Finite Group Databasebeta

← C47×#24435 #26064133

Subgroups — C47×#24435 #26064133

Order 12032.

1550 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#550C211yesmaximal, characteristic, complemented
2C2×C47×#466C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic, complemented
4C2×C47×#449C211yesmaximal, characteristic, complemented
5C2×C47×#416C211yesmaximal, characteristic, complemented
6C47×#2414C211yesmaximal, characteristic, complemented
7C47×#2041C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#2011C211yesmaximal, characteristic, complemented
10C47×#1999C211yesmaximal, characteristic, complemented
11C47×#1880C211yesmaximal, characteristic, complemented
12C47×#1875C211yesmaximal, characteristic, complemented
13C47×#1869C211yesmaximal, characteristic, complemented
14C47×#1863C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C22×D8×C47C2211yescharacteristic
21C23×C8×C47C2211yescharacteristic
22C47×#550—24no—
23C47×#550—24no—
24C2×#127×C47—21no—
25C2×#127×C47C2211yescharacteristic
26C2×#121×C47—21no—
27C2×#121×C47—21no—
28C2×#121×C47C2211yescharacteristic
29C2×#121×C47C2211yescharacteristic
30C2×#121×C47C2211yescharacteristic
31C2×#121×C47C2211yescharacteristic
32C2×C4×Q8×C47C2211yescharacteristic
33C2×C4×D4×C47—21no—
34C2×C4×D4×C47C2211yescharacteristic
35C2×#117×C47C2211yescharacteristic
36C47×#466—24no—
37C47×#449—24no—
38C47×#449—24no—
39C2×#107×C47C2211yescharacteristic
40C47×#416—24no—
41C2×#103×C47C2211yescharacteristic
42C2×#103×C47C2211yescharacteristic
43C2×#103×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
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
54C47×#394—21no—
55C47×#392—21no—
56C47×#390—21no—
57C47×#390C2211yescharacteristic
58C47×#389C2211yescharacteristic
59C47×#388—21no—
60C47×#380C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#336C2211yescharacteristic
64C47×#336C2211yescharacteristic
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—22no—
70C2×#41×C47—22no—
71C2×#41×C47—22no—
72C2×#41×C47—41no—
73C2×#41×C47—41no—
74C2×#41×C47—41no—
75C2×#41×C47—41no—
76C2×#41×C47D414yescomplemented
77C22×Q8×C47C2311yescharacteristic
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47—21no—
83C22×D4×C47—21no—
84C22×D4×C47—21no—
85C22×D4×C47—21no—
86C22×D4×C47D411yescharacteristic
87C22×D4×C47C2311yescharacteristic
88C22×D4×C47C2311yescharacteristic
89C22×D4×C47C2311yescharacteristic
90C23×C4×C47—21no—
91C23×C4×C47—21no—
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2311yescharacteristic
94C2×SD16×C47—22no—
95C2×SD16×C47—22no—
96C2×SD16×C47—22no—
97C2×D8×C47—22no—
98C2×D8×C47—22no—
99C2×D8×C47—22no—
100C2×D8×C47—41no—
101C2×D8×C47—41no—
102C2×D8×C47—41no—
103C22×C8×C47—22no—
104C22×C8×C47—22no—
105C22×C8×C47—41no—
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C22×C8×C47C2311yescharacteristic
109C22×C8×C47C2311yescharacteristic
110#127×C47—28no—
111#127×C47—22no—
112#127×C47—22no—
113#121×C47—28no—
114#121×C47—28no—
115#121×C47—22no—
116#121×C47—22no—
117#121×C47—22no—
118#121×C47—22no—
119#121×C47—22no—
120#121×C47—22no—
121#121×C47—41no—
122#121×C47D414yescomplemented
123C4×Q8×C47—22no—
124C4×Q8×C47—22no—
125C4×D4×C47—28no—
126C4×D4×C47—22no—
127C4×D4×C47—22no—
128#117×C47—22no—
129#117×C47—41no—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47D411yescharacteristic
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
148C2×C42×C47—21no—
149C2×C42×C47C2311yescharacteristic
150#107×C47—22no—
151#103×C47—22no—
152#103×C47—22no—
153#103×C47D414yescomplemented
154#102×C47—22no—
155#102×C47—22no—
156#102×C47—22no—
157#102×C47—22no—
158#102×C47—22no—
159#102×C47—22no—
160#102×C47—41no—
161C22⋊C8×C47—22no—
162C22⋊C8×C47—22no—
163C22⋊C8×C47—41no—
164#95×C47—21no—
165#95×C47—21no—
166C24×C47—21no—
167C24×C47—21no—
168C24×C47—21no—
169C24×C47C2×D411yescharacteristic
170C24×C47C2×D411yescharacteristic
171#41×C47—28no—
172#41×C47—44no—
173#41×C47—44no—
174#41×C47—44no—
175#41×C47—44no—
176#41×C47—44no—
177#41×C47—44no—
178#41×C47—44no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47C2×D412yes—
183C2×Q8×C47C2×D412yes—
184C2×Q8×C47#4112yes—
185C2×D4×C47—24no—
186C2×D4×C47—24no—
187C2×D4×C47—22no—
188C2×D4×C47—24no—
189C2×D4×C47—24no—
190C2×D4×C47—24no—
191C2×D4×C47—24no—
192C2×D4×C47—22no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
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—21no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—41no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—42no—
215C2×D4×C47—42no—
216C2×D4×C47—42no—
217C2×D4×C47—42no—
218C2×D4×C47—42no—
219C2×D4×C47—81no—
220C2×D4×C47—81no—
221C2×D4×C47—81no—
222C2×D4×C47—81no—
223C2×D4×C47—81no—
224C2×D4×C47—81no—
225C2×D4×C47—81no—
226C2×D4×C47—81no—
227C2×D4×C47—81no—
228C2×D4×C47C2×D412yes—
229C2×D4×C47C2×D412yes—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—24no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—24no—
239C22×C4×C47—21no—
240C22×C4×C47—21no—
241C22×C4×C47—21no—
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—42no—
248C22×C4×C47—42no—
249C22×C4×C47—42no—
250C22×C4×C47—42no—
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47C2×D412yes—
255C22×C4×C47C2×D412yes—
256C22×C4×C47C2×D411yescharacteristic
257C22×C4×C47C2411yescharacteristic
258SD16×C47—44no—
259D8×C47—44no—
260D8×C47—44no—
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×C47—21no—
269C2×C8×C47—21no—
270C2×C8×C47—21no—
271C2×C8×C47—21no—
272C2×C8×C47—44no—
273C2×C8×C47C2×D412yes—
274C4⋊C4×C47—24no—
275C4⋊C4×C47—22no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—81no—
283C4⋊C4×C47C2×D412yes—
284C4⋊C4×C47C2×D412yes—
285C22⋊C4×C47—24no—
286C22⋊C4×C47—22no—
287C22⋊C4×C47—24no—
288C22⋊C4×C47—22no—
289C22⋊C4×C47—42no—
290C22⋊C4×C47—42no—
291C22⋊C4×C47—42no—
292C22⋊C4×C47—42no—
293C22⋊C4×C47—81no—
294C22⋊C4×C47—81no—
295C42×C47—24no—
296C42×C47—21no—
297C42×C47—21no—
298C42×C47—42no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—21no—
303C23×C47—21no—
304C23×C47—21no—
305C23×C47—21no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—21no—
309C23×C47—21no—
310C23×C47—21no—
311C23×C47—21no—
312C23×C47—21no—
313C23×C47—21no—
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—41no—
324C23×C47—41no—
325C23×C47—41no—
326C23×C47—41no—
327C23×C47—41no—
328C23×C47—41no—
329C23×C47—41no—
330C23×C47—41no—
331C23×C47—41no—
332C23×C47—41no—
333C23×C47#12012yes—
334C23×C47C22×D411yescharacteristic
335Q8×C47—22no—
336Q8×C47—22no—
337Q8×C47—22no—
338Q8×C47#12114yes—
339D4×C47—22no—
340D4×C47—22no—
341D4×C47—22no—
342D4×C47—22no—
343D4×C47—44no—
344D4×C47—48no—
345D4×C47—48no—
346D4×C47—48no—
347D4×C47—41no—
348D4×C47—41no—
349D4×C47—41no—
350D4×C47—41no—
351D4×C47—41no—
352D4×C47—41no—
353D4×C47—41no—
354D4×C47—41no—
355D4×C47—84no—
356D4×C47—84no—
357D4×C47—84no—
358D4×C47—84no—
359D4×C47—84no—
360C2×C4×C47—21no—
361C2×C4×C47—22no—
362C2×C4×C47—21no—
363C2×C4×C47—22no—
364C2×C4×C47—21no—
365C2×C4×C47—22no—
366C2×C4×C47—21no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—21no—
372C2×C4×C47—22no—
373C2×C4×C47—21no—
374C2×C4×C47—22no—
375C2×C4×C47—21no—
376C2×C4×C47—21no—
377C2×C4×C47—21no—
378C2×C4×C47—21no—
379C2×C4×C47—48no—
380C2×C4×C47—48no—
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—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47#12012yes—
396C2×C4×C47#13512yes—
397C2×C4×C47C22×D411yescharacteristic
398C2×C4×C47C22×D411yescharacteristic
399C2×C4×C47C22×D411yescharacteristic
400C2×C4×C47C2×#4111yescharacteristic
401C2×C4×C47H(5,𝔽2)11yescharacteristic
402C2×C4×C47H(5,𝔽2)11yescharacteristic
403C8×C47—22no—
404C8×C47—41no—
405C8×C47—41no—
406C8×C47—41no—
407#24435C4711yesmaximal, characteristic, direct product factor, Sylow
408C22×C47—22no—
409C22×C47—22no—
410C22×C47—22no—
411C22×C47—41no—
412C22×C47—41no—
413C22×C47—41no—
414C22×C47—41no—
415C22×C47—42no—
416C22×C47—42no—
417C22×C47—41no—
418C22×C47—41no—
419C22×C47—42no—
420C22×C47—42no—
421C22×C47—41no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47—41no—
425C22×C47—41no—
426C22×C47—41no—
427C22×C47—41no—
428C22×C47—81no—
429C22×C47—81no—
430C22×C47—81no—
431C22×C47—81no—
432C22×C47—81no—
433C22×C47—81no—
434C22×C47—81no—
435C22×C47—81no—
436C22×C47—81no—
437C22×C47—81no—
438C22×C47—81no—
439C22×C47—81no—
440C22×C47—81no—
441C22×C47—81no—
442C22×C47—81no—
443C22×C47C2×#12011yescharacteristic
444C22×C47D4211yescharacteristic
445C22×C47#54611yescharacteristic
446C22×C47C2×#13511yescharacteristic
447C22×C47#57511yescharacteristic
448C22×C47#57611yescharacteristic
449C22×C47#57611yescharacteristic
450C4×C47—22no—
451C4×C47—24no—
452C4×C47—22no—
453C4×C47—41no—
454C4×C47—41no—
455C4×C47—42no—
456C4×C47—42no—
457C4×C47—81no—
458C4×C47—81no—
459C4×C47C2×#12111yescharacteristic
460C4×C47#53411yescharacteristic
461C4×C47D4211yescharacteristic
462C4×C47#54611yescharacteristic
463C2×#550C2×C4711yescharacteristic, complemented
464C2×#466C2×C4711yescharacteristic, complemented
465C2×#449C2×C4711yescharacteristic, complemented
466C2×#449C2×C4711yescharacteristic, complemented
467C2×#416C2×C4711yescharacteristic, complemented
468#2414C2×C4711yescharacteristic, complemented
469#2041C2×C4711yescharacteristic, complemented
470#2033C2×C4711yescharacteristic, complemented
471#2011C2×C4711yescharacteristic, complemented
472#1999C2×C4711yescharacteristic, complemented
473#1880C2×C4711yescharacteristic, complemented
474#1875C2×C4711yescharacteristic, complemented
475#1869C2×C4711yescharacteristic, complemented
476#1863C2×C4711yescharacteristic, complemented
477#1788C2×C4711yescharacteristic, complemented
478C2×C47—42no—
479C2×C47—81no—
480C2×C47—82no—
481C2×C47—82no—
482C2×C47—161no—
483C2×C47#241011yescharacteristic
484C2×C47#300211yescharacteristic
485C2×C47#300811yescharacteristic
486C2×C47#326811yescharacteristic
487C2×C47#328711yescharacteristic
488C2×C47#330511yescharacteristic
489C2×C47#330911yescharacteristic
490C22×#41C22×C4711yescharacteristic
491C22×#41C22×C4711yescharacteristic
492C22×SD16C22×C4711yescharacteristic
493C22×D8C22×C4711yescharacteristic
494C22×D8C22×C4711yescharacteristic
495C23×C8C22×C4711yescharacteristic
496#550—24no—
497#550—24no—
498C2×#127—21no—
499C2×#127C22×C4711yescharacteristic
500C2×#121—21no—
501C2×#121—21no—
502C2×#121C22×C4711yescharacteristic
503C2×#121C22×C4711yescharacteristic
504C2×#121C22×C4711yescharacteristic
505C2×#121C22×C4711yescharacteristic
506C2×C4×Q8C22×C4711yescharacteristic
507C2×C4×D4—21no—
508C2×C4×D4C22×C4711yescharacteristic
509C2×#117C22×C4711yescharacteristic
510#466—24no—
511#449—24no—
512#449—24no—
513C2×#107C22×C4711yescharacteristic
514#416—24no—
515C2×#103C22×C4711yescharacteristic
516C2×#103C22×C4711yescharacteristic
517C2×#103C22×C4711yescharacteristic
518C2×#102C22×C4711yescharacteristic
519C2×#102C22×C4711yescharacteristic
520C2×#102C22×C4711yescharacteristic
521C2×#102C22×C4711yescharacteristic
522C2×#102C22×C4711yescharacteristic
523C2×#102C22×C4711yescharacteristic
524C2×#102C22×C4711yescharacteristic
525C2×C22⋊C8C22×C4711yescharacteristic
526C2×C22⋊C8C22×C4711yescharacteristic
527C2×C22⋊C8C22×C4711yescharacteristic
528#394—21no—
529#392—21no—
530#390—21no—
531#390C22×C4711yescharacteristic
532#389C22×C4711yescharacteristic
533#388—21no—
534#380C22×C4711yescharacteristic
535#340C22×C4711yescharacteristic
536#340C22×C4711yescharacteristic
537#336C22×C4711yescharacteristic
538#336C22×C4711yescharacteristic
539C47#2443511yescharacteristic, direct product factor, Sylow
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—41no—
548C2×#41—41no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41D4×C4714yescomplemented
552C22×Q8C23×C4711yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4D4×C4711yescharacteristic
562C22×D4C23×C4711yescharacteristic
563C22×D4C23×C4711yescharacteristic
564C22×D4C23×C4711yescharacteristic
565C23×C4—21no—
566C23×C4—21no—
567C23×C4C23×C4711yescharacteristic
568C23×C4C23×C4711yescharacteristic
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—41no—
576C2×D8—41no—
577C2×D8—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C4711yescharacteristic
582C22×C8C23×C4711yescharacteristic
583C22×C8C23×C4711yescharacteristic
584C22×C8C23×C4711yescharacteristic
585#127—28no—
586#127—22no—
587#127—22no—
588#121—28no—
589#121—28no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121D4×C4714yescomplemented
598C4×Q8—22no—
599C4×Q8—22no—
600C4×D4—28no—
601C4×D4—22no—
602C4×D4—22no—
603#117—22no—
604#117—41no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4D4×C4711yescharacteristic
608C2×C4⋊C4C23×C4711yescharacteristic
609C2×C4⋊C4C23×C4711yescharacteristic
610C2×C4⋊C4C23×C4711yescharacteristic
611C2×C4⋊C4C23×C4711yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4D4×C4711yescharacteristic
621C2×C22⋊C4D4×C4711yescharacteristic
622C2×C42—21no—
623C2×C42—21no—
624C2×C42C23×C4711yescharacteristic
625#107—22no—
626#103—22no—
627#103—22no—
628#103D4×C4714yescomplemented
629#102—22no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—41no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24C2×D4×C4711yescharacteristic
645C24C2×D4×C4711yescharacteristic
646#41—28no—
647#41—44no—
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C4712yes—
658C2×Q8C2×D4×C4712yes—
659C2×Q8#41×C4712yes—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—41no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C4712yes—
704C2×D4C2×D4×C4712yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—24no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4C2×D4×C4711yescharacteristic
727C22×C4C2×D4×C4711yescharacteristic
728C22×C4C2×D4×C4711yescharacteristic
729C22×C4C2×D4×C4712yes—
730C22×C4C2×D4×C4712yes—
731C22×C4C2×D4×C4711yescharacteristic
732C22×C4C24×C4711yescharacteristic
733SD16—44no—
734D8—44no—
735D8—44no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—44no—
748C2×C8C2×D4×C4712yes—
749C4⋊C4—24no—
750C4⋊C4—22no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—81no—
758C4⋊C4C2×D4×C4712yes—
759C4⋊C4C2×D4×C4712yes—
760C22⋊C4—24no—
761C22⋊C4—22no—
762C22⋊C4—24no—
763C22⋊C4—22no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C42—24no—
771C42—21no—
772C42—21no—
773C42—42no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23#120×C4712yes—
809C23C22×D4×C4711yescharacteristic
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8#121×C4714yes—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—22no—
818D4—44no—
819D4—48no—
820D4—48no—
821D4—48no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—48no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4#120×C4712yes—
871C2×C4#135×C4712yes—
872C2×C4C22×D4×C4711yescharacteristic
873C2×C4C22×D4×C4711yescharacteristic
874C2×C4C22×D4×C4711yescharacteristic
875C2×C4C2×#41×C4711yescharacteristic
876C2×C4H(5,𝔽2)×C4711yescharacteristic
877C2×C4H(5,𝔽2)×C4711yescharacteristic
878C8—22no—
879C8—41no—
880C8—41no—
881C8—41no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×#120×C4711yescharacteristic
918C22D42×C4711yescharacteristic
919C22C47×#54611yescharacteristic
920C22C2×#135×C4711yescharacteristic
921C22C47×#57511yescharacteristic
922C22C47×#57611yescharacteristic
923C22C47×#57611yescharacteristic
924C4—22no—
925C4—24no—
926C4—22no—
927C4—41no—
928C4—41no—
929C4—42no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×#121×C4711yescharacteristic
934C4C47×#53411yescharacteristic
935C4D42×C4711yescharacteristic
936C4C47×#54611yescharacteristic
937C2—42no—
938C2—81no—
939C2—82no—
940C2—82no—
941C2—161no—
942C2C47×#241011yescharacteristic
943C2C47×#300211yescharacteristic
944C2C47×#300811yescharacteristic
945C2C47×#326811yescharacteristic
946C2C47×#328711yescharacteristic
947C2C47×#330511yescharacteristic
948C2C47×#330911yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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
1. C2×C47×#550C2semidirect
2. C2×C47×#466C2semidirect
3. C2×C47×#449C2semidirect
4. C2×C47×#449C2semidirect
5. C2×C47×#416C2semidirect
6. C47×#2414C2semidirect
7. C47×#2041C2semidirect
8. C47×#2033C2semidirect
9. C47×#2011C2semidirect
10. C47×#1999C2semidirect
11. C47×#1880C2semidirect
12. C47×#1875C2semidirect
13. C47×#1869C2semidirect
14. C47×#1863C2semidirect
15. C47×#1788C2semidirect
76. C2×#41×C47D4semidirect
122. #121×C47D4semidirect
153. #103×C47D4semidirect
407. #24435C47direct (N × H)
463. C2×#550C2×C47semidirect
464. C2×#466C2×C47semidirect
465. C2×#449C2×C47semidirect
466. C2×#449C2×C47semidirect
467. C2×#416C2×C47semidirect
468. #2414C2×C47semidirect
469. #2041C2×C47semidirect
470. #2033C2×C47semidirect
471. #2011C2×C47semidirect
472. #1999C2×C47semidirect
473. #1880C2×C47semidirect
474. #1875C2×C47semidirect
475. #1869C2×C47semidirect
476. #1863C2×C47semidirect
477. #1788C2×C47semidirect
539. C47#24435direct (N × H)
551. C2×#41D4×C47semidirect
597. #121D4×C47semidirect
628. #103D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5502
C2×C47×#4662
C2×C47×#4492
C2×C47×#4162
C47×#24142
C47×#20412
C47×#20332
C47×#20112
C47×#19992
C47×#18802
C47×#18752
C47×#18692
C47×#18632
C47×#17882
#2443547