Finite Group Databasebeta

← C2×#20247742 #26385725

Subgroups — C2×#20247742 #26385725

Order 12032.

3158 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094015C211yesmaximal, characteristic, complemented
2#20247742C2116yesmaximal, direct product factor
3C2×#15689048C212yesmaximal, complemented
4C2×#15689037C212yesmaximal, complemented
5C2×#15689026C211yesmaximal, characteristic, complemented
6C2×#15689026C211yesmaximal, characteristic, complemented
7C2×#15689026C212yesmaximal, complemented
8C2×#15689017C212yesmaximal, complemented
9C2×#15688983C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
12C22×#121×C47C211yesmaximal, characteristic
13C2×#13094015—28no—
14C2×#13094015C2218yescomplemented
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2212yes—
18C22×Dic47⋊C4C2212yes—
19C22×C22⋊Dic47C2212yes—
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2211yescharacteristic
22C22×C22⋊Dic47C2212yes—
23C22×C22⋊Dic47C2212yes—
24C22×C22⋊Dic47C2212yes—
25C22×C22⋊Dic47C2212yes—
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28C22×C4×Dic47C2212yes—
29#15689048C22116yescomplemented
30#15689037C22116yescomplemented
31#15689026C2218yescomplemented
32#15689026C2218yescomplemented
33#15689026C22116yescomplemented
34#15689017C22116yescomplemented
35#15688983C2218yescomplemented
36C4⋊C4×Dic47C2218yescomplemented
37C4×C22⋊Dic47C2218yescomplemented
38C2×C47⋊#95C2212yes—
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2212yes—
41C2×C47⋊#95C2211yescharacteristic
42C23×D4×C47C2211yescharacteristic
43C23×D4×C47C2212yes—
44C24×C4×C47C2211yescharacteristic
45C2×#121×C47—28no—
46C2×#121×C47C2218yes—
47C22×C4⋊C4×C47C2211yescharacteristic
48C22×C22⋊C4×C47C2212yes—
49C23×Dic47C2311yescharacteristic
50C23×Dic47C2312yes—
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2312yes—
54C23×Dic47C2311yescharacteristic
55#13094015—232no—
56C2×C4⋊Dic47—28no—
57C2×C4⋊Dic47—24no—
58C2×C4⋊Dic47—24no—
59C2×C4⋊Dic47C2314yes—
60C2×C4⋊Dic47C2314yes—
61C2×C4⋊Dic47C2318yes—
62C2×Dic47⋊C4—28no—
63C2×Dic47⋊C4C2318yes—
64C2×C22⋊Dic47—24no—
65C2×C22⋊Dic47—24no—
66C2×C22⋊Dic47—28no—
67C2×C22⋊Dic47—44no—
68C2×C22⋊Dic47—44no—
69C2×C22⋊Dic47—44no—
70C2×C22⋊Dic47—44no—
71C2×C22⋊Dic47C2314yes—
72C2×C22⋊Dic47C2314yes—
73C2×C22⋊Dic47C2318yes—
74C2×C22⋊Dic47C2318yes—
75C2×C22⋊Dic47C2318yes—
76C2×C22⋊Dic47C2318yes—
77C2×C22⋊Dic47C2318yes—
78C2×C4×Dic47—24no—
79C2×C4×Dic47—24no—
80C2×C4×Dic47—44no—
81C2×C4×Dic47C2314yes—
82C2×C4×Dic47C2314yes—
83C2×C4×Dic47C2318yes—
84C47⋊#95C2314yes—
85C47⋊#95C2314yes—
86C47⋊#95C2318yes—
87C47⋊#95C2318yes—
88C25×C47C2312yes—
89C25×C47C2311yescharacteristic
90C22×D4×C47—28no—
91C22×D4×C47—28no—
92C22×D4×C47—24no—
93C22×D4×C47—24no—
94C22×D4×C47—24no—
95C22×D4×C47—44no—
96C22×D4×C47C2314yes—
97C22×D4×C47C2318yes—
98C23×C4×C47—24no—
99C23×C4×C47—24no—
100C23×C4×C47—24no—
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2314yes—
103C23×C4×C47C2312yes—
104C23×C4×C47C2311yescharacteristic
105#121×C47—232no—
106C2×C4⋊C4×C47D418yes—
107C2×C4⋊C4×C47C2314yes—
108C2×C22⋊C4×C47—28no—
109C2×C22⋊C4×C47C2318yes—
110C24×C47—22no—
111C24×C47—22no—
112C24×C47—22no—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—24no—
117C24×C47—24no—
118C24×C47—24no—
119C24×C47—24no—
120C24×C47—24no—
121C24×C47—24no—
122C24×C47—24no—
123C24×C47#4114yes—
124C24×C47C2414yes—
125C24×C47C2412yes—
126C24×C47C2411yescharacteristic
127C2×D4×C47—216no—
128C2×D4×C47—216no—
129C2×D4×C47—28no—
130C2×D4×C47—28no—
131C2×D4×C47—28no—
132C2×D4×C47—48no—
133C2×D4×C47—432no—
134C2×D4×C47—416no—
135C22×C4×C47—24no—
136C22×C4×C47—24no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—28no—
141C22×C4×C47—28no—
142C22×C4×C47—28no—
143C22×C4×C47—416no—
144C22×C4×C47C2×D418yes—
145C22×C4×C47C2×D414yes—
146C22×C4×C47#4114yes—
147C22×C4×C47#4114yes—
148C22×C4×C47C2412yes—
149C22×C4×C47C2414yes—
150C22×C4×C47C2412yes—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—24no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—24no—
160C22×Dic47—22no—
161C22×Dic47—24no—
162C22×Dic47—24no—
163C22×Dic47—24no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—24no—
167C22×Dic47—22no—
168C22×Dic47#4114yes—
169C22×Dic47C2412yes—
170C22×Dic47C2414yes—
171C22×Dic47C2412yes—
172C22×Dic47C2412yes—
173C22×Dic47C2414yes—
174C22×Dic47C2412yes—
175C4⋊C4×C47C2×D4116yes—
176C22⋊C4×C47—216no—
177C22⋊Dic47—28no—
178C22⋊Dic47—28no—
179C22⋊Dic47—216no—
180C22⋊Dic47—48no—
181C22⋊Dic47—48no—
182C22⋊Dic47—48no—
183C22⋊Dic47—48no—
184C4⋊Dic47—216no—
185C4⋊Dic47—28no—
186C4⋊Dic47—28no—
187Dic47⋊C4—216no—
188C4×Dic47—28no—
189C4×Dic47—28no—
190C4×Dic47—48no—
191C23×C47—28no—
192C23×C47—28no—
193C23×C47—28no—
194C23×C47—22no—
195C23×C47—22no—
196C23×C47—22no—
197C23×C47—22no—
198C23×C47—22no—
199C23×C47—22no—
200C23×C47—24no—
201C23×C47—24no—
202C23×C47—24no—
203C23×C47—24no—
204C23×C47—24no—
205C23×C47—24no—
206C23×C47—24no—
207C23×C47—44no—
208C23×C47—44no—
209C23×C47—44no—
210C23×C47—44no—
211C23×C47—48no—
212C23×C47—48no—
213C23×C47—48no—
214C23×C47—48no—
215C23×C47—48no—
216C23×C47—48no—
217C23×C47—48no—
218C23×C47C22×D412yes—
219C23×C47C2×#4112yes—
220C23×C47C2×#4114yes—
221C23×C47C2×#4112yes—
222C23×C47C2×#4112yes—
223C23×C47C2×#4112yes—
224C23×C47H(5,𝔽2)12yes—
225C23×C47H(5,𝔽2)12yes—
226C23×C47C2511yescharacteristic
227D4×C47—432no—
228D4×C47—416no—
229C2×C4×C47—216no—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—44no—
236C2×C4×C47—416no—
237C2×C4×C47#124116yes—
238C2×C4×C47C22×D418yes—
239C2×C4×C47C22×D414yes—
240C2×C4×C47C2×#4114yes—
241C2×C4×C47C2×#4114yes—
242C2×Dic47—28no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—24no—
248C2×Dic47—22no—
249C2×Dic47—24no—
250C2×Dic47—22no—
251C2×Dic47—24no—
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—24no—
255C2×Dic47—22no—
256C2×Dic47—24no—
257C2×Dic47—22no—
258C2×Dic47—24no—
259C2×Dic47—22no—
260C2×Dic47—48no—
261C2×Dic47—44no—
262C2×Dic47—44no—
263C2×Dic47—48no—
264C2×Dic47—44no—
265C2×Dic47C2×#4114yes—
266C2×#2490—471nomaximal, Sylow
267C22×C47—24no—
268C22×C47—24no—
269C22×C47—24no—
270C22×C47—42no—
271C22×C47—42no—
272C22×C47—42no—
273C22×C47—42no—
274C22×C47—416no—
275C22×C47—44no—
276C22×C47—44no—
277C22×C47—44no—
278C22×C47—44no—
279C22×C47—44no—
280C22×C47—44no—
281C22×C47—44no—
282C22×C47—816no—
283C22×C47C2×#12414yes—
284C22×C47#52914yes—
285C22×C47#54014yes—
286C22×C47#54614yes—
287C22×C47#55014yes—
288C22×C47#55314yes—
289C22×C47#55314yes—
290C22×C47C23×D411yescharacteristic
291C22×C47C22×#4111yescharacteristic
292C22×C47C22×#4111yescharacteristic
293C22×C47C22×#4111yescharacteristic
294C22×C47C22×#4111yescharacteristic
295C22×C47C2×H(5,𝔽2)11yescharacteristic
296C22×C47C2×H(5,𝔽2)11yescharacteristic
297C4×C47—28no—
298C4×C47—42no—
299C4×C47C2×#12418yes—
300Dic47—24no—
301Dic47—44no—
302Dic47—42no—
303Dic47—42no—
304Dic47—44no—
305Dic47—42no—
306C22×#125—471no—
307C22×#121D4711yescharacteristic
308#2490—4716no—
309C2×#397—472no—
310C2×#394—472no—
311C2×#390—472no—
312C2×#390—471no—
313C2×#390—471no—
314C2×#388—472no—
315C2×#380—471no—
316C2×C4×C4⋊C4—471no—
317C2×C4×C22⋊C4—471no—
318C2×C47—44no—
319C2×C47—84no—
320C2×C47#249018yescomplemented
321C2×C47C22×#12411yescharacteristic
322C2×C47C2×#52911yescharacteristic
323C2×C47C2×#54011yescharacteristic
324C2×C47C2×#54611yescharacteristic
325C2×C47C2×#55011yescharacteristic
326C2×C47C2×#55311yescharacteristic
327C2×C47C2×#55311yescharacteristic
328C23×D4C2×D4711yescharacteristic
329C23×D4C2×D4712yes—
330C24×C4C2×D4711yescharacteristic
331C2×#125—478no—
332C2×#125—948no—
333C2×#121—28no—
334C2×#121C2×D4718yes—
335C22×C4⋊C4—472no—
336C22×C4⋊C4—472no—
337C22×C4⋊C4—471no—
338C22×C4⋊C4—471no—
339C22×C4⋊C4C2×D4711yescharacteristic
340C22×C22⋊C4—471no—
341C22×C22⋊C4—471no—
342C22×C22⋊C4—472no—
343C22×C22⋊C4—472no—
344C22×C22⋊C4—472no—
345C22×C22⋊C4—472no—
346C22×C22⋊C4—472no—
347C22×C22⋊C4C2×D4712yes—
348C22×C42—471no—
349C22×C42—471no—
350C22×C42—472no—
351#397—4716no—
352#394—4716no—
353#390—478no—
354#390—478no—
355#390—4716no—
356#388—4716no—
357#380—478no—
358C4×C4⋊C4—478no—
359C4×C22⋊C4—478no—
360C2×#95—472no—
361C2×#95—471no—
362C2×#95—472no—
363C2×#95—471no—
364C47C2×#249011yescharacteristic, complemented, Sylow
365C25C22×D4712yes—
366C25C22×D4711yescharacteristic
367C22×D4—28no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—28no—
371C22×D4—24no—
372C22×D4—44no—
373C22×D4C22×D4714yes—
374C22×D4C22×D4718yes—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—471no—
379C23×C4—472no—
380C23×C4—471no—
381C23×C4—471no—
382C23×C4—472no—
383C23×C4—471no—
384C23×C4C22×D4714yes—
385C23×C4C22×D4711yescharacteristic
386C23×C4C22×D4712yes—
387C23×C4C22×D4711yescharacteristic
388#125—9432no—
389#121—232no—
390C2×C4⋊C4—478no—
391C2×C4⋊C4—474no—
392C2×C4⋊C4—478no—
393C2×C4⋊C4—474no—
394C2×C4⋊C4—944no—
395C2×C4⋊C4—948no—
396C2×C4⋊C4—948no—
397C2×C4⋊C4—944no—
398C2×C4⋊C4C22⋊D4718yes—
399C2×C4⋊C4C22×D4714yes—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—474no—
402C2×C22⋊C4—474no—
403C2×C22⋊C4—478no—
404C2×C22⋊C4—478no—
405C2×C22⋊C4—478no—
406C2×C22⋊C4—478no—
407C2×C22⋊C4—478no—
408C2×C22⋊C4—944no—
409C2×C22⋊C4—948no—
410C2×C22⋊C4—944no—
411C2×C22⋊C4—1884no—
412C2×C22⋊C4—1884no—
413C2×C22⋊C4—1884no—
414C2×C22⋊C4—1884no—
415C2×C22⋊C4C22×D4718yes—
416C2×C42—474no—
417C2×C42—474no—
418C2×C42—478no—
419C2×C42—944no—
420C2×C42—944no—
421C2×C42—1884no—
422#95—474no—
423#95—474no—
424#95—478no—
425#95—478no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—24no—
438C24—24no—
439C24#1062535214yes—
440C24C23×D4714yes—
441C24C23×D4712yes—
442C24C23×D4711yescharacteristic
443C2×D4—216no—
444C2×D4—216no—
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—48no—
449C2×D4—432no—
450C2×D4—416no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—416no—
460C22×C4—474no—
461C22×C4—472no—
462C22×C4—472no—
463C22×C4—474no—
464C22×C4—472no—
465C22×C4—472no—
466C22×C4—474no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—944no—
472C22×C4—944no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—944no—
478C22×C4—944no—
479C22×C4—942no—
480C22×C4—944no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—944no—
484C22×C4#1062535214yes—
485C22×C4#1062535214yes—
486C22×C4C2×C22⋊D4718yes—
487C22×C4C2×C22⋊D4714yes—
488C22×C4C23×D4712yes—
489C22×C4C23×D4714yes—
490C22×C4C23×D4712yes—
491C4⋊C4—9416no—
492C4⋊C4—9416no—
493C4⋊C4—948no—
494C4⋊C4—948no—
495C4⋊C4C2×C22⋊D47116yes—
496C22⋊C4—216no—
497C22⋊C4—948no—
498C22⋊C4—9416no—
499C22⋊C4—948no—
500C22⋊C4—1888no—
501C22⋊C4—1888no—
502C22⋊C4—1888no—
503C22⋊C4—1888no—
504C42—948no—
505C42—948no—
506C42—1888no—
507C23—28no—
508C23—28no—
509C23—28no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—48no—
528C23—48no—
529C23—48no—
530C23—48no—
531C23—48no—
532C23—48no—
533C23—48no—
534C23C22×C22⋊D4712yes—
535C23#41×D4712yes—
536C23C2×#1062535214yes—
537C23C2×#1062535212yes—
538C23C2×#1062535212yes—
539C23C2×#1062535212yes—
540C23#1309406912yes—
541C23#1309407012yes—
542C23C24×D4711yescharacteristic
543D4—432no—
544D4—416no—
545C2×C4—216no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—44no—
552C2×C4—416no—
553C2×C4—474no—
554C2×C4—948no—
555C2×C4—942no—
556C2×C4—942no—
557C2×C4—942no—
558C2×C4—942no—
559C2×C4—944no—
560C2×C4—942no—
561C2×C4—944no—
562C2×C4—942no—
563C2×C4—942no—
564C2×C4—942no—
565C2×C4—944no—
566C2×C4—944no—
567C2×C4—942no—
568C2×C4—942no—
569C2×C4—944no—
570C2×C4—942no—
571C2×C4—944no—
572C2×C4—1884no—
573C2×C4—1884no—
574C2×C4—1888no—
575C2×C4—1884no—
576C2×C4—1888no—
577C2×C4#13094011116yes—
578C2×C4C22×C22⋊D4718yes—
579C2×C4C22×C22⋊D4714yes—
580C2×C4C2×#1062535214yes—
581C2×C4C2×#1062535214yes—
582C22—24no—
583C22—24no—
584C22—24no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—416no—
589C22—42no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—816no—
598C22C2×#1309401114yes—
599C22#1568965414yes—
600C22#1568972614yes—
601C22#1568976714yes—
602C22#1568979214yes—
603C22#1568982014yes—
604C22#1568982514yes—
605C22C23×C22⋊D4711yescharacteristic
606C22C2×#41×D4711yescharacteristic
607C22C22×#1062535211yescharacteristic
608C22C22×#1062535211yescharacteristic
609C22C22×#1062535211yescharacteristic
610C22C2×#1309406911yescharacteristic
611C22C2×#1309407011yescharacteristic
612C4—28no—
613C4—42no—
614C4—944no—
615C4—1882no—
616C4—1882no—
617C4—1884no—
618C4—1882no—
619C4—1884no—
620C4C2×#1309401118yes—
621C2—44no—
622C2—84no—
623C2#2024774218yesdirect product factor
624C2C22×#1309401111yescharacteristic
625C2C2×#1568965411yescharacteristic
626C2C2×#1568972611yescharacteristic
627C2C2×#1568976711yescharacteristic
628C2C2×#1568979211yescharacteristic
629C2C2×#1568982011yescharacteristic
630C2C2×#1568982511yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
Fitting, prime radicalC22×#121×C47C2
socleC24×C47C24
hypercenterC22×#121D47
hypocenterC47C2×#2490
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#13094015C2semidirect
2. #20247742C2direct (N × H)
3. C2×#15689048C2semidirect
4. C2×#15689037C2semidirect
5. C2×#15689026C2semidirect
6. C2×#15689026C2semidirect
7. C2×#15689026C2semidirect
8. C2×#15689017C2semidirect
9. C2×#15688983C2semidirect
10. C2×C4⋊C4×Dic47C2semidirect
11. C2×C4×C22⋊Dic47C2semidirect
14. C2×#13094015C22semidirect
29. #15689048C22semidirect
30. #15689037C22semidirect
31. #15689026C22semidirect
32. #15689026C22semidirect
33. #15689026C22semidirect
34. #15689017C22semidirect
35. #15688983C22semidirect
36. C4⋊C4×Dic47C22semidirect
37. C4×C22⋊Dic47C22semidirect
320. C2×C47#2490semidirect
364. C47C2×#2490semidirect
623. C2#20247742direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940152
#202477422
C2×#156890482
C2×#156890372
C2×#156890262
C2×#156890172
C2×#156889832
C2×C4⋊C4×Dic472
C2×C4×C22⋊Dic472
C22×#121×C472
C2×#249047