Finite Group Databasebeta

← C47×#24474 #26064172

Subgroups — C47×#24474 #26064172

Order 12032.

1298 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3586C211yesmaximal, characteristic
2C47×#3069C211yesmaximal, characteristic, complemented
3C47×#3039C211yesmaximal, characteristic, complemented
4C47×#3022C211yesmaximal, characteristic, complemented
5C2×C47×#456C211yesmaximal, characteristic, complemented
6C47×#2901C211yesmaximal, characteristic, complemented
7C47×#2050C211yesmaximal, characteristic, complemented
8C47×#2049C211yesmaximal, characteristic, complemented
9C47×#2009C211yesmaximal, characteristic, complemented
10C47×#2005C211yesmaximal, characteristic, complemented
11C47×#1906C211yesmaximal, characteristic, complemented
12C47×#1902C211yesmaximal, characteristic, complemented
13C47×#1902C211yesmaximal, characteristic, complemented
14C47×#1861C211yesmaximal, characteristic, complemented
15C47×#1796C211yesmaximal, characteristic, complemented
16C47×#585C2211yescharacteristic
17C2×2−1+4×C47C2211yescharacteristic
18C47×#578—22no—
19C47×#578—22no—
20C47×#577—22no—
21C47×#577—22no—
22C47×#575—22no—
23C47×#575C2211yescharacteristic
24C47×#575C2211yescharacteristic
25C2×#137×C47—22no—
26C2×#137×C47C2211yescharacteristic
27C2×#137×C47C2211yescharacteristic
28C2×#137×C47C2211yescharacteristic
29C2×#137×C47C2211yescharacteristic
30C2×#137×C47C2211yescharacteristic, complemented
31C47×#568C2211yescharacteristic
32C47×#568C2211yescharacteristic
33C47×#536C2211yescharacteristic
34C2×C4⋊Q8×C47C2211yescharacteristic, complemented
35C4×#41×C47C2211yescharacteristic
36C47×#473—22no—
37C47×#471—22no—
38C47×#462—22no—
39C47×#461—22no—
40C47×#456—22no—
41C47×#456—22no—
42C47×#456—22no—
43C47×#455—22no—
44C47×#430C2211yescharacteristic, complemented
45C47×#423C2211yescharacteristic, complemented
46C47×#421—22no—
47C47×#421C2211yescharacteristic
48C47×#421C2211yescharacteristic
49C47×#421C2211yescharacteristic
50C47×#421C2211yescharacteristic
51C2×#104×C47—22no—
52C2×#104×C47C2211yescharacteristic
53C2×#104×C47C2211yescharacteristic
54C2×#104×C47C2211yescharacteristic, complemented
55C47×#419C2211yescharacteristic, complemented
56C47×#419C2211yescharacteristic, complemented
57C47×#419C2211yescharacteristic, complemented
58C47×#413C2211yescharacteristic
59C47×#413C2211yescharacteristic, complemented
60C2×#101×C47C2211yescharacteristic, complemented
61C2×#101×C47C2211yescharacteristic, complemented
62C47×#410C2211yescharacteristic, complemented
63C47×#344C2211yescharacteristic, complemented
64C47×#344C2211yescharacteristic, complemented
65C47×#339C2211yescharacteristic, complemented
66C47×#338C2211yescharacteristic, complemented
672−1+4×C47—22no—
682−1+4×C47—22no—
692−1+4×C47—21no—
702−1+4×C47—21no—
712−1+4×C47—22no—
722−1+4×C47—41no—
732−1+4×C47D412yes—
74H(5,𝔽2)×C47—21no—
75H(5,𝔽2)×C47—21no—
76H(5,𝔽2)×C47—41no—
77H(5,𝔽2)×C47D412yes—
78C2×#41×C47—22no—
79C2×#41×C47—22no—
80C2×#41×C47—21no—
81C2×#41×C47—21no—
82C2×#41×C47—41no—
83C2×#41×C47—41no—
84C2×#41×C47C2311yescharacteristic
85C2×#41×C47C2311yescharacteristic
86C2×#41×C47C2311yescharacteristic
87C2×#41×C47C2311yescharacteristic
88C22×Q8×C47—21no—
89C22×Q8×C47—21no—
90C22×Q8×C47C2311yescharacteristic
91C22×Q8×C47C2311yescharacteristic
92#137×C47—24no—
93#137×C47—24no—
94#137×C47—24no—
95#137×C47—22no—
96#137×C47—22no—
97#137×C47—21no—
98#137×C47—22no—
99#137×C47—21no—
100#137×C47—21no—
101#137×C47—22no—
102#137×C47—22no—
103#137×C47—22no—
104#137×C47—22no—
105#137×C47—22no—
106#137×C47—22no—
107#137×C47—41no—
108#137×C47D412yes—
109AGL(1,ℤ/8)×C47—24no—
110AGL(1,ℤ/8)×C47—21no—
111AGL(1,ℤ/8)×C47—21no—
112AGL(1,ℤ/8)×C47—21no—
113AGL(1,ℤ/8)×C47D412yes—
114#135×C47—24no—
115#135×C47—24no—
116#135×C47—22no—
117#135×C47—22no—
118C2×Q16×C47—24no—
119C2×Q16×C47—21no—
120C2×Q16×C47—21no—
121C2×Q16×C47—21no—
122C2×Q16×C47—21no—
123C2×Q16×C47D412yes—
124C2×SD16×C47—24no—
125C2×SD16×C47—21no—
126C2×SD16×C47—21no—
127C2×SD16×C47—21no—
128C2×SD16×C47—21no—
129C2×SD16×C47D412yes—
130#131×C47—22no—
131#131×C47—22no—
132#131×C47—22no—
133#131×C47—41no—
134C2×M16×C47—22no—
135C2×M16×C47—22no—
136C2×M16×C47C2311yescharacteristic
137C2×M16×C47C2311yescharacteristic
138C2×M16×C47C2311yescharacteristic
139C2×M16×C47C2311yescharacteristic
140C2×M16×C47C2311yescharacteristic
141C2×M16×C47C2311yescharacteristic
142C4⋊Q8×C47—21no—
143C4⋊Q8×C47—22no—
144C4⋊Q8×C47—21no—
145C4⋊Q8×C47—21no—
146#124×C47—21no—
147#123×C47—41no—
148C22⋊Q8×C47—41no—
149C4×Q8×C47—21no—
150C4×D4×C47—21no—
151C4×D4×C47—41no—
152#117×C47—21no—
153#117×C47C2311yescharacteristic
154#117×C47C2311yescharacteristic
155C2×C4⋊C4×C47—41no—
156C2×C42×C47—21no—
157C2×C42×C47C2311yescharacteristic
158#108×C47—22no—
159C4⋊C8×C47—22no—
160#104×C47—22no—
161#104×C47—22no—
162#104×C47—22no—
163#104×C47—22no—
164#104×C47—21no—
165#104×C47—21no—
166#104×C47—21no—
167#104×C47—21no—
168#104×C47D412yes—
169#104×C47D412yes—
170#103×C47—22no—
171#103×C47—22no—
172#103×C47—41no—
173#101×C47—21no—
174#101×C47—21no—
175#101×C47—22no—
176#101×C47—22no—
177#100×C47—21no—
178#100×C47—21no—
179#99×C47—41no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—21no—
183#41×C47—21no—
184#41×C47—24no—
185#41×C47—22no—
186#41×C47—22no—
187#41×C47—22no—
188#41×C47—22no—
189#41×C47—21no—
190#41×C47—21no—
191#41×C47—21no—
192#41×C47—21no—
193#41×C47—21no—
194#41×C47—21no—
195#41×C47—21no—
196#41×C47—21no—
197#41×C47—42no—
198#41×C47—42no—
199#41×C47—42no—
200#41×C47—42no—
201#41×C47—42no—
202#41×C47—44no—
203#41×C47—42no—
204#41×C47—41no—
205#41×C47—41no—
206#41×C47—44no—
207#41×C47—42no—
208#41×C47C2×D412yes—
209#41×C47C2×D412yes—
210#41×C47C2×D412yes—
211#41×C47C2×D412yes—
212C2×Q8×C47—21no—
213C2×Q8×C47—24no—
214C2×Q8×C47—22no—
215C2×Q8×C47—22no—
216C2×Q8×C47—21no—
217C2×Q8×C47—21no—
218C2×Q8×C47—21no—
219C2×Q8×C47—21no—
220C2×Q8×C47—21no—
221C2×Q8×C47—21no—
222C2×Q8×C47—21no—
223C2×Q8×C47—21no—
224C2×Q8×C47—21no—
225C2×Q8×C47—21no—
226C2×Q8×C47—41no—
227C2×Q8×C47—42no—
228C2×Q8×C47—42no—
229C2×Q8×C47—41no—
230C2×Q8×C47—42no—
231C2×Q8×C47C2×D412yes—
232C2×Q8×C47C2×D411yescharacteristic
233C2×Q8×C47C2×D411yescharacteristic
234C2×Q8×C47C2×D411yescharacteristic
235C2×Q8×C47#4111yescharacteristic
236C2×D4×C47—21no—
237C2×D4×C47—21no—
238C2×D4×C47—22no—
239C2×D4×C47—22no—
240C2×D4×C47—21no—
241C2×D4×C47—21no—
242C2×D4×C47—42no—
243C2×D4×C47—41no—
244C2×D4×C47—42no—
245C2×D4×C47—42no—
246C2×D4×C47—41no—
247C2×D4×C47C2×D411yescharacteristic
248C2×D4×C47C2×D411yescharacteristic
249C2×D4×C47C2×D411yescharacteristic
250C2×D4×C47#4111yescharacteristic
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—21no—
258C22×C4×C47—42no—
259C22×C4×C47—41no—
260C22×C4×C47—41no—
261C22×C4×C47—41no—
262C22×C4×C47C2411yescharacteristic
263Q16×C47—24no—
264Q16×C47—22no—
265Q16×C47—22no—
266Q16×C47—24no—
267Q16×C47—42no—
268Q16×C47—42no—
269Q16×C47—42no—
270SD16×C47—24no—
271SD16×C47—22no—
272SD16×C47—22no—
273SD16×C47—22no—
274SD16×C47—22no—
275SD16×C47—24no—
276SD16×C47—42no—
277SD16×C47—42no—
278SD16×C47—42no—
279D8×C47—22no—
280D8×C47—22no—
281M16×C47—24no—
282M16×C47—21no—
283M16×C47—21no—
284M16×C47—21no—
285M16×C47—21no—
286M16×C47—21no—
287M16×C47—21no—
288M16×C47—21no—
289M16×C47—21no—
290M16×C47—21no—
291M16×C47—21no—
292M16×C47—42no—
293M16×C47C2×D412yes—
294M16×C47C2×D412yes—
295C2×C8×C47—24no—
296C2×C8×C47—21no—
297C2×C8×C47—21no—
298C2×C8×C47—21no—
299C2×C8×C47—21no—
300C2×C8×C47—21no—
301C2×C8×C47—42no—
302C2×C8×C47C2×D412yes—
303C4⋊C4×C47—21no—
304C4⋊C4×C47—21no—
305C4⋊C4×C47—42no—
306C4⋊C4×C47—42no—
307C4⋊C4×C47—41no—
308C4⋊C4×C47—42no—
309C22⋊C4×C47—21no—
310C22⋊C4×C47—21no—
311C22⋊C4×C47—41no—
312C22⋊C4×C47—42no—
313C42×C47—21no—
314C42×C47—21no—
315C42×C47—21no—
316C42×C47—41no—
317C42×C47C2×D411yescharacteristic
318C42×C47C2×D411yescharacteristic
319C23×C47—21no—
320C23×C47—21no—
321C23×C47—21no—
322C23×C47—21no—
323C23×C47—42no—
324C23×C47H(5,𝔽2)11yescharacteristic
325Q8×C47—21no—
326Q8×C47—21no—
327Q8×C47—21no—
328Q8×C47—22no—
329Q8×C47—21no—
330Q8×C47—21no—
331Q8×C47—21no—
332Q8×C47—22no—
333Q8×C47—42no—
334Q8×C47—44no—
335Q8×C47—41no—
336Q8×C47—41no—
337Q8×C47—41no—
338Q8×C47—41no—
339Q8×C47—41no—
340Q8×C47—41no—
341Q8×C47#12012yes—
342Q8×C47#12112yes—
343D4×C47—22no—
344D4×C47—22no—
345D4×C47—22no—
346D4×C47—22no—
347D4×C47—21no—
348D4×C47—21no—
349D4×C47—21no—
350D4×C47—21no—
351D4×C47—21no—
352D4×C47—21no—
353D4×C47—42no—
354D4×C47—42no—
355D4×C47—42no—
356D4×C47—44no—
357D4×C47—41no—
358D4×C47—41no—
359D4×C47—41no—
360D4×C47—41no—
361D4×C47#12012yes—
362D4×C47#12112yes—
363C2×C4×C47—21no—
364C2×C4×C47—21no—
365C2×C4×C47—21no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—21no—
371C2×C4×C47—21no—
372C2×C4×C47—22no—
373C2×C4×C47—21no—
374C2×C4×C47—42no—
375C2×C4×C47—42no—
376C2×C4×C47—42no—
377C2×C4×C47—42no—
378C2×C4×C47—44no—
379C2×C4×C47—44no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—82no—
392C2×C4×C47C22×D411yescharacteristic
393C2×C4×C47C22×D411yescharacteristic
394C2×C4×C47C22×D411yescharacteristic
395C2×C4×C47C22×D411yescharacteristic
396C2×C4×C47C2×#4111yescharacteristic
397C2×C4×C47H(5,𝔽2)11yescharacteristic
398C8×C47—22no—
399C8×C47—22no—
400C8×C47—22no—
401C8×C47—41no—
402C8×C47—41no—
403C8×C47—41no—
404#24474C4711yesmaximal, characteristic, direct product factor, Sylow
405C22×C47—22no—
406C22×C47—22no—
407C22×C47—41no—
408C22×C47—41no—
409C22×C47—41no—
410C22×C47—81no—
411C22×C47—81no—
412C22×C47—81no—
413C22×C47—81no—
414C22×C47—162no—
415C22×C47#53411yescharacteristic
416C22×C47D4211yescharacteristic
417C22×C47#54611yescharacteristic
418C4×C47—22no—
419C4×C47—22no—
420C4×C47—22no—
421C4×C47—41no—
422C4×C47—41no—
423C4×C47—42no—
424C4×C47—41no—
425C4×C47—81no—
426C4×C47—81no—
427C4×C47—81no—
428C4×C47C2×#12011yescharacteristic
429C4×C47C2×#12111yescharacteristic
430C4×C47D4211yescharacteristic
431C4×C47#54611yescharacteristic
432#3586C2×C4711yescharacteristic
433#3069C2×C4711yescharacteristic, complemented
434#3039C2×C4711yescharacteristic, complemented
435#3022C2×C4711yescharacteristic, complemented
436C2×#456C2×C4711yescharacteristic, complemented
437#2901C2×C4711yescharacteristic, complemented
438#2050C2×C4711yescharacteristic, complemented
439#2049C2×C4711yescharacteristic, complemented
440#2009C2×C4711yescharacteristic, complemented
441#2005C2×C4711yescharacteristic, complemented
442#1906C2×C4711yescharacteristic, complemented
443#1902C2×C4711yescharacteristic, complemented
444#1902C2×C4711yescharacteristic, complemented
445#1861C2×C4711yescharacteristic, complemented
446#1796C2×C4711yescharacteristic, complemented
447C2×C47—21no—
448C2×C47—21no—
449C2×C47—21no—
450C2×C47—42no—
451C2×C47—42no—
452C2×C47—81no—
453C2×C47—81no—
454C2×C47#241011yescharacteristic
455#585C22×C4711yescharacteristic
456C2×2−1+4C22×C4711yescharacteristic
457#578—22no—
458#578—22no—
459#577—22no—
460#577—22no—
461#575—22no—
462#575C22×C4711yescharacteristic
463#575C22×C4711yescharacteristic
464C2×#137—22no—
465C2×#137C22×C4711yescharacteristic
466C2×#137C22×C4711yescharacteristic
467C2×#137C22×C4711yescharacteristic
468C2×#137C22×C4711yescharacteristic
469C2×#137C22×C4711yescharacteristic, complemented
470#568C22×C4711yescharacteristic
471#568C22×C4711yescharacteristic
472#536C22×C4711yescharacteristic
473C2×C4⋊Q8C22×C4711yescharacteristic, complemented
474C4×#41C22×C4711yescharacteristic
475#473—22no—
476#471—22no—
477#462—22no—
478#461—22no—
479#456—22no—
480#456—22no—
481#456—22no—
482#455—22no—
483#430C22×C4711yescharacteristic, complemented
484#423C22×C4711yescharacteristic, complemented
485#421—22no—
486#421C22×C4711yescharacteristic
487#421C22×C4711yescharacteristic
488#421C22×C4711yescharacteristic
489#421C22×C4711yescharacteristic
490C2×#104—22no—
491C2×#104C22×C4711yescharacteristic
492C2×#104C22×C4711yescharacteristic
493C2×#104C22×C4711yescharacteristic, complemented
494#419C22×C4711yescharacteristic, complemented
495#419C22×C4711yescharacteristic, complemented
496#419C22×C4711yescharacteristic, complemented
497#413C22×C4711yescharacteristic
498#413C22×C4711yescharacteristic, complemented
499C2×#101C22×C4711yescharacteristic, complemented
500C2×#101C22×C4711yescharacteristic, complemented
501#410C22×C4711yescharacteristic, complemented
502#344C22×C4711yescharacteristic, complemented
503#344C22×C4711yescharacteristic, complemented
504#339C22×C4711yescharacteristic, complemented
505#338C22×C4711yescharacteristic, complemented
506C47#2447411yescharacteristic, direct product factor, Sylow
5072−1+4—22no—
5082−1+4—22no—
5092−1+4—21no—
5102−1+4—21no—
5112−1+4—22no—
5122−1+4—41no—
5132−1+4D4×C4712yes—
514H(5,𝔽2)—21no—
515H(5,𝔽2)—21no—
516H(5,𝔽2)—41no—
517H(5,𝔽2)D4×C4712yes—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C4711yescharacteristic
525C2×#41C23×C4711yescharacteristic
526C2×#41C23×C4711yescharacteristic
527C2×#41C23×C4711yescharacteristic
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8C23×C4711yescharacteristic
531C22×Q8C23×C4711yescharacteristic
532#137—24no—
533#137—24no—
534#137—24no—
535#137—22no—
536#137—22no—
537#137—21no—
538#137—22no—
539#137—21no—
540#137—21no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—41no—
548#137D4×C4712yes—
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)D4×C4712yes—
554#135—24no—
555#135—24no—
556#135—22no—
557#135—22no—
558C2×Q16—24no—
559C2×Q16—21no—
560C2×Q16—21no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16D4×C4712yes—
564C2×SD16—24no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16D4×C4712yes—
570#131—22no—
571#131—22no—
572#131—22no—
573#131—41no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16C23×C4711yescharacteristic
577C2×M16C23×C4711yescharacteristic
578C2×M16C23×C4711yescharacteristic
579C2×M16C23×C4711yescharacteristic
580C2×M16C23×C4711yescharacteristic
581C2×M16C23×C4711yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—21no—
585C4⋊Q8—21no—
586#124—21no—
587#123—41no—
588C22⋊Q8—41no—
589C4×Q8—21no—
590C4×D4—21no—
591C4×D4—41no—
592#117—21no—
593#117C23×C4711yescharacteristic
594#117C23×C4711yescharacteristic
595C2×C4⋊C4—41no—
596C2×C42—21no—
597C2×C42C23×C4711yescharacteristic
598#108—22no—
599C4⋊C8—22no—
600#104—22no—
601#104—22no—
602#104—22no—
603#104—22no—
604#104—21no—
605#104—21no—
606#104—21no—
607#104—21no—
608#104D4×C4712yes—
609#104D4×C4712yes—
610#103—22no—
611#103—22no—
612#103—41no—
613#101—21no—
614#101—21no—
615#101—22no—
616#101—22no—
617#100—21no—
618#100—21no—
619#99—41no—
620#41—21no—
621#41—21no—
622#41—21no—
623#41—21no—
624#41—24no—
625#41—22no—
626#41—22no—
627#41—22no—
628#41—22no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—42no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—42no—
642#41—44no—
643#41—42no—
644#41—41no—
645#41—41no—
646#41—44no—
647#41—42no—
648#41C2×D4×C4712yes—
649#41C2×D4×C4712yes—
650#41C2×D4×C4712yes—
651#41C2×D4×C4712yes—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—41no—
667C2×Q8—42no—
668C2×Q8—42no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8C2×D4×C4711yescharacteristic
672C2×Q8C2×D4×C4711yescharacteristic
673C2×Q8C2×D4×C4712yes—
674C2×Q8C2×D4×C4711yescharacteristic
675C2×Q8#41×C4711yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—42no—
683C2×D4—41no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—41no—
687C2×D4C2×D4×C4711yescharacteristic
688C2×D4C2×D4×C4711yescharacteristic
689C2×D4C2×D4×C4711yescharacteristic
690C2×D4#41×C4711yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4C24×C4711yescharacteristic
703Q16—24no—
704Q16—22no—
705Q16—22no—
706Q16—24no—
707Q16—42no—
708Q16—42no—
709Q16—42no—
710SD16—24no—
711SD16—22no—
712SD16—22no—
713SD16—22no—
714SD16—22no—
715SD16—24no—
716SD16—42no—
717SD16—42no—
718SD16—42no—
719D8—22no—
720D8—22no—
721M16—24no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—42no—
733M16C2×D4×C4712yes—
734M16C2×D4×C4712yes—
735C2×C8—24no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—42no—
742C2×C8C2×D4×C4712yes—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—41no—
748C4⋊C4—42no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—41no—
752C22⋊C4—42no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—41no—
757C42C2×D4×C4711yescharacteristic
758C42C2×D4×C4711yescharacteristic
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—42no—
764C23H(5,𝔽2)×C4711yescharacteristic
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—22no—
769Q8—21no—
770Q8—21no—
771Q8—21no—
772Q8—22no—
773Q8—42no—
774Q8—44no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8#120×C4712yes—
782Q8#121×C4712yes—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—44no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4#120×C4712yes—
802D4#121×C4712yes—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—82no—
832C2×C4C22×D4×C4711yescharacteristic
833C2×C4C22×D4×C4711yescharacteristic
834C2×C4C22×D4×C4711yescharacteristic
835C2×C4C22×D4×C4711yescharacteristic
836C2×C4C2×#41×C4711yescharacteristic
837C2×C4H(5,𝔽2)×C4711yescharacteristic
838C8—22no—
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—162no—
854C22C47×#53411yescharacteristic
855C22D42×C4711yescharacteristic
856C22C47×#54611yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—42no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4C2×#120×C4711yescharacteristic
868C4C2×#121×C4711yescharacteristic
869C4D42×C4711yescharacteristic
870C4C47×#54611yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—42no—
875C2—42no—
876C2—81no—
877C2—81no—
878C2C47×#241011yescharacteristic
subgroupG/H
center, socleC2×C47#2410
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3586C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#3069C2semidirect
3. C47×#3039C2semidirect
4. C47×#3022C2semidirect
5. C2×C47×#456C2semidirect
6. C47×#2901C2semidirect
7. C47×#2050C2semidirect
8. C47×#2049C2semidirect
9. C47×#2009C2semidirect
10. C47×#2005C2semidirect
11. C47×#1906C2semidirect
12. C47×#1902C2semidirect
13. C47×#1902C2semidirect
14. C47×#1861C2semidirect
15. C47×#1796C2semidirect
30. C2×#137×C47C22semidirect
34. C2×C4⋊Q8×C47C22semidirect
44. C47×#430C22semidirect
45. C47×#423C22semidirect
54. C2×#104×C47C22semidirect
55. C47×#419C22semidirect
56. C47×#419C22semidirect
57. C47×#419C22semidirect
59. C47×#413C22semidirect
60. C2×#101×C47C22semidirect
61. C2×#101×C47C22semidirect
62. C47×#410C22semidirect
63. C47×#344C22semidirect
64. C47×#344C22semidirect
65. C47×#339C22semidirect
66. C47×#338C22semidirect
404. #24474C47direct (N × H)
433. #3069C2×C47semidirect
434. #3039C2×C47semidirect
435. #3022C2×C47semidirect
436. C2×#456C2×C47semidirect
437. #2901C2×C47semidirect
438. #2050C2×C47semidirect
439. #2049C2×C47semidirect
440. #2009C2×C47semidirect
441. #2005C2×C47semidirect
442. #1906C2×C47semidirect
443. #1902C2×C47semidirect
444. #1902C2×C47semidirect
445. #1861C2×C47semidirect
446. #1796C2×C47semidirect
469. C2×#137C22×C47semidirect
473. C2×C4⋊Q8C22×C47semidirect
483. #430C22×C47semidirect
484. #423C22×C47semidirect
493. C2×#104C22×C47semidirect
494. #419C22×C47semidirect
495. #419C22×C47semidirect
496. #419C22×C47semidirect
498. #413C22×C47semidirect
499. C2×#101C22×C47semidirect
500. C2×#101C22×C47semidirect
501. #410C22×C47semidirect
502. #344C22×C47semidirect
503. #344C22×C47semidirect
504. #339C22×C47semidirect
505. #338C22×C47semidirect
506. C47#24474direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35862
C47×#30692
C47×#30392
C47×#30222
C2×C47×#4562
C47×#29012
C47×#20502
C47×#20492
C47×#20092
C47×#20052
C47×#19062
C47×#19022
C47×#18612
C47×#17962
#2447447