Finite Group Databasebeta

← C47×#26418 #26066116

Subgroups — C47×#26418 #26066116

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2442C211yesmaximal, characteristic
2C47×#2360C211yesmaximal, characteristic
3C47×#2101C211yesmaximal, characteristic, complemented
4C47×#2086C211yesmaximal, characteristic, complemented
5C47×#2068C211yesmaximal, characteristic, complemented
6C47×#2026C211yesmaximal, characteristic, complemented
7C47×#1989C211yesmaximal, characteristic, complemented
8C47×#1918C211yesmaximal, characteristic, complemented
9C47×#1892C211yesmaximal, characteristic
10C47×#1872C211yesmaximal, characteristic
11C47×#1863C211yesmaximal, characteristic, complemented
12C47×#1852C211yesmaximal, characteristic
13C47×#1850C211yesmaximal, characteristic
14C47×#1805C211yesmaximal, characteristic, complemented
15C2×C47×#340C211yesmaximal, characteristic
16C23×C8×C47C2211yescharacteristic
17C2×#125×C47C2211yescharacteristic
18C2×C22⋊Q8×C47C2211yescharacteristic
19C2×C4×Q8×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C4⋊C4×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×#103×C47C2211yescharacteristic
27C2×#103×C47C2211yescharacteristic
28C2×#103×C47C2211yescharacteristic
29C2×#103×C47C2211yescharacteristic
30C2×C22⋊C8×C47C2211yescharacteristic
31C47×#400—21no—
32C47×#398—21no—
33C47×#391C2211yescharacteristic
34C47×#389—21no—
35C47×#389C2211yescharacteristic
36C47×#389C2211yescharacteristic
37C47×#389C2211yescharacteristic
38C47×#387—21no—
39C47×#385—21no—
40C47×#385—21no—
41C47×#382C2211yescharacteristic
42C47×#380—21no—
43C47×#380C2211yescharacteristic
44C4×C4⋊C4×C47C2211yescharacteristic
45C4×C22⋊C4×C47—21no—
46C4×C22⋊C4×C47C2211yescharacteristic
47C47×#340C2211yescharacteristic
48C47×#340C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Q8×C47C2311yescharacteristic
60C23×C4×C47—21no—
61C23×C4×C47—21no—
62C23×C4×C47C2311yescharacteristic
63C22×C8×C47—22no—
64C22×C8×C47—41no—
65C22×C8×C47—41no—
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C22×C8×C47C2311yescharacteristic
69C22×C8×C47C2311yescharacteristic
70#125×C47—22no—
71#125×C47—41no—
72C22⋊Q8×C47—22no—
73C22⋊Q8×C47Q814yes—
74C4×Q8×C47—22no—
75C4×Q8×C47—41no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—22no—
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47—21no—
85C2×C4⋊C4×C47—21no—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—41no—
88C2×C4⋊C4×C47—41no—
89C2×C4⋊C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47C2311yescharacteristic
91C2×C4⋊C4×C47C2311yescharacteristic
92C2×C4⋊C4×C47C2311yescharacteristic
93C2×C4⋊C4×C47C2311yescharacteristic
94C2×C4⋊C4×C47C2311yescharacteristic
95C2×C4⋊C4×C47C2311yescharacteristic
96C2×C22⋊C4×C47—21no—
97C2×C22⋊C4×C47—21no—
98C2×C22⋊C4×C47D411yescharacteristic
99C2×C22⋊C4×C47D411yescharacteristic
100C2×C42×C47—21no—
101C2×C42×C47—21no—
102C2×C42×C47C2311yescharacteristic
103C2×C42×C47C2311yescharacteristic
104#107×C47—22no—
105#107×C47—41no—
106C4⋊C8×C47—41no—
107C4⋊C8×C47—41no—
108#103×C47—22no—
109#103×C47—41no—
110#103×C47—41no—
111#103×C47—41no—
112C22⋊C8×C47—22no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119#95×C47—21no—
120#95×C47—21no—
121#95×C47—21no—
122#95×C47D411yescharacteristic
123#95×C47D411yescharacteristic
124C24×C47C2×D411yescharacteristic
125C2×Q8×C47—21no—
126C2×Q8×C47—21no—
127C2×Q8×C47—21no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47C2×Q812yes—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—42no—
144C22×C4×C47—42no—
145C22×C4×C47—42no—
146C22×C4×C47—42no—
147C22×C4×C47—81no—
148C22×C4×C47—81no—
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×Q812yes—
155C22×C4×C47#4112yes—
156C22×C4×C47C2411yescharacteristic
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—44no—
170C4⋊C4×C47—24no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—42no—
183C4⋊C4×C47—42no—
184C4⋊C4×C47—42no—
185C4⋊C4×C47—42no—
186C4⋊C4×C47—42no—
187C4⋊C4×C47—81no—
188C4⋊C4×C47—81no—
189C4⋊C4×C47—81no—
190C4⋊C4×C47C2×Q812yes—
191C4⋊C4×C47#4112yes—
192C4⋊C4×C47#4112yes—
193C22⋊C4×C47—24no—
194C22⋊C4×C47—22no—
195C22⋊C4×C47—22no—
196C22⋊C4×C47—42no—
197C42×C47—21no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—42no—
202C42×C47—81no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47C22⋊Q812yes—
208C23×C47#13512yes—
209C23×C47#13712yes—
210C23×C47C22×D411yescharacteristic
211Q8×C47—22no—
212Q8×C47—22no—
213Q8×C47—41no—
214Q8×C47—41no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—84no—
258C2×C4×C47—84no—
259C2×C4×C47C22⋊Q812yes—
260C2×C4×C47C22×Q811yescharacteristic
261C2×C4×C47C2×#4111yescharacteristic
262C2×C4×C47C2×#4111yescharacteristic
263C2×C4×C47C2×#4111yescharacteristic
264C2×C4×C47H(5,𝔽2)11yescharacteristic
265C2×C4×C47H(5,𝔽2)11yescharacteristic
266C8×C47—41no—
267C8×C47—41no—
268C8×C47—41no—
269C8×C47—41no—
270#26418C4711yesmaximal, characteristic, direct product factor, Sylow
271C22×C47—22no—
272C22×C47—22no—
273C22×C47—22no—
274C22×C47—22no—
275C22×C47—22no—
276C22×C47—22no—
277C22×C47#47914yes—
278C22×C47C2×C22⋊Q811yescharacteristic
279C22×C47#54611yescharacteristic
280C22×C47#54611yescharacteristic
281C22×C47C2×#13511yescharacteristic
282C22×C47C2×#13711yescharacteristic
283C22×C47#57611yescharacteristic
284C22×C47#57811yescharacteristic
285C4×C47—22no—
286C4×C47—42no—
287C4×C47—42no—
288C4×C47—41no—
289C4×C47—42no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—42no—
294C4×C47—81no—
295C4×C47—81no—
296C4×C47—81no—
297C4×C47—81no—
298C4×C47#52911yescharacteristic
299C4×C47#53811yescharacteristic
300C4×C47#55411yescharacteristic
301C4×C47#55411yescharacteristic
302#2442C2×C4711yescharacteristic
303#2360C2×C4711yescharacteristic
304#2101C2×C4711yescharacteristic, complemented
305#2086C2×C4711yescharacteristic, complemented
306#2068C2×C4711yescharacteristic, complemented
307#2026C2×C4711yescharacteristic, complemented
308#1989C2×C4711yescharacteristic, complemented
309#1918C2×C4711yescharacteristic, complemented
310#1892C2×C4711yescharacteristic
311#1872C2×C4711yescharacteristic
312#1863C2×C4711yescharacteristic, complemented
313#1852C2×C4711yescharacteristic
314#1850C2×C4711yescharacteristic
315#1805C2×C4711yescharacteristic, complemented
316C2×#340C2×C4711yescharacteristic
317C2×C47—24no—
318C2×C47#245011yescharacteristic
319C2×C47C2×#47911yescharacteristic
320C2×C47#308311yescharacteristic
321C2×C47#329711yescharacteristic
322C2×C47#330011yescharacteristic
323C2×C47#331211yescharacteristic
324C2×C47#331411yescharacteristic
325C23×C8C22×C4711yescharacteristic
326C2×#125C22×C4711yescharacteristic
327C2×C22⋊Q8C22×C4711yescharacteristic
328C2×C4×Q8C22×C4711yescharacteristic
329C22×C4⋊C4C22×C4711yescharacteristic
330C22×C4⋊C4C22×C4711yescharacteristic
331C2×#107C22×C4711yescharacteristic
332C2×#107C22×C4711yescharacteristic
333C2×C4⋊C8C22×C4711yescharacteristic
334C2×C4⋊C8C22×C4711yescharacteristic
335C2×#103C22×C4711yescharacteristic
336C2×#103C22×C4711yescharacteristic
337C2×#103C22×C4711yescharacteristic
338C2×#103C22×C4711yescharacteristic
339C2×C22⋊C8C22×C4711yescharacteristic
340#400—21no—
341#398—21no—
342#391C22×C4711yescharacteristic
343#389—21no—
344#389C22×C4711yescharacteristic
345#389C22×C4711yescharacteristic
346#389C22×C4711yescharacteristic
347#387—21no—
348#385—21no—
349#385—21no—
350#382C22×C4711yescharacteristic
351#380—21no—
352#380C22×C4711yescharacteristic
353C4×C4⋊C4C22×C4711yescharacteristic
354C4×C22⋊C4—21no—
355C4×C22⋊C4C22×C4711yescharacteristic
356#340C22×C4711yescharacteristic
357#340C22×C4711yescharacteristic
358#340C22×C4711yescharacteristic
359#340C22×C4711yescharacteristic
360#340C22×C4711yescharacteristic
361#340C22×C4711yescharacteristic
362#340C22×C4711yescharacteristic
363#340C22×C4711yescharacteristic
364#340C22×C4711yescharacteristic
365#340C22×C4711yescharacteristic
366#336C22×C4711yescharacteristic
367#336C22×C4711yescharacteristic
368C47#2641811yescharacteristic, direct product factor, Sylow
369C22×Q8C23×C4711yescharacteristic
370C23×C4—21no—
371C23×C4—21no—
372C23×C4C23×C4711yescharacteristic
373C22×C8—22no—
374C22×C8—41no—
375C22×C8—41no—
376C22×C8C23×C4711yescharacteristic
377C22×C8C23×C4711yescharacteristic
378C22×C8C23×C4711yescharacteristic
379C22×C8C23×C4711yescharacteristic
380#125—22no—
381#125—41no—
382C22⋊Q8—22no—
383C22⋊Q8Q8×C4714yes—
384C4×Q8—22no—
385C4×Q8—41no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4C23×C4711yescharacteristic
400C2×C4⋊C4C23×C4711yescharacteristic
401C2×C4⋊C4C23×C4711yescharacteristic
402C2×C4⋊C4C23×C4711yescharacteristic
403C2×C4⋊C4C23×C4711yescharacteristic
404C2×C4⋊C4C23×C4711yescharacteristic
405C2×C4⋊C4C23×C4711yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4D4×C4711yescharacteristic
409C2×C22⋊C4D4×C4711yescharacteristic
410C2×C42—21no—
411C2×C42—21no—
412C2×C42C23×C4711yescharacteristic
413C2×C42C23×C4711yescharacteristic
414#107—22no—
415#107—41no—
416C4⋊C8—41no—
417C4⋊C8—41no—
418#103—22no—
419#103—41no—
420#103—41no—
421#103—41no—
422C22⋊C8—22no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95D4×C4711yescharacteristic
433#95D4×C4711yescharacteristic
434C24C2×D4×C4711yescharacteristic
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×Q8×C4712yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—81no—
458C22×C4—81no—
459C22×C4C2×D4×C4711yescharacteristic
460C22×C4C2×D4×C4711yescharacteristic
461C22×C4C2×D4×C4711yescharacteristic
462C22×C4C2×D4×C4711yescharacteristic
463C22×C4C2×D4×C4711yescharacteristic
464C22×C4C2×Q8×C4712yes—
465C22×C4#41×C4712yes—
466C22×C4C24×C4711yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—44no—
480C4⋊C4—24no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—81no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4C2×Q8×C4712yes—
501C4⋊C4#41×C4712yes—
502C4⋊C4#41×C4712yes—
503C22⋊C4—24no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—42no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—81no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C22⋊Q8×C4712yes—
518C23#135×C4712yes—
519C23#137×C4712yes—
520C23C22×D4×C4711yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—41no—
524Q8—41no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—84no—
569C2×C4C22⋊Q8×C4712yes—
570C2×C4C22×Q8×C4711yescharacteristic
571C2×C4C2×#41×C4711yescharacteristic
572C2×C4C2×#41×C4711yescharacteristic
573C2×C4C2×#41×C4711yescharacteristic
574C2×C4H(5,𝔽2)×C4711yescharacteristic
575C2×C4H(5,𝔽2)×C4711yescharacteristic
576C8—41no—
577C8—41no—
578C8—41no—
579C8—41no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22C47×#47914yes—
587C22C2×C22⋊Q8×C4711yescharacteristic
588C22C47×#54611yescharacteristic
589C22C47×#54611yescharacteristic
590C22C2×#135×C4711yescharacteristic
591C22C2×#137×C4711yescharacteristic
592C22C47×#57611yescharacteristic
593C22C47×#57811yescharacteristic
594C4—22no—
595C4—41no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C47×#52911yescharacteristic
608C4C47×#53811yescharacteristic
609C4C47×#55411yescharacteristic
610C4C47×#55411yescharacteristic
611C2—24no—
612C2C47×#245011yescharacteristic
613C2C2×C47×#47911yescharacteristic
614C2C47×#308311yescharacteristic
615C2C47×#329711yescharacteristic
616C2C47×#330011yescharacteristic
617C2C47×#331211yescharacteristic
618C2C47×#331411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC24×C47C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#2101C2semidirect
4. C47×#2086C2semidirect
5. C47×#2068C2semidirect
6. C47×#2026C2semidirect
7. C47×#1989C2semidirect
8. C47×#1918C2semidirect
11. C47×#1863C2semidirect
14. C47×#1805C2semidirect
270. #26418C47direct (N × H)
304. #2101C2×C47semidirect
305. #2086C2×C47semidirect
306. #2068C2×C47semidirect
307. #2026C2×C47semidirect
308. #1989C2×C47semidirect
309. #1918C2×C47semidirect
312. #1863C2×C47semidirect
315. #1805C2×C47semidirect
368. C47#26418direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#24422
C47×#23602
C47×#21012
C47×#20862
C47×#20682
C47×#20262
C47×#19892
C47×#19182
C47×#18922
C47×#18722
C47×#18632
C47×#18522
C47×#18502
C47×#18052
C2×C47×#3402
#2641847