Finite Group Databasebeta

← C4×#15689048 #26138096

Subgroups — C4×#15689048 #26138096

Order 12032.

1790 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689048C211yesmaximal, characteristic
2C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic47C212yesmaximal
4#20241655C211yesmaximal, characteristic, complemented
5#20241648C212yesmaximal, complemented
6#20241644C211yesmaximal, characteristic, complemented
7#20241635C212yesmaximal
8#20241633C211yesmaximal, characteristic
9C4×C47⋊#95C212yesmaximal, complemented
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C22⋊Dic47C2212yes—
15C22×C22⋊Dic47C2212yes—
16C22×C4×Dic47C2212yes—
17C22×C4×Dic47C2212yes—
18#15689048C418yesdirect product factor
19C4×C4⋊Dic47—24no—
20C4×C22⋊Dic47—28no—
21C2×C47⋊#95C2212yes—
22C2×C47⋊#95C2211yescharacteristic
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2212yes—
31C24×C4×C47C2211yescharacteristic
32C22×C22⋊C4×C47C2211yescharacteristic
33C22×C22⋊C4×C47C2211yescharacteristic
34C22×C42×C47C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C4×C22⋊C4×C47—24no—
37C2×#95×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C23×Dic47C2312yes—
40C23×Dic47C2312yes—
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C2×C4⋊Dic47—22no—
44C2×C4⋊Dic47—22no—
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—24no—
47C2×C4⋊Dic47C2×C414yescomplemented
48C2×C22⋊Dic47—24no—
49C2×C22⋊Dic47—24no—
50C2×C22⋊Dic47—24no—
51C2×C22⋊Dic47—24no—
52C2×C22⋊Dic47—24no—
53C2×C22⋊Dic47C2×C418yes—
54C2×C4×Dic47—24no—
55C2×C4×Dic47—24no—
56C2×C4×Dic47—24no—
57C2×C4×Dic47—24no—
58C2×C4×Dic47—24no—
59C2×C4×Dic47—24no—
60C47⋊#95—24no—
61C47⋊#95—24no—
62C47⋊#95—24no—
63C47⋊#95—24no—
64C47⋊#95—22no—
65C47⋊#95—24no—
66C47⋊#95—24no—
67C47⋊#95—24no—
68C47⋊#95C2×C414yescomplemented
69C47⋊#95C2×C418yescomplemented
70C25×C47C2311yescharacteristic
71C23×C4×C47—22no—
72C23×C4×C47—22no—
73C23×C4×C47—24no—
74C23×C4×C47—24no—
75C23×C4×C47D414yes—
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C23×C4×C47C2311yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C23×C4×C47C2311yescharacteristic
82C2×C22⋊C4×C47—22no—
83C2×C22⋊C4×C47—22no—
84C2×C22⋊C4×C47—22no—
85C2×C22⋊C4×C47—22no—
86C2×C22⋊C4×C47—22no—
87C2×C22⋊C4×C47C2×C414yes—
88C2×C42×C47—24no—
89C2×C42×C47—22no—
90C2×C42×C47—24no—
91C2×C42×C47D414yes—
92#95×C47—22no—
93#95×C47—22no—
94C24×C47—21no—
95C24×C47—21no—
96C24×C47—21no—
97C24×C47—21no—
98C24×C47—22no—
99C24×C47—22no—
100C24×C47—22no—
101C24×C47—22no—
102C24×C47C22×C412yes—
103C24×C47C2×D412yes—
104C24×C47#4112yes—
105C24×C47C2411yescharacteristic
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—28no—
125C22×C4×C47—216no—
126C22×C4×C47—44no—
127C22×C4×C47—44no—
128C22×C4×C47—48no—
129C22×C4×C47C22×C412yes—
130C22×C4×C47C22×C412yes—
131C22×C4×C47C2×D412yes—
132C22×C4×C47C2×D412yes—
133C22×C4×C47C2×D412yes—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47#4112yes—
137C22×C4×C47#4112yes—
138C22×C4×C47#4112yes—
139C22×C4×C47#4114yes—
140C22×C4×C47#4114yes—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47C22×C414yes—
166C22×Dic47C22×C414yes—
167C22×Dic47#4114yes—
168C22×Dic47#4114yes—
169C22⋊C4×C47—28no—
170C22⋊C4×C47—28no—
171C42×C47—28no—
172C42×C47—44no—
173C22⋊Dic47—216no—
174C22⋊Dic47—216no—
175C4⋊Dic47—28no—
176C4⋊Dic47—28no—
177C4×Dic47—48no—
178C4×Dic47—48no—
179C23×C47—22no—
180C23×C47—24no—
181C23×C47—24no—
182C23×C47—22no—
183C23×C47—22no—
184C23×C47—24no—
185C23×C47—24no—
186C23×C47—22no—
187C23×C47—24no—
188C23×C47—24no—
189C23×C47—22no—
190C23×C47—22no—
191C23×C47—41no—
192C23×C47—41no—
193C23×C47—41no—
194C23×C47—42no—
195C23×C47—42no—
196C23×C47—42no—
197C23×C47—42no—
198C23×C47—42no—
199C23×C47—42no—
200C23×C47—41no—
201C23×C47C4×D414yes—
202C23×C47C23×C411yescharacteristic
203C23×C47C22×D411yescharacteristic
204C23×C47C22×D411yescharacteristic
205C23×C47C2×#4112yes—
206C23×C47C2×#4112yes—
207C23×C47C2×#4112yes—
208C23×C47C2×#4112yes—
209C23×C47C2×#4111yescharacteristic
210C23×C47C2×#4111yescharacteristic
211C23×C47C2×#4111yescharacteristic
212C23×C47C2×#4111yescharacteristic
213C2×C4×C47—24no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—24no—
217C2×C4×C47—22no—
218C2×C4×C47—24no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—24no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—24no—
225C2×C4×C47—22no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47—41no—
237C2×C4×C47—416no—
238C2×C4×C47C4×D414yes—
239C2×C4×C47#12114yes—
240C2×C4×C47#12314yes—
241C2×C4×C47#12318yes—
242C2×C4×C47#12414yes—
243C2×C4×C47#12618yes—
244C2×Dic47—24no—
245C2×Dic47—24no—
246C2×Dic47—24no—
247C2×Dic47—24no—
248C2×Dic47—24no—
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—24no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—42no—
260C2×Dic47—42no—
261C2×Dic47—42no—
262C2×Dic47—42no—
263C2×Dic47—42no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266C2×Dic47—42no—
267C2×Dic47—42no—
268C2×Dic47—42no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C4×#397—471nomaximal, Sylow
273C22×C47—24no—
274C22×C47—28no—
275C22×C47—44no—
276C22×C47—42no—
277C22×C47—42no—
278C22×C47—42no—
279C22×C47—44no—
280C22×C47—42no—
281C22×C47—44no—
282C22×C47—42no—
283C22×C47—42no—
284C22×C47C2×C4×D411yescharacteristic
285C22×C47C2×C4×D411yescharacteristic
286C22×C47C4×#4112yes—
287C22×C47C4×#4112yes—
288C22×C47C4×#4111yescharacteristic
289C22×C47C2×#12111yescharacteristic
290C22×C47C2×#12311yescharacteristic
291C22×C47C2×#12312yes—
292C22×C47#52511yescharacteristic
293C22×C47#52511yescharacteristic
294C22×C47#52512yes—
295C22×C47C2×#12411yescharacteristic
296C22×C47C2×#12612yes—
297C22×C47#52912yes—
298C22×C47#52912yes—
299C22×C47#52912yes—
300C22×C47#52912yes—
301C22×C47#52912yes—
302C22×C47#52912yes—
303C22×C47#52912yes—
304C22×C47#52911yescharacteristic
305C22×C47#53211yescharacteristic
306C22×C47#53211yescharacteristic
307C4×C47—24no—
308C4×C47—42no—
309C4×C47—42no—
310C4×C47—42no—
311C4×C47—42no—
312C4×C47#39718yescomplemented
313Dic47—44no—
314Dic47—44no—
315Dic47—44no—
316Dic47—44no—
317C2×#397—471no—
318C2×C4×C4⋊C4—471no—
319C2×C4×C22⋊C4—472no—
320C2×C4×C22⋊C4D4711yescharacteristic
321#1445—471no—
322#1443—472no—
323#1442—471no—
324#1440—472no—
325#1439—471no—
326C4×#95—471no—
327C4×#95—472no—
328C2×C47—44no—
329C2×C47C4×#12111yescharacteristic
330C2×C47C4×#12311yescharacteristic
331C2×C47C4×#12312yes—
332C2×C47C4×#12411yescharacteristic
333C2×C47C4×#12612yes—
334C2×C47C2×#39711yescharacteristic
335C2×C47#239211yescharacteristic
336C2×C47#239511yescharacteristic
337C2×C47#239512yes—
338C2×C47#239811yescharacteristic
339C2×C47#240112yes—
340C24×C4C2×D4711yescharacteristic
341C22×C4⋊C4—471no—
342C22×C4⋊C4—471no—
343C22×C22⋊C4—472no—
344C22×C22⋊C4—472no—
345C22×C22⋊C4C2×D4711yescharacteristic
346C22×C22⋊C4C2×D4711yescharacteristic
347C22×C42—472no—
348C22×C42—472no—
349C22×C42C2×D4711yescharacteristic
350C22×C42C2×D4711yescharacteristic
351#397—478no—
352C4×C4⋊C4—944no—
353C4×C22⋊C4—24no—
354C4×C22⋊C4—948no—
355C2×#95—471no—
356C2×#95—472no—
357C2×#95—472no—
358C2×#95—471no—
359C2×#95—472no—
360C2×#95—472no—
361C2×#95—472no—
362C2×#95—472no—
363C2×#95—472no—
364C2×#95—472no—
365C2×#95C2×D4711yescharacteristic
366C2×#95C2×D4711yescharacteristic
367C47C4×#39711yescharacteristic, complemented, Sylow
368C25C22×D4711yescharacteristic
369C23×C4—22no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—22no—
373C23×C4—472no—
374C23×C4—472no—
375C23×C4—472no—
376C23×C4—472no—
377C23×C4D18814yes—
378C23×C4C22×D4711yescharacteristic
379C23×C4C22×D4711yescharacteristic
380C23×C4C22×D4711yescharacteristic
381C23×C4C22×D4711yescharacteristic
382C23×C4C22×D4711yescharacteristic
383C23×C4C22×D4711yescharacteristic
384C2×C4⋊C4—474no—
385C2×C4⋊C4—944no—
386C2×C4⋊C4—942no—
387C2×C4⋊C4—942no—
388C2×C4⋊C4—942no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—478no—
395C2×C22⋊C4—944no—
396C2×C22⋊C4—944no—
397C2×C22⋊C4—944no—
398C2×C22⋊C4—944no—
399C2×C22⋊C4—944no—
400C2×C22⋊C4C4×D4714yes—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—22no—
404C2×C42—944no—
405C2×C42—944no—
406C2×C42—944no—
407C2×C42—944no—
408C2×C42—944no—
409C2×C42—944no—
410C2×C42C22⋊D4714yes—
411#95—22no—
412#95—22no—
413#95—474no—
414#95—478no—
415#95—944no—
416#95—944no—
417#95—944no—
418#95—944no—
419#95—944no—
420#95—944no—
421#95—942no—
422#95—944no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24C2×C4×D4712yes—
432C24C2×D18812yes—
433C24#1062535012yes—
434C24C23×D4711yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—28no—
454C22×C4—216no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—48no—
458C22×C4—474no—
459C22×C4—474no—
460C22×C4—474no—
461C22×C4—474no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4C2×C4×D4712yes—
487C22×C4C2×C4×D4712yes—
488C22×C4C2×D18812yes—
489C22×C4C2×D18812yes—
490C22×C4#1062535012yes—
491C22×C4#1062535012yes—
492C22×C4#1062535012yes—
493C22×C4#1062535214yes—
494C22×C4#1062535214yes—
495C22×C4C2×C22⋊D4712yes—
496C22×C4C2×C22⋊D4712yes—
497C22×C4C2×C22⋊D4712yes—
498C4⋊C4—948no—
499C4⋊C4—948no—
500C22⋊C4—28no—
501C22⋊C4—28no—
502C22⋊C4—9416no—
503C22⋊C4—9416no—
504C42—28no—
505C42—44no—
506C42—1888no—
507C42—1888no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—22no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—22no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23C4×D18814yes—
531C23C22×C4×D4711yescharacteristic
532C23C22×C22⋊D4711yescharacteristic
533C23C22×D18811yescharacteristic
534C23#41×D4712yes—
535C23#41×D4712yes—
536C23C2×#1062535212yes—
537C23C2×#1062535212yes—
538C23C2×#1062535011yescharacteristic
539C23C2×#1062535011yescharacteristic
540C23C2×#1062535011yescharacteristic
541C23C2×#1062535011yescharacteristic
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—416no—
567C2×C4—944no—
568C2×C4—944no—
569C2×C4—944no—
570C2×C4—944no—
571C2×C4—944no—
572C2×C4—944no—
573C2×C4—944no—
574C2×C4—944no—
575C2×C4—944no—
576C2×C4—944no—
577C2×C4—944no—
578C2×C4—944no—
579C2×C4—1882no—
580C2×C4—1882no—
581C2×C4—1882no—
582C2×C4—1882no—
583C2×C4—1882no—
584C2×C4—1882no—
585C2×C4—1882no—
586C2×C4—1882no—
587C2×C4—1882no—
588C2×C4—1882no—
589C2×C4—1882no—
590C2×C4—1882no—
591C2×C4—1882no—
592C2×C4—1882no—
593C2×C4—1882no—
594C2×C4—1882no—
595C2×C4C4×C22⋊D4714yes—
596C2×C4#1309399814yes—
597C2×C4#1309400514yes—
598C2×C4#1309400818yes—
599C2×C4#1309401114yes—
600C2×C4#1309401718yes—
601C22—24no—
602C22—28no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—44no—
607C22—42no—
608C22—42no—
609C22—44no—
610C22—42no—
611C22—44no—
612C22C2×C4×C22⋊D4711yescharacteristic
613C22C2×C4×D18811yescharacteristic
614C22C4×#1062535212yes—
615C22C4×#1062535212yes—
616C22C4×#1062535011yescharacteristic
617C22C2×#1309399811yescharacteristic
618C22C2×#1309400511yescharacteristic
619C22C2×#1309400812yes—
620C22#1568963011yescharacteristic
621C22#1568963411yescharacteristic
622C22#1568963512yes—
623C22C2×#1309401111yescharacteristic
624C22C2×#1309401712yes—
625C22#1568965112yes—
626C22#1568965312yes—
627C22#1568965312yes—
628C22#1568965312yes—
629C22#1568965312yes—
630C22#1568965512yes—
631C22#1568965512yes—
632C22#1568965711yescharacteristic
633C22#1568966911yescharacteristic
634C22#1568967311yescharacteristic
635C4—24no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—1884no—
641C4—1884no—
642C4—1884no—
643C4—1884no—
644C4#1568904818yesdirect product factor
645C2—44no—
646C2C4×#1309399811yescharacteristic
647C2C4×#1309400511yescharacteristic
648C2C4×#1309400812yes—
649C2C4×#1309401111yescharacteristic
650C2C4×#1309401712yes—
651C2C2×#1568904811yescharacteristic
652C2#2024662411yescharacteristic
653C2#2024664711yescharacteristic
654C2#2024664812yes—
655C2#2024667211yescharacteristic
656C2#2024668812yes—
subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C4×#397
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic47C2semidirect
4. #20241655C2semidirect
5. #20241648C2semidirect
6. #20241644C2semidirect
9. C4×C47⋊#95C2semidirect
10. C4×C47⋊#95C2semidirect
18. #15689048C4direct (N × H)
47. C2×C4⋊Dic47C2×C4semidirect
68. C47⋊#95C2×C4semidirect
69. C47⋊#95C2×C4semidirect
312. C4×C47#397semidirect
367. C47C4×#397semidirect
644. C4#15689048direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156890482
C2×C4×C4⋊Dic472
C2×C4×C22⋊Dic472
#202416552
#202416482
#202416442
#202416352
#202416332
C4×C47⋊#952
C2×C4×C22⋊C4×C472
C4×#39747