Finite Group Databasebeta

← C2×#20241958 #26183591

Subgroups — C2×#20241958 #26183591

Order 12032.

1522 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D47C211yesmaximal, characteristic
2C2×C22⋊C8×D47C211yesmaximal, characteristic
3C2×#15688982C211yesmaximal, characteristic
4#20241958C218yesmaximal, direct product factor
5C2×#15688861C211yesmaximal, characteristic, complemented
6C2×#15688860C211yesmaximal, characteristic, complemented
7C2×#15688859C211yesmaximal, characteristic, complemented
8C2×C47×#328C211yesmaximal, characteristic, complemented
9C22×Q8×D47C411yescharacteristic, complemented
10C23×C4×D47C2211yescharacteristic
11C22×C8×D47—21no—
12C2×#13094004C411yescharacteristic, complemented
13C2×#13094003C2211yescharacteristic
14C2×#13094002—21no—
15C2×#13094001—21no—
16C2×#13094000C411yescharacteristic, complemented
17C22⋊Q8×D47—22no—
18C22⋊Q8×D47—22no—
19C22⋊Q8×D47C414yescomplemented
20C22⋊Q8×D47C2214yes—
21C22×Dic47⋊C4—21no—
22C2×C4⋊C4×D47—21no—
23C2×C4⋊C4×D47C411yescharacteristic, complemented
24C22×(C2×D47)⋊C4—21no—
25C2×C22⋊C4×D47—21no—
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×(C2×D47)⋊C8—21no—
28C22⋊C8×D47—22no—
29C22⋊C8×D47C2214yes—
30#15688982—22no—
31#15688982C2214yes—
32C2×C47⋊#95C2211yescharacteristic
33#15688861C2214yescomplemented
34#15688860C2214yescomplemented
35#15688859C2214yescomplemented
36C2×C22⋊Q8×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C47×#328C2214yescomplemented
40C24×D47D411yescharacteristic
41C22×Dic94—21no—
42C22×Dic94C2×C411yescharacteristic
43C2×Q8×D47—22no—
44C2×Q8×D47—44no—
45C2×Q8×D47C2×C414yescomplemented
46C23×Dic47—21no—
47C23×Dic47D411yescharacteristic
48C22×C4×D47—21no—
49C22×C4×D47—21no—
50C22×C4×D47—44no—
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47C2×C412yes—
53C22×C4×D47C2×C411yescharacteristic
54C22×C4×D47D411yescharacteristic
55C22×C4×D47D412yes—
56C22×C4×D47D411yescharacteristic
57C22×C4×D47D412yes—
58C22×C4×D47C2312yes—
59C22×C47⋊C8—21no—
60C2×C8×D47—24no—
61C2×C8×D47—44no—
62#13094004—22no—
63#13094004C2×C414yescomplemented
64#13094003—21no—
65#13094003—21no—
66#13094003C2×C412yes—
67#13094003C2312yes—
68#13094002—24no—
69#13094002—24no—
70#13094001—24no—
71#13094001—24no—
72#13094000—22no—
73#13094000C2×C414yescomplemented
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47C2×C411yescharacteristic
76C2×Dic47⋊C4—21no—
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—24no—
80C2×Dic47⋊C4—44no—
81C4⋊C4×D47—24no—
82C4⋊C4×D47—22no—
83C4⋊C4×D47—24no—
84C4⋊C4×D47C2×C414yescomplemented
85C2×C22⋊Dic47—21no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×(C2×D47)⋊C4—24no—
89C2×(C2×D47)⋊C4—44no—
90C22⋊C4×D47—24no—
91C22⋊C4×D47—24no—
92C22⋊(C47⋊C8)—21no—
93C22⋊(C47⋊C8)C2312yes—
94(C2×D47)⋊C8—24no—
95C47⋊#95—21no—
96C47⋊#95C2312yes—
97C22×Q8×C47C2×C411yescharacteristic
98C23×C4×C47—21no—
99C23×C4×C47C2311yescharacteristic
100C22×C8×C47—21no—
101C22⋊Q8×C47—21no—
102C22⋊Q8×C47—21no—
103C22⋊Q8×C47C2×C412yes—
104C22⋊Q8×C47C2312yes—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47C2×C411yescharacteristic
107C2×C22⋊C4×C47—21no—
108C22⋊C8×C47—21no—
109C22⋊C8×C47C2312yes—
110#95×C47—21no—
111#95×C47C2312yes—
112C24×C47C2×D411yescharacteristic
113C23×D47—42no—
114C23×D47—42no—
115C23×D47C22⋊C411yescharacteristic
116C23×D47C22⋊C411yescharacteristic
117C23×D47C22⋊C412yes—
118C23×D47SD1614yes—
119C23×D47Q1614yes—
120C23×D47C2×D412yes—
121C2×Q8×C47—21no—
122C2×Q8×C47—42no—
123C2×Q8×C47C22×C412yes—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—22no—
127C22×C4×C47—42no—
128C22×C4×C47—42no—
129C22×C4×C47—42no—
130C22×C4×C47—42no—
131C22×C4×C47C22×C411yescharacteristic
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2411yescharacteristic
137C22×Dic47—24no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—22no—
141C22×Dic47—42no—
142C22×Dic47—42no—
143C22×Dic47—42no—
144C22×Dic47C22⋊C411yescharacteristic
145C22×Dic47C22⋊C412yes—
146C22×Dic47C22⋊C411yescharacteristic
147C22×Dic47C2×D412yes—
148Q8×D47—48no—
149Q8×D47—48no—
150C2×C4×D47—24no—
151C2×C4×D47—24no—
152C2×C4×D47—24no—
153C2×C4×D47—24no—
154C2×C4×D47—44no—
155C2×C4×D47—44no—
156C2×C4×D47—44no—
157C2×C4×D47—44no—
158C2×C4×D47—42no—
159C2×C4×D47—42no—
160C2×C4×D47—44no—
161C2×C4×D47—44no—
162C2×C4×D47C22⋊C412yes—
163C2×C4×D47C22⋊C412yes—
164C2×C4×D47C22⋊C412yes—
165C2×C4×D47C22⋊C412yes—
166C2×C4×D47C22×C412yes—
167C2×C4×D47C22×C412yes—
168C2×C4×D47C2×D412yes—
169C2×C4×D47C2×D412yes—
170C2×Dic94—21no—
171C2×Dic94—24no—
172C2×Dic94—44no—
173C2×Dic94—42no—
174C2×Dic94C22×C412yes—
175C2×C8×C47—22no—
176C2×C8×C47—42no—
177C4⋊C4×C47—22no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—22no—
180C4⋊C4×C47C22×C412yes—
181C22⋊C4×C47—22no—
182C22⋊C4×C47—22no—
183C22⋊Dic47—22no—
184C22⋊Dic47—22no—
185(C2×D47)⋊C4—24no—
186(C2×D47)⋊C4—24no—
187(C2×D47)⋊C4—48no—
188C4⋊Dic47—21no—
189C4⋊Dic47—24no—
190C4⋊Dic47C22×C412yes—
191Dic47⋊C4—22no—
192Dic47⋊C4—22no—
193Dic47⋊C4—24no—
194Dic47⋊C4—24no—
195Dic47⋊C4—48no—
196C2×C47⋊C8—22no—
197C2×C47⋊C8—42no—
198C8×D47—48no—
199C23×C47—22no—
200C23×C47—22no—
201C23×C47C2×C22⋊C411yescharacteristic
202C23×C47C2×C22⋊C411yescharacteristic
203C23×C47C2×SD1612yes—
204C23×C47C2×Q1612yes—
205C23×C47C22×D411yescharacteristic
206C22×D47—22no—
207C22×D47—22no—
208C22×D47—22no—
209C22×D47—22no—
210C22×D47—42no—
211C22×D47—42no—
212C22×D47—42no—
213C22×D47—48no—
214C22×D47—48no—
215C22×D47—42no—
216C22×D47#10314yes—
217C22×D47#10314yes—
218C22×D47#10318yes—
219C22×D47C2×C22⋊C412yes—
220C22×D47C2×C22⋊C412yes—
221C22×D47C2×SD1614yes—
222C22×D47C2×Q1614yes—
223Q8×C47—42no—
224Q8×C47—42no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47—84no—
239C2×C4×C47C2×C22⋊C411yescharacteristic
240C2×C4×C47C2×C22⋊C411yescharacteristic
241C2×C4×C47C23×C411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×Dic47—22no—
244C2×Dic47—24no—
245C2×Dic47—24no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—84no—
254C2×Dic47#9914yes—
255C2×Dic47C2×C22⋊C412yes—
256C2×Dic47C2×C22⋊C412yes—
257C4×D47—24no—
258C4×D47—24no—
259C4×D47—24no—
260C4×D47—24no—
261C4×D47—42no—
262C4×D47—42no—
263C4×D47—42no—
264C4×D47—42no—
265C4×D47—48no—
266C4×D47—48no—
267Dic94—42no—
268Dic94—48no—
269Dic94—42no—
270C8×C47—42no—
271C47⋊C8—42no—
272C2×#1520—471nomaximal, Sylow
273C22×C47—21no—
274C22×C47—21no—
275C22×C47—21no—
276C22×C47—21no—
277C22×C47—24no—
278C22×C47—24no—
279C22×C47C2×#9912yes—
280C22×C47C2×#10312yes—
281C22×C47C2×#10312yes—
282C22×C47#42112yes—
283C22×C47C22×C22⋊C411yescharacteristic
284C22×C47C22×SD1611yescharacteristic
285C22×C47C22×Q1611yescharacteristic
286C2×D47—22no—
287C2×D47—22no—
288C2×D47—22no—
289C2×D47—22no—
290C2×D47—28no—
291C2×D47—28no—
292C2×D47—48no—
293C2×D47—44no—
294C2×D47—44no—
295C2×D47C2×#10314yes—
296C2×D47C2×#10314yes—
297C4×C47—21no—
298C4×C47—21no—
299C4×C47—21no—
300C4×C47—21no—
301C4×C47—42no—
302C4×C47—42no—
303C4×C47—82no—
304Dic47—22no—
305Dic47—42no—
306Dic47—42no—
307Dic47—82no—
308Dic47C2×#9914yes—
309C22×C22⋊Q8—471no—
310C22×C22⋊C8—471no—
311C2×#380—471no—
312#1520—478no—
313C2×#328—471no—
314C2×#328—471no—
315C2×#328—471no—
316C2×#328D4711yescharacteristic, complemented
317C2×C47—21no—
318C2×C47—21no—
319C2×C47—22no—
320C2×C47#152014yescomplemented
321C2×C47C22×#9911yescharacteristic
322C2×C47C22×#10311yescharacteristic
323C2×C47C2×#42111yescharacteristic
324D47—24no—
325D47—24no—
326C23×Q8—471no—
327C24×C4—471no—
328C23×C8—941no—
329C2×C22⋊Q8—471no—
330C2×C22⋊Q8—471no—
331C2×C22⋊Q8—474no—
332C2×C22⋊Q8—474no—
333C2×C22⋊Q8—471no—
334C2×C22⋊Q8—941no—
335C2×C22⋊Q8—941no—
336C2×C22⋊Q8—942no—
337C2×C22⋊Q8—942no—
338C2×C22⋊Q8C2×D4711yescharacteristic
339C22×C4⋊C4—471no—
340C22×C4⋊C4—941no—
341C22×C4⋊C4—941no—
342C22×C22⋊C4—941no—
343C22×C22⋊C4—941no—
344C2×C22⋊C8—471no—
345C2×C22⋊C8—474no—
346C2×C22⋊C8—942no—
347C2×C22⋊C8—941no—
348C2×C22⋊C8C2×D4711yescharacteristic
349#380—474no—
350#380—942no—
351C2×#95—471no—
352C2×#95C2×D4711yescharacteristic
353#328—474no—
354#328—474no—
355#328—474no—
356#328C2×D4714yescomplemented
357C47C2×#152011yescharacteristic, complemented, Sylow
358C25—471no—
359C22×Q8—474no—
360C22×Q8—471no—
361C22×Q8—941no—
362C22×Q8—942no—
363C22×Q8—1884no—
364C22×Q8C4×D4711yescharacteristic
365C23×C4—21no—
366C23×C4—471no—
367C23×C4—471no—
368C23×C4—471no—
369C23×C4—472no—
370C23×C4—471no—
371C23×C4—471no—
372C23×C4—472no—
373C23×C4—472no—
374C23×C4—472no—
375C23×C4—941no—
376C23×C4—941no—
377C23×C4—941no—
378C23×C4—1884no—
379C23×C4C22×D4711yescharacteristic
380C22×C8—21no—
381C22×C8—944no—
382C22×C8—941no—
383C22×C8—1884no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—474no—
387C22⋊Q8—472no—
388C22⋊Q8—472no—
389C22⋊Q8—474no—
390C22⋊Q8—944no—
391C22⋊Q8—944no—
392C22⋊Q8—944no—
393C22⋊Q8—944no—
394C22⋊Q8—942no—
395C22⋊Q8—942no—
396C22⋊Q8—941no—
397C22⋊Q8—941no—
398C22⋊Q8C4×D4712yes—
399C22⋊Q8C22×D4712yes—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—471no—
402C2×C4⋊C4—474no—
403C2×C4⋊C4—942no—
404C2×C4⋊C4—944no—
405C2×C4⋊C4—944no—
406C2×C4⋊C4—941no—
407C2×C4⋊C4—941no—
408C2×C4⋊C4—941no—
409C2×C4⋊C4—941no—
410C2×C4⋊C4—944no—
411C2×C4⋊C4—1884no—
412C2×C4⋊C4C4×D4711yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—944no—
415C2×C22⋊C4—944no—
416C2×C22⋊C4—941no—
417C2×C22⋊C4—941no—
418C2×C22⋊C4—941no—
419C2×C22⋊C4—944no—
420C2×C22⋊C4—1884no—
421C22⋊C8—21no—
422C22⋊C8—472no—
423C22⋊C8—944no—
424C22⋊C8—941no—
425C22⋊C8C22×D4712yes—
426#95—21no—
427#95—472no—
428#95—941no—
429#95C22×D4712yes—
430C24—471no—
431C24—471no—
432C24—472no—
433C24—474no—
434C24—474no—
435C24—472no—
436C24—1882no—
437C24—1882no—
438C24D4×D4711yescharacteristic
439C2×Q8—21no—
440C2×Q8—42no—
441C2×Q8—472no—
442C2×Q8—944no—
443C2×Q8—941no—
444C2×Q8—1882no—
445C2×Q8—1884no—
446C2×Q8—1888no—
447C2×Q8—1888no—
448C2×Q8C2×C4×D4712yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—471no—
457C22×C4—472no—
458C22×C4—471no—
459C22×C4—472no—
460C22×C4—472no—
461C22×C4—472no—
462C22×C4—472no—
463C22×C4—472no—
464C22×C4—472no—
465C22×C4—472no—
466C22×C4—472no—
467C22×C4—472no—
468C22×C4—944no—
469C22×C4—944no—
470C22×C4—944no—
471C22×C4—944no—
472C22×C4—944no—
473C22×C4—941no—
474C22×C4—941no—
475C22×C4—942no—
476C22×C4—1882no—
477C22×C4—1882no—
478C22×C4—1884no—
479C22×C4—1884no—
480C22×C4—1884no—
481C22×C4—1884no—
482C22×C4—1884no—
483C22×C4—1884no—
484C22×C4—1882no—
485C22×C4—1882no—
486C22×C4—1882no—
487C22×C4C2×C4×D4711yescharacteristic
488C22×C4C2×C4×D4711yescharacteristic
489C22×C4D4×D4711yescharacteristic
490C22×C4D4×D4711yescharacteristic
491C22×C4D4×D4711yescharacteristic
492C22×C4C23×D4711yescharacteristic
493C2×C8—22no—
494C2×C8—42no—
495C2×C8—942no—
496C2×C8—1888no—
497C2×C8—1882no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—472no—
502C4⋊C4—944no—
503C4⋊C4—944no—
504C4⋊C4—944no—
505C4⋊C4—942no—
506C4⋊C4—941no—
507C4⋊C4—942no—
508C4⋊C4—1888no—
509C4⋊C4C2×C4×D4712yes—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—944no—
513C22⋊C4—944no—
514C22⋊C4—942no—
515C22⋊C4—942no—
516C22⋊C4—1888no—
517C23—22no—
518C23—22no—
519C23—472no—
520C23—472no—
521C23—474no—
522C23—474no—
523C23—478no—
524C23—474no—
525C23—474no—
526C23—942no—
527C23—942no—
528C23—942no—
529C23—942no—
530C23—1882no—
531C23—1882no—
532C23—1882no—
533C23—1882no—
534C23—1888no—
535C23—1888no—
536C23C22⋊C4×D4711yescharacteristic
537C23C22⋊C4×D4711yescharacteristic
538C23SD16×D4712yes—
539C23Q16×D4712yes—
540C23C2×D4×D4711yescharacteristic
541Q8—42no—
542Q8—42no—
543Q8—1882no—
544Q8—1882no—
545Q8—1888no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—84no—
560C2×C4—472no—
561C2×C4—474no—
562C2×C4—472no—
563C2×C4—944no—
564C2×C4—944no—
565C2×C4—944no—
566C2×C4—944no—
567C2×C4—944no—
568C2×C4—944no—
569C2×C4—942no—
570C2×C4—942no—
571C2×C4—942no—
572C2×C4—3764no—
573C2×C4—1882no—
574C2×C4—1882no—
575C2×C4—1882no—
576C2×C4—1882no—
577C2×C4—1888no—
578C2×C4—1888no—
579C2×C4—1882no—
580C2×C4—1882no—
581C2×C4—1882no—
582C2×C4—1882no—
583C2×C4—1882no—
584C2×C4C22⋊C4×D4711yescharacteristic
585C2×C4C22⋊C4×D4711yescharacteristic
586C2×C4C22×C4×D4711yescharacteristic
587C2×C4C2×D4×D4711yescharacteristic
588C8—42no—
589C8—1882no—
590C22—21no—
591C22—21no—
592C22—24no—
593C22—24no—
594C22—21no—
595C22—21no—
596C22—474no—
597C22—474no—
598C22—942no—
599C22—942no—
600C22—948no—
601C22—948no—
602C22—942no—
603C22—942no—
604C22—1884no—
605C22—1888no—
606C22—1884no—
607C22#99×D4712yes—
608C22#103×D4712yes—
609C22#103×D4712yes—
610C22#1568913812yes—
611C22C2×C22⋊C4×D4711yescharacteristic
612C22C2×SD16×D4711yescharacteristic
613C22C2×Q16×D4711yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—42no—
620C4—82no—
621C4—474no—
622C4—942no—
623C4—3762no—
624C4—1882no—
625C4—1882no—
626C2—21no—
627C2—22no—
628C2—21no—
629C2—944no—
630C2—944no—
631C2#2024195814yesdirect product factor
632C2C2×#99×D4711yescharacteristic
633C2C2×#103×D4711yescharacteristic
634C2C2×#1568913811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#328C2
socleC23×C47C2×C22⋊C4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenterC2×#328D47
hypocenterC47C2×#1520
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. #20241958C2direct (N × H)
5. C2×#15688861C2semidirect
6. C2×#15688860C2semidirect
7. C2×#15688859C2semidirect
8. C2×C47×#328C2semidirect
9. C22×Q8×D47C4semidirect
12. C2×#13094004C4semidirect
16. C2×#13094000C4semidirect
19. C22⋊Q8×D47C4semidirect
23. C2×C4⋊C4×D47C4semidirect
33. #15688861C22semidirect
34. #15688860C22semidirect
35. #15688859C22semidirect
39. C47×#328C22semidirect
45. C2×Q8×D47C2×C4semidirect
63. #13094004C2×C4semidirect
73. #13094000C2×C4semidirect
84. C4⋊C4×D47C2×C4semidirect
316. C2×#328D47semidirect
320. C2×C47#1520semidirect
356. #328C2×D47semidirect
357. C47C2×#1520semidirect
631. C2#20241958direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D472
C2×C22⋊C8×D472
C2×#156889822
#202419582
C2×#156888612
C2×#156888602
C2×#156888592
C2×C47×#3282
C2×#152047