Finite Group Databasebeta

← C2×C47×#2121 #26073042

Subgroups — C2×C47×#2121 #26073042

Order 12032.

1494 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#534C211yesmaximal, characteristic
2C22×#100×C47C211yesmaximal, characteristic, complemented
3C22×#99×C47C211yesmaximal, characteristic, complemented
4C47×#2121C218yesmaximal, direct product factor
5C2×C47×#352C212yesmaximal, complemented
6C2×C47×AΣL(1,𝔽16)C212yesmaximal, complemented
7C23×D4×C47C411yescharacteristic, complemented
8C23×D4×C47C2211yescharacteristic
9C22×M16×C47—21no—
10C47×#534—22no—
11C47×#534—22no—
12C47×#534C414yescomplemented
13C47×#534C2214yes—
14C2×#123×C47—21no—
15C2×#123×C47C411yescharacteristic, complemented
16C2×#123×C47C2211yescharacteristic
17C2×#121×C47—21no—
18C2×#121×C47—21no—
19C2×#120×C47—21no—
20C2×#120×C47C411yescharacteristic, complemented
21C2×#120×C47C2211yescharacteristic
22C22×C22⋊C4×C47—21no—
23C22×C22⋊C4×C47C411yescharacteristic, complemented
24C2×#100×C47—21no—
25C2×#100×C47—22no—
26C2×#100×C47C2212yes—
27C2×#100×C47C2214yescomplemented
28C2×#99×C47—21no—
29C2×#99×C47—22no—
30C2×#99×C47C2212yes—
31C2×#99×C47C2214yescomplemented
32C47×#352C2218yescomplemented
33C47×AΣL(1,𝔽16)C2218yescomplemented
34C25×C47C2×C411yescharacteristic
35C25×C47C2×C411yescharacteristic, complemented
36C25×C47D411yescharacteristic
37C22×D4×C47—21no—
38C22×D4×C47—22no—
39C22×D4×C47—21no—
40C22×D4×C47—21no—
41C22×D4×C47—21no—
42C22×D4×C47—41no—
43C22×D4×C47—41no—
44C22×D4×C47—42no—
45C22×D4×C47—42no—
46C22×D4×C47—41no—
47C22×D4×C47—41no—
48C22×D4×C47C2×C411yescharacteristic
49C22×D4×C47C2×C412yes—
50C22×D4×C47C2×C414yescomplemented
51C22×D4×C47D411yescharacteristic
52C22×D4×C47D412yes—
53C22×D4×C47D411yescharacteristic
54C22×D4×C47D412yes—
55C22×D4×C47C2311yescharacteristic
56C22×D4×C47C2312yes—
57C23×C4×C47—21no—
58C23×C4×C47—41no—
59C23×C4×C47C2×C411yescharacteristic, complemented
60C23×C4×C47D411yescharacteristic
61C2×M16×C47—22no—
62C2×M16×C47—24no—
63C2×M16×C47—42no—
64C2×M16×C47—41no—
65C22×C8×C47—41no—
66#123×C47—22no—
67#123×C47—21no—
68#123×C47—21no—
69#123×C47—24no—
70#123×C47—24no—
71#123×C47C2×C414yescomplemented
72#123×C47C2×C412yescomplemented
73#123×C47C2312yes—
74#121×C47—24no—
75#121×C47—24no—
76#121×C47—24no—
77#121×C47—24no—
78#120×C47—24no—
79#120×C47—24no—
80#120×C47—22no—
81#120×C47—21no—
82#120×C47—21no—
83#120×C47C2×C414yescomplemented
84#120×C47C2×C412yescomplemented
85#120×C47C2312yes—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—21no—
88C2×C22⋊C4×C47—22no—
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C22⋊C4×C47—21no—
94C2×C22⋊C4×C47—22no—
95C2×C22⋊C4×C47—24no—
96C2×C22⋊C4×C47—42no—
97C2×C22⋊C4×C47—41no—
98C2×C22⋊C4×C47C2×C411yescharacteristic, complemented
99C2×C22⋊C4×C47C2×C411yescharacteristic, complemented
100C2×C22⋊C4×C47C2×C414yescomplemented
101#100×C47—22no—
102#100×C47—24no—
103#100×C47C2314yes—
104#99×C47—22no—
105#99×C47—24no—
106#99×C47C2314yes—
107C24×C47—21no—
108C24×C47—22no—
109C24×C47—21no—
110C24×C47—22no—
111C24×C47—21no—
112C24×C47—21no—
113C24×C47—21no—
114C24×C47—21no—
115C24×C47—41no—
116C24×C47—41no—
117C24×C47—82no—
118C24×C47—82no—
119C24×C47—82no—
120C24×C47C22⋊C411yescharacteristic
121C24×C47C22⋊C411yescharacteristic
122C24×C47C22⋊C412yes—
123C24×C47C22⋊C412yes—
124C24×C47C22⋊C411yescharacteristic
125C24×C47C22×C411yescharacteristic
126C24×C47C22×C412yes—
127C24×C47C22×C412yescomplemented
128C24×C47C2×D411yescharacteristic
129C24×C47C2×D412yes—
130C2×D4×C47—24no—
131C2×D4×C47—24no—
132C2×D4×C47—22no—
133C2×D4×C47—24no—
134C2×D4×C47—22no—
135C2×D4×C47—41no—
136C2×D4×C47—42no—
137C2×D4×C47—42no—
138C2×D4×C47—41no—
139C2×D4×C47—42no—
140C2×D4×C47—41no—
141C2×D4×C47—42no—
142C2×D4×C47—42no—
143C2×D4×C47—41no—
144C2×D4×C47—42no—
145C2×D4×C47—41no—
146C2×D4×C47—41no—
147C2×D4×C47—42no—
148C2×D4×C47—42no—
149C2×D4×C47—41no—
150C2×D4×C47—41no—
151C2×D4×C47—44no—
152C2×D4×C47—44no—
153C2×D4×C47—42no—
154C2×D4×C47—42no—
155C2×D4×C47—42no—
156C2×D4×C47—41no—
157C2×D4×C47—41no—
158C2×D4×C47—44no—
159C2×D4×C47—44no—
160C2×D4×C47—82no—
161C2×D4×C47—82no—
162C2×D4×C47C22⋊C412yes—
163C2×D4×C47C22⋊C412yes—
164C2×D4×C47C22⋊C412yes—
165C2×D4×C47C22×C412yes—
166C2×D4×C47C22×C411yescharacteristic
167C2×D4×C47C2×D411yescharacteristic
168C2×D4×C47C2×D412yes—
169C2×D4×C47C2×D411yescharacteristic
170C2×D4×C47C2×D412yes—
171C2×D4×C47C2411yescharacteristic
172C22×C4×C47—21no—
173C22×C4×C47—22no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—24no—
180C22×C4×C47—41no—
181C22×C4×C47—41no—
182C22×C4×C47—44no—
183C22×C4×C47—42no—
184C22×C4×C47—82no—
185C22×C4×C47—84no—
186C22×C4×C47C22⋊C411yescharacteristic
187C22×C4×C47C22⋊C412yes—
188C22×C4×C47C22×C412yescomplemented
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D412yes—
191M16×C47—24no—
192M16×C47—42no—
193M16×C47—44no—
194C2×C8×C47—44no—
195C2×C8×C47—42no—
196C4⋊C4×C47—24no—
197C4⋊C4×C47—22no—
198C4⋊C4×C47—22no—
199C22⋊C4×C47—21no—
200C22⋊C4×C47—21no—
201C22⋊C4×C47—24no—
202C22⋊C4×C47—24no—
203C22⋊C4×C47—22no—
204C22⋊C4×C47—22no—
205C22⋊C4×C47—24no—
206C22⋊C4×C47—22no—
207C22⋊C4×C47—22no—
208C22⋊C4×C47—24no—
209C22⋊C4×C47—42no—
210C22⋊C4×C47—44no—
211C22⋊C4×C47C22×C412yescomplemented
212C22⋊C4×C47C22×C412yescomplemented
213C23×C47—22no—
214C23×C47—21no—
215C23×C47—21no—
216C23×C47—22no—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—21no—
220C23×C47—21no—
221C23×C47—21no—
222C23×C47—22no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—22no—
227C23×C47—21no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—42no—
231C23×C47—42no—
232C23×C47—42no—
233C23×C47—44no—
234C23×C47—42no—
235C23×C47—42no—
236C23×C47—42no—
237C23×C47—42no—
238C23×C47—42no—
239C23×C47—42no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—82no—
243C23×C47—82no—
244C23×C47—82no—
245C23×C47—82no—
246C23×C47—82no—
247C23×C47—82no—
248C23×C47—82no—
249C23×C47—82no—
250C23×C47—84no—
251C23×C47—84no—
252C23×C47—82no—
253C23×C47—84no—
254C23×C47—84no—
255C23×C47#9911yescharacteristic
256C23×C47#9911yescharacteristic
257C23×C47#9912yes—
258C23×C47C2×C22⋊C411yescharacteristic
259C23×C47C2×C22⋊C411yescharacteristic
260C23×C47C2×C22⋊C412yes—
261C23×C47C2×C22⋊C411yescharacteristic
262C23×C47C2×C22⋊C412yes—
263C23×C47C2×C22⋊C412yes—
264C23×C47C23×C411yescharacteristic
265C23×C47C22×D411yescharacteristic
266D4×C47—42no—
267D4×C47—42no—
268D4×C47—42no—
269D4×C47—42no—
270D4×C47—41no—
271D4×C47—41no—
272D4×C47—42no—
273D4×C47—41no—
274D4×C47—42no—
275D4×C47—41no—
276D4×C47—48no—
277D4×C47—44no—
278D4×C47—44no—
279D4×C47—84no—
280D4×C47—82no—
281D4×C47—82no—
282C2×C4×C47—22no—
283C2×C4×C47—21no—
284C2×C4×C47—22no—
285C2×C4×C47—21no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—42no—
299C2×C4×C47—44no—
300C2×C4×C47—84no—
301C2×C4×C47—88no—
302C2×C4×C47—84no—
303C2×C4×C47C2×C22⋊C412yes—
304C2×C4×C47C2×C22⋊C411yescharacteristic
305C2×C4×C47C22×D411yescharacteristic
306C8×C47—44no—
307C2×#2121C4711yesmaximal, characteristic, direct product factor, Sylow
308C22×C47—22no—
309C22×C47—22no—
310C22×C47—22no—
311C22×C47—21no—
312C22×C47—21no—
313C22×C47—21no—
314C22×C47—22no—
315C22×C47—22no—
316C22×C47—21no—
317C22×C47—42no—
318C22×C47—42no—
319C22×C47—42no—
320C22×C47—42no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47—41no—
325C22×C47—44no—
326C22×C47—42no—
327C22×C47—44no—
328C22×C47—42no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—81no—
337C22×C47—81no—
338C22×C47—82no—
339C22×C47—82no—
340C22×C47—82no—
341C22×C47—82no—
342C22×C47—82no—
343C22×C47—82no—
344C22×C47—82no—
345C22×C47—84no—
346C22×C47—84no—
347C22×C47—82no—
348C22×C47C2×#9911yescharacteristic
349C22×C47C2×#9912yes—
350C22×C47C2×#9912yes—
351C22×C47C2×#9911yescharacteristic
352C22×C47C22×C22⋊C411yescharacteristic
353C4×C47—21no—
354C4×C47—22no—
355C4×C47—21no—
356C4×C47—42no—
357C4×C47—42no—
358C4×C47—42no—
359C4×C47—84no—
360C2×#534C2×C4711yescharacteristic
361C22×#100C2×C4711yescharacteristic, complemented
362C22×#99C2×C4711yescharacteristic, complemented
363#2121C2×C4718yesdirect product factor
364C2×#352C2×C4712yescomplemented
365C2×AΣL(1,𝔽16)C2×C4712yescomplemented
366C2×C47—21no—
367C2×C47—21no—
368C2×C47—22no—
369C2×C47—22no—
370C2×C47—41no—
371C2×C47—42no—
372C2×C47—41no—
373C2×C47—42no—
374C2×C47—41no—
375C2×C47—41no—
376C2×C47—82no—
377C2×C47#212112yesdirect product factor
378C2×C47C22×#9911yescharacteristic
379C23×D4C4×C4711yescharacteristic, complemented
380C23×D4C22×C4711yescharacteristic
381C22×M16—21no—
382#534—22no—
383#534—22no—
384#534C4×C4714yescomplemented
385#534C22×C4714yes—
386C2×#123—21no—
387C2×#123C4×C4711yescharacteristic, complemented
388C2×#123C22×C4711yescharacteristic
389C2×#121—21no—
390C2×#121—21no—
391C2×#120—21no—
392C2×#120C4×C4711yescharacteristic, complemented
393C2×#120C22×C4711yescharacteristic
394C22×C22⋊C4—21no—
395C22×C22⋊C4C4×C4711yescharacteristic, complemented
396C2×#100—22no—
397C2×#100—21no—
398C2×#100C22×C4712yes—
399C2×#100C22×C4714yescomplemented
400C2×#99—22no—
401C2×#99—21no—
402C2×#99C22×C4712yes—
403C2×#99C22×C4714yescomplemented
404#352C22×C4718yescomplemented
405AΣL(1,𝔽16)C22×C4718yescomplemented
406C47C2×#212111yescharacteristic, direct product factor, Sylow
407C25C2×C4×C4711yescharacteristic
408C25C2×C4×C4711yescharacteristic, complemented
409C25D4×C4711yescharacteristic
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—22no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—41no—
416C22×D4—41no—
417C22×D4—42no—
418C22×D4—41no—
419C22×D4—41no—
420C22×D4—42no—
421C22×D4C2×C4×C4711yescharacteristic
422C22×D4C2×C4×C4712yes—
423C22×D4C2×C4×C4714yescomplemented
424C22×D4D4×C4711yescharacteristic
425C22×D4D4×C4712yes—
426C22×D4D4×C4711yescharacteristic
427C22×D4D4×C4712yes—
428C22×D4C23×C4711yescharacteristic
429C22×D4C23×C4712yes—
430C23×C4—21no—
431C23×C4—41no—
432C23×C4C2×C4×C4711yescharacteristic, complemented
433C23×C4D4×C4711yescharacteristic
434C2×M16—22no—
435C2×M16—24no—
436C2×M16—41no—
437C2×M16—42no—
438C22×C8—41no—
439#123—22no—
440#123—21no—
441#123—21no—
442#123—24no—
443#123—24no—
444#123C2×C4×C4714yescomplemented
445#123C2×C4×C4712yescomplemented
446#123C23×C4712yes—
447#121—24no—
448#121—24no—
449#121—24no—
450#121—24no—
451#120—24no—
452#120—24no—
453#120—22no—
454#120—21no—
455#120—21no—
456#120C2×C4×C4714yescomplemented
457#120C2×C4×C4712yescomplemented
458#120C23×C4712yes—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—41no—
471C2×C22⋊C4C2×C4×C4711yescharacteristic, complemented
472C2×C22⋊C4C2×C4×C4711yescharacteristic, complemented
473C2×C22⋊C4C2×C4×C4714yescomplemented
474#100—22no—
475#100—24no—
476#100C23×C4714yes—
477#99—22no—
478#99—24no—
479#99C23×C4714yes—
480C24—21no—
481C24—21no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—22no—
486C24—21no—
487C24—21no—
488C24—41no—
489C24—41no—
490C24—82no—
491C24—82no—
492C24—82no—
493C24C22⋊C4×C4711yescharacteristic
494C24C22⋊C4×C4711yescharacteristic
495C24C22⋊C4×C4712yes—
496C24C22⋊C4×C4712yes—
497C24C22⋊C4×C4711yescharacteristic
498C24C22×C4×C4711yescharacteristic
499C24C22×C4×C4712yes—
500C24C22×C4×C4712yescomplemented
501C24C2×D4×C4711yescharacteristic
502C24C2×D4×C4712yes—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—22no—
506C2×D4—24no—
507C2×D4—22no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—41no—
513C2×D4—42no—
514C2×D4—41no—
515C2×D4—42no—
516C2×D4—41no—
517C2×D4—42no—
518C2×D4—41no—
519C2×D4—42no—
520C2×D4—41no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—41no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—42no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—82no—
534C2×D4—82no—
535C2×D4C22⋊C4×C4712yes—
536C2×D4C22⋊C4×C4712yes—
537C2×D4C22⋊C4×C4712yes—
538C2×D4C22×C4×C4712yes—
539C2×D4C22×C4×C4711yescharacteristic
540C2×D4C2×D4×C4711yescharacteristic
541C2×D4C2×D4×C4712yes—
542C2×D4C2×D4×C4711yescharacteristic
543C2×D4C2×D4×C4712yes—
544C2×D4C24×C4711yescharacteristic
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—44no—
557C22×C4—82no—
558C22×C4—84no—
559C22×C4C22⋊C4×C4711yescharacteristic
560C22×C4C22⋊C4×C4712yes—
561C22×C4C22×C4×C4712yescomplemented
562C22×C4C2×D4×C4711yescharacteristic
563C22×C4C2×D4×C4712yes—
564M16—24no—
565M16—42no—
566M16—44no—
567C2×C8—42no—
568C2×C8—44no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—24no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—24no—
582C22⋊C4—42no—
583C22⋊C4—44no—
584C22⋊C4C22×C4×C4712yescomplemented
585C22⋊C4C22×C4×C4712yescomplemented
586C23—22no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—22no—
593C23—21no—
594C23—21no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—21no—
601C23—22no—
602C23—22no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—44no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23—82no—
620C23—82no—
621C23—82no—
622C23—82no—
623C23—84no—
624C23—84no—
625C23—82no—
626C23—84no—
627C23—84no—
628C23#99×C4711yescharacteristic
629C23#99×C4711yescharacteristic
630C23#99×C4712yes—
631C23C2×C22⋊C4×C4711yescharacteristic
632C23C2×C22⋊C4×C4711yescharacteristic
633C23C2×C22⋊C4×C4712yes—
634C23C2×C22⋊C4×C4711yescharacteristic
635C23C2×C22⋊C4×C4712yes—
636C23C2×C22⋊C4×C4712yes—
637C23C23×C4×C4711yescharacteristic
638C23C22×D4×C4711yescharacteristic
639D4—42no—
640D4—42no—
641D4—42no—
642D4—42no—
643D4—41no—
644D4—41no—
645D4—42no—
646D4—41no—
647D4—42no—
648D4—41no—
649D4—48no—
650D4—44no—
651D4—44no—
652D4—84no—
653D4—82no—
654D4—82no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—84no—
674C2×C4—88no—
675C2×C4—84no—
676C2×C4C2×C22⋊C4×C4712yes—
677C2×C4C2×C22⋊C4×C4711yescharacteristic
678C2×C4C22×D4×C4711yescharacteristic
679C8—44no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—22no—
687C22—22no—
688C22—21no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—44no—
698C22—42no—
699C22—42no—
700C22—44no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22—82no—
717C22—84no—
718C22—84no—
719C22—82no—
720C22C2×#99×C4711yescharacteristic
721C22C2×#99×C4712yes—
722C22C2×#99×C4712yes—
723C22C2×#99×C4711yescharacteristic
724C22C22×C22⋊C4×C4711yescharacteristic
725C4—21no—
726C4—22no—
727C4—21no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—84no—
732C2—21no—
733C2—21no—
734C2—22no—
735C2—22no—
736C2—41no—
737C2—42no—
738C2—41no—
739C2—41no—
740C2—41no—
741C2—42no—
742C2—82no—
743C2C47×#212112yesdirect product factor
744C2C22×#99×C4711yescharacteristic
subgroupG/H
center, socleC22×C47C2×#99
commutatorC23C23×C4×C47
Frattini, cosocleC2×D4C24×C47
prime radicalC2×C47×#534C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C24×C47 ◁ C23×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#100×C47C2semidirect
3. C22×#99×C47C2semidirect
4. C47×#2121C2direct (N × H)
5. C2×C47×#352C2semidirect
6. C2×C47×AΣL(1,𝔽16)C2semidirect
7. C23×D4×C47C4semidirect
12. C47×#534C4semidirect
15. C2×#123×C47C4semidirect
20. C2×#120×C47C4semidirect
23. C22×C22⋊C4×C47C4semidirect
27. C2×#100×C47C22semidirect
31. C2×#99×C47C22semidirect
32. C47×#352C22semidirect
33. C47×AΣL(1,𝔽16)C22semidirect
35. C25×C47C2×C4semidirect
50. C22×D4×C47C2×C4semidirect
59. C23×C4×C47C2×C4semidirect
71. #123×C47C2×C4semidirect
72. #123×C47C2×C4semidirect
83. #120×C47C2×C4semidirect
84. #120×C47C2×C4semidirect
98. C2×C22⋊C4×C47C2×C4semidirect
99. C2×C22⋊C4×C47C2×C4semidirect
100. C2×C22⋊C4×C47C2×C4semidirect
127. C24×C47C22×C4semidirect
188. C22×C4×C47C22×C4semidirect
211. C22⋊C4×C47C22×C4semidirect
212. C22⋊C4×C47C22×C4semidirect
307. C2×#2121C47direct (N × H)
361. C22×#100C2×C47semidirect
362. C22×#99C2×C47semidirect
363. #2121C2×C47direct (N × H)
364. C2×#352C2×C47semidirect
365. C2×AΣL(1,𝔽16)C2×C47semidirect
377. C2×C47#2121direct (N × H)
379. C23×D4C4×C47semidirect
384. #534C4×C47semidirect
387. C2×#123C4×C47semidirect
392. C2×#120C4×C47semidirect
395. C22×C22⋊C4C4×C47semidirect
399. C2×#100C22×C47semidirect
403. C2×#99C22×C47semidirect
404. #352C22×C47semidirect
405. AΣL(1,𝔽16)C22×C47semidirect
406. C47C2×#2121direct (N × H)
408. C25C2×C4×C47semidirect
423. C22×D4C2×C4×C47semidirect
432. C23×C4C2×C4×C47semidirect
444. #123C2×C4×C47semidirect
445. #123C2×C4×C47semidirect
456. #120C2×C4×C47semidirect
457. #120C2×C4×C47semidirect
471. C2×C22⋊C4C2×C4×C47semidirect
472. C2×C22⋊C4C2×C4×C47semidirect
473. C2×C22⋊C4C2×C4×C47semidirect
500. C24C22×C4×C47semidirect
561. C22×C4C22×C4×C47semidirect
584. C22⋊C4C22×C4×C47semidirect
585. C22⋊C4C22×C4×C47semidirect
743. C2C47×#2121direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5342
C22×#100×C472
C22×#99×C472
C47×#21212
C2×C47×#3522
C2×C47×AΣL(1,𝔽16)2
C2×#212147