Finite Group Databasebeta

← C2×C47×#3232 #26100538

Subgroups — C2×C47×#3232 #26100538

Order 12032.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#529C211yesmaximal, characteristic
2C22×#125×C47C211yesmaximal, characteristic, complemented
3C47×#3232C2116yesmaximal, direct product factor
4C2×C47×#499C212yesmaximal, complemented
5C2×C47×#488C212yesmaximal, complemented
6C2×C47×#484C211yesmaximal, characteristic, complemented
7C2×C47×#481C211yesmaximal, characteristic
8C2×C47×#483C211yesmaximal, characteristic, complemented
9C2×C47×#480C211yesmaximal, characteristic
10C2×C47×#479C212yesmaximal, complemented
11C2×C47×#478C212yesmaximal, complemented
12C2×C47×#431C211yesmaximal, characteristic, complemented
13C47×#529—24no—
14C47×#529C2218yes—
15C2×#126×C47—21no—
16C2×#125×C47—21no—
17C2×#125×C47—21no—
18C2×#125×C47—24no—
19C2×#125×C47C2212yes—
20C2×#125×C47C2212yes—
21C2×#125×C47C2211yescharacteristic
22C2×#125×C47C2218yescomplemented
23C2×#124×C47C2211yescharacteristic
24C2×#123×C47—21no—
25C2×C22⋊Q8×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×C4×Q8×C47C2211yescharacteristic
28C2×C4×D4×C47—21no—
29C2×C4×D4×C47C2211yescharacteristic
30C2×#117×C47—21no—
31C22×C4⋊C4×C47—21no—
32C22×C4⋊C4×C47—21no—
33C22×C4⋊C4×C47C2211yescharacteristic
34C22×C4⋊C4×C47C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C47×#499C22116yescomplemented
37C47×#488C22116yescomplemented
38C47×#484C2218yescomplemented
39C47×#483C2218yescomplemented
40C47×#481C2218yes—
41C47×#480C2218yes—
42C47×#479C22116yescomplemented
43C47×#478C22116yescomplemented
44C47×#431C2218yescomplemented
45C2×#107×C47C2212yes—
46C2×#107×C47C2212yes—
47C2×#106×C47C2212yes—
48C2×#106×C47C2212yes—
49C2×C4⋊C8×C47C2212yes—
50C2×#103×C47C2212yes—
51C2×#103×C47C2212yes—
52C2×#102×C47C2212yes—
53C2×#102×C47C2212yes—
54C2×C22⋊C8×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic
56C2×C4×C8×C47C2212yes—
57C22×Q8×C47C2311yescharacteristic
58C22×D4×C47—21no—
59C22×D4×C47C2311yescharacteristic
60C23×C4×C47—21no—
61C23×C4×C47—21no—
62C23×C4×C47—21no—
63C23×C4×C47D411yescharacteristic
64C23×C4×C47D411yescharacteristic
65C23×C4×C47C2311yescharacteristic
66C22×C8×C47C2312yes—
67C22×C8×C47C2312yes—
68#126×C47—28no—
69#125×C47—24no—
70#125×C47—24no—
71#125×C47—28no—
72#125×C47—28no—
73#125×C47—22no—
74#125×C47C2318yes—
75#125×C47C2318yes—
76#125×C47C2314yes—
77#124×C47—22no—
78#124×C47C2314yes—
79#123×C47—28no—
80C22⋊Q8×C47—22no—
81C22⋊Q8×C47C2314yes—
82#121×C47—22no—
83#121×C47C2314yes—
84C4×Q8×C47—22no—
85C4×Q8×C47C2314yes—
86C4×D4×C47—28no—
87C4×D4×C47—22no—
88C4×D4×C47C2314yes—
89#117×C47—28no—
90C2×C4⋊C4×C47—22no—
91C2×C4⋊C4×C47—22no—
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47—22no—
94C2×C4⋊C4×C47—28no—
95C2×C4⋊C4×C47—28no—
96C2×C4⋊C4×C47—22no—
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47C2314yes—
105C2×C4⋊C4×C47C2314yes—
106C2×C4⋊C4×C47C2312yes—
107C2×C4⋊C4×C47C2312yes—
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C42×C47—21no—
116C2×C42×C47D411yescharacteristic
117C2×C42×C47D411yescharacteristic
118C2×C42×C47D414yes—
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121C2×C42×C47C2314yes—
122#107×C47C2318yes—
123#107×C47C2318yes—
124#106×C47C2318yes—
125#106×C47C2318yes—
126C4⋊C8×C47C2318yes—
127#103×C47C2318yes—
128#103×C47C2318yes—
129#102×C47C2318yes—
130#102×C47C2318yes—
131C22⋊C8×C47C2314yes—
132C22⋊C8×C47C2314yes—
133C4×C8×C47C2318yes—
134C24×C47—21no—
135C24×C47C2×D411yescharacteristic
136C2×Q8×C47—21no—
137C2×Q8×C47—24no—
138C2×Q8×C47C2412yes—
139C2×D4×C47—24no—
140C2×D4×C47—21no—
141C2×D4×C47—24no—
142C2×D4×C47—44no—
143C2×D4×C47C2412yes—
144C22×C4×C47—24no—
145C22×C4×C47—24no—
146C22×C4×C47—24no—
147C22×C4×C47—24no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—24no—
154C22×C4×C47—42no—
155C22×C4×C47—44no—
156C22×C4×C47—44no—
157C22×C4×C47—44no—
158C22×C4×C47C2×D412yes—
159C22×C4×C47C2×D414yes—
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2×D414yes—
166C22×C4×C47C2412yes—
167C22×C4×C47C2411yescharacteristic
168C2×C8×C47—24no—
169C2×C8×C47—24no—
170C2×C8×C47C2414yes—
171C2×C8×C47C2414yes—
172C4⋊C4×C47—28no—
173C4⋊C4×C47—28no—
174C4⋊C4×C47—28no—
175C4⋊C4×C47—28no—
176C4⋊C4×C47—24no—
177C4⋊C4×C47—24no—
178C4⋊C4×C47—22no—
179C4⋊C4×C47—22no—
180C4⋊C4×C47—24no—
181C4⋊C4×C47—24no—
182C4⋊C4×C47—24no—
183C4⋊C4×C47—24no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47C2414yes—
187C4⋊C4×C47C2414yes—
188C4⋊C4×C47C2412yes—
189C4⋊C4×C47C2412yes—
190C22⋊C4×C47—24no—
191C22⋊C4×C47—24no—
192C22⋊C4×C47—24no—
193C22⋊C4×C47—24no—
194C22⋊C4×C47—24no—
195C42×C47—24no—
196C42×C47C2×D414yes—
197C42×C47C2×D412yes—
198C42×C47C2×D412yes—
199C42×C47C2×D414yes—
200C42×C47C2412yes—
201C42×C47C2412yes—
202C23×C47—22no—
203C23×C47—22no—
204C23×C47—22no—
205C23×C47—42no—
206C23×C47—42no—
207C23×C47—42no—
208C23×C47#13514yes—
209C23×C47C22×D412yes—
210C23×C47C22×D411yescharacteristic
211Q8×C47—24no—
212Q8×C47—42no—
213D4×C47—24no—
214D4×C47—48no—
215D4×C47—42no—
216C2×C4×C47—22no—
217C2×C4×C47—28no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—24no—
223C2×C4×C47—24no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—24no—
228C2×C4×C47—24no—
229C2×C4×C47—44no—
230C2×C4×C47—48no—
231C2×C4×C47—48no—
232C2×C4×C47—42no—
233C2×C4×C47—48no—
234C2×C4×C47—44no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47—44no—
238C2×C4×C47C22×D412yes—
239C2×C4×C47C22×D412yes—
240C2×C4×C47C22×D412yes—
241C2×C4×C47C22×D412yes—
242C2×C4×C47C22×D412yes—
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C472−1+414yes—
245C2×C4×C47C2511yescharacteristic
246C8×C47—24no—
247C8×C47—24no—
248C2×#3232C4711yesmaximal, characteristic, direct product factor, Sylow
249C22×C47—22no—
250C22×C47—28no—
251C22×C47—22no—
252C22×C47—42no—
253C22×C47—42no—
254C22×C47—42no—
255C22×C47—84no—
256C22×C47#53612yes—
257C22×C47C2×#13514yes—
258C22×C47C2×#13512yes—
259C22×C47#57512yes—
260C22×C47C23×D411yescharacteristic
261C4×C47—22no—
262C4×C47—22no—
263C4×C47—22no—
264C4×C47—22no—
265C4×C47—22no—
266C4×C47—42no—
267C4×C47—44no—
268C4×C47—42no—
269C4×C47—42no—
270C4×C47—44no—
271C4×C47#53612yes—
272C4×C47C2×2−1+412yes—
273C2×#529C2×C4711yescharacteristic
274C22×#125C2×C4711yescharacteristic, complemented
275#3232C2×C47116yesdirect product factor
276C2×#499C2×C4712yescomplemented
277C2×#488C2×C4712yescomplemented
278C2×#484C2×C4711yescharacteristic, complemented
279C2×#481C2×C4711yescharacteristic
280C2×#483C2×C4711yescharacteristic, complemented
281C2×#480C2×C4711yescharacteristic
282C2×#479C2×C4712yescomplemented
283C2×#478C2×C4712yescomplemented
284C2×#431C2×C4711yescharacteristic, complemented
285C2×C47—24no—
286C2×C47—82no—
287C2×C47#323214yesdirect product factor
288C2×C47C2×#53611yescharacteristic
289C2×C47C22×#13511yescharacteristic
290C2×C47C2×#57511yescharacteristic
291#529—24no—
292#529C22×C4718yes—
293C2×#126—21no—
294C2×#125—21no—
295C2×#125—21no—
296C2×#125—24no—
297C2×#125C22×C4712yes—
298C2×#125C22×C4712yes—
299C2×#125C22×C4711yescharacteristic
300C2×#125C22×C4718yescomplemented
301C2×#124C22×C4711yescharacteristic
302C2×#123—21no—
303C2×C22⋊Q8C22×C4711yescharacteristic
304C2×#121C22×C4711yescharacteristic
305C2×C4×Q8C22×C4711yescharacteristic
306C2×C4×D4—21no—
307C2×C4×D4C22×C4711yescharacteristic
308C2×#117—21no—
309C22×C4⋊C4—21no—
310C22×C4⋊C4—21no—
311C22×C4⋊C4C22×C4711yescharacteristic
312C22×C4⋊C4C22×C4711yescharacteristic
313C22×C42C22×C4711yescharacteristic
314#499C22×C47116yescomplemented
315#488C22×C47116yescomplemented
316#484C22×C4718yescomplemented
317#483C22×C4718yescomplemented
318#481C22×C4718yes—
319#480C22×C4718yes—
320#479C22×C47116yescomplemented
321#478C22×C47116yescomplemented
322#431C22×C4718yescomplemented
323C2×#107C22×C4712yes—
324C2×#107C22×C4712yes—
325C2×#106C22×C4712yes—
326C2×#106C22×C4712yes—
327C2×C4⋊C8C22×C4712yes—
328C2×#103C22×C4712yes—
329C2×#103C22×C4712yes—
330C2×#102C22×C4712yes—
331C2×#102C22×C4712yes—
332C2×C22⋊C8C22×C4711yescharacteristic
333C2×C22⋊C8C22×C4711yescharacteristic
334C2×C4×C8C22×C4712yes—
335C47C2×#323211yescharacteristic, direct product factor, Sylow
336C22×Q8C23×C4711yescharacteristic
337C22×D4—21no—
338C22×D4C23×C4711yescharacteristic
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4D4×C4711yescharacteristic
343C23×C4D4×C4711yescharacteristic
344C23×C4C23×C4711yescharacteristic
345C22×C8C23×C4712yes—
346C22×C8C23×C4712yes—
347#126—28no—
348#125—24no—
349#125—24no—
350#125—28no—
351#125—28no—
352#125—22no—
353#125C23×C4718yes—
354#125C23×C4718yes—
355#125C23×C4714yes—
356#124—22no—
357#124C23×C4714yes—
358#123—28no—
359C22⋊Q8—22no—
360C22⋊Q8C23×C4714yes—
361#121—22no—
362#121C23×C4714yes—
363C4×Q8—22no—
364C4×Q8C23×C4714yes—
365C4×D4—28no—
366C4×D4—22no—
367C4×D4C23×C4714yes—
368#117—28no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4C23×C4712yes—
384C2×C4⋊C4C23×C4712yes—
385C2×C4⋊C4C23×C4714yes—
386C2×C4⋊C4C23×C4714yes—
387C2×C4⋊C4C23×C4711yescharacteristic
388C2×C4⋊C4C23×C4711yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C2×C42D4×C4711yescharacteristic
396C2×C42D4×C4711yescharacteristic
397C2×C42D4×C4714yes—
398C2×C42C23×C4711yescharacteristic
399C2×C42C23×C4711yescharacteristic
400C2×C42C23×C4714yes—
401#107C23×C4718yes—
402#107C23×C4718yes—
403#106C23×C4718yes—
404#106C23×C4718yes—
405C4⋊C8C23×C4718yes—
406#103C23×C4718yes—
407#103C23×C4718yes—
408#102C23×C4718yes—
409#102C23×C4718yes—
410C22⋊C8C23×C4714yes—
411C22⋊C8C23×C4714yes—
412C4×C8C23×C4718yes—
413C24—21no—
414C24C2×D4×C4711yescharacteristic
415C2×Q8—21no—
416C2×Q8—24no—
417C2×Q8C24×C4712yes—
418C2×D4—24no—
419C2×D4—21no—
420C2×D4—24no—
421C2×D4—44no—
422C2×D4C24×C4712yes—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—42no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4C2×D4×C4711yescharacteristic
438C22×C4C2×D4×C4711yescharacteristic
439C22×C4C2×D4×C4712yes—
440C22×C4C2×D4×C4711yescharacteristic
441C22×C4C2×D4×C4711yescharacteristic
442C22×C4C2×D4×C4711yescharacteristic
443C22×C4C2×D4×C4714yes—
444C22×C4C2×D4×C4714yes—
445C22×C4C24×C4712yes—
446C22×C4C24×C4711yescharacteristic
447C2×C8—24no—
448C2×C8—24no—
449C2×C8C24×C4714yes—
450C2×C8C24×C4714yes—
451C4⋊C4—28no—
452C4⋊C4—28no—
453C4⋊C4—28no—
454C4⋊C4—28no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4C24×C4714yes—
466C4⋊C4C24×C4714yes—
467C4⋊C4C24×C4712yes—
468C4⋊C4C24×C4712yes—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C42—24no—
475C42C2×D4×C4714yes—
476C42C2×D4×C4712yes—
477C42C2×D4×C4712yes—
478C42C2×D4×C4714yes—
479C42C24×C4712yes—
480C42C24×C4712yes—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23#135×C4714yes—
488C23C22×D4×C4712yes—
489C23C22×D4×C4711yescharacteristic
490Q8—24no—
491Q8—42no—
492D4—24no—
493D4—48no—
494D4—42no—
495C2×C4—22no—
496C2×C4—28no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—44no—
509C2×C4—48no—
510C2×C4—48no—
511C2×C4—42no—
512C2×C4—48no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4C22×D4×C4712yes—
518C2×C4C22×D4×C4712yes—
519C2×C4C22×D4×C4712yes—
520C2×C4C22×D4×C4712yes—
521C2×C4C22×D4×C4712yes—
522C2×C4C22×D4×C4711yescharacteristic
523C2×C42−1+4×C4714yes—
524C2×C4C25×C4711yescharacteristic
525C8—24no—
526C8—24no—
527C22—22no—
528C22—22no—
529C22—28no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22C47×#53612yes—
535C22C2×#135×C4714yes—
536C22C2×#135×C4712yes—
537C22C47×#57512yes—
538C22C23×D4×C4711yescharacteristic
539C4—22no—
540C4—22no—
541C4—22no—
542C4—22no—
543C4—22no—
544C4—44no—
545C4—42no—
546C4—42no—
547C4—44no—
548C4—42no—
549C4C47×#53612yes—
550C4C2×2−1+4×C4712yes—
551C2—24no—
552C2—82no—
553C2C47×#323214yesdirect product factor
554C2C2×C47×#53611yescharacteristic
555C2C22×#135×C4711yescharacteristic
556C2C2×C47×#57511yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC2×C4C25×C47
prime radicalC2×#121×C47C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#125×C47C2semidirect
3. C47×#3232C2direct (N × H)
4. C2×C47×#499C2semidirect
5. C2×C47×#488C2semidirect
6. C2×C47×#484C2semidirect
8. C2×C47×#483C2semidirect
10. C2×C47×#479C2semidirect
11. C2×C47×#478C2semidirect
12. C2×C47×#431C2semidirect
22. C2×#125×C47C22semidirect
36. C47×#499C22semidirect
37. C47×#488C22semidirect
38. C47×#484C22semidirect
39. C47×#483C22semidirect
42. C47×#479C22semidirect
43. C47×#478C22semidirect
44. C47×#431C22semidirect
248. C2×#3232C47direct (N × H)
274. C22×#125C2×C47semidirect
275. #3232C2×C47direct (N × H)
276. C2×#499C2×C47semidirect
277. C2×#488C2×C47semidirect
278. C2×#484C2×C47semidirect
280. C2×#483C2×C47semidirect
282. C2×#479C2×C47semidirect
283. C2×#478C2×C47semidirect
284. C2×#431C2×C47semidirect
287. C2×C47#3232direct (N × H)
300. C2×#125C22×C47semidirect
314. #499C22×C47semidirect
315. #488C22×C47semidirect
316. #484C22×C47semidirect
317. #483C22×C47semidirect
320. #479C22×C47semidirect
321. #478C22×C47semidirect
322. #431C22×C47semidirect
335. C47C2×#3232direct (N × H)
553. C2C47×#3232direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5292
C22×#125×C472
C47×#32322
C2×C47×#4992
C2×C47×#4882
C2×C47×#4842
C2×C47×#4812
C2×C47×#4832
C2×C47×#4802
C2×C47×#4792
C2×C47×#4782
C2×C47×#4312
C2×#323247