Finite Group Databasebeta

← #26138076

Subgroups — #26138076

Order 12032.

2550 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic47C211yesmaximal, characteristic
2C2×#15689037C211yesmaximal, characteristic
3C2×#15688974C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic47C212yesmaximal, complemented
5C2×C22⋊C4×Dic47C212yesmaximal, complemented
6#20241644C211yesmaximal, characteristic, complemented
7#20241642C211yesmaximal, characteristic, complemented
8#20241635C212yesmaximal, complemented
9#20241631C212yesmaximal, complemented
10#95×Dic47C211yesmaximal, characteristic, complemented
11C47×#1438C211yesmaximal, characteristic
12C24×Dic47C2212yes—
13C2×D4×Dic47—28no—
14C2×D4×Dic47—24no—
15C22×C4⋊Dic47C2211yescharacteristic
16C22×Dic47⋊C4C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×C22⋊Dic47C2212yes—
19C22×C22⋊Dic47C2212yes—
20C22×C22⋊Dic47C2212yes—
21C22×C4×Dic47C2212yes—
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25#15689037C418yescomplemented
26#15688974—24no—
27C22⋊C4×Dic47—28no—
28C22⋊C4×Dic47—28no—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C23×D4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2212yes—
38C22×C22⋊C4×C47C2212yes—
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2211yescharacteristic
41C23×Dic47—24no—
42C23×Dic47—24no—
43C23×Dic47—24no—
44C23×Dic47—24no—
45C23×Dic47—24no—
46C23×Dic47—24no—
47C23×Dic47D418yes—
48C23×Dic47C2312yes—
49C23×Dic47C2311yescharacteristic
50C23×Dic47C2312yes—
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54D4×Dic47—232no—
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—24no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4—22no—
62C2×Dic47⋊C4C2×C414yescomplemented
63C2×C22⋊Dic47—24no—
64C2×C22⋊Dic47—24no—
65C2×C22⋊Dic47—24no—
66C2×C22⋊Dic47—24no—
67C2×C22⋊Dic47—24no—
68C2×C22⋊Dic47—24no—
69C2×C22⋊Dic47—24no—
70C2×C22⋊Dic47C2×C418yescomplemented
71C2×C22⋊Dic47C2×C418yescomplemented
72C2×C4×Dic47—22no—
73C2×C4×Dic47—24no—
74C2×C4×Dic47—22no—
75C2×C4×Dic47—24no—
76C2×C4×Dic47—24no—
77C2×C4×Dic47—24no—
78C2×C4×Dic47—22no—
79C2×C4×Dic47—24no—
80C2×C4×Dic47D414yes—
81C2×C4×Dic47D414yescomplemented
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—24no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C47⋊#95—22no—
88C47⋊#95C2×C414yescomplemented
89C25×C47C2312yes—
90C22×D4×C47—24no—
91C22×D4×C47—24no—
92C22×D4×C47—22no—
93C22×D4×C47—22no—
94C22×D4×C47C2×C414yes—
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2312yes—
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C2×C22⋊C4×C47—24no—
100C2×C22⋊C4×C47—24no—
101C2×C22⋊C4×C47—24no—
102C2×C22⋊C4×C47—24no—
103C2×C22⋊C4×C47—24no—
104C2×C22⋊C4×C47—24no—
105#95×C47—22no—
106#95×C47—22no—
107C24×C47—22no—
108C24×C47—22no—
109C24×C47—22no—
110C24×C47—22no—
111C24×C47—22no—
112C24×C47—22no—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47C22×C414yes—
120C24×C47C2×D414yes—
121C24×C47#4114yes—
122C24×C47C2411yescharacteristic
123C2×D4×C47—28no—
124C2×D4×C47—216no—
125C2×D4×C47—28no—
126C2×D4×C47—216no—
127C2×D4×C47—28no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—21no—
143C22×C4×C47—22no—
144C22×C4×C47C22×C412yes—
145C22×C4×C47C2×D412yes—
146C22×C4×C47C2×D412yes—
147C22×C4×C47#4114yes—
148C22×C4×C47#4112yes—
149C22×C4×C47#4112yes—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—21no—
159C22×Dic47—22no—
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—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—216no—
175C22×Dic47—216no—
176C22×Dic47—216no—
177C22×Dic47—48no—
178C22×Dic47—48no—
179C22×Dic47—48no—
180C22×Dic47—48no—
181C22×Dic47C22×C414yes—
182C22×Dic47C22×C412yes—
183C22×Dic47C22×C412yes—
184C22×Dic47C2×D414yes—
185C22×Dic47C2×D412yes—
186C22×Dic47C2×D412yes—
187C22×Dic47C2×D414yes—
188C22×Dic47C2×D412yes—
189C22×Dic47C2×D412yes—
190C22×Dic47#4112yes—
191C22×Dic47#4112yes—
192C22×Dic47#4114yes—
193C22⋊C4×C47—216no—
194C22⋊C4×C47—216no—
195C22⋊Dic47—216no—
196C22⋊Dic47—216no—
197C22⋊Dic47—216no—
198C4⋊Dic47—28no—
199Dic47⋊C4—28no—
200Dic47⋊C4—28no—
201C4×Dic47—28no—
202C4×Dic47—28no—
203C4×Dic47—44no—
204C4×Dic47—48no—
205C23×C47—24no—
206C23×C47—24no—
207C23×C47—24no—
208C23×C47—24no—
209C23×C47—24no—
210C23×C47—24no—
211C23×C47—24no—
212C23×C47—24no—
213C23×C47—24no—
214C23×C47—24no—
215C23×C47—24no—
216C23×C47—24no—
217C23×C47—24no—
218C23×C47—24no—
219C23×C47—24no—
220C23×C47—24no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—42no—
224C23×C47—42no—
225C23×C47—42no—
226C23×C47—42no—
227C23×C47—42no—
228C23×C47—42no—
229C23×C47—42no—
230C23×C47—42no—
231C23×C47—42no—
232C23×C47—42no—
233C23×C47—42no—
234C23×C47—42no—
235C23×C47—42no—
236C23×C47—42no—
237C23×C47—42no—
238C23×C47—42no—
239C23×C47C4×D418yes—
240C23×C47C23×C411yescharacteristic
241C23×C47C22×D412yes—
242C23×C47C22×D411yescharacteristic
243C23×C47C22×D411yescharacteristic
244C23×C47C2×#4111yescharacteristic
245C23×C47C2×#4111yescharacteristic
246C23×C47C2×#4112yes—
247C23×C47C2×#4112yes—
248C23×C47C2×#4111yescharacteristic
249C23×C47C2×#4111yescharacteristic
250C23×C47C2×#4112yes—
251D4×C47—232no—
252C2×C4×C47—24no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—24no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—24no—
259C2×C4×C47—24no—
260C2×C4×C47—24no—
261C2×C4×C47—24no—
262C2×C4×C47—24no—
263C2×C4×C47—41no—
264C2×C4×C47—42no—
265C2×C4×C47—42no—
266C2×C4×C47—41no—
267C2×C4×C47—42no—
268C2×C4×C47—42no—
269C2×C4×C47—42no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—42no—
273C2×C4×C47C4×D414yes—
274C2×Dic47—22no—
275C2×Dic47—22no—
276C2×Dic47—22no—
277C2×Dic47—22no—
278C2×Dic47—22no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—24no—
282C2×Dic47—24no—
283C2×Dic47—24no—
284C2×Dic47—24no—
285C2×Dic47—22no—
286C2×Dic47—24no—
287C2×Dic47—24no—
288C2×Dic47—24no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—41no—
292C2×Dic47—42no—
293C2×Dic47—42no—
294C2×Dic47—42no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—41no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—432no—
305C2×Dic47C4×D414yescomplemented
306C2×Dic47#12014yes—
307C2×Dic47#12114yes—
308C2×Dic47#12118yes—
309C2×Dic47#12318yes—
310C2×Dic47#12414yes—
311C4×#394—471nomaximal, Sylow
312C22×C47—28no—
313C22×C47—28no—
314C22×C47—28no—
315C22×C47—44no—
316C22×C47—44no—
317C22×C47—44no—
318C22×C47—44no—
319C22×C47—44no—
320C22×C47—44no—
321C22×C47—44no—
322C22×C47—44no—
323C22×C47—44no—
324C22×C47—44no—
325C22×C47—44no—
326C22×C47—44no—
327C22×C47C2×C4×D411yescharacteristic
328C22×C47C2×C4×D412yes—
329C22×C47C2×C4×D411yescharacteristic
330C22×C47C4×#4111yescharacteristic
331C22×C47C4×#4112yes—
332C22×C47C2×#12011yescharacteristic
333C22×C47C2×#12111yescharacteristic
334C22×C47C2×#12112yes—
335C22×C47C2×#12312yes—
336C22×C47#52512yes—
337C22×C47#52512yes—
338C22×C47#52512yes—
339C22×C47#52511yescharacteristic
340C22×C47#52511yescharacteristic
341C22×C47C2×#12411yescharacteristic
342C22×C47#52912yes—
343C22×C47#52911yescharacteristic
344C22×C47#52912yes—
345C22×C47#52912yes—
346C22×C47#52912yes—
347C22×C47#53212yes—
348C22×C47#53211yescharacteristic
349C22×C47#53211yescharacteristic
350C4×C47—24no—
351C4×C47—42no—
352C4×C47—42no—
353C4×C47—44no—
354Dic47—24no—
355Dic47—44no—
356Dic47—42no—
357Dic47—42no—
358Dic47—44no—
359Dic47#39418yescomplemented
360C22×C4×D4—471no—
361C2×#394—471no—
362C2×C4×C4⋊C4—471no—
363C2×C4×C22⋊C4—472no—
364C2×C4×C22⋊C4—472no—
365#1442—471no—
366#1441—471no—
367#1440—472no—
368#1439—472no—
369#1438D4711yescharacteristic
370C4×#95—471no—
371C2×C47—48no—
372C2×C47C4×#12011yescharacteristic
373C2×C47C4×#12112yes—
374C2×C47C4×#12111yescharacteristic
375C2×C47C4×#12312yes—
376C2×C47C4×#12411yescharacteristic
377C2×C47C2×#39411yescharacteristic
378C2×C47#238811yescharacteristic
379C2×C47#239211yescharacteristic
380C2×C47#239212yes—
381C2×C47#239512yes—
382C2×C47#239811yescharacteristic
383C23×D4C2×D4711yescharacteristic
384C24×C4—472no—
385C2×C4×D4—944no—
386C2×C4×D4—948no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4—471no—
389C22×C4⋊C4—471no—
390C22×C22⋊C4—472no—
391C22×C22⋊C4—472no—
392C22×C22⋊C4—472no—
393C22×C22⋊C4C2×D4712yes—
394C22×C22⋊C4C2×D4712yes—
395C22×C42—471no—
396C22×C42—471no—
397C22×C42—472no—
398C22×C42—471no—
399#394—478no—
400C4×C4⋊C4—944no—
401C4×C22⋊C4—948no—
402C4×C22⋊C4—948no—
403C2×#95—471no—
404C2×#95—472no—
405C2×#95—472no—
406C2×#95—472no—
407C2×#95—471no—
408C2×#95—472no—
409C2×#95—472no—
410C2×#95C2×D4711yescharacteristic
411C2×#95C2×D4711yescharacteristic
412C47C4×#39411yescharacteristic, complemented, Sylow
413C25C22×D4712yes—
414C22×D4—24no—
415C22×D4—24no—
416C22×D4—22no—
417C22×D4—22no—
418C22×D4C4×D4714yes—
419C23×C4—471no—
420C23×C4—471no—
421C23×C4—478no—
422C23×C4—471no—
423C23×C4—471no—
424C23×C4—472no—
425C23×C4—472no—
426C23×C4—944no—
427C23×C4—944no—
428C23×C4—944no—
429C23×C4—944no—
430C23×C4—944no—
431C23×C4—944no—
432C23×C4C22×D4711yescharacteristic
433C23×C4C22×D4711yescharacteristic
434C23×C4C22×D4712yes—
435C23×C4C22×D4711yescharacteristic
436C4×D4—9432no—
437C2×C4⋊C4—474no—
438C2×C4⋊C4—944no—
439C2×C4⋊C4—942no—
440C2×C4⋊C4—942no—
441C2×C4⋊C4—942no—
442C2×C4⋊C4—942no—
443C2×C4⋊C4—942no—
444C2×C4⋊C4—942no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—478no—
452C2×C22⋊C4—478no—
453C2×C22⋊C4—944no—
454C2×C22⋊C4—944no—
455C2×C22⋊C4—944no—
456C2×C22⋊C4—944no—
457C2×C22⋊C4—944no—
458C2×C22⋊C4—944no—
459C2×C22⋊C4—944no—
460C2×C42—474no—
461C2×C42—474no—
462C2×C42—944no—
463C2×C42—942no—
464C2×C42—942no—
465C2×C42—944no—
466C2×C42—944no—
467C2×C42—944no—
468C2×C42—942no—
469C2×C42—944no—
470#95—22no—
471#95—22no—
472#95—474no—
473#95—944no—
474#95—944no—
475#95—944no—
476#95—942no—
477#95—944no—
478#95—944no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24C2×C4×D4714yes—
492C24D4×D4714yes—
493C24#1062535214yes—
494C24C23×D4711yescharacteristic
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—216no—
498C2×D4—216no—
499C2×D4—28no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—472no—
517C22×C4—472no—
518C22×C4—474no—
519C22×C4—472no—
520C22×C4—474no—
521C22×C4—472no—
522C22×C4—472no—
523C22×C4—472no—
524C22×C4—474no—
525C22×C4—472no—
526C22×C4—474no—
527C22×C4—472no—
528C22×C4—9416no—
529C22×C4—9416no—
530C22×C4—9416no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—941no—
534C22×C4—941no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—941no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—941no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—1888no—
556C22×C4—1888no—
557C22×C4—1888no—
558C22×C4—1888no—
559C22×C4C2×C4×D4712yes—
560C22×C4D4×D4712yes—
561C22×C4D4×D4712yes—
562C22×C4#1062535214yes—
563C22×C4#1062535212yes—
564C22×C4#1062535212yes—
565C4⋊C4—948no—
566C4⋊C4—948no—
567C4⋊C4—948no—
568C22⋊C4—216no—
569C22⋊C4—216no—
570C22⋊C4—9416no—
571C22⋊C4—9416no—
572C22⋊C4—9416no—
573C42—948no—
574C42—948no—
575C42—1884no—
576C42—1888no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23(C22⋊D47)⋊C418yes—
612C23C22×C4×D4711yescharacteristic
613C23C2×D4×D4711yescharacteristic
614C23C2×D4×D4712yes—
615C23C2×D4×D4711yescharacteristic
616C23#41×D4711yescharacteristic
617C23#41×D4711yescharacteristic
618C23#41×D4712yes—
619C23C2×#1062535212yes—
620C23C2×#1062535211yescharacteristic
621C23C2×#1062535211yescharacteristic
622C23C2×#1062535212yes—
623D4—232no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—474no—
646C2×C4—474no—
647C2×C4—478no—
648C2×C4—478no—
649C2×C4—474no—
650C2×C4—474no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—944no—
658C2×C4—944no—
659C2×C4—944no—
660C2×C4—942no—
661C2×C4—944no—
662C2×C4—942no—
663C2×C4—944no—
664C2×C4—944no—
665C2×C4—944no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—18832no—
669C2×C4—1881no—
670C2×C4—1882no—
671C2×C4—1882no—
672C2×C4—1882no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4—1881no—
677C2×C4—1882no—
678C2×C4—1882no—
679C2×C4—1882no—
680C2×C4—1882no—
681C2×C4—1882no—
682C2×C4(C22⋊D47)⋊C414yes—
683C22—28no—
684C22—28no—
685C22—28no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—44no—
698C22C4×D4×D4711yescharacteristic
699C22C2×(C22⋊D47)⋊C412yes—
700C22C2×(C22⋊D47)⋊C411yescharacteristic
701C22C4×#1062535212yes—
702C22C4×#1062535211yescharacteristic
703C22#120×D4711yescharacteristic
704C22#121×D4712yes—
705C22#121×D4711yescharacteristic
706C22#123×D4712yes—
707C22#1568962912yes—
708C22#1568962912yes—
709C22#1568962912yes—
710C22#1568962911yescharacteristic
711C22#1568963311yescharacteristic
712C22#124×D4711yescharacteristic
713C22#1568965012yes—
714C22#1568965211yescharacteristic
715C22#1568965412yes—
716C22#1568965412yes—
717C22#1568965412yes—
718C22#1568966812yes—
719C22#1568967111yescharacteristic
720C22#1568967111yescharacteristic
721C4—24no—
722C4—42no—
723C4—42no—
724C4—44no—
725C4—478no—
726C4—944no—
727C4—1884no—
728C4—1882no—
729C4—1882no—
730C4—1884no—
731C2—48no—
732C2#2024588711yescharacteristic
733C2#2024589812yes—
734C2#2024590411yescharacteristic
735C2#2024591312yes—
736C2#2024593511yescharacteristic
737C2#394×D4711yescharacteristic
738C2#2024660011yescharacteristic
739C2#2024662312yes—
740C2#2024662311yescharacteristic
741C2#2024664412yes—
742C2#2024667611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1438C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenter#1438D47
hypocenterC47C4×#394
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
3. C2×#15688974C2semidirect
4. C2×C22⋊C4×Dic47C2semidirect
5. C2×C22⋊C4×Dic47C2semidirect
6. #20241644C2semidirect
7. #20241642C2semidirect
8. #20241635C2semidirect
9. #20241631C2semidirect
10. #95×Dic47C2semidirect
25. #15689037C4semidirect
62. C2×Dic47⋊C4C2×C4semidirect
70. C2×C22⋊Dic47C2×C4semidirect
71. C2×C22⋊Dic47C2×C4semidirect
81. C2×C4×Dic47D4semidirect
88. C47⋊#95C2×C4semidirect
305. C2×Dic47C4×D4semidirect
359. Dic47#394semidirect
412. C47C4×#394semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic472
C2×#156890372
C2×#156889742
C2×C22⋊C4×Dic472
#202416442
#202416422
#202416352
#202416312
#95×Dic472
C47×#14382
C4×#39447