristic
277C2×#117—118no—
278C2×#117—228no—
279C22×C4⋊C4—111no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4C2×D1112yescomplemented
283C22×C22⋊C4—111no—
284C22×C22⋊C4—111no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—118no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—228no—
293C22×C22⋊C4C2×D1111yescharacteristic
294C22×C22⋊C4C2×D1111yescharacteristic
295C22×C42—111no—
296C22×C42—111no—
297#399—1116no—
298#397—1116no—
299#388—1116no—
300#388—1116no—
301#385—118no—
302#385C2×D1118yescomplemented
303#381—118no—
304#379—118no—
305#379—118no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95C2×D1112yescomplemented
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—28no—
313C22×C11—28no—
314C22×C11—232no—
315C22×C11C2×#12318yes—
316C22×C11C2×#12314yes—
317C22×C11#52514yes—
318C22×C11#53514yes—
319C22×C11#55118yes—
320C22×C11#55118yes—
321C22×C11C23×D411yescharacteristic
322C22×C11C22×#4111yescharacteristic
323C22×C11C22×#4111yescharacteristic
324C22×C11C22×#4112yes—
325C22×C11C2×H(5,𝔽2)12yes—
326C2×D11—28no—
327C2×D11—28no—
328C2×D11—28no—
329C2×D11—464no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—432no—
335C4×C11—42no—
336C4×C11—42no—
337C4×C11—44no—
338C4×C11—44no—
339Dic11—24no—
340Dic11—24no—
341Dic11—42no—
342Dic11—42no—
343Dic11—44no—
344C25—112no—
345C25—114no—
346C25—228no—
347C25—224no—
348C25—224no—
349C25—224no—
350C25—444no—
351C25C22×D1111yescharacteristic
352C23×C4—24no—
353C23×C4—44no—
354C23×C4—118no—
355C23×C4—114no—
356C23×C4—111no—
357C23×C4—111no—
358C23×C4—111no—
359C23×C4—112no—
360C23×C4—111no—
361C23×C4—224no—
362C23×C4—224no—
363C23×C4C22×D1111yescharacteristic
364C23×C4C22×D1111yescharacteristic
365C23×C4C22×D1112yes—
366C23×C4C22×D1112yes—
367C23×C4C22×D1114yes—
368#117—2232no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—444no—
376C2×C4⋊C4C22×D1118yescomplemented
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—228no—
388C2×C22⋊C4—228no—
389C2×C22⋊C4—2232no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—228no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—444no—
395C2×C22⋊C4—444no—
396C2×C22⋊C4C22×D1114yes—
397C2×C22⋊C4C22×D1114yes—
398C2×C42—114no—
399C2×C42—114no—
400C2×C42—224no—
401C2×C42—224no—
402#95—118no—
403#95—118no—
404#95—118no—
405#95C22×D1118yescomplemented
406C2×C11—28no—
407C2×C11#248218yescomplemented
408C2×C11C22×#12311yescharacteristic
409C2×C11C2×#52511yescharacteristic
410C2×C11C2×#53511yescharacteristic
411C2×C11C2×#55112yes—
412C2×C11C2×#55112yes—
413D11—48no—
414C24—24no—
415C24—24no—
416C24—118no—
417C24—114no—
418C24—2216no—
419C24—2232no—
420C24—224no—
421C24—228no—
422C24—224no—
423C24—224no—
424C24—224no—
425C24—224no—
426C24—224no—
427C24—228no—
428C24—228no—
429C24—448no—
430C24—4432no—
431C24—4432no—
432C24—4416no—
433C24—4416no—
434C24#433914yes—
435C24D4×D1114yes—
436C24#434314yes—
437C24C23×D1112yes—
438C24C23×D1111yescharacteristic
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—28no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—48no—
451C22×C4—416no—
452C22×C4—114no—
453C22×C4—114no—
454C22×C4—1116no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—2232no—
461C22×C4—228no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—228no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4C23×D1114yes—
475C22×C4C23×D1114yes—
476C22×C4C23×D1112yes—
477C22×C4C23×D1112yes—
478C4⋊C4—48no—
479C4⋊C4—228no—
480C4⋊C4—228no—
481C4⋊C4—448no—
482C22⋊C4—28no—
483C22⋊C4—28no—
484C22⋊C4—2216no—
485C22⋊C4—2216no—
486C22⋊C4—2216no—
487C22⋊C4—2216no—
488C22⋊C4—228no—
489C22⋊C4—228no—
490C22⋊C4—448no—
491C22⋊C4—448no—
492C42—228no—
493C42—228no—
494C11C2×#248211yescharacteristic, complemented, Sylow
495C23—216no—
496C23—28no—
497C23—216no—
498C23—28no—
499C23—24no—
500C23—24no—
501C23—118no—
502C23—2232no—
503C23—2216no—
504C23—2216no—
505C23—2216no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—4432no—
513C23—4432no—
514C23—4416no—
515C23—44128no—
516C23—4416no—
517C23—448no—
518C23—448no—
519C23—448no—
520C23—448no—
521C23#66947116yes—
522C23C2×#433914yes—
523C23C2×#433912yes—
524C23C2×D4×D1114yes—
525C23C2×D4×D1112yes—
526C23#6703714yes—
527C23C2×#434314yes—
528C23C2×#434312yes—
529C23#41×D1114yes—
530C23C24×D1111yescharacteristic
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—416no—
542C2×C4—48no—
543C2×C4—44no—
544C2×C4—48no—
545C2×C4—44no—
546C2×C4—114no—
547C2×C4—114no—
548C2×C4—2232no—
549C2×C4—228no—
550C2×C4—228no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—444no—
563C2×C4—448no—
564C2×C4—444no—
565C22—28no—
566C22—28no—
567C22—24no—
568C22—232no—
569C22—24no—
570C22—228no—
571C22—228no—
572C22—228no—
573C22—4464no—
574C22—444no—
575C22—444no—
576C22—444no—
577C22—4432no—
578C22—444no—
579C22C2×#6694718yes—
580C22C2×#6694714yes—
581C22#1062308718yes—
582C22#1062312314yes—
583C22#1062316818yes—
584C22#1062318714yes—
585C22C22×#433911yescharacteristic
586C22C22×D4×D1111yescharacteristic
587C22C2×#6703712yes—
588C22C22×#434311yescharacteristic
589C22C2×#41×D1112yes—
590C4—44no—
591C4—44no—
592C4—42no—
593C4—42no—
594C4—224no—
595C4—224no—
596C4—444no—
597C4—442no—
598C4—442no—
599C2—28no—
600C2—448no—
601C2#1307288918yesdirect product factor
602C2C22×#6694711yescharacteristic
603C2C2×#1062318711yescharacteristic
604C2C2×#1062312311yescharacteristic
605C2C2×#1062316812yes—
606C2C2×#1062308712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#385D11
hypocenterC11C2×#2482
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#66930C2semidirect
3. #13072889C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622288C2semidirect
6. C2×#10622603C2semidirect
7. C2×#10622282C2semidirect
8. C2×#10622823C2semidirect
9. C2×#10622556C2semidirect
12. C2×C11×#385C2semidirect
16. C22×C11×C4⋊C4C22semidirect
29. C22×Dic11⋊C4C22semidirect
30. C22×Dic11⋊C4C22semidirect
31. C22×Dic11⋊C4C22semidirect
32. C22×C4×Dic11C22semidirect
33. C22×C4×Dic11C22semidirect
35. C2×#66930C22semidirect
36. C11×#385C22semidirect
37. C2×C11×#95C22semidirect
38. #10622823C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
42. #10622605C22semidirect
43. #10622603C22semidirect
46. #10622556C22semidirect
47. #10622288C22semidirect
48. #10622282C22semidirect
74. C2×C11×C4⋊C4C23semidirect
99. C2×Dic11⋊C4C23semidirect
100. C2×Dic11⋊C4C23semidirect
101. C2×Dic11⋊C4C23semidirect
104. C2×C4×Dic11C23semidirect
105. C2×C4×Dic11C23semidirect
107. C11×#95C23semidirect
108. C11⋊#95C23semidirect
109. C11⋊#95C23semidirect
110. C11⋊#95C23semidirect
200. C2×#385D11semidirect
282. C22×C4⋊C4C2×D11semidirect
302. #385C2×D11semidirect
309. C2×#95C2×D11semidirect
376. C2×C4⋊C4C22×D11semidirect
405. #95C22×D11semidirect
407. C2×C11#2482semidirect
494. C11C2×#2482semidirect
601. C2#13072889direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669302
C23×(C2×D11)⋊C42
#130728892
C2×#106226052
C2×#106222882
C2×#106226032
C2×#106222822
C2×#106228232
C2×#106225562
C2×#106225682
C2×C11×#3852
C2×#248211