Finite Group Databasebeta

← C47×#24364 #26064062

Subgroups — C47×#24364 #26064062

Order 12032.

1512 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C47C211yesmaximal, characteristic, complemented
2C2×C47×#463C211yesmaximal, characteristic, complemented
3C2×C47×#459C211yesmaximal, characteristic, complemented
4C2×C47×#449C211yesmaximal, characteristic, complemented
5C47×#2431C211yesmaximal, characteristic, complemented
6C47×#2339C211yesmaximal, characteristic, complemented
7C47×#2056C211yesmaximal, characteristic, complemented
8C47×#2055C211yesmaximal, characteristic, complemented
9C47×#2015C211yesmaximal, characteristic, complemented
10C47×#2014C211yesmaximal, characteristic, complemented
11C47×#1893C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic, complemented
13C47×#1877C211yesmaximal, characteristic, complemented
14C47×#1850C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C2×#135×C47—24no—
19C2×#135×C47—24no—
20C2×#135×C47—24no—
21C22×Q16×C47C2211yescharacteristic
22C22×SD16×C47C2211yescharacteristic
23C22×SD16×C47C2211yescharacteristic
24C22×SD16×C47C2211yescharacteristic
25C22×D8×C47C2211yescharacteristic
26C22×D8×C47C2211yescharacteristic
27C23×C8×C47C2211yescharacteristic
28C2×#127×C47C2211yescharacteristic
29C2×#124×C47C2211yescharacteristic
30C2×#121×C47C2211yescharacteristic
31C2×C4×D4×C47C2211yescharacteristic
32C2×C4×D4×C47C2211yescharacteristic
33C47×#463—24no—
34C47×#459—24no—
35C47×#449—24no—
36C2×C4⋊C8×C47C2211yescharacteristic
37C2×C4⋊C8×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C47×#392—21no—
48C47×#392—21no—
49C47×#391C2211yescharacteristic
50C47×#391C2211yescharacteristic
51C47×#391C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#386—21no—
54C47×#386—21no—
55C47×#386—21no—
56C47×#386—21no—
57C47×#381—21no—
58C47×#380C2211yescharacteristic
59C4×C22⋊C4×C47C2211yescharacteristic
60C2×#95×C47—21no—
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×Q8×C47C2311yescharacteristic
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47—21no—
83C22×D4×C47—21no—
84C22×D4×C47C2311yescharacteristic
85C22×D4×C47C2311yescharacteristic
86C22×D4×C47C2311yescharacteristic
87C23×C4×C47—21no—
88C23×C4×C47—21no—
89C23×C4×C47—21no—
90C23×C4×C47—21no—
91C23×C4×C47C2311yescharacteristic
92#135×C47—232no—
93C2×Q16×C47—22no—
94C2×Q16×C47—22no—
95C2×Q16×C47—22no—
96C2×SD16×C47—22no—
97C2×SD16×C47—22no—
98C2×SD16×C47—22no—
99C2×SD16×C47—22no—
100C2×SD16×C47—22no—
101C2×SD16×C47—22no—
102C2×SD16×C47—41no—
103C2×SD16×C47—41no—
104C2×SD16×C47D414yescomplemented
105C2×D8×C47—22no—
106C2×D8×C47—22no—
107C2×D8×C47—22no—
108C2×D8×C47—22no—
109C2×D8×C47—22no—
110C2×D8×C47D414yescomplemented
111C22×C8×C47—22no—
112C22×C8×C47—22no—
113C22×C8×C47—22no—
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117C22×C8×C47C2311yescharacteristic
118#127×C47—22no—
119#127×C47—41no—
120#124×C47—22no—
121#124×C47—41no—
122#121×C47—22no—
123#121×C47—22no—
124C4×D4×C47—22no—
125C4×D4×C47—22no—
126C4×D4×C47—41no—
127C4×D4×C47—41no—
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—21no—
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47D411yescharacteristic
140C2×C22⋊C4×C47D411yescharacteristic
141C2×C42×C47C2311yescharacteristic
142C2×C42×C47C2311yescharacteristic
143C4⋊C8×C47—22no—
144C4⋊C8×C47—22no—
145#103×C47—22no—
146#103×C47—22no—
147#103×C47—41no—
148#102×C47—22no—
149#102×C47—22no—
150#102×C47—22no—
151#102×C47—22no—
152#102×C47—41no—
153C22⋊C8×C47—22no—
154#95×C47—21no—
155#95×C47—21no—
156#95×C47—21no—
157#95×C47—21no—
158#95×C47—21no—
159#95×C47—21no—
160#95×C47—21no—
161#95×C47D411yescharacteristic
162#95×C47D411yescharacteristic
163C24×C47—21no—
164C24×C47—21no—
165C24×C47—21no—
166C24×C47C2×D411yescharacteristic
167#41×C47—28no—
168#41×C47—28no—
169#41×C47—44no—
170#41×C47—44no—
171#41×C47—44no—
172#41×C47—44no—
173#41×C47—44no—
174#41×C47—44no—
175C2×Q8×C47—21no—
176C2×Q8×C47—21no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47C2×D412yes—
186C2×Q8×C47C2×D412yes—
187C2×D4×C47—24no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
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—42no—
203C2×D4×C47—42no—
204C2×D4×C47—42no—
205C2×D4×C47—42no—
206C2×D4×C47—42no—
207C2×D4×C47—42no—
208C2×D4×C47—42no—
209C2×D4×C47—42no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—81no—
213C2×D4×C47—81no—
214C2×D4×C47—81no—
215C2×D4×C47—81no—
216C2×D4×C47C2×D412yes—
217C2×D4×C47C2×D412yes—
218C2×D4×C47C2×D412yes—
219C2×D4×C47C2×D412yes—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—24no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—42no—
231C22×C4×C47—42no—
232C22×C4×C47—42no—
233C22×C4×C47—42no—
234C22×C4×C47—42no—
235C22×C4×C47—42no—
236C22×C4×C47—42no—
237C22×C4×C47—42no—
238C22×C4×C47—42no—
239C22×C4×C47—81no—
240C22×C4×C47—81no—
241C22×C4×C47C2×D411yescharacteristic
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D412yes—
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47#4112yes—
248C22×C4×C47C2411yescharacteristic
249Q16×C47—28no—
250SD16×C47—28no—
251SD16×C47—28no—
252SD16×C47—44no—
253D8×C47—28no—
254D8×C47—44no—
255C2×C8×C47—28no—
256C2×C8×C47—21no—
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×C47C2×D412yes—
267C2×C8×C47C2×D412yes—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C22⋊C4×C47—22no—
275C22⋊C4×C47—41no—
276C22⋊C4×C47—42no—
277C22⋊C4×C47—42no—
278C22⋊C4×C47—42no—
279C22⋊C4×C47—42no—
280C22⋊C4×C47—42no—
281C22⋊C4×C47—81no—
282C22⋊C4×C47—81no—
283C22⋊C4×C47—81no—
284C42×C47—21no—
285C42×C47—21no—
286C42×C47—21no—
287C42×C47—21no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—21no—
292C23×C47—21no—
293C23×C47—21no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—21no—
297C23×C47—22no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47#12112yes—
316C23×C47C22×D411yescharacteristic
317Q8×C47—22no—
318Q8×C47—22no—
319Q8×C47—22no—
320Q8×C47—22no—
321Q8×C47—41no—
322Q8×C47—41no—
323Q8×C47—41no—
324Q8×C47—41no—
325D4×C47—22no—
326D4×C47—22no—
327D4×C47—22no—
328D4×C47—22no—
329D4×C47—22no—
330D4×C47—48no—
331D4×C47—48no—
332D4×C47—41no—
333D4×C47—41no—
334D4×C47—41no—
335D4×C47—41no—
336D4×C47—41no—
337D4×C47—41no—
338D4×C47—84no—
339D4×C47—84no—
340D4×C47—84no—
341D4×C47#12014yes—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—21no—
352C2×C4×C47—21no—
353C2×C4×C47—21no—
354C2×C4×C47—22no—
355C2×C4×C47—21no—
356C2×C4×C47—21no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—21no—
360C2×C4×C47—21no—
361C2×C4×C47—48no—
362C2×C4×C47—48no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
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—84no—
377C2×C4×C47—84no—
378C2×C4×C47#12112yes—
379C2×C4×C47#13512yescomplemented
380C2×C4×C47C22×D411yescharacteristic
381C2×C4×C47C22×D411yescharacteristic
382C2×C4×C47C22×D411yescharacteristic
383C2×C4×C47C2×#4111yescharacteristic
384C2×C4×C47H(5,𝔽2)11yescharacteristic
385C2×C4×C47H(5,𝔽2)11yescharacteristic
386C8×C47—22no—
387C8×C47—22no—
388C8×C47—41no—
389C8×C47—41no—
390#24364C4711yesmaximal, characteristic, direct product factor, Sylow
391C22×C47—22no—
392C22×C47—24no—
393C22×C47—22no—
394C22×C47—22no—
395C22×C47—41no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—41no—
399C22×C47—42no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—42no—
403C22×C47—42no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—42no—
408C22×C47—81no—
409C22×C47—81no—
410C22×C47—81no—
411C22×C47—81no—
412C22×C47—81no—
413C22×C47—81no—
414C22×C47—81no—
415C22×C47—81no—
416C22×C47—81no—
417C22×C47—81no—
418C22×C47—81no—
419C22×C47C2×#12111yescharacteristic
420C22×C47D4211yescharacteristic
421C22×C47D4211yescharacteristic
422C22×C47C2×#13511yescharacteristic
423C22×C47#57511yescharacteristic
424C22×C47#57611yescharacteristic
425C22×C47#57711yescharacteristic
426C4×C47—22no—
427C4×C47—22no—
428C4×C47—42no—
429C4×C47—42no—
430C4×C47—41no—
431C4×C47—41no—
432C4×C47—41no—
433C4×C47—81no—
434C4×C47—81no—
435C4×C47—81no—
436C4×C47C2×#12011yescharacteristic
437C4×C47#53411yescharacteristic
438C4×C47#54611yescharacteristic
439C4×C47#54611yescharacteristic
440C22×#135C2×C4711yescharacteristic, complemented
441C2×#463C2×C4711yescharacteristic, complemented
442C2×#459C2×C4711yescharacteristic, complemented
443C2×#449C2×C4711yescharacteristic, complemented
444#2431C2×C4711yescharacteristic, complemented
445#2339C2×C4711yescharacteristic, complemented
446#2056C2×C4711yescharacteristic, complemented
447#2055C2×C4711yescharacteristic, complemented
448#2015C2×C4711yescharacteristic, complemented
449#2014C2×C4711yescharacteristic, complemented
450#1893C2×C4711yescharacteristic, complemented
451#1879C2×C4711yescharacteristic, complemented
452#1877C2×C4711yescharacteristic, complemented
453#1850C2×C4711yescharacteristic, complemented
454#1788C2×C4711yescharacteristic, complemented
455C2×C47—42no—
456C2×C47—44no—
457C2×C47—82no—
458C2×C47—161no—
459C2×C47#241011yescharacteristic
460C2×C47#303511yescharacteristic
461C2×C47#304511yescharacteristic
462C2×C47#326711yescharacteristic
463C2×C47#326811yescharacteristic
464C2×C47#328011yescharacteristic
465C2×C47#328411yescharacteristic
466C22×#41C22×C4711yescharacteristic
467C22×#41C22×C4711yescharacteristic
468C2×#135—24no—
469C2×#135—24no—
470C2×#135—24no—
471C22×Q16C22×C4711yescharacteristic
472C22×SD16C22×C4711yescharacteristic
473C22×SD16C22×C4711yescharacteristic
474C22×SD16C22×C4711yescharacteristic
475C22×D8C22×C4711yescharacteristic
476C22×D8C22×C4711yescharacteristic
477C23×C8C22×C4711yescharacteristic
478C2×#127C22×C4711yescharacteristic
479C2×#124C22×C4711yescharacteristic
480C2×#121C22×C4711yescharacteristic
481C2×C4×D4C22×C4711yescharacteristic
482C2×C4×D4C22×C4711yescharacteristic
483#463—24no—
484#459—24no—
485#449—24no—
486C2×C4⋊C8C22×C4711yescharacteristic
487C2×C4⋊C8C22×C4711yescharacteristic
488C2×#103C22×C4711yescharacteristic
489C2×#103C22×C4711yescharacteristic
490C2×#103C22×C4711yescharacteristic
491C2×#102C22×C4711yescharacteristic
492C2×#102C22×C4711yescharacteristic
493C2×#102C22×C4711yescharacteristic
494C2×#102C22×C4711yescharacteristic
495C2×#102C22×C4711yescharacteristic
496C2×C22⋊C8C22×C4711yescharacteristic
497#392—21no—
498#392—21no—
499#391C22×C4711yescharacteristic
500#391C22×C4711yescharacteristic
501#391C22×C4711yescharacteristic
502#390C22×C4711yescharacteristic
503#386—21no—
504#386—21no—
505#386—21no—
506#386—21no—
507#381—21no—
508#380C22×C4711yescharacteristic
509C4×C22⋊C4C22×C4711yescharacteristic
510C2×#95—21no—
511#340C22×C4711yescharacteristic
512#340C22×C4711yescharacteristic
513#336C22×C4711yescharacteristic
514#336C22×C4711yescharacteristic
515C47#2436411yescharacteristic, direct product factor, Sylow
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41—41no—
527C2×#41D4×C4714yescomplemented
528C22×Q8C23×C4711yescharacteristic
529C22×Q8C23×C4711yescharacteristic
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4C23×C4711yescharacteristic
536C22×D4C23×C4711yescharacteristic
537C22×D4C23×C4711yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C23×C4711yescharacteristic
543#135—232no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16D4×C4714yescomplemented
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8D4×C4714yescomplemented
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8C23×C4711yescharacteristic
566C22×C8C23×C4711yescharacteristic
567C22×C8C23×C4711yescharacteristic
568C22×C8C23×C4711yescharacteristic
569#127—22no—
570#127—41no—
571#124—22no—
572#124—41no—
573#121—22no—
574#121—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—41no—
578C4×D4—41no—
579C2×C4⋊C4C23×C4711yescharacteristic
580C2×C4⋊C4C23×C4711yescharacteristic
581C2×C4⋊C4C23×C4711yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C4711yescharacteristic
591C2×C22⋊C4D4×C4711yescharacteristic
592C2×C42C23×C4711yescharacteristic
593C2×C42C23×C4711yescharacteristic
594C4⋊C8—22no—
595C4⋊C8—22no—
596#103—22no—
597#103—22no—
598#103—41no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95—21no—
611#95—21no—
612#95D4×C4711yescharacteristic
613#95D4×C4711yescharacteristic
614C24—21no—
615C24—21no—
616C24—21no—
617C24C2×D4×C4711yescharacteristic
618#41—28no—
619#41—28no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624#41—44no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8C2×D4×C4712yes—
637C2×Q8C2×D4×C4712yes—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C4712yes—
668C2×D4C2×D4×C4712yes—
669C2×D4C2×D4×C4712yes—
670C2×D4C2×D4×C4712yes—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—81no—
691C22×C4—81no—
692C22×C4C2×D4×C4711yescharacteristic
693C22×C4C2×D4×C4711yescharacteristic
694C22×C4C2×D4×C4711yescharacteristic
695C22×C4C2×D4×C4711yescharacteristic
696C22×C4C2×D4×C4712yes—
697C22×C4C2×D4×C4711yescharacteristic
698C22×C4#41×C4712yes—
699C22×C4C24×C4711yescharacteristic
700Q16—28no—
701SD16—28no—
702SD16—28no—
703SD16—44no—
704D8—28no—
705D8—44no—
706C2×C8—28no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8C2×D4×C4712yes—
718C2×C8C2×D4×C4712yes—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C22⋊C4—22no—
726C22⋊C4—41no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C22⋊C4—81no—
733C22⋊C4—81no—
734C22⋊C4—81no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23#121×C4712yes—
767C23C22×D4×C4711yescharacteristic
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—22no—
772Q8—41no—
773Q8—41no—
774Q8—41no—
775Q8—41no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—48no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4#120×C4714yes—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—84no—
828C2×C4—84no—
829C2×C4#121×C4712yes—
830C2×C4#135×C4712yescomplemented
831C2×C4C22×D4×C4711yescharacteristic
832C2×C4C22×D4×C4711yescharacteristic
833C2×C4C22×D4×C4711yescharacteristic
834C2×C4C2×#41×C4711yescharacteristic
835C2×C4H(5,𝔽2)×C4711yescharacteristic
836C2×C4H(5,𝔽2)×C4711yescharacteristic
837C8—22no—
838C8—22no—
839C8—41no—
840C8—41no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—41no—
851C22—42no—
852C22—41no—
853C22—41no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22C2×#121×C4711yescharacteristic
870C22D42×C4711yescharacteristic
871C22D42×C4711yescharacteristic
872C22C2×#135×C4711yescharacteristic
873C22C47×#57511yescharacteristic
874C22C47×#57611yescharacteristic
875C22C47×#57711yescharacteristic
876C4—22no—
877C4—22no—
878C4—42no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4C2×#120×C4711yescharacteristic
887C4C47×#53411yescharacteristic
888C4C47×#54611yescharacteristic
889C4C47×#54611yescharacteristic
890C2—42no—
891C2—44no—
892C2—82no—
893C2—161no—
894C2C47×#241011yescharacteristic
895C2C47×#303511yescharacteristic
896C2C47×#304511yescharacteristic
897C2C47×#326711yescharacteristic
898C2C47×#326811yescharacteristic
899C2C47×#328011yescharacteristic
900C2C47×#328411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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
1. C22×#135×C47C2semidirect
2. C2×C47×#463C2semidirect
3. C2×C47×#459C2semidirect
4. C2×C47×#449C2semidirect
5. C47×#2431C2semidirect
6. C47×#2339C2semidirect
7. C47×#2056C2semidirect
8. C47×#2055C2semidirect
9. C47×#2015C2semidirect
10. C47×#2014C2semidirect
11. C47×#1893C2semidirect
12. C47×#1879C2semidirect
13. C47×#1877C2semidirect
14. C47×#1850C2semidirect
15. C47×#1788C2semidirect
76. C2×#41×C47D4semidirect
104. C2×SD16×C47D4semidirect
110. C2×D8×C47D4semidirect
379. C2×C4×C47#135semidirect
390. #24364C47direct (N × H)
440. C22×#135C2×C47semidirect
441. C2×#463C2×C47semidirect
442. C2×#459C2×C47semidirect
443. C2×#449C2×C47semidirect
444. #2431C2×C47semidirect
445. #2339C2×C47semidirect
446. #2056C2×C47semidirect
447. #2055C2×C47semidirect
448. #2015C2×C47semidirect
449. #2014C2×C47semidirect
450. #1893C2×C47semidirect
451. #1879C2×C47semidirect
452. #1877C2×C47semidirect
453. #1850C2×C47semidirect
454. #1788C2×C47semidirect
515. C47#24364direct (N × H)
527. C2×#41D4×C47semidirect
555. C2×SD16D4×C47semidirect
561. C2×D8D4×C47semidirect
830. C2×C4#135×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C472
C2×C47×#4632
C2×C47×#4592
C2×C47×#4492
C47×#24312
C47×#23392
C47×#20562
C47×#20552
C47×#20152
C47×#20142
C47×#18932
C47×#18792
C47×#18772
C47×#18502
C47×#17882
#2436447