Finite Group Databasebeta

← C2×#13072191 #14921915

Subgroups — C2×#13072191 #14921915

Order 2816.

3894 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66928C211yesmaximal, characteristic, complemented
2C22×#66950C211yesmaximal, characteristic, complemented
3C22×#66948C211yesmaximal, characteristic
4C22×#66946C211yesmaximal, characteristic, complemented
5#13072191C2116yesmaximal, direct product factor
6C2×#10622287C212yesmaximal, complemented
7C2×#10622604C212yesmaximal, complemented
8C2×#10622587C211yesmaximal, characteristic, complemented
9C2×#10622278C212yesmaximal, complemented
10C2×#10622600C212yesmaximal, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×D44C2212yes—
14C23×D44C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2212yes—
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×C4⋊Dic11C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C2×#66950—28no—
32C2×#66950C2218yescomplemented
33C2×#66948—28no—
34C2×#66948C2218yes—
35C2×#66946—28no—
36C2×#66946C2218yescomplemented
37C2×#66928—28no—
38C2×#66928C2218yescomplemented
39C11×#389C2218yescomplemented
40C2×C11×#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622604C22116yescomplemented
46#10622600C22116yescomplemented
47#10622587C2218yescomplemented
48C4×(C2×D11)⋊C4C2218yescomplemented
49#10622287C22116yescomplemented
50#10622278C22116yescomplemented
51C24×D11C2312yes—
52C24×D11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C22×D44—24no—
63C22×D44—24no—
64C22×D44—28no—
65C22×D44—28no—
66C22×D44—44no—
67C22×D44D418yes—
68C22×D44C2318yes—
69C22×D44C2314yes—
70C22×C4×D11—28no—
71C22×C4×D11—24no—
72C22×C4×D11—24no—
73C22×C4×D11—24no—
74C22×C4×D11—28no—
75C22×C4×D11—44no—
76C22×C4×D11C2314yes—
77C22×C4×D11C2318yes—
78C22×Dic22—24no—
79C22×Dic22—24no—
80C22×Dic22—24no—
81C22×Dic22C2314yes—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4—44no—
84C2×C11×C4⋊C4D418yescomplemented
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C4⋊C4C2318yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C42×C11—24no—
89C2×C42×C11C2314yes—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—28no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—28no—
95C2×(C2×D11)⋊C4—28no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×C4⋊Dic11—28no—
105C2×C4⋊Dic11C2318yes—
106C2×C4×Dic11—24no—
107C2×C4×Dic11C2314yes—
108#66950—232no—
109#66948—232no—
110#66946—232no—
111#66928—232no—
112C11×#95C2318yes—
113C11⋊#95C2318yes—
114C11⋊#95C2314yes—
115C11⋊#95C2318yes—
116C11⋊#95C2314yes—
117C2×#2427—111nomaximal, Sylow
118C24×C11C2411yescharacteristic
119C23×D11—22no—
120C23×D11—24no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—22no—
129C23×D11—24no—
130C23×D11—22no—
131C23×D11C2×D418yes—
132C23×D11#4114yes—
133C23×D11C2414yes—
134C23×D11C2412yes—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—22no—
146C22×C4×C11C2×D418yes—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11#4114yes—
150C22×C4×C11C2414yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2412yes—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11#4114yes—
167C22×Dic11C2412yes—
168C22×Dic11C2412yes—
169C22×Dic11C2414yes—
170C22×Dic11C2412yes—
171C2×D44—216no—
172C2×D44—216no—
173C2×D44—232no—
174C2×D44—28no—
175C2×D44—28no—
176C2×D44—48no—
177C2×D44—432no—
178C2×D44C2×D4116yes—
179C2×C4×D11—216no—
180C2×C4×D11—216no—
181C2×C4×D11—28no—
182C2×C4×D11—28no—
183C2×C4×D11—28no—
184C2×C4×D11—48no—
185C2×C4×D11—432no—
186C2×C4×D11—416no—
187C2×Dic22—28no—
188C2×Dic22—28no—
189C2×Dic22—28no—
190C2×Dic22—416no—
191C11×C4⋊C4—28no—
192C11×C4⋊C4—48no—
193C11×C4⋊C4C2×D4116yescomplemented
194C42×C11—28no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—216no—
198(C2×D11)⋊C4—216no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—216no—
201(C2×D11)⋊C4—216no—
202C4⋊Dic11—216no—
203C4×Dic11—28no—
204C22×#124—111no—
205C22×C22⋊Q8—111no—
206C22×#121—111no—
207C22×C4×D4—111no—
208#2427—1116no—
209C2×#397—112no—
210C2×#394—112no—
211C2×#391—111no—
212C2×#389D1111yescharacteristic, complemented
213C2×#386—112no—
214C2×#380—112no—
215C2×C4×C22⋊C4—111no—
216C23×C11C22×D412yes—
217C23×C11C22×D412yes—
218C23×C11C2×#4112yes—
219C23×C11C2×#4112yes—
220C23×C11C2×#4112yes—
221C23×C11H(5,𝔽2)12yes—
222C23×C112−1+412yes—
223C23×C11C2511yescharacteristic
224C22×D11—216no—
225C22×D11—28no—
226C22×D11—28no—
227C22×D11—216no—
228C22×D11—216no—
229C22×D11—28no—
230C22×D11—22no—
231C22×D11—24no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—22no—
240C22×D11—24no—
241C22×D11—22no—
242C22×D11—44no—
243C22×D11—48no—
244C22×D11—44no—
245C22×D11—48no—
246C22×D11—48no—
247C22×D11—44no—
248C22×D11—44no—
249C22×D11—48no—
250C22×D11C22×D418yes—
251C22×D11C2×#4114yes—
252C2×C4×C11—216no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—48no—
265C2×C4×C11—44no—
266C2×C4×C11—44no—
267C2×C4×C11#121116yes—
268C2×C4×C11C22×D418yes—
269C2×C4×C11C22×D414yes—
270C2×C4×C11C22×D414yes—
271C2×C4×C11C2×#4114yes—
272C2×Dic11—28no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—48no—
285C2×Dic11—44no—
286C2×Dic11—44no—
287C2×Dic11C2×#4114yes—
288D44—232no—
289D44—432no—
290C4×D11—432no—
291C4×D11—416no—
292Dic22—416no—
293C23×Q8—111no—
294C23×D4—111no—
295C23×D4—112no—
296C24×C4—111no—
297C24×C4—112no—
298C2×#124—118no—
299C2×#124—228no—
300C2×C22⋊Q8—118no—
301C2×C22⋊Q8—228no—
302C2×#121—118no—
303C2×#121—228no—
304C2×C4×D4—118no—
305C2×C4×D4—228no—
306C22×C4⋊C4—112no—
307C22×C4⋊C4C2×D1111yescharacteristic
308C22×C4⋊C4C2×D1112yes—
309C22×C4⋊C4C2×D1111yescharacteristic
310C22×C22⋊C4—111no—
311C22×C22⋊C4—112no—
312C22×C22⋊C4—112no—
313C22×C22⋊C4—112no—
314C22×C22⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4—111no—
317C22×C42—111no—
318C22×C42C2×D1111yescharacteristic
319#397—1116no—
320#394—1116no—
321#391—118no—
322#389C2×D1118yescomplemented
323#386—1116no—
324#380—1116no—
325C4×C22⋊C4—118no—
326C2×#95—112no—
327C2×#95—111no—
328C2×#95—111no—
329C2×#95—112no—
330C2×#95C2×D1112yes—
331C22×C11C2×#12114yes—
332C22×C11#52914yes—
333C22×C11#54214yes—
334C22×C11#54614yes—
335C22×C11#54614yes—
336C22×C11#54714yes—
337C22×C11#54814yes—
338C22×C11C23×D411yescharacteristic
339C22×C11C23×D411yescharacteristic
340C22×C11C22×#4111yescharacteristic
341C22×C11C22×#4111yescharacteristic
342C22×C11C22×#4111yescharacteristic
343C22×C11C2×H(5,𝔽2)11yescharacteristic
344C22×C11C2×2−1+411yescharacteristic
345C2×D11—28no—
346C2×D11—24no—
347C2×D11—28no—
348C2×D11—24no—
349C2×D11—28no—
350C2×D11—24no—
351C2×D11—42no—
352C2×D11—44no—
353C2×D11—432no—
354C2×D11—416no—
355C2×D11—42no—
356C2×D11—44no—
357C2×D11—42no—
358C2×D11—44no—
359C2×D11—42no—
360C2×D11—44no—
361C4×C11—28no—
362C4×C11—42no—
363C4×C11—44no—
364C4×C11—42no—
365C4×C11C2×#12118yes—
366Dic11—24no—
367Dic11—44no—
368Dic11—42no—
369Dic11—42no—
370C25—112no—
371C25—111no—
372C22×Q8—114no—
373C22×Q8—224no—
374C22×Q8—224no—
375C22×Q8—224no—
376C22×D4—118no—
377C22×D4—114no—
378C22×D4—118no—
379C22×D4—228no—
380C22×D4—228no—
381C22×D4—224no—
382C22×D4—224no—
383C22×D4—444no—
384C23×C4—111no—
385C23×C4—112no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—114no—
389C23×C4—118no—
390C23×C4—228no—
391C23×C4—228no—
392C23×C4—224no—
393C23×C4—224no—
394C23×C4—224no—
395C23×C4—444no—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1112yes—
399C23×C4C22×D1112yes—
400C23×C4C22×D1111yescharacteristic
401#124—2232no—
402C22⋊Q8—2232no—
403#121—2232no—
404C4×D4—2232no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4—118no—
408C2×C4⋊C4—228no—
409C2×C4⋊C4D4418yescomplemented
410C2×C4⋊C4C22×D1114yes—
411C2×C4⋊C4C22×D1118yes—
412C2×C4⋊C4C22×D1114yes—
413C2×C22⋊C4—118no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—118no—
418C2×C22⋊C4—114no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—224no—
421C2×C22⋊C4—228no—
422C2×C22⋊C4—228no—
423C2×C22⋊C4—228no—
424C2×C22⋊C4—224no—
425C2×C22⋊C4—228no—
426C2×C22⋊C4—228no—
427C2×C42—24no—
428C2×C42—114no—
429C2×C42—224no—
430C2×C42C22×D1114yes—
431#95—114no—
432#95—114no—
433#95—118no—
434#95—118no—
435#95C22×D1118yes—
436C2×C11#242718yescomplemented
437C2×C11C22×#12111yescharacteristic
438C2×C11C2×#52911yescharacteristic
439C2×C11C2×#54211yescharacteristic
440C2×C11C2×#54611yescharacteristic
441C2×C11C2×#54611yescharacteristic
442C2×C11C2×#54711yescharacteristic
443C2×C11C2×#54811yescharacteristic
444D11—48no—
445D11—44no—
446C24—118no—
447C24—114no—
448C24—114no—
449C24—112no—
450C24—222no—
451C24—224no—
452C24—222no—
453C24—224no—
454C24—222no—
455C24—222no—
456C24—224no—
457C24—222no—
458C24—224no—
459C24—222no—
460C24—224no—
461C24—224no—
462C24C23×D1111yescharacteristic
463C2×Q8—228no—
464C2×Q8—228no—
465C2×Q8—228no—
466C2×Q8—4416no—
467C2×D4—1116no—
468C2×D4—2216no—
469C2×D4—2216no—
470C2×D4—2232no—
471C2×D4—228no—
472C2×D4—228no—
473C2×D4—448no—
474C2×D4—4432no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—114no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—114no—
490C22×C4—112no—
491C22×C4—2216no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—224no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—224no—
499C22×C4—222no—
500C22×C4—224no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—2216no—
504C22×C4—228no—
505C22×C4—228no—
506C22×C4—228no—
507C22×C4—448no—
508C22×C4—4432no—
509C22×C4—4416no—
510C22×C4C2×D4418yes—
511C22×C4C2×D4414yes—
512C22×C4D4×D1114yes—
513C22×C4#434314yes—
514C22×C4C23×D1114yes—
515C22×C4C23×D1112yes—
516C22×C4C23×D1112yes—
517C22×C4C23×D1114yes—
518C22×C4C23×D1112yes—
519C4⋊C4—28no—
520C4⋊C4—48no—
521C4⋊C4—2216no—
522C4⋊C4C2×D44116yescomplemented
523C22⋊C4—228no—
524C22⋊C4—2216no—
525C22⋊C4—2216no—
526C22⋊C4—2216no—
527C22⋊C4—228no—
528C22⋊C4—2216no—
529C22⋊C4—2216no—
530C42—28no—
531C42—228no—
532C11C2×#242711yescharacteristic, complemented, Sylow
533C23—118no—
534C23—114no—
535C23—2216no—
536C23—228no—
537C23—228no—
538C23—2216no—
539C23—2216no—
540C23—222no—
541C23—224no—
542C23—222no—
543C23—224no—
544C23—222no—
545C23—222no—
546C23—224no—
547C23—224no—
548C23—222no—
549C23—222no—
550C23—224no—
551C23—224no—
552C23—228no—
553C23—448no—
554C23—444no—
555C23—444no—
556C23—448no—
557C23—444no—
558C23—448no—
559C23—444no—
560C23—448no—
561C23C22×D4412yes—
562C23C2×D4×D1112yes—
563C23#6703712yes—
564C23C2×#434312yes—
565C23#6704012yes—
566C23#41×D1112yes—
567C23#41×D1112yes—
568C23C24×D1111yescharacteristic
569Q8—4416no—
570D4—2232no—
571D4—4432no—
572C2×C4—216no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—48no—
586C2×C4—44no—
587C2×C4—114no—
588C2×C4—228no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—224no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—224no—
596C2×C4—222no—
597C2×C4—224no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—4432no—
601C2×C4—444no—
602C2×C4—448no—
603C2×C4—444no—
604C2×C4—4416no—
605C2×C4#66948116yes—
606C2×C4C22×D4418yes—
607C2×C4C22×D4414yes—
608C2×C4C2×D4×D1114yes—
609C2×C4C2×#434314yes—
610C22—224no—
611C22—224no—
612C22—228no—
613C22—228no—
614C22—224no—
615C22—228no—
616C22—444no—
617C22—4432no—
618C22—4416no—
619C22—444no—
620C22—442no—
621C22—444no—
622C22—442no—
623C22—442no—
624C22—444no—
625C22—442no—
626C22C2×#6694814yes—
627C22#1062308514yes—
628C22#1062310714yes—
629C22#1062314314yes—
630C22#1062316214yes—
631C22#1062322214yes—
632C22#1062326414yes—
633C22C23×D4411yescharacteristic
634C22C22×D4×D1111yescharacteristic
635C22C2×#6703711yescharacteristic
636C22C22×#434311yescharacteristic
637C22C2×#6704011yescharacteristic
638C22C2×#41×D1111yescharacteristic
639C22C2×#41×D1111yescharacteristic
640C4—28no—
641C4—44no—
642C4—42no—
643C4—42no—
644C4—224no—
645C4—442no—
646C4—442no—
647C4—444no—
648C4C2×#6694818yes—
649C2—444no—
650C2—448no—
651C2#1307219118yesdirect product factor
652C2C22×#6694811yescharacteristic
653C2C2×#1062322211yescharacteristic
654C2C2×#1062326411yescharacteristic
655C2C2×#1062308511yescharacteristic
656C2C2×#1062314311yescharacteristic
657C2C2×#1062316211yescharacteristic
658C2C2×#1062310711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC22×#66948C2
hypercenterC2×#389D11
hypocenterC11C2×#2427
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#66928C2semidirect
2. C22×#66950C2semidirect
4. C22×#66946C2semidirect
5. #13072191C2direct (N × H)
6. C2×#10622287C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622587C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622600C2semidirect
11. C2×C4×(C2×D11)⋊C4C2semidirect
12. C2×C11×#389C2semidirect
32. C2×#66950C22semidirect
36. C2×#66946C22semidirect
38. C2×#66928C22semidirect
39. C11×#389C22semidirect
45. #10622604C22semidirect
46. #10622600C22semidirect
47. #10622587C22semidirect
48. C4×(C2×D11)⋊C4C22semidirect
49. #10622287C22semidirect
50. #10622278C22semidirect
84. C2×C11×C4⋊C4D4semidirect
193. C11×C4⋊C4C2×D4semidirect
212. C2×#389D11semidirect
322. #389C2×D11semidirect
409. C2×C4⋊C4D44semidirect
436. C2×C11#2427semidirect
522. C4⋊C4C2×D44semidirect
532. C11C2×#2427semidirect
651. C2#13072191direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669282
C22×#669502
C22×#669482
C22×#669462
#130721912
C2×#106222872
C2×#106226042
C2×#106225872
C2×#106222782
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×C11×#3892
C2×#242711