Finite Group Databasebeta

← C47×#24452 #26064150

Subgroups — C47×#24452 #26064150

Order 12032.

1592 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#546C211yesmaximal, characteristic
2C2×C47×#468C211yesmaximal, characteristic, complemented
3C2×C47×#452C211yesmaximal, characteristic, complemented
4C2×C47×#450C211yesmaximal, characteristic, complemented
5C2×C47×#417C211yesmaximal, characteristic, complemented
6C47×#2417C211yesmaximal, characteristic, complemented
7C47×#2042C211yesmaximal, characteristic, complemented
8C47×#2036C211yesmaximal, characteristic, complemented
9C47×#2015C211yesmaximal, characteristic, complemented
10C47×#2001C211yesmaximal, characteristic, complemented
11C47×#1877C211yesmaximal, characteristic, complemented
12C47×#1874C211yesmaximal, characteristic, complemented
13C47×#1870C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C22×Q16×C47C2211yescharacteristic, complemented
19C22×SD16×C47C2211yescharacteristic
20C22×SD16×C47C2211yescharacteristic
21C22×M16×C47C2211yescharacteristic, complemented
22C47×#546—24no—
23C47×#546—24no—
24C2×#124×C47C2211yescharacteristic
25C2×#123×C47—21no—
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×C22⋊Q8×C47C2211yescharacteristic, complemented
29C2×#121×C47—21no—
30C2×#121×C47C2211yescharacteristic
31C2×#120×C47—21no—
32C2×C4×D4×C47C2211yescharacteristic
33C2×C4×D4×C47C2211yescharacteristic
34C22×C4⋊C4×C47C2211yescharacteristic, complemented
35C22×C22⋊C4×C47—21no—
36C47×#468—24no—
37C47×#452—24no—
38C47×#450—24no—
39C2×#107×C47C2211yescharacteristic, complemented
40C47×#417—24no—
41C2×#103×C47C2211yescharacteristic, complemented
42C2×#103×C47C2211yescharacteristic, complemented
43C2×#103×C47C2211yescharacteristic, complemented
44C2×#103×C47C2211yescharacteristic, complemented
45C2×#102×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C2×#102×C47C2211yescharacteristic
48C2×#102×C47C2211yescharacteristic
49C2×#102×C47C2211yescharacteristic
50C2×#102×C47C2211yescharacteristic
51C2×C22⋊C8×C47C2211yescharacteristic
52C2×C22⋊C8×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic, complemented
54C47×#398—21no—
55C47×#396—21no—
56C47×#391C2211yescharacteristic, complemented
57C47×#389C2211yescharacteristic, complemented
58C47×#386—21no—
59C47×#380—21no—
60C47×#380C2211yescharacteristic
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C47×#336C2211yescharacteristic, complemented
64C47×#336C2211yescharacteristic, complemented
65C25×C47—21no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—41no—
70C2×#41×C47—41no—
71C2×#41×C47D414yes—
72C22×Q8×C47C2311yescharacteristic
73C22×Q8×C47C2311yescharacteristic
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—22no—
77C22×D4×C47—22no—
78C22×D4×C47—22no—
79C22×D4×C47—22no—
80C22×D4×C47—21no—
81C22×D4×C47—41no—
82C22×D4×C47—41no—
83C22×D4×C47D411yescharacteristic
84C22×D4×C47C2311yescharacteristic
85C22×D4×C47C2311yescharacteristic
86C23×C4×C47—21no—
87C23×C4×C47—21no—
88C23×C4×C47—21no—
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C2×Q16×C47—22no—
92C2×Q16×C47—41no—
93C2×Q16×C47—41no—
94C2×SD16×C47—22no—
95C2×SD16×C47—22no—
96C2×SD16×C47—22no—
97C2×SD16×C47—22no—
98C2×SD16×C47—22no—
99C2×SD16×C47—41no—
100C2×M16×C47—22no—
101C2×M16×C47—22no—
102C2×M16×C47—41no—
103C22×C8×C47C2311yescharacteristic
104C22×C8×C47C2311yescharacteristic
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107#124×C47—22no—
108#124×C47—22no—
109#123×C47—28no—
110C22⋊Q8×C47—22no—
111C22⋊Q8×C47—22no—
112C22⋊Q8×C47—22no—
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47—22no—
115C22⋊Q8×C47—41no—
116#121×C47—28no—
117#121×C47—22no—
118#121×C47D414yes—
119#120×C47—28no—
120C4×D4×C47—22no—
121C4×D4×C47—22no—
122C4×D4×C47—22no—
123C4×D4×C47—22no—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—22no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47—21no—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47—41no—
131C2×C4⋊C4×C47D411yescharacteristic
132C2×C4⋊C4×C47C2311yescharacteristic
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C22⋊C4×C47—28no—
137C2×C22⋊C4×C47—21no—
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47—21no—
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47—21no—
143C2×C22⋊C4×C47—21no—
144C2×C22⋊C4×C47—21no—
145C2×C22⋊C4×C47D411yescharacteristic
146C2×C22⋊C4×C47D411yescharacteristic
147C2×C42×C47C2311yescharacteristic
148#107×C47—22no—
149#103×C47—22no—
150#103×C47—22no—
151#103×C47—22no—
152#103×C47—22no—
153#102×C47—22no—
154#102×C47—22no—
155#102×C47—22no—
156#102×C47—22no—
157#102×C47—41no—
158#102×C47D414yescomplemented
159C22⋊C8×C47—22no—
160C22⋊C8×C47—22no—
161C22⋊C8×C47—41no—
162#95×C47—21no—
163#95×C47—21no—
164#95×C47—21no—
165#95×C47—21no—
166C24×C47—21no—
167C24×C47—24no—
168C24×C47—21no—
169C24×C47—42no—
170C24×C47—42no—
171C24×C47—42no—
172C24×C47—42no—
173C24×C47—81no—
174C24×C47—81no—
175C24×C47C2×D411yescharacteristic
176C24×C47C2×D411yescharacteristic
177#41×C47—28no—
178#41×C47—44no—
179#41×C47—44no—
180#41×C47—44no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47C2×D412yes—
193C2×D4×C47—24no—
194C2×D4×C47—22no—
195C2×D4×C47—24no—
196C2×D4×C47—22no—
197C2×D4×C47—24no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—41no—
207C2×D4×C47—42no—
208C2×D4×C47—42no—
209C2×D4×C47—44no—
210C2×D4×C47—44no—
211C2×D4×C47—44no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—44no—
215C2×D4×C47—81no—
216C2×D4×C47—81no—
217C2×D4×C47C2×D412yes—
218C2×D4×C47C2×D412yes—
219C2×D4×C47C2×D412yes—
220C2×D4×C47#4112yes—
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—24no—
229C22×C4×C47—24no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—42no—
240C22×C4×C47—42no—
241C22×C4×C47—42no—
242C22×C4×C47—42no—
243C22×C4×C47—81no—
244C22×C4×C47—81no—
245C22×C4×C47—81no—
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D412yes—
251C22×C4×C47C2×D412yes—
252C22×C4×C47C2411yescharacteristic
253Q16×C47—44no—
254SD16×C47—44no—
255SD16×C47—44no—
256M16×C47—44no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
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×C47C2×D412yes—
269C4⋊C4×C47—24no—
270C4⋊C4×C47—22no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—42no—
278C4⋊C4×C47—42no—
279C4⋊C4×C47—42no—
280C4⋊C4×C47—81no—
281C4⋊C4×C47C2×D412yes—
282C4⋊C4×C47C2×D412yes—
283C22⋊C4×C47—24no—
284C22⋊C4×C47—24no—
285C22⋊C4×C47—24no—
286C22⋊C4×C47—24no—
287C22⋊C4×C47—22no—
288C22⋊C4×C47—22no—
289C22⋊C4×C47—24no—
290C22⋊C4×C47—42no—
291C22⋊C4×C47—42no—
292C22⋊C4×C47—81no—
293C42×C47—21no—
294C42×C47—21no—
295C23×C47—21no—
296C23×C47—22no—
297C23×C47—21no—
298C23×C47—21no—
299C23×C47—22no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—22no—
303C23×C47—21no—
304C23×C47—21no—
305C23×C47—21no—
306C23×C47—21no—
307C23×C47—21no—
308C23×C47—21no—
309C23×C47—21no—
310C23×C47—22no—
311C23×C47—48no—
312C23×C47—48no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—41no—
319C23×C47—41no—
320C23×C47—41no—
321C23×C47—41no—
322C23×C47—41no—
323C23×C47—84no—
324C23×C47—84no—
325C23×C47—84no—
326C23×C47—84no—
327C23×C47—84no—
328C23×C47#12012yes—
329C23×C47#13712yes—
330C23×C47C22×D411yescharacteristic
331Q8×C47—22no—
332Q8×C47—22no—
333Q8×C47—41no—
334Q8×C47—41no—
335Q8×C47—41no—
336Q8×C47—41no—
337Q8×C47—41no—
338Q8×C47—41no—
339D4×C47—22no—
340D4×C47—22no—
341D4×C47—22no—
342D4×C47—22no—
343D4×C47—22no—
344D4×C47—44no—
345D4×C47—48no—
346D4×C47—48no—
347D4×C47—41no—
348D4×C47—41no—
349D4×C47—84no—
350D4×C47#12114yes—
351C2×C4×C47—21no—
352C2×C4×C47—21no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—21no—
362C2×C4×C47—22no—
363C2×C4×C47—21no—
364C2×C4×C47—21no—
365C2×C4×C47—21no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47—48no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—84no—
390C2×C4×C47—84no—
391C2×C4×C47#12012yes—
392C2×C4×C47C22×D411yescharacteristic
393C2×C4×C47C22×D411yescharacteristic
394C2×C4×C47C22×D411yescharacteristic
395C2×C4×C47C2×#4111yescharacteristic
396C2×C4×C47H(5,𝔽2)11yescharacteristic
397C2×C4×C47H(5,𝔽2)11yescharacteristic
398C8×C47—22no—
399C8×C47—41no—
400C8×C47—41no—
401C8×C47—41no—
402#24452C4711yesmaximal, characteristic, direct product factor, Sylow
403C22×C47—22no—
404C22×C47—24no—
405C22×C47—22no—
406C22×C47—22no—
407C22×C47—22no—
408C22×C47—22no—
409C22×C47—22no—
410C22×C47—41no—
411C22×C47—42no—
412C22×C47—41no—
413C22×C47—42no—
414C22×C47—42no—
415C22×C47—41no—
416C22×C47—41no—
417C22×C47—41no—
418C22×C47—42no—
419C22×C47—41no—
420C22×C47—42no—
421C22×C47—41no—
422C22×C47—41no—
423C22×C47—42no—
424C22×C47—42no—
425C22×C47—42no—
426C22×C47—42no—
427C22×C47—816no—
428C22×C47—81no—
429C22×C47—81no—
430C22×C47—81no—
431C22×C47—81no—
432C22×C47C2×#12011yescharacteristic
433C22×C47D4211yescharacteristic
434C22×C47#54611yescharacteristic
435C22×C47C2×#13711yescharacteristic
436C22×C47#57511yescharacteristic
437C22×C47#57611yescharacteristic
438C22×C47#57711yescharacteristic
439C4×C47—22no—
440C4×C47—41no—
441C4×C47—42no—
442C4×C47—41no—
443C4×C47—41no—
444C4×C47—42no—
445C4×C47—42no—
446C4×C47—81no—
447C4×C47—81no—
448C4×C47—81no—
449C4×C47C2×#12111yescharacteristic
450C4×C47#53411yescharacteristic
451C4×C47D4211yescharacteristic
452C4×C47#54611yescharacteristic
453C2×#546C2×C4711yescharacteristic
454C2×#468C2×C4711yescharacteristic, complemented
455C2×#452C2×C4711yescharacteristic, complemented
456C2×#450C2×C4711yescharacteristic, complemented
457C2×#417C2×C4711yescharacteristic, complemented
458#2417C2×C4711yescharacteristic, complemented
459#2042C2×C4711yescharacteristic, complemented
460#2036C2×C4711yescharacteristic, complemented
461#2015C2×C4711yescharacteristic, complemented
462#2001C2×C4711yescharacteristic, complemented
463#1877C2×C4711yescharacteristic, complemented
464#1874C2×C4711yescharacteristic, complemented
465#1870C2×C4711yescharacteristic, complemented
466#1862C2×C4711yescharacteristic, complemented
467#1786C2×C4711yescharacteristic, complemented
468C2×C47—42no—
469C2×C47—42no—
470C2×C47—44no—
471C2×C47—82no—
472C2×C47#241011yescharacteristic
473C2×C47#300711yescharacteristic
474C2×C47#301211yescharacteristic
475C2×C47#326611yescharacteristic
476C2×C47#327311yescharacteristic
477C2×C47#331411yescharacteristic
478C2×C47#332311yescharacteristic
479C22×#41C22×C4711yescharacteristic
480C23×D4C22×C4711yescharacteristic
481C22×Q16C22×C4711yescharacteristic, complemented
482C22×SD16C22×C4711yescharacteristic
483C22×SD16C22×C4711yescharacteristic
484C22×M16C22×C4711yescharacteristic, complemented
485#546—24no—
486#546—24no—
487C2×#124C22×C4711yescharacteristic
488C2×#123—21no—
489C2×C22⋊Q8C22×C4711yescharacteristic
490C2×C22⋊Q8C22×C4711yescharacteristic
491C2×C22⋊Q8C22×C4711yescharacteristic, complemented
492C2×#121—21no—
493C2×#121C22×C4711yescharacteristic
494C2×#120—21no—
495C2×C4×D4C22×C4711yescharacteristic
496C2×C4×D4C22×C4711yescharacteristic
497C22×C4⋊C4C22×C4711yescharacteristic, complemented
498C22×C22⋊C4—21no—
499#468—24no—
500#452—24no—
501#450—24no—
502C2×#107C22×C4711yescharacteristic, complemented
503#417—24no—
504C2×#103C22×C4711yescharacteristic, complemented
505C2×#103C22×C4711yescharacteristic, complemented
506C2×#103C22×C4711yescharacteristic, complemented
507C2×#103C22×C4711yescharacteristic, complemented
508C2×#102C22×C4711yescharacteristic
509C2×#102C22×C4711yescharacteristic
510C2×#102C22×C4711yescharacteristic
511C2×#102C22×C4711yescharacteristic
512C2×#102C22×C4711yescharacteristic
513C2×#102C22×C4711yescharacteristic
514C2×C22⋊C8C22×C4711yescharacteristic
515C2×C22⋊C8C22×C4711yescharacteristic
516C2×C22⋊C8C22×C4711yescharacteristic, complemented
517#398—21no—
518#396—21no—
519#391C22×C4711yescharacteristic, complemented
520#389C22×C4711yescharacteristic, complemented
521#386—21no—
522#380—21no—
523#380C22×C4711yescharacteristic
524#340C22×C4711yescharacteristic, complemented
525#340C22×C4711yescharacteristic, complemented
526#336C22×C4711yescharacteristic, complemented
527#336C22×C4711yescharacteristic, complemented
528C47#2445211yescharacteristic, direct product factor, Sylow
529C25—21no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C4714yes—
536C22×Q8C23×C4711yescharacteristic
537C22×Q8C23×C4711yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—21no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4D4×C4711yescharacteristic
548C22×D4C23×C4711yescharacteristic
549C22×D4C23×C4711yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C23×C4711yescharacteristic
554C23×C4C23×C4711yescharacteristic
555C2×Q16—22no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C22×C8C23×C4711yescharacteristic
568C22×C8C23×C4711yescharacteristic
569C22×C8C23×C4711yescharacteristic
570C22×C8C23×C4711yescharacteristic
571#124—22no—
572#124—22no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580#121—28no—
581#121—22no—
582#121D4×C4714yes—
583#120—28no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4D4×C4711yescharacteristic
596C2×C4⋊C4C23×C4711yescharacteristic
597C2×C4⋊C4C23×C4711yescharacteristic
598C2×C4⋊C4C23×C4711yescharacteristic
599C2×C4⋊C4C23×C4711yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4D4×C4711yescharacteristic
610C2×C22⋊C4D4×C4711yescharacteristic
611C2×C42C23×C4711yescharacteristic
612#107—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—22no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—41no—
622#102D4×C4714yescomplemented
623C22⋊C8—22no—
624C22⋊C8—22no—
625C22⋊C8—41no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630C24—21no—
631C24—24no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×D4×C4711yescharacteristic
640C24C2×D4×C4711yescharacteristic
641#41—28no—
642#41—44no—
643#41—44no—
644#41—44no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8C2×D4×C4712yes—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—24no—
660C2×D4—22no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—41no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—44no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4C2×D4×C4712yes—
682C2×D4C2×D4×C4712yes—
683C2×D4C2×D4×C4712yes—
684C2×D4#41×C4712yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—81no—
708C22×C4—81no—
709C22×C4—81no—
710C22×C4C2×D4×C4711yescharacteristic
711C22×C4C2×D4×C4711yescharacteristic
712C22×C4C2×D4×C4711yescharacteristic
713C22×C4C2×D4×C4711yescharacteristic
714C22×C4C2×D4×C4712yes—
715C22×C4C2×D4×C4712yes—
716C22×C4C24×C4711yescharacteristic
717Q16—44no—
718SD16—44no—
719SD16—44no—
720M16—44no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C4712yes—
733C4⋊C4—24no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—81no—
745C4⋊C4C2×D4×C4712yes—
746C4⋊C4C2×D4×C4712yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—81no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—22no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—48no—
776C23—48no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23—84no—
792C23#120×C4712yes—
793C23#137×C4712yes—
794C23C22×D4×C4711yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—44no—
809D4—48no—
810D4—48no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#121×C4714yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—84no—
854C2×C4—84no—
855C2×C4#120×C4712yes—
856C2×C4C22×D4×C4711yescharacteristic
857C2×C4C22×D4×C4711yescharacteristic
858C2×C4C22×D4×C4711yescharacteristic
859C2×C4C2×#41×C4711yescharacteristic
860C2×C4H(5,𝔽2)×C4711yescharacteristic
861C2×C4H(5,𝔽2)×C4711yescharacteristic
862C8—22no—
863C8—41no—
864C8—41no—
865C8—41no—
866C22—22no—
867C22—22no—
868C22—24no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—816no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22C2×#120×C4711yescharacteristic
896C22D42×C4711yescharacteristic
897C22C47×#54611yescharacteristic
898C22C2×#137×C4711yescharacteristic
899C22C47×#57511yescharacteristic
900C22C47×#57611yescharacteristic
901C22C47×#57711yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4C2×#121×C4711yescharacteristic
913C4C47×#53411yescharacteristic
914C4D42×C4711yescharacteristic
915C4C47×#54611yescharacteristic
916C2—42no—
917C2—42no—
918C2—44no—
919C2—82no—
920C2C47×#241011yescharacteristic
921C2C47×#300711yescharacteristic
922C2C47×#301211yescharacteristic
923C2C47×#326611yescharacteristic
924C2C47×#327311yescharacteristic
925C2C47×#331411yescharacteristic
926C2C47×#332311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#468C2semidirect
3. C2×C47×#452C2semidirect
4. C2×C47×#450C2semidirect
5. C2×C47×#417C2semidirect
6. C47×#2417C2semidirect
7. C47×#2042C2semidirect
8. C47×#2036C2semidirect
9. C47×#2015C2semidirect
10. C47×#2001C2semidirect
11. C47×#1877C2semidirect
12. C47×#1874C2semidirect
13. C47×#1870C2semidirect
14. C47×#1862C2semidirect
15. C47×#1786C2semidirect
18. C22×Q16×C47C22semidirect
21. C22×M16×C47C22semidirect
28. C2×C22⋊Q8×C47C22semidirect
34. C22×C4⋊C4×C47C22semidirect
39. C2×#107×C47C22semidirect
41. C2×#103×C47C22semidirect
42. C2×#103×C47C22semidirect
43. C2×#103×C47C22semidirect
44. C2×#103×C47C22semidirect
53. C2×C22⋊C8×C47C22semidirect
56. C47×#391C22semidirect
57. C47×#389C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
63. C47×#336C22semidirect
64. C47×#336C22semidirect
158. #102×C47D4semidirect
402. #24452C47direct (N × H)
454. C2×#468C2×C47semidirect
455. C2×#452C2×C47semidirect
456. C2×#450C2×C47semidirect
457. C2×#417C2×C47semidirect
458. #2417C2×C47semidirect
459. #2042C2×C47semidirect
460. #2036C2×C47semidirect
461. #2015C2×C47semidirect
462. #2001C2×C47semidirect
463. #1877C2×C47semidirect
464. #1874C2×C47semidirect
465. #1870C2×C47semidirect
466. #1862C2×C47semidirect
467. #1786C2×C47semidirect
481. C22×Q16C22×C47semidirect
484. C22×M16C22×C47semidirect
491. C2×C22⋊Q8C22×C47semidirect
497. C22×C4⋊C4C22×C47semidirect
502. C2×#107C22×C47semidirect
504. C2×#103C22×C47semidirect
505. C2×#103C22×C47semidirect
506. C2×#103C22×C47semidirect
507. C2×#103C22×C47semidirect
516. C2×C22⋊C8C22×C47semidirect
519. #391C22×C47semidirect
520. #389C22×C47semidirect
524. #340C22×C47semidirect
525. #340C22×C47semidirect
526. #336C22×C47semidirect
527. #336C22×C47semidirect
528. C47#24452direct (N × H)
622. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5462
C2×C47×#4682
C2×C47×#4522
C2×C47×#4502
C2×C47×#4172
C47×#24172
C47×#20422
C47×#20362
C47×#20152
C47×#20012
C47×#18772
C47×#18742
C47×#18702
C47×#18622
C47×#17862
#2445247