Finite Group Databasebeta

← C47×#22886 #26062584

Subgroups — C47×#22886 #26062584

Order 12032.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3002C211yesmaximal, characteristic
2C2×C47×#444C211yesmaximal, characteristic, complemented
3C47×#2933C211yesmaximal, characteristic, complemented
4C22×#104×C47C211yesmaximal, characteristic, complemented
5C47×#2880C211yesmaximal, characteristic, complemented
6C47×#1975C211yesmaximal, characteristic, complemented
7C47×#1938C211yesmaximal, characteristic, complemented
8C47×#1929C211yesmaximal, characteristic, complemented
9C47×#1896C211yesmaximal, characteristic, complemented
10C47×#1876C211yesmaximal, characteristic, complemented
11C47×#1876C211yesmaximal, characteristic, complemented
12C47×#1866C211yesmaximal, characteristic, complemented
13C47×#1855C211yesmaximal, characteristic, complemented
14C47×#1765C211yesmaximal, characteristic, complemented
15C47×#1749C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C2×#135×C47C2211yescharacteristic
18C2×#135×C47C2211yescharacteristic
19C2×#131×C47C2211yescharacteristic
20C2×#131×C47C2211yescharacteristic
21C2×#131×C47C2211yescharacteristic, complemented
22C22×M16×C47C2211yescharacteristic
23C47×#525C2211yescharacteristic
24C22×C42×C47C2211yescharacteristic
25C47×#452C411yescharacteristic, complemented
26C47×#452C411yescharacteristic, complemented
27C47×#451C411yescharacteristic, complemented
28C47×#450C411yescharacteristic, complemented
29C47×#449C411yescharacteristic, complemented
30C47×#449C411yescharacteristic, complemented
31C47×#448C411yescharacteristic, complemented
32C47×#447C411yescharacteristic, complemented
33C47×#444—24no—
34C47×#436—21no—
35C47×#435—21no—
36C47×#435—21no—
37C8×D4×C47—21no—
38C2×#108×C47C2211yescharacteristic, complemented
39C2×#108×C47C2211yescharacteristic, complemented
40C47×#424C2211yescharacteristic, complemented
41C2×#104×C47—24no—
42C2×#104×C47C2211yescharacteristic
43C2×#104×C47C2211yescharacteristic
44C2×#104×C47C2211yescharacteristic
45C2×#104×C47C2211yescharacteristic
46C2×#104×C47C2211yescharacteristic, complemented
47C2×#104×C47C2211yescharacteristic, complemented
48C47×#416C2211yescharacteristic
49C47×#416C2211yescharacteristic
50C47×#408—21no—
51C47×#408—21no—
52C47×#408C2211yescharacteristic
53C47×#408C2211yescharacteristic
54C47×#408C2211yescharacteristic, complemented
55C47×#407—21no—
56C47×#407C2211yescharacteristic
57C2×C22⋊C8×C47—21no—
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C47×#405C2211yescharacteristic, complemented
61C2×#97×C47C2211yescharacteristic, complemented
62C2×#97×C47C2211yescharacteristic, complemented
63C47×#341C2211yescharacteristic, complemented
64C47×#341C2211yescharacteristic, complemented
65C47×#339C2211yescharacteristic, complemented
66C47×#339C2211yescharacteristic, complemented
67C47×#336C2211yescharacteristic, complemented
68C47×#336C2211yescharacteristic, complemented
69C2×#41×C47—21no—
70C2×#41×C47—21no—
71C2×#41×C47—22no—
72C2×#41×C47—22no—
73C2×#41×C47—41no—
74C2×#41×C47—41no—
75C2×#41×C47C2×C411yescharacteristic
76C2×#41×C47C2×C411yescharacteristic
77C2×#41×C47C2311yescharacteristic
78C2×#41×C47C2311yescharacteristic
79C2×#41×C47C2311yescharacteristic
80C22×Q8×C47C2×C411yescharacteristic
81C22×D4×C47—21no—
82C22×D4×C47C2×C411yescharacteristic
83C23×C4×C47—21no—
84C23×C4×C47—21no—
85C23×C4×C47C2311yescharacteristic
86#135×C47—22no—
87#135×C47—22no—
88#135×C47—41no—
89#135×C47—41no—
90C2×Q16×C47C2×C411yescharacteristic, complemented
91C2×Q16×C47C2×C411yescharacteristic, complemented
92C2×SD16×C47C2×C411yescharacteristic, complemented
93C2×SD16×C47C2×C411yescharacteristic, complemented
94C2×SD16×C47C2×C411yescharacteristic, complemented
95C2×SD16×C47C2×C411yescharacteristic, complemented
96C2×D8×C47C2×C411yescharacteristic, complemented
97C2×D8×C47C2×C411yescharacteristic, complemented
98#131×C47—22no—
99#131×C47—22no—
100#131×C47—22no—
101#131×C47—41no—
102#131×C47—41no—
103#131×C47—41no—
104C2×M16×C47—21no—
105C2×M16×C47—21no—
106C2×M16×C47—21no—
107C2×M16×C47—21no—
108C2×M16×C47—22no—
109C2×M16×C47—41no—
110C2×M16×C47C2311yescharacteristic
111C2×M16×C47C2311yescharacteristic
112C2×M16×C47C2311yescharacteristic
113C2×M16×C47C2311yescharacteristic
114C22×C8×C47—21no—
115C22×C8×C47—21no—
116C22×C8×C47—21no—
117C22×C8×C47—21no—
118C22×C8×C47C2311yescharacteristic
119C22×C8×C47C2311yescharacteristic
120C22×C8×C47C2311yescharacteristic
121C22×C8×C47C2311yescharacteristic
122#123×C47—21no—
123C22⋊Q8×C47C2×C411yescharacteristic
124C22⋊Q8×C47C2×C411yescharacteristic
125#121×C47C2×C411yescharacteristic
126#121×C47C2×C411yescharacteristic
127#120×C47—21no—
128C4×D4×C47—21no—
129C4×D4×C47—21no—
130#117×C47C2311yescharacteristic
131C2×C42×C47—22no—
132C2×C42×C47—21no—
133C2×C42×C47—41no—
134C2×C42×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136#108×C47—22no—
137#108×C47—41no—
138C4⋊C8×C47—21no—
139C4⋊C8×C47—21no—
140#104×C47—22no—
141#104×C47—22no—
142#104×C47—22no—
143#104×C47—22no—
144#104×C47—41no—
145#104×C47D414yescomplemented
146#103×C47C2×C411yescharacteristic, complemented
147#103×C47C2×C411yescharacteristic, complemented
148#103×C47C2×C411yescharacteristic, complemented
149#103×C47C2×C411yescharacteristic, complemented
150#102×C47C2×C411yescharacteristic, complemented
151#102×C47C2×C411yescharacteristic, complemented
152#102×C47C2×C411yescharacteristic, complemented
153#102×C47C2×C411yescharacteristic, complemented
154C22⋊C8×C47—21no—
155C22⋊C8×C47—21no—
156C22⋊C8×C47—21no—
157C22⋊C8×C47—21no—
158C22⋊C8×C47—21no—
159C22⋊C8×C47—21no—
160C22⋊C8×C47—21no—
161C22⋊C8×C47—21no—
162C22⋊C8×C47C2×C411yescharacteristic
163C22⋊C8×C47C2×C411yescharacteristic
164C22⋊C8×C47C2×C411yescharacteristic
165C22⋊C8×C47C2×C411yescharacteristic
166C22⋊C8×C47D411yescharacteristic
167C22⋊C8×C47D411yescharacteristic
168C22⋊C8×C47D411yescharacteristic
169C22⋊C8×C47D411yescharacteristic
170#97×C47—21no—
171#97×C47—22no—
172#97×C47—41no—
173C4×C8×C47—21no—
174C24×C47—21no—
175C24×C47#4111yescharacteristic
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—22no—
179#41×C47—22no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—21no—
183#41×C47—21no—
184#41×C47—21no—
185#41×C47—21no—
186#41×C47—21no—
187#41×C47—21no—
188#41×C47—42no—
189#41×C47—42no—
190#41×C47—41no—
191#41×C47—41no—
192#41×C47—42no—
193#41×C47—42no—
194#41×C47C2×D412yes—
195#41×C47#4112yes—
196C2×Q8×C47—21no—
197C2×Q8×C47—22no—
198C2×Q8×C47—41no—
199C2×Q8×C47C22×C411yescharacteristic
200C2×Q8×C47C22×C411yescharacteristic
201C2×Q8×C47C22×C411yescharacteristic
202C2×D4×C47—21no—
203C2×D4×C47—22no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—21no—
210C2×D4×C47—21no—
211C2×D4×C47—41no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47C22×C411yescharacteristic
215C2×D4×C47C22×C411yescharacteristic
216C2×D4×C47C22×C411yescharacteristic
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—42no—
230C22×C4×C47—42no—
231C22×C4×C47—42no—
232C22×C4×C47—42no—
233C22×C4×C47—42no—
234C22×C4×C47C22×C411yescharacteristic
235C22×C4×C47C22×C411yescharacteristic
236C22×C4×C47C2×D411yescharacteristic
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47#4111yescharacteristic
239C22×C4×C47C2411yescharacteristic
240Q16×C47—22no—
241Q16×C47—41no—
242SD16×C47—22no—
243SD16×C47—22no—
244SD16×C47—41no—
245SD16×C47—41no—
246D8×C47—22no—
247D8×C47—41no—
248M16×C47—21no—
249M16×C47—21no—
250M16×C47—21no—
251M16×C47—21no—
252M16×C47—21no—
253M16×C47—21no—
254M16×C47—21no—
255M16×C47—42no—
256M16×C47—42no—
257M16×C47—42no—
258M16×C47—42no—
259M16×C47C2×D412yes—
260C2×C8×C47—21no—
261C2×C8×C47—21no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—21no—
266C2×C8×C47—21no—
267C2×C8×C47—21no—
268C2×C8×C47—21no—
269C2×C8×C47—21no—
270C2×C8×C47—21no—
271C2×C8×C47—21no—
272C2×C8×C47—42no—
273C2×C8×C47—42no—
274C2×C8×C47—42no—
275C2×C8×C47—42no—
276C2×C8×C47C22×C411yescharacteristic
277C2×C8×C47C22×C411yescharacteristic
278C2×C8×C47C22×C411yescharacteristic
279C2×C8×C47C22×C411yescharacteristic
280C2×C8×C47C2×D411yescharacteristic
281C2×C8×C47C2×D411yescharacteristic
282C2×C8×C47C2×D411yescharacteristic
283C2×C8×C47C2×D411yescharacteristic
284C4⋊C4×C47—21no—
285C4⋊C4×C47—21no—
286C4⋊C4×C47C22×C411yescharacteristic
287C4⋊C4×C47C22×C411yescharacteristic
288C22⋊C4×C47—21no—
289C22⋊C4×C47—21no—
290C22⋊C4×C47—21no—
291C22⋊C4×C47—21no—
292C22⋊C4×C47—21no—
293C42×C47—21no—
294C42×C47—21no—
295C42×C47—21no—
296C42×C47—21no—
297C42×C47—42no—
298C42×C47C2×D412yes—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—22no—
303C23×C47—21no—
304C23×C47—21no—
305C23×C47—41no—
306C23×C47—42no—
307C23×C47—42no—
308C23×C47—81no—
309C23×C47C4×D411yescharacteristic
310C23×C47C4×D411yescharacteristic
311C23×C47C2×#4111yescharacteristic
312Q8×C47—21no—
313Q8×C47—21no—
314Q8×C47—21no—
315Q8×C47—21no—
316Q8×C47—21no—
317Q8×C47—42no—
318Q8×C47C4×D412yes—
319D4×C47—22no—
320D4×C47—22no—
321D4×C47—21no—
322D4×C47—21no—
323D4×C47—21no—
324D4×C47—21no—
325D4×C47—21no—
326D4×C47—42no—
327D4×C47—42no—
328D4×C47—42no—
329D4×C47—41no—
330D4×C47—41no—
331D4×C47—41no—
332D4×C47—41no—
333D4×C47—42no—
334D4×C47—81no—
335D4×C47C4×D412yes—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—22no—
345C2×C4×C47—21no—
346C2×C4×C47—22no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—22no—
350C2×C4×C47—21no—
351C2×C4×C47—21no—
352C2×C4×C47—21no—
353C2×C4×C47—21no—
354C2×C4×C47—22no—
355C2×C4×C47—42no—
356C2×C4×C47—42no—
357C2×C4×C47—42no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—48no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47C4×D411yescharacteristic
368C2×C4×C47C4×D411yescharacteristic
369C2×C4×C47C23×C411yescharacteristic
370C2×C4×C47C22×D411yescharacteristic
371C2×C4×C47C22×D411yescharacteristic
372C2×C4×C47C2×#4111yescharacteristic
373C2×C4×C47H(5,𝔽2)11yescharacteristic
374C2×C4×C47H(5,𝔽2)11yescharacteristic
375C8×C47—21no—
376C8×C47—21no—
377C8×C47—21no—
378C8×C47—21no—
379C8×C47—21no—
380C8×C47—21no—
381C8×C47—22no—
382C8×C47—21no—
383C8×C47—21no—
384C8×C47—41no—
385C8×C47—41no—
386C8×C47—41no—
387#22886C4711yesmaximal, characteristic, direct product factor, Sylow
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—22no—
394C22×C47—21no—
395C22×C47—21no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—41no—
399C22×C47—41no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—41no—
403C22×C47—41no—
404C22×C47—41no—
405C22×C47—41no—
406C22×C47—84no—
407C22×C47#44412yescomplemented
408C22×C47C2×C4×D411yescharacteristic
409C22×C47#54611yescharacteristic
410C22×C47#55111yescharacteristic
411C4×C47—21no—
412C4×C47—21no—
413C4×C47—22no—
414C4×C47—42no—
415C4×C47—42no—
416C4×C47—41no—
417C4×C47—41no—
418C4×C47—41no—
419C4×C47—41no—
420C4×C47C2×C4×D411yescharacteristic
421C4×C47#51811yescharacteristic
422C4×C47D4211yescharacteristic
423C4×C47#54611yescharacteristic
424#3002C2×C4711yescharacteristic
425C2×#444C2×C4711yescharacteristic, complemented
426#2933C2×C4711yescharacteristic, complemented
427C22×#104C2×C4711yescharacteristic, complemented
428#2880C2×C4711yescharacteristic, complemented
429#1975C2×C4711yescharacteristic, complemented
430#1938C2×C4711yescharacteristic, complemented
431#1929C2×C4711yescharacteristic, complemented
432#1896C2×C4711yescharacteristic, complemented
433#1876C2×C4711yescharacteristic, complemented
434#1876C2×C4711yescharacteristic, complemented
435#1866C2×C4711yescharacteristic, complemented
436#1855C2×C4711yescharacteristic, complemented
437#1765C2×C4711yescharacteristic, complemented
438#1749C2×C4711yescharacteristic, complemented
439C2×C47—21no—
440C2×C47—22no—
441C2×C47—21no—
442C2×C47—41no—
443C2×C47—42no—
444C2×C47—81no—
445C2×C47—81no—
446C2×C47#235811yescharacteristic
447C2×C47C2×#44411yescharacteristic
448C2×C47#295611yescharacteristic
449C22×#41C22×C4711yescharacteristic
450C2×#135C22×C4711yescharacteristic
451C2×#135C22×C4711yescharacteristic
452C2×#131C22×C4711yescharacteristic
453C2×#131C22×C4711yescharacteristic
454C2×#131C22×C4711yescharacteristic, complemented
455C22×M16C22×C4711yescharacteristic
456#525C22×C4711yescharacteristic
457C22×C42C22×C4711yescharacteristic
458#452C4×C4711yescharacteristic, complemented
459#452C4×C4711yescharacteristic, complemented
460#451C4×C4711yescharacteristic, complemented
461#450C4×C4711yescharacteristic, complemented
462#449C4×C4711yescharacteristic, complemented
463#449C4×C4711yescharacteristic, complemented
464#448C4×C4711yescharacteristic, complemented
465#447C4×C4711yescharacteristic, complemented
466#444—24no—
467#436—21no—
468#435—21no—
469#435—21no—
470C8×D4—21no—
471C2×#108C22×C4711yescharacteristic, complemented
472C2×#108C22×C4711yescharacteristic, complemented
473#424C22×C4711yescharacteristic, complemented
474C2×#104—24no—
475C2×#104C22×C4711yescharacteristic
476C2×#104C22×C4711yescharacteristic
477C2×#104C22×C4711yescharacteristic
478C2×#104C22×C4711yescharacteristic
479C2×#104C22×C4711yescharacteristic, complemented
480C2×#104C22×C4711yescharacteristic, complemented
481#416C22×C4711yescharacteristic
482#416C22×C4711yescharacteristic
483#408—21no—
484#408—21no—
485#408C22×C4711yescharacteristic
486#408C22×C4711yescharacteristic
487#408C22×C4711yescharacteristic, complemented
488#407—21no—
489#407C22×C4711yescharacteristic
490C2×C22⋊C8—21no—
491C2×C22⋊C8C22×C4711yescharacteristic
492C2×C22⋊C8C22×C4711yescharacteristic
493#405C22×C4711yescharacteristic, complemented
494C2×#97C22×C4711yescharacteristic, complemented
495C2×#97C22×C4711yescharacteristic, complemented
496#341C22×C4711yescharacteristic, complemented
497#341C22×C4711yescharacteristic, complemented
498#339C22×C4711yescharacteristic, complemented
499#339C22×C4711yescharacteristic, complemented
500#336C22×C4711yescharacteristic, complemented
501#336C22×C4711yescharacteristic, complemented
502C47#2288611yescharacteristic, direct product factor, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×C4×C4711yescharacteristic
510C2×#41C2×C4×C4711yescharacteristic
511C2×#41C23×C4711yescharacteristic
512C2×#41C23×C4711yescharacteristic
513C2×#41C23×C4711yescharacteristic
514C22×Q8C2×C4×C4711yescharacteristic
515C22×D4—21no—
516C22×D4C2×C4×C4711yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C4711yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×C4×C4711yescharacteristic, complemented
525C2×Q16C2×C4×C4711yescharacteristic, complemented
526C2×SD16C2×C4×C4711yescharacteristic, complemented
527C2×SD16C2×C4×C4711yescharacteristic, complemented
528C2×SD16C2×C4×C4711yescharacteristic, complemented
529C2×SD16C2×C4×C4711yescharacteristic, complemented
530C2×D8C2×C4×C4711yescharacteristic, complemented
531C2×D8C2×C4×C4711yescharacteristic, complemented
532#131—22no—
533#131—22no—
534#131—22no—
535#131—41no—
536#131—41no—
537#131—41no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—21no—
541C2×M16—21no—
542C2×M16—22no—
543C2×M16—41no—
544C2×M16C23×C4711yescharacteristic
545C2×M16C23×C4711yescharacteristic
546C2×M16C23×C4711yescharacteristic
547C2×M16C23×C4711yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8—21no—
552C22×C8C23×C4711yescharacteristic
553C22×C8C23×C4711yescharacteristic
554C22×C8C23×C4711yescharacteristic
555C22×C8C23×C4711yescharacteristic
556#123—21no—
557C22⋊Q8C2×C4×C4711yescharacteristic
558C22⋊Q8C2×C4×C4711yescharacteristic
559#121C2×C4×C4711yescharacteristic
560#121C2×C4×C4711yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C23×C4711yescharacteristic
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C23×C4711yescharacteristic
569C2×C42C23×C4711yescharacteristic
570#108—22no—
571#108—41no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—22no—
578#104—41no—
579#104D4×C4714yescomplemented
580#103C2×C4×C4711yescharacteristic, complemented
581#103C2×C4×C4711yescharacteristic, complemented
582#103C2×C4×C4711yescharacteristic, complemented
583#103C2×C4×C4711yescharacteristic, complemented
584#102C2×C4×C4711yescharacteristic, complemented
585#102C2×C4×C4711yescharacteristic, complemented
586#102C2×C4×C4711yescharacteristic, complemented
587#102C2×C4×C4711yescharacteristic, complemented
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8C2×C4×C4711yescharacteristic
597C22⋊C8C2×C4×C4711yescharacteristic
598C22⋊C8C2×C4×C4711yescharacteristic
599C22⋊C8C2×C4×C4711yescharacteristic
600C22⋊C8D4×C4711yescharacteristic
601C22⋊C8D4×C4711yescharacteristic
602C22⋊C8D4×C4711yescharacteristic
603C22⋊C8D4×C4711yescharacteristic
604#97—21no—
605#97—22no—
606#97—41no—
607C4×C8—21no—
608C24—21no—
609C24#41×C4711yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41C2×D4×C4712yes—
629#41#41×C4712yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×C4×C4711yescharacteristic
634C2×Q8C22×C4×C4711yescharacteristic
635C2×Q8C22×C4×C4711yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×C4×C4711yescharacteristic
649C2×D4C22×C4×C4711yescharacteristic
650C2×D4C22×C4×C4711yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22×C4×C4711yescharacteristic
669C22×C4C22×C4×C4711yescharacteristic
670C22×C4C2×D4×C4711yescharacteristic
671C22×C4C2×D4×C4711yescharacteristic
672C22×C4#41×C4711yescharacteristic
673C22×C4C24×C4711yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—42no—
690M16—42no—
691M16—42no—
692M16—42no—
693M16C2×D4×C4712yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—42no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—42no—
710C2×C8C22×C4×C4711yescharacteristic
711C2×C8C22×C4×C4711yescharacteristic
712C2×C8C22×C4×C4711yescharacteristic
713C2×C8C22×C4×C4711yescharacteristic
714C2×C8C2×D4×C4711yescharacteristic
715C2×C8C2×D4×C4711yescharacteristic
716C2×C8C2×D4×C4711yescharacteristic
717C2×C8C2×D4×C4711yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×C4×C4711yescharacteristic
721C4⋊C4C22×C4×C4711yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42C2×D4×C4712yes—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23C4×D4×C4711yescharacteristic
744C23C4×D4×C4711yescharacteristic
745C23C2×#41×C4711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8C4×D4×C4712yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—42no—
768D4—81no—
769D4C4×D4×C4712yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4C4×D4×C4711yescharacteristic
802C2×C4C4×D4×C4711yescharacteristic
803C2×C4C23×C4×C4711yescharacteristic
804C2×C4C22×D4×C4711yescharacteristic
805C2×C4C22×D4×C4711yescharacteristic
806C2×C4C2×#41×C4711yescharacteristic
807C2×C4H(5,𝔽2)×C4711yescharacteristic
808C2×C4H(5,𝔽2)×C4711yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—22no—
816C8—21no—
817C8—21no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22C47×#44412yescomplemented
841C22C2×C4×D4×C4711yescharacteristic
842C22C47×#54611yescharacteristic
843C22C47×#55111yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4C2×C4×D4×C4711yescharacteristic
854C4C47×#51811yescharacteristic
855C4D42×C4711yescharacteristic
856C4C47×#54611yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2C47×#235811yescharacteristic
865C2C2×C47×#44411yescharacteristic
866C2C47×#295611yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC22×C47C2×C4×D4
prime radicalC47×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C2×C22⋊C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#444C2semidirect
3. C47×#2933C2semidirect
4. C22×#104×C47C2semidirect
5. C47×#2880C2semidirect
6. C47×#1975C2semidirect
7. C47×#1938C2semidirect
8. C47×#1929C2semidirect
9. C47×#1896C2semidirect
10. C47×#1876C2semidirect
11. C47×#1876C2semidirect
12. C47×#1866C2semidirect
13. C47×#1855C2semidirect
14. C47×#1765C2semidirect
15. C47×#1749C2semidirect
21. C2×#131×C47C22semidirect
25. C47×#452C4semidirect
26. C47×#452C4semidirect
27. C47×#451C4semidirect
28. C47×#450C4semidirect
29. C47×#449C4semidirect
30. C47×#449C4semidirect
31. C47×#448C4semidirect
32. C47×#447C4semidirect
38. C2×#108×C47C22semidirect
39. C2×#108×C47C22semidirect
40. C47×#424C22semidirect
46. C2×#104×C47C22semidirect
47. C2×#104×C47C22semidirect
54. C47×#408C22semidirect
60. C47×#405C22semidirect
61. C2×#97×C47C22semidirect
62. C2×#97×C47C22semidirect
63. C47×#341C22semidirect
64. C47×#341C22semidirect
65. C47×#339C22semidirect
66. C47×#339C22semidirect
67. C47×#336C22semidirect
68. C47×#336C22semidirect
90. C2×Q16×C47C2×C4semidirect
91. C2×Q16×C47C2×C4semidirect
92. C2×SD16×C47C2×C4semidirect
93. C2×SD16×C47C2×C4semidirect
94. C2×SD16×C47C2×C4semidirect
95. C2×SD16×C47C2×C4semidirect
96. C2×D8×C47C2×C4semidirect
97. C2×D8×C47C2×C4semidirect
145. #104×C47D4semidirect
146. #103×C47C2×C4semidirect
147. #103×C47C2×C4semidirect
148. #103×C47C2×C4semidirect
149. #103×C47C2×C4semidirect
150. #102×C47C2×C4semidirect
151. #102×C47C2×C4semidirect
152. #102×C47C2×C4semidirect
153. #102×C47C2×C4semidirect
387. #22886C47direct (N × H)
407. C22×C47#444semidirect
425. C2×#444C2×C47semidirect
426. #2933C2×C47semidirect
427. C22×#104C2×C47semidirect
428. #2880C2×C47semidirect
429. #1975C2×C47semidirect
430. #1938C2×C47semidirect
431. #1929C2×C47semidirect
432. #1896C2×C47semidirect
433. #1876C2×C47semidirect
434. #1876C2×C47semidirect
435. #1866C2×C47semidirect
436. #1855C2×C47semidirect
437. #1765C2×C47semidirect
438. #1749C2×C47semidirect
454. C2×#131C22×C47semidirect
458. #452C4×C47semidirect
459. #452C4×C47semidirect
460. #451C4×C47semidirect
461. #450C4×C47semidirect
462. #449C4×C47semidirect
463. #449C4×C47semidirect
464. #448C4×C47semidirect
465. #447C4×C47semidirect
471. C2×#108C22×C47semidirect
472. C2×#108C22×C47semidirect
473. #424C22×C47semidirect
479. C2×#104C22×C47semidirect
480. C2×#104C22×C47semidirect
487. #408C22×C47semidirect
493. #405C22×C47semidirect
494. C2×#97C22×C47semidirect
495. C2×#97C22×C47semidirect
496. #341C22×C47semidirect
497. #341C22×C47semidirect
498. #339C22×C47semidirect
499. #339C22×C47semidirect
500. #336C22×C47semidirect
501. #336C22×C47semidirect
502. C47#22886direct (N × H)
524. C2×Q16C2×C4×C47semidirect
525. C2×Q16C2×C4×C47semidirect
526. C2×SD16C2×C4×C47semidirect
527. C2×SD16C2×C4×C47semidirect
528. C2×SD16C2×C4×C47semidirect
529. C2×SD16C2×C4×C47semidirect
530. C2×D8C2×C4×C47semidirect
531. C2×D8C2×C4×C47semidirect
579. #104D4×C47semidirect
580. #103C2×C4×C47semidirect
581. #103C2×C4×C47semidirect
582. #103C2×C4×C47semidirect
583. #103C2×C4×C47semidirect
584. #102C2×C4×C47semidirect
585. #102C2×C4×C47semidirect
586. #102C2×C4×C47semidirect
587. #102C2×C4×C47semidirect
840. C22C47×#444semidirect

Maximal subgroups

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

subgroupindex
C47×#30022
C2×C47×#4442
C47×#29332
C22×#104×C472
C47×#28802
C47×#19752
C47×#19382
C47×#19292
C47×#18962
C47×#18762
C47×#18662
C47×#18552
C47×#17652
C47×#17492
#2288647