Finite Group Databasebeta

← #26138181

Subgroups — #26138181

Order 12032.

2950 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C2×#15689002C212yesmaximal
3C2×#15688983C211yesmaximal, characteristic, complemented
4C2×#15688980C212yesmaximal, complemented
5#20241638C212yesmaximal, complemented
6#20241630C212yesmaximal, complemented
7#20241617C212yesmaximal, complemented
8#20241611C212yesmaximal, complemented
9C23×C4⋊C4×C47C211yesmaximal, characteristic, complemented
10C23×C22⋊D47C2211yescharacteristic
11C23×C4×D47C2211yescharacteristic
12C2×C4×C22⋊D47—24no—
13C2×C4×C22⋊D47—24no—
14C2×C4×C22⋊D47C418yescomplemented
15C22×C4⋊Dic47C2212yes—
16C22×Dic47⋊C4C2211yescharacteristic
17C22×C22⋊Dic47C2212yes—
18C22×C22⋊Dic47C2211yescharacteristic
19C22×(C2×D47)⋊C4C2214yes—
20C22×(C2×D47)⋊C4C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22#15689002—28no—
23#15688983—24no—
24#15688980—28no—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2214yes—
27C2×C47⋊#95C2214yes—
28C2×C47⋊#95C2214yes—
29C24×C4×C47C2212yes—
30C24×C4×C47C2211yescharacteristic
31C22×C4⋊C4×C47—24no—
32C22×C4⋊C4×C47—28no—
33C22×C4⋊C4×C47C2212yes—
34C22×C4⋊C4×C47C2212yes—
35C24×D47C2311yescharacteristic
36C22×C22⋊D47—22no—
37C22×C22⋊D47—22no—
38C22×C22⋊D47—22no—
39C22×C22⋊D47—22no—
40C22×C22⋊D47C2×C414yes—
41C22×C22⋊D47D414yes—
42C22×C22⋊D47Q814yes—
43C23×Dic47C2314yes—
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2311yescharacteristic
46C23×Dic47C2311yescharacteristic
47C22×C4×D47—24no—
48C22×C4×D47—22no—
49C22×C4×D47—22no—
50C22×C4×D47—24no—
51C22×C4×D47C2×C414yescomplemented
52C4×C22⋊D47—232no—
53C2×C4⋊Dic47—24no—
54C2×C4⋊Dic47—24no—
55C2×C4⋊Dic47—24no—
56C2×Dic47⋊C4—22no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4C2×C414yescomplemented
59C2×C22⋊Dic47—22no—
60C2×C22⋊Dic47—22no—
61C2×C22⋊Dic47—24no—
62C2×C22⋊Dic47—24no—
63C2×C22⋊Dic47—24no—
64C2×C22⋊Dic47C2×C414yes—
65C2×(C2×D47)⋊C4—22no—
66C2×(C2×D47)⋊C4—22no—
67C2×(C2×D47)⋊C4—28no—
68C2×(C2×D47)⋊C4—28no—
69C2×(C2×D47)⋊C4—44no—
70C2×(C2×D47)⋊C4C2×C414yescomplemented
71C2×C4×Dic47—22no—
72C2×C4×Dic47—22no—
73C2×C4×Dic47C2×C414yescomplemented
74C47⋊#95—28no—
75C47⋊#95—24no—
76C47⋊#95—28no—
77C47⋊#95—44no—
78C25×C47C2311yescharacteristic
79C23×C4×C47—24no—
80C23×C4×C47—24no—
81C23×C4×C47—24no—
82C23×C4×C47—28no—
83C23×C4×C47—24no—
84C23×C4×C47—24no—
85C23×C4×C47—44no—
86C23×C4×C47C2×C414yes—
87C23×C4×C47D414yes—
88C23×C4×C47D414yes—
89C23×C4×C47C2314yes—
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C2×C4⋊C4×C47—232no—
93C2×C4⋊C4×C47—28no—
94C2×C4⋊C4×C47—24no—
95C2×C4⋊C4×C47—24no—
96C2×C4⋊C4×C47—24no—
97C2×C4⋊C4×C47D418yescomplemented
98C24×C47—22no—
99C24×C47—22no—
100C24×C47—22no—
101C24×C47—22no—
102C24×C47C22×C412yes—
103C24×C47C2×D412yes—
104C24×C47C2×D412yes—
105C24×C47C2×D412yes—
106C24×C47C2×Q812yes—
107C24×C47#4112yes—
108C24×C47#4112yes—
109C24×C47C2411yescharacteristic
110C23×D47—22no—
111C23×D47—21no—
112C23×D47—21no—
113C23×D47—22no—
114C23×D47—21no—
115C23×D47—21no—
116C23×D47—22no—
117C23×D47—22no—
118C23×D47C22×C412yes—
119C23×D47C2×D412yes—
120C23×D47C2×Q812yes—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—216no—
124C22×C4×C47—28no—
125C22×C4×C47—216no—
126C22×C4×C47—28no—
127C22×C4×C47—216no—
128C22×C4×C47—24no—
129C22×C4×C47—24no—
130C22×C4×C47—24no—
131C22×C4×C47—24no—
132C22×C4×C47—24no—
133C22×C4×C47—24no—
134C22×C4×C47—416no—
135C22×C4×C47—416no—
136C22×C4×C47—48no—
137C22×C4×C47—48no—
138C22×C4×C47C22⋊C4116yescomplemented
139C22×C4×C47C22×C412yes—
140C22×C4×C47C22×C412yes—
141C22×C4×C47C2×D418yes—
142C22×C4×C47C2×D412yes—
143C22×C4×C47C2×D412yes—
144C22×C4×C47C2×D412yes—
145C22×C4×C47C2×D412yes—
146C22×C4×C47C2×D414yes—
147C22×C4×C47#4114yes—
148C2×C22⋊D47—28no—
149C2×C22⋊D47—28no—
150C2×C22⋊D47—28no—
151C2×C22⋊D47—28no—
152C2×C22⋊D47—28no—
153C2×C22⋊D47—28no—
154C2×C22⋊D47C4⋊C4116yescomplemented
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—21no—
159C22×Dic47—22no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—24no—
168C22×Dic47—24no—
169C22×Dic47—24no—
170C22×Dic47—24no—
171C22×Dic47—24no—
172C22×Dic47—24no—
173C22×Dic47—24no—
174C22×Dic47C22×C412yes—
175C22×Dic47C22×C412yes—
176C22×Dic47C22×C412yes—
177C22×Dic47C2×D412yes—
178C22×Dic47C2×Q812yes—
179C2×C4×D47—28no—
180C2×C4×D47—216no—
181C2×C4×D47—44no—
182C2×C4×D47—48no—
183C2×C4×D47—44no—
184C4⋊C4×C47—216no—
185C4⋊C4×C47—216no—
186C22⋊Dic47—28no—
187C22⋊Dic47—48no—
188(C2×D47)⋊C4—28no—
189(C2×D47)⋊C4—416no—
190C4⋊Dic47—48no—
191Dic47⋊C4—28no—
192C4×Dic47—28no—
193C23×C47—24no—
194C23×C47—24no—
195C23×C47—22no—
196C23×C47—24no—
197C23×C47—22no—
198C23×C47—22no—
199C23×C47—22no—
200C23×C47—24no—
201C23×C47—24no—
202C23×C47—24no—
203C23×C47—24no—
204C23×C47—24no—
205C23×C47—24no—
206C23×C47—24no—
207C23×C47—24no—
208C23×C47—24no—
209C23×C47C2×C22⋊C414yes—
210C23×C47C2×C4⋊C414yes—
211C23×C47#11714yes—
212C23×C47#12114yes—
213C23×C47#12114yes—
214C23×C47C22⋊Q814yes—
215C23×C47C22⋊Q814yes—
216C23×C47C23×C411yescharacteristic
217C23×C47C22×D411yescharacteristic
218C23×C47C22×D411yescharacteristic
219C23×C47C22×D412yes—
220C23×C47C22×D411yescharacteristic
221C23×C47C22×Q811yescharacteristic
222C23×C47C2×#4111yescharacteristic
223C23×C47C2×#4112yes—
224C23×C47C2×#4111yescharacteristic
225C23×C47H(5,𝔽2)12yes—
226C23×C472−1+412yes—
227C22×D47—22no—
228C22×D47—22no—
229C22×D47—24no—
230C22×D47—24no—
231C22×D47—22no—
232C22×D47—22no—
233C22×D47—22no—
234C22×D47—22no—
235C22×D47—24no—
236C22×D47—24no—
237C22×D47—24no—
238C22×D47—24no—
239C22×D47—41no—
240C22×D47—42no—
241C22×D47—41no—
242C22×D47—41no—
243C22×D47—41no—
244C22×D47—42no—
245C22×D47—42no—
246C22×D47—42no—
247C22×D47—42no—
248C22×D47—42no—
249C22×D47C2×C4⋊C414yescomplemented
250C2×C4×C47—24no—
251C2×C4×C47—22no—
252C2×C4×C47—24no—
253C2×C4×C47—22no—
254C2×C4×C47—232no—
255C2×C4×C47—28no—
256C2×C4×C47—28no—
257C2×C4×C47—28no—
258C2×C4×C47—432no—
259C2×C4×C47—44no—
260C2×C4×C47—44no—
261C2×C4×C47—44no—
262C2×C4×C47—44no—
263C2×C4×C47C2×C22⋊C414yes—
264C2×C4×C47C2×C22⋊C414yes—
265C2×C4×C47C4×D418yes—
266C2×C4×C47#12014yes—
267C2×C4×C47#12118yes—
268C2×C4×C47#12314yes—
269C22⋊D47—232no—
270C2×Dic47—22no—
271C2×Dic47—22no—
272C2×Dic47—22no—
273C2×Dic47—22no—
274C2×Dic47—22no—
275C2×Dic47—22no—
276C2×Dic47—22no—
277C2×Dic47—22no—
278C2×Dic47—24no—
279C2×Dic47—24no—
280C2×Dic47—41no—
281C2×Dic47—42no—
282C2×Dic47—41no—
283C2×Dic47—41no—
284C2×Dic47—41no—
285C2×Dic47—42no—
286C2×Dic47—44no—
287C2×Dic47—44no—
288C2×Dic47—44no—
289C2×Dic47—44no—
290C2×Dic47—44no—
291C2×Dic47—44no—
292C2×Dic47—44no—
293C2×Dic47C2×C4⋊C414yescomplemented
294C4×D47—416no—
295#13872—471nomaximal, Sylow
296C22×C47—24no—
297C22×C47—28no—
298C22×C47—28no—
299C22×C47—24no—
300C22×C47—24no—
301C22×C47—28no—
302C22×C47—28no—
303C22×C47—24no—
304C22×C47—24no—
305C22×C47—24no—
306C22×C47#38018yescomplemented
307C22×C47C22×C22⋊C411yescharacteristic
308C22×C47C22×C4⋊C411yescharacteristic
309C22×C47C2×#11711yescharacteristic
310C22×C47C2×C4×D412yes—
311C22×C47#52012yes—
312C22×C47C2×#12011yescharacteristic
313C22×C47C2×#12111yescharacteristic
314C22×C47C2×#12112yes—
315C22×C47C2×#12111yescharacteristic
316C22×C47C2×C22⋊Q811yescharacteristic
317C22×C47C2×C22⋊Q811yescharacteristic
318C22×C47C2×#12311yescharacteristic
319C22×C47#53511yescharacteristic
320C22×C47#53611yescharacteristic
321C22×C47#53712yes—
322C22×C47D4212yes—
323C22×C47#54612yes—
324C22×C47#54712yes—
325C22×C47#54812yes—
326C22×C47D4×Q812yes—
327C22×C47#55212yes—
328C22×C47#55312yes—
329C22×C47#55412yes—
330C2×D47—28no—
331C2×D47—24no—
332C2×D47—42no—
333C2×D47—44no—
334C2×D47—42no—
335C2×D47—42no—
336C2×D47—44no—
337C2×D47—44no—
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—42no—
341C4×C47—24no—
342C4×C47—48no—
343C4×C47#38618yescomplemented
344Dic47—24no—
345Dic47—42no—
346Dic47—42no—
347Dic47—84no—
348C22×C4×D4—471no—
349C23×C4⋊C4D4711yescharacteristic, complemented
350C2×#386—472no—
351C2×#380—471no—
352C2×#380—472no—
353#1441—472no—
354#1439—472no—
355C4⋊#95—472no—
356C22⋊#95—472no—
357C2×C47—28no—
358C2×C47C2×#38011yescharacteristic
359C2×C47C2×#38611yescharacteristic
360C2×C47#231111yescharacteristic
361C2×C47D4×C4⋊C412yes—
362C2×C47#235212yes—
363C2×C47#240811yescharacteristic
364C2×C47#240911yescharacteristic
365C2×C47#241612yes—
366C2×C47#241712yes—
367C2×C47#248611yescharacteristic
368C2×C47#248711yescharacteristic
369D47—44no—
370C23×D4—471no—
371C24×C4—471no—
372C24×C4C2×D4712yes—
373C24×C4C2×D4711yescharacteristic
374C2×C4×D4—478no—
375C2×C4×D4—944no—
376C2×C4×D4—944no—
377C22×C4⋊C4—24no—
378C22×C4⋊C4—28no—
379C22×C4⋊C4—471no—
380C22×C4⋊C4—472no—
381C22×C4⋊C4C2×D4712yes—
382C22×C4⋊C4C2×D4712yes—
383C22×C22⋊C4—471no—
384C22×C22⋊C4—471no—
385C22×C22⋊C4—472no—
386C22×C22⋊C4—474no—
387C22×C42—471no—
388#386—948no—
389#380—944no—
390#380—948no—
391C2×#95—474no—
392C2×#95—474no—
393C2×#95—472no—
394C2×#95—474no—
395C47#1387211yescharacteristic, complemented, Sylow
396C25—471no—
397C25C22×D4711yescharacteristic
398C22×D4—474no—
399C22×D4—474no—
400C22×D4—474no—
401C22×D4—942no—
402C22×D4—942no—
403C22×D4—942no—
404C22×D4—942no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—28no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—44no—
412C23×C4—471no—
413C23×C4—471no—
414C23×C4—471no—
415C23×C4—474no—
416C23×C4—474no—
417C23×C4—942no—
418C23×C4—944no—
419C23×C4—942no—
420C23×C4—944no—
421C23×C4C4×D4714yes—
422C23×C4D18814yes—
423C23×C4C22⋊D4714yes—
424C23×C4C22×D4714yes—
425C23×C4C22×D4711yescharacteristic
426C23×C4C22×D4711yescharacteristic
427C4×D4—9432no—
428C2×C4⋊C4—232no—
429C2×C4⋊C4—28no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—474no—
434C2×C4⋊C4—942no—
435C2×C4⋊C4—942no—
436C2×C4⋊C4—944no—
437C2×C4⋊C4—944no—
438C2×C4⋊C4—944no—
439C2×C4⋊C4C22⋊D4718yescomplemented
440C2×C22⋊C4—474no—
441C2×C22⋊C4—474no—
442C2×C22⋊C4—942no—
443C2×C22⋊C4—942no—
444C2×C22⋊C4—942no—
445C2×C22⋊C4—942no—
446C2×C22⋊C4—948no—
447C2×C22⋊C4—944no—
448C2×C22⋊C4—944no—
449C2×C22⋊C4—944no—
450C2×C22⋊C4—948no—
451C2×C22⋊C4—1884no—
452C2×C42—474no—
453C2×C42—942no—
454C2×C42—942no—
455#95—948no—
456#95—944no—
457#95—948no—
458#95—1884no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—472no—
464C24—472no—
465C24—472no—
466C24—942no—
467C24—941no—
468C24—941no—
469C24—941no—
470C24—942no—
471C24—941no—
472C24—942no—
473C24—942no—
474C24C2×C4×D4712yes—
475C24C2×D18812yes—
476C24D4×D4712yes—
477C24#1062535212yes—
478C24Q8×D4712yes—
479C24#1062535412yes—
480C24C2×C22⋊D4712yes—
481C24C23×D4711yescharacteristic
482C2×D4—4716no—
483C2×D4—948no—
484C2×D4—948no—
485C2×D4—948no—
486C2×D4—948no—
487C2×D4—948no—
488C2×D4—948no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—216no—
492C22×C4—28no—
493C22×C4—216no—
494C22×C4—28no—
495C22×C4—216no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—416no—
503C22×C4—416no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—472no—
507C22×C4—472no—
508C22×C4—472no—
509C22×C4—472no—
510C22×C4—472no—
511C22×C4—941no—
512C22×C4—941no—
513C22×C4—941no—
514C22×C4—941no—
515C22×C4—942no—
516C22×C4—941no—
517C22×C4—941no—
518C22×C4—941no—
519C22×C4—941no—
520C22×C4—942no—
521C22×C4—942no—
522C22×C4—942no—
523C22×C4—948no—
524C22×C4—9416no—
525C22×C4—944no—
526C22×C4—944no—
527C22×C4—944no—
528C22×C4—944no—
529C22×C4—944no—
530C22×C4—944no—
531C22×C4—944no—
532C22×C4—1884no—
533C22×C4—1888no—
534C22×C4—1884no—
535C22×C4(C2×D47)⋊C4116yescomplemented
536C22×C4C2×C4×D4712yes—
537C22×C4C2×C4×D4712yes—
538C22×C4C2×D18812yes—
539C22×C4C2×D18812yes—
540C22×C4#1062535014yes—
541C22×C4C2×C22⋊D4718yes—
542C22×C4C2×C22⋊D4712yes—
543C22×C4C2×C22⋊D4712yes—
544C22×C4C2×C22⋊D4714yes—
545C4⋊C4—216no—
546C4⋊C4—216no—
547C4⋊C4—948no—
548C4⋊C4—1888no—
549C22⋊C4—948no—
550C22⋊C4—948no—
551C22⋊C4—18816no—
552C22⋊C4—1888no—
553C42—948no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—22no—
565C23—24no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—24no—
570C23—474no—
571C23—944no—
572C23—944no—
573C23—944no—
574C23—942no—
575C23—944no—
576C23—942no—
577C23—944no—
578C23—944no—
579C23—942no—
580C23—942no—
581C23—942no—
582C23—942no—
583C23—1882no—
584C23—1882no—
585C23—1882no—
586C23—1882no—
587C23—1881no—
588C23—1882no—
589C23—1881no—
590C23—1881no—
591C23—1881no—
592C23—1882no—
593C23C2×(C2×D47)⋊C414yes—
594C23C4⋊C4×D4714yes—
595C23#1309398214yes—
596C23#1309399514yes—
597C23#1309399914yes—
598C23#1309400014yes—
599C23#1309400414yes—
600C23C22×C4×D4711yescharacteristic
601C23C2×D4×D4711yescharacteristic
602C23C22×C22⋊D4712yes—
603C23C22×C22⋊D4711yescharacteristic
604C23C22×D18811yescharacteristic
605C23C2×Q8×D4711yescharacteristic
606C23C2×#1062535211yescharacteristic
607C23C2×#1062535012yes—
608C23C2×#1062535411yescharacteristic
609C23#1309406912yes—
610C23#1309407212yes—
611D4—9432no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—232no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—432no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—474no—
626C2×C4—942no—
627C2×C4—942no—
628C2×C4—942no—
629C2×C4—942no—
630C2×C4—942no—
631C2×C4—942no—
632C2×C4—942no—
633C2×C4—942no—
634C2×C4—944no—
635C2×C4—944no—
636C2×C4—1884no—
637C2×C4—1884no—
638C2×C4—1884no—
639C2×C4—1884no—
640C2×C4—1884no—
641C2×C4—1884no—
642C2×C4—1884no—
643C2×C4—1881no—
644C2×C4—1882no—
645C2×C4—1881no—
646C2×C4—1881no—
647C2×C4—1881no—
648C2×C4—1882no—
649C2×C4—18816no—
650C2×C4C2×(C2×D47)⋊C414yes—
651C2×C4C2×(C2×D47)⋊C414yes—
652C2×C4C4×C22⋊D4718yes—
653C2×C4#1309399314yes—
654C2×C4#1309399818yes—
655C2×C4#1309400714yes—
656C22—28no—
657C22—28no—
658C22—28no—
659C22—24no—
660C22—28no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—24no—
666C22—948no—
667C22—944no—
668C22—1884no—
669C22—1884no—
670C22—1882no—
671C22—1884no—
672C22—1882no—
673C22—1882no—
674C22—1882no—
675C22—1882no—
676C22—1882no—
677C22#1568898018yescomplemented
678C22C22×(C2×D47)⋊C411yescharacteristic
679C22C2×C4⋊C4×D4711yescharacteristic
680C22C2×#1309398211yescharacteristic
681C22C2×C4×C22⋊D4712yes—
682C22#1568960412yes—
683C22C2×#1309399311yescharacteristic
684C22C2×#1309399511yescharacteristic
685C22C2×#1309399812yes—
686C22C2×#1309399911yescharacteristic
687C22C2×#1309400011yescharacteristic
688C22C2×#1309400411yescharacteristic
689C22C2×#1309400711yescharacteristic
690C22#1568969011yescharacteristic
691C22#1568969711yescharacteristic
692C22#1568970412yes—
693C22D4×C22⋊D4712yes—
694C22#1568976712yes—
695C22#1568977412yes—
696C22#1568978412yes—
697C22Q8×C22⋊D4712yes—
698C22#1568980812yes—
699C22#1568982112yes—
700C22#1568982812yes—
701C4—24no—
702C4—48no—
703C4—944no—
704C4—3764no—
705C4—1882no—
706C4—1882no—
707C4#1568900218yescomplemented
708C2—28no—
709C2—1884no—
710C2C2×#1568898011yescharacteristic
711C2C2×#1568900211yescharacteristic
712C2#2024598111yescharacteristic
713C2C4⋊C4×C22⋊D4712yes—
714C2#2024631312yes—
715C2#2024673811yescharacteristic
716C2#2024674711yescharacteristic
717C2#2024682212yes—
718C2#2024683312yes—
719C2#2024769011yescharacteristic
720C2#2024769911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC23×C4⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC23×C4⋊C4D47
hypocenterC47#13872
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#15688983C2semidirect
4. C2×#15688980C2semidirect
5. #20241638C2semidirect
6. #20241630C2semidirect
7. #20241617C2semidirect
8. #20241611C2semidirect
9. C23×C4⋊C4×C47C2semidirect
14. C2×C4×C22⋊D47C4semidirect
51. C22×C4×D47C2×C4semidirect
58. C2×Dic47⋊C4C2×C4semidirect
70. C2×(C2×D47)⋊C4C2×C4semidirect
73. C2×C4×Dic47C2×C4semidirect
97. C2×C4⋊C4×C47D4semidirect
138. C22×C4×C47C22⋊C4semidirect
154. C2×C22⋊D47C4⋊C4semidirect
249. C22×D47C2×C4⋊C4semidirect
293. C2×Dic47C2×C4⋊C4semidirect
306. C22×C47#380semidirect
343. C4×C47#386semidirect
349. C23×C4⋊C4D47semidirect
395. C47#13872semidirect
439. C2×C4⋊C4C22⋊D47semidirect
535. C22×C4(C2×D47)⋊C4semidirect
677. C22#15688980semidirect
707. C4#15689002semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C2×#156890022
C2×#156889832
C2×#156889802
#202416382
#202416302
#202416172
#202416112
C23×C4⋊C4×C472
#1387247