Finite Group Databasebeta

← C2×#20241893 #26183419

Subgroups — C2×#20241893 #26183419

Order 12032.

1834 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C22×C47⋊#95C211yesmaximal, characteristic, complemented
3#20241893C218yesmaximal, direct product factor
4C2×#15688861C212yesmaximal, complemented
5C2×#15688858C212yesmaximal, complemented
6C2×C47×#407C211yesmaximal, characteristic, complemented
7C22×#10625350C411yescharacteristic, complemented
8C24×Dic47—21no—
9#15689634—22no—
10#15689634—22no—
11#15689634C414yescomplemented
12#15689634C2214yes—
13C2×#13094007—21no—
14C2×#13094003C411yescharacteristic, complemented
15C2×#13094003C2211yescharacteristic
16C2×#13093998C411yescharacteristic, complemented
17C2×#13093998C2211yescharacteristic
18C2×#13093993—21no—
19C2×C4×C22⋊D47—21no—
20C2×C4×C22⋊D47—21no—
21C2×#13093983C411yescharacteristic, complemented
22C2×C47⋊#95—21no—
23C2×C47⋊#95—22no—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2214yescomplemented
26#15688861C2218yescomplemented
27#15688858C2218yescomplemented
28C24×C4×C47C2211yescharacteristic
29C22×M16×C47—21no—
30C47×#407—22no—
31C47×#407C2214yescomplemented
32C2×C22⋊C8×C47—21no—
33C2×C22⋊C8×C47C2212yes—
34C2×#10625350—22no—
35C2×#10625350—44no—
36C2×#10625350C2×C414yescomplemented
37C22×Dic94C2×C411yescharacteristic, complemented
38C22×D188C2×C411yescharacteristic, complemented
39C22×C22⋊D47—21no—
40C22×C22⋊D47—21no—
41C22×C22⋊D47—21no—
42C23×Dic47—28no—
43C23×Dic47—22no—
44C23×Dic47—24no—
45C23×Dic47—44no—
46C23×Dic47—44no—
47C22×C4×D47—21no—
48#13094007—24no—
49#13094007—24no—
50#13094003—22no—
51#13094003—21no—
52#13094003—21no—
53#13094003C2×C414yescomplemented
54#13094003C2×C412yescomplemented
55#13094003C2312yes—
56#13093998—22no—
57#13093998—21no—
58#13093998—21no—
59#13093998C2×C414yescomplemented
60#13093998C2×C412yescomplemented
61#13093998C2312yes—
62#13093993—24no—
63#13093993—24no—
64C4×C22⋊D47—24no—
65C4×C22⋊D47—24no—
66C4×C22⋊D47—24no—
67C4×C22⋊D47—24no—
68#13093983—22no—
69#13093983C2×C414yescomplemented
70C2×C4⋊Dic47C2×C411yescharacteristic, complemented
71C2×C4⋊Dic47C2×C411yescharacteristic, complemented
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×C22⋊Dic47—21no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×C4×Dic47—21no—
80C47⋊#95—22no—
81C47⋊#95—24no—
82C47⋊#95C2314yes—
83C25×C47D411yescharacteristic
84C23×C4×C47—44no—
85C23×C4×C47C2×C411yescharacteristic
86C23×C4×C47C2×C411yescharacteristic
87C23×C4×C47C2×C412yes—
88C23×C4×C47D411yescharacteristic
89C23×C4×C47D411yescharacteristic
90C23×C4×C47D412yes—
91C23×C4×C47D411yescharacteristic
92C23×C4×C47D412yes—
93C23×C4×C47C2311yescharacteristic
94C23×C4×C47C2312yes—
95C2×M16×C47—24no—
96C2×M16×C47—44no—
97C22×C8×C47—22no—
98C22⋊C8×C47—24no—
99C22⋊C8×C47—22no—
100C22⋊C8×C47C2314yes—
101C24×C47—24no—
102C24×C47—24no—
103C24×C47—22no—
104C24×C47—22no—
105C24×C47C22⋊C412yes—
106C24×C47C22⋊C411yescharacteristic
107C24×C47C22⋊C411yescharacteristic
108C24×C47C2×D412yes—
109C24×C47C2×D411yescharacteristic
110C23×D47—21no—
111C22×C4×C47—24no—
112C22×C4×C47—24no—
113C22×C4×C47—42no—
114C22×C4×C47—44no—
115C22×C4×C47—42no—
116C22×C4×C47—44no—
117C22×C4×C47—42no—
118C22×C4×C47—44no—
119C22×C4×C47—42no—
120C22×C4×C47—44no—
121C22×C4×C47C22⋊C411yescharacteristic
122C22×C4×C47C22⋊C411yescharacteristic
123C22×C4×C47C22⋊C412yes—
124C22×C4×C47C22⋊C412yes—
125C22×C4×C47C22⋊C412yes—
126C22×C4×C47C22⋊C412yes—
127C22×C4×C47C22⋊C412yes—
128C22×C4×C47C22×C411yescharacteristic
129C22×C4×C47C22×C412yes—
130C22×C4×C47C22×C411yescharacteristic
131C22×C4×C47C22×C412yes—
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D412yes—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2411yescharacteristic
139C2×C22⋊D47—22no—
140C2×C22⋊D47—24no—
141C2×C22⋊D47—24no—
142C2×C22⋊D47—22no—
143C2×C22⋊D47—44no—
144C2×C22⋊D47—44no—
145C2×C22⋊D47—42no—
146C2×C22⋊D47—42no—
147C22×Dic47—28no—
148C22×Dic47—216no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—24no—
153C22×Dic47—432no—
154C22×Dic47—44no—
155C22×Dic47—48no—
156C22×Dic47—48no—
157C22×Dic47—44no—
158#10625350—48no—
159#10625350—48no—
160C2×D188—21no—
161C2×D188—42no—
162C2×D188C22×C412yescomplemented
163C2×C4×D47—24no—
164C2×C4×D47—44no—
165C2×Dic94—21no—
166C2×Dic94—42no—
167C2×Dic94C22×C412yescomplemented
168M16×C47—48no—
169C2×C8×C47—24no—
170C2×C8×C47—44no—
171C22⋊Dic47—24no—
172C22⋊Dic47—22no—
173C22⋊Dic47—24no—
174C22⋊Dic47—22no—
175(C2×D47)⋊C4—24no—
176(C2×D47)⋊C4—22no—
177(C2×D47)⋊C4—22no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47C22×C412yescomplemented
181C4⋊Dic47C22×C412yescomplemented
182Dic47⋊C4—24no—
183Dic47⋊C4—22no—
184Dic47⋊C4—22no—
185C4×Dic47—24no—
186C23×C47—216no—
187C23×C47—216no—
188C23×C47—22no—
189C23×C47—22no—
190C23×C47—24no—
191C23×C47—22no—
192C23×C47—24no—
193C23×C47—22no—
194C23×C47—24no—
195C23×C47—22no—
196C23×C47—22no—
197C23×C47—24no—
198C23×C47—22no—
199C23×C47—24no—
200C23×C47—22no—
201C23×C47#9914yes—
202C23×C47#10414yes—
203C23×C47C2×C22⋊C412yes—
204C23×C47C2×C22⋊C411yescharacteristic
205C23×C47C2×C22⋊C412yes—
206C23×C47C2×C22⋊C411yescharacteristic
207C23×C47AGL(1,ℤ/8)12yes—
208C23×C47#13712yes—
209C23×C47C22×D411yescharacteristic
210C22×D47—22no—
211C22×D47—42no—
212C22×D47—42no—
213C22×D47—42no—
214C2×C4×C47—22no—
215C2×C4×C47—24no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—24no—
219C2×C4×C47—24no—
220C2×C4×C47—24no—
221C2×C4×C47—22no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—41no—
226C2×C4×C47—42no—
227C2×C4×C47—41no—
228C2×C4×C47—42no—
229C2×C4×C47—41no—
230C2×C4×C47—42no—
231C2×C4×C47—41no—
232C2×C4×C47C2×C22⋊C412yes—
233C2×C4×C47C2×C22⋊C412yes—
234C2×C4×C47C2×C22⋊C411yescharacteristic
235C2×C4×C47C2×C22⋊C411yescharacteristic
236C2×C4×C47C23×C411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C22⋊D47—42no—
239C22⋊D47—42no—
240C22⋊D47—48no—
241C22⋊D47—44no—
242C22⋊D47—48no—
243C2×Dic47—28no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—432no—
248C2×Dic47—44no—
249C2×Dic47—416no—
250C2×Dic47—44no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254D188—42no—
255D188—42no—
256C4×D47—48no—
257Dic94—42no—
258Dic94—42no—
259C8×C47—44no—
260C2×#1504—471nomaximal, Sylow
261C22×C47—28no—
262C22×C47—28no—
263C22×C47—216no—
264C22×C47—21no—
265C22×C47—21no—
266C22×C47—22no—
267C22×C47—22no—
268C22×C47—22no—
269C22×C47—21no—
270C22×C47—22no—
271C22×C47—21no—
272C22×C47—24no—
273C22×C47—28no—
274C22×C47—28no—
275C22×C47—24no—
276C22×C47C2×#9914yes—
277C22×C47C2×#9912yes—
278C22×C47#41712yes—
279C22×C47#41712yes—
280C22×C47C2×#10414yes—
281C22×C47C2×#10412yes—
282C22×C47C22×C22⋊C411yescharacteristic
283C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C47C2×#13711yescharacteristic
285C2×D47—42no—
286C2×D47—42no—
287C2×D47—42no—
288C2×D47—84no—
289C4×C47—21no—
290C4×C47—21no—
291C4×C47—21no—
292C4×C47—22no—
293C4×C47—21no—
294C4×C47—22no—
295Dic47—48no—
296Dic47—42no—
297Dic47—42no—
298Dic47—42no—
299C2×#525—471no—
300C2×#407D4711yescharacteristic, complemented
301C22×#95—471no—
302#1504—478no—
303C2×#328—472no—
304C2×#327—472no—
305C2×C47—21no—
306C2×C47—21no—
307C2×C47—24no—
308C2×C47—22no—
309C2×C47—24no—
310C2×C47#150414yescomplemented
311C2×C47C22×#9911yescharacteristic
312C2×C47C2×#41711yescharacteristic
313C2×C47C22×#10411yescharacteristic
314D47—82no—
315C22×#41—471no—
316C24×C4—941no—
317C24×C4C2×D4711yescharacteristic
318C22×M16—21no—
319#525—474no—
320#525—474no—
321#525—942no—
322#525—942no—
323C2×#123—941no—
324C2×C22⋊Q8—471no—
325C2×C22⋊Q8—471no—
326C2×#121—471no—
327C2×#121—471no—
328C2×#120—941no—
329C2×C4×D4—941no—
330C2×C4×D4—941no—
331C2×#117—471no—
332#407—22no—
333#407C2×D4714yescomplemented
334C2×C22⋊C8—21no—
335C2×C22⋊C8C2×D4712yes—
336C2×#95—472no—
337C2×#95—474no—
338C2×#95—941no—
339C2×#95—942no—
340#328—478no—
341#327—478no—
342C47C2×#150411yescharacteristic, complemented, Sylow
343C25D18811yescharacteristic
344C2×#41—474no—
345C2×#41—942no—
346C2×#41—1884no—
347C22×Q8—471no—
348C22×D4—471no—
349C22×D4—941no—
350C22×D4—941no—
351C22×D4—941no—
352C23×C4—44no—
353C23×C4—948no—
354C23×C4—944no—
355C23×C4—942no—
356C23×C4—941no—
357C23×C4—1884no—
358C23×C4—1884no—
359C23×C4C4×D4711yescharacteristic
360C23×C4C4×D4711yescharacteristic
361C23×C4C4×D4712yes—
362C23×C4D18811yescharacteristic
363C23×C4D18812yes—
364C23×C4C22⋊D4711yescharacteristic
365C23×C4C22⋊D4711yescharacteristic
366C23×C4C22⋊D4712yes—
367C23×C4C22×D4711yescharacteristic
368C23×C4C22×D4712yes—
369C2×M16—24no—
370C2×M16—44no—
371C22×C8—22no—
372#123—944no—
373#123—944no—
374C22⋊Q8—474no—
375C22⋊Q8—472no—
376C22⋊Q8—472no—
377C22⋊Q8—942no—
378C22⋊Q8—941no—
379C22⋊Q8—941no—
380#121—474no—
381#121—472no—
382#121—472no—
383#121—942no—
384#121—941no—
385#121—941no—
386#120—944no—
387#120—944no—
388C4×D4—944no—
389C4×D4—944no—
390C4×D4—944no—
391C4×D4—944no—
392#117—474no—
393#117—942no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C22⋊C4—941no—
399C2×C22⋊C4—941no—
400C2×C22⋊C4—941no—
401C2×C22⋊C4—941no—
402C2×C22⋊C4—941no—
403C2×C42—941no—
404C22⋊C8—24no—
405C22⋊C8—22no—
406C22⋊C8C22×D4714yes—
407#95—474no—
408#95—944no—
409#95—942no—
410C24—24no—
411C24—24no—
412C24—22no—
413C24—22no—
414C24—941no—
415C24(C2×D47)⋊C412yes—
416C24(C2×D47)⋊C411yescharacteristic
417C24(C2×D47)⋊C411yescharacteristic
418C24C2×D18812yes—
419C24C2×D18811yescharacteristic
420#41—1888no—
421#41—1888no—
422C2×Q8—472no—
423C2×Q8—941no—
424C2×Q8—1882no—
425C2×D4—472no—
426C2×D4—942no—
427C2×D4—944no—
428C2×D4—944no—
429C2×D4—942no—
430C2×D4—941no—
431C2×D4—1882no—
432C2×D4—1884no—
433C2×D4—1884no—
434C2×D4—1882no—
435C2×D4—1882no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—42no—
439C22×C4—44no—
440C22×C4—42no—
441C22×C4—44no—
442C22×C4—42no—
443C22×C4—44no—
444C22×C4—42no—
445C22×C4—44no—
446C22×C4—9416no—
447C22×C4—948no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—944no—
452C22×C4—944no—
453C22×C4—1884no—
454C22×C4—18832no—
455C22×C4—1888no—
456C22×C4—1884no—
457C22×C4—1888no—
458C22×C4—1884no—
459C22×C4(C2×D47)⋊C412yes—
460C22×C4(C2×D47)⋊C412yes—
461C22×C4(C2×D47)⋊C411yescharacteristic
462C22×C4(C2×D47)⋊C411yescharacteristic
463C22×C4(C2×D47)⋊C412yes—
464C22×C4(C2×D47)⋊C412yes—
465C22×C4(C2×D47)⋊C412yes—
466C22×C4C2×C4×D4712yes—
467C22×C4C2×C4×D4711yescharacteristic
468C22×C4C2×C4×D4711yescharacteristic
469C22×C4C2×C4×D4712yes—
470C22×C4C2×D18812yes—
471C22×C4C2×D18811yescharacteristic
472C22×C4C2×C22⋊D4712yes—
473C22×C4C2×C22⋊D4711yescharacteristic
474C22×C4C2×C22⋊D4712yes—
475C22×C4C2×C22⋊D4711yescharacteristic
476C22×C4C23×D4711yescharacteristic
477M16—48no—
478C2×C8—24no—
479C2×C8—44no—
480C4⋊C4—472no—
481C4⋊C4—472no—
482C4⋊C4—944no—
483C4⋊C4—942no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—942no—
487C22⋊C4—944no—
488C22⋊C4—942no—
489C22⋊C4—944no—
490C22⋊C4—942no—
491C22⋊C4—944no—
492C22⋊C4—942no—
493C22⋊C4—942no—
494C42—944no—
495C23—216no—
496C23—216no—
497C23—24no—
498C23—22no—
499C23—24no—
500C23—22no—
501C23—24no—
502C23—22no—
503C23—22no—
504C23—24no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—942no—
511C23—1882no—
512C23—1882no—
513C23—1882no—
514C23#1309393814yes—
515C23#1309395014yes—
516C23C2×(C2×D47)⋊C412yes—
517C23C2×(C2×D47)⋊C411yescharacteristic
518C23C2×(C2×D47)⋊C412yes—
519C23C2×(C2×D47)⋊C411yescharacteristic
520C23#1309405212yes—
521C23#1309405712yes—
522C23C22×D18811yescharacteristic
523Q8—1882no—
524Q8—1882no—
525D4—1882no—
526D4—1882no—
527D4—1888no—
528D4—1884no—
529D4—1888no—
530D4—1882no—
531D4—1882no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—948no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—1888no—
555C2×C4—18832no—
556C2×C4—1884no—
557C2×C4—18816no—
558C2×C4—1882no—
559C2×C4—1882no—
560C2×C4—1882no—
561C2×C4—1884no—
562C2×C4C2×(C2×D47)⋊C412yes—
563C2×C4C2×(C2×D47)⋊C411yescharacteristic
564C2×C4C2×(C2×D47)⋊C412yes—
565C2×C4C2×(C2×D47)⋊C411yescharacteristic
566C2×C4C22×C4×D4711yescharacteristic
567C2×C4C22×C22⋊D4711yescharacteristic
568C8—44no—
569C22—28no—
570C22—216no—
571C22—28no—
572C22—21no—
573C22—22no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—22no—
578C22—24no—
579C22—28no—
580C22—28no—
581C22—24no—
582C22—22no—
583C22—22no—
584C22—3764no—
585C22—1882no—
586C22—1882no—
587C22—1882no—
588C22C2×#1309393814yes—
589C22C2×#1309393812yes—
590C22#1568912512yes—
591C22#1568912512yes—
592C22C2×#1309395014yes—
593C22C2×#1309395012yes—
594C22C22×(C2×D47)⋊C411yescharacteristic
595C22C2×#1309405211yescharacteristic
596C22C2×#1309405711yescharacteristic
597C4—21no—
598C4—22no—
599C4—21no—
600C4—21no—
601C4—22no—
602C4—21no—
603C4—1888no—
604C4—1882no—
605C4—1882no—
606C4—1882no—
607C2—21no—
608C2—24no—
609C2—22no—
610C2—24no—
611C2—21no—
612C2—3762no—
613C2#2024189314yesdirect product factor
614C2C22×#1309393811yescharacteristic
615C2C2×#1568912511yescharacteristic
616C2C22×#1309395011yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#407C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenterC2×#407D47
hypocenterC47C2×#1504
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×C47⋊#95C2semidirect
3. #20241893C2direct (N × H)
4. C2×#15688861C2semidirect
5. C2×#15688858C2semidirect
6. C2×C47×#407C2semidirect
7. C22×#10625350C4semidirect
11. #15689634C4semidirect
14. C2×#13094003C4semidirect
16. C2×#13093998C4semidirect
21. C2×#13093983C4semidirect
25. C2×C47⋊#95C22semidirect
26. #15688861C22semidirect
27. #15688858C22semidirect
31. C47×#407C22semidirect
36. C2×#10625350C2×C4semidirect
37. C22×Dic94C2×C4semidirect
38. C22×D188C2×C4semidirect
53. #13094003C2×C4semidirect
54. #13094003C2×C4semidirect
59. #13093998C2×C4semidirect
60. #13093998C2×C4semidirect
69. #13093983C2×C4semidirect
70. C2×C4⋊Dic47C2×C4semidirect
71. C2×C4⋊Dic47C2×C4semidirect
162. C2×D188C22×C4semidirect
167. C2×Dic94C22×C4semidirect
180. C4⋊Dic47C22×C4semidirect
181. C4⋊Dic47C22×C4semidirect
300. C2×#407D47semidirect
310. C2×C47#1504semidirect
333. #407C2×D47semidirect
342. C47C2×#1504semidirect
613. C2#20241893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896342
C22×C47⋊#952
#202418932
C2×#156888612
C2×#156888582
C2×C47×#4072
C2×#150447