Finite Group Databasebeta

← C47×#24459 #26064157

Subgroups — C47×#24459 #26064157

Order 12032.

1362 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#576C211yesmaximal, characteristic
2C2×C47×#471C211yesmaximal, characteristic, complemented
3C47×#3046C211yesmaximal, characteristic, complemented
4C2×C47×#455C211yesmaximal, characteristic, complemented
5C47×#3009C211yesmaximal, characteristic, complemented
6C47×#2897C211yesmaximal, characteristic, complemented
7C47×#2051C211yesmaximal, characteristic, complemented
8C47×#2045C211yesmaximal, characteristic, complemented
9C47×#2012C211yesmaximal, characteristic, complemented
10C47×#2003C211yesmaximal, characteristic, complemented
11C47×#1908C211yesmaximal, characteristic, complemented
12C47×#1883C211yesmaximal, characteristic, complemented
13C47×#1876C211yesmaximal, characteristic, complemented
14C47×#1866C211yesmaximal, characteristic, complemented
15C47×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C47C2211yescharacteristic
17C2×H(5,𝔽2)×C47C2211yescharacteristic
18C47×#576—24no—
19C47×#576—24no—
20C2×#137×C47C2211yescharacteristic
21C2×#137×C47C2211yescharacteristic, complemented
22C2×AGL(1,ℤ/8)×C47—21no—
23C2×AGL(1,ℤ/8)×C47—21no—
24C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
26C2×#135×C47—21no—
27C2×#135×C47C2211yescharacteristic
28C22×SD16×C47C2211yescharacteristic, complemented
29C22×D8×C47—21no—
30C22×D8×C47C2211yescharacteristic
31C2×#131×C47C2211yescharacteristic
32C2×#131×C47C2211yescharacteristic, complemented
33C47×#536C2211yescharacteristic, complemented
34C2×#124×C47C2211yescharacteristic, complemented
35C47×#520C2211yescharacteristic, complemented
36C47×#471—24no—
37C47×#464—21no—
38C47×#463—21no—
39C47×#462—21no—
40C47×#461—21no—
41C47×#455—24no—
42C47×#452—21no—
43C47×#452—21no—
44C47×#450—21no—
45C47×#450—21no—
46C2×#108×C47C2211yescharacteristic, complemented
47C47×#424C2211yescharacteristic, complemented
48C2×#104×C47C2211yescharacteristic
49C2×#104×C47C2211yescharacteristic, complemented
50C2×#104×C47C2211yescharacteristic, complemented
51C47×#418—21no—
52C47×#418C2211yescharacteristic, complemented
53C47×#418C2211yescharacteristic, complemented
54C47×#417—21no—
55C47×#417C2211yescharacteristic
56C47×#417C2211yescharacteristic, complemented
57C47×#416—21no—
58C47×#416C2211yescharacteristic
59C2×#103×C47C2211yescharacteristic, complemented
60C2×#102×C47—21no—
61C2×#102×C47C2211yescharacteristic, complemented
62C2×#101×C47C2211yescharacteristic, complemented
63C2×#100×C47C2211yescharacteristic, complemented
64C2×#100×C47C2211yescharacteristic, complemented
65C47×#408C2211yescharacteristic, complemented
66C47×#390C2211yescharacteristic, complemented
67C47×#343C2211yescharacteristic, complemented
68C47×#341C2211yescharacteristic, complemented
69C47×#339C2211yescharacteristic, complemented
70C47×#336C2211yescharacteristic, complemented
71H(5,𝔽2)×C47—22no—
72H(5,𝔽2)×C47—22no—
73H(5,𝔽2)×C47—22no—
74H(5,𝔽2)×C47—22no—
75H(5,𝔽2)×C47—22no—
76H(5,𝔽2)×C47—41no—
77H(5,𝔽2)×C47—41no—
78H(5,𝔽2)×C47D414yes—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47—21no—
82C2×#41×C47—21no—
83C2×#41×C47C2311yescharacteristic
84C2×#41×C47C2311yescharacteristic
85C2×#41×C47C2311yescharacteristic
86C22×Q8×C47C2311yescharacteristic
87C22×D4×C47—21no—
88C22×D4×C47—21no—
89C22×D4×C47—21no—
90C22×D4×C47—21no—
91C22×D4×C47—41no—
92C22×D4×C47—41no—
93C22×D4×C47C2311yescharacteristic
94C22×D4×C47C2311yescharacteristic
95#137×C47—22no—
96#137×C47—22no—
97#137×C47—22no—
98#137×C47—22no—
99AGL(1,ℤ/8)×C47—28no—
100AGL(1,ℤ/8)×C47—28no—
101AGL(1,ℤ/8)×C47—22no—
102AGL(1,ℤ/8)×C47—22no—
103AGL(1,ℤ/8)×C47—22no—
104AGL(1,ℤ/8)×C47D414yes—
105#135×C47—28no—
106#135×C47—22no—
107#135×C47—22no—
108C2×Q16×C47—21no—
109C2×Q16×C47—21no—
110C2×Q16×C47D411yescharacteristic
111C2×SD16×C47—21no—
112C2×SD16×C47—21no—
113C2×SD16×C47—21no—
114C2×SD16×C47—21no—
115C2×SD16×C47—22no—
116C2×SD16×C47—21no—
117C2×SD16×C47—21no—
118C2×SD16×C47—41no—
119C2×SD16×C47D411yescharacteristic
120C2×SD16×C47D411yescharacteristic
121C2×D8×C47—28no—
122C2×D8×C47—21no—
123C2×D8×C47—21no—
124C2×D8×C47—22no—
125C2×D8×C47—22no—
126C2×D8×C47—21no—
127C2×D8×C47—21no—
128C2×D8×C47D411yescharacteristic
129#131×C47—22no—
130#131×C47—22no—
131#131×C47—22no—
132#131×C47—41no—
133C2×M16×C47—21no—
134C2×M16×C47—21no—
135C2×M16×C47C2311yescharacteristic
136C2×M16×C47C2311yescharacteristic
137C2×M16×C47C2311yescharacteristic
138C2×M16×C47C2311yescharacteristic
139C22×C8×C47—21no—
140C22×C8×C47—21no—
141C22×C8×C47C2311yescharacteristic
142C22×C8×C47C2311yescharacteristic
143C4⋊Q8×C47—21no—
144#124×C47—22no—
145#124×C47—21no—
146#124×C47—41no—
147#123×C47—41no—
148C22⋊Q8×C47—21no—
149C22⋊Q8×C47—21no—
150C4×Q8×C47—21no—
151C4×D4×C47—21no—
152C4×D4×C47—41no—
153#117×C47—21no—
154#117×C47C2311yescharacteristic
155C2×C4⋊C4×C47—21no—
156C2×C4⋊C4×C47C2311yescharacteristic
157C2×C22⋊C4×C47—41no—
158C2×C22⋊C4×C47—41no—
159C2×C42×C47C2311yescharacteristic
160#108×C47—22no—
161C4⋊C8×C47—21no—
162C4⋊C8×C47—21no—
163#104×C47—22no—
164#104×C47—22no—
165#104×C47—41no—
166#103×C47—21no—
167#103×C47—21no—
168#103×C47—21no—
169#103×C47—21no—
170#103×C47D411yescharacteristic
171#103×C47D411yescharacteristic
172#102×C47—21no—
173#102×C47—21no—
174#102×C47—21no—
175#102×C47—21no—
176#102×C47—21no—
177#102×C47—21no—
178#102×C47—21no—
179#102×C47—21no—
180#102×C47D411yescharacteristic
181#102×C47D411yescharacteristic
182#101×C47—22no—
183#100×C47—22no—
184#100×C47—22no—
185C22⋊C8×C47—21no—
186C22⋊C8×C47—21no—
187C24×C47—21no—
188C24×C47—21no—
189C24×C47—41no—
190C24×C47—41no—
191#41×C47—21no—
192#41×C47—21no—
193#41×C47—21no—
194#41×C47—21no—
195#41×C47—24no—
196#41×C47—24no—
197#41×C47—24no—
198#41×C47—21no—
199#41×C47—21no—
200#41×C47—21no—
201#41×C47—21no—
202#41×C47—42no—
203#41×C47—42no—
204#41×C47—42no—
205#41×C47—42no—
206#41×C47—42no—
207#41×C47C2×D412yes—
208#41×C47C2×D412yes—
209#41×C47C2×D412yes—
210#41×C47#4112yes—
211C2×Q8×C47—21no—
212C2×Q8×C47—21no—
213C2×Q8×C47—21no—
214C2×Q8×C47—21no—
215C2×Q8×C47—21no—
216C2×Q8×C47—21no—
217C2×Q8×C47C2×D411yescharacteristic
218C2×Q8×C47C2×D411yescharacteristic
219C2×Q8×C47C2×D411yescharacteristic
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—24no—
223C2×D4×C47—24no—
224C2×D4×C47—24no—
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47—21no—
228C2×D4×C47—21no—
229C2×D4×C47—21no—
230C2×D4×C47—21no—
231C2×D4×C47—21no—
232C2×D4×C47—21no—
233C2×D4×C47—21no—
234C2×D4×C47—21no—
235C2×D4×C47—21no—
236C2×D4×C47—42no—
237C2×D4×C47—42no—
238C2×D4×C47—42no—
239C2×D4×C47—41no—
240C2×D4×C47—41no—
241C2×D4×C47—41no—
242C2×D4×C47—41no—
243C2×D4×C47—44no—
244C2×D4×C47—42no—
245C2×D4×C47—44no—
246C2×D4×C47—44no—
247C2×D4×C47—44no—
248C2×D4×C47—42no—
249C2×D4×C47C2×D411yescharacteristic
250C2×D4×C47C2×D412yes—
251C2×D4×C47C2×D412yes—
252C2×D4×C47C2×D411yescharacteristic
253C2×D4×C47C2×D411yescharacteristic
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—21no—
258C22×C4×C47—21no—
259C22×C4×C47—21no—
260C22×C4×C47—41no—
261C22×C4×C47—41no—
262C22×C4×C47—41no—
263C22×C4×C47C2411yescharacteristic
264Q16×C47—22no—
265Q16×C47—42no—
266Q16×C47—42no—
267SD16×C47—24no—
268SD16×C47—24no—
269SD16×C47—22no—
270SD16×C47—22no—
271SD16×C47—42no—
272SD16×C47—42no—
273SD16×C47—42no—
274SD16×C47—42no—
275D8×C47—24no—
276D8×C47—24no—
277D8×C47—24no—
278D8×C47—22no—
279D8×C47—24no—
280M16×C47—24no—
281M16×C47—21no—
282M16×C47—21no—
283M16×C47—21no—
284M16×C47—21no—
285M16×C47—21no—
286M16×C47—21no—
287M16×C47—21no—
288M16×C47—42no—
289M16×C47C2×D412yes—
290C2×C8×C47—24no—
291C2×C8×C47—21no—
292C2×C8×C47—21no—
293C2×C8×C47—21no—
294C2×C8×C47—21no—
295C2×C8×C47—21no—
296C2×C8×C47—21no—
297C2×C8×C47—21no—
298C2×C8×C47—21no—
299C2×C8×C47—42no—
300C2×C8×C47C2×D411yescharacteristic
301C2×C8×C47C2×D411yescharacteristic
302C2×C8×C47C2×D411yescharacteristic
303C2×C8×C47C2×D411yescharacteristic
304C4⋊C4×C47—21no—
305C4⋊C4×C47—21no—
306C4⋊C4×C47—41no—
307C4⋊C4×C47—41no—
308C4⋊C4×C47—41no—
309C4⋊C4×C47C2×D411yescharacteristic
310C4⋊C4×C47C2×D411yescharacteristic
311C22⋊C4×C47—21no—
312C22⋊C4×C47—41no—
313C22⋊C4×C47—41no—
314C22⋊C4×C47—41no—
315C22⋊C4×C47—44no—
316C22⋊C4×C47—82no—
317C42×C47—21no—
318C42×C47—21no—
319C42×C47—21no—
320C42×C47—41no—
321C23×C47—21no—
322C23×C47—21no—
323C23×C47—21no—
324C23×C47—22no—
325C23×C47—22no—
326C23×C47—44no—
327C23×C47—44no—
328C23×C47—41no—
329C23×C47—41no—
330C23×C47—41no—
331C23×C47—41no—
332C23×C47—81no—
333C23×C47—81no—
334C23×C47—81no—
335C23×C47—81no—
336C23×C47—161no—
337C23×C47—161no—
338C23×C47—161no—
339C23×C47—161no—
340C23×C47H(5,𝔽2)11yescharacteristic
341Q8×C47—21no—
342Q8×C47—21no—
343Q8×C47—21no—
344Q8×C47—21no—
345Q8×C47—41no—
346Q8×C47—41no—
347Q8×C47—41no—
348Q8×C47—41no—
349Q8×C47#12012yes—
350Q8×C47#12112yes—
351D4×C47—22no—
352D4×C47—22no—
353D4×C47—22no—
354D4×C47—22no—
355D4×C47—22no—
356D4×C47—22no—
357D4×C47—21no—
358D4×C47—22no—
359D4×C47—21no—
360D4×C47—22no—
361D4×C47—21no—
362D4×C47—21no—
363D4×C47—44no—
364D4×C47—44no—
365D4×C47—44no—
366D4×C47—44no—
367D4×C47—41no—
368D4×C47—41no—
369D4×C47—41no—
370D4×C47—41no—
371D4×C47—41no—
372D4×C47—41no—
373D4×C47#12012yes—
374D4×C47#12112yes—
375C2×C4×C47—21no—
376C2×C4×C47—21no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—21no—
382C2×C4×C47—21no—
383C2×C4×C47—21no—
384C2×C4×C47—44no—
385C2×C4×C47—44no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47—81no—
396C2×C4×C47—161no—
397C2×C4×C47C22×D411yescharacteristic
398C2×C4×C47C22×D411yescharacteristic
399C2×C4×C47C22×D411yescharacteristic
400C2×C4×C47C22×D411yescharacteristic
401C2×C4×C47C2×#4111yescharacteristic
402C2×C4×C47H(5,𝔽2)11yescharacteristic
403C8×C47—21no—
404C8×C47—22no—
405C8×C47—21no—
406C8×C47—21no—
407C8×C47—21no—
408C8×C47—41no—
409C8×C47—41no—
410C8×C47—41no—
411#24459C4711yesmaximal, characteristic, direct product factor, Sylow
412C22×C47—21no—
413C22×C47—21no—
414C22×C47—22no—
415C22×C47—22no—
416C22×C47—41no—
417C22×C47—41no—
418C22×C47—41no—
419C22×C47—41no—
420C22×C47—41no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—41no—
424C22×C47—41no—
425C22×C47—82no—
426C22×C47—82no—
427C22×C47—81no—
428C22×C47—81no—
429C22×C47—81no—
430C22×C47—81no—
431C22×C47—161no—
432C22×C47—161no—
433C22×C47—164no—
434C22×C47—164no—
435C22×C47#53411yescharacteristic
436C22×C47D4211yescharacteristic
437C22×C47#54611yescharacteristic
438C4×C47—22no—
439C4×C47—22no—
440C4×C47—41no—
441C4×C47—41no—
442C4×C47—41no—
443C4×C47—81no—
444C4×C47—81no—
445C4×C47—81no—
446C4×C47C2×#12011yescharacteristic
447C4×C47C2×#12111yescharacteristic
448C4×C47D4211yescharacteristic
449C4×C47#54611yescharacteristic
450C2×#576C2×C4711yescharacteristic
451C2×#471C2×C4711yescharacteristic, complemented
452#3046C2×C4711yescharacteristic, complemented
453C2×#455C2×C4711yescharacteristic, complemented
454#3009C2×C4711yescharacteristic, complemented
455#2897C2×C4711yescharacteristic, complemented
456#2051C2×C4711yescharacteristic, complemented
457#2045C2×C4711yescharacteristic, complemented
458#2012C2×C4711yescharacteristic, complemented
459#2003C2×C4711yescharacteristic, complemented
460#1908C2×C4711yescharacteristic, complemented
461#1883C2×C4711yescharacteristic, complemented
462#1876C2×C4711yescharacteristic, complemented
463#1866C2×C4711yescharacteristic, complemented
464#1792C2×C4711yescharacteristic, complemented
465C2×C47—21no—
466C2×C47—21no—
467C2×C47—42no—
468C2×C47—42no—
469C2×C47—81no—
470C2×C47—82no—
471C2×C47—82no—
472C2×C47#241011yescharacteristic
473C2×C47#328811yescharacteristic
474C2×C47#329011yescharacteristic
475C2×H(5,𝔽2)C22×C4711yescharacteristic
476C2×H(5,𝔽2)C22×C4711yescharacteristic
477#576—24no—
478#576—24no—
479C2×#137C22×C4711yescharacteristic
480C2×#137C22×C4711yescharacteristic, complemented
481C2×AGL(1,ℤ/8)—21no—
482C2×AGL(1,ℤ/8)—21no—
483C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
484C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
485C2×#135—21no—
486C2×#135C22×C4711yescharacteristic
487C22×SD16C22×C4711yescharacteristic, complemented
488C22×D8—21no—
489C22×D8C22×C4711yescharacteristic
490C2×#131C22×C4711yescharacteristic
491C2×#131C22×C4711yescharacteristic, complemented
492#536C22×C4711yescharacteristic, complemented
493C2×#124C22×C4711yescharacteristic, complemented
494#520C22×C4711yescharacteristic, complemented
495#471—24no—
496#464—21no—
497#463—21no—
498#462—21no—
499#461—21no—
500#455—24no—
501#452—21no—
502#452—21no—
503#450—21no—
504#450—21no—
505C2×#108C22×C4711yescharacteristic, complemented
506#424C22×C4711yescharacteristic, complemented
507C2×#104C22×C4711yescharacteristic
508C2×#104C22×C4711yescharacteristic, complemented
509C2×#104C22×C4711yescharacteristic, complemented
510#418—21no—
511#418C22×C4711yescharacteristic, complemented
512#418C22×C4711yescharacteristic, complemented
513#417—21no—
514#417C22×C4711yescharacteristic
515#417C22×C4711yescharacteristic, complemented
516#416—21no—
517#416C22×C4711yescharacteristic
518C2×#103C22×C4711yescharacteristic, complemented
519C2×#102—21no—
520C2×#102C22×C4711yescharacteristic, complemented
521C2×#101C22×C4711yescharacteristic, complemented
522C2×#100C22×C4711yescharacteristic, complemented
523C2×#100C22×C4711yescharacteristic, complemented
524#408C22×C4711yescharacteristic, complemented
525#390C22×C4711yescharacteristic, complemented
526#343C22×C4711yescharacteristic, complemented
527#341C22×C4711yescharacteristic, complemented
528#339C22×C4711yescharacteristic, complemented
529#336C22×C4711yescharacteristic, complemented
530C47#2445911yescharacteristic, direct product factor, Sylow
531H(5,𝔽2)—22no—
532H(5,𝔽2)—22no—
533H(5,𝔽2)—22no—
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—41no—
537H(5,𝔽2)—41no—
538H(5,𝔽2)D4×C4714yes—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41C23×C4711yescharacteristic
544C2×#41C23×C4711yescharacteristic
545C2×#41C23×C4711yescharacteristic
546C22×Q8C23×C4711yescharacteristic
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4C23×C4711yescharacteristic
554C22×D4C23×C4711yescharacteristic
555#137—22no—
556#137—22no—
557#137—22no—
558#137—22no—
559AGL(1,ℤ/8)—28no—
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)D4×C4714yes—
565#135—28no—
566#135—22no—
567#135—22no—
568C2×Q16—21no—
569C2×Q16—21no—
570C2×Q16D4×C4711yescharacteristic
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—41no—
579C2×SD16D4×C4711yescharacteristic
580C2×SD16D4×C4711yescharacteristic
581C2×D8—28no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—21no—
587C2×D8—21no—
588C2×D8D4×C4711yescharacteristic
589#131—22no—
590#131—22no—
591#131—22no—
592#131—41no—
593C2×M16—21no—
594C2×M16—21no—
595C2×M16C23×C4711yescharacteristic
596C2×M16C23×C4711yescharacteristic
597C2×M16C23×C4711yescharacteristic
598C2×M16C23×C4711yescharacteristic
599C22×C8—21no—
600C22×C8—21no—
601C22×C8C23×C4711yescharacteristic
602C22×C8C23×C4711yescharacteristic
603C4⋊Q8—21no—
604#124—22no—
605#124—21no—
606#124—41no—
607#123—41no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C4×Q8—21no—
611C4×D4—21no—
612C4×D4—41no—
613#117—21no—
614#117C23×C4711yescharacteristic
615C2×C4⋊C4—21no—
616C2×C4⋊C4C23×C4711yescharacteristic
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C42C23×C4711yescharacteristic
620#108—22no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623#104—22no—
624#104—22no—
625#104—41no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103D4×C4711yescharacteristic
631#103D4×C4711yescharacteristic
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102D4×C4711yescharacteristic
641#102D4×C4711yescharacteristic
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C24—21no—
648C24—21no—
649C24—41no—
650C24—41no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—42no—
663#41—42no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41C2×D4×C4712yes—
668#41C2×D4×C4712yes—
669#41C2×D4×C4712yes—
670#41#41×C4712yes—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8C2×D4×C4711yescharacteristic
678C2×Q8C2×D4×C4711yescharacteristic
679C2×Q8C2×D4×C4711yescharacteristic
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—42no—
709C2×D4C2×D4×C4712yes—
710C2×D4C2×D4×C4712yes—
711C2×D4C2×D4×C4711yescharacteristic
712C2×D4C2×D4×C4711yescharacteristic
713C2×D4C2×D4×C4711yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4C24×C4711yescharacteristic
724Q16—22no—
725Q16—42no—
726Q16—42no—
727SD16—24no—
728SD16—24no—
729SD16—22no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—24no—
737D8—24no—
738D8—22no—
739D8—24no—
740M16—24no—
741M16—21no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—42no—
749M16C2×D4×C4712yes—
750C2×C8—24no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—42no—
760C2×C8C2×D4×C4711yescharacteristic
761C2×C8C2×D4×C4711yescharacteristic
762C2×C8C2×D4×C4711yescharacteristic
763C2×C8C2×D4×C4711yescharacteristic
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—41no—
767C4⋊C4—41no—
768C4⋊C4—41no—
769C4⋊C4C2×D4×C4711yescharacteristic
770C4⋊C4C2×D4×C4711yescharacteristic
771C22⋊C4—21no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—41no—
775C22⋊C4—44no—
776C22⋊C4—82no—
777C42—21no—
778C42—21no—
779C42—21no—
780C42—41no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—81no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—161no—
797C23—161no—
798C23—161no—
799C23—161no—
800C23H(5,𝔽2)×C4711yescharacteristic
801Q8—21no—
802Q8—21no—
803Q8—21no—
804Q8—21no—
805Q8—41no—
806Q8—41no—
807Q8—41no—
808Q8—41no—
809Q8#120×C4712yes—
810Q8#121×C4712yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—21no—
818D4—22no—
819D4—21no—
820D4—22no—
821D4—21no—
822D4—21no—
823D4—44no—
824D4—44no—
825D4—44no—
826D4—44no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4#120×C4712yes—
834D4#121×C4712yes—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—81no—
856C2×C4—161no—
857C2×C4C22×D4×C4711yescharacteristic
858C2×C4C22×D4×C4711yescharacteristic
859C2×C4C22×D4×C4711yescharacteristic
860C2×C4C22×D4×C4711yescharacteristic
861C2×C4C2×#41×C4711yescharacteristic
862C2×C4H(5,𝔽2)×C4711yescharacteristic
863C8—21no—
864C8—22no—
865C8—21no—
866C8—21no—
867C8—21no—
868C8—41no—
869C8—41no—
870C8—41no—
871C22—21no—
872C22—21no—
873C22—22no—
874C22—22no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—42no—
884C22—82no—
885C22—82no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—161no—
891C22—161no—
892C22—164no—
893C22—164no—
894C22C47×#53411yescharacteristic
895C22D42×C4711yescharacteristic
896C22C47×#54611yescharacteristic
897C4—22no—
898C4—22no—
899C4—41no—
900C4—41no—
901C4—41no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4C2×#120×C4711yescharacteristic
906C4C2×#121×C4711yescharacteristic
907C4D42×C4711yescharacteristic
908C4C47×#54611yescharacteristic
909C2—21no—
910C2—21no—
911C2—42no—
912C2—42no—
913C2—81no—
914C2—82no—
915C2—82no—
916C2C47×#241011yescharacteristic
917C2C47×#328811yescharacteristic
918C2C47×#329011yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#576C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#471C2semidirect
3. C47×#3046C2semidirect
4. C2×C47×#455C2semidirect
5. C47×#3009C2semidirect
6. C47×#2897C2semidirect
7. C47×#2051C2semidirect
8. C47×#2045C2semidirect
9. C47×#2012C2semidirect
10. C47×#2003C2semidirect
11. C47×#1908C2semidirect
12. C47×#1883C2semidirect
13. C47×#1876C2semidirect
14. C47×#1866C2semidirect
15. C47×#1792C2semidirect
21. C2×#137×C47C22semidirect
28. C22×SD16×C47C22semidirect
32. C2×#131×C47C22semidirect
33. C47×#536C22semidirect
34. C2×#124×C47C22semidirect
35. C47×#520C22semidirect
46. C2×#108×C47C22semidirect
47. C47×#424C22semidirect
49. C2×#104×C47C22semidirect
50. C2×#104×C47C22semidirect
52. C47×#418C22semidirect
53. C47×#418C22semidirect
56. C47×#417C22semidirect
59. C2×#103×C47C22semidirect
61. C2×#102×C47C22semidirect
62. C2×#101×C47C22semidirect
63. C2×#100×C47C22semidirect
64. C2×#100×C47C22semidirect
65. C47×#408C22semidirect
66. C47×#390C22semidirect
67. C47×#343C22semidirect
68. C47×#341C22semidirect
69. C47×#339C22semidirect
70. C47×#336C22semidirect
411. #24459C47direct (N × H)
451. C2×#471C2×C47semidirect
452. #3046C2×C47semidirect
453. C2×#455C2×C47semidirect
454. #3009C2×C47semidirect
455. #2897C2×C47semidirect
456. #2051C2×C47semidirect
457. #2045C2×C47semidirect
458. #2012C2×C47semidirect
459. #2003C2×C47semidirect
460. #1908C2×C47semidirect
461. #1883C2×C47semidirect
462. #1876C2×C47semidirect
463. #1866C2×C47semidirect
464. #1792C2×C47semidirect
480. C2×#137C22×C47semidirect
487. C22×SD16C22×C47semidirect
491. C2×#131C22×C47semidirect
492. #536C22×C47semidirect
493. C2×#124C22×C47semidirect
494. #520C22×C47semidirect
505. C2×#108C22×C47semidirect
506. #424C22×C47semidirect
508. C2×#104C22×C47semidirect
509. C2×#104C22×C47semidirect
511. #418C22×C47semidirect
512. #418C22×C47semidirect
515. #417C22×C47semidirect
518. C2×#103C22×C47semidirect
520. C2×#102C22×C47semidirect
521. C2×#101C22×C47semidirect
522. C2×#100C22×C47semidirect
523. C2×#100C22×C47semidirect
524. #408C22×C47semidirect
525. #390C22×C47semidirect
526. #343C22×C47semidirect
527. #341C22×C47semidirect
528. #339C22×C47semidirect
529. #336C22×C47semidirect
530. C47#24459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5762
C2×C47×#4712
C47×#30462
C2×C47×#4552
C47×#30092
C47×#28972
C47×#20512
C47×#20452
C47×#20122
C47×#20032
C47×#19082
C47×#18832
C47×#18762
C47×#18662
C47×#17922
#2445947