Finite Group Databasebeta

← C2×#20244605 #26243871

Subgroups — C2×#20244605 #26243871

Order 12032.

1434 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689697C211yesmaximal, characteristic
2C2×#15689163C211yesmaximal, characteristic, complemented
3C22×#13093952C211yesmaximal, characteristic
4C2×#15689122C211yesmaximal, characteristic
5C22×#13093943C211yesmaximal, characteristic, complemented
6#20244605C218yesmaximal, direct product factor
7C2×#15688883C211yesmaximal, characteristic, complemented
8C2×C47×#391C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12#15689697—22no—
13#15689697—22no—
14#15689697—22no—
15#15689697C2214yes—
16C2×#13094022—21no—
17C2×#13094013—21no—
18C2×#13094007—22no—
19C2×#13094000—21no—
20C2×#13094000—21no—
21C2×#13093983C2211yescharacteristic
22#15689163—22no—
23#15689163C2214yescomplemented
24C2×#13093957—21no—
25C2×#13093955—21no—
26C2×#13093952—24no—
27C2×#13093952C2214yes—
28#15689122—22no—
29#15689122C2214yes—
30C2×#13093947—21no—
31C2×#13093944—21no—
32C2×#13093943—24no—
33C2×#13093943C2214yescomplemented
34#15688883C2214yescomplemented
35C23×Q8×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C47×#391—22no—
39C47×#391C2214yescomplemented
40C2×#95×C47—22no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—22no—
44C2×#10625350—22no—
45C2×#10625350—22no—
46C2×#10625350—22no—
47C2×#10625350D412yes—
48C2×#10625350C2312yes—
49C22×Dic94D411yescharacteristic
50C22×D188D411yescharacteristic
51C22×C22⋊D47—21no—
52C22×C4×D47—21no—
53C2×#10625329—21no—
54C2×#10625329—22no—
55C2×#10625329—21no—
56C2×#10625329—22no—
57C2×#10625329—22no—
58C2×#10625329D414yes—
59C2×#10625329C2312yes—
60C2×#10625329C2312yes—
61C22×C47⋊C8—21no—
62C22×C47⋊C8—21no—
63#13094022—24no—
64#13094022—24no—
65#13094013—24no—
66#13094013—24no—
67#13094007—28no—
68#13094007—28no—
69#13094000—24no—
70#13094000—24no—
71#13094000—24no—
72#13094000—24no—
73#13093983—21no—
74#13093983—21no—
75#13093983D412yes—
76#13093983C2312yes—
77C2×C4⋊Dic47D411yescharacteristic
78C2×C4⋊Dic47D411yescharacteristic
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—22no—
81C2×C22⋊Dic47—21no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—22no—
84C2×C4×Dic47—21no—
85#13093957—24no—
86#13093955—24no—
87#13093952—28no—
88#13093947—24no—
89#13093944—24no—
90#13093943—28no—
91C22×Q8×C47—22no—
92C22×Q8×C47—21no—
93C22×Q8×C47—21no—
94C22×Q8×C47—21no—
95C22×Q8×C47—21no—
96C22×Q8×C47—22no—
97C22×Q8×C47—22no—
98C22×Q8×C47—22no—
99C22×Q8×C47D412yes—
100C22×Q8×C47C2312yes—
101C23×C4×C47—21no—
102C23×C4×C47—21no—
103C23×C4×C47D412yes—
104C23×C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47C2312yes—
111C2×C42×C47—22no—
112C2×C42×C47—22no—
113C2×C42×C47—21no—
114C2×C42×C47C2312yes—
115#95×C47—28no—
116C24×C47C2×D411yescharacteristic
117C23×D47—21no—
118C2×Q8×C47—22no—
119C2×Q8×C47—22no—
120C2×Q8×C47—24no—
121C2×Q8×C47—24no—
122C2×Q8×C47—22no—
123C2×Q8×C47—22no—
124C2×Q8×C47—22no—
125C2×Q8×C47—22no—
126C2×Q8×C47—22no—
127C2×Q8×C47—22no—
128C2×Q8×C47—42no—
129C2×Q8×C47—42no—
130C2×Q8×C47—42no—
131C2×Q8×C47—42no—
132C2×Q8×C47—42no—
133C2×Q8×C47—42no—
134C2×Q8×C47—42no—
135C2×Q8×C47—42no—
136C22×C4×C47—24no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—24no—
140C22×C4×C47—24no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—42no—
144C22×C4×C47—42no—
145C22×C4×C47—44no—
146C22×C4×C47—41no—
147C22×C4×C47—41no—
148C22×C4×C47C2×D414yes—
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D412yes—
155C22×C4×C47#4112yes—
156C22×C4×C47#4112yes—
157C22×C4×C47#4112yes—
158C22×C4×C47C2411yescharacteristic
159C2×C22⋊D47—22no—
160C2×C22⋊D47—22no—
161C2×C22⋊D47—42no—
162C2×C22⋊D47—42no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166#10625350—24no—
167#10625350—24no—
168#10625350—22no—
169#10625350—22no—
170#10625350—22no—
171#10625350—22no—
172#10625350—42no—
173#10625350—42no—
174#10625350—42no—
175#10625350—42no—
176C2×D188—22no—
177C2×D188—22no—
178C2×D188—21no—
179C2×D188C2×D412yes—
180C2×C4×D47—22no—
181C2×C4×D47—22no—
182C2×C4×D47—42no—
183C2×C4×D47—42no—
184C2×Dic94—22no—
185C2×Dic94—22no—
186C2×Dic94—21no—
187C2×Dic94C2×D412yes—
188C4⋊C4×C47—22no—
189C4⋊C4×C47—22no—
190C4⋊C4×C47—41no—
191C4⋊C4×C47—41no—
192C42×C47—22no—
193C42×C47—22no—
194C42×C47—42no—
195C22⋊Dic47—22no—
196C22⋊Dic47—22no—
197(C2×D47)⋊C4—28no—
198(C2×D47)⋊C4—28no—
199C4⋊Dic47—21no—
200C4⋊Dic47—21no—
201C4⋊Dic47C2×D412yes—
202C4⋊Dic47C2×D412yes—
203Dic47⋊C4—28no—
204Dic47⋊C4—28no—
205C4×Dic47—22no—
206C4×Dic47—22no—
207#10625329—24no—
208#10625329—22no—
209#10625329—22no—
210#10625329—22no—
211#10625329—42no—
212#10625329C2×D414yes—
213C2×C47⋊C8—24no—
214C2×C47⋊C8—22no—
215C2×C47⋊C8—22no—
216C2×C47⋊C8—42no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47#12011yescharacteristic
220C23×C47#12011yescharacteristic
221C23×C47#12112yes—
222C23×C47#12312yes—
223C23×C47C22×D411yescharacteristic
224C22×D47—22no—
225C22×D47—42no—
226C22×D47—42no—
227C22×D47—42no—
228Q8×C47—42no—
229Q8×C47—42no—
230Q8×C47—42no—
231Q8×C47—42no—
232Q8×C47—44no—
233Q8×C47—44no—
234C2×C4×C47—24no—
235C2×C4×C47—24no—
236C2×C4×C47—24no—
237C2×C4×C47—24no—
238C2×C4×C47—42no—
239C2×C4×C47—48no—
240C2×C4×C47—42no—
241C2×C4×C47—44no—
242C2×C4×C47—44no—
243C2×C4×C47—44no—
244C2×C4×C47—42no—
245C2×C4×C47—82no—
246C2×C4×C47—82no—
247C2×C4×C47#12011yescharacteristic
248C2×C4×C47#12011yescharacteristic
249C2×C4×C47#12112yes—
250C2×C4×C47#12112yes—
251C2×C4×C47#12112yes—
252C2×C4×C47#12112yes—
253C2×C4×C47#12112yes—
254C2×C4×C47#12312yes—
255C2×C4×C47#12312yes—
256C2×C4×C47#12312yes—
257C2×C4×C47#12412yes—
258C2×C4×C47#12412yes—
259C2×C4×C47C22×D411yescharacteristic
260C2×C4×C47C22×D411yescharacteristic
261C2×C4×C47C22×D411yescharacteristic
262C2×C4×C47C2×#4111yescharacteristic
263C2×C4×C47C2×#4111yescharacteristic
264C2×C4×C47C2×#4111yescharacteristic
265C22⋊D47—42no—
266C22⋊D47—42no—
267C22⋊D47—44no—
268C2×Dic47—22no—
269C2×Dic47—22no—
270C2×Dic47—22no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—42no—
274D188—22no—
275D188—22no—
276D188—42no—
277C4×D47—42no—
278C4×D47—42no—
279C4×D47—44no—
280Dic94—22no—
281Dic94—22no—
282Dic94—42no—
283C47⋊C8—24no—
284C47⋊C8—42no—
285C2×#2038—471nomaximal, Sylow
286C22×C47—21no—
287C22×C47—21no—
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—24no—
291C22×C47—24no—
292C22×C47#39412yes—
293C22×C47#39412yes—
294C22×C47#45412yes—
295C22×C47#45612yes—
296C22×C47C2×#12011yescharacteristic
297C22×C47C2×#12111yescharacteristic
298C22×C47C2×#12311yescharacteristic
299C2×D47—42no—
300C2×D47—42no—
301C2×D47—42no—
302C2×D47—84no—
303C4×C47—44no—
304C4×C47—44no—
305C4×C47—82no—
306C4×C47#39412yes—
307C4×C47#39412yes—
308C4×C47C2×#12111yescharacteristic
309C4×C47C2×#12111yescharacteristic
310C4×C47C2×#12311yescharacteristic
311C4×C47C2×#12411yescharacteristic
312Dic47—42no—
313Dic47—42no—
314Dic47—42no—
315C2×#536—471no—
316C2×#428—471no—
317C22×#104—471no—
318C2×#417—471no—
319C22×#101—471no—
320C2×#391D4711yescharacteristic, complemented
321#2038—478no—
322C2×#339—471no—
323C2×C47—21no—
324C2×C47—21no—
325C2×C47—22no—
326C2×C47#203814yescomplemented
327C2×C47C2×#39411yescharacteristic
328C2×C47C2×#45411yescharacteristic
329C2×C47C2×#45611yescharacteristic
330D47—82no—
331C22×#41—471no—
332C23×Q8C2×D4711yescharacteristic
333C22×M16—471no—
334C22×M16—471no—
335#536—474no—
336#536—942no—
337#536—942no—
338#536—942no—
339C2×C4⋊Q8—941no—
340C2×#124—941no—
341C2×#123—942no—
342C2×C22⋊Q8—941no—
343C2×C22⋊Q8—941no—
344C2×#117—471no—
345C22×C4⋊C4C2×D4711yescharacteristic
346C22×C42C2×D4711yescharacteristic
347#428—474no—
348#428—942no—
349C2×#107—941no—
350C2×#106—941no—
351C2×#104—474no—
352C2×#104—944no—
353#417—474no—
354#417—942no—
355C2×#103—941no—
356C2×#102—941no—
357C2×#101—474no—
358C2×#101—944no—
359#391—22no—
360#391C2×D4714yescomplemented
361C2×#95—22no—
362#339—474no—
363C47C2×#203811yescharacteristic, complemented, Sylow
364C2×#41—472no—
365C2×#41—472no—
366C2×#41—941no—
367C2×#41—941no—
368C2×#41—942no—
369C2×#41—942no—
370C2×#41—942no—
371C2×#41—942no—
372C22×Q8—22no—
373C22×Q8—22no—
374C22×Q8—21no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—21no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—471no—
381C22×Q8C22⋊D4712yes—
382C22×Q8C22×D4712yes—
383C22×D4—471no—
384C22×D4—941no—
385C23×C4—21no—
386C23×C4—21no—
387C23×C4—941no—
388C23×C4C22⋊D4712yes—
389C23×C4C22×D4711yescharacteristic
390C2×M16—474no—
391C2×M16—472no—
392C2×M16—472no—
393C2×M16—942no—
394C2×M16—941no—
395C2×M16—941no—
396C2×M16—942no—
397C2×M16—942no—
398C22×C8—941no—
399C22×C8—941no—
400C4⋊Q8—944no—
401C4⋊Q8—944no—
402#124—944no—
403#124—944no—
404#123—948no—
405#123—948no—
406C22⋊Q8—944no—
407C22⋊Q8—944no—
408C22⋊Q8—944no—
409C22⋊Q8—944no—
410#117—472no—
411#117—472no—
412#117—941no—
413#117—941no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—471no—
420C2×C4⋊C4—471no—
421C2×C4⋊C4—942no—
422C2×C4⋊C4—942no—
423C2×C4⋊C4C22×D4712yes—
424C2×C22⋊C4—942no—
425C2×C22⋊C4—942no—
426C2×C22⋊C4—941no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—21no—
430C2×C42—941no—
431C2×C42C22×D4712yes—
432#107—944no—
433#106—944no—
434#104—948no—
435#103—944no—
436#102—944no—
437#101—948no—
438#95—28no—
439C24—941no—
440C24C2×C22⋊D4711yescharacteristic
441#41—944no—
442#41—944no—
443#41—942no—
444#41—942no—
445#41—942no—
446#41—942no—
447#41—1882no—
448#41—1882no—
449#41—1882no—
450#41—1882no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—24no—
454C2×Q8—24no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—472no—
470C2×Q8—941no—
471C2×Q8—942no—
472C2×Q8—942no—
473C2×D4—472no—
474C2×D4—942no—
475C2×D4—942no—
476C2×D4—941no—
477C2×D4—942no—
478C2×D4—942no—
479C2×D4—1882no—
480C2×D4—1882no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—44no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—941no—
494C22×C4—941no—
495C22×C4—941no—
496C22×C4—942no—
497C22×C4—942no—
498C22×C4—1882no—
499C22×C4—1882no—
500C22×C4#1062535012yes—
501C22×C4#1062535012yes—
502C22×C4D4×D4711yescharacteristic
503C22×C4D4×D4711yescharacteristic
504C22×C4D4×D4711yescharacteristic
505C22×C4D4×D4711yescharacteristic
506C22×C4D4×D4712yes—
507C22×C4#1062535212yes—
508C22×C4C2×C22⋊D4714yes—
509C22×C4C2×C22⋊D4711yescharacteristic
510C22×C4C23×D4711yescharacteristic
511M16—474no—
512M16—944no—
513M16—942no—
514M16—942no—
515M16—942no—
516M16—1882no—
517C2×C8—944no—
518C2×C8—942no—
519C2×C8—942no—
520C2×C8—1882no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—472no—
526C4⋊C4—472no—
527C4⋊C4—948no—
528C4⋊C4—948no—
529C4⋊C4—941no—
530C4⋊C4—941no—
531C22⋊C4—948no—
532C22⋊C4—948no—
533C22⋊C4—942no—
534C22⋊C4—942no—
535C42—22no—
536C42—22no—
537C42—42no—
538C42—942no—
539C42—942no—
540C23—22no—
541C23—22no—
542C23—942no—
543C23—1882no—
544C23—1882no—
545C23—1882no—
546C23#1309399211yescharacteristic
547C23#1309399211yescharacteristic
548C23#1309399612yes—
549C23#1309400712yes—
550C23C22×C22⋊D4711yescharacteristic
551Q8—44no—
552Q8—44no—
553Q8—42no—
554Q8—42no—
555Q8—42no—
556Q8—42no—
557Q8—942no—
558Q8—942no—
559Q8—1882no—
560D4—942no—
561D4—942no—
562D4—1884no—
563D4—1882no—
564D4—1882no—
565D4—1882no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—42no—
571C2×C4—48no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—42no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—942no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—1882no—
583C2×C4—1882no—
584C2×C4—1882no—
585C2×C4—1884no—
586C2×C4—1882no—
587C2×C4—1882no—
588C2×C4#1309399211yescharacteristic
589C2×C4#1309399211yescharacteristic
590C2×C4#1309399612yes—
591C2×C4#1309399712yes—
592C2×C4#1309399712yes—
593C2×C4#1309399712yes—
594C2×C4#1309399712yes—
595C2×C4#1309400612yes—
596C2×C4#1309400612yes—
597C2×C4#1309400712yes—
598C2×C4#1309401012yes—
599C2×C4#1309401012yes—
600C2×C4C2×D4×D4711yescharacteristic
601C2×C4C2×D4×D4711yescharacteristic
602C2×C4C2×D4×D4711yescharacteristic
603C2×C4C2×#1062535211yescharacteristic
604C2×C4C2×#1062535011yescharacteristic
605C2×C4C2×#1062535011yescharacteristic
606C8—944no—
607C8—1882no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—24no—
613C22—24no—
614C22—3764no—
615C22—1882no—
616C22—1882no—
617C22—1882no—
618C22#1568903812yes—
619C22#1568903812yes—
620C22#1568929512yes—
621C22#1568930512yes—
622C22C2×#1309399211yescharacteristic
623C22C2×#1309399611yescharacteristic
624C22C2×#1309400711yescharacteristic
625C4—44no—
626C4—44no—
627C4—82no—
628C4—1882no—
629C4—1882no—
630C4—1882no—
631C4#1568903812yes—
632C4#1568903812yes—
633C4C2×#1309399711yescharacteristic
634C4C2×#1309399711yescharacteristic
635C4C2×#1309400611yescharacteristic
636C4C2×#1309401011yescharacteristic
637C2—21no—
638C2—22no—
639C2—21no—
640C2—3762no—
641C2#2024460514yesdirect product factor
642C2C2×#1568903811yescharacteristic
643C2C2×#1568929511yescharacteristic
644C2C2×#1568930511yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#391C2
socleC23×C47#120
prime radicalC22×#10625350C22
hypercenterC2×#391D47
hypocenterC47C2×#2038
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#15689163C2semidirect
5. C22×#13093943C2semidirect
6. #20244605C2direct (N × H)
7. C2×#15688883C2semidirect
8. C2×C47×#391C2semidirect
23. #15689163C22semidirect
33. C2×#13093943C22semidirect
34. #15688883C22semidirect
39. C47×#391C22semidirect
320. C2×#391D47semidirect
326. C2×C47#2038semidirect
360. #391C2×D47semidirect
363. C47C2×#2038semidirect
641. C2#20244605direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896972
C2×#156891632
C22×#130939522
C2×#156891222
C22×#130939432
#202446052
C2×#156888832
C2×C47×#3912
C2×#203847