Finite Group Databasebeta

← C47×#24031 #26063729

Subgroups — C47×#24031 #26063729

Order 12032.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3488C211yesmaximal, characteristic
2C47×#3093C211yesmaximal, characteristic, complemented
3C47×#2896C211yesmaximal, characteristic, complemented
4C47×#2500C211yesmaximal, characteristic, complemented
5C47×#2040C211yesmaximal, characteristic, complemented
6C47×#2039C211yesmaximal, characteristic, complemented
7C47×#2037C211yesmaximal, characteristic, complemented
8C47×#2037C211yesmaximal, characteristic, complemented
9C47×#1900C211yesmaximal, characteristic, complemented
10C47×#1871C211yesmaximal, characteristic, complemented
11C47×#1860C211yesmaximal, characteristic, complemented
12C47×#1859C211yesmaximal, characteristic, complemented
13C47×#1792C211yesmaximal, characteristic, complemented
14C47×#1792C211yesmaximal, characteristic, complemented
15C47×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic, complemented
19C47×#550—21no—
20C47×#548—21no—
21C47×#546—21no—
22C47×#546—22no—
23D42×C47—22no—
24D42×C47—21no—
25C47×#537—21no—
26C47×#537C2211yescharacteristic
27C47×#535—21no—
28C47×#535C2211yescharacteristic
29C47×#525—21no—
30C47×#525C2211yescharacteristic
31C2×#121×C47—21no—
32C2×#121×C47C2211yescharacteristic
33C47×#520C2211yescharacteristic
34C2×#117×C47C2211yescharacteristic, complemented
35C47×#485—21no—
36C47×#485—21no—
37C47×#482—21no—
38C47×#482—21no—
39C47×#428C2211yescharacteristic, complemented
40C47×#428C2211yescharacteristic, complemented
41C2×#104×C47C2211yescharacteristic
42C2×#104×C47C2211yescharacteristic
43C2×#104×C47C2211yescharacteristic, complemented
44C2×#104×C47C2211yescharacteristic, complemented
45C2×#104×C47C2211yescharacteristic, complemented
46C2×#104×C47C2211yescharacteristic, complemented
47C47×#419—21no—
48C47×#418—21no—
49C47×#417C2211yescharacteristic
50C47×#417C2211yescharacteristic
51C47×#417C2211yescharacteristic, complemented
52C47×#417C2211yescharacteristic, complemented
53C47×#417C2211yescharacteristic, complemented
54C47×#417C2211yescharacteristic, complemented
55C47×#416—21no—
56C47×#416—21no—
57C2×#100×C47C2211yescharacteristic, complemented
58C2×#100×C47C2211yescharacteristic, complemented
59C47×#407C2211yescharacteristic, complemented
60C47×#394—22no—
61C47×#390C2211yescharacteristic, complemented
62C47×#390C2211yescharacteristic, complemented
63C47×#388—22no—
64C47×#384C2211yescharacteristic, complemented
65C47×#382C2211yescharacteristic, complemented
66C4×C22⋊C4×C47C2211yescharacteristic, complemented
67C47×#343C2211yescharacteristic, complemented
68C47×#343C2211yescharacteristic, complemented
69C47×#339C2211yescharacteristic, complemented
70C47×#339C2211yescharacteristic, complemented
71H(5,𝔽2)×C47—22no—
72H(5,𝔽2)×C47—22no—
73H(5,𝔽2)×C47—41no—
74H(5,𝔽2)×C47—41no—
75C2×#41×C47—21no—
76C2×#41×C47—21no—
77C2×#41×C47—21no—
78C2×#41×C47—21no—
79C2×#41×C47—22no—
80C2×#41×C47—22no—
81C2×#41×C47—41no—
82C2×#41×C47—41no—
83C2×#41×C47D411yescharacteristic
84C2×#41×C47D411yescharacteristic
85C2×#41×C47C2311yescharacteristic
86C2×#41×C47C2311yescharacteristic
87C2×#41×C47C2311yescharacteristic
88C22×Q8×C47D411yescharacteristic
89C22×D4×C47—21no—
90C22×D4×C47—22no—
91C22×D4×C47—22no—
92C22×D4×C47—21no—
93C22×D4×C47—21no—
94C22×D4×C47D411yescharacteristic
95C22×D4×C47D412yes—
96C22×D4×C47C2311yescharacteristic
97C23×C4×C47—21no—
98C23×C4×C47C2311yescharacteristic
99C2×M16×C47—21no—
100C2×M16×C47—41no—
101C2×M16×C47—41no—
102C2×M16×C47C2311yescharacteristic
103C2×M16×C47C2311yescharacteristic
104C2×M16×C47C2311yescharacteristic
105C2×M16×C47C2311yescharacteristic
106C22×C8×C47—21no—
107#127×C47—22no—
108#127×C47—21no—
109#124×C47—22no—
110#124×C47—21no—
111#123×C47—22no—
112#123×C47—21no—
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47—21no—
115C22⋊Q8×C47—21no—
116C22⋊Q8×C47D411yescharacteristic
117C22⋊Q8×C47D411yescharacteristic
118#121×C47—22no—
119#121×C47—22no—
120#121×C47—22no—
121#121×C47—22no—
122#121×C47—22no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—21no—
127#121×C47—21no—
128#121×C47—21no—
129#121×C47—22no—
130#121×C47—21no—
131#121×C47—21no—
132#121×C47D411yescharacteristic
133#121×C47D411yescharacteristic
134#120×C47—22no—
135#120×C47—22no—
136#120×C47—22no—
137#120×C47—21no—
138#120×C47—22no—
139C4×Q8×C47—21no—
140C4×D4×C47—22no—
141C4×D4×C47—22no—
142C4×D4×C47—21no—
143C4×D4×C47—22no—
144C4×D4×C47—21no—
145C4×D4×C47—21no—
146#117×C47—21no—
147#117×C47—21no—
148#117×C47—21no—
149#117×C47—21no—
150#117×C47—21no—
151#117×C47C2311yescharacteristic
152C2×C4⋊C4×C47—21no—
153C2×C4⋊C4×C47—22no—
154C2×C4⋊C4×C47C2311yescharacteristic
155C2×C4⋊C4×C47C2311yescharacteristic
156C2×C4⋊C4×C47C2311yescharacteristic
157C2×C22⋊C4×C47—22no—
158C2×C22⋊C4×C47—21no—
159C2×C22⋊C4×C47—21no—
160C2×C22⋊C4×C47—22no—
161C2×C22⋊C4×C47—22no—
162C2×C22⋊C4×C47D412yes—
163C2×C42×C47—21no—
164C2×C42×C47C2311yescharacteristic
165C2×C42×C47C2311yescharacteristic
166#107×C47—21no—
167#107×C47—21no—
168#106×C47—21no—
169#106×C47—21no—
170#104×C47—22no—
171#104×C47—22no—
172#104×C47—41no—
173#104×C47—41no—
174#104×C47—41no—
175#104×C47—41no—
176#103×C47—21no—
177#103×C47—21no—
178#103×C47—21no—
179#103×C47—21no—
180#103×C47—21no—
181#103×C47—21no—
182#102×C47—21no—
183#102×C47—21no—
184#102×C47—21no—
185#102×C47—21no—
186#102×C47—21no—
187#102×C47—21no—
188#100×C47—41no—
189#100×C47—41no—
190C22⋊C8×C47—21no—
191C22⋊C8×C47—21no—
192#95×C47—21no—
193#95×C47—22no—
194C24×C47—22no—
195C24×C47—21no—
196C24×C47C2×D412yes—
197C24×C47C2×D411yescharacteristic
198#41×C47—21no—
199#41×C47—21no—
200#41×C47—22no—
201#41×C47—22no—
202#41×C47—21no—
203#41×C47—21no—
204#41×C47—21no—
205#41×C47—21no—
206#41×C47—21no—
207#41×C47—21no—
208#41×C47—21no—
209#41×C47—21no—
210#41×C47—42no—
211#41×C47—42no—
212#41×C47—41no—
213#41×C47—41no—
214#41×C47—42no—
215#41×C47—42no—
216#41×C47—42no—
217#41×C47—42no—
218#41×C47—42no—
219#41×C47—42no—
220#41×C47#4112yes—
221#41×C47#4112yes—
222C2×Q8×C47—21no—
223C2×Q8×C47—22no—
224C2×Q8×C47—41no—
225C2×Q8×C47C2×D411yescharacteristic
226C2×Q8×C47C2×D411yescharacteristic
227C2×Q8×C47C2×D411yescharacteristic
228C2×D4×C47—21no—
229C2×D4×C47—22no—
230C2×D4×C47—22no—
231C2×D4×C47—22no—
232C2×D4×C47—22no—
233C2×D4×C47—21no—
234C2×D4×C47—21no—
235C2×D4×C47—21no—
236C2×D4×C47—21no—
237C2×D4×C47—21no—
238C2×D4×C47—22no—
239C2×D4×C47—22no—
240C2×D4×C47—22no—
241C2×D4×C47—21no—
242C2×D4×C47—22no—
243C2×D4×C47—21no—
244C2×D4×C47—21no—
245C2×D4×C47—21no—
246C2×D4×C47—21no—
247C2×D4×C47—21no—
248C2×D4×C47—21no—
249C2×D4×C47—21no—
250C2×D4×C47—41no—
251C2×D4×C47—42no—
252C2×D4×C47—42no—
253C2×D4×C47—42no—
254C2×D4×C47—42no—
255C2×D4×C47—44no—
256C2×D4×C47—44no—
257C2×D4×C47—42no—
258C2×D4×C47—42no—
259C2×D4×C47—82no—
260C2×D4×C47—84no—
261C2×D4×C47C2×D411yescharacteristic
262C2×D4×C47C2×D411yescharacteristic
263C2×D4×C47C2×D411yescharacteristic
264C22×C4×C47—21no—
265C22×C4×C47—21no—
266C22×C4×C47—21no—
267C22×C4×C47—21no—
268C22×C4×C47—21no—
269C22×C4×C47—22no—
270C22×C4×C47—21no—
271C22×C4×C47—21no—
272C22×C4×C47—22no—
273C22×C4×C47—21no—
274C22×C4×C47—21no—
275C22×C4×C47—21no—
276C22×C4×C47—21no—
277C22×C4×C47—21no—
278C22×C4×C47—21no—
279C22×C4×C47—21no—
280C22×C4×C47—42no—
281C22×C4×C47—42no—
282C22×C4×C47C2×D411yescharacteristic
283C22×C4×C47C2×D411yescharacteristic
284C22×C4×C47C2×D411yescharacteristic
285C22×C4×C47C2×D411yescharacteristic
286C22×C4×C47C2×D411yescharacteristic
287C22×C4×C47C2×D412yes—
288C22×C4×C47C2411yescharacteristic
289M16×C47—21no—
290M16×C47—21no—
291M16×C47—21no—
292M16×C47—21no—
293M16×C47—21no—
294M16×C47—21no—
295M16×C47—21no—
296M16×C47—21no—
297M16×C47—42no—
298C2×C8×C47—21no—
299C2×C8×C47—21no—
300C2×C8×C47—21no—
301C2×C8×C47—21no—
302C2×C8×C47—42no—
303C4⋊C4×C47—22no—
304C4⋊C4×C47—22no—
305C4⋊C4×C47—21no—
306C4⋊C4×C47—21no—
307C4⋊C4×C47—21no—
308C4⋊C4×C47—21no—
309C4⋊C4×C47—21no—
310C4⋊C4×C47—21no—
311C4⋊C4×C47—21no—
312C4⋊C4×C47—21no—
313C4⋊C4×C47—82no—
314C4⋊C4×C47C2×D411yescharacteristic
315C4⋊C4×C47C2×D411yescharacteristic
316C22⋊C4×C47—22no—
317C22⋊C4×C47—22no—
318C22⋊C4×C47—22no—
319C22⋊C4×C47—22no—
320C22⋊C4×C47—22no—
321C22⋊C4×C47—21no—
322C22⋊C4×C47—21no—
323C22⋊C4×C47—21no—
324C22⋊C4×C47—21no—
325C22⋊C4×C47—22no—
326C22⋊C4×C47—22no—
327C22⋊C4×C47—21no—
328C22⋊C4×C47—42no—
329C22⋊C4×C47—44no—
330C22⋊C4×C47—41no—
331C22⋊C4×C47—41no—
332C22⋊C4×C47—82no—
333C42×C47—22no—
334C42×C47—21no—
335C42×C47—21no—
336C42×C47—21no—
337C42×C47—21no—
338C42×C47—21no—
339C42×C47—41no—
340C42×C47—41no—
341C23×C47—21no—
342C23×C47—21no—
343C23×C47—21no—
344C23×C47—22no—
345C23×C47—21no—
346C23×C47—21no—
347C23×C47—22no—
348C23×C47—22no—
349C23×C47—41no—
350C23×C47—41no—
351C23×C47—42no—
352C23×C47—42no—
353C23×C47—44no—
354C23×C47—42no—
355C23×C47—42no—
356C23×C47—81no—
357C23×C47—82no—
358C23×C47—82no—
359C23×C47#12011yescharacteristic
360C23×C47#12011yescharacteristic
361C23×C47C22×D411yescharacteristic
362Q8×C47—21no—
363Q8×C47—21no—
364Q8×C47—21no—
365Q8×C47—21no—
366Q8×C47—21no—
367Q8×C47—42no—
368Q8×C47#12312yes—
369D4×C47—22no—
370D4×C47—22no—
371D4×C47—21no—
372D4×C47—21no—
373D4×C47—21no—
374D4×C47—21no—
375D4×C47—21no—
376D4×C47—42no—
377D4×C47—42no—
378D4×C47—44no—
379D4×C47—42no—
380D4×C47—44no—
381D4×C47—44no—
382D4×C47—42no—
383D4×C47—41no—
384D4×C47—41no—
385D4×C47—41no—
386D4×C47—41no—
387D4×C47—41no—
388D4×C47—41no—
389D4×C47—41no—
390D4×C47—41no—
391D4×C47—81no—
392D4×C47—82no—
393D4×C47—82no—
394D4×C47—82no—
395D4×C47—82no—
396D4×C47#12312yes—
397C2×C4×C47—21no—
398C2×C4×C47—21no—
399C2×C4×C47—21no—
400C2×C4×C47—21no—
401C2×C4×C47—21no—
402C2×C4×C47—21no—
403C2×C4×C47—21no—
404C2×C4×C47—21no—
405C2×C4×C47—21no—
406C2×C4×C47—21no—
407C2×C4×C47—21no—
408C2×C4×C47—22no—
409C2×C4×C47—22no—
410C2×C4×C47—22no—
411C2×C4×C47—21no—
412C2×C4×C47—22no—
413C2×C4×C47—21no—
414C2×C4×C47—21no—
415C2×C4×C47—21no—
416C2×C4×C47—42no—
417C2×C4×C47—42no—
418C2×C4×C47—42no—
419C2×C4×C47—44no—
420C2×C4×C47—41no—
421C2×C4×C47—41no—
422C2×C4×C47—41no—
423C2×C4×C47—41no—
424C2×C4×C47—41no—
425C2×C4×C47—41no—
426C2×C4×C47—42no—
427C2×C4×C47—41no—
428C2×C4×C47—42no—
429C2×C4×C47—41no—
430C2×C4×C47—42no—
431C2×C4×C47—41no—
432C2×C4×C47—41no—
433C2×C4×C47—41no—
434C2×C4×C47—82no—
435C2×C4×C47#12011yescharacteristic
436C2×C4×C47#12011yescharacteristic
437C2×C4×C47C22×D411yescharacteristic
438C2×C4×C47C22×D411yescharacteristic
439C2×C4×C47C2×#4111yescharacteristic
440C2×C4×C47C2×#4111yescharacteristic
441C2×C4×C47H(5,𝔽2)11yescharacteristic
442C2×C4×C47H(5,𝔽2)11yescharacteristic
443C8×C47—41no—
444C8×C47—41no—
445C8×C47—41no—
446C8×C47—41no—
447#24031C4711yesmaximal, characteristic, direct product factor, Sylow
448C22×C47—21no—
449C22×C47—21no—
450C22×C47—21no—
451C22×C47—21no—
452C22×C47—22no—
453C22×C47—21no—
454C22×C47—21no—
455C22×C47—21no—
456C22×C47—21no—
457C22×C47—41no—
458C22×C47—41no—
459C22×C47—41no—
460C22×C47—41no—
461C22×C47—42no—
462C22×C47—41no—
463C22×C47—42no—
464C22×C47—41no—
465C22×C47—42no—
466C22×C47—41no—
467C22×C47—41no—
468C22×C47—81no—
469C22×C47—81no—
470C22×C47—82no—
471C22×C47—82no—
472C22×C47—84no—
473C22×C47—164no—
474C22×C47C2×#12011yescharacteristic
475C22×C47#54611yescharacteristic
476C22×C47#54611yescharacteristic
477C4×C47—21no—
478C4×C47—21no—
479C4×C47—22no—
480C4×C47—42no—
481C4×C47—41no—
482C4×C47—41no—
483C4×C47—41no—
484C4×C47—42no—
485C4×C47—41no—
486C4×C47—81no—
487C4×C47—81no—
488C4×C47—81no—
489C4×C47C2×#12311yescharacteristic
490C4×C47#53411yescharacteristic
491C4×C47#54611yescharacteristic
492C4×C47#54611yescharacteristic
493#3488C2×C4711yescharacteristic
494#3093C2×C4711yescharacteristic, complemented
495#2896C2×C4711yescharacteristic, complemented
496#2500C2×C4711yescharacteristic, complemented
497#2040C2×C4711yescharacteristic, complemented
498#2039C2×C4711yescharacteristic, complemented
499#2037C2×C4711yescharacteristic, complemented
500#2037C2×C4711yescharacteristic, complemented
501#1900C2×C4711yescharacteristic, complemented
502#1871C2×C4711yescharacteristic, complemented
503#1860C2×C4711yescharacteristic, complemented
504#1859C2×C4711yescharacteristic, complemented
505#1792C2×C4711yescharacteristic, complemented
506#1792C2×C4711yescharacteristic, complemented
507#1789C2×C4711yescharacteristic, complemented
508C2×C47—21no—
509C2×C47—21no—
510C2×C47—41no—
511C2×C47—41no—
512C2×C47—42no—
513C2×C47—81no—
514C2×C47—82no—
515C2×C47—81no—
516C2×C47#240511yescharacteristic
517C2×C47#301811yescharacteristic
518C2×C47#301911yescharacteristic
519C2×H(5,𝔽2)C22×C4711yescharacteristic
520C22×#41C22×C4711yescharacteristic
521C22×M16C22×C4711yescharacteristic, complemented
522#550—21no—
523#548—21no—
524#546—21no—
525#546—22no—
526D42—22no—
527D42—21no—
528#537—21no—
529#537C22×C4711yescharacteristic
530#535—21no—
531#535C22×C4711yescharacteristic
532#525—21no—
533#525C22×C4711yescharacteristic
534C2×#121—21no—
535C2×#121C22×C4711yescharacteristic
536#520C22×C4711yescharacteristic
537C2×#117C22×C4711yescharacteristic, complemented
538#485—21no—
539#485—21no—
540#482—21no—
541#482—21no—
542#428C22×C4711yescharacteristic, complemented
543#428C22×C4711yescharacteristic, complemented
544C2×#104C22×C4711yescharacteristic
545C2×#104C22×C4711yescharacteristic
546C2×#104C22×C4711yescharacteristic, complemented
547C2×#104C22×C4711yescharacteristic, complemented
548C2×#104C22×C4711yescharacteristic, complemented
549C2×#104C22×C4711yescharacteristic, complemented
550#419—21no—
551#418—21no—
552#417C22×C4711yescharacteristic
553#417C22×C4711yescharacteristic
554#417C22×C4711yescharacteristic, complemented
555#417C22×C4711yescharacteristic, complemented
556#417C22×C4711yescharacteristic, complemented
557#417C22×C4711yescharacteristic, complemented
558#416—21no—
559#416—21no—
560C2×#100C22×C4711yescharacteristic, complemented
561C2×#100C22×C4711yescharacteristic, complemented
562#407C22×C4711yescharacteristic, complemented
563#394—22no—
564#390C22×C4711yescharacteristic, complemented
565#390C22×C4711yescharacteristic, complemented
566#388—22no—
567#384C22×C4711yescharacteristic, complemented
568#382C22×C4711yescharacteristic, complemented
569C4×C22⋊C4C22×C4711yescharacteristic, complemented
570#343C22×C4711yescharacteristic, complemented
571#343C22×C4711yescharacteristic, complemented
572#339C22×C4711yescharacteristic, complemented
573#339C22×C4711yescharacteristic, complemented
574C47#2403111yescharacteristic, direct product factor, Sylow
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C4711yescharacteristic
588C2×#41D4×C4711yescharacteristic
589C2×#41C23×C4711yescharacteristic
590C2×#41C23×C4711yescharacteristic
591C2×#41C23×C4711yescharacteristic
592C22×Q8D4×C4711yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C4711yescharacteristic
599C22×D4D4×C4712yes—
600C22×D4C23×C4711yescharacteristic
601C23×C4—21no—
602C23×C4C23×C4711yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C4711yescharacteristic
607C2×M16C23×C4711yescharacteristic
608C2×M16C23×C4711yescharacteristic
609C2×M16C23×C4711yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C4711yescharacteristic
621C22⋊Q8D4×C4711yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C4711yescharacteristic
637#121D4×C4711yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C4711yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C4711yescharacteristic
659C2×C4⋊C4C23×C4711yescharacteristic
660C2×C4⋊C4C23×C4711yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C4712yes—
667C2×C42—21no—
668C2×C42C23×C4711yescharacteristic
669C2×C42C23×C4711yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C4712yes—
701C24C2×D4×C4711yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C4712yes—
725#41#41×C4712yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C4711yescharacteristic
730C2×Q8C2×D4×C4711yescharacteristic
731C2×Q8C2×D4×C4711yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C4711yescharacteristic
766C2×D4C2×D4×C4711yescharacteristic
767C2×D4C2×D4×C4711yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C4711yescharacteristic
787C22×C4C2×D4×C4711yescharacteristic
788C22×C4C2×D4×C4711yescharacteristic
789C22×C4C2×D4×C4711yescharacteristic
790C22×C4C2×D4×C4711yescharacteristic
791C22×C4C2×D4×C4712yes—
792C22×C4C24×C4711yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C4711yescharacteristic
819C4⋊C4C2×D4×C4711yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C4711yescharacteristic
864C23#120×C4711yescharacteristic
865C23C22×D4×C4711yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C4712yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—81no—
896D4—82no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C4712yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C4711yescharacteristic
940C2×C4#120×C4711yescharacteristic
941C2×C4C22×D4×C4711yescharacteristic
942C2×C4C22×D4×C4711yescharacteristic
943C2×C4C2×#41×C4711yescharacteristic
944C2×C4C2×#41×C4711yescharacteristic
945C2×C4H(5,𝔽2)×C4711yescharacteristic
946C2×C4H(5,𝔽2)×C4711yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C4711yescharacteristic
978C22C47×#54611yescharacteristic
979C22C47×#54611yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C4711yescharacteristic
993C4C47×#53411yescharacteristic
994C4C47×#54611yescharacteristic
995C4C47×#54611yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C47×#240511yescharacteristic
1005C2C47×#301811yescharacteristic
1006C2C47×#301911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3488C2
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
2. C47×#3093C2semidirect
3. C47×#2896C2semidirect
4. C47×#2500C2semidirect
5. C47×#2040C2semidirect
6. C47×#2039C2semidirect
7. C47×#2037C2semidirect
8. C47×#2037C2semidirect
9. C47×#1900C2semidirect
10. C47×#1871C2semidirect
11. C47×#1860C2semidirect
12. C47×#1859C2semidirect
13. C47×#1792C2semidirect
14. C47×#1792C2semidirect
15. C47×#1789C2semidirect
18. C22×M16×C47C22semidirect
34. C2×#117×C47C22semidirect
39. C47×#428C22semidirect
40. C47×#428C22semidirect
43. C2×#104×C47C22semidirect
44. C2×#104×C47C22semidirect
45. C2×#104×C47C22semidirect
46. C2×#104×C47C22semidirect
51. C47×#417C22semidirect
52. C47×#417C22semidirect
53. C47×#417C22semidirect
54. C47×#417C22semidirect
57. C2×#100×C47C22semidirect
58. C2×#100×C47C22semidirect
59. C47×#407C22semidirect
61. C47×#390C22semidirect
62. C47×#390C22semidirect
64. C47×#384C22semidirect
65. C47×#382C22semidirect
66. C4×C22⋊C4×C47C22semidirect
67. C47×#343C22semidirect
68. C47×#343C22semidirect
69. C47×#339C22semidirect
70. C47×#339C22semidirect
447. #24031C47direct (N × H)
494. #3093C2×C47semidirect
495. #2896C2×C47semidirect
496. #2500C2×C47semidirect
497. #2040C2×C47semidirect
498. #2039C2×C47semidirect
499. #2037C2×C47semidirect
500. #2037C2×C47semidirect
501. #1900C2×C47semidirect
502. #1871C2×C47semidirect
503. #1860C2×C47semidirect
504. #1859C2×C47semidirect
505. #1792C2×C47semidirect
506. #1792C2×C47semidirect
507. #1789C2×C47semidirect
521. C22×M16C22×C47semidirect
537. C2×#117C22×C47semidirect
542. #428C22×C47semidirect
543. #428C22×C47semidirect
546. C2×#104C22×C47semidirect
547. C2×#104C22×C47semidirect
548. C2×#104C22×C47semidirect
549. C2×#104C22×C47semidirect
554. #417C22×C47semidirect
555. #417C22×C47semidirect
556. #417C22×C47semidirect
557. #417C22×C47semidirect
560. C2×#100C22×C47semidirect
561. C2×#100C22×C47semidirect
562. #407C22×C47semidirect
564. #390C22×C47semidirect
565. #390C22×C47semidirect
567. #384C22×C47semidirect
568. #382C22×C47semidirect
569. C4×C22⋊C4C22×C47semidirect
570. #343C22×C47semidirect
571. #343C22×C47semidirect
572. #339C22×C47semidirect
573. #339C22×C47semidirect
574. C47#24031direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34882
C47×#30932
C47×#28962
C47×#25002
C47×#20402
C47×#20392
C47×#20372
C47×#19002
C47×#18712
C47×#18602
C47×#18592
C47×#17922
C47×#17892
#2403147