Finite Group Databasebeta

← C2×C47×#1890 #26060656

Subgroups — C2×C47×#1890 #26060656

Order 12032.

2102 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C47C211yesmaximal, characteristic
2C2×C47×#518C211yesmaximal, characteristic
3C22×#99×C47C211yesmaximal, characteristic
4C2×C47×#381C212yesmaximal, complemented
5C47×#1890C218yesmaximal, direct product factor
6C2×C47×#342C212yesmaximal, complemented
7C23×D4×C47C2211yescharacteristic
8C24×C4×C47C2211yescharacteristic
9C2×#123×C47—24no—
10C2×#123×C47—22no—
11C2×#123×C47C418yescomplemented
12C2×#123×C47C2214yes—
13C47×#518—22no—
14C47×#518—24no—
15C47×#518C2214yes—
16C2×C4×D4×C47—24no—
17C2×#117×C47—21no—
18C22×C4⋊C4×C47—21no—
19C22×C22⋊C4×C47—21no—
20C22×C22⋊C4×C47—21no—
21C22×C22⋊C4×C47C2212yes—
22C22×C22⋊C4×C47C2212yes—
23C22×C22⋊C4×C47C2211yescharacteristic
24C2×#99×C47—24no—
25C2×#99×C47C2214yes—
26C47×#381—24no—
27C47×#381C2218yescomplemented
28C2×#95×C47—24no—
29C47×#342C2218yescomplemented
30C25×C47D411yescharacteristic
31C25×C47C2311yescharacteristic
32C22×D4×C47—22no—
33C22×D4×C47—22no—
34C22×D4×C47—24no—
35C22×D4×C47C2×C414yes—
36C22×D4×C47D414yes—
37C22×D4×C47D412yes—
38C22×D4×C47C2312yes—
39C23×C4×C47—21no—
40C23×C4×C47—21no—
41C23×C4×C47—22no—
42C23×C4×C47—21no—
43C23×C4×C47—22no—
44C23×C4×C47—22no—
45C23×C4×C47—24no—
46C23×C4×C47—22no—
47C23×C4×C47—22no—
48C23×C4×C47C2×C414yescomplemented
49C23×C4×C47D411yescharacteristic
50C23×C4×C47D414yes—
51C23×C4×C47C2312yes—
52#123×C47—216no—
53#123×C47—28no—
54#123×C47C2×C4116yescomplemented
55C4×D4×C47—216no—
56C4×D4×C47—216no—
57#117×C47—24no—
58#117×C47—24no—
59C2×C4⋊C4×C47—22no—
60C2×C4⋊C4×C47—28no—
61C2×C4⋊C4×C47—24no—
62C2×C22⋊C4×C47—22no—
63C2×C22⋊C4×C47—24no—
64C2×C22⋊C4×C47—28no—
65C2×C22⋊C4×C47—22no—
66C2×C22⋊C4×C47—24no—
67C2×C22⋊C4×C47—24no—
68C2×C22⋊C4×C47—22no—
69C2×C22⋊C4×C47—22no—
70C2×C22⋊C4×C47—22no—
71C2×C22⋊C4×C47—21no—
72C2×C22⋊C4×C47—22no—
73C2×C22⋊C4×C47—24no—
74C2×C22⋊C4×C47—24no—
75C2×C22⋊C4×C47—22no—
76C2×C22⋊C4×C47C2×C414yescomplemented
77C2×C22⋊C4×C47D414yes—
78C2×C22⋊C4×C47C2314yes—
79C2×C22⋊C4×C47C2314yes—
80C2×C22⋊C4×C47C2312yes—
81C2×C42×C47—22no—
82#99×C47—28no—
83#95×C47—216no—
84C24×C47—21no—
85C24×C47—21no—
86C24×C47—22no—
87C24×C47—44no—
88C24×C47—44no—
89C24×C47C22⋊C414yes—
90C24×C47C22×C412yes—
91C24×C47C2×D411yescharacteristic
92C24×C47C2×D412yes—
93C24×C47C2×D412yes—
94C24×C47C2×D411yescharacteristic
95C24×C47C2×D412yes—
96C24×C47C2×D412yes—
97C24×C47#4114yes—
98C24×C47C2411yescharacteristic
99C2×D4×C47—28no—
100C2×D4×C47—28no—
101C2×D4×C47—24no—
102C2×D4×C47—28no—
103C2×D4×C47—28no—
104C2×D4×C47—24no—
105C2×D4×C47—24no—
106C2×D4×C47—24no—
107C2×D4×C47C22⋊C418yes—
108C2×D4×C47C22×C414yes—
109C2×D4×C47C2×D414yes—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—22no—
113C22×C4×C47—24no—
114C22×C4×C47—24no—
115C22×C4×C47—24no—
116C22×C4×C47—28no—
117C22×C4×C47—28no—
118C22×C4×C47—24no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—24no—
123C22×C4×C47—24no—
124C22×C4×C47—28no—
125C22×C4×C47—24no—
126C22×C4×C47—24no—
127C22×C4×C47—44no—
128C22×C4×C47—41no—
129C22×C4×C47—42no—
130C22×C4×C47—41no—
131C22×C4×C47—44no—
132C22×C4×C47—44no—
133C22×C4×C47—42no—
134C22×C4×C47—42no—
135C22×C4×C47—48no—
136C22×C4×C47—48no—
137C22×C4×C47—44no—
138C22×C4×C47—84no—
139C22×C4×C47C22⋊C414yes—
140C22×C4×C47C22×C414yescomplemented
141C22×C4×C47C2×D412yes—
142C22×C4×C47C2×D418yes—
143C4⋊C4×C47—28no—
144C4⋊C4×C47—216no—
145C22⋊C4×C47—28no—
146C22⋊C4×C47—216no—
147C22⋊C4×C47—24no—
148C22⋊C4×C47—24no—
149C22⋊C4×C47—24no—
150C22⋊C4×C47—24no—
151C22⋊C4×C47—24no—
152C22⋊C4×C47—22no—
153C22⋊C4×C47—24no—
154C22⋊C4×C47—24no—
155C22⋊C4×C47—44no—
156C22⋊C4×C47C22×C414yescomplemented
157C42×C47—28no—
158C23×C47—28no—
159C23×C47—24no—
160C23×C47—22no—
161C23×C47—24no—
162C23×C47—22no—
163C23×C47—24no—
164C23×C47—44no—
165C23×C47—44no—
166C23×C47—44no—
167C23×C47—42no—
168C23×C47—48no—
169C23×C47—42no—
170C23×C47—48no—
171C23×C47—44no—
172C23×C47—44no—
173C23×C47—84no—
174C23×C47—82no—
175C23×C47C2×C22⋊C412yes—
176C23×C47C2×C22⋊C414yes—
177C23×C47C2×C22⋊C412yes—
178C23×C47C4×D414yes—
179C23×C47C4×D414yes—
180C23×C47#12011yescharacteristic
181C23×C47#12012yes—
182C23×C47#12011yescharacteristic
183C23×C47#12114yes—
184C23×C47#12114yes—
185C23×C47#12312yes—
186C23×C47#12312yes—
187C23×C47C23×C411yescharacteristic
188C23×C47C22×D411yescharacteristic
189C23×C47C22×D412yes—
190C23×C47C22×D411yescharacteristic
191C23×C47C2×#4112yes—
192D4×C47—28no—
193D4×C47—28no—
194D4×C47—216no—
195C2×C4×C47—22no—
196C2×C4×C47—22no—
197C2×C4×C47—24no—
198C2×C4×C47—24no—
199C2×C4×C47—24no—
200C2×C4×C47—24no—
201C2×C4×C47—28no—
202C2×C4×C47—28no—
203C2×C4×C47—48no—
204C2×C4×C47—44no—
205C2×C4×C47—42no—
206C2×C4×C47—44no—
207C2×C4×C47—42no—
208C2×C4×C47—44no—
209C2×C4×C47—48no—
210C2×C4×C47—44no—
211C2×C4×C47—48no—
212C2×C4×C47—48no—
213C2×C4×C47—48no—
214C2×C4×C47—44no—
215C2×C4×C47—84no—
216C2×C4×C47—88no—
217C2×C4×C47—88no—
218C2×C4×C47C2×C22⋊C414yes—
219C2×#1890C4711yesmaximal, characteristic, direct product factor, Sylow
220C22×C47—24no—
221C22×C47—28no—
222C22×C47—24no—
223C22×C47—28no—
224C22×C47—24no—
225C22×C47—22no—
226C22×C47—24no—
227C22×C47—22no—
228C22×C47—24no—
229C22×C47—42no—
230C22×C47—44no—
231C22×C47—44no—
232C22×C47—42no—
233C22×C47—41no—
234C22×C47—41no—
235C22×C47—42no—
236C22×C47—44no—
237C22×C47—48no—
238C22×C47—44no—
239C22×C47—82no—
240C22×C47—84no—
241C22×C47#38612yes—
242C22×C47#38614yes—
243C22×C47#38612yes—
244C22×C47#45814yes—
245C22×C47C22×C22⋊C411yescharacteristic
246C22×C47C2×C4×D412yes—
247C22×C47C2×#12011yescharacteristic
248C22×C47C2×#12112yes—
249C22×C47C2×#12311yescharacteristic
250C4×C47—24no—
251C4×C47—44no—
252C4×C47—48no—
253C4×C47—44no—
254C4×C47—84no—
255C22×#123C2×C4711yescharacteristic
256C2×#518C2×C4711yescharacteristic
257C22×#99C2×C4711yescharacteristic
258C2×#381C2×C4712yescomplemented
259#1890C2×C4718yesdirect product factor
260C2×#342C2×C4712yescomplemented
261C2×C47—21no—
262C2×C47—22no—
263C2×C47—21no—
264C2×C47—22no—
265C2×C47—22no—
266C2×C47—24no—
267C2×C47—44no—
268C2×C47#189014yesdirect product factor
269C2×C47C2×#38611yescharacteristic
270C2×C47C2×#45812yes—
271C23×D4C22×C4711yescharacteristic
272C24×C4C22×C4711yescharacteristic
273C2×#123—24no—
274C2×#123—22no—
275C2×#123C4×C4718yescomplemented
276C2×#123C22×C4714yes—
277#518—22no—
278#518—24no—
279#518C22×C4714yes—
280C2×C4×D4—24no—
281C2×#117—21no—
282C22×C4⋊C4—21no—
283C22×C22⋊C4—21no—
284C22×C22⋊C4—21no—
285C22×C22⋊C4C22×C4712yes—
286C22×C22⋊C4C22×C4712yes—
287C22×C22⋊C4C22×C4711yescharacteristic
288C2×#99—24no—
289C2×#99C22×C4714yes—
290#381—24no—
291#381C22×C4718yescomplemented
292C2×#95—24no—
293#342C22×C4718yescomplemented
294C47C2×#189011yescharacteristic, direct product factor, Sylow
295C25D4×C4711yescharacteristic
296C25C23×C4711yescharacteristic
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—24no—
300C22×D4C2×C4×C4714yes—
301C22×D4D4×C4714yes—
302C22×D4D4×C4712yes—
303C22×D4C23×C4712yes—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—22no—
307C23×C4—21no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—24no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4C2×C4×C4714yescomplemented
314C23×C4D4×C4711yescharacteristic
315C23×C4D4×C4714yes—
316C23×C4C23×C4712yes—
317#123—216no—
318#123—28no—
319#123C2×C4×C47116yescomplemented
320C4×D4—216no—
321C4×D4—216no—
322#117—24no—
323#117—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—24no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4C2×C4×C4714yescomplemented
342C2×C22⋊C4D4×C4714yes—
343C2×C22⋊C4C23×C4714yes—
344C2×C22⋊C4C23×C4714yes—
345C2×C22⋊C4C23×C4712yes—
346C2×C42—22no—
347#99—28no—
348#95—216no—
349C24—21no—
350C24—21no—
351C24—22no—
352C24—44no—
353C24—44no—
354C24C22⋊C4×C4714yes—
355C24C22×C4×C4712yes—
356C24C2×D4×C4711yescharacteristic
357C24C2×D4×C4712yes—
358C24C2×D4×C4712yes—
359C24C2×D4×C4711yescharacteristic
360C24C2×D4×C4712yes—
361C24C2×D4×C4712yes—
362C24#41×C4714yes—
363C24C24×C4711yescharacteristic
364C2×D4—28no—
365C2×D4—28no—
366C2×D4—24no—
367C2×D4—28no—
368C2×D4—28no—
369C2×D4—24no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4C22⋊C4×C4718yes—
373C2×D4C22×C4×C4714yes—
374C2×D4C2×D4×C4714yes—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—28no—
382C22×C4—28no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—28no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—44no—
393C22×C4—41no—
394C22×C4—42no—
395C22×C4—41no—
396C22×C4—44no—
397C22×C4—44no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—48no—
401C22×C4—48no—
402C22×C4—44no—
403C22×C4—84no—
404C22×C4C22⋊C4×C4714yes—
405C22×C4C22×C4×C4714yescomplemented
406C22×C4C2×D4×C4712yes—
407C22×C4C2×D4×C4718yes—
408C4⋊C4—28no—
409C4⋊C4—216no—
410C22⋊C4—28no—
411C22⋊C4—216no—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—22no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—44no—
421C22⋊C4C22×C4×C4714yescomplemented
422C42—28no—
423C23—28no—
424C23—24no—
425C23—22no—
426C23—24no—
427C23—22no—
428C23—24no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—42no—
433C23—48no—
434C23—42no—
435C23—48no—
436C23—44no—
437C23—44no—
438C23—84no—
439C23—82no—
440C23C2×C22⋊C4×C4712yes—
441C23C2×C22⋊C4×C4714yes—
442C23C2×C22⋊C4×C4712yes—
443C23C4×D4×C4714yes—
444C23C4×D4×C4714yes—
445C23#120×C4711yescharacteristic
446C23#120×C4712yes—
447C23#120×C4711yescharacteristic
448C23#121×C4714yes—
449C23#121×C4714yes—
450C23#123×C4712yes—
451C23#123×C4712yes—
452C23C23×C4×C4711yescharacteristic
453C23C22×D4×C4711yescharacteristic
454C23C22×D4×C4712yes—
455C23C22×D4×C4711yescharacteristic
456C23C2×#41×C4712yes—
457D4—28no—
458D4—28no—
459D4—216no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—28no—
467C2×C4—28no—
468C2×C4—48no—
469C2×C4—44no—
470C2×C4—48no—
471C2×C4—42no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—48no—
476C2×C4—44no—
477C2×C4—48no—
478C2×C4—48no—
479C2×C4—44no—
480C2×C4—84no—
481C2×C4—88no—
482C2×C4—88no—
483C2×C4C2×C22⋊C4×C4714yes—
484C22—24no—
485C22—28no—
486C22—24no—
487C22—28no—
488C22—24no—
489C22—22no—
490C22—24no—
491C22—22no—
492C22—24no—
493C22—42no—
494C22—44no—
495C22—44no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—42no—
500C22—44no—
501C22—48no—
502C22—44no—
503C22—82no—
504C22—84no—
505C22C47×#38612yes—
506C22C47×#38614yes—
507C22C47×#38612yes—
508C22C47×#45814yes—
509C22C22×C22⋊C4×C4711yescharacteristic
510C22C2×C4×D4×C4712yes—
511C22C2×#120×C4711yescharacteristic
512C22C2×#121×C4712yes—
513C22C2×#123×C4711yescharacteristic
514C4—24no—
515C4—44no—
516C4—44no—
517C4—48no—
518C4—84no—
519C2—21no—
520C2—22no—
521C2—21no—
522C2—22no—
523C2—22no—
524C2—24no—
525C2—44no—
526C2C47×#189014yesdirect product factor
527C2C2×C47×#38611yescharacteristic
528C2C2×C47×#45812yes—
subgroupG/H
center, socleC23×C47#120
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC23×D4×C47C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C47×#381C2semidirect
5. C47×#1890C2direct (N × H)
6. C2×C47×#342C2semidirect
11. C2×#123×C47C4semidirect
27. C47×#381C22semidirect
29. C47×#342C22semidirect
48. C23×C4×C47C2×C4semidirect
54. #123×C47C2×C4semidirect
76. C2×C22⋊C4×C47C2×C4semidirect
140. C22×C4×C47C22×C4semidirect
156. C22⋊C4×C47C22×C4semidirect
219. C2×#1890C47direct (N × H)
258. C2×#381C2×C47semidirect
259. #1890C2×C47direct (N × H)
260. C2×#342C2×C47semidirect
268. C2×C47#1890direct (N × H)
275. C2×#123C4×C47semidirect
291. #381C22×C47semidirect
293. #342C22×C47semidirect
294. C47C2×#1890direct (N × H)
313. C23×C4C2×C4×C47semidirect
319. #123C2×C4×C47semidirect
341. C2×C22⋊C4C2×C4×C47semidirect
405. C22×C4C22×C4×C47semidirect
421. C22⋊C4C22×C4×C47semidirect
526. C2C47×#1890direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C472
C2×C47×#5182
C22×#99×C472
C2×C47×#3812
C47×#18902
C2×C47×#3422
C2×#189047