Finite Group Databasebeta

← C47×#33552 #26073250

Subgroups — C47×#33552 #26073250

Order 12032.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3533C211yesmaximal, characteristic, complemented
2C47×#3026C211yesmaximal, characteristic, complemented
3C2×C47×#458C211yesmaximal, characteristic, complemented
4C47×#3019C211yesmaximal, characteristic, complemented
5C47×#2201C212yesmaximal, complemented
6C47×#2200C212yesmaximal, complemented
7C47×#2198C212yesmaximal, complemented
8C47×#2197C212yesmaximal, complemented
9C47×#2127C211yesmaximal, characteristic, complemented
10C47×#2121C211yesmaximal, characteristic, complemented
11C2×C47×#352C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C47C2211yescharacteristic
13C47×#575—21no—
14C47×#563C2211yescharacteristic, complemented
15C47×#562—21no—
16C47×#560C2211yescharacteristic, complemented
17C47×#559C2211yescharacteristic, complemented
18C47×#553—21no—
19C47×#552—21no—
20C47×#551—21no—
21C47×#551C2211yescharacteristic, complemented
22C47×#547—21no—
23C47×#546—21no—
24C47×#542—21no—
25C47×#540—21no—
26C47×#539—21no—
27C47×#538—21no—
28C47×#538—21no—
29C47×#535C2211yescharacteristic
30C47×#534—21no—
31C47×#534C2211yescharacteristic
32C47×#525—21no—
33C2×#123×C47—21no—
34C2×#123×C47C2211yescharacteristic
35C47×#458—21no—
36C47×#458—21no—
37C47×#458—21no—
38C47×#458C2212yes—
39C47×#458C2212yes—
40C47×#458C2212yes—
41C47×B(4,𝔽2)—21no—
42C47×B(4,𝔽2)C2212yes—
43C47×#455—21no—
44C47×#455C2212yes—
45C47×#453—21no—
46C47×#453C2212yes—
47C47×#421—21no—
48C2×#100×C47C2211yescharacteristic
49C2×#99×C47—21no—
50C2×#99×C47—21no—
51C2×#99×C47C2211yescharacteristic
52C2×#99×C47C2211yescharacteristic
53C47×#354C2212yescomplemented
54C47×#353C2212yescomplemented
55C47×#352C2212yescomplemented
56C47×#352C2212yescomplemented
57C47×#352C2212yescomplemented
58C47×AΣL(1,𝔽16)C2212yescomplemented
59H(5,𝔽2)×C47—21no—
60H(5,𝔽2)×C47—21no—
61H(5,𝔽2)×C47—21no—
62H(5,𝔽2)×C47—42no—
63H(5,𝔽2)×C47C2312yes—
64C2×#41×C47—21no—
65C2×#41×C47—21no—
66C2×#41×C47—41no—
67C2×#41×C47D411yescharacteristic, complemented
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—41no—
71C22×D4×C47D411yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C23×C4×C47D411yescharacteristic, complemented
74#137×C47—22no—
75#137×C47—41no—
76AGL(1,ℤ/8)×C47—22no—
77AGL(1,ℤ/8)×C47—41no—
78#135×C47—42no—
79C2×M16×C47—21no—
80C4⋊Q8×C47—21no—
81#127×C47D411yescharacteristic, complemented
82#127×C47C2311yescharacteristic
83#126×C47—21no—
84#126×C47—21no—
85#126×C47—21no—
86#126×C47—21no—
87#126×C47—21no—
88#126×C47—21no—
89#125×C47—21no—
90#125×C47—21no—
91#125×C47—21no—
92#124×C47—21no—
93#124×C47—21no—
94#124×C47—21no—
95#124×C47—21no—
96#124×C47D411yescharacteristic, complemented
97#124×C47C2311yescharacteristic
98#123×C47—21no—
99#123×C47—21no—
100#123×C47—21no—
101#123×C47—21no—
102#123×C47—21no—
103#123×C47—21no—
104#123×C47—21no—
105#123×C47—21no—
106#123×C47—21no—
107#123×C47—21no—
108#123×C47—21no—
109#123×C47—21no—
110#123×C47—22no—
111#123×C47—22no—
112#123×C47—22no—
113#123×C47—41no—
114#123×C47—42no—
115#123×C47D411yescharacteristic
116#123×C47D411yescharacteristic, complemented
117#123×C47D411yescharacteristic, complemented
118#123×C47C2311yescharacteristic
119#123×C47C2311yescharacteristic
120#123×C47C2311yescharacteristic
121C22⋊Q8×C47—21no—
122C22⋊Q8×C47—21no—
123C22⋊Q8×C47—21no—
124C22⋊Q8×C47—21no—
125C22⋊Q8×C47—21no—
126C22⋊Q8×C47—21no—
127C22⋊Q8×C47—21no—
128C22⋊Q8×C47—21no—
129#121×C47—21no—
130#121×C47—21no—
131#121×C47—21no—
132#121×C47—21no—
133#121×C47—21no—
134#121×C47—21no—
135#121×C47—21no—
136#121×C47—21no—
137#121×C47—21no—
138#121×C47—21no—
139#121×C47—21no—
140#121×C47—21no—
141#121×C47—42no—
142#120×C47—21no—
143#120×C47—21no—
144#120×C47—21no—
145#120×C47—21no—
146#120×C47—22no—
147#120×C47—41no—
148#120×C47D411yescharacteristic
149#120×C47C2311yescharacteristic
150C4×Q8×C47—21no—
151C4×D4×C47—21no—
152C4×D4×C47—21no—
153C4×D4×C47—21no—
154C4×D4×C47—21no—
155C4×D4×C47—21no—
156C4×D4×C47—21no—
157C4×D4×C47—21no—
158C4×D4×C47—21no—
159C4×D4×C47—21no—
160#117×C47—21no—
161#117×C47—21no—
162#117×C47—21no—
163#117×C47D411yescharacteristic, complemented
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—41no—
167C2×C22⋊C4×C47—21no—
168C2×C22⋊C4×C47—21no—
169C2×C22⋊C4×C47—21no—
170C2×C22⋊C4×C47—21no—
171C2×C22⋊C4×C47—41no—
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic, complemented
174#104×C47—22no—
175#104×C47—22no—
176#100×C47—21no—
177#100×C47C2312yes—
178#99×C47—21no—
179#99×C47—21no—
180#99×C47—22no—
181#99×C47—22no—
182#99×C47—22no—
183#99×C47—22no—
184#99×C47C2312yes—
185#99×C47C2312yes—
186C24×C47—21no—
187C24×C47—21no—
188C24×C47C2×D411yescharacteristic
189C24×C47C2×D411yescharacteristic
190C24×C47C2×D411yescharacteristic
191#41×C47—22no—
192#41×C47—22no—
193#41×C47—42no—
194#41×C47—41no—
195#41×C47—42no—
196#41×C47—42no—
197#41×C47—41no—
198#41×C47—41no—
199#41×C47—42no—
200#41×C47—41no—
201#41×C47—81no—
202#41×C47—81no—
203C2×Q8×C47—21no—
204C2×Q8×C47—21no—
205C2×Q8×C47—21no—
206C2×Q8×C47C2×D411yescharacteristic
207C2×D4×C47—21no—
208C2×D4×C47—22no—
209C2×D4×C47—22no—
210C2×D4×C47—21no—
211C2×D4×C47—21no—
212C2×D4×C47—22no—
213C2×D4×C47—22no—
214C2×D4×C47—21no—
215C2×D4×C47—21no—
216C2×D4×C47—21no—
217C2×D4×C47—21no—
218C2×D4×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—41no—
224C2×D4×C47—41no—
225C2×D4×C47—42no—
226C2×D4×C47—42no—
227C2×D4×C47—41no—
228C2×D4×C47—41no—
229C2×D4×C47—41no—
230C2×D4×C47—41no—
231C2×D4×C47—42no—
232C2×D4×C47—42no—
233C2×D4×C47—41no—
234C2×D4×C47—41no—
235C2×D4×C47—41no—
236C2×D4×C47—41no—
237C2×D4×C47—41no—
238C2×D4×C47—42no—
239C2×D4×C47C2×D411yescharacteristic
240C2×D4×C47C2×D411yescharacteristic
241C2×D4×C47C2×D411yescharacteristic
242C2×D4×C47C2×D411yescharacteristic
243C2×D4×C47C2411yescharacteristic
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—41no—
256C22×C4×C47—41no—
257C22×C4×C47—41no—
258C22×C4×C47—41no—
259C22×C4×C47—41no—
260C22×C4×C47C2×D411yescharacteristic
261C22×C4×C47C2×D411yescharacteristic
262C22×C4×C47C2×D411yescharacteristic
263C22×C4×C47C2×D411yescharacteristic
264Q16×C47—42no—
265SD16×C47—42no—
266SD16×C47—42no—
267D8×C47—42no—
268M16×C47—22no—
269M16×C47—41no—
270C2×C8×C47—41no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47—21no—
285C4⋊C4×C47—21no—
286C4⋊C4×C47—21no—
287C4⋊C4×C47—21no—
288C4⋊C4×C47—21no—
289C4⋊C4×C47—21no—
290C4⋊C4×C47—42no—
291C4⋊C4×C47—42no—
292C4⋊C4×C47—42no—
293C22⋊C4×C47—21no—
294C22⋊C4×C47—21no—
295C22⋊C4×C47—21no—
296C22⋊C4×C47—21no—
297C22⋊C4×C47—21no—
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—21no—
305C22⋊C4×C47—21no—
306C22⋊C4×C47—21no—
307C22⋊C4×C47—21no—
308C22⋊C4×C47—21no—
309C22⋊C4×C47—21no—
310C22⋊C4×C47—21no—
311C22⋊C4×C47—21no—
312C22⋊C4×C47—21no—
313C22⋊C4×C47—21no—
314C22⋊C4×C47—21no—
315C22⋊C4×C47—21no—
316C22⋊C4×C47—22no—
317C22⋊C4×C47—22no—
318C22⋊C4×C47—42no—
319C22⋊C4×C47—41no—
320C22⋊C4×C47—41no—
321C22⋊C4×C47—42no—
322C22⋊C4×C47—42no—
323C22⋊C4×C47—42no—
324C22⋊C4×C47C2×D411yescharacteristic
325C22⋊C4×C47C2×D411yescharacteristic
326C22⋊C4×C47C2×D411yescharacteristic
327C22⋊C4×C47C2×D411yescharacteristic
328C42×C47—21no—
329C42×C47—21no—
330C42×C47—21no—
331C42×C47—21no—
332C42×C47C2×D411yescharacteristic
333C42×C47C2×D411yescharacteristic
334C23×C47—21no—
335C23×C47—21no—
336C23×C47—21no—
337C23×C47—21no—
338C23×C47—22no—
339C23×C47—22no—
340C23×C47—21no—
341C23×C47—21no—
342C23×C47—41no—
343C23×C47—41no—
344C23×C47—41no—
345C23×C47—41no—
346C23×C47—81no—
347C23×C47—81no—
348C23×C47—81no—
349C23×C47—82no—
350C23×C47—161no—
351C23×C47#12011yescharacteristic
352C23×C47#12011yescharacteristic
353C23×C47#12011yescharacteristic
354C23×C47C22×D411yescharacteristic
355C23×C47C22×D411yescharacteristic
356Q8×C47—22no—
357Q8×C47—41no—
358Q8×C47—41no—
359Q8×C47—81no—
360Q8×C47—81no—
361D4×C47—22no—
362D4×C47—41no—
363D4×C47—41no—
364D4×C47—41no—
365D4×C47—41no—
366D4×C47—41no—
367D4×C47—41no—
368D4×C47—42no—
369D4×C47—42no—
370D4×C47—42no—
371D4×C47—42no—
372D4×C47—42no—
373D4×C47—42no—
374D4×C47—41no—
375D4×C47—41no—
376D4×C47—41no—
377D4×C47—41no—
378D4×C47—81no—
379D4×C47—81no—
380D4×C47—81no—
381D4×C47—81no—
382D4×C47—81no—
383D4×C47—81no—
384D4×C47—81no—
385D4×C47—81no—
386D4×C47—81no—
387D4×C47—162no—
388C2×C4×C47—21no—
389C2×C4×C47—21no—
390C2×C4×C47—22no—
391C2×C4×C47—22no—
392C2×C4×C47—21no—
393C2×C4×C47—21no—
394C2×C4×C47—21no—
395C2×C4×C47—21no—
396C2×C4×C47—21no—
397C2×C4×C47—21no—
398C2×C4×C47—21no—
399C2×C4×C47—21no—
400C2×C4×C47—21no—
401C2×C4×C47—21no—
402C2×C4×C47—42no—
403C2×C4×C47—42no—
404C2×C4×C47—41no—
405C2×C4×C47—41no—
406C2×C4×C47—41no—
407C2×C4×C47—41no—
408C2×C4×C47—41no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—42no—
413C2×C4×C47—42no—
414C2×C4×C47—81no—
415C2×C4×C47—81no—
416C2×C4×C47—81no—
417C2×C4×C47—81no—
418C2×C4×C47—81no—
419C2×C4×C47—81no—
420C2×C4×C47—81no—
421C2×C4×C47—81no—
422C2×C4×C47—82no—
423C2×C4×C47—161no—
424C2×C4×C47#12011yescharacteristic
425C2×C4×C47C22×D411yescharacteristic
426C8×C47—42no—
427#33552C4711yesmaximal, characteristic, direct product factor, Sylow
428C22×C47—21no—
429C22×C47—21no—
430C22×C47—21no—
431C22×C47—21no—
432C22×C47—41no—
433C22×C47—41no—
434C22×C47—41no—
435C22×C47—41no—
436C22×C47—41no—
437C22×C47—42no—
438C22×C47—41no—
439C22×C47—41no—
440C22×C47—41no—
441C22×C47—41no—
442C22×C47—42no—
443C22×C47—41no—
444C22×C47—41no—
445C22×C47—81no—
446C22×C47—81no—
447C22×C47—81no—
448C22×C47—82no—
449C22×C47—82no—
450C22×C47—82no—
451C22×C47—82no—
452C22×C47—161no—
453C22×C47—161no—
454C22×C47B(4,𝔽2)11yescharacteristic
455C22×C47B(4,𝔽2)11yescharacteristic
456C22×C47C2×#12011yescharacteristic
457C4×C47—21no—
458C4×C47—21no—
459C4×C47—41no—
460C4×C47—41no—
461C4×C47—41no—
462C4×C47—41no—
463C4×C47—41no—
464C4×C47—41no—
465C4×C47—42no—
466C4×C47—41no—
467C4×C47—41no—
468C4×C47—41no—
469C4×C47—41no—
470C4×C47—82no—
471C4×C47—82no—
472#3533C2×C4711yescharacteristic, complemented
473#3026C2×C4711yescharacteristic, complemented
474C2×#458C2×C4711yescharacteristic, complemented
475#3019C2×C4711yescharacteristic, complemented
476#2201C2×C4712yescomplemented
477#2200C2×C4712yescomplemented
478#2198C2×C4712yescomplemented
479#2197C2×C4712yescomplemented
480#2127C2×C4711yescharacteristic, complemented
481#2121C2×C4711yescharacteristic, complemented
482C2×#352C2×C4711yescharacteristic, complemented
483C2×C47—21no—
484C2×C47—21no—
485C2×C47—21no—
486C2×C47—41no—
487C2×C47—41no—
488C2×C47—41no—
489C2×C47—41no—
490C2×C47—81no—
491C2×C47—81no—
492C2×C47—82no—
493C2×C47C2×B(4,𝔽2)11yescharacteristic
494C2×H(5,𝔽2)C22×C4711yescharacteristic
495#575—21no—
496#563C22×C4711yescharacteristic, complemented
497#562—21no—
498#560C22×C4711yescharacteristic, complemented
499#559C22×C4711yescharacteristic, complemented
500#553—21no—
501#552—21no—
502#551—21no—
503#551C22×C4711yescharacteristic, complemented
504#547—21no—
505#546—21no—
506#542—21no—
507#540—21no—
508#539—21no—
509#538—21no—
510#538—21no—
511#535C22×C4711yescharacteristic
512#534—21no—
513#534C22×C4711yescharacteristic
514#525—21no—
515C2×#123—21no—
516C2×#123C22×C4711yescharacteristic
517#458—21no—
518#458—21no—
519#458—21no—
520#458C22×C4712yes—
521#458C22×C4712yes—
522#458C22×C4712yes—
523B(4,𝔽2)—21no—
524B(4,𝔽2)C22×C4712yes—
525#455—21no—
526#455C22×C4712yes—
527#453—21no—
528#453C22×C4712yes—
529#421—21no—
530C2×#100C22×C4711yescharacteristic
531C2×#99—21no—
532C2×#99—21no—
533C2×#99C22×C4711yescharacteristic
534C2×#99C22×C4711yescharacteristic
535#354C22×C4712yescomplemented
536#353C22×C4712yescomplemented
537#352C22×C4712yescomplemented
538#352C22×C4712yescomplemented
539#352C22×C4712yescomplemented
540AΣL(1,𝔽16)C22×C4712yescomplemented
541C47#3355211yescharacteristic, direct product factor, Sylow
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C4712yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C4711yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C4711yescharacteristic
555C22×D4C23×C4711yescharacteristic
556C23×C4D4×C4711yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C4711yescharacteristic, complemented
565#127C23×C4711yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C4711yescharacteristic, complemented
580#124C23×C4711yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C4711yescharacteristic
599#123D4×C4711yescharacteristic, complemented
600#123D4×C4711yescharacteristic, complemented
601#123C23×C4711yescharacteristic
602#123C23×C4711yescharacteristic
603#123C23×C4711yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C4711yescharacteristic
632#120C23×C4711yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C4711yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C4711yescharacteristic
656C2×C22⋊C4D4×C4711yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C4712yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C4712yes—
668#99C23×C4712yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C4711yescharacteristic
672C24C2×D4×C4711yescharacteristic
673C24C2×D4×C4711yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C4711yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C4711yescharacteristic
723C2×D4C2×D4×C4711yescharacteristic
724C2×D4C2×D4×C4711yescharacteristic
725C2×D4C2×D4×C4711yescharacteristic
726C2×D4C24×C4711yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C4711yescharacteristic
744C22×C4C2×D4×C4711yescharacteristic
745C22×C4C2×D4×C4711yescharacteristic
746C22×C4C2×D4×C4711yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C4711yescharacteristic
808C22⋊C4C2×D4×C4711yescharacteristic
809C22⋊C4C2×D4×C4711yescharacteristic
810C22⋊C4C2×D4×C4711yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C4711yescharacteristic
816C42C2×D4×C4711yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C4711yescharacteristic
835C23#120×C4711yescharacteristic
836C23#120×C4711yescharacteristic
837C23C22×D4×C4711yescharacteristic
838C23C22×D4×C4711yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—42no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C4711yescharacteristic
908C2×C4C22×D4×C4711yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22C47×B(4,𝔽2)11yescharacteristic
937C22C47×B(4,𝔽2)11yescharacteristic
938C22C2×#120×C4711yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×C47×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C47C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C47
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C23×C47 ◁ C22×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3533C2semidirect
2. C47×#3026C2semidirect
3. C2×C47×#458C2semidirect
4. C47×#3019C2semidirect
5. C47×#2201C2semidirect
6. C47×#2200C2semidirect
7. C47×#2198C2semidirect
8. C47×#2197C2semidirect
9. C47×#2127C2semidirect
10. C47×#2121C2semidirect
11. C2×C47×#352C2semidirect
14. C47×#563C22semidirect
16. C47×#560C22semidirect
17. C47×#559C22semidirect
21. C47×#551C22semidirect
53. C47×#354C22semidirect
54. C47×#353C22semidirect
55. C47×#352C22semidirect
56. C47×#352C22semidirect
57. C47×#352C22semidirect
58. C47×AΣL(1,𝔽16)C22semidirect
67. C2×#41×C47D4semidirect
73. C23×C4×C47D4semidirect
81. #127×C47D4semidirect
96. #124×C47D4semidirect
116. #123×C47D4semidirect
117. #123×C47D4semidirect
163. #117×C47D4semidirect
173. C2×C22⋊C4×C47D4semidirect
427. #33552C47direct (N × H)
472. #3533C2×C47semidirect
473. #3026C2×C47semidirect
474. C2×#458C2×C47semidirect
475. #3019C2×C47semidirect
476. #2201C2×C47semidirect
477. #2200C2×C47semidirect
478. #2198C2×C47semidirect
479. #2197C2×C47semidirect
480. #2127C2×C47semidirect
481. #2121C2×C47semidirect
482. C2×#352C2×C47semidirect
496. #563C22×C47semidirect
498. #560C22×C47semidirect
499. #559C22×C47semidirect
503. #551C22×C47semidirect
535. #354C22×C47semidirect
536. #353C22×C47semidirect
537. #352C22×C47semidirect
538. #352C22×C47semidirect
539. #352C22×C47semidirect
540. AΣL(1,𝔽16)C22×C47semidirect
541. C47#33552direct (N × H)
550. C2×#41D4×C47semidirect
556. C23×C4D4×C47semidirect
564. #127D4×C47semidirect
579. #124D4×C47semidirect
599. #123D4×C47semidirect
600. #123D4×C47semidirect
646. #117D4×C47semidirect
656. C2×C22⋊C4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35332
C47×#30262
C2×C47×#4582
C47×#30192
C47×#22012
C47×#22002
C47×#21982
C47×#21972
C47×#21272
C47×#21212
C2×C47×#3522
#3355247