Finite Group Databasebeta

← C2×#20243374 #26215671

Subgroups — C2×#20243374 #26215671

Order 12032.

2066 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×D4×Dic47C211yesmaximal, characteristic
2C22×#13093939C211yesmaximal, characteristic
3C2×#15688981C212yesmaximal, complemented
4#20243374C218yesmaximal, direct product factor
5C2×#15688889C212yesmaximal, complemented
6C22×#99×C47C211yesmaximal, characteristic
7C24×Dic47C411yescharacteristic, complemented
8C24×Dic47C2211yescharacteristic
9C2×D4×Dic47—22no—
10C2×D4×Dic47—22no—
11C2×D4×Dic47—24no—
12C2×D4×Dic47C414yescomplemented
13C2×D4×Dic47C2214yes—
14C22×C4⋊Dic47C411yescharacteristic, complemented
15C22×Dic47⋊C4—22no—
16C22×C22⋊Dic47C411yescharacteristic, complemented
17C22×C22⋊Dic47C2212yes—
18C22×C22⋊Dic47C2211yescharacteristic
19C22×C4×Dic47C411yescharacteristic, complemented
20C2×#13093939—24no—
21C2×#13093939C2214yes—
22#15688981—24no—
23#15688981C2218yescomplemented
24C2×C47⋊#95—22no—
25#15688889C2218yescomplemented
26C23×D4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2212yes—
28C2×#99×C47—24no—
29C2×#99×C47C2214yes—
30C23×Dic47—22no—
31C23×Dic47—21no—
32C23×Dic47—21no—
33C23×Dic47—22no—
34C23×Dic47—44no—
35C23×Dic47—44no—
36C23×Dic47C2×C411yescharacteristic
37C23×Dic47C2×C411yescharacteristic
38C23×Dic47C2×C411yescharacteristic
39C23×Dic47C2×C411yescharacteristic
40C23×Dic47C2×C412yes—
41C23×Dic47C2×C414yescomplemented
42C23×Dic47D412yes—
43C23×Dic47D412yes—
44C23×Dic47D414yes—
45C23×Dic47C2312yes—
46D4×Dic47—28no—
47D4×Dic47—28no—
48D4×Dic47—28no—
49D4×Dic47—28no—
50C2×C4⋊Dic47—22no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47C2×C414yescomplemented
53C2×Dic47⋊C4—28no—
54C2×Dic47⋊C4—48no—
55C2×C22⋊Dic47—22no—
56C2×C22⋊Dic47—22no—
57C2×C22⋊Dic47—22no—
58C2×C22⋊Dic47—22no—
59C2×C22⋊Dic47—24no—
60C2×C22⋊Dic47—24no—
61C2×C22⋊Dic47—22no—
62C2×C22⋊Dic47C2×C412yes—
63C2×C22⋊Dic47C2×C414yescomplemented
64C2×C22⋊Dic47C2314yes—
65C2×C22⋊Dic47C2312yes—
66C2×C4×Dic47—21no—
67C2×C4×Dic47—22no—
68C2×C4×Dic47—21no—
69C2×C4×Dic47C2×C414yescomplemented
70#13093939—28no—
71C47⋊#95—28no—
72C25×C47C2×C411yescharacteristic
73C25×C47C2311yescharacteristic
74C22×D4×C47—22no—
75C22×D4×C47—22no—
76C22×D4×C47—24no—
77C22×D4×C47C2×C412yes—
78C22×D4×C47D414yes—
79C22×D4×C47Q814yes—
80C22×D4×C47C2312yes—
81C23×C4×C47—22no—
82C23×C4×C47C2×C411yescharacteristic
83C2×C22⋊C4×C47—24no—
84C2×C22⋊C4×C47—24no—
85C2×C22⋊C4×C47—22no—
86C2×C22⋊C4×C47C2314yes—
87#99×C47—28no—
88C24×C47—21no—
89C24×C47—21no—
90C24×C47—22no—
91C24×C47—42no—
92C24×C47—42no—
93C24×C47—42no—
94C24×C47—42no—
95C24×C47C4⋊C414yescomplemented
96C24×C47C22×C411yescharacteristic
97C24×C47C22×C412yes—
98C24×C47C22×C411yescharacteristic
99C24×C47C2×D412yes—
100C24×C47C2×D412yes—
101C24×C47C2×D412yes—
102C24×C47C2×Q812yes—
103C24×C47#4114yes—
104C24×C47C2411yescharacteristic
105C2×D4×C47—24no—
106C2×D4×C47—24no—
107C2×D4×C47—28no—
108C2×D4×C47—28no—
109C2×D4×C47—28no—
110C2×D4×C47—28no—
111C2×D4×C47—24no—
112C2×D4×C47—24no—
113C2×D4×C47C4⋊C418yescomplemented
114C2×D4×C47C2×D414yes—
115C2×D4×C47C2×Q814yes—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—22no—
119C22×C4×C47—24no—
120C22×C4×C47—44no—
121C22×C4×C47—44no—
122C22×C4×C47—44no—
123C22×C4×C47C4⋊C414yescomplemented
124C22×C4×C47C22×C412yes—
125C22×Dic47—28no—
126C22×Dic47—24no—
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—21no—
131C22×Dic47—24no—
132C22×Dic47—24no—
133C22×Dic47—24no—
134C22×Dic47—44no—
135C22×Dic47—48no—
136C22×Dic47—44no—
137C22×Dic47—42no—
138C22×Dic47—44no—
139C22×Dic47—44no—
140C22×Dic47—48no—
141C22×Dic47—48no—
142C22×Dic47—44no—
143C22×Dic47—42no—
144C22×Dic47—42no—
145C22×Dic47—44no—
146C22×Dic47—44no—
147C22×Dic47—44no—
148C22×Dic47C22⋊C411yescharacteristic
149C22×Dic47C22⋊C412yes—
150C22×Dic47C22⋊C412yes—
151C22×Dic47C22⋊C414yes—
152C22×Dic47C22⋊C412yes—
153C22×Dic47C22⋊C414yes—
154C22×Dic47C22⋊C411yescharacteristic
155C22×Dic47C22×C412yes—
156C22×Dic47C22×C412yes—
157C22×Dic47C22×C412yes—
158C22×Dic47C22×C412yes—
159C22×Dic47C2×D414yes—
160C22×Dic47C2×D414yes—
161C22⋊C4×C47—24no—
162C22⋊C4×C47—24no—
163C22⋊C4×C47—44no—
164C22⋊Dic47—24no—
165C22⋊Dic47—24no—
166C22⋊Dic47—28no—
167C22⋊Dic47—24no—
168C22⋊Dic47—24no—
169C22⋊Dic47—44no—
170C4⋊Dic47—28no—
171Dic47⋊C4—416no—
172C4×Dic47—24no—
173C4×Dic47—24no—
174C23×C47—24no—
175C23×C47—22no—
176C23×C47—24no—
177C23×C47—22no—
178C23×C47—22no—
179C23×C47—22no—
180C23×C47—24no—
181C23×C47—24no—
182C23×C47—41no—
183C23×C47—42no—
184C23×C47—41no—
185C23×C47—41no—
186C23×C47—42no—
187C23×C47—44no—
188C23×C47—44no—
189C23×C47—48no—
190C23×C47—41no—
191C23×C47—42no—
192C23×C47—48no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47—48no—
196C23×C47—42no—
197C23×C47—42no—
198C23×C47—42no—
199C23×C47C2×C22⋊C412yes—
200C23×C47C2×C22⋊C411yescharacteristic
201C23×C47C2×C22⋊C411yescharacteristic
202C23×C47C2×C4⋊C412yes—
203C23×C47C2×C4⋊C412yes—
204C23×C47C2×C4⋊C414yescomplemented
205C23×C47#11712yes—
206C23×C47#11712yes—
207C23×C47#12114yes—
208C23×C47#12114yes—
209C23×C47C22⋊Q814yes—
210C23×C47C22⋊Q814yes—
211C23×C47C23×C411yescharacteristic
212C23×C47C22×D412yes—
213C23×C47C22×D411yescharacteristic
214C23×C47C22×Q811yescharacteristic
215C23×C47C2×#4112yes—
216D4×C47—28no—
217D4×C47—28no—
218D4×C47—216no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—24no—
222C2×C4×C47—24no—
223C2×C4×C47—44no—
224C2×C4×C47—44no—
225C2×C4×C47—44no—
226C2×C4×C47—88no—
227C2×C4×C47C2×C4⋊C414yescomplemented
228C2×Dic47—22no—
229C2×Dic47—24no—
230C2×Dic47—28no—
231C2×Dic47—24no—
232C2×Dic47—24no—
233C2×Dic47—28no—
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—44no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—44no—
240C2×Dic47—48no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245C2×Dic47—48no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—44no—
249C2×Dic47—44no—
250C2×Dic47—44no—
251C2×Dic47—88no—
252C2×Dic47#9914yescomplemented
253C2×Dic47C2×C22⋊C412yes—
254C2×Dic47C2×C22⋊C414yes—
255C2×Dic47C2×C22⋊C412yes—
256C2×#1799—471nomaximal, Sylow
257C22×C47—28no—
258C22×C47—24no—
259C22×C47—24no—
260C22×C47—28no—
261C22×C47—22no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—22no—
265C22×C47—22no—
266C22×C47—21no—
267C22×C47—21no—
268C22×C47—22no—
269C22×C47—24no—
270C22×C47—42no—
271C22×C47—42no—
272C22×C47—44no—
273C22×C47—44no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—42no—
277C22×C47—44no—
278C22×C47—44no—
279C22×C47—48no—
280C22×C47—48no—
281C22×C47—42no—
282C22×C47—42no—
283C22×C47#38012yes—
284C22×C47#38014yes—
285C22×C47#38012yes—
286C22×C47C2×#9912yes—
287C22×C47#41012yes—
288C22×C47C22×C22⋊C411yescharacteristic
289C22×C47C22×C4⋊C411yescharacteristic
290C22×C47C2×#11711yescharacteristic
291C22×C47C2×#12112yes—
292C22×C47C2×C22⋊Q812yes—
293C4×C47—24no—
294C4×C47—84no—
295Dic47—22no—
296Dic47—24no—
297Dic47—42no—
298Dic47—42no—
299Dic47—84no—
300Dic47C2×#9914yescomplemented
301C22×C4×D4—471no—
302C22×#99—471no—
303C22×#99D4711yescharacteristic
304C2×#380—472no—
305#1799—478no—
306C2×#342—472no—
307C2×C47—22no—
308C2×C47—21no—
309C2×C47—21no—
310C2×C47—22no—
311C2×C47—22no—
312C2×C47—24no—
313C2×C47—44no—
314C2×C47#179914yescomplemented
315C2×C47C2×#38011yescharacteristic
316C2×C47C22×#9911yescharacteristic
317C2×C47C2×#41011yescharacteristic
318C23×D4C2×D4711yescharacteristic
319C24×C4—471no—
320C24×C4—471no—
321C2×C4×D4—474no—
322C2×C4×D4—474no—
323C2×C4×D4—942no—
324C2×C4×D4—942no—
325C2×C4×D4—944no—
326C22×C4⋊C4—471no—
327C22×C4⋊C4—942no—
328C22×C22⋊C4—471no—
329C22×C22⋊C4—471no—
330C22×C22⋊C4—472no—
331C22×C22⋊C4C2×D4712yes—
332C22×C42—471no—
333C2×#99—24no—
334C2×#99—474no—
335C2×#99—944no—
336C2×#99C2×D4714yes—
337#380—478no—
338#380—944no—
339C2×#95—942no—
340#342—478no—
341C47C2×#179911yescharacteristic, complemented, Sylow
342C25C4×D4711yescharacteristic
343C25C22×D4711yescharacteristic
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4Dic9414yes—
348C22×D4C4×D4712yes—
349C22×D4C22⋊D4714yes—
350C22×D4C22×D4712yes—
351C23×C4—22no—
352C23×C4—471no—
353C23×C4—472no—
354C23×C4—471no—
355C23×C4—472no—
356C23×C4—472no—
357C23×C4—474no—
358C23×C4—472no—
359C23×C4—471no—
360C23×C4—471no—
361C23×C4—474no—
362C23×C4—941no—
363C23×C4—942no—
364C23×C4—941no—
365C23×C4—942no—
366C23×C4—1884no—
367C23×C4—1884no—
368C23×C4C4×D4711yescharacteristic
369C4×D4—948no—
370C4×D4—948no—
371C4×D4—948no—
372C4×D4—948no—
373C2×C4⋊C4—474no—
374C2×C4⋊C4—942no—
375C2×C4⋊C4—942no—
376C2×C4⋊C4—948no—
377C2×C4⋊C4—1888no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—472no—
382C2×C22⋊C4—474no—
383C2×C22⋊C4—472no—
384C2×C22⋊C4—474no—
385C2×C22⋊C4—942no—
386C2×C22⋊C4—942no—
387C2×C22⋊C4—942no—
388C2×C22⋊C4—942no—
389C2×C22⋊C4—944no—
390C2×C22⋊C4—944no—
391C2×C22⋊C4—942no—
392C2×C22⋊C4C22×D4714yes—
393C2×C42—474no—
394C2×C42—942no—
395C2×C42—941no—
396C2×C42—941no—
397#99—28no—
398#99—948no—
399#95—948no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24Dic47⋊C414yescomplemented
408C24C2×Dic9412yes—
409C24C2×C4×D4711yescharacteristic
410C24C2×C4×D4712yes—
411C24C2×C4×D4711yescharacteristic
412C24D4×D4712yes—
413C24D4×D4712yes—
414C24#1062535214yes—
415C24C2×C22⋊D4712yes—
416C24C23×D4711yescharacteristic
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4Dic47⋊C418yescomplemented
426C2×D4C2×Dic9414yes—
427C2×D4C2×C22⋊D4714yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—471no—
436C22×C4—472no—
437C22×C4—474no—
438C22×C4—471no—
439C22×C4—472no—
440C22×C4—472no—
441C22×C4—474no—
442C22×C4—472no—
443C22×C4—474no—
444C22×C4—472no—
445C22×C4—474no—
446C22×C4—472no—
447C22×C4—472no—
448C22×C4—948no—
449C22×C4—944no—
450C22×C4—944no—
451C22×C4—944no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4—944no—
457C22×C4—1884no—
458C22×C4—1884no—
459C22×C4—1888no—
460C22×C4—1884no—
461C22×C4—1882no—
462C22×C4—1884no—
463C22×C4—1888no—
464C22×C4—1884no—
465C22×C4—1888no—
466C22×C4—1884no—
467C22×C4—1884no—
468C22×C4—1884no—
469C22×C4—1882no—
470C22×C4—1882no—
471C22×C4Dic47⋊C414yescomplemented
472C22×C4C2×C4×D4712yes—
473C4⋊C4—948no—
474C4⋊C4—18816no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—44no—
478C22⋊C4—948no—
479C22⋊C4—944no—
480C22⋊C4—944no—
481C22⋊C4—944no—
482C22⋊C4—944no—
483C22⋊C4—1884no—
484C42—944no—
485C42—944no—
486C23—24no—
487C23—22no—
488C23—24no—
489C23—22no—
490C23—24no—
491C23—24no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—44no—
498C23—41no—
499C23—42no—
500C23—48no—
501C23—44no—
502C23—41no—
503C23—42no—
504C23—48no—
505C23—42no—
506C23—42no—
507C23—48no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23C22⋊C4×D4712yes—
512C23C22⋊C4×D4711yescharacteristic
513C23C22⋊C4×D4711yescharacteristic
514C23C2×Dic47⋊C412yes—
515C23C2×Dic47⋊C412yes—
516C23C2×Dic47⋊C414yescomplemented
517C23#1309398012yes—
518C23#1309398012yes—
519C23#1309399614yes—
520C23#1309399614yes—
521C23#1309400114yes—
522C23#1309400114yes—
523C23C22×C4×D4711yescharacteristic
524C23C2×D4×D4712yes—
525C23C22×C22⋊D4711yescharacteristic
526C23C22×Dic9411yescharacteristic
527C23C2×#1062535212yes—
528D4—216no—
529D4—28no—
530D4—28no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—88no—
539C2×C4—472no—
540C2×C4—474no—
541C2×C4—472no—
542C2×C4—474no—
543C2×C4—948no—
544C2×C4—948no—
545C2×C4—944no—
546C2×C4—944no—
547C2×C4—944no—
548C2×C4—942no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—3768no—
552C2×C4—1888no—
553C2×C4—1884no—
554C2×C4—1884no—
555C2×C4—1882no—
556C2×C4—1882no—
557C2×C4—1888no—
558C2×C4—1884no—
559C2×C4—1884no—
560C2×C4—1884no—
561C2×C4—1882no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4—1882no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4C2×Dic47⋊C414yescomplemented
568C22—28no—
569C22—24no—
570C22—24no—
571C22—28no—
572C22—22no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—22no—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—24no—
581C22—42no—
582C22—42no—
583C22—44no—
584C22—44no—
585C22—41no—
586C22—41no—
587C22—42no—
588C22—44no—
589C22—48no—
590C22—44no—
591C22—48no—
592C22—42no—
593C22—42no—
594C22#1568898112yes—
595C22#1568898114yes—
596C22#1568898112yes—
597C22#99×D4712yes—
598C22#1568909512yes—
599C22C2×C22⋊C4×D4711yescharacteristic
600C22C22×Dic47⋊C411yescharacteristic
601C22C2×#1309398011yescharacteristic
602C22C2×#1309399612yes—
603C22C2×#1309400112yes—
604C4—24no—
605C4—84no—
606C4—474no—
607C4—942no—
608C4—944no—
609C4—3764no—
610C4—1882no—
611C4—1882no—
612C2—22no—
613C2—22no—
614C2—21no—
615C2—21no—
616C2—24no—
617C2—22no—
618C2—44no—
619C2#2024337414yesdirect product factor
620C2C2×#1568898111yescharacteristic
621C2C2×#99×D4711yescharacteristic
622C2C2×#1568909511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC22×#99×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D4×C47C22
cosocleC24×C47C24
hypercenterC22×#99D47
hypocenterC47C2×#1799
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. C2×#15688981C2semidirect
4. #20243374C2direct (N × H)
5. C2×#15688889C2semidirect
7. C24×Dic47C4semidirect
12. C2×D4×Dic47C4semidirect
14. C22×C4⋊Dic47C4semidirect
16. C22×C22⋊Dic47C4semidirect
19. C22×C4×Dic47C4semidirect
23. #15688981C22semidirect
25. #15688889C22semidirect
41. C23×Dic47C2×C4semidirect
52. C2×C4⋊Dic47C2×C4semidirect
63. C2×C22⋊Dic47C2×C4semidirect
69. C2×C4×Dic47C2×C4semidirect
95. C24×C47C4⋊C4semidirect
113. C2×D4×C47C4⋊C4semidirect
123. C22×C4×C47C4⋊C4semidirect
204. C23×C47C2×C4⋊C4semidirect
227. C2×C4×C47C2×C4⋊C4semidirect
252. C2×Dic47#99semidirect
300. Dic47C2×#99semidirect
314. C2×C47#1799semidirect
341. C47C2×#1799semidirect
407. C24Dic47⋊C4semidirect
425. C2×D4Dic47⋊C4semidirect
471. C22×C4Dic47⋊C4semidirect
516. C23C2×Dic47⋊C4semidirect
567. C2×C4C2×Dic47⋊C4semidirect
619. C2#20243374direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic472
C22×#130939392
C2×#156889812
#202433742
C2×#156888892
C22×#99×C472
C2×#179947