Finite Group Databasebeta

← C47×#24124 #26063822

Subgroups — C47×#24124 #26063822

Order 12032.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#553C211yesmaximal, characteristic, complemented
2C2×C47×#478C211yesmaximal, characteristic, complemented
3C2×C4×D8×C47C211yesmaximal, characteristic, complemented
4C47×#2535C211yesmaximal, characteristic, complemented
5C47×#2034C211yesmaximal, characteristic, complemented
6C47×#2033C211yesmaximal, characteristic, complemented
7C47×#1999C211yesmaximal, characteristic, complemented
8C47×#1999C211yesmaximal, characteristic, complemented
9C47×#1991C211yesmaximal, characteristic, complemented
10C47×#1954C211yesmaximal, characteristic, complemented
11C47×#1875C211yesmaximal, characteristic, complemented
12C47×#1874C211yesmaximal, characteristic, complemented
13C47×#1854C211yesmaximal, characteristic, complemented
14C47×#1852C211yesmaximal, characteristic, complemented
15C47×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C47×#553—24no—
18C47×#553—24no—
19C2×#126×C47—21no—
20C2×#125×C47C2211yescharacteristic
21C2×#123×C47—21no—
22C2×#121×C47—21no—
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×C4×D4×C47—21no—
28C2×C4×D4×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C2×C4×D4×C47C2211yescharacteristic
31C2×#117×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C47×#478—24no—
34C4×D8×C47—24no—
35C2×#107×C47C2211yescharacteristic
36C2×#107×C47C2211yescharacteristic
37C2×#106×C47C2211yescharacteristic
38C2×C4⋊C8×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C2×C22⋊C8×C47C2211yescharacteristic
49C2×C4×C8×C47C2211yescharacteristic
50C47×#397—21no—
51C47×#392—21no—
52C47×#386—21no—
53C47×#386—21no—
54C47×#382C2211yescharacteristic
55C47×#380C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×D4×C47—21no—
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47D411yescharacteristic
68C22×D4×C47C2311yescharacteristic
69C22×D4×C47C2311yescharacteristic
70C23×C4×C47—21no—
71C23×C4×C47—21no—
72C23×C4×C47—21no—
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C2×D8×C47—22no—
76C2×D8×C47—22no—
77C2×D8×C47—22no—
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82#126×C47—28no—
83#125×C47—22no—
84#125×C47D414yescomplemented
85#123×C47—28no—
86#121×C47—28no—
87#121×C47—22no—
88#121×C47—22no—
89#121×C47—22no—
90#121×C47—22no—
91#121×C47—22no—
92#121×C47—22no—
93#121×C47—41no—
94#121×C47—41no—
95C4×D4×C47—28no—
96C4×D4×C47—22no—
97C4×D4×C47—22no—
98C4×D4×C47—22no—
99C4×D4×C47—22no—
100C4×D4×C47—22no—
101C4×D4×C47D414yescomplemented
102#117×C47—22no—
103#117×C47—22no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47—22no—
109C2×C4⋊C4×C47D411yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C22⋊C4×C47—21no—
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×C47D411yescharacteristic
126C2×C22⋊C4×C47D411yescharacteristic
127C2×C42×C47—21no—
128C2×C42×C47C2311yescharacteristic
129#107×C47—22no—
130#107×C47—22no—
131#106×C47—22no—
132C4⋊C8×C47—22no—
133#102×C47—22no—
134#102×C47—22no—
135#102×C47—22no—
136#102×C47—22no—
137#102×C47—41no—
138#102×C47—41no—
139C22⋊C8×C47—22no—
140C22⋊C8×C47—22no—
141C22⋊C8×C47—41no—
142C22⋊C8×C47—41no—
143C4×C8×C47—22no—
144#95×C47—21no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47C2×D411yescharacteristic
151C24×C47C2×D411yescharacteristic
152C2×D4×C47—24no—
153C2×D4×C47—22no—
154C2×D4×C47—24no—
155C2×D4×C47—22no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—41no—
167C2×D4×C47—42no—
168C2×D4×C47—42no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47—42no—
172C2×D4×C47—42no—
173C2×D4×C47—81no—
174C2×D4×C47—81no—
175C2×D4×C47—81no—
176C2×D4×C47—81no—
177C2×D4×C47C2×D412yes—
178C2×D4×C47#4112yes—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—24no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—24no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—42no—
200C22×C4×C47—81no—
201C22×C4×C47—81no—
202C22×C4×C47—81no—
203C22×C4×C47—81no—
204C22×C4×C47—81no—
205C22×C4×C47—81no—
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2411yescharacteristic
211D8×C47—28no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47#4112yes—
224C4⋊C4×C47—24no—
225C4⋊C4×C47—24no—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—22no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47C2×D412yes—
238C4⋊C4×C47C2×D412yes—
239C4⋊C4×C47C2×D412yes—
240C22⋊C4×C47—24no—
241C22⋊C4×C47—24no—
242C22⋊C4×C47—24no—
243C22⋊C4×C47—24no—
244C22⋊C4×C47—22no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—42no—
247C22⋊C4×C47—42no—
248C22⋊C4×C47—42no—
249C22⋊C4×C47—81no—
250C22⋊C4×C47—81no—
251C42×C47—24no—
252C42×C47C2×D412yes—
253C42×C47C2×D412yes—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47#13512yes—
282C23×C47C22×D411yescharacteristic
283D4×C47—22no—
284D4×C47—22no—
285D4×C47—22no—
286D4×C47—22no—
287D4×C47—44no—
288D4×C47—48no—
289D4×C47—41no—
290D4×C47—41no—
291D4×C47—41no—
292D4×C47—41no—
293D4×C47—84no—
294D4×C47—84no—
295D4×C47—84no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—21no—
304C2×C4×C47—22no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—84no—
333C2×C4×C47—84no—
334C2×C4×C47—84no—
335C2×C4×C47#12012yes—
336C2×C4×C47#12012yes—
337C2×C4×C47C22×D411yescharacteristic
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C2×#4111yescharacteristic
340C2×C4×C47C2×#4111yescharacteristic
341C2×C4×C47H(5,𝔽2)11yescharacteristic
342C2×C4×C472−1+411yescharacteristic
343C8×C47—22no—
344C8×C47—41no—
345C8×C47—41no—
346C8×C47—41no—
347#24124C4711yesmaximal, characteristic, direct product factor, Sylow
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—41no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—41no—
364C22×C47—42no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—42no—
368C22×C47—81no—
369C22×C47—81no—
370C22×C47—81no—
371C22×C47—81no—
372C22×C47—81no—
373C22×C47—81no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47C2×#12011yescharacteristic
377C22×C47#54611yescharacteristic
378C22×C47#54711yescharacteristic
379C22×C47C2×#13511yescharacteristic
380C22×C47#57511yescharacteristic
381C22×C47#57611yescharacteristic
382C22×C47#57611yescharacteristic
383C4×C47—22no—
384C4×C47—22no—
385C4×C47—41no—
386C4×C47—41no—
387C4×C47—42no—
388C4×C47—42no—
389C4×C47—42no—
390C4×C47—81no—
391C4×C47—81no—
392C4×C47—81no—
393C4×C47#52511yescharacteristic
394C4×C47#53711yescharacteristic
395C4×C47#54811yescharacteristic
396C4×C47#55011yescharacteristic
397C2×#553C2×C4711yescharacteristic, complemented
398C2×#478C2×C4711yescharacteristic, complemented
399C2×C4×D8C2×C4711yescharacteristic, complemented
400#2535C2×C4711yescharacteristic, complemented
401#2034C2×C4711yescharacteristic, complemented
402#2033C2×C4711yescharacteristic, complemented
403#1999C2×C4711yescharacteristic, complemented
404#1999C2×C4711yescharacteristic, complemented
405#1991C2×C4711yescharacteristic, complemented
406#1954C2×C4711yescharacteristic, complemented
407#1875C2×C4711yescharacteristic, complemented
408#1874C2×C4711yescharacteristic, complemented
409#1854C2×C4711yescharacteristic, complemented
410#1852C2×C4711yescharacteristic, complemented
411#1804C2×C4711yescharacteristic, complemented
412C2×C47—42no—
413C2×C47—81no—
414C2×C47—82no—
415C2×C47—82no—
416C2×C47#240711yescharacteristic
417C2×C47#300211yescharacteristic
418C2×C47#300811yescharacteristic
419C2×C47#329711yescharacteristic
420C2×C47#332211yescharacteristic
421C2×C47#333911yescharacteristic
422C2×C47#335511yescharacteristic
423C22×D8C22×C4711yescharacteristic
424#553—24no—
425#553—24no—
426C2×#126—21no—
427C2×#125C22×C4711yescharacteristic
428C2×#123—21no—
429C2×#121—21no—
430C2×#121C22×C4711yescharacteristic
431C2×#121C22×C4711yescharacteristic
432C2×#121C22×C4711yescharacteristic
433C2×#121C22×C4711yescharacteristic
434C2×C4×D4—21no—
435C2×C4×D4C22×C4711yescharacteristic
436C2×C4×D4C22×C4711yescharacteristic
437C2×C4×D4C22×C4711yescharacteristic
438C2×#117C22×C4711yescharacteristic
439C22×C4⋊C4C22×C4711yescharacteristic
440#478—24no—
441C4×D8—24no—
442C2×#107C22×C4711yescharacteristic
443C2×#107C22×C4711yescharacteristic
444C2×#106C22×C4711yescharacteristic
445C2×C4⋊C8C22×C4711yescharacteristic
446C2×#102C22×C4711yescharacteristic
447C2×#102C22×C4711yescharacteristic
448C2×#102C22×C4711yescharacteristic
449C2×#102C22×C4711yescharacteristic
450C2×#102C22×C4711yescharacteristic
451C2×#102C22×C4711yescharacteristic
452C2×C22⋊C8C22×C4711yescharacteristic
453C2×C22⋊C8C22×C4711yescharacteristic
454C2×C22⋊C8C22×C4711yescharacteristic
455C2×C22⋊C8C22×C4711yescharacteristic
456C2×C4×C8C22×C4711yescharacteristic
457#397—21no—
458#392—21no—
459#386—21no—
460#386—21no—
461#382C22×C4711yescharacteristic
462#380C22×C4711yescharacteristic
463#380C22×C4711yescharacteristic
464#340C22×C4711yescharacteristic
465#340C22×C4711yescharacteristic
466#340C22×C4711yescharacteristic
467#340C22×C4711yescharacteristic
468#340C22×C4711yescharacteristic
469#340C22×C4711yescharacteristic
470C47#2412411yescharacteristic, direct product factor, Sylow
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C4711yescharacteristic
476C22×D4C23×C4711yescharacteristic
477C22×D4C23×C4711yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C4711yescharacteristic
482C23×C4C23×C4711yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C4711yescharacteristic
487C22×C8C23×C4711yescharacteristic
488C22×C8C23×C4711yescharacteristic
489C22×C8C23×C4711yescharacteristic
490#126—28no—
491#125—22no—
492#125D4×C4714yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C4714yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4D4×C4711yescharacteristic
518C2×C4⋊C4C23×C4711yescharacteristic
519C2×C4⋊C4C23×C4711yescharacteristic
520C2×C4⋊C4C23×C4711yescharacteristic
521C2×C4⋊C4C23×C4711yescharacteristic
522C2×C4⋊C4C23×C4711yescharacteristic
523C2×C4⋊C4C23×C4711yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4D4×C4711yescharacteristic
534C2×C22⋊C4D4×C4711yescharacteristic
535C2×C42—21no—
536C2×C42C23×C4711yescharacteristic
537#107—22no—
538#107—22no—
539#106—22no—
540C4⋊C8—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C4711yescharacteristic
559C24C2×D4×C4711yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C2×D4×C4712yes—
586C2×D4#41×C4712yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C4711yescharacteristic
615C22×C4C2×D4×C4711yescharacteristic
616C22×C4C2×D4×C4711yescharacteristic
617C22×C4C2×D4×C4711yescharacteristic
618C22×C4C24×C4711yescharacteristic
619D8—28no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8#41×C4712yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4C2×D4×C4712yes—
646C4⋊C4C2×D4×C4712yes—
647C4⋊C4C2×D4×C4712yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C4712yes—
661C42C2×D4×C4712yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#135×C4712yes—
690C23C22×D4×C4711yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#120×C4712yes—
744C2×C4#120×C4712yes—
745C2×C4C22×D4×C4711yescharacteristic
746C2×C4C22×D4×C4711yescharacteristic
747C2×C4C2×#41×C4711yescharacteristic
748C2×C4C2×#41×C4711yescharacteristic
749C2×C4H(5,𝔽2)×C4711yescharacteristic
750C2×C42−1+4×C4711yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C4711yescharacteristic
784C22C47×#54611yescharacteristic
785C22C47×#54711yescharacteristic
786C22C2×#135×C4711yescharacteristic
787C22C47×#57511yescharacteristic
788C22C47×#57611yescharacteristic
789C22C47×#57611yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4C47×#52511yescharacteristic
801C4C47×#53711yescharacteristic
802C4C47×#54811yescharacteristic
803C4C47×#55011yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2C47×#240711yescharacteristic
809C2C47×#300211yescharacteristic
810C2C47×#300811yescharacteristic
811C2C47×#329711yescharacteristic
812C2C47×#332211yescharacteristic
813C2C47×#333911yescharacteristic
814C2C47×#335511yescharacteristic
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×#553C2semidirect
2. C2×C47×#478C2semidirect
3. C2×C4×D8×C47C2semidirect
4. C47×#2535C2semidirect
5. C47×#2034C2semidirect
6. C47×#2033C2semidirect
7. C47×#1999C2semidirect
8. C47×#1999C2semidirect
9. C47×#1991C2semidirect
10. C47×#1954C2semidirect
11. C47×#1875C2semidirect
12. C47×#1874C2semidirect
13. C47×#1854C2semidirect
14. C47×#1852C2semidirect
15. C47×#1804C2semidirect
84. #125×C47D4semidirect
101. C4×D4×C47D4semidirect
347. #24124C47direct (N × H)
397. C2×#553C2×C47semidirect
398. C2×#478C2×C47semidirect
399. C2×C4×D8C2×C47semidirect
400. #2535C2×C47semidirect
401. #2034C2×C47semidirect
402. #2033C2×C47semidirect
403. #1999C2×C47semidirect
404. #1999C2×C47semidirect
405. #1991C2×C47semidirect
406. #1954C2×C47semidirect
407. #1875C2×C47semidirect
408. #1874C2×C47semidirect
409. #1854C2×C47semidirect
410. #1852C2×C47semidirect
411. #1804C2×C47semidirect
470. C47#24124direct (N × H)
492. #125D4×C47semidirect
509. C4×D4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5532
C2×C47×#4782
C2×C4×D8×C472
C47×#25352
C47×#20342
C47×#20332
C47×#19992
C47×#19912
C47×#19542
C47×#18752
C47×#18742
C47×#18542
C47×#18522
C47×#18042
#2412447