Finite Group Databasebeta

← C47×#24468 #26064166

Subgroups — C47×#24468 #26064166

Order 12032.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3488C211yesmaximal, characteristic, complemented
2C47×#3055C211yesmaximal, characteristic, complemented
3C2×C47×#453C211yesmaximal, characteristic, complemented
4C47×#3006C211yesmaximal, characteristic, complemented
5C2×C47×#421C211yesmaximal, characteristic, complemented
6C47×#2619C211yesmaximal, characteristic, complemented
7C47×#2040C211yesmaximal, characteristic, complemented
8C47×#2037C211yesmaximal, characteristic, complemented
9C47×#2006C211yesmaximal, characteristic, complemented
10C47×#2002C211yesmaximal, characteristic, complemented
11C47×#1900C211yesmaximal, characteristic, complemented
12C47×#1897C211yesmaximal, characteristic, complemented
13C47×#1883C211yesmaximal, characteristic, complemented
14C47×#1860C211yesmaximal, characteristic, complemented
15C47×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
21C22×M16×C47C2211yescharacteristic, complemented
22C47×#550—21no—
23C47×#548—21no—
24C47×#546—21no—
25C47×#546—22no—
26D42×C47—22no—
27D42×C47—21no—
28C47×#537—21no—
29C47×#537C2211yescharacteristic
30C47×#535—21no—
31C47×#535C2211yescharacteristic
32C2×#127×C47C2211yescharacteristic, complemented
33C47×#525—21no—
34C47×#525C2211yescharacteristic
35C2×#121×C47—21no—
36C2×#121×C47C2211yescharacteristic
37C2×#121×C47C2211yescharacteristic, complemented
38C47×#520C2211yescharacteristic
39C2×#117×C47C2211yescharacteristic, complemented
40C47×#469—21no—
41C47×#468—21no—
42C47×#466—21no—
43C47×#465—21no—
44C47×#453—24no—
45C47×#449—21no—
46C47×#449—21no—
47C47×#448—21no—
48C47×#447—21no—
49C47×#428C2211yescharacteristic, complemented
50C47×#421—24no—
51C2×#104×C47C2211yescharacteristic
52C2×#104×C47C2211yescharacteristic
53C2×#104×C47C2211yescharacteristic, complemented
54C2×#104×C47C2211yescharacteristic, complemented
55C2×#104×C47C2211yescharacteristic, complemented
56C2×#104×C47C2211yescharacteristic, complemented
57C47×#418C2211yescharacteristic, complemented
58C47×#417C2211yescharacteristic
59C47×#417C2211yescharacteristic, complemented
60C47×#417C2211yescharacteristic, complemented
61C2×#100×C47C2211yescharacteristic, complemented
62C2×#100×C47C2211yescharacteristic, complemented
63C47×#407C2211yescharacteristic, complemented
64C47×#394—22no—
65C47×#392—22no—
66C47×#390C2211yescharacteristic, complemented
67C47×#390C2211yescharacteristic, complemented
68C47×#382C2211yescharacteristic, complemented
69C47×#343C2211yescharacteristic, complemented
70C47×#343C2211yescharacteristic, complemented
71C47×#339C2211yescharacteristic, complemented
72C47×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C47—22no—
74H(5,𝔽2)×C47—22no—
75H(5,𝔽2)×C47—41no—
76H(5,𝔽2)×C47—41no—
77C2×#41×C47—21no—
78C2×#41×C47—21no—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47—22no—
82C2×#41×C47—22no—
83C2×#41×C47—41no—
84C2×#41×C47—41no—
85C2×#41×C47D411yescharacteristic, complemented
86C2×#41×C47D411yescharacteristic, complemented
87C2×#41×C47C2311yescharacteristic
88C2×#41×C47C2311yescharacteristic
89C2×#41×C47C2311yescharacteristic
90C22×Q8×C47D411yescharacteristic, complemented
91C22×D4×C47—21no—
92C22×D4×C47—22no—
93C22×D4×C47—22no—
94C22×D4×C47—21no—
95C22×D4×C47—21no—
96C22×D4×C47—21no—
97C22×D4×C47—22no—
98C22×D4×C47D412yes—
99C22×D4×C47D411yescharacteristic, complemented
100C22×D4×C47C2311yescharacteristic
101C22×D4×C47C2311yescharacteristic
102C23×C4×C47—21no—
103C23×C4×C47C2311yescharacteristic
104AGL(1,ℤ/8)×C47—22no—
105AGL(1,ℤ/8)×C47—22no—
106AGL(1,ℤ/8)×C47—22no—
107AGL(1,ℤ/8)×C47—41no—
108AGL(1,ℤ/8)×C47—41no—
109AGL(1,ℤ/8)×C47—41no—
110C2×SD16×C47—21no—
111C2×SD16×C47—21no—
112C2×SD16×C47—21no—
113C2×D8×C47—21no—
114C2×D8×C47—21no—
115C2×D8×C47—21no—
116C2×M16×C47—21no—
117C2×M16×C47—22no—
118C2×M16×C47—41no—
119C2×M16×C47C2311yescharacteristic
120C2×M16×C47C2311yescharacteristic
121C2×M16×C47C2311yescharacteristic
122C2×M16×C47C2311yescharacteristic
123C22×C8×C47—21no—
124#127×C47—22no—
125#127×C47—21no—
126#127×C47—22no—
127#127×C47—41no—
128#124×C47—22no—
129#124×C47—21no—
130#123×C47—22no—
131#123×C47—21no—
132C22⋊Q8×C47—22no—
133C22⋊Q8×C47—21no—
134C22⋊Q8×C47—21no—
135C22⋊Q8×C47D411yescharacteristic, complemented
136C22⋊Q8×C47D411yescharacteristic, complemented
137#121×C47—22no—
138#121×C47—22no—
139#121×C47—22no—
140#121×C47—22no—
141#121×C47—22no—
142#121×C47—21no—
143#121×C47—21no—
144#121×C47—21no—
145#121×C47—21no—
146#121×C47—21no—
147#121×C47—21no—
148#121×C47—22no—
149#121×C47—21no—
150#121×C47—21no—
151#121×C47—21no—
152#121×C47—21no—
153#121×C47—21no—
154#121×C47—21no—
155#121×C47D411yescharacteristic, complemented
156#121×C47D411yescharacteristic, complemented
157#120×C47—22no—
158#120×C47—22no—
159#120×C47—22no—
160#120×C47—21no—
161#120×C47—22no—
162C4×Q8×C47—21no—
163C4×D4×C47—22no—
164C4×D4×C47—22no—
165C4×D4×C47—21no—
166C4×D4×C47—22no—
167C4×D4×C47—21no—
168C4×D4×C47—21no—
169#117×C47—21no—
170#117×C47—22no—
171#117×C47—41no—
172#117×C47C2311yescharacteristic
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—22no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—22no—
181C2×C22⋊C4×C47—22no—
182C2×C22⋊C4×C47D412yes—
183C2×C42×C47C2311yescharacteristic
184C2×C42×C47C2311yescharacteristic
185#107×C47—21no—
186#106×C47—21no—
187#104×C47—22no—
188#104×C47—22no—
189#104×C47—22no—
190#104×C47—22no—
191#104×C47—41no—
192#104×C47D414yescomplemented
193#103×C47—21no—
194#103×C47—21no—
195#103×C47—21no—
196#102×C47—21no—
197#102×C47—21no—
198#102×C47—21no—
199#102×C47—21no—
200#102×C47—21no—
201#100×C47—22no—
202#100×C47—41no—
203C22⋊C8×C47—21no—
204C22⋊C8×C47—21no—
205#95×C47—22no—
206C24×C47—22no—
207C24×C47—21no—
208C24×C47—21no—
209C24×C47C2×D412yes—
210C24×C47C2×D411yescharacteristic
211#41×C47—21no—
212#41×C47—21no—
213#41×C47—22no—
214#41×C47—22no—
215#41×C47—21no—
216#41×C47—21no—
217#41×C47—21no—
218#41×C47—21no—
219#41×C47—21no—
220#41×C47—21no—
221#41×C47—21no—
222#41×C47—21no—
223#41×C47—42no—
224#41×C47—42no—
225#41×C47—41no—
226#41×C47—41no—
227#41×C47—42no—
228#41×C47—42no—
229#41×C47—42no—
230#41×C47—42no—
231#41×C47—42no—
232#41×C47—42no—
233#41×C47C2×D412yes—
234#41×C47#4112yes—
235C2×Q8×C47—21no—
236C2×Q8×C47—22no—
237C2×Q8×C47—41no—
238C2×Q8×C47C2×D411yescharacteristic
239C2×Q8×C47C2×D411yescharacteristic
240C2×Q8×C47C2×D411yescharacteristic
241C2×D4×C47—21no—
242C2×D4×C47—22no—
243C2×D4×C47—22no—
244C2×D4×C47—22no—
245C2×D4×C47—22no—
246C2×D4×C47—21no—
247C2×D4×C47—21no—
248C2×D4×C47—21no—
249C2×D4×C47—21no—
250C2×D4×C47—21no—
251C2×D4×C47—22no—
252C2×D4×C47—22no—
253C2×D4×C47—22no—
254C2×D4×C47—21no—
255C2×D4×C47—22no—
256C2×D4×C47—21no—
257C2×D4×C47—21no—
258C2×D4×C47—21no—
259C2×D4×C47—21no—
260C2×D4×C47—21no—
261C2×D4×C47—21no—
262C2×D4×C47—21no—
263C2×D4×C47—21no—
264C2×D4×C47—21no—
265C2×D4×C47—21no—
266C2×D4×C47—21no—
267C2×D4×C47—21no—
268C2×D4×C47—21no—
269C2×D4×C47—41no—
270C2×D4×C47—42no—
271C2×D4×C47—42no—
272C2×D4×C47—44no—
273C2×D4×C47—42no—
274C2×D4×C47—42no—
275C2×D4×C47—44no—
276C2×D4×C47—44no—
277C2×D4×C47—42no—
278C2×D4×C47—42no—
279C2×D4×C47—41no—
280C2×D4×C47—41no—
281C2×D4×C47—82no—
282C2×D4×C47—82no—
283C2×D4×C47—82no—
284C2×D4×C47—82no—
285C2×D4×C47—84no—
286C2×D4×C47C2×D411yescharacteristic
287C2×D4×C47C2×D411yescharacteristic
288C2×D4×C47C2×D411yescharacteristic
289C22×C4×C47—21no—
290C22×C4×C47—21no—
291C22×C4×C47—21no—
292C22×C4×C47—21no—
293C22×C4×C47—21no—
294C22×C4×C47—22no—
295C22×C4×C47—21no—
296C22×C4×C47—21no—
297C22×C4×C47—22no—
298C22×C4×C47—21no—
299C22×C4×C47—21no—
300C22×C4×C47—21no—
301C22×C4×C47—21no—
302C22×C4×C47—21no—
303C22×C4×C47—21no—
304C22×C4×C47—42no—
305C22×C4×C47—42no—
306C22×C4×C47C2×D411yescharacteristic
307C22×C4×C47C2×D411yescharacteristic
308C22×C4×C47C2×D411yescharacteristic
309C22×C4×C47C2×D411yescharacteristic
310C22×C4×C47C2×D411yescharacteristic
311C22×C4×C47C2×D412yes—
312C22×C4×C47C2411yescharacteristic
313SD16×C47—42no—
314SD16×C47—42no—
315SD16×C47—42no—
316D8×C47—42no—
317D8×C47—42no—
318D8×C47—42no—
319M16×C47—21no—
320M16×C47—21no—
321M16×C47—21no—
322M16×C47—21no—
323M16×C47—21no—
324M16×C47—21no—
325M16×C47—21no—
326M16×C47—42no—
327M16×C47C2×D412yescomplemented
328C2×C8×C47—21no—
329C2×C8×C47—21no—
330C2×C8×C47—21no—
331C2×C8×C47—21no—
332C2×C8×C47—42no—
333C4⋊C4×C47—22no—
334C4⋊C4×C47—22no—
335C4⋊C4×C47—21no—
336C4⋊C4×C47—21no—
337C4⋊C4×C47—21no—
338C4⋊C4×C47—21no—
339C4⋊C4×C47—21no—
340C4⋊C4×C47—21no—
341C4⋊C4×C47—42no—
342C4⋊C4×C47C2×D411yescharacteristic
343C4⋊C4×C47C2×D411yescharacteristic
344C22⋊C4×C47—22no—
345C22⋊C4×C47—22no—
346C22⋊C4×C47—22no—
347C22⋊C4×C47—22no—
348C22⋊C4×C47—22no—
349C22⋊C4×C47—21no—
350C22⋊C4×C47—21no—
351C22⋊C4×C47—21no—
352C22⋊C4×C47—21no—
353C22⋊C4×C47—22no—
354C22⋊C4×C47—22no—
355C22⋊C4×C47—21no—
356C22⋊C4×C47—42no—
357C22⋊C4×C47—41no—
358C22⋊C4×C47—41no—
359C22⋊C4×C47—82no—
360C22⋊C4×C47—82no—
361C42×C47—22no—
362C42×C47—21no—
363C42×C47—21no—
364C42×C47—21no—
365C42×C47—21no—
366C42×C47C2×D412yescomplemented
367C23×C47—21no—
368C23×C47—21no—
369C23×C47—21no—
370C23×C47—22no—
371C23×C47—21no—
372C23×C47—21no—
373C23×C47—22no—
374C23×C47—22no—
375C23×C47—41no—
376C23×C47—41no—
377C23×C47—42no—
378C23×C47—42no—
379C23×C47—44no—
380C23×C47—42no—
381C23×C47—42no—
382C23×C47—42no—
383C23×C47—42no—
384C23×C47—41no—
385C23×C47—41no—
386C23×C47—41no—
387C23×C47—81no—
388C23×C47—82no—
389C23×C47—82no—
390C23×C47#12011yescharacteristic
391C23×C47#12011yescharacteristic
392C23×C47C22×D411yescharacteristic
393Q8×C47—21no—
394Q8×C47—21no—
395Q8×C47—21no—
396Q8×C47—21no—
397Q8×C47—21no—
398Q8×C47—42no—
399Q8×C47#12112yes—
400D4×C47—22no—
401D4×C47—22no—
402D4×C47—21no—
403D4×C47—21no—
404D4×C47—21no—
405D4×C47—21no—
406D4×C47—21no—
407D4×C47—42no—
408D4×C47—42no—
409D4×C47—44no—
410D4×C47—42no—
411D4×C47—44no—
412D4×C47—44no—
413D4×C47—42no—
414D4×C47—41no—
415D4×C47—41no—
416D4×C47—41no—
417D4×C47—41no—
418D4×C47—41no—
419D4×C47—41no—
420D4×C47—41no—
421D4×C47—41no—
422D4×C47—41no—
423D4×C47—41no—
424D4×C47—41no—
425D4×C47—41no—
426D4×C47—81no—
427D4×C47—82no—
428D4×C47—82no—
429D4×C47—82no—
430D4×C47—82no—
431D4×C47—88no—
432D4×C47—82no—
433D4×C47—82no—
434D4×C47#12112yes—
435C2×C4×C47—21no—
436C2×C4×C47—21no—
437C2×C4×C47—21no—
438C2×C4×C47—21no—
439C2×C4×C47—21no—
440C2×C4×C47—21no—
441C2×C4×C47—21no—
442C2×C4×C47—21no—
443C2×C4×C47—21no—
444C2×C4×C47—22no—
445C2×C4×C47—21no—
446C2×C4×C47—21no—
447C2×C4×C47—22no—
448C2×C4×C47—21no—
449C2×C4×C47—22no—
450C2×C4×C47—21no—
451C2×C4×C47—21no—
452C2×C4×C47—21no—
453C2×C4×C47—22no—
454C2×C4×C47—42no—
455C2×C4×C47—42no—
456C2×C4×C47—42no—
457C2×C4×C47—44no—
458C2×C4×C47—41no—
459C2×C4×C47—41no—
460C2×C4×C47—41no—
461C2×C4×C47—41no—
462C2×C4×C47—41no—
463C2×C4×C47—41no—
464C2×C4×C47—42no—
465C2×C4×C47—41no—
466C2×C4×C47—41no—
467C2×C4×C47—42no—
468C2×C4×C47—41no—
469C2×C4×C47—41no—
470C2×C4×C47—82no—
471C2×C4×C47#12011yescharacteristic
472C2×C4×C47#12011yescharacteristic
473C2×C4×C47C22×D411yescharacteristic
474C2×C4×C47C22×D411yescharacteristic
475C2×C4×C47C22×D411yescharacteristic
476C2×C4×C47C2×#4111yescharacteristic
477C2×C4×C47H(5,𝔽2)11yescharacteristic
478C2×C4×C47H(5,𝔽2)11yescharacteristic
479C8×C47—22no—
480C8×C47—41no—
481C8×C47—41no—
482C8×C47—41no—
483#24468C4711yesmaximal, characteristic, direct product factor, Sylow
484C22×C47—21no—
485C22×C47—21no—
486C22×C47—21no—
487C22×C47—21no—
488C22×C47—22no—
489C22×C47—21no—
490C22×C47—21no—
491C22×C47—21no—
492C22×C47—21no—
493C22×C47—41no—
494C22×C47—41no—
495C22×C47—41no—
496C22×C47—41no—
497C22×C47—42no—
498C22×C47—42no—
499C22×C47—41no—
500C22×C47—41no—
501C22×C47—41no—
502C22×C47—42no—
503C22×C47—41no—
504C22×C47—81no—
505C22×C47—81no—
506C22×C47—82no—
507C22×C47—82no—
508C22×C47—82no—
509C22×C47—82no—
510C22×C47—84no—
511C22×C47—81no—
512C22×C47—81no—
513C22×C47—81no—
514C22×C47—164no—
515C22×C47C2×#12011yescharacteristic
516C22×C47D4211yescharacteristic
517C22×C47#54611yescharacteristic
518C4×C47—21no—
519C4×C47—21no—
520C4×C47—22no—
521C4×C47—42no—
522C4×C47—41no—
523C4×C47—41no—
524C4×C47—42no—
525C4×C47—41no—
526C4×C47—41no—
527C4×C47—81no—
528C4×C47—81no—
529C4×C47C2×#12111yescharacteristic
530C4×C47#53411yescharacteristic
531C4×C47D4211yescharacteristic
532C4×C47#54611yescharacteristic
533#3488C2×C4711yescharacteristic, complemented
534#3055C2×C4711yescharacteristic, complemented
535C2×#453C2×C4711yescharacteristic, complemented
536#3006C2×C4711yescharacteristic, complemented
537C2×#421C2×C4711yescharacteristic, complemented
538#2619C2×C4711yescharacteristic, complemented
539#2040C2×C4711yescharacteristic, complemented
540#2037C2×C4711yescharacteristic, complemented
541#2006C2×C4711yescharacteristic, complemented
542#2002C2×C4711yescharacteristic, complemented
543#1900C2×C4711yescharacteristic, complemented
544#1897C2×C4711yescharacteristic, complemented
545#1883C2×C4711yescharacteristic, complemented
546#1860C2×C4711yescharacteristic, complemented
547#1792C2×C4711yescharacteristic, complemented
548C2×C47—21no—
549C2×C47—21no—
550C2×C47—41no—
551C2×C47—41no—
552C2×C47—42no—
553C2×C47—81no—
554C2×C47—82no—
555C2×C47—81no—
556C2×C47—161no—
557C2×C47#241011yescharacteristic
558C2×C47#301911yescharacteristic
559C2×C47#302111yescharacteristic
560C2×H(5,𝔽2)C22×C4711yescharacteristic
561C22×#41C22×C4711yescharacteristic
562C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
563C2×AGL(1,ℤ/8)C22×C4711yescharacteristic, complemented
564C2×AGL(1,ℤ/8)C22×C4711yescharacteristic, complemented
565C22×M16C22×C4711yescharacteristic, complemented
566#550—21no—
567#548—21no—
568#546—21no—
569#546—22no—
570D42—22no—
571D42—21no—
572#537—21no—
573#537C22×C4711yescharacteristic
574#535—21no—
575#535C22×C4711yescharacteristic
576C2×#127C22×C4711yescharacteristic, complemented
577#525—21no—
578#525C22×C4711yescharacteristic
579C2×#121—21no—
580C2×#121C22×C4711yescharacteristic
581C2×#121C22×C4711yescharacteristic, complemented
582#520C22×C4711yescharacteristic
583C2×#117C22×C4711yescharacteristic, complemented
584#469—21no—
585#468—21no—
586#466—21no—
587#465—21no—
588#453—24no—
589#449—21no—
590#449—21no—
591#448—21no—
592#447—21no—
593#428C22×C4711yescharacteristic, complemented
594#421—24no—
595C2×#104C22×C4711yescharacteristic
596C2×#104C22×C4711yescharacteristic
597C2×#104C22×C4711yescharacteristic, complemented
598C2×#104C22×C4711yescharacteristic, complemented
599C2×#104C22×C4711yescharacteristic, complemented
600C2×#104C22×C4711yescharacteristic, complemented
601#418C22×C4711yescharacteristic, complemented
602#417C22×C4711yescharacteristic
603#417C22×C4711yescharacteristic, complemented
604#417C22×C4711yescharacteristic, complemented
605C2×#100C22×C4711yescharacteristic, complemented
606C2×#100C22×C4711yescharacteristic, complemented
607#407C22×C4711yescharacteristic, complemented
608#394—22no—
609#392—22no—
610#390C22×C4711yescharacteristic, complemented
611#390C22×C4711yescharacteristic, complemented
612#382C22×C4711yescharacteristic, complemented
613#343C22×C4711yescharacteristic, complemented
614#343C22×C4711yescharacteristic, complemented
615#339C22×C4711yescharacteristic, complemented
616#339C22×C4711yescharacteristic, complemented
617C47#2446811yescharacteristic, direct product factor, Sylow
618H(5,𝔽2)—22no—
619H(5,𝔽2)—22no—
620H(5,𝔽2)—41no—
621H(5,𝔽2)—41no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—22no—
627C2×#41—22no—
628C2×#41—41no—
629C2×#41—41no—
630C2×#41D4×C4711yescharacteristic, complemented
631C2×#41D4×C4711yescharacteristic, complemented
632C2×#41C23×C4711yescharacteristic
633C2×#41C23×C4711yescharacteristic
634C2×#41C23×C4711yescharacteristic
635C22×Q8D4×C4711yescharacteristic, complemented
636C22×D4—21no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—21no—
642C22×D4—22no—
643C22×D4D4×C4712yes—
644C22×D4D4×C4711yescharacteristic, complemented
645C22×D4C23×C4711yescharacteristic
646C22×D4C23×C4711yescharacteristic
647C23×C4—21no—
648C23×C4C23×C4711yescharacteristic
649AGL(1,ℤ/8)—22no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—22no—
652AGL(1,ℤ/8)—41no—
653AGL(1,ℤ/8)—41no—
654AGL(1,ℤ/8)—41no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×D8—21no—
661C2×M16—21no—
662C2×M16—22no—
663C2×M16—41no—
664C2×M16C23×C4711yescharacteristic
665C2×M16C23×C4711yescharacteristic
666C2×M16C23×C4711yescharacteristic
667C2×M16C23×C4711yescharacteristic
668C22×C8—21no—
669#127—22no—
670#127—21no—
671#127—22no—
672#127—41no—
673#124—22no—
674#124—21no—
675#123—22no—
676#123—21no—
677C22⋊Q8—22no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8D4×C4711yescharacteristic, complemented
681C22⋊Q8D4×C4711yescharacteristic, complemented
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—22no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—21no—
700#121D4×C4711yescharacteristic, complemented
701#121D4×C4711yescharacteristic, complemented
702#120—22no—
703#120—22no—
704#120—22no—
705#120—21no—
706#120—22no—
707C4×Q8—21no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—21no—
711C4×D4—22no—
712C4×D4—21no—
713C4×D4—21no—
714#117—21no—
715#117—22no—
716#117—41no—
717#117C23×C4711yescharacteristic
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4C23×C4711yescharacteristic
721C2×C4⋊C4C23×C4711yescharacteristic
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4D4×C4712yes—
728C2×C42C23×C4711yescharacteristic
729C2×C42C23×C4711yescharacteristic
730#107—21no—
731#106—21no—
732#104—22no—
733#104—22no—
734#104—22no—
735#104—22no—
736#104—41no—
737#104D4×C4714yescomplemented
738#103—21no—
739#103—21no—
740#103—21no—
741#102—21no—
742#102—21no—
743#102—21no—
744#102—21no—
745#102—21no—
746#100—22no—
747#100—41no—
748C22⋊C8—21no—
749C22⋊C8—21no—
750#95—22no—
751C24—22no—
752C24—21no—
753C24—21no—
754C24C2×D4×C4712yes—
755C24C2×D4×C4711yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41C2×D4×C4712yes—
779#41#41×C4712yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×D4×C4711yescharacteristic
784C2×Q8C2×D4×C4711yescharacteristic
785C2×Q8C2×D4×C4711yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—84no—
831C2×D4C2×D4×C4711yescharacteristic
832C2×D4C2×D4×C4711yescharacteristic
833C2×D4C2×D4×C4711yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×D4×C4711yescharacteristic
852C22×C4C2×D4×C4711yescharacteristic
853C22×C4C2×D4×C4711yescharacteristic
854C22×C4C2×D4×C4711yescharacteristic
855C22×C4C2×D4×C4711yescharacteristic
856C22×C4C2×D4×C4712yes—
857C22×C4C24×C4711yescharacteristic
858SD16—42no—
859SD16—42no—
860SD16—42no—
861D8—42no—
862D8—42no—
863D8—42no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—42no—
872M16C2×D4×C4712yescomplemented
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—42no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4C2×D4×C4711yescharacteristic
888C4⋊C4C2×D4×C4711yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—42no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C42—22no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42C2×D4×C4712yescomplemented
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23#120×C4711yescharacteristic
936C23#120×C4711yescharacteristic
937C23C22×D4×C4711yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8#121×C4712yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—81no—
972D4—82no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4#121×C4712yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4#120×C4711yescharacteristic
1017C2×C4#120×C4711yescharacteristic
1018C2×C4C22×D4×C4711yescharacteristic
1019C2×C4C22×D4×C4711yescharacteristic
1020C2×C4C22×D4×C4711yescharacteristic
1021C2×C4C2×#41×C4711yescharacteristic
1022C2×C4H(5,𝔽2)×C4711yescharacteristic
1023C2×C4H(5,𝔽2)×C4711yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—41no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×#120×C4711yescharacteristic
1060C22D42×C4711yescharacteristic
1061C22C47×#54611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—42no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×#121×C4711yescharacteristic
1074C4C47×#53411yescharacteristic
1075C4D42×C4711yescharacteristic
1076C4C47×#54611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2C47×#241011yescharacteristic
1087C2C47×#301911yescharacteristic
1088C2C47×#302111yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3488C2semidirect
2. C47×#3055C2semidirect
3. C2×C47×#453C2semidirect
4. C47×#3006C2semidirect
5. C2×C47×#421C2semidirect
6. C47×#2619C2semidirect
7. C47×#2040C2semidirect
8. C47×#2037C2semidirect
9. C47×#2006C2semidirect
10. C47×#2002C2semidirect
11. C47×#1900C2semidirect
12. C47×#1897C2semidirect
13. C47×#1883C2semidirect
14. C47×#1860C2semidirect
15. C47×#1792C2semidirect
19. C2×AGL(1,ℤ/8)×C47C22semidirect
20. C2×AGL(1,ℤ/8)×C47C22semidirect
21. C22×M16×C47C22semidirect
32. C2×#127×C47C22semidirect
37. C2×#121×C47C22semidirect
39. C2×#117×C47C22semidirect
49. C47×#428C22semidirect
53. C2×#104×C47C22semidirect
54. C2×#104×C47C22semidirect
55. C2×#104×C47C22semidirect
56. C2×#104×C47C22semidirect
57. C47×#418C22semidirect
59. C47×#417C22semidirect
60. C47×#417C22semidirect
61. C2×#100×C47C22semidirect
62. C2×#100×C47C22semidirect
63. C47×#407C22semidirect
66. C47×#390C22semidirect
67. C47×#390C22semidirect
68. C47×#382C22semidirect
69. C47×#343C22semidirect
70. C47×#343C22semidirect
71. C47×#339C22semidirect
72. C47×#339C22semidirect
85. C2×#41×C47D4semidirect
86. C2×#41×C47D4semidirect
90. C22×Q8×C47D4semidirect
99. C22×D4×C47D4semidirect
135. C22⋊Q8×C47D4semidirect
136. C22⋊Q8×C47D4semidirect
155. #121×C47D4semidirect
156. #121×C47D4semidirect
192. #104×C47D4semidirect
327. M16×C47C2×D4semidirect
366. C42×C47C2×D4semidirect
483. #24468C47direct (N × H)
533. #3488C2×C47semidirect
534. #3055C2×C47semidirect
535. C2×#453C2×C47semidirect
536. #3006C2×C47semidirect
537. C2×#421C2×C47semidirect
538. #2619C2×C47semidirect
539. #2040C2×C47semidirect
540. #2037C2×C47semidirect
541. #2006C2×C47semidirect
542. #2002C2×C47semidirect
543. #1900C2×C47semidirect
544. #1897C2×C47semidirect
545. #1883C2×C47semidirect
546. #1860C2×C47semidirect
547. #1792C2×C47semidirect
563. C2×AGL(1,ℤ/8)C22×C47semidirect
564. C2×AGL(1,ℤ/8)C22×C47semidirect
565. C22×M16C22×C47semidirect
576. C2×#127C22×C47semidirect
581. C2×#121C22×C47semidirect
583. C2×#117C22×C47semidirect
593. #428C22×C47semidirect
597. C2×#104C22×C47semidirect
598. C2×#104C22×C47semidirect
599. C2×#104C22×C47semidirect
600. C2×#104C22×C47semidirect
601. #418C22×C47semidirect
603. #417C22×C47semidirect
604. #417C22×C47semidirect
605. C2×#100C22×C47semidirect
606. C2×#100C22×C47semidirect
607. #407C22×C47semidirect
610. #390C22×C47semidirect
611. #390C22×C47semidirect
612. #382C22×C47semidirect
613. #343C22×C47semidirect
614. #343C22×C47semidirect
615. #339C22×C47semidirect
616. #339C22×C47semidirect
617. C47#24468direct (N × H)
630. C2×#41D4×C47semidirect
631. C2×#41D4×C47semidirect
635. C22×Q8D4×C47semidirect
644. C22×D4D4×C47semidirect
680. C22⋊Q8D4×C47semidirect
681. C22⋊Q8D4×C47semidirect
700. #121D4×C47semidirect
701. #121D4×C47semidirect
737. #104D4×C47semidirect
872. M16C2×D4×C47semidirect
911. C42C2×D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#34882
C47×#30552
C2×C47×#4532
C47×#30062
C2×C47×#4212
C47×#26192
C47×#20402
C47×#20372
C47×#20062
C47×#20022
C47×#19002
C47×#18972
C47×#18832
C47×#18602
C47×#17922
#2446847