Finite Group Databasebeta

← C47×#26007 #26065705

Subgroups — C47×#26007 #26065705

Order 12032.

740 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2440C211yesmaximal, characteristic
2C47×#2347C211yesmaximal, characteristic
3C47×#2099C211yesmaximal, characteristic, complemented
4C47×#2088C211yesmaximal, characteristic, complemented
5C47×#2086C211yesmaximal, characteristic, complemented
6C47×#2058C211yesmaximal, characteristic, complemented
7C47×#1987C211yesmaximal, characteristic, complemented
8C47×#1948C211yesmaximal, characteristic, complemented
9C47×#1921C211yesmaximal, characteristic, complemented
10C47×#1919C211yesmaximal, characteristic, complemented
11C47×#1853C211yesmaximal, characteristic
12C47×#1851C211yesmaximal, characteristic
13C47×#1825C211yesmaximal, characteristic
14C47×#1809C211yesmaximal, characteristic
15C47×#1736C211yesmaximal, characteristic
16C22×M16×C47C2211yescharacteristic
17C2×C4⋊Q8×C47C2211yescharacteristic
18C2×C22⋊Q8×C47—21no—
19C2×#117×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C2×#106×C47C2211yescharacteristic
23C2×#106×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C22⋊C8×C47C2211yescharacteristic
28C47×#398—21no—
29C47×#395—21no—
30C47×#389C2211yescharacteristic
31C47×#389C2211yescharacteristic
32C47×#389C2211yescharacteristic
33C47×#389C2211yescharacteristic
34C47×#388—21no—
35C47×#388—21no—
36C47×#385—21no—
37C47×#384C2211yescharacteristic
38C47×#383—21no—
39C47×#380C2211yescharacteristic
40C47×#380C2211yescharacteristic
41C4×C4⋊C4×C47—21no—
42C4×C4⋊C4×C47C2211yescharacteristic
43C4×C4⋊C4×C47C2211yescharacteristic
44C4×C22⋊C4×C47C2211yescharacteristic
45C47×#340C2211yescharacteristic
46C47×#340C2211yescharacteristic
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×C47—21no—
60C23×C4×C47—21no—
61C23×C4×C47C2311yescharacteristic
62C2×M16×C47—22no—
63C2×M16×C47—22no—
64C2×M16×C47—41no—
65C22×C8×C47C2311yescharacteristic
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C22×C8×C47C2311yescharacteristic
69C4⋊Q8×C47—22no—
70C4⋊Q8×C47—41no—
71C22⋊Q8×C47—44no—
72#117×C47—22no—
73#117×C47Q814yescomplemented
74C2×C4⋊C4×C47—22no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47—41no—
84C2×C4⋊C4×C47C2311yescharacteristic
85C2×C4⋊C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47C2311yescharacteristic
87C2×C4⋊C4×C47C2311yescharacteristic
88C2×C4⋊C4×C47C2311yescharacteristic
89C2×C4⋊C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47C2311yescharacteristic
91C2×C4⋊C4×C47C2311yescharacteristic
92C2×C22⋊C4×C47—21no—
93C2×C22⋊C4×C47—21no—
94C2×C22⋊C4×C47—21no—
95C2×C22⋊C4×C47D411yescharacteristic
96C2×C22⋊C4×C47D411yescharacteristic
97C2×C42×C47—21no—
98C2×C42×C47—21no—
99C2×C42×C47—21no—
100C2×C42×C47C2311yescharacteristic
101C2×C42×C47C2311yescharacteristic
102#107×C47—22no—
103#106×C47—22no—
104#106×C47—41no—
105#106×C47—41no—
106C4⋊C8×C47—22no—
107C4⋊C8×C47—41no—
108C22⋊C8×C47—22no—
109#95×C47—21no—
110#95×C47—21no—
111#95×C47—21no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47D411yescharacteristic
118#95×C47D411yescharacteristic
119C24×C47C2×D411yescharacteristic
120C2×Q8×C47—42no—
121C2×Q8×C47—42no—
122C2×Q8×C47—81no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—42no—
136C22×C4×C47—42no—
137C22×C4×C47—81no—
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×Q812yes—
144C22×C4×C47#4112yes—
145C22×C4×C47C2411yescharacteristic
146M16×C47—44no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47#4112yes—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—42no—
173C4⋊C4×C47—42no—
174C4⋊C4×C47—42no—
175C4⋊C4×C47—42no—
176C4⋊C4×C47—42no—
177C4⋊C4×C47—42no—
178C4⋊C4×C47—42no—
179C4⋊C4×C47—81no—
180C4⋊C4×C47C2×Q812yes—
181C4⋊C4×C47C2×Q812yes—
182C4⋊C4×C47#4112yes—
183C22⋊C4×C47—24no—
184C22⋊C4×C47—22no—
185C22⋊C4×C47—22no—
186C22⋊C4×C47—42no—
187C22⋊C4×C47—81no—
188C42×C47—24no—
189C42×C47—21no—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—81no—
194C42×C47—81no—
195C23×C47—21no—
196C23×C47—21no—
197C23×C47—21no—
198C23×C47—21no—
199C23×C47—21no—
200C23×C47—21no—
201C23×C47C22⋊Q812yes—
202C23×C47C22×D411yescharacteristic
203Q8×C47—84no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—21no—
217C2×C4×C47—22no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
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—84no—
245C2×C4×C47C22⋊Q812yes—
246C2×C4×C47AGL(1,ℤ/8)12yes—
247C2×C4×C47#13712yes—
248C2×C4×C47C22×Q811yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C2×C4×C47H(5,𝔽2)11yescharacteristic
253C2×C4×C472−1+411yescharacteristic
254C8×C47—22no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258#26007C4711yesmaximal, characteristic, direct product factor, Sylow
259C22×C47—22no—
260C22×C47—22no—
261C22×C47—22no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47C2×C22⋊Q811yescharacteristic
267C22×C47#54611yescharacteristic
268C22×C47#54711yescharacteristic
269C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C47C2×#13711yescharacteristic
271C22×C47#57711yescharacteristic
272C22×C47#57711yescharacteristic
273C4×C47—22no—
274C4×C47—22no—
275C4×C47—22no—
276C4×C47—42no—
277C4×C47—42no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—42no—
281C4×C47—81no—
282C4×C47—81no—
283C4×C47—81no—
284C4×C47—81no—
285C4×C47—81no—
286C4×C47#53311yescharacteristic
287C4×C47#54411yescharacteristic
288C4×C47#55111yescharacteristic
289C4×C47#55211yescharacteristic
290#2440C2×C4711yescharacteristic
291#2347C2×C4711yescharacteristic
292#2099C2×C4711yescharacteristic, complemented
293#2088C2×C4711yescharacteristic, complemented
294#2086C2×C4711yescharacteristic, complemented
295#2058C2×C4711yescharacteristic, complemented
296#1987C2×C4711yescharacteristic, complemented
297#1948C2×C4711yescharacteristic, complemented
298#1921C2×C4711yescharacteristic, complemented
299#1919C2×C4711yescharacteristic, complemented
300#1853C2×C4711yescharacteristic
301#1851C2×C4711yescharacteristic
302#1825C2×C4711yescharacteristic
303#1809C2×C4711yescharacteristic
304#1736C2×C4711yescharacteristic
305C2×C47—42no—
306C2×C47#243811yescharacteristic
307C2×C47#307911yescharacteristic
308C2×C47#308411yescharacteristic
309C2×C47#332011yescharacteristic
310C2×C47#332411yescharacteristic
311C2×C47#334511yescharacteristic
312C2×C47#335611yescharacteristic
313C22×M16C22×C4711yescharacteristic
314C2×C4⋊Q8C22×C4711yescharacteristic
315C2×C22⋊Q8—21no—
316C2×#117C22×C4711yescharacteristic
317C22×C4⋊C4C22×C4711yescharacteristic
318C2×#107C22×C4711yescharacteristic
319C2×#106C22×C4711yescharacteristic
320C2×#106C22×C4711yescharacteristic
321C2×#106C22×C4711yescharacteristic
322C2×C4⋊C8C22×C4711yescharacteristic
323C2×C4⋊C8C22×C4711yescharacteristic
324C2×C22⋊C8C22×C4711yescharacteristic
325#398—21no—
326#395—21no—
327#389C22×C4711yescharacteristic
328#389C22×C4711yescharacteristic
329#389C22×C4711yescharacteristic
330#389C22×C4711yescharacteristic
331#388—21no—
332#388—21no—
333#385—21no—
334#384C22×C4711yescharacteristic
335#383—21no—
336#380C22×C4711yescharacteristic
337#380C22×C4711yescharacteristic
338C4×C4⋊C4—21no—
339C4×C4⋊C4C22×C4711yescharacteristic
340C4×C4⋊C4C22×C4711yescharacteristic
341C4×C22⋊C4C22×C4711yescharacteristic
342#340C22×C4711yescharacteristic
343#340C22×C4711yescharacteristic
344#340C22×C4711yescharacteristic
345#340C22×C4711yescharacteristic
346#340C22×C4711yescharacteristic
347#340C22×C4711yescharacteristic
348#340C22×C4711yescharacteristic
349#340C22×C4711yescharacteristic
350#340C22×C4711yescharacteristic
351#340C22×C4711yescharacteristic
352#340C22×C4711yescharacteristic
353#340C22×C4711yescharacteristic
354#336C22×C4711yescharacteristic
355#336C22×C4711yescharacteristic
356C47#2600711yescharacteristic, direct product factor, Sylow
357C22×Q8—21no—
358C23×C4—21no—
359C23×C4C23×C4711yescharacteristic
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—41no—
363C22×C8C23×C4711yescharacteristic
364C22×C8C23×C4711yescharacteristic
365C22×C8C23×C4711yescharacteristic
366C22×C8C23×C4711yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8—41no—
369C22⋊Q8—44no—
370#117—22no—
371#117Q8×C4714yescomplemented
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4C23×C4711yescharacteristic
383C2×C4⋊C4C23×C4711yescharacteristic
384C2×C4⋊C4C23×C4711yescharacteristic
385C2×C4⋊C4C23×C4711yescharacteristic
386C2×C4⋊C4C23×C4711yescharacteristic
387C2×C4⋊C4C23×C4711yescharacteristic
388C2×C4⋊C4C23×C4711yescharacteristic
389C2×C4⋊C4C23×C4711yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4D4×C4711yescharacteristic
394C2×C22⋊C4D4×C4711yescharacteristic
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C4711yescharacteristic
399C2×C42C23×C4711yescharacteristic
400#107—22no—
401#106—22no—
402#106—41no—
403#106—41no—
404C4⋊C8—22no—
405C4⋊C8—41no—
406C22⋊C8—22no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95D4×C4711yescharacteristic
416#95D4×C4711yescharacteristic
417C24C2×D4×C4711yescharacteristic
418C2×Q8—42no—
419C2×Q8—42no—
420C2×Q8—81no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—81no—
436C22×C4C2×D4×C4711yescharacteristic
437C22×C4C2×D4×C4711yescharacteristic
438C22×C4C2×D4×C4711yescharacteristic
439C22×C4C2×D4×C4711yescharacteristic
440C22×C4C2×D4×C4711yescharacteristic
441C22×C4C2×Q8×C4712yes—
442C22×C4#41×C4712yes—
443C22×C4C24×C4711yescharacteristic
444M16—44no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8#41×C4712yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—81no—
478C4⋊C4C2×Q8×C4712yes—
479C4⋊C4C2×Q8×C4712yes—
480C4⋊C4#41×C4712yes—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—42no—
485C22⋊C4—81no—
486C42—24no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—81no—
492C42—81no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23C22⋊Q8×C4712yes—
500C23C22×D4×C4711yescharacteristic
501Q8—84no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—84no—
543C2×C4C22⋊Q8×C4712yes—
544C2×C4AGL(1,ℤ/8)×C4712yes—
545C2×C4#137×C4712yes—
546C2×C4C22×Q8×C4711yescharacteristic
547C2×C4C2×#41×C4711yescharacteristic
548C2×C4C2×#41×C4711yescharacteristic
549C2×C4C2×#41×C4711yescharacteristic
550C2×C4H(5,𝔽2)×C4711yescharacteristic
551C2×C42−1+4×C4711yescharacteristic
552C8—22no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C2×C22⋊Q8×C4711yescharacteristic
564C22C47×#54611yescharacteristic
565C22C47×#54711yescharacteristic
566C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
567C22C2×#137×C4711yescharacteristic
568C22C47×#57711yescharacteristic
569C22C47×#57711yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—41no—
574C4—42no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4C47×#53311yescharacteristic
584C4C47×#54411yescharacteristic
585C4C47×#55111yescharacteristic
586C4C47×#55211yescharacteristic
587C2—42no—
588C2C47×#243811yescharacteristic
589C2C47×#307911yescharacteristic
590C2C47×#308411yescharacteristic
591C2C47×#332011yescharacteristic
592C2C47×#332411yescharacteristic
593C2C47×#334511yescharacteristic
594C2C47×#335611yescharacteristic
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×#2099C2semidirect
4. C47×#2088C2semidirect
5. C47×#2086C2semidirect
6. C47×#2058C2semidirect
7. C47×#1987C2semidirect
8. C47×#1948C2semidirect
9. C47×#1921C2semidirect
10. C47×#1919C2semidirect
73. #117×C47Q8semidirect
258. #26007C47direct (N × H)
292. #2099C2×C47semidirect
293. #2088C2×C47semidirect
294. #2086C2×C47semidirect
295. #2058C2×C47semidirect
296. #1987C2×C47semidirect
297. #1948C2×C47semidirect
298. #1921C2×C47semidirect
299. #1919C2×C47semidirect
356. C47#26007direct (N × H)
371. #117Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#24402
C47×#23472
C47×#20992
C47×#20882
C47×#20862
C47×#20582
C47×#19872
C47×#19482
C47×#19212
C47×#19192
C47×#18532
C47×#18512
C47×#18252
C47×#18092
C47×#17362
#2600747