Finite Group Databasebeta

← C4×#15689262 #26221869

Subgroups — C4×#15689262 #26221869

Order 12032.

1532 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689262C211yesmaximal, characteristic
2C2×C4×#10625336C212yesmaximal, complemented
3C4×#13093998C211yesmaximal, characteristic
4#20243743C212yesmaximal, complemented
5#20243705C211yesmaximal, characteristic
6#20243656C212yesmaximal, complemented
7#20243581C211yesmaximal, characteristic, complemented
8#20243323C211yesmaximal, characteristic, complemented
9C4×#13093948C212yesmaximal, complemented
10C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
11C22×C4×Q8×C47C211yesmaximal, characteristic, complemented
12C22×#10625336C2212yes—
13C2×#13093998C2211yescharacteristic
14C2×C4×D188C2211yescharacteristic
15C2×C4×C22⋊D47—21no—
16#15689262C418yesdirect product factor
17C4×#10625336—28no—
18C2×#13093955C2212yes—
19C2×#13093948C2212yes—
20C2×#13093948C2212yes—
21C2×#13093948C2212yes—
22C2×#13093944C2212yes—
23C2×C22⋊(C47⋊C8)C2211yescharacteristic
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25C2×C4×C47⋊C8C2212yes—
26#15689025C2211yescharacteristic
27#15689021C2211yescharacteristic
28#15689014—21no—
29#15689002—21no—
30#15688983C2211yescharacteristic
31C4×C4⋊Dic47C2211yescharacteristic
32C4×(C2×D47)⋊C4—21no—
33#15688885C2212yes—
34#15688885C2212yes—
35#15688878C2212yes—
36C23×Q8×C47C2211yescharacteristic
37C2×C4×Q8×C47—28no—
38C2×C4×Q8×C47—21no—
39C2×C4×Q8×C47—21no—
40C2×C4×Q8×C47C2212yes—
41C2×C4×Q8×C47C2212yes—
42C22×C4⋊C4×C47—21no—
43C22×C4⋊C4×C47C2211yescharacteristic
44C22×C42×C47—21no—
45C22×C42×C47C2211yescharacteristic
46C22×D188C2311yescharacteristic
47C22×C22⋊D47—21no—
48C22×C4×D47—21no—
49C2×#10625336—24no—
50C2×#10625336—24no—
51C2×#10625336C2×C418yescomplemented
52C22×C47⋊C8C2312yes—
53C22×C47⋊C8C2312yes—
54#13093998—22no—
55#13093998C2×C414yes—
56C4×D188—24no—
57C4×C22⋊D47—44no—
58C2×C4⋊Dic47C2311yescharacteristic
59C2×C4⋊Dic47C2311yescharacteristic
60C2×C4⋊Dic47C2311yescharacteristic
61C2×Dic47⋊C4—21no—
62C2×C22⋊Dic47—21no—
63C2×(C2×D47)⋊C4—21no—
64C2×(C2×D47)⋊C4—21no—
65C2×(C2×D47)⋊C4—21no—
66C2×(C2×D47)⋊C4—21no—
67C2×C4×Dic47—21no—
68#13093955—24no—
69#13093948—24no—
70#13093948—24no—
71#13093948C2×C418yescomplemented
72#13093944—24no—
73C22⋊(C47⋊C8)—22no—
74C22⋊(C47⋊C8)C2×C414yescomplemented
75C4×C47⋊C8—24no—
76C47⋊#95—21no—
77C47⋊#95—21no—
78C47⋊#95—21no—
79C22×Q8×C47—24no—
80C22×Q8×C47—24no—
81C22×Q8×C47—21no—
82C22×Q8×C47—22no—
83C22×Q8×C47C2×C414yescomplemented
84C22×Q8×C47C2312yes—
85C23×C4×C47—21no—
86C23×C4×C47—21no—
87C23×C4×C47D411yescharacteristic
88C23×C4×C47D411yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C4×Q8×C47—28no—
91C4×Q8×C47—28no—
92C4×Q8×C47—24no—
93C4×Q8×C47—24no—
94C4×Q8×C47—24no—
95C4×Q8×C47D418yescomplemented
96C2×C4⋊C4×C47—28no—
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47—22no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—24no—
101C2×C4⋊C4×C47C2312yes—
102C2×C42×C47—28no—
103C2×C42×C47—22no—
104C2×C42×C47—22no—
105C2×C42×C47—24no—
106C2×C42×C47D411yescharacteristic
107C2×C42×C47D411yescharacteristic
108C2×C42×C47C2311yescharacteristic
109C2×C42×C47C2311yescharacteristic
110C24×C47C2×D411yescharacteristic
111C23×D47—21no—
112C2×Q8×C47—24no—
113C2×Q8×C47—216no—
114C2×Q8×C47—24no—
115C2×Q8×C47—216no—
116C2×Q8×C47—24no—
117C2×Q8×C47—22no—
118C2×Q8×C47—22no—
119C2×Q8×C47—22no—
120C2×Q8×C47C22×C414yes—
121C2×Q8×C47C2×D414yes—
122C2×Q8×C47#4114yes—
123C22×C4×C47—24no—
124C22×C4×C47—24no—
125C22×C4×C47—24no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—24no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—41no—
136C22×C4×C47—42no—
137C22×C4×C47—42no—
138C22×C4×C47SD1614yescomplemented
139C22×C4×C47C22×C412yes—
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47#4112yes—
146C22×C4×C47C2411yescharacteristic
147C2×C22⋊D47—24no—
148C2×C22⋊D47—42no—
149C2×C22⋊D47—42no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C2×D188—22no—
154C2×D188—22no—
155C2×D188—21no—
156C2×D188C22×C412yes—
157C2×C4×D47—42no—
158C2×C4×D47—42no—
159C2×C4×D47—42no—
160C4⋊C4×C47—28no—
161C4⋊C4×C47—24no—
162C4⋊C4×C47—28no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47C2×D414yes—
165C42×C47—28no—
166C42×C47—28no—
167C42×C47—22no—
168C42×C47—22no—
169C42×C47—22no—
170C42×C47C2×D414yes—
171C22⋊Dic47—42no—
172#10625336—216no—
173(C2×D47)⋊C4—24no—
174(C2×D47)⋊C4—42no—
175(C2×D47)⋊C4—42no—
176(C2×D47)⋊C4—42no—
177C4⋊Dic47—21no—
178C4⋊Dic47—22no—
179C4⋊Dic47—22no—
180C4⋊Dic47C22×C412yes—
181Dic47⋊C4—42no—
182C4×Dic47—42no—
183C2×C47⋊C8—22no—
184C2×C47⋊C8—22no—
185C2×C47⋊C8—22no—
186C2×C47⋊C8—22no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8C22×C414yes—
189C23×C47—21no—
190C23×C47—21no—
191C23×C47—21no—
192C23×C47—21no—
193C23×C47C4×D412yes—
194C23×C47C2×SD1612yes—
195C23×C47#13512yes—
196C23×C47C22×D411yescharacteristic
197C22×D47—22no—
198C22×D47—41no—
199C22×D47—41no—
200C22×D47—41no—
201C22×D47—41no—
202C22×D47—41no—
203C22×D47—41no—
204Q8×C47—216no—
205Q8×C47—24no—
206Q8×C47—24no—
207Q8×C47—24no—
208Q8×C47C4×D418yescomplemented
209C2×C4×C47—216no—
210C2×C4×C47—24no—
211C2×C4×C47—21no—
212C2×C4×C47—24no—
213C2×C4×C47—21no—
214C2×C4×C47—24no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—24no—
220C2×C4×C47—24no—
221C2×C4×C47—28no—
222C2×C4×C47—21no—
223C2×C4×C47—24no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—44no—
227C2×C4×C47—48no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47C4×D412yes—
231C2×C4×C47#12012yes—
232C2×C4×C47#12012yes—
233C2×C4×C47C2×SD1612yes—
234C2×C4×C47C2×SD1612yes—
235C2×C4×C47#13712yes—
236C2×C4×C47C23×C411yescharacteristic
237C2×C4×C47C22×D412yes—
238C2×C4×C47C2×#4112yes—
239C2×C4×C47C2×#4111yescharacteristic
240C22⋊D47—48no—
241C2×Dic47—22no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250D188—24no—
251D188—42no—
252C4×D47—84no—
253C47⋊C8—24no—
254C47⋊C8—42no—
255C4×#448—471nomaximal, Sylow
256C22×C47—22no—
257C22×C47—22no—
258C22×C47—22no—
259C22×C47—22no—
260C22×C47—22no—
261C22×C47—22no—
262C22×C47C4×SD1614yescomplemented
263C22×C47C2×C4×D411yescharacteristic
264C22×C47C2×#12011yescharacteristic
265C22×C47#52511yescharacteristic
266C22×C47C22×SD1611yescharacteristic
267C22×C47C2×#13511yescharacteristic
268C22×C47C2×#13711yescharacteristic
269C22×C47#57511yescharacteristic
270C2×D47—42no—
271C2×D47—42no—
272C2×D47—42no—
273C2×D47—81no—
274C2×D47—81no—
275C2×D47—81no—
276C2×D47—81no—
277C4×C47—22no—
278C4×C47—22no—
279C4×C47—28no—
280C4×C47—22no—
281C4×C47—41no—
282C4×C47—44no—
283C4×C47#44814yescomplemented
284C4×C47C2×C4×D412yes—
285C4×C47#52512yes—
286Dic47—42no—
287Dic47—81no—
288Dic47—81no—
289C22×C4×Q8D4711yescharacteristic, complemented
290C2×#448—471no—
291C2×C4×SD16—472no—
292C4×#121—471no—
293#1880—472no—
294#1874—471no—
295#1865—472no—
296#1853—471no—
297#1787—471no—
298C4×#103—472no—
299C4×C22⋊C8—471no—
300C2×C47—24no—
301C2×C47C4×#12011yescharacteristic
302C2×C47C2×C4×SD1611yescharacteristic
303C2×C47C4×#13711yescharacteristic
304C2×C47C2×#44811yescharacteristic
305C2×C47#300211yescharacteristic
306C2×C47#310311yescharacteristic
307C2×C47#310811yescharacteristic
308D47—82no—
309C23×Q8C2×D4711yescharacteristic
310C22×SD16—472no—
311C2×#121—471no—
312C2×C4×Q8—28no—
313C2×C4×Q8—21no—
314C2×C4×Q8—21no—
315C2×C4×Q8C2×D4712yes—
316C2×C4×Q8C2×D4712yes—
317C2×C4×D4—471no—
318C2×C4×D4—941no—
319C22×C4⋊C4—21no—
320C22×C4⋊C4C2×D4711yescharacteristic
321C22×C42—21no—
322C22×C42C2×D4711yescharacteristic
323#448—478no—
324C4×SD16—948no—
325C2×#106—472no—
326C2×#103—472no—
327C2×#103—472no—
328C2×#103—472no—
329C2×#102—472no—
330C2×C22⋊C8—471no—
331C2×C22⋊C8—471no—
332C2×C4×C8—472no—
333#390—471no—
334#389—471no—
335#388—941no—
336#386—941no—
337#380—471no—
338C4×C4⋊C4—471no—
339C4×C22⋊C4—941no—
340#340—472no—
341#340—472no—
342#336—472no—
343C47C4×#44811yescharacteristic, complemented, Sylow
344C22×Q8—24no—
345C22×Q8—24no—
346C22×Q8—22no—
347C22×Q8—21no—
348C22×Q8C4×D4714yescomplemented
349C22×Q8C22×D4712yes—
350C22×D4—471no—
351C22×D4—941no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—941no—
355C23×C4C22⋊D4711yescharacteristic
356C23×C4C22⋊D4711yescharacteristic
357C23×C4C22×D4711yescharacteristic
358C2×SD16—478no—
359C2×SD16—944no—
360C2×SD16—944no—
361C22×C8—472no—
362C22×C8—472no—
363#121—474no—
364#121—942no—
365C4×Q8—28no—
366C4×Q8—28no—
367C4×Q8—24no—
368C4×Q8—24no—
369C4×Q8—24no—
370C4×Q8C22⋊D4718yescomplemented
371C4×D4—944no—
372C4×D4—1884no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—471no—
379C2×C4⋊C4—471no—
380C2×C4⋊C4—471no—
381C2×C4⋊C4—941no—
382C2×C4⋊C4C22×D4712yes—
383C2×C22⋊C4—941no—
384C2×C22⋊C4—941no—
385C2×C22⋊C4—941no—
386C2×C22⋊C4—941no—
387C2×C22⋊C4—941no—
388C2×C42—28no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—941no—
393C2×C42C22⋊D4711yescharacteristic
394C2×C42C22⋊D4711yescharacteristic
395C2×C42C22×D4711yescharacteristic
396C2×C42C22×D4711yescharacteristic
397#106—944no—
398#103—478no—
399#103—944no—
400#103—944no—
401#102—944no—
402C22⋊C8—474no—
403C22⋊C8—942no—
404C4×C8—944no—
405#95—941no—
406#95—941no—
407#95—941no—
408C24—941no—
409C24C2×C22⋊D4711yescharacteristic
410C2×Q8—24no—
411C2×Q8—216no—
412C2×Q8—24no—
413C2×Q8—216no—
414C2×Q8—24no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8C2×C4×D4714yes—
419C2×Q8#1062535014yes—
420C2×Q8C2×C22⋊D4714yes—
421C2×D4—472no—
422C2×D4—944no—
423C2×D4—942no—
424C2×D4—942no—
425C2×D4—941no—
426C2×D4—1882no—
427C2×D4—1882no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—941no—
444C22×C4—941no—
445C22×C4—941no—
446C22×C4—1882no—
447C22×C4—1882no—
448C22×C4—1882no—
449C22×C4#1062533614yescomplemented
450C22×C4C2×C4×D4712yes—
451C22×C4#1062535012yes—
452C22×C4C2×C22⋊D4711yescharacteristic
453C22×C4C2×C22⋊D4711yescharacteristic
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C2×C22⋊D4711yescharacteristic
457C22×C4C23×D4711yescharacteristic
458SD16—9416no—
459C2×C8—474no—
460C2×C8—942no—
461C2×C8—942no—
462C2×C8—942no—
463C2×C8—942no—
464C2×C8—942no—
465C4⋊C4—28no—
466C4⋊C4—24no—
467C4⋊C4—28no—
468C4⋊C4—22no—
469C4⋊C4—472no—
470C4⋊C4—941no—
471C4⋊C4—942no—
472C4⋊C4—942no—
473C4⋊C4—1882no—
474C4⋊C4C2×C22⋊D4714yes—
475C22⋊C4—944no—
476C22⋊C4—1882no—
477C22⋊C4—1882no—
478C22⋊C4—1882no—
479C22⋊C4—1882no—
480C42—28no—
481C42—28no—
482C42—22no—
483C42—22no—
484C42—22no—
485C42—1882no—
486C42C2×C22⋊D4714yes—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—942no—
492C23—1881no—
493C23—1881no—
494C23—1881no—
495C23—1881no—
496C23—1881no—
497C23—1881no—
498C23C4×C22⋊D4712yes—
499C23C2×#1062533612yes—
500C23#1309404412yes—
501C23C22×C22⋊D4711yescharacteristic
502Q8—216no—
503Q8—24no—
504Q8—24no—
505Q8—24no—
506Q8C4×C22⋊D4718yescomplemented
507D4—944no—
508D4—1888no—
509D4—1882no—
510C2×C4—216no—
511C2×C4—24no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—24no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—28no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—21no—
524C2×C4—24no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—44no—
528C2×C4—48no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—942no—
532C2×C4—3764no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4—1881no—
538C2×C4—1881no—
539C2×C4—1881no—
540C2×C4—1881no—
541C2×C4C4×C22⋊D4712yes—
542C2×C4#1309399312yes—
543C2×C4#1309399312yes—
544C2×C4C2×#1062533612yes—
545C2×C4C2×#1062533612yes—
546C2×C4#1309405512yes—
547C2×C4C22×C4×D4711yescharacteristic
548C2×C4C22×C22⋊D4712yes—
549C2×C4C2×#1062535012yes—
550C2×C4C2×#1062535011yescharacteristic
551C8—944no—
552C8—1882no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—3761no—
560C22—3761no—
561C22—3761no—
562C22—3761no—
563C22—1882no—
564C22—1882no—
565C22—1882no—
566C22C4×#1062533614yescomplemented
567C22C2×C4×C22⋊D4711yescharacteristic
568C22C2×#1309399311yescharacteristic
569C22#1568963411yescharacteristic
570C22C22×#1062533611yescharacteristic
571C22C2×#1309404411yescharacteristic
572C22C2×#1309405511yescharacteristic
573C22#1568992111yescharacteristic
574C4—28no—
575C4—22no—
576C4—22no—
577C4—22no—
578C4—41no—
579C4—44no—
580C4—3761no—
581C4—3761no—
582C4—1882no—
583C4#1568926214yesdirect product factor
584C4C2×C4×C22⋊D4712yes—
585C4#1568963412yes—
586C2—24no—
587C2—3762no—
588C2C4×#1309399311yescharacteristic
589C2C2×C4×#1062533611yescharacteristic
590C2C4×#1309405511yescharacteristic
591C2C2×#1568926211yescharacteristic
592C2#2025260611yescharacteristic
593C2#2025341911yescharacteristic
594C2#2025346811yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×C4×Q8×C47C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenterC22×C4×Q8D47
hypocenterC47C4×#448
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625336C2semidirect
4. #20243743C2semidirect
6. #20243656C2semidirect
7. #20243581C2semidirect
8. #20243323C2semidirect
9. C4×#13093948C2semidirect
10. C4×C22⋊(C47⋊C8)C2semidirect
11. C22×C4×Q8×C47C2semidirect
16. #15689262C4direct (N × H)
51. C2×#10625336C2×C4semidirect
71. #13093948C2×C4semidirect
74. C22⋊(C47⋊C8)C2×C4semidirect
83. C22×Q8×C47C2×C4semidirect
95. C4×Q8×C47D4semidirect
138. C22×C4×C47SD16semidirect
208. Q8×C47C4×D4semidirect
262. C22×C47C4×SD16semidirect
283. C4×C47#448semidirect
289. C22×C4×Q8D47semidirect
343. C47C4×#448semidirect
348. C22×Q8C4×D47semidirect
370. C4×Q8C22⋊D47semidirect
449. C22×C4#10625336semidirect
506. Q8C4×C22⋊D47semidirect
566. C22C4×#10625336semidirect
583. C4#15689262direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156892622
C2×C4×#106253362
C4×#130939982
#202437432
#202437052
#202436562
#202435812
#202433232
C4×#130939482
C4×C22⋊(C47⋊C8)2
C22×C4×Q8×C472
C4×#44847