Finite Group Databasebeta

← C47×#13996 #26053694

Subgroups — C47×#13996 #26053694

Order 12032.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C47C211yesmaximal, characteristic
2C2×C47×#386C211yesmaximal, characteristic
3C2×C47×#386C211yesmaximal, characteristic
4C2×C47×#385C211yesmaximal, characteristic, complemented
5C2×C47×#381C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
7C22×#95×C47C211yesmaximal, characteristic, complemented
8C47×#1445C212yesmaximal, complemented
9C47×#1439C212yesmaximal, complemented
10C47×#1437C212yesmaximal, complemented
11C47×C4⋊#95C212yesmaximal, complemented
12C23×D4×C47C2211yescharacteristic
13C24×C4×C47C2211yescharacteristic
14C24×C4×C47C2211yescharacteristic
15C24×C4×C47C2211yescharacteristic
16C2×#123×C47—24no—
17C2×#123×C47—24no—
18C2×#123×C47C418yescomplemented
19C22×C4⋊C4×C47C2212yes—
20C22×C4⋊C4×C47C2212yes—
21C22×C22⋊C4×C47C2211yescharacteristic
22C22×C22⋊C4×C47C2211yescharacteristic
23C22×C22⋊C4×C47C2212yes—
24C22×C22⋊C4×C47C2212yes—
25C22×C22⋊C4×C47C2211yescharacteristic
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2211yescharacteristic
28C22×C42×C47C2212yes—
29C47×#386—24no—
30C47×#386—24no—
31C47×#385—24no—
32C47×#381—24no—
33C4×C22⋊C4×C47—24no—
34C2×#95×C47—24no—
35C2×#95×C47C2212yes—
36C2×#95×C47C2212yes—
37C2×#95×C47C2212yes—
38C2×#95×C47C2212yes—
39C2×#95×C47C2212yes—
40C2×#95×C47C2212yes—
41C2×#95×C47C2211yescharacteristic
42C2×#95×C47C2212yes—
43C2×#95×C47C2211yescharacteristic
44C25×C47C2311yescharacteristic
45C25×C47C2311yescharacteristic
46C22×D4×C47—22no—
47C22×D4×C47—22no—
48C22×D4×C47—22no—
49C22×D4×C47—22no—
50C22×D4×C47—22no—
51C22×D4×C47—22no—
52C22×D4×C47C2×C414yes—
53C23×C4×C47—22no—
54C23×C4×C47—22no—
55C23×C4×C47—22no—
56C23×C4×C47—22no—
57C23×C4×C47—22no—
58C23×C4×C47—22no—
59C23×C4×C47—22no—
60C23×C4×C47—22no—
61C23×C4×C47—22no—
62C23×C4×C47—24no—
63C23×C4×C47—24no—
64C23×C4×C47—22no—
65C23×C4×C47—22no—
66C23×C4×C47—42no—
67C23×C4×C47—42no—
68C23×C4×C47C2×C414yes—
69C23×C4×C47D414yes—
70C23×C4×C47C2311yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C23×C4×C47C2312yes—
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2312yes—
75C23×C4×C47C2311yescharacteristic
76C23×C4×C47C2312yes—
77C23×C4×C47C2312yes—
78C23×C4×C47C2311yescharacteristic
79#123×C47—232no—
80C2×C4⋊C4×C47—24no—
81C2×C4⋊C4×C47—24no—
82C2×C4⋊C4×C47—24no—
83C2×C4⋊C4×C47—24no—
84C2×C4⋊C4×C47—42no—
85C2×C4⋊C4×C47C2×C418yescomplemented
86C2×C22⋊C4×C47—22no—
87C2×C22⋊C4×C47—22no—
88C2×C22⋊C4×C47—24no—
89C2×C22⋊C4×C47—24no—
90C2×C22⋊C4×C47—22no—
91C2×C22⋊C4×C47—22no—
92C2×C22⋊C4×C47—22no—
93C2×C22⋊C4×C47—24no—
94C2×C22⋊C4×C47—22no—
95C2×C22⋊C4×C47—22no—
96C2×C22⋊C4×C47—24no—
97C2×C22⋊C4×C47—24no—
98C2×C22⋊C4×C47—42no—
99C2×C22⋊C4×C47—42no—
100C2×C22⋊C4×C47C2×C414yes—
101C2×C22⋊C4×C47C2×C418yescomplemented
102C2×C22⋊C4×C47D414yes—
103C2×C22⋊C4×C47D414yes—
104C2×C22⋊C4×C47D414yes—
105C2×C42×C47—24no—
106C2×C42×C47—24no—
107C2×C42×C47—42no—
108#95×C47—24no—
109#95×C47—24no—
110#95×C47—24no—
111#95×C47—24no—
112#95×C47—24no—
113#95×C47—24no—
114#95×C47—24no—
115#95×C47—22no—
116#95×C47—22no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47—22no—
120C24×C47—22no—
121C24×C47—21no—
122C24×C47—21no—
123C24×C47—21no—
124C24×C47—21no—
125C24×C47—22no—
126C24×C47—22no—
127C24×C47—21no—
128C24×C47—21no—
129C24×C47—22no—
130C24×C47—22no—
131C24×C47C22×C412yes—
132C24×C47C22×C412yes—
133C24×C47C2×D412yes—
134C24×C47C2×D412yes—
135C24×C47C2×D412yes—
136C24×C47C2×D412yes—
137C24×C47#4112yes—
138C24×C47#4112yes—
139C24×C47C2411yescharacteristic
140C2×D4×C47—28no—
141C2×D4×C47—28no—
142C2×D4×C47—28no—
143C2×D4×C47—44no—
144C2×D4×C47—44no—
145C2×D4×C47—44no—
146C2×D4×C47—44no—
147C22×C4×C47—21no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—21no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—28no—
155C22×C4×C47—28no—
156C22×C4×C47—28no—
157C22×C4×C47—28no—
158C22×C4×C47—28no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—21no—
169C22×C4×C47—22no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—21no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—28no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—44no—
199C22×C4×C47—48no—
200C22×C4×C47—48no—
201C22×C4×C47—48no—
202C22×C4×C47—48no—
203C22×C4×C47—44no—
204C22×C4×C47—44no—
205C22×C4×C47—44no—
206C22×C4×C47—44no—
207C22×C4×C47—44no—
208C22×C4×C47—44no—
209C22×C4×C47C22×C414yes—
210C22×C4×C47C22×C412yes—
211C22×C4×C47C22×C414yes—
212C22×C4×C47C2×D414yes—
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2×D414yes—
215C22×C4×C47C2×D414yes—
216C22×C4×C47C2×D412yes—
217C22×C4×C47#4114yes—
218C22×C4×C47#4114yes—
219C4⋊C4×C47—216no—
220C4⋊C4×C47—48no—
221C22⋊C4×C47—28no—
222C22⋊C4×C47—216no—
223C22⋊C4×C47—48no—
224C22⋊C4×C47—44no—
225C22⋊C4×C47—44no—
226C22⋊C4×C47—44no—
227C22⋊C4×C47C22⋊C4116yescomplemented
228C42×C47—48no—
229C23×C47—24no—
230C23×C47—24no—
231C23×C47—22no—
232C23×C47—22no—
233C23×C47—24no—
234C23×C47—22no—
235C23×C47—22no—
236C23×C47—24no—
237C23×C47—24no—
238C23×C47—24no—
239C23×C47—24no—
240C23×C47—24no—
241C23×C47—24no—
242C23×C47—24no—
243C23×C47—24no—
244C23×C47—24no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—22no—
248C23×C47—24no—
249C23×C47—24no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—42no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—42no—
260C23×C47—42no—
261C23×C47—42no—
262C23×C47—42no—
263C23×C47—42no—
264C23×C47—42no—
265C23×C47—42no—
266C23×C47—42no—
267C23×C47—42no—
268C23×C47C2×C22⋊C414yes—
269C23×C47C4×D414yes—
270C23×C47C4×D414yes—
271C23×C47#12114yes—
272C23×C47#12114yes—
273C23×C47#12414yes—
274C23×C47#12714yes—
275C23×C47C23×C411yescharacteristic
276C23×C47C22×D411yescharacteristic
277C23×C47C22×D411yescharacteristic
278C23×C47C22×D411yescharacteristic
279C23×C47C22×D411yescharacteristic
280C23×C47C2×#4111yescharacteristic
281C23×C47C2×#4111yescharacteristic
282C23×C47C2×#4112yes—
283C23×C47C2×#4112yes—
284C23×C47H(5,𝔽2)12yes—
285C23×C472−1+412yes—
286D4×C47—416no—
287C2×C4×C47—24no—
288C2×C4×C47—24no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—24no—
292C2×C4×C47—24no—
293C2×C4×C47—24no—
294C2×C4×C47—24no—
295C2×C4×C47—24no—
296C2×C4×C47—24no—
297C2×C4×C47—24no—
298C2×C4×C47—22no—
299C2×C4×C47—24no—
300C2×C4×C47—24no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—24no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—24no—
307C2×C4×C47—22no—
308C2×C4×C47—24no—
309C2×C4×C47—24no—
310C2×C4×C47—24no—
311C2×C4×C47—24no—
312C2×C4×C47—416no—
313C2×C4×C47—416no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—42no—
319C2×C4×C47—41no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47—41no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47—42no—
328C2×C4×C47—42no—
329C2×C4×C47—42no—
330C2×C4×C47—42no—
331C2×C4×C47—42no—
332C2×C4×C47—416no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—42no—
340C2×C4×C47—42no—
341C2×C4×C47—42no—
342C2×C4×C47—42no—
343C2×C4×C47C2×C22⋊C418yes—
344C2×C4×C47#12314yescomplemented
345#13996C4711yesmaximal, characteristic, direct product factor, Sylow
346C22×C47—24no—
347C22×C47—28no—
348C22×C47—28no—
349C22×C47—24no—
350C22×C47—24no—
351C22×C47—28no—
352C22×C47—28no—
353C22×C47—24no—
354C22×C47—24no—
355C22×C47—24no—
356C22×C47—42no—
357C22×C47—44no—
358C22×C47—44no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—81no—
362C22×C47—81no—
363C22×C47—82no—
364C22×C47—82no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47#39018yes—
368C22×C47C22×C22⋊C411yescharacteristic
369C22×C47C2×C4×D411yescharacteristic
370C22×C47C2×C4×D411yescharacteristic
371C22×C47C4×#4112yes—
372C22×C47#52012yes—
373C22×C47C2×#12111yescharacteristic
374C22×C47C2×#12111yescharacteristic
375C22×C47C2×#12311yescharacteristic
376C22×C47#52511yescharacteristic
377C22×C47C2×#12411yescharacteristic
378C22×C47#52912yes—
379C22×C47C2×#12711yescharacteristic
380C22×C47#53411yescharacteristic
381C22×C47#53611yescharacteristic
382C22×C47#53912yes—
383C22×C47#54612yes—
384C22×C47#54612yes—
385C22×C47#54612yes—
386C22×C47#54712yes—
387C22×C47#54712yes—
388C22×C47#54712yes—
389C22×C47#55112yes—
390C22×C47#55212yes—
391C4×C47—28no—
392C4×C47—24no—
393C4×C47—42no—
394C4×C47—44no—
395C4×C47—44no—
396C4×C47—44no—
397C4×C47—42no—
398C4×C47—81no—
399C4×C47—81no—
400C22×#123C2×C4711yescharacteristic
401C2×#386C2×C4711yescharacteristic
402C2×#386C2×C4711yescharacteristic
403C2×#385C2×C4711yescharacteristic, complemented
404C2×#381C2×C4711yescharacteristic, complemented
405C2×C4×C22⋊C4C2×C4711yescharacteristic, complemented
406C22×#95C2×C4711yescharacteristic, complemented
407#1445C2×C4712yescomplemented
408#1439C2×C4712yescomplemented
409#1437C2×C4712yescomplemented
410C4⋊#95C2×C4712yescomplemented
411C2×C47—28no—
412C2×C47—82no—
413C2×C47C2×#39011yescharacteristic
414C2×C47C4×#12311yescharacteristic
415C2×C47#232211yescharacteristic
416C2×C47#233912yes—
417C2×C47#235912yes—
418C2×C47#241211yescharacteristic
419C2×C47#241311yescharacteristic
420C2×C47#242512yes—
421C2×C47#248812yes—
422C2×C47#250111yescharacteristic
423C2×C47#253911yescharacteristic
424C23×D4C22×C4711yescharacteristic
425C24×C4C22×C4711yescharacteristic
426C24×C4C22×C4711yescharacteristic
427C24×C4C22×C4711yescharacteristic
428C2×#123—24no—
429C2×#123—24no—
430C2×#123C4×C4718yescomplemented
431C22×C4⋊C4C22×C4712yes—
432C22×C4⋊C4C22×C4712yes—
433C22×C22⋊C4C22×C4711yescharacteristic
434C22×C22⋊C4C22×C4711yescharacteristic
435C22×C22⋊C4C22×C4712yes—
436C22×C22⋊C4C22×C4712yes—
437C22×C22⋊C4C22×C4711yescharacteristic
438C22×C22⋊C4C22×C4711yescharacteristic
439C22×C22⋊C4C22×C4711yescharacteristic
440C22×C42C22×C4712yes—
441#386—24no—
442#386—24no—
443#385—24no—
444#381—24no—
445C4×C22⋊C4—24no—
446C2×#95—24no—
447C2×#95C22×C4711yescharacteristic
448C2×#95C22×C4712yes—
449C2×#95C22×C4712yes—
450C2×#95C22×C4712yes—
451C2×#95C22×C4712yes—
452C2×#95C22×C4712yes—
453C2×#95C22×C4712yes—
454C2×#95C22×C4712yes—
455C2×#95C22×C4711yescharacteristic
456C47#1399611yescharacteristic, direct product factor, Sylow
457C25C23×C4711yescharacteristic
458C25C23×C4711yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×C4×C4714yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4C2×C4×C4714yes—
482C23×C4D4×C4714yes—
483C23×C4C23×C4711yescharacteristic
484C23×C4C23×C4711yescharacteristic
485C23×C4C23×C4712yes—
486C23×C4C23×C4711yescharacteristic
487C23×C4C23×C4712yes—
488C23×C4C23×C4711yescharacteristic
489C23×C4C23×C4712yes—
490C23×C4C23×C4712yes—
491C23×C4C23×C4711yescharacteristic
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4C2×C4×C4718yescomplemented
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4C2×C4×C4714yes—
514C2×C22⋊C4C2×C4×C4718yescomplemented
515C2×C22⋊C4D4×C4714yes—
516C2×C22⋊C4D4×C4714yes—
517C2×C22⋊C4D4×C4714yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—22no—
529#95—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C4712yes—
545C24C22×C4×C4712yes—
546C24C2×D4×C4712yes—
547C24C2×D4×C4712yes—
548C24C2×D4×C4712yes—
549C24C2×D4×C4712yes—
550C24#41×C4712yes—
551C24#41×C4712yes—
552C24C24×C4711yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C4714yes—
623C22×C4C22×C4×C4712yes—
624C22×C4C22×C4×C4714yes—
625C22×C4C2×D4×C4714yes—
626C22×C4C2×D4×C4712yes—
627C22×C4C2×D4×C4714yes—
628C22×C4C2×D4×C4714yes—
629C22×C4C2×D4×C4712yes—
630C22×C4#41×C4714yes—
631C22×C4#41×C4714yes—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4C22⋊C4×C47116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊C4×C4714yes—
682C23C4×D4×C4714yes—
683C23C4×D4×C4714yes—
684C23#121×C4714yes—
685C23#121×C4714yes—
686C23#124×C4714yes—
687C23#127×C4714yes—
688C23C23×C4×C4711yescharacteristic
689C23C22×D4×C4711yescharacteristic
690C23C22×D4×C4711yescharacteristic
691C23C22×D4×C4711yescharacteristic
692C23C22×D4×C4711yescharacteristic
693C23C2×#41×C4711yescharacteristic
694C23C2×#41×C4711yescharacteristic
695C23C2×#41×C4712yes—
696C23C2×#41×C4712yes—
697C23H(5,𝔽2)×C4712yes—
698C232−1+4×C4712yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—416no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C2×C22⋊C4×C4718yes—
757C2×C4#123×C4714yescomplemented
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—24no—
765C22—28no—
766C22—28no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—82no—
777C22—82no—
778C22—81no—
779C22C47×#39018yes—
780C22C22×C22⋊C4×C4711yescharacteristic
781C22C2×C4×D4×C4711yescharacteristic
782C22C2×C4×D4×C4711yescharacteristic
783C22C4×#41×C4712yes—
784C22C47×#52012yes—
785C22C2×#121×C4711yescharacteristic
786C22C2×#121×C4711yescharacteristic
787C22C2×#123×C4711yescharacteristic
788C22C47×#52511yescharacteristic
789C22C2×#124×C4711yescharacteristic
790C22C47×#52912yes—
791C22C2×#127×C4711yescharacteristic
792C22C47×#53411yescharacteristic
793C22C47×#53611yescharacteristic
794C22C47×#53912yes—
795C22C47×#54612yes—
796C22C47×#54612yes—
797C22C47×#54612yes—
798C22C47×#54712yes—
799C22C47×#54712yes—
800C22C47×#54712yes—
801C22C47×#55112yes—
802C22C47×#55212yes—
803C4—28no—
804C4—24no—
805C4—44no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×C47×#39011yescharacteristic
815C2C4×#123×C4711yescharacteristic
816C2C47×#232211yescharacteristic
817C2C47×#233912yes—
818C2C47×#235912yes—
819C2C47×#241211yescharacteristic
820C2C47×#241311yescharacteristic
821C2C47×#242512yes—
822C2C47×#248812yes—
823C2C47×#250111yescharacteristic
824C2C47×#253911yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC23×D4×C47C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C47×#385C2semidirect
5. C2×C47×#381C2semidirect
6. C2×C4×C22⋊C4×C47C2semidirect
7. C22×#95×C47C2semidirect
8. C47×#1445C2semidirect
9. C47×#1439C2semidirect
10. C47×#1437C2semidirect
11. C47×C4⋊#95C2semidirect
18. C2×#123×C47C4semidirect
85. C2×C4⋊C4×C47C2×C4semidirect
101. C2×C22⋊C4×C47C2×C4semidirect
227. C22⋊C4×C47C22⋊C4semidirect
344. C2×C4×C47#123semidirect
345. #13996C47direct (N × H)
403. C2×#385C2×C47semidirect
404. C2×#381C2×C47semidirect
405. C2×C4×C22⋊C4C2×C47semidirect
406. C22×#95C2×C47semidirect
407. #1445C2×C47semidirect
408. #1439C2×C47semidirect
409. #1437C2×C47semidirect
410. C4⋊#95C2×C47semidirect
430. C2×#123C4×C47semidirect
456. C47#13996direct (N × H)
498. C2×C4⋊C4C2×C4×C47semidirect
514. C2×C22⋊C4C2×C4×C47semidirect
640. C22⋊C4C22⋊C4×C47semidirect
757. C2×C4#123×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C472
C2×C47×#3862
C2×C47×#3852
C2×C47×#3812
C2×C4×C22⋊C4×C472
C22×#95×C472
C47×#14452
C47×#14392
C47×#14372
C47×C4⋊#952
#1399647