Finite Group Databasebeta

← C2×#20244397 #26243075

Subgroups — C2×#20244397 #26243075

Order 12032.

2182 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
1C23×#10625337C211yesmaximal, characteristic, complemented
2C22×#13094004C211yesmaximal, characteristic
3C22×#13094000C211yesmaximal, characteristic
4C22×#13093949C211yesmaximal, characteristic, complemented
5C22×(C2×D47)⋊C8C211yesmaximal, characteristic
6#20244397C218yesmaximal, direct product factor
7C2×#15688885C211yesmaximal, characteristic, complemented
8C22×#103×C47C211yesmaximal, characteristic, complemented
9C23×Dic94C2211yescharacteristic
10C23×C4×D47C2211yescharacteristic
11C22×#10625337—24no—
12C22×#10625337—24no—
13C22×#10625337—24no—
14C22×#10625337C2214yescomplemented
15C23×C47⋊C8C2211yescharacteristic
16C2×#13094004—24no—
17C2×#13094004—22no—
18C2×#13094004—24no—
19C2×#13094004C2214yes—
20C2×#13094000—22no—
21C2×#13094000—24no—
22C2×#13094000—24no—
23C2×#13094000C2214yes—
24C22×C4⋊Dic47—21no—
25C22×C4⋊Dic47C2211yescharacteristic
26C22×Dic47⋊C4—21no—
27C22×(C2×D47)⋊C4—21no—
28C22×(C2×D47)⋊C4—21no—
29C2×#13093949—24no—
30C2×#13093949C2214yescomplemented
31C2×(C2×D47)⋊C8—24no—
32C2×(C2×D47)⋊C8C2214yes—
33#15688885C2214yescomplemented
34C23×Q8×C47C2211yescharacteristic
35C23×C8×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C2×#103×C47—24no—
38C2×#103×C47C2214yescomplemented
39C24×D47D411yescharacteristic
40C22×Dic94—22no—
41C22×Dic94—22no—
42C22×Dic94—22no—
43C22×Dic94—22no—
44C22×Dic94—21no—
45C22×Dic94—22no—
46C22×Dic94D414yes—
47C22×Dic94C2312yes—
48C23×Dic47—21no—
49C23×Dic47—21no—
50C23×Dic47D411yescharacteristic
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47—22no—
54C22×C4×D47—22no—
55C22×C4×D47—22no—
56C22×C4×D47—22no—
57C22×C4×D47D412yes—
58C22×C4×D47C2312yes—
59C2×#10625337—232no—
60C2×#10625337—28no—
61C2×#10625337—28no—
62C2×#10625337—28no—
63C22×C47⋊C8—22no—
64C22×C47⋊C8—22no—
65C22×C47⋊C8D414yes—
66C22×C47⋊C8C2312yes—
67#13094004—216no—
68#13094004—28no—
69#13094004—28no—
70#13094000—216no—
71#13094000—28no—
72#13094000—28no—
73C2×C4⋊Dic47—28no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—22no—
76C2×C4⋊Dic47—24no—
77C2×C4⋊Dic47D414yes—
78C2×C4⋊Dic47C2312yes—
79C2×Dic47⋊C4—28no—
80C2×Dic47⋊C4—24no—
81C2×(C2×D47)⋊C4—28no—
82C2×(C2×D47)⋊C4—28no—
83C2×(C2×D47)⋊C4—24no—
84C2×(C2×D47)⋊C4—24no—
85#13093949—28no—
86(C2×D47)⋊C8—28no—
87C22×Q8×C47—22no—
88C22×Q8×C47—21no—
89C22×Q8×C47—22no—
90C22×Q8×C47—22no—
91C22×Q8×C47—22no—
92C22×Q8×C47—22no—
93C22×Q8×C47D414yes—
94C22×Q8×C47C2312yes—
95C23×C4×C47—21no—
96C23×C4×C47—21no—
97C23×C4×C47C2311yescharacteristic
98C22×C8×C47—22no—
99C22×C8×C47—22no—
100C22×C8×C47—22no—
101C22×C8×C47C2312yes—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47D414yes—
105C2×C4⋊C4×C47C2312yes—
106#103×C47—28no—
107C24×C47C2×D411yescharacteristic
108C23×D47—22no—
109C23×D47—22no—
110C23×D47—22no—
111C23×D47—22no—
112C23×D47—22no—
113C23×D47—22no—
114C23×D47Q1614yescomplemented
115C23×D47C2×D412yes—
116C2×Q8×C47—24no—
117C2×Q8×C47—22no—
118C2×Q8×C47—28no—
119C2×Q8×C47—28no—
120C2×Q8×C47—22no—
121C2×Q8×C47—22no—
122C2×Q8×C47—22no—
123C2×Q8×C47—22no—
124C2×Q8×C47—42no—
125C2×Q8×C47—42no—
126C2×Q8×C47—44no—
127C2×Q8×C47—44no—
128C2×Q8×C47C2×D414yes—
129C22×C4×C47—24no—
130C22×C4×C47—24no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—42no—
134C22×C4×C47—42no—
135C22×C4×C47—42no—
136C22×C4×C47—42no—
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D412yes—
139C22×C4×C47C2×D412yes—
140C22×C4×C47C2×D412yes—
141C22×C4×C47C2×D412yes—
142C22×C4×C47C2×D412yes—
143C22×C4×C47#4112yes—
144C22×C4×C47C2411yescharacteristic
145C22×Dic47—24no—
146C22×Dic47—24no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—42no—
153C22×Dic47—42no—
154C22×Dic47—42no—
155C22×Dic47—42no—
156C22×Dic47C2×D412yes—
157C2×C4×D47—24no—
158C2×C4×D47—24no—
159C2×C4×D47—24no—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—44no—
167C2×C4×D47—44no—
168C2×C4×D47—44no—
169C2×C4×D47—44no—
170C2×Dic94—28no—
171C2×Dic94—28no—
172C2×Dic94—22no—
173C2×Dic94—22no—
174C2×Dic94—22no—
175C2×Dic94—22no—
176C2×Dic94—24no—
177C2×Dic94—22no—
178C2×Dic94—42no—
179C2×Dic94—44no—
180C2×Dic94—42no—
181C2×Dic94—44no—
182C2×Dic94C2×D414yes—
183C2×C8×C47—22no—
184C2×C8×C47—22no—
185C2×C8×C47—22no—
186C2×C8×C47—44no—
187C4⋊C4×C47—24no—
188C4⋊C4×C47—22no—
189C4⋊C4×C47C2×D414yes—
190#10625337—232no—
191(C2×D47)⋊C4—216no—
192(C2×D47)⋊C4—216no—
193C4⋊Dic47—216no—
194C4⋊Dic47—24no—
195C4⋊Dic47—22no—
196C4⋊Dic47C2×D414yes—
197Dic47⋊C4—216no—
198C2×C47⋊C8—28no—
199C2×C47⋊C8—22no—
200C2×C47⋊C8—22no—
201C2×C47⋊C8C2×D414yes—
202C23×C47#12012yes—
203C23×C47#12012yes—
204C23×C47#12112yes—
205C23×C47C2×Q1612yes—
206C23×C47#13512yes—
207C23×C47#13712yes—
208C23×C47#13712yes—
209C23×C47C22×D411yescharacteristic
210C22×D47—22no—
211C22×D47—22no—
212C22×D47—22no—
213C22×D47—22no—
214C22×D47—22no—
215C22×D47—22no—
216C22×D47—28no—
217C22×D47—28no—
218C22×D47—28no—
219C22×D47—44no—
220C22×D47—44no—
221C22×D47—44no—
222C22×D47—44no—
223C22×D47C2×Q1614yescomplemented
224Q8×C47—24no—
225Q8×C47—24no—
226Q8×C47—42no—
227Q8×C47—42no—
228Q8×C47—48no—
229C2×C4×C47—24no—
230C2×C4×C47—24no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—48no—
236C2×C4×C47—48no—
237C2×C4×C47#12012yes—
238C2×C4×C47#12014yes—
239C2×C4×C47#12012yes—
240C2×C4×C47#12114yes—
241C2×C4×C47#12112yes—
242C2×C4×C47#12114yes—
243C2×C4×C47#12714yes—
244C2×C4×C47C22×D411yescharacteristic
245C2×C4×C47C22×D411yescharacteristic
246C2×C4×C47C22×D411yescharacteristic
247C2×C4×C47C22×D411yescharacteristic
248C2×C4×C47C22×D411yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×Dic47—22no—
251C2×Dic47—24no—
252C2×Dic47—22no—
253C2×Dic47—24no—
254C2×Dic47—22no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—48no—
260C2×Dic47—44no—
261C2×Dic47—48no—
262C4×D47—42no—
263C4×D47—42no—
264C4×D47—42no—
265C4×D47—42no—
266C4×D47—48no—
267Dic94—24no—
268Dic94—24no—
269Dic94—42no—
270Dic94—42no—
271Dic94—48no—
272C8×C47—42no—
273C47⋊C8—24no—
274C2×#2001—471nomaximal, Sylow
275C22×C47#39214yes—
276C22×C47#45114yes—
277C22×C47#45114yes—
278C22×C47#45214yes—
279C22×C47#45214yes—
280C22×C47#46714yes—
281C22×C47#47014yes—
282C22×C47C2×#12011yescharacteristic
283C22×C47C2×#12011yescharacteristic
284C22×C47C2×#12111yescharacteristic
285C22×C47C22×Q1611yescharacteristic
286C22×C47C2×#13511yescharacteristic
287C22×C47C2×#13711yescharacteristic
288C22×C47C2×#13711yescharacteristic
289C2×D47—24no—
290C2×D47—24no—
291C2×D47—24no—
292C2×D47—42no—
293C2×D47—42no—
294C2×D47—42no—
295C2×D47—416no—
296C2×D47—42no—
297C4×C47—44no—
298C4×C47—44no—
299C4×C47#39214yes—
300C4×C47C2×#12011yescharacteristic
301C4×C47C2×#12111yescharacteristic
302C4×C47C2×#12111yescharacteristic
303C4×C47C2×#12711yescharacteristic
304Dic47—44no—
305Dic47—42no—
306Dic47—44no—
307C23×Q16—471no—
308C22×C22⋊Q8—471no—
309C22×C22⋊Q8—471no—
310C22×#103—471no—
311C22×#103D4711yescharacteristic, complemented
312C22×C22⋊C8—471no—
313#2001—478no—
314C2×#340—471no—
315C2×C47#200118yescomplemented
316C2×C47C2×#39211yescharacteristic
317C2×C47C2×#45111yescharacteristic
318C2×C47C2×#45111yescharacteristic
319C2×C47C2×#45211yescharacteristic
320C2×C47C2×#45211yescharacteristic
321C2×C47C2×#46711yescharacteristic
322C2×C47C2×#47011yescharacteristic
323D47—44no—
324C23×Q8—471no—
325C23×Q8C2×D4711yescharacteristic
326C24×C4—471no—
327C22×Q16—474no—
328C22×Q16—944no—
329C22×Q16—944no—
330C22×Q16—944no—
331C23×C8—471no—
332C23×C8C2×D4711yescharacteristic
333C2×C22⋊Q8—474no—
334C2×C22⋊Q8—474no—
335C2×C22⋊Q8—942no—
336C2×C22⋊Q8—944no—
337C2×C22⋊Q8—944no—
338C2×C22⋊Q8—942no—
339C2×C22⋊Q8—944no—
340C2×C22⋊Q8—944no—
341C22×C4⋊C4—471no—
342C22×C4⋊C4—941no—
343C22×C4⋊C4—941no—
344C22×C4⋊C4C2×D4711yescharacteristic
345C22×C22⋊C4—941no—
346C22×C22⋊C4—941no—
347C2×#103—24no—
348C2×#103—474no—
349C2×#103—944no—
350C2×#103C2×D4714yescomplemented
351C2×C22⋊C8—474no—
352C2×C22⋊C8—944no—
353#340—474no—
354C47C2×#200111yescharacteristic, complemented, Sylow
355C25—471no—
356C22×Q8—22no—
357C22×Q8—21no—
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—474no—
363C22×Q8—472no—
364C22×Q8—941no—
365C22×Q8—942no—
366C22×Q8—942no—
367C22×Q8—942no—
368C22×Q8—942no—
369C22×Q8—942no—
370C22×Q8D18814yes—
371C22×Q8C22×D4712yes—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—471no—
375C23×C4—472no—
376C23×C4—472no—
377C23×C4—941no—
378C23×C4—941no—
379C23×C4—942no—
380C23×C4—942no—
381C23×C4—942no—
382C23×C4—942no—
383C23×C4—942no—
384C23×C4—942no—
385C23×C4C22×D4711yescharacteristic
386C2×Q16—948no—
387C2×Q16—948no—
388C2×Q16—9432no—
389C2×Q16—948no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8—474no—
394C22×C8—472no—
395C22×C8—942no—
396C22×C8—942no—
397C22×C8C22×D4712yes—
398C22⋊Q8—948no—
399C22⋊Q8—9416no—
400C22⋊Q8—948no—
401C22⋊Q8—9416no—
402C22⋊Q8—948no—
403C22⋊Q8—948no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—474no—
407C2×C4⋊C4—472no—
408C2×C4⋊C4—944no—
409C2×C4⋊C4—944no—
410C2×C4⋊C4—948no—
411C2×C4⋊C4—948no—
412C2×C4⋊C4—942no—
413C2×C4⋊C4—941no—
414C2×C4⋊C4C22⋊D4714yes—
415C2×C4⋊C4C22×D4712yes—
416C2×C22⋊C4—944no—
417C2×C22⋊C4—944no—
418C2×C22⋊C4—948no—
419C2×C22⋊C4—948no—
420#103—28no—
421#103—948no—
422C22⋊C8—948no—
423C24—474no—
424C24—472no—
425C24—942no—
426C24—942no—
427C24—942no—
428C24—942no—
429C24—942no—
430C24—942no—
431C24D4×D4711yescharacteristic
432C2×Q8—24no—
433C2×Q8—22no—
434C2×Q8—28no—
435C2×Q8—28no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—42no—
441C2×Q8—44no—
442C2×Q8—42no—
443C2×Q8—44no—
444C2×Q8—474no—
445C2×Q8—944no—
446C2×Q8—942no—
447C2×Q8—948no—
448C2×Q8—948no—
449C2×Q8—942no—
450C2×Q8—942no—
451C2×Q8—942no—
452C2×Q8—942no—
453C2×Q8—1882no—
454C2×Q8—1882no—
455C2×Q8—1884no—
456C2×Q8—1884no—
457C2×Q8C2×D18814yes—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—472no—
467C22×C4—944no—
468C22×C4—942no—
469C22×C4—944no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—944no—
475C22×C4—944no—
476C22×C4—944no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—1882no—
484C22×C4—1882no—
485C22×C4—1882no—
486C22×C4—1882no—
487C22×C4—1884no—
488C22×C4—1884no—
489C22×C4—1884no—
490C22×C4—1884no—
491C22×C4C2×D18812yes—
492C22×C4#1062535012yes—
493C22×C4D4×D4711yescharacteristic
494C22×C4D4×D4712yes—
495C22×C4D4×D4712yes—
496C22×C4D4×D4712yes—
497C22×C4C2×C22⋊D4712yes—
498C22×C4C23×D4711yescharacteristic
499Q16—9432no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—44no—
504C2×C8—474no—
505C2×C8—948no—
506C2×C8—942no—
507C2×C8—942no—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—474no—
511C4⋊C4—9416no—
512C4⋊C4—9416no—
513C4⋊C4—944no—
514C4⋊C4—942no—
515C4⋊C4C2×C22⋊D4714yes—
516C22⋊C4—9416no—
517C22⋊C4—9416no—
518C23—474no—
519C23—948no—
520C23—948no—
521C23—942no—
522C23—942no—
523C23—942no—
524C23—948no—
525C23—942no—
526C23—942no—
527C23—942no—
528C23—1884no—
529C23—1884no—
530C23—1884no—
531C23—1884no—
532C23#1309399212yes—
533C23#1309399412yes—
534C23#1309399712yes—
535C23Q16×D4712yes—
536C23#1309404512yes—
537C23#1309405312yes—
538C23#1309405612yes—
539C23C2×D4×D4711yescharacteristic
540Q8—24no—
541Q8—24no—
542Q8—48no—
543Q8—42no—
544Q8—42no—
545Q8—944no—
546Q8—944no—
547Q8—1888no—
548Q8—1882no—
549Q8—1882no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—48no—
553C2×C4—48no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—944no—
559C2×C4—942no—
560C2×C4—944no—
561C2×C4—942no—
562C2×C4—942no—
563C2×C4—1884no—
564C2×C4—1888no—
565C2×C4—1888no—
566C2×C4—1882no—
567C2×C4—1882no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4—1888no—
571C2×C4—1882no—
572C2×C4—1882no—
573C2×C4—1882no—
574C2×C4—1882no—
575C2×C4#1309399212yes—
576C2×C4#1309399412yes—
577C2×C4#1309399414yes—
578C2×C4#1309399712yes—
579C2×C4#1309399714yes—
580C2×C4#1309399814yes—
581C2×C4#1309402014yes—
582C2×C4C2×D4×D4711yescharacteristic
583C2×C4C2×D4×D4711yescharacteristic
584C2×C4C2×D4×D4711yescharacteristic
585C2×C4C22×C22⋊D4711yescharacteristic
586C2×C4C22×D18811yescharacteristic
587C2×C4C2×#1062535011yescharacteristic
588C8—42no—
589C8—944no—
590C22—944no—
591C22—944no—
592C22—944no—
593C22—1882no—
594C22—1882no—
595C22—18816no—
596C22—1882no—
597C22—1882no—
598C22#1568903214yes—
599C22#1568927714yes—
600C22#1568928014yes—
601C22#1568928214yes—
602C22#1568928814yes—
603C22#1568936314yes—
604C22#1568938014yes—
605C22C2×#1309399211yescharacteristic
606C22C2×#1309399411yescharacteristic
607C22C2×#1309399711yescharacteristic
608C22C2×Q16×D4711yescharacteristic
609C22C2×#1309404511yescharacteristic
610C22C2×#1309405311yescharacteristic
611C22C2×#1309405611yescharacteristic
612C4—44no—
613C4—44no—
614C4—1882no—
615C4—1884no—
616C4—1884no—
617C4#1568903214yes—
618C4C2×#1309399411yescharacteristic
619C4C2×#1309399711yescharacteristic
620C4C2×#1309399811yescharacteristic
621C4C2×#1309402011yescharacteristic
622C2—1884no—
623C2#2024439718yesdirect product factor
624C2C2×#1568903211yescharacteristic
625C2C2×#1568927711yescharacteristic
626C2C2×#1568928011yescharacteristic
627C2C2×#1568928211yescharacteristic
628C2C2×#1568928811yescharacteristic
629C2C2×#1568936311yescharacteristic
630C2C2×#1568938011yescharacteristic
subgroupG/H
centerC24D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#103×C47C2
socleC24×C47C2×D4
prime radicalC24×D47D4
hypercenterC22×#103D47
hypocenterC47C2×#2001
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C23×#10625337C2semidirect
4. C22×#13093949C2semidirect
6. #20244397C2direct (N × H)
7. C2×#15688885C2semidirect
8. C22×#103×C47C2semidirect
14. C22×#10625337C22semidirect
30. C2×#13093949C22semidirect
33. #15688885C22semidirect
38. C2×#103×C47C22semidirect
114. C23×D47Q16semidirect
223. C22×D47C2×Q16semidirect
311. C22×#103D47semidirect
315. C2×C47#2001semidirect
350. C2×#103C2×D47semidirect
354. C47C2×#2001semidirect
623. C2#20244397direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106253372
C22×#130940042
C22×#130940002
C22×#130939492
C22×(C2×D47)⋊C82
#202443972
C2×#156888852
C22×#103×C472
C2×#200147