Finite Group Databasebeta

← C2×#13072916 #14923293

Subgroups — C2×#13072916 #14923293

Order 2816.

3070 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
1C22×C4×D44C211yesmaximal, characteristic
2C22×#66945C211yesmaximal, characteristic, complemented
3#13072916C2116yesmaximal, direct product factor
4C2×#10622606C212yesmaximal, complemented
5C2×#10622285C212yesmaximal
6C2×#10622541C211yesmaximal, characteristic, complemented
7C2×#10622603C212yesmaximal, complemented
8C2×#10622268C212yesmaximal, complemented
9C2×#10622600C211yesmaximal, characteristic, complemented
10C2×#10622600C211yesmaximal, characteristic, complemented
11C2×#10622600C211yesmaximal, characteristic, complemented
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2212yes—
31C2×#66945—28no—
32C2×#66945C2218yescomplemented
33C2×C4×D44—28no—
34C2×C4×D44C2218yes—
35C11×#389C2218yescomplemented
36C2×C11×#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622606C22116yescomplemented
42#10622603C22116yescomplemented
43#10622600C2218yescomplemented
44#10622600C2218yescomplemented
45#10622600C2218yescomplemented
46#10622541C2218yescomplemented
47#10622285C22116yes—
48#10622268C22116yescomplemented
49C24×D11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×D44—24no—
61C22×D44—24no—
62C22×D44—24no—
63C22×D44C2314yes—
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11—24no—
67C22×C4×D11—24no—
68C22×C4×D11—24no—
69C22×C4×D11D418yes—
70C22×C4×D11C2314yes—
71C22×C4×D11C2314yes—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—44no—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2318yes—
78C2×C42×C11—24no—
79C2×C42×C11C2314yes—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2314yes—
97C2×C4⋊Dic11C2314yes—
98C2×Dic11⋊C4—28no—
99C2×Dic11⋊C4C2318yes—
100C2×C4×Dic11—28no—
101C2×C4×Dic11C2318yes—
102#66945—232no—
103C4×D44—232no—
104C11×#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C2×#2485—111nomaximal, Sylow
110C24×C11C2411yescharacteristic
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11C2×D414yes—
124C23×D11#4114yes—
125C23×D11C2412yes—
126C23×D11C2412yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11C2×D414yes—
139C22×C4×C11#4114yes—
140C22×C4×C11#4114yes—
141C22×C4×C11#4114yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11C2×D414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2414yes—
161C22×Dic11C2414yes—
162C22×Dic11C2412yes—
163C2×D44—232no—
164C2×D44—28no—
165C2×D44—28no—
166C2×D44—28no—
167C2×C4×D11—232no—
168C2×C4×D11—28no—
169C2×C4×D11—28no—
170C2×C4×D11—28no—
171C2×C4×D11—28no—
172C2×C4×D11—28no—
173C2×C4×D11—416no—
174C2×C4×D11C2×D4116yes—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—28no—
177C11×C4⋊C4—48no—
178C42×C11—28no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—48no—
184(C2×D11)⋊C4—48no—
185C4⋊Dic11—28no—
186C4⋊Dic11—28no—
187C4⋊Dic11—28no—
188Dic11⋊C4—216no—
189C4×Dic11—216no—
190C22×C4×D4—111no—
191C22×#117—111no—
192#2485—1116no—
193C2×#397—112no—
194C2×#394—112no—
195C2×#389—111no—
196C2×#389D1111yescharacteristic, complemented
197C2×#388—112no—
198C2×#387—112no—
199C2×#380—111no—
200C2×#380—111no—
201C2×#380—111no—
202C23×C11C22×D412yes—
203C23×C11C2×#4112yes—
204C23×C11C2×#4112yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4112yes—
207C23×C11H(5,𝔽2)12yes—
208C23×C112−1+412yes—
209C23×C11C2511yescharacteristic
210C22×D11—28no—
211C22×D11—28no—
212C22×D11—28no—
213C22×D11—28no—
214C22×D11—28no—
215C22×D11—28no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—44no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11C22×D414yes—
237C22×D11C2×#4114yes—
238C2×C4×C11—28no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—48no—
251C2×C4×C11—44no—
252C2×C4×C11—48no—
253C2×C4×C11#123116yes—
254C2×C4×C11C22×D414yes—
255C2×C4×C11C2×#4114yes—
256C2×C4×C11C2×#4114yes—
257C2×C4×C11C2×#4114yes—
258C2×Dic11—28no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—44no—
271C2×Dic11—48no—
272C2×Dic11—48no—
273C2×Dic11C22×D414yes—
274D44—232no—
275C4×D11—232no—
276C4×D11—416no—
277C23×D4—111no—
278C24×C4—111no—
279C24×C4—111no—
280C2×C4×D4—118no—
281C2×C4×D4—228no—
282C2×#117—118no—
283C2×#117—228no—
284C22×C4⋊C4—112no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4C2×D1111yescharacteristic
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C4⋊C4C2×D1112yes—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—111no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C42—112no—
298C22×C42C2×D1111yescharacteristic
299#397—1116no—
300#394—1116no—
301#389—118no—
302#389C2×D1118yescomplemented
303#388—1116no—
304#387—1116no—
305#380—118no—
306#380—118no—
307#380—118no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95C2×D1112yes—
313C22×C11C2×#12314yes—
314C22×C11#52514yes—
315C22×C11#53714yes—
316C22×C11#55214yes—
317C22×C11#55314yes—
318C22×C11#55514yes—
319C22×C11#55614yes—
320C22×C11C23×D411yescharacteristic
321C22×C11C22×#4111yescharacteristic
322C22×C11C22×#4111yescharacteristic
323C22×C11C22×#4111yescharacteristic
324C22×C11C22×#4111yescharacteristic
325C22×C11C2×H(5,𝔽2)11yescharacteristic
326C22×C11C2×2−1+411yescharacteristic
327C2×D11—24no—
328C2×D11—24no—
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11—24no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—416no—
342C2×D11—416no—
343C4×C11—24no—
344C4×C11—44no—
345C4×C11—42no—
346C4×C11—44no—
347C4×C11C2×#12318yes—
348Dic11—24no—
349Dic11—42no—
350Dic11—44no—
351Dic11—44no—
352C25—111no—
353C25—111no—
354C22×D4—114no—
355C22×D4—224no—
356C22×D4—224no—
357C22×D4—224no—
358C23×C4—111no—
359C23×C4—118no—
360C23×C4—114no—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4—111no—
364C23×C4—114no—
365C23×C4—224no—
366C23×C4—224no—
367C23×C4—224no—
368C23×C4—224no—
369C23×C4—224no—
370C23×C4C22×D1112yes—
371C23×C4C22×D1111yescharacteristic
372C23×C4C22×D1112yes—
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C4×D4—2232no—
376#117—2232no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—118no—
384C2×C4⋊C4—224no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—228no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4C22×D1114yes—
389C2×C4⋊C4C22×D1114yes—
390C2×C4⋊C4C22×D1118yes—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—228no—
401C2×C22⋊C4—444no—
402C2×C22⋊C4—444no—
403C2×C42—24no—
404C2×C42—118no—
405C2×C42—228no—
406C2×C42C22×D1114yes—
407#95—118no—
408#95—118no—
409#95—118no—
410#95—118no—
411#95C22×D1118yes—
412C2×C11#248518yescomplemented
413C2×C11C22×#12311yescharacteristic
414C2×C11C2×#52511yescharacteristic
415C2×C11C2×#53711yescharacteristic
416C2×C11C2×#55211yescharacteristic
417C2×C11C2×#55311yescharacteristic
418C2×C11C2×#55511yescharacteristic
419C2×C11C2×#55611yescharacteristic
420D11—44no—
421D11—44no—
422C24—114no—
423C24—114no—
424C24—112no—
425C24—112no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—222no—
430C24—222no—
431C24—222no—
432C24—222no—
433C24—222no—
434C24—222no—
435C24—222no—
436C24—222no—
437C24—222no—
438C24C23×D1111yescharacteristic
439C2×D4—228no—
440C2×D4—228no—
441C2×D4—2232no—
442C2×D4—228no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—114no—
455C22×C4—112no—
456C22×C4—1116no—
457C22×C4—112no—
458C22×C4—114no—
459C22×C4—114no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—2232no—
463C22×C4—228no—
464C22×C4—228no—
465C22×C4—222no—
466C22×C4—224no—
467C22×C4—222no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—222no—
473C22×C4—224no—
474C22×C4—228no—
475C22×C4—228no—
476C22×C4—228no—
477C22×C4—4416no—
478C22×C4#433914yes—
479C22×C4D4×D1114yes—
480C22×C4#434314yes—
481C22×C4#434314yes—
482C22×C4C23×D1114yes—
483C22×C4C23×D1112yes—
484C22×C4C23×D1114yes—
485C22×C4C23×D1112yes—
486C22×C4C23×D1112yes—
487C4⋊C4—28no—
488C4⋊C4—28no—
489C4⋊C4—48no—
490C4⋊C4—228no—
491C4⋊C4—228no—
492C4⋊C4—2216no—
493C4⋊C4—228no—
494C22⋊C4—228no—
495C22⋊C4—2216no—
496C22⋊C4—228no—
497C22⋊C4—2216no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C42—28no—
501C42—2216no—
502C11C2×#248511yescharacteristic, complemented, Sylow
503C23—114no—
504C23—114no—
505C23—228no—
506C23—228no—
507C23—228no—
508C23—228no—
509C23—228no—
510C23—222no—
511C23—222no—
512C23—222no—
513C23—222no—
514C23—222no—
515C23—222no—
516C23—222no—
517C23—222no—
518C23—222no—
519C23—222no—
520C23—222no—
521C23—222no—
522C23—228no—
523C23—444no—
524C23—444no—
525C23—444no—
526C23—444no—
527C23—444no—
528C23—444no—
529C23—444no—
530C23—444no—
531C23C2×#433912yes—
532C23C2×D4×D1112yes—
533C23#6703712yes—
534C23C2×#434312yes—
535C23C2×#434312yes—
536C23#41×D1112yes—
537C23#6704312yes—
538C23C24×D1111yescharacteristic
539D4—2232no—
540C2×C4—28no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—48no—
553C2×C4—44no—
554C2×C4—48no—
555C2×C4—114no—
556C2×C4—228no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—2232no—
560C2×C4—222no—
561C2×C4—224no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—222no—
568C2×C4—224no—
569C2×C4—448no—
570C2×C4—444no—
571C2×C4—448no—
572C2×C4—4416no—
573C2×C4#66947116yes—
574C2×C4C2×#433914yes—
575C2×C4C2×D4×D1114yes—
576C2×C4C2×#434314yes—
577C2×C4C2×#434314yes—
578C22—224no—
579C22—224no—
580C22—224no—
581C22—224no—
582C22—224no—
583C22—224no—
584C22—442no—
585C22—4416no—
586C22—4416no—
587C22—442no—
588C22—442no—
589C22—442no—
590C22—442no—
591C22—442no—
592C22—442no—
593C22—442no—
594C22C2×#6694714yes—
595C22#1062308914yes—
596C22#1062311514yes—
597C22#1062313914yes—
598C22#1062315814yes—
599C22#1062322514yes—
600C22#1062326514yes—
601C22C22×#433911yescharacteristic
602C22C22×D4×D1111yescharacteristic
603C22C2×#6703711yescharacteristic
604C22C22×#434311yescharacteristic
605C22C22×#434311yescharacteristic
606C22C2×#41×D1111yescharacteristic
607C22C2×#6704311yescharacteristic
608C4—24no—
609C4—44no—
610C4—42no—
611C4—44no—
612C4—224no—
613C4—444no—
614C4—444no—
615C4—442no—
616C4C2×#6694718yes—
617C2—444no—
618C2—444no—
619C2#1307291618yesdirect product factor
620C2C22×#6694711yescharacteristic
621C2C2×#1062315811yescharacteristic
622C2C2×#1062313911yescharacteristic
623C2C2×#1062322511yescharacteristic
624C2C2×#1062308911yescharacteristic
625C2C2×#1062326511yescharacteristic
626C2C2×#1062311511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#389D11
hypocenterC11C2×#2485
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×#66945C2semidirect
3. #13072916C2direct (N × H)
4. C2×#10622606C2semidirect
6. C2×#10622541C2semidirect
7. C2×#10622603C2semidirect
8. C2×#10622268C2semidirect
9. C2×#10622600C2semidirect
10. C2×#10622600C2semidirect
11. C2×#10622600C2semidirect
12. C2×C11×#389C2semidirect
32. C2×#66945C22semidirect
35. C11×#389C22semidirect
41. #10622606C22semidirect
42. #10622603C22semidirect
43. #10622600C22semidirect
44. #10622600C22semidirect
45. #10622600C22semidirect
46. #10622541C22semidirect
48. #10622268C22semidirect
196. C2×#389D11semidirect
302. #389C2×D11semidirect
412. C2×C11#2485semidirect
502. C11C2×#2485semidirect
619. C2#13072916direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D442
C22×#669452
#130729162
C2×#106226062
C2×#106222852
C2×#106225412
C2×#106226032
C2×#106222682
C2×#106226002
C2×C11×#3892
C2×#248511