Finite Group Databasebeta

← C47×#25132 #26064830

Subgroups — C47×#25132 #26064830

Order 12032.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#469C211yesmaximal, characteristic, complemented
2C2×C47×#447C211yesmaximal, characteristic, complemented
3C2×C47×#436C211yesmaximal, characteristic, complemented
4C2×C47×#418C211yesmaximal, characteristic, complemented
5C47×#2414C211yesmaximal, characteristic, complemented
6C47×#2408C211yesmaximal, characteristic, complemented
7C47×#2065C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic, complemented
9C47×#2033C211yesmaximal, characteristic, complemented
10C47×#1999C211yesmaximal, characteristic, complemented
11C47×#1970C211yesmaximal, characteristic, complemented
12C47×#1934C211yesmaximal, characteristic, complemented
13C47×#1895C211yesmaximal, characteristic, complemented
14C47×#1895C211yesmaximal, characteristic, complemented
15C47×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C22×M16×C47C2211yescharacteristic, complemented
21C2×#121×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic, complemented
25C2×#120×C47—21no—
26C2×C4×D4×C47C2211yescharacteristic
27C2×#117×C47C2211yescharacteristic
28C47×#469—24no—
29C47×#447—24no—
30C47×#436—24no—
31C2×#107×C47C2211yescharacteristic, complemented
32C2×#106×C47C2211yescharacteristic, complemented
33C2×C4⋊C8×C47C2211yescharacteristic, complemented
34C47×#418—24no—
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic, complemented
42C2×#102×C47C2211yescharacteristic, complemented
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic, complemented
45C2×C4×C8×C47C2211yescharacteristic, complemented
46C47×#394—21no—
47C47×#394—21no—
48C47×#392—21no—
49C47×#392—21no—
50C47×#390—21no—
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#390C2211yescharacteristic, complemented
54C47×#389C2211yescharacteristic, complemented
55C47×#388—21no—
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic, complemented
58C47×#379—21no—
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C25×C47—21no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—22no—
71C22×D4×C47—21no—
72C22×D4×C47—22no—
73C22×D4×C47—41no—
74C22×D4×C47—41no—
75C22×D4×C47D411yescharacteristic
76C22×D4×C47C2311yescharacteristic
77C22×D4×C47C2311yescharacteristic
78C22×D4×C47C2311yescharacteristic
79C23×C4×C47C2311yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C2×D8×C47—22no—
82C2×D8×C47—22no—
83C2×D8×C47—22no—
84C2×D8×C47—22no—
85C2×D8×C47—41no—
86C2×D8×C47—41no—
87C2×M16×C47—22no—
88C2×M16×C47—22no—
89C2×M16×C47—22no—
90C2×M16×C47—22no—
91C2×M16×C47—41no—
92C2×M16×C47—41no—
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96C22×C8×C47C2311yescharacteristic
97#121×C47—22no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—22no—
101#121×C47—22no—
102#121×C47—41no—
103#121×C47—41no—
104#121×C47—41no—
105#120×C47—44no—
106C4×D4×C47—22no—
107C4×D4×C47—22no—
108#117×C47—22no—
109#117×C47—41no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47D411yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47D411yescharacteristic
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C42×C47—21no—
133C2×C42×C47C2311yescharacteristic
134#107×C47—41no—
135#106×C47—22no—
136C4⋊C8×C47—22no—
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—
144#102×C47D414yescomplemented
145C22⋊C8×C47—22no—
146C22⋊C8×C47D414yescomplemented
147C4×C8×C47—22no—
148#95×C47—21no—
149#95×C47—21no—
150#95×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—42no—
155C24×C47—42no—
156C24×C47—42no—
157C24×C47—42no—
158C24×C47—42no—
159C24×C47—81no—
160C24×C47—81no—
161C24×C47C2×D411yescharacteristic
162C24×C47C2×D411yescharacteristic
163C2×D4×C47—28no—
164C2×D4×C47—22no—
165C2×D4×C47—22no—
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—44no—
183C2×D4×C47—44no—
184C2×D4×C47—41no—
185C2×D4×C47—42no—
186C2×D4×C47—42no—
187C2×D4×C47—44no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—42no—
191C2×D4×C47—42no—
192C2×D4×C47—42no—
193C2×D4×C47—42no—
194C2×D4×C47—42no—
195C2×D4×C47—42no—
196C2×D4×C47—81no—
197C2×D4×C47—81no—
198C2×D4×C47—81no—
199C2×D4×C47—81no—
200C2×D4×C47—81no—
201C2×D4×C47C2×D412yes—
202C2×D4×C47#4112yes—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D412yes—
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47#4112yes—
224C22×C4×C47C2411yescharacteristic
225D8×C47—44no—
226D8×C47—44no—
227M16×C47—44no—
228M16×C47—44no—
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×C47C2×D412yes—
239C2×C8×C47C2×D412yes—
240C2×C8×C47C2×D412yes—
241C4⋊C4×C47—22no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—81no—
252C4⋊C4×C47C2×D412yes—
253C22⋊C4×C47—22no—
254C22⋊C4×C47—22no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—42no—
257C22⋊C4×C47—42no—
258C22⋊C4×C47—42no—
259C22⋊C4×C47—42no—
260C22⋊C4×C47—42no—
261C22⋊C4×C47—42no—
262C22⋊C4×C47—42no—
263C22⋊C4×C47—42no—
264C22⋊C4×C47—81no—
265C22⋊C4×C47—81no—
266C22⋊C4×C47—81no—
267C22⋊C4×C47—81no—
268C42×C47—21no—
269C42×C47—21no—
270C42×C47—42no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—22no—
279C23×C47—21no—
280C23×C47—22no—
281C23×C47—21no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—48no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
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—84no—
307C23×C47—84no—
308C23×C47—84no—
309C23×C47—84no—
310C23×C47—84no—
311C23×C47—84no—
312C23×C47#12112yes—
313C23×C47C22×D411yescharacteristic
314D4×C47—22no—
315D4×C47—22no—
316D4×C47—22no—
317D4×C47—22no—
318D4×C47—44no—
319D4×C47—48no—
320D4×C47—41no—
321D4×C47—41no—
322D4×C47—41no—
323D4×C47—41no—
324D4×C47—41no—
325D4×C47—41no—
326D4×C47—41no—
327D4×C47—41no—
328D4×C47—84no—
329D4×C47—84no—
330D4×C47—84no—
331D4×C47—84no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—22no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47#12112yes—
366C2×C4×C47AGL(1,ℤ/8)12yes—
367C2×C4×C47C22×D411yescharacteristic
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47C2×#4111yescharacteristic
370C2×C4×C47C2×#4111yescharacteristic
371C2×C4×C47H(5,𝔽2)11yescharacteristic
372C2×C4×C47H(5,𝔽2)11yescharacteristic
373C8×C47—22no—
374C8×C47—22no—
375C8×C47—22no—
376C8×C47—41no—
377#25132C4711yesmaximal, characteristic, direct product factor, Sylow
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—41no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—42no—
387C22×C47—42no—
388C22×C47—41no—
389C22×C47—42no—
390C22×C47—41no—
391C22×C47—42no—
392C22×C47—41no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—42no—
396C22×C47—41no—
397C22×C47—42no—
398C22×C47—816no—
399C22×C47—81no—
400C22×C47—81no—
401C22×C47—81no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47—81no—
405C22×C47—81no—
406C22×C47—81no—
407C22×C47—81no—
408C22×C47—81no—
409C22×C47—81no—
410C22×C47—81no—
411C22×C47—81no—
412C22×C47—81no—
413C22×C47—81no—
414C22×C47C2×#12111yescharacteristic
415C22×C47D4211yescharacteristic
416C22×C47#54611yescharacteristic
417C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
418C22×C47#57511yescharacteristic
419C22×C47#57611yescharacteristic
420C22×C47#57611yescharacteristic
421C4×C47—22no—
422C4×C47—22no—
423C4×C47—41no—
424C4×C47—42no—
425C4×C47—41no—
426C4×C47—81no—
427C4×C47—81no—
428C4×C47—81no—
429C4×C47—81no—
430C4×C47#52511yescharacteristic
431C4×C47#53811yescharacteristic
432C4×C47D4211yescharacteristic
433C4×C47#54611yescharacteristic
434C2×#469C2×C4711yescharacteristic, complemented
435C2×#447C2×C4711yescharacteristic, complemented
436C2×#436C2×C4711yescharacteristic, complemented
437C2×#418C2×C4711yescharacteristic, complemented
438#2414C2×C4711yescharacteristic, complemented
439#2408C2×C4711yescharacteristic, complemented
440#2065C2×C4711yescharacteristic, complemented
441#2054C2×C4711yescharacteristic, complemented
442#2033C2×C4711yescharacteristic, complemented
443#1999C2×C4711yescharacteristic, complemented
444#1970C2×C4711yescharacteristic, complemented
445#1934C2×C4711yescharacteristic, complemented
446#1895C2×C4711yescharacteristic, complemented
447#1895C2×C4711yescharacteristic, complemented
448#1854C2×C4711yescharacteristic, complemented
449C2×C47—42no—
450C2×C47—81no—
451C2×C47—82no—
452C2×C47—82no—
453C2×C47—161no—
454C2×C47#242411yescharacteristic
455C2×C47#305511yescharacteristic
456C2×C47#305811yescharacteristic
457C2×C47#327311yescharacteristic
458C2×C47#327411yescharacteristic
459C2×C47#332211yescharacteristic
460C2×C47#332511yescharacteristic
461C23×D4C22×C4711yescharacteristic
462C22×D8C22×C4711yescharacteristic
463C22×D8C22×C4711yescharacteristic
464C22×M16C22×C4711yescharacteristic
465C22×M16C22×C4711yescharacteristic, complemented
466C2×#121C22×C4711yescharacteristic
467C2×#121C22×C4711yescharacteristic
468C2×#121C22×C4711yescharacteristic
469C2×#121C22×C4711yescharacteristic, complemented
470C2×#120—21no—
471C2×C4×D4C22×C4711yescharacteristic
472C2×#117C22×C4711yescharacteristic
473#469—24no—
474#447—24no—
475#436—24no—
476C2×#107C22×C4711yescharacteristic, complemented
477C2×#106C22×C4711yescharacteristic, complemented
478C2×C4⋊C8C22×C4711yescharacteristic, complemented
479#418—24no—
480C2×#102C22×C4711yescharacteristic
481C2×#102C22×C4711yescharacteristic
482C2×#102C22×C4711yescharacteristic
483C2×#102C22×C4711yescharacteristic
484C2×#102C22×C4711yescharacteristic
485C2×#102C22×C4711yescharacteristic
486C2×#102C22×C4711yescharacteristic, complemented
487C2×#102C22×C4711yescharacteristic, complemented
488C2×C22⋊C8C22×C4711yescharacteristic
489C2×C22⋊C8C22×C4711yescharacteristic, complemented
490C2×C4×C8C22×C4711yescharacteristic, complemented
491#394—21no—
492#394—21no—
493#392—21no—
494#392—21no—
495#390—21no—
496#390C22×C4711yescharacteristic
497#390C22×C4711yescharacteristic
498#390C22×C4711yescharacteristic, complemented
499#389C22×C4711yescharacteristic, complemented
500#388—21no—
501#380C22×C4711yescharacteristic
502#380C22×C4711yescharacteristic, complemented
503#379—21no—
504#340C22×C4711yescharacteristic, complemented
505#340C22×C4711yescharacteristic, complemented
506#340C22×C4711yescharacteristic, complemented
507#340C22×C4711yescharacteristic, complemented
508C47#2513211yescharacteristic, direct product factor, Sylow
509C25—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4D4×C4711yescharacteristic
522C22×D4C23×C4711yescharacteristic
523C22×D4C23×C4711yescharacteristic
524C22×D4C23×C4711yescharacteristic
525C23×C4C23×C4711yescharacteristic
526C23×C4C23×C4711yescharacteristic
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—41no—
532C2×D8—41no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8C23×C4711yescharacteristic
540C22×C8C23×C4711yescharacteristic
541C22×C8C23×C4711yescharacteristic
542C22×C8C23×C4711yescharacteristic
543#121—22no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—41no—
549#121—41no—
550#121—41no—
551#120—44no—
552C4×D4—22no—
553C4×D4—22no—
554#117—22no—
555#117—41no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C4711yescharacteristic
558C2×C4⋊C4C23×C4711yescharacteristic
559C2×C4⋊C4C23×C4711yescharacteristic
560C2×C4⋊C4C23×C4711yescharacteristic
561C2×C4⋊C4C23×C4711yescharacteristic
562C2×C4⋊C4C23×C4711yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4D4×C4711yescharacteristic
577C2×C22⋊C4D4×C4711yescharacteristic
578C2×C42—21no—
579C2×C42C23×C4711yescharacteristic
580#107—41no—
581#106—22no—
582C4⋊C8—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—22no—
589#102—41no—
590#102D4×C4714yescomplemented
591C22⋊C8—22no—
592C22⋊C8D4×C4714yescomplemented
593C4×C8—22no—
594#95—21no—
595#95—21no—
596#95—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—42no—
601C24—42no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—81no—
606C24—81no—
607C24C2×D4×C4711yescharacteristic
608C24C2×D4×C4711yescharacteristic
609C2×D4—28no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C2×D4×C4712yes—
648C2×D4#41×C4712yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4C2×D4×C4711yescharacteristic
665C22×C4C2×D4×C4711yescharacteristic
666C22×C4C2×D4×C4711yescharacteristic
667C22×C4C2×D4×C4712yes—
668C22×C4C2×D4×C4711yescharacteristic
669C22×C4#41×C4712yes—
670C22×C4C24×C4711yescharacteristic
671D8—44no—
672D8—44no—
673M16—44no—
674M16—44no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8C2×D4×C4712yes—
685C2×C8C2×D4×C4712yes—
686C2×C8C2×D4×C4712yes—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—81no—
698C4⋊C4C2×D4×C4712yes—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C42—42no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23#121×C4712yes—
759C23C22×D4×C4711yescharacteristic
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—44no—
765D4—48no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—84no—
775D4—84no—
776D4—84no—
777D4—84no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4#121×C4712yes—
812C2×C4AGL(1,ℤ/8)×C4712yes—
813C2×C4C22×D4×C4711yescharacteristic
814C2×C4C22×D4×C4711yescharacteristic
815C2×C4C2×#41×C4711yescharacteristic
816C2×C4C2×#41×C4711yescharacteristic
817C2×C4H(5,𝔽2)×C4711yescharacteristic
818C2×C4H(5,𝔽2)×C4711yescharacteristic
819C8—22no—
820C8—22no—
821C8—22no—
822C8—41no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—816no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C2×#121×C4711yescharacteristic
860C22D42×C4711yescharacteristic
861C22C47×#54611yescharacteristic
862C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
863C22C47×#57511yescharacteristic
864C22C47×#57611yescharacteristic
865C22C47×#57611yescharacteristic
866C4—22no—
867C4—22no—
868C4—41no—
869C4—41no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4C47×#52511yescharacteristic
876C4C47×#53811yescharacteristic
877C4D42×C4711yescharacteristic
878C4C47×#54611yescharacteristic
879C2—42no—
880C2—81no—
881C2—82no—
882C2—82no—
883C2—161no—
884C2C47×#242411yescharacteristic
885C2C47×#305511yescharacteristic
886C2C47×#305811yescharacteristic
887C2C47×#327311yescharacteristic
888C2C47×#327411yescharacteristic
889C2C47×#332211yescharacteristic
890C2C47×#332511yescharacteristic
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×#469C2semidirect
2. C2×C47×#447C2semidirect
3. C2×C47×#436C2semidirect
4. C2×C47×#418C2semidirect
5. C47×#2414C2semidirect
6. C47×#2408C2semidirect
7. C47×#2065C2semidirect
8. C47×#2054C2semidirect
9. C47×#2033C2semidirect
10. C47×#1999C2semidirect
11. C47×#1970C2semidirect
12. C47×#1934C2semidirect
13. C47×#1895C2semidirect
14. C47×#1895C2semidirect
15. C47×#1854C2semidirect
20. C22×M16×C47C22semidirect
24. C2×#121×C47C22semidirect
31. C2×#107×C47C22semidirect
32. C2×#106×C47C22semidirect
33. C2×C4⋊C8×C47C22semidirect
41. C2×#102×C47C22semidirect
42. C2×#102×C47C22semidirect
44. C2×C22⋊C8×C47C22semidirect
45. C2×C4×C8×C47C22semidirect
53. C47×#390C22semidirect
54. C47×#389C22semidirect
57. C47×#380C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
144. #102×C47D4semidirect
146. C22⋊C8×C47D4semidirect
377. #25132C47direct (N × H)
434. C2×#469C2×C47semidirect
435. C2×#447C2×C47semidirect
436. C2×#436C2×C47semidirect
437. C2×#418C2×C47semidirect
438. #2414C2×C47semidirect
439. #2408C2×C47semidirect
440. #2065C2×C47semidirect
441. #2054C2×C47semidirect
442. #2033C2×C47semidirect
443. #1999C2×C47semidirect
444. #1970C2×C47semidirect
445. #1934C2×C47semidirect
446. #1895C2×C47semidirect
447. #1895C2×C47semidirect
448. #1854C2×C47semidirect
465. C22×M16C22×C47semidirect
469. C2×#121C22×C47semidirect
476. C2×#107C22×C47semidirect
477. C2×#106C22×C47semidirect
478. C2×C4⋊C8C22×C47semidirect
486. C2×#102C22×C47semidirect
487. C2×#102C22×C47semidirect
489. C2×C22⋊C8C22×C47semidirect
490. C2×C4×C8C22×C47semidirect
498. #390C22×C47semidirect
499. #389C22×C47semidirect
502. #380C22×C47semidirect
504. #340C22×C47semidirect
505. #340C22×C47semidirect
506. #340C22×C47semidirect
507. #340C22×C47semidirect
508. C47#25132direct (N × H)
590. #102D4×C47semidirect
592. C22⋊C8D4×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×#4472
C2×C47×#4362
C2×C47×#4182
C47×#24142
C47×#24082
C47×#20652
C47×#20542
C47×#20332
C47×#19992
C47×#19702
C47×#19342
C47×#18952
C47×#18542
#2513247