Finite Group Databasebeta

← C47×#25106 #26064804

Subgroups — C47×#25106 #26064804

Order 12032.

1230 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#469C211yesmaximal, characteristic, complemented
2C2×C47×#463C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic, complemented
4C2×C47×#417C211yesmaximal, characteristic, complemented
5C47×#2431C211yesmaximal, characteristic, complemented
6C47×#2361C211yesmaximal, characteristic, complemented
7C47×#2065C211yesmaximal, characteristic, complemented
8C47×#2055C211yesmaximal, characteristic, complemented
9C47×#2042C211yesmaximal, characteristic, complemented
10C47×#2011C211yesmaximal, characteristic, complemented
11C47×#1982C211yesmaximal, characteristic, complemented
12C47×#1927C211yesmaximal, characteristic, complemented
13C47×#1879C211yesmaximal, characteristic, complemented
14C47×#1874C211yesmaximal, characteristic, complemented
15C47×#1851C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C22×M16×C47C2211yescharacteristic
21C2×#127×C47C2211yescharacteristic
22C2×#124×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×C4×D4×C47—21no—
26C2×C4×D4×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C47×#469—24no—
29C47×#463—24no—
30C47×#449—24no—
31C2×#106×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C47×#417—24no—
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C47×#392—21no—
47C47×#392—21no—
48C47×#391C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#388—21no—
53C47×#386—21no—
54C47×#386—21no—
55C47×#386—21no—
56C47×#385—21no—
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C2×#41×C47—22no—
64C2×#41×C47—22no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—41no—
68C2×#41×C47—41no—
69C22×Q8×C47C2311yescharacteristic
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47C2311yescharacteristic
76C22×D4×C47C2311yescharacteristic
77C22×D4×C47C2311yescharacteristic
78C23×C4×C47—21no—
79C23×C4×C47—21no—
80C23×C4×C47—21no—
81C23×C4×C47C2311yescharacteristic
82C2×SD16×C47—22no—
83C2×SD16×C47—22no—
84C2×SD16×C47—41no—
85C2×D8×C47—22no—
86C2×D8×C47—22no—
87C2×D8×C47—22no—
88C2×D8×C47—22no—
89C2×D8×C47—41no—
90C2×D8×C47—41no—
91C2×M16×C47—22no—
92C2×M16×C47—22no—
93C2×M16×C47—41no—
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98#127×C47—22no—
99#127×C47—41no—
100#124×C47—22no—
101#124×C47—41no—
102#121×C47—22no—
103#121×C47—22no—
104#121×C47—22no—
105#121×C47D414yescomplemented
106C4×D4×C47—22no—
107C4×D4×C47—41no—
108C4×D4×C47—44no—
109C2×C4⋊C4×C47—22no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—41no—
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47D411yescharacteristic
127C2×C22⋊C4×C47D411yescharacteristic
128C2×C42×C47—21no—
129C2×C42×C47C2311yescharacteristic
130C2×C42×C47C2311yescharacteristic
131#106×C47—22no—
132C4⋊C8×C47—22no—
133C4⋊C8×C47—41no—
134#103×C47—22no—
135#103×C47—22no—
136#103×C47D414yescomplemented
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47—41no—
144C22⋊C8×C47—22no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47D411yescharacteristic
150#95×C47D411yescharacteristic
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47C2×D411yescharacteristic
155#41×C47—28no—
156#41×C47—44no—
157#41×C47—44no—
158#41×C47—44no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47C2×D412yes—
165C2×D4×C47—24no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—42no—
183C2×D4×C47—42no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
186C2×D4×C47—42no—
187C2×D4×C47—42no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—42no—
191C2×D4×C47—42no—
192C2×D4×C47—81no—
193C2×D4×C47—81no—
194C2×D4×C47—81no—
195C2×D4×C47—81no—
196C2×D4×C47C2×D412yes—
197C2×D4×C47#4112yes—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—42no—
208C22×C4×C47—42no—
209C22×C4×C47—42no—
210C22×C4×C47—42no—
211C22×C4×C47—42no—
212C22×C4×C47—42no—
213C22×C4×C47—42no—
214C22×C4×C47—81no—
215C22×C4×C47—81no—
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D412yes—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47#4112yes—
223C22×C4×C47C2411yescharacteristic
224SD16×C47—44no—
225D8×C47—44no—
226D8×C47—44no—
227M16×C47—44no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47C2×D412yes—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—42no—
247C4⋊C4×C47—42no—
248C4⋊C4×C47C2×D412yes—
249C4⋊C4×C47C2×D412yes—
250C22⋊C4×C47—24no—
251C22⋊C4×C47—22no—
252C22⋊C4×C47—41no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—42no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—42no—
257C22⋊C4×C47—42no—
258C22⋊C4×C47—81no—
259C22⋊C4×C47—81no—
260C22⋊C4×C47—81no—
261C42×C47—21no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47—21no—
265C42×C47—42no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47#12112yes—
294C23×C47C22×D411yescharacteristic
295Q8×C47—22no—
296Q8×C47—22no—
297Q8×C47—41no—
298Q8×C47—41no—
299D4×C47—22no—
300D4×C47—22no—
301D4×C47—22no—
302D4×C47—22no—
303D4×C47—48no—
304D4×C47—48no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—84no—
314D4×C47—84no—
315D4×C47—84no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—48no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—84no—
350C2×C4×C47—84no—
351C2×C4×C47#12112yes—
352C2×C4×C47AGL(1,ℤ/8)12yes—
353C2×C4×C47C22×D411yescharacteristic
354C2×C4×C47C22×D411yescharacteristic
355C2×C4×C47C2×#4111yescharacteristic
356C2×C4×C47C2×#4111yescharacteristic
357C2×C4×C47H(5,𝔽2)11yescharacteristic
358C2×C4×C47H(5,𝔽2)11yescharacteristic
359C8×C47—22no—
360C8×C47—41no—
361C8×C47—41no—
362C8×C47—41no—
363#25106C4711yesmaximal, characteristic, direct product factor, Sylow
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47—81no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47—81no—
386C22×C47—81no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47C2×#12111yescharacteristic
393C22×C47D4211yescharacteristic
394C22×C47#54611yescharacteristic
395C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C47#57511yescharacteristic
397C22×C47#57611yescharacteristic
398C22×C47#57711yescharacteristic
399C4×C47—22no—
400C4×C47—22no—
401C4×C47—42no—
402C4×C47—41no—
403C4×C47—41no—
404C4×C47—42no—
405C4×C47—42no—
406C4×C47—41no—
407C4×C47—81no—
408C4×C47—81no—
409C4×C47#52511yescharacteristic
410C4×C47#53811yescharacteristic
411C4×C47D4211yescharacteristic
412C4×C47#54611yescharacteristic
413C2×#469C2×C4711yescharacteristic, complemented
414C2×#463C2×C4711yescharacteristic, complemented
415C2×#449C2×C4711yescharacteristic, complemented
416C2×#417C2×C4711yescharacteristic, complemented
417#2431C2×C4711yescharacteristic, complemented
418#2361C2×C4711yescharacteristic, complemented
419#2065C2×C4711yescharacteristic, complemented
420#2055C2×C4711yescharacteristic, complemented
421#2042C2×C4711yescharacteristic, complemented
422#2011C2×C4711yescharacteristic, complemented
423#1982C2×C4711yescharacteristic, complemented
424#1927C2×C4711yescharacteristic, complemented
425#1879C2×C4711yescharacteristic, complemented
426#1874C2×C4711yescharacteristic, complemented
427#1851C2×C4711yescharacteristic, complemented
428C2×C47—42no—
429C2×C47—82no—
430C2×C47—82no—
431C2×C47—161no—
432C2×C47#242411yescharacteristic
433C2×C47#303611yescharacteristic
434C2×C47#304511yescharacteristic
435C2×C47#327111yescharacteristic
436C2×C47#327411yescharacteristic
437C2×C47#330611yescharacteristic
438C2×C47#332211yescharacteristic
439C22×#41C22×C4711yescharacteristic
440C22×SD16C22×C4711yescharacteristic
441C22×D8C22×C4711yescharacteristic
442C22×D8C22×C4711yescharacteristic
443C22×M16C22×C4711yescharacteristic
444C2×#127C22×C4711yescharacteristic
445C2×#124C22×C4711yescharacteristic
446C2×#121C22×C4711yescharacteristic
447C2×#121C22×C4711yescharacteristic
448C2×C4×D4—21no—
449C2×C4×D4C22×C4711yescharacteristic
450C22×C4⋊C4C22×C4711yescharacteristic
451#469—24no—
452#463—24no—
453#449—24no—
454C2×#106C22×C4711yescharacteristic
455C2×C4⋊C8C22×C4711yescharacteristic
456C2×C4⋊C8C22×C4711yescharacteristic
457#417—24no—
458C2×#103C22×C4711yescharacteristic
459C2×#103C22×C4711yescharacteristic
460C2×#103C22×C4711yescharacteristic
461C2×#102C22×C4711yescharacteristic
462C2×#102C22×C4711yescharacteristic
463C2×#102C22×C4711yescharacteristic
464C2×#102C22×C4711yescharacteristic
465C2×#102C22×C4711yescharacteristic
466C2×#102C22×C4711yescharacteristic
467C2×#102C22×C4711yescharacteristic
468C2×C22⋊C8C22×C4711yescharacteristic
469#392—21no—
470#392—21no—
471#391C22×C4711yescharacteristic
472#390C22×C4711yescharacteristic
473#390C22×C4711yescharacteristic
474#389C22×C4711yescharacteristic
475#388—21no—
476#386—21no—
477#386—21no—
478#386—21no—
479#385—21no—
480C4×C4⋊C4C22×C4711yescharacteristic
481C4×C22⋊C4C22×C4711yescharacteristic
482#340C22×C4711yescharacteristic
483#340C22×C4711yescharacteristic
484#336C22×C4711yescharacteristic
485#336C22×C4711yescharacteristic
486C47#2510611yescharacteristic, direct product factor, Sylow
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8C23×C4711yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C23×C4711yescharacteristic
500C22×D4C23×C4711yescharacteristic
501C22×D4C23×C4711yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C23×C4711yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—41no—
518C22×C8C23×C4711yescharacteristic
519C22×C8C23×C4711yescharacteristic
520C22×C8C23×C4711yescharacteristic
521C22×C8C23×C4711yescharacteristic
522#127—22no—
523#127—41no—
524#124—22no—
525#124—41no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121D4×C4714yescomplemented
530C4×D4—22no—
531C4×D4—41no—
532C4×D4—44no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4C23×C4711yescharacteristic
538C2×C4⋊C4C23×C4711yescharacteristic
539C2×C4⋊C4C23×C4711yescharacteristic
540C2×C4⋊C4C23×C4711yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C4711yescharacteristic
551C2×C22⋊C4D4×C4711yescharacteristic
552C2×C42—21no—
553C2×C42C23×C4711yescharacteristic
554C2×C42C23×C4711yescharacteristic
555#106—22no—
556C4⋊C8—22no—
557C4⋊C8—41no—
558#103—22no—
559#103—22no—
560#103D4×C4714yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—41no—
568C22⋊C8—22no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95D4×C4711yescharacteristic
574#95D4×C4711yescharacteristic
575C24—21no—
576C24—21no—
577C24—21no—
578C24C2×D4×C4711yescharacteristic
579#41—28no—
580#41—44no—
581#41—44no—
582#41—44no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8C2×D4×C4712yes—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4C2×D4×C4712yes—
621C2×D4#41×C4712yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4C2×D4×C4711yescharacteristic
641C22×C4C2×D4×C4711yescharacteristic
642C22×C4C2×D4×C4711yescharacteristic
643C22×C4C2×D4×C4711yescharacteristic
644C22×C4C2×D4×C4712yes—
645C22×C4C2×D4×C4711yescharacteristic
646C22×C4#41×C4712yes—
647C22×C4C24×C4711yescharacteristic
648SD16—44no—
649D8—44no—
650D8—44no—
651M16—44no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8C2×D4×C4712yes—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C4712yes—
673C4⋊C4C2×D4×C4712yes—
674C22⋊C4—24no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—42no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23#121×C4712yes—
718C23C22×D4×C4711yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—48no—
728D4—48no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—84no—
738D4—84no—
739D4—84no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—48no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4#121×C4712yes—
776C2×C4AGL(1,ℤ/8)×C4712yes—
777C2×C4C22×D4×C4711yescharacteristic
778C2×C4C22×D4×C4711yescharacteristic
779C2×C4C2×#41×C4711yescharacteristic
780C2×C4C2×#41×C4711yescharacteristic
781C2×C4H(5,𝔽2)×C4711yescharacteristic
782C2×C4H(5,𝔽2)×C4711yescharacteristic
783C8—22no—
784C8—41no—
785C8—41no—
786C8—41no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C4711yescharacteristic
816C22D42×C4711yescharacteristic
817C22C47×#54611yescharacteristic
818C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
819C22C47×#57511yescharacteristic
820C22C47×#57611yescharacteristic
821C22C47×#57711yescharacteristic
822C4—22no—
823C4—22no—
824C4—42no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—42no—
830C4—81no—
831C4—81no—
832C4C47×#52511yescharacteristic
833C4C47×#53811yescharacteristic
834C4D42×C4711yescharacteristic
835C4C47×#54611yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—161no—
840C2C47×#242411yescharacteristic
841C2C47×#303611yescharacteristic
842C2C47×#304511yescharacteristic
843C2C47×#327111yescharacteristic
844C2C47×#327411yescharacteristic
845C2C47×#330611yescharacteristic
846C2C47×#332211yescharacteristic
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. C2×C47×#469C2semidirect
2. C2×C47×#463C2semidirect
3. C2×C47×#449C2semidirect
4. C2×C47×#417C2semidirect
5. C47×#2431C2semidirect
6. C47×#2361C2semidirect
7. C47×#2065C2semidirect
8. C47×#2055C2semidirect
9. C47×#2042C2semidirect
10. C47×#2011C2semidirect
11. C47×#1982C2semidirect
12. C47×#1927C2semidirect
13. C47×#1879C2semidirect
14. C47×#1874C2semidirect
15. C47×#1851C2semidirect
105. #121×C47D4semidirect
136. #103×C47D4semidirect
363. #25106C47direct (N × H)
413. C2×#469C2×C47semidirect
414. C2×#463C2×C47semidirect
415. C2×#449C2×C47semidirect
416. C2×#417C2×C47semidirect
417. #2431C2×C47semidirect
418. #2361C2×C47semidirect
419. #2065C2×C47semidirect
420. #2055C2×C47semidirect
421. #2042C2×C47semidirect
422. #2011C2×C47semidirect
423. #1982C2×C47semidirect
424. #1927C2×C47semidirect
425. #1879C2×C47semidirect
426. #1874C2×C47semidirect
427. #1851C2×C47semidirect
486. C47#25106direct (N × H)
529. #121D4×C47semidirect
560. #103D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4692
C2×C47×#4632
C2×C47×#4492
C2×C47×#4172
C47×#24312
C47×#23612
C47×#20652
C47×#20552
C47×#20422
C47×#20112
C47×#19822
C47×#19272
C47×#18792
C47×#18742
C47×#18512
#2510647