Finite Group Databasebeta

← C2×#20246966 #26384423

Subgroups — C2×#20246966 #26384423

Order 12032.

3894 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094013C211yesmaximal, characteristic, complemented
2C22×#13094000C211yesmaximal, characteristic, complemented
3C22×#13093999C211yesmaximal, characteristic
4C22×C4×D188C211yesmaximal, characteristic, complemented
5#20246966C2116yesmaximal, direct product factor
6C2×#15689052C212yesmaximal, complemented
7C2×#15689041C212yesmaximal, complemented
8C2×#15689019C211yesmaximal, characteristic, complemented
9C2×#15689001C212yesmaximal, complemented
10C2×#15688982C212yesmaximal, complemented
11C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
12C2×C47×#391C211yesmaximal, characteristic, complemented
13C23×D188C2212yes—
14C23×D188C2211yescharacteristic
15C23×C4×D47C2211yescharacteristic
16C23×C4×D47C2212yes—
17C2×#13094013—28no—
18C2×#13094013C2218yescomplemented
19C2×#13094000—28no—
20C2×#13094000C2218yescomplemented
21C2×#13093999—28no—
22C2×#13093999C2218yes—
23C2×C4×D188—28no—
24C2×C4×D188C2218yescomplemented
25C22×C4⋊Dic47C2211yescharacteristic
26C22×Dic47⋊C4C2212yes—
27C22×Dic47⋊C4C2212yes—
28C22×(C2×D47)⋊C4C2212yes—
29C22×(C2×D47)⋊C4C2212yes—
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2212yes—
32C22×(C2×D47)⋊C4C2212yes—
33C22×(C2×D47)⋊C4C2212yes—
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36#15689052C22116yescomplemented
37#15689041C22116yescomplemented
38#15689019C2218yescomplemented
39#15689001C22116yescomplemented
40#15688982C22116yescomplemented
41C4×(C2×D47)⋊C4C2218yescomplemented
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2212yes—
44C2×C47⋊#95C2211yescharacteristic
45C23×Q8×C47C2211yescharacteristic
46C22×C4⋊C4×C47C2211yescharacteristic
47C22×C42×C47C2211yescharacteristic
48C47×#391C2218yescomplemented
49C2×#95×C47C2212yes—
50C2×#95×C47C2212yes—
51C24×D47C2312yes—
52C24×D47C2311yescharacteristic
53C22×D188—24no—
54C22×D188—24no—
55C22×D188—28no—
56C22×D188—28no—
57C22×D188—44no—
58C22×D188D418yes—
59C22×D188C2318yes—
60C22×D188C2314yes—
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2312yes—
65C22×C4×D47—24no—
66C22×C4×D47—24no—
67C22×C4×D47—28no—
68C22×C4×D47—24no—
69C22×C4×D47—28no—
70C22×C4×D47—44no—
71C22×C4×D47C2314yes—
72C22×C4×D47C2318yes—
73#13094013—232no—
74#13094000—232no—
75#13093999—232no—
76C4×D188—232no—
77C2×C4⋊Dic47D418yescomplemented
78C2×C4⋊Dic47C2314yes—
79C2×Dic47⋊C4—28no—
80C2×Dic47⋊C4—44no—
81C2×Dic47⋊C4C2318yes—
82C2×Dic47⋊C4C2318yes—
83C2×(C2×D47)⋊C4—28no—
84C2×(C2×D47)⋊C4—28no—
85C2×(C2×D47)⋊C4—28no—
86C2×(C2×D47)⋊C4—24no—
87C2×(C2×D47)⋊C4—24no—
88C2×(C2×D47)⋊C4—28no—
89C2×(C2×D47)⋊C4—28no—
90C2×(C2×D47)⋊C4C2314yes—
91C2×(C2×D47)⋊C4C2314yes—
92C2×(C2×D47)⋊C4C2318yes—
93C2×(C2×D47)⋊C4C2318yes—
94C2×(C2×D47)⋊C4C2318yes—
95C2×(C2×D47)⋊C4C2318yes—
96C2×(C2×D47)⋊C4C2318yes—
97C2×C4×Dic47—24no—
98C2×C4×Dic47C2314yes—
99C47⋊#95C2314yes—
100C47⋊#95C2314yes—
101C47⋊#95C2318yes—
102C22×Q8×C47—24no—
103C22×Q8×C47—24no—
104C22×Q8×C47—24no—
105C22×Q8×C47C2314yes—
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2312yes—
108C23×C4×C47C2312yes—
109C23×C4×C47C2311yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47—24no—
112C2×C4⋊C4×C47C2314yes—
113C2×C42×C47—24no—
114C2×C42×C47C2314yes—
115#95×C47C2318yes—
116#95×C47C2318yes—
117C24×C47C2411yescharacteristic
118C23×D47—22no—
119C23×D47—24no—
120C23×D47—22no—
121C23×D47—22no—
122C23×D47—22no—
123C23×D47—24no—
124C23×D47—24no—
125C23×D47—24no—
126C23×D47—24no—
127C23×D47—22no—
128C23×D47—24no—
129C23×D47—22no—
130C23×D47C2×D418yes—
131C23×D47#4114yes—
132C23×D47C2414yes—
133C23×D47C2412yes—
134C2×Q8×C47—28no—
135C2×Q8×C47—28no—
136C2×Q8×C47—28no—
137C2×Q8×C47—416no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—24no—
142C22×C4×C47—24no—
143C22×C4×C47—24no—
144C22×C4×C47—24no—
145C22×C4×C47—22no—
146C22×C4×C47—24no—
147C22×C4×C47—24no—
148C22×C4×C47—22no—
149C22×C4×C47C2×D414yes—
150C22×C4×C47C2×D414yes—
151C22×C4×C47#4114yes—
152C22×C4×C47#4114yes—
153C22×C4×C47C2412yes—
154C22×C4×C47C2414yes—
155C22×C4×C47C2414yes—
156C22×C4×C47C2412yes—
157C22×C4×C47C2412yes—
158C22×Dic47—24no—
159C22×Dic47—24no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47C2×D418yes—
170C22×Dic47C2412yes—
171C22×Dic47C2412yes—
172C22×Dic47C2412yes—
173C22×Dic47C2414yes—
174C2×D188—232no—
175C2×D188—28no—
176C2×D188—28no—
177C2×D188—216no—
178C2×D188—216no—
179C2×D188—48no—
180C2×D188—432no—
181C2×D188C2×D4116yes—
182C2×C4×D47—28no—
183C2×C4×D47—28no—
184C2×C4×D47—216no—
185C2×C4×D47—28no—
186C2×C4×D47—216no—
187C2×C4×D47—48no—
188C2×C4×D47—432no—
189C2×C4×D47—416no—
190C4⋊C4×C47—28no—
191C42×C47—28no—
192(C2×D47)⋊C4—216no—
193(C2×D47)⋊C4—216no—
194(C2×D47)⋊C4—216no—
195(C2×D47)⋊C4—28no—
196(C2×D47)⋊C4—28no—
197(C2×D47)⋊C4—216no—
198(C2×D47)⋊C4—216no—
199C4⋊Dic47C2×D4116yescomplemented
200Dic47⋊C4—216no—
201Dic47⋊C4—48no—
202C4×Dic47—28no—
203C23×C47C22×D412yes—
204C23×C47C22×D412yes—
205C23×C47C2×#4112yes—
206C23×C47C2×#4112yes—
207C23×C47C2×#4112yes—
208C23×C47H(5,𝔽2)12yes—
209C23×C472−1+412yes—
210C23×C47C2511yescharacteristic
211C22×D47—216no—
212C22×D47—28no—
213C22×D47—28no—
214C22×D47—216no—
215C22×D47—216no—
216C22×D47—28no—
217C22×D47—22no—
218C22×D47—24no—
219C22×D47—22no—
220C22×D47—22no—
221C22×D47—22no—
222C22×D47—24no—
223C22×D47—24no—
224C22×D47—24no—
225C22×D47—24no—
226C22×D47—22no—
227C22×D47—24no—
228C22×D47—22no—
229C22×D47—44no—
230C22×D47—48no—
231C22×D47—44no—
232C22×D47—48no—
233C22×D47—48no—
234C22×D47—44no—
235C22×D47—44no—
236C22×D47—48no—
237C22×D47C22×D418yes—
238C22×D47C2×#4114yes—
239Q8×C47—416no—
240C2×C4×C47—28no—
241C2×C4×C47—22no—
242C2×C4×C47—22no—
243C2×C4×C47—24no—
244C2×C4×C47—22no—
245C2×C4×C47—24no—
246C2×C4×C47—24no—
247C2×C4×C47—22no—
248C2×C4×C47—24no—
249C2×C4×C47—24no—
250C2×C4×C47—24no—
251C2×C4×C47—22no—
252C2×C4×C47—48no—
253C2×C4×C47—48no—
254C2×C4×C47—44no—
255C2×C4×C47#121116yes—
256C2×C4×C47C22×D414yes—
257C2×C4×C47C22×D414yes—
258C2×C4×C47C2×#4114yes—
259C2×C4×C47C2×#4114yes—
260C2×Dic47—216no—
261C2×Dic47—24no—
262C2×Dic47—24no—
263C2×Dic47—22no—
264C2×Dic47—22no—
265C2×Dic47—22no—
266C2×Dic47—22no—
267C2×Dic47—22no—
268C2×Dic47—22no—
269C2×Dic47—22no—
270C2×Dic47—22no—
271C2×Dic47—22no—
272C2×Dic47—44no—
273C2×Dic47—44no—
274C2×Dic47—44no—
275C2×Dic47C22×D418yes—
276D188—232no—
277D188—432no—
278C4×D47—432no—
279C4×D47—416no—
280C2×#2427—471nomaximal, Sylow
281C22×C47C2×#12114yes—
282C22×C47#52914yes—
283C22×C47#54214yes—
284C22×C47#54614yes—
285C22×C47#54614yes—
286C22×C47#54714yes—
287C22×C47#54814yes—
288C22×C47C23×D411yescharacteristic
289C22×C47C23×D411yescharacteristic
290C22×C47C22×#4111yescharacteristic
291C22×C47C22×#4111yescharacteristic
292C22×C47C22×#4111yescharacteristic
293C22×C47C2×H(5,𝔽2)11yescharacteristic
294C22×C47C2×2−1+411yescharacteristic
295C2×D47—28no—
296C2×D47—24no—
297C2×D47—24no—
298C2×D47—28no—
299C2×D47—28no—
300C2×D47—24no—
301C2×D47—42no—
302C2×D47—44no—
303C2×D47—432no—
304C2×D47—416no—
305C2×D47—42no—
306C2×D47—44no—
307C2×D47—44no—
308C2×D47—42no—
309C2×D47—42no—
310C2×D47—44no—
311C4×C47—24no—
312C4×C47—44no—
313C4×C47—44no—
314C4×C47—42no—
315C4×C47C2×#12118yes—
316Dic47—28no—
317Dic47—42no—
318Dic47—42no—
319Dic47—42no—
320C22×#124—471no—
321C22×C22⋊Q8—471no—
322C22×#121—471no—
323C22×C4×D4—471no—
324#2427—4716no—
325C2×#397—472no—
326C2×#394—472no—
327C2×#391D4711yescharacteristic, complemented
328C2×#389—471no—
329C2×#386—472no—
330C2×#380—472no—
331C2×C4×C22⋊C4—471no—
332C2×C47#242718yescomplemented
333C2×C47C22×#12111yescharacteristic
334C2×C47C2×#52911yescharacteristic
335C2×C47C2×#54211yescharacteristic
336C2×C47C2×#54611yescharacteristic
337C2×C47C2×#54611yescharacteristic
338C2×C47C2×#54711yescharacteristic
339C2×C47C2×#54811yescharacteristic
340D47—48no—
341D47—44no—
342C23×Q8C2×D4711yescharacteristic
343C23×D4—471no—
344C23×D4—472no—
345C24×C4—471no—
346C24×C4—472no—
347C2×#124—478no—
348C2×#124—948no—
349C2×C22⋊Q8—478no—
350C2×C22⋊Q8—948no—
351C2×#121—478no—
352C2×#121—948no—
353C2×C4×D4—478no—
354C2×C4×D4—948no—
355C22×C4⋊C4—471no—
356C22×C4⋊C4—472no—
357C22×C4⋊C4—472no—
358C22×C4⋊C4C2×D4711yescharacteristic
359C22×C22⋊C4—471no—
360C22×C22⋊C4—472no—
361C22×C22⋊C4—472no—
362C22×C22⋊C4—472no—
363C22×C22⋊C4—472no—
364C22×C22⋊C4—472no—
365C22×C22⋊C4—471no—
366C22×C42—471no—
367C22×C42C2×D4711yescharacteristic
368#397—4716no—
369#394—4716no—
370#391C2×D4718yescomplemented
371#389—478no—
372#386—4716no—
373#380—4716no—
374C4×C22⋊C4—478no—
375C2×#95—471no—
376C2×#95—472no—
377C2×#95—471no—
378C2×#95C2×D4712yes—
379C2×#95C2×D4712yes—
380C47C2×#242711yescharacteristic, complemented, Sylow
381C25—472no—
382C25—471no—
383C22×Q8—24no—
384C22×Q8—24no—
385C22×Q8—24no—
386C22×Q8C22×D4714yes—
387C22×D4—478no—
388C22×D4—474no—
389C22×D4—478no—
390C22×D4—948no—
391C22×D4—948no—
392C22×D4—944no—
393C22×D4—944no—
394C22×D4—1884no—
395C23×C4—472no—
396C23×C4—471no—
397C23×C4—471no—
398C23×C4—471no—
399C23×C4—474no—
400C23×C4—478no—
401C23×C4—948no—
402C23×C4—944no—
403C23×C4—944no—
404C23×C4—944no—
405C23×C4—948no—
406C23×C4—1884no—
407C23×C4C22×D4712yes—
408C23×C4C22×D4711yescharacteristic
409C23×C4C22×D4712yes—
410C23×C4C22×D4711yescharacteristic
411C23×C4C22×D4711yescharacteristic
412#124—9432no—
413C22⋊Q8—9432no—
414#121—9432no—
415C4×D4—9432no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—478no—
418C2×C4⋊C4—474no—
419C2×C4⋊C4—478no—
420C2×C4⋊C4—478no—
421C2×C4⋊C4—948no—
422C2×C4⋊C4—1884no—
423C2×C4⋊C4C22×D4714yes—
424C2×C22⋊C4—478no—
425C2×C22⋊C4—478no—
426C2×C22⋊C4—478no—
427C2×C22⋊C4—478no—
428C2×C22⋊C4—478no—
429C2×C22⋊C4—474no—
430C2×C22⋊C4—474no—
431C2×C22⋊C4—948no—
432C2×C22⋊C4—948no—
433C2×C22⋊C4—948no—
434C2×C22⋊C4—948no—
435C2×C22⋊C4—948no—
436C2×C22⋊C4—944no—
437C2×C22⋊C4—944no—
438C2×C42—24no—
439C2×C42—474no—
440C2×C42—944no—
441C2×C42C22×D4714yes—
442#95—474no—
443#95—474no—
444#95—478no—
445#95C22×D4718yes—
446#95C22×D4718yes—
447C24—478no—
448C24—474no—
449C24—474no—
450C24—472no—
451C24—942no—
452C24—944no—
453C24—942no—
454C24—944no—
455C24—942no—
456C24—944no—
457C24—942no—
458C24—944no—
459C24—944no—
460C24—942no—
461C24—944no—
462C24—942no—
463C24C23×D4711yescharacteristic
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—416no—
468C2×D4—4716no—
469C2×D4—9416no—
470C2×D4—9416no—
471C2×D4—9432no—
472C2×D4—948no—
473C2×D4—948no—
474C2×D4—1888no—
475C2×D4—18832no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—478no—
488C22×C4—474no—
489C22×C4—472no—
490C22×C4—472no—
491C22×C4—472no—
492C22×C4—9416no—
493C22×C4—944no—
494C22×C4—944no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4—942no—
498C22×C4—942no—
499C22×C4—942no—
500C22×C4—942no—
501C22×C4—942no—
502C22×C4—942no—
503C22×C4—942no—
504C22×C4—948no—
505C22×C4—948no—
506C22×C4—948no—
507C22×C4—9416no—
508C22×C4—1888no—
509C22×C4—18832no—
510C22×C4—18816no—
511C22×C4#1062535014yes—
512C22×C4D4×D4714yes—
513C22×C4D4×D4714yes—
514C22×C4#1062535414yes—
515C22×C4C23×D4712yes—
516C22×C4C23×D4714yes—
517C22×C4C23×D4714yes—
518C22×C4C23×D4712yes—
519C22×C4C23×D4712yes—
520C4⋊C4—28no—
521C4⋊C4—4716no—
522C4⋊C4—9416no—
523C4⋊C4—1888no—
524C22⋊C4—9416no—
525C22⋊C4—9416no—
526C22⋊C4—948no—
527C22⋊C4—9416no—
528C22⋊C4—9416no—
529C22⋊C4—9416no—
530C22⋊C4—948no—
531C42—28no—
532C42—948no—
533C23—478no—
534C23—474no—
535C23—948no—
536C23—9416no—
537C23—9416no—
538C23—948no—
539C23—9416no—
540C23—948no—
541C23—942no—
542C23—944no—
543C23—942no—
544C23—944no—
545C23—942no—
546C23—944no—
547C23—942no—
548C23—944no—
549C23—944no—
550C23—942no—
551C23—944no—
552C23—942no—
553C23—1884no—
554C23—1888no—
555C23—1888no—
556C23—1884no—
557C23—1884no—
558C23—1888no—
559C23—1884no—
560C23—1888no—
561C23C2×D4×D4712yes—
562C23C2×D4×D4712yes—
563C23#41×D4712yes—
564C23C2×#1062535012yes—
565C23C2×#1062535412yes—
566C23#1309407012yes—
567C23#1309407212yes—
568C23C24×D4711yescharacteristic
569Q8—416no—
570D4—9432no—
571D4—18832no—
572C2×C4—28no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—48no—
585C2×C4—44no—
586C2×C4—48no—
587C2×C4—478no—
588C2×C4—9416no—
589C2×C4—944no—
590C2×C4—944no—
591C2×C4—942no—
592C2×C4—942no—
593C2×C4—942no—
594C2×C4—942no—
595C2×C4—942no—
596C2×C4—942no—
597C2×C4—942no—
598C2×C4—942no—
599C2×C4—942no—
600C2×C4—18832no—
601C2×C4—1884no—
602C2×C4—1884no—
603C2×C4—1884no—
604C2×C4—18816no—
605C2×C4#13093997116yes—
606C2×C4C2×D4×D4714yes—
607C2×C4C2×D4×D4714yes—
608C2×C4C2×#1062535014yes—
609C2×C4C2×#1062535414yes—
610C22—944no—
611C22—948no—
612C22—948no—
613C22—944no—
614C22—948no—
615C22—944no—
616C22—1884no—
617C22—1882no—
618C22—1882no—
619C22—1884no—
620C22—1882no—
621C22—1884no—
622C22—18816no—
623C22—18832no—
624C22—1882no—
625C22—1884no—
626C22C2×#1309399714yes—
627C22#1568966014yes—
628C22#1568974514yes—
629C22#1568976414yes—
630C22#1568976614yes—
631C22#1568977614yes—
632C22#1568978314yes—
633C22C22×D4×D4711yescharacteristic
634C22C22×D4×D4711yescharacteristic
635C22C2×#41×D4711yescharacteristic
636C22C22×#1062535011yescharacteristic
637C22C22×#1062535411yescharacteristic
638C22C2×#1309407011yescharacteristic
639C22C2×#1309407211yescharacteristic
640C4—24no—
641C4—44no—
642C4—42no—
643C4—44no—
644C4—948no—
645C4—1882no—
646C4—1882no—
647C4—1882no—
648C4C2×#1309399718yes—
649C2—1884no—
650C2—1888no—
651C2#2024696618yesdirect product factor
652C2C22×#1309399711yescharacteristic
653C2C2×#1568966011yescharacteristic
654C2C2×#1568974511yescharacteristic
655C2C2×#1568976411yescharacteristic
656C2C2×#1568976611yescharacteristic
657C2C2×#1568977611yescharacteristic
658C2C2×#1568978311yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#391C2
socleC24×C47C24
prime radicalC22×#13093999C2
hypercenterC2×#391D47
hypocenterC47C2×#2427
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. C22×#13094013C2semidirect
2. C22×#13094000C2semidirect
4. C22×C4×D188C2semidirect
5. #20246966C2direct (N × H)
6. C2×#15689052C2semidirect
7. C2×#15689041C2semidirect
8. C2×#15689019C2semidirect
9. C2×#15689001C2semidirect
10. C2×#15688982C2semidirect
11. C2×C4×(C2×D47)⋊C4C2semidirect
12. C2×C47×#391C2semidirect
18. C2×#13094013C22semidirect
20. C2×#13094000C22semidirect
24. C2×C4×D188C22semidirect
36. #15689052C22semidirect
37. #15689041C22semidirect
38. #15689019C22semidirect
39. #15689001C22semidirect
40. #15688982C22semidirect
41. C4×(C2×D47)⋊C4C22semidirect
48. C47×#391C22semidirect
77. C2×C4⋊Dic47D4semidirect
199. C4⋊Dic47C2×D4semidirect
327. C2×#391D47semidirect
332. C2×C47#2427semidirect
370. #391C2×D47semidirect
380. C47C2×#2427semidirect
651. C2#20246966direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940132
C22×#130940002
C22×#130939992
C22×C4×D1882
#202469662
C2×#156890522
C2×#156890412
C2×#156890192
C2×#156890012
C2×#156889822
C2×C4×(C2×D47)⋊C42
C2×C47×#3912
C2×#242747