Finite Group Databasebeta

← C47×#25557 #26065255

Subgroups — C47×#25557 #26065255

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#552C211yesmaximal, characteristic
2C2×C47×#484C211yesmaximal, characteristic, complemented
3C2×C47×#470C211yesmaximal, characteristic, complemented
4C47×#2415C211yesmaximal, characteristic
5C47×#2059C211yesmaximal, characteristic, complemented
6C47×#2036C211yesmaximal, characteristic, complemented
7C47×#2026C211yesmaximal, characteristic, complemented
8C47×#2001C211yesmaximal, characteristic, complemented
9C47×#1878C211yesmaximal, characteristic, complemented
10C47×#1873C211yesmaximal, characteristic, complemented
11C47×#1873C211yesmaximal, characteristic, complemented
12C47×#1870C211yesmaximal, characteristic
13C47×#1863C211yesmaximal, characteristic, complemented
14C47×#1854C211yesmaximal, characteristic, complemented
15C47×#1736C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C47×#552—24no—
19C47×#552—24no—
20C2×#126×C47—21no—
21C2×#125×C47—21no—
22C2×#125×C47C2211yescharacteristic
23C2×#123×C47—21no—
24C2×C22⋊Q8×C47C2211yescharacteristic
25C2×C22⋊Q8×C47C2211yescharacteristic
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×C4×Q8×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C2×#117×C47—21no—
31C2×#117×C47C2211yescharacteristic
32C2×#117×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C47×#484—24no—
35C47×#470—24no—
36C2×#107×C47C2211yescharacteristic
37C2×#107×C47C2211yescharacteristic
38C2×#106×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#103×C47C2211yescharacteristic
42C2×#103×C47C2211yescharacteristic
43C2×#103×C47C2211yescharacteristic
44C2×#103×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#397—21no—
49C47×#394—21no—
50C47×#391C2211yescharacteristic
51C47×#389—21no—
52C47×#389C2211yescharacteristic
53C47×#388—21no—
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47D411yescharacteristic
66C23×C4×C47—21no—
67C23×C4×C47C2311yescharacteristic
68C23×C4×C47C2311yescharacteristic
69C2×Q16×C47—22no—
70C2×Q16×C47—22no—
71C2×Q16×C47—41no—
72C2×M16×C47—22no—
73C2×M16×C47—22no—
74C2×M16×C47—41no—
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79#126×C47—28no—
80#125×C47—28no—
81#125×C47—22no—
82#125×C47—22no—
83#123×C47—28no—
84C22⋊Q8×C47—22no—
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—22no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47—22no—
89C22⋊Q8×C47—22no—
90C22⋊Q8×C47—41no—
91C22⋊Q8×C47D414yes—
92C4×Q8×C47—22no—
93C4×Q8×C47—22no—
94C4×D4×C47—22no—
95C4×D4×C47—22no—
96#117×C47—28no—
97#117×C47—22no—
98#117×C47—22no—
99#117×C47—22no—
100#117×C47—41no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47D411yescharacteristic
112C2×C4⋊C4×C47D414yes—
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
130C2×C42×C47—21no—
131C2×C42×C47C2311yescharacteristic
132#107×C47—22no—
133#107×C47—22no—
134#106×C47—22no—
135#103×C47—22no—
136#103×C47—22no—
137#103×C47—22no—
138#103×C47—22no—
139#103×C47—22no—
140#103×C47—41no—
141C22⋊C8×C47—22no—
142C22⋊C8×C47—22no—
143C22⋊C8×C47—41no—
144#95×C47—21no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148C24×C47C2×D411yescharacteristic
149C24×C47C2×D411yescharacteristic
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47C2×D412yes—
162C2×D4×C47—22no—
163C2×D4×C47—41no—
164C2×D4×C47—41no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—24no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—42no—
185C22×C4×C47—42no—
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D412yes—
191C22×C4×C47C2×D412yes—
192C22×C4×C47C2411yescharacteristic
193Q16×C47—44no—
194M16×C47—44no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47#4112yes—
207C4⋊C4×C47—24no—
208C4⋊C4×C47—24no—
209C4⋊C4×C47—24no—
210C4⋊C4×C47—24no—
211C4⋊C4×C47—24no—
212C4⋊C4×C47—24no—
213C4⋊C4×C47—22no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—42no—
223C4⋊C4×C47—42no—
224C4⋊C4×C47—42no—
225C4⋊C4×C47C2×D412yes—
226C4⋊C4×C47C2×D412yes—
227C4⋊C4×C47C2×D412yes—
228C4⋊C4×C47#4112yes—
229C22⋊C4×C47—24no—
230C22⋊C4×C47—24no—
231C22⋊C4×C47—24no—
232C22⋊C4×C47—22no—
233C22⋊C4×C47—22no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C42×C47—24no—
239C42×C47—24no—
240C42×C47—21no—
241C42×C47—21no—
242C42×C47—42no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47#12012yes—
257C23×C47C22×D411yescharacteristic
258Q8×C47—22no—
259Q8×C47—22no—
260Q8×C47—41no—
261Q8×C47—41no—
262Q8×C47—41no—
263Q8×C47—41no—
264Q8×C47—41no—
265Q8×C47—41no—
266D4×C47—44no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—21no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—48no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47#12012yes—
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C2×#4111yescharacteristic
315C2×C4×C47C2×#4111yescharacteristic
316C2×C4×C47H(5,𝔽2)11yescharacteristic
317C2×C4×C472−1+411yescharacteristic
318C8×C47—22no—
319C8×C47—41no—
320C8×C47—41no—
321C8×C47—41no—
322#25557C4711yesmaximal, characteristic, direct product factor, Sylow
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47C2×#12011yescharacteristic
338C22×C47#54611yescharacteristic
339C22×C47#54711yescharacteristic
340C22×C47#57511yescharacteristic
341C22×C47#57511yescharacteristic
342C22×C47#57811yescharacteristic
343C22×C47#57811yescharacteristic
344C4×C47—22no—
345C4×C47—41no—
346C4×C47—42no—
347C4×C47—41no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47—41no—
351C4×C47—42no—
352C4×C47—42no—
353C4×C47—81no—
354C4×C47—81no—
355C4×C47—81no—
356C4×C47#53211yescharacteristic
357C4×C47#53711yescharacteristic
358C4×C47#54611yescharacteristic
359C4×C47#54711yescharacteristic
360C2×#552C2×C4711yescharacteristic
361C2×#484C2×C4711yescharacteristic, complemented
362C2×#470C2×C4711yescharacteristic, complemented
363#2415C2×C4711yescharacteristic
364#2059C2×C4711yescharacteristic, complemented
365#2036C2×C4711yescharacteristic, complemented
366#2026C2×C4711yescharacteristic, complemented
367#2001C2×C4711yescharacteristic, complemented
368#1878C2×C4711yescharacteristic, complemented
369#1873C2×C4711yescharacteristic, complemented
370#1873C2×C4711yescharacteristic, complemented
371#1870C2×C4711yescharacteristic
372#1863C2×C4711yescharacteristic, complemented
373#1854C2×C4711yescharacteristic, complemented
374#1736C2×C4711yescharacteristic, complemented
375C2×C47—42no—
376C2×C47—81no—
377C2×C47#243011yescharacteristic
378C2×C47#300511yescharacteristic
379C2×C47#301111yescharacteristic
380C2×C47#331511yescharacteristic
381C2×C47#332711yescharacteristic
382C2×C47#334911yescharacteristic
383C2×C47#335211yescharacteristic
384C22×Q16C22×C4711yescharacteristic
385C22×M16C22×C4711yescharacteristic
386#552—24no—
387#552—24no—
388C2×#126—21no—
389C2×#125—21no—
390C2×#125C22×C4711yescharacteristic
391C2×#123—21no—
392C2×C22⋊Q8C22×C4711yescharacteristic
393C2×C22⋊Q8C22×C4711yescharacteristic
394C2×C22⋊Q8C22×C4711yescharacteristic
395C2×C22⋊Q8C22×C4711yescharacteristic
396C2×C4×Q8C22×C4711yescharacteristic
397C2×C4×D4C22×C4711yescharacteristic
398C2×#117—21no—
399C2×#117C22×C4711yescharacteristic
400C2×#117C22×C4711yescharacteristic
401C22×C4⋊C4C22×C4711yescharacteristic
402#484—24no—
403#470—24no—
404C2×#107C22×C4711yescharacteristic
405C2×#107C22×C4711yescharacteristic
406C2×#106C22×C4711yescharacteristic
407C2×#103C22×C4711yescharacteristic
408C2×#103C22×C4711yescharacteristic
409C2×#103C22×C4711yescharacteristic
410C2×#103C22×C4711yescharacteristic
411C2×#103C22×C4711yescharacteristic
412C2×#103C22×C4711yescharacteristic
413C2×C22⋊C8C22×C4711yescharacteristic
414C2×C22⋊C8C22×C4711yescharacteristic
415C2×C22⋊C8C22×C4711yescharacteristic
416#397—21no—
417#394—21no—
418#391C22×C4711yescharacteristic
419#389—21no—
420#389C22×C4711yescharacteristic
421#388—21no—
422#380C22×C4711yescharacteristic
423#340C22×C4711yescharacteristic
424#340C22×C4711yescharacteristic
425#340C22×C4711yescharacteristic
426#340C22×C4711yescharacteristic
427#340C22×C4711yescharacteristic
428#340C22×C4711yescharacteristic
429#336C22×C4711yescharacteristic
430#336C22×C4711yescharacteristic
431C47#2555711yescharacteristic, direct product factor, Sylow
432C22×Q8C23×C4711yescharacteristic
433C22×Q8C23×C4711yescharacteristic
434C22×D4D4×C4711yescharacteristic
435C23×C4—21no—
436C23×C4C23×C4711yescharacteristic
437C23×C4C23×C4711yescharacteristic
438C2×Q16—22no—
439C2×Q16—22no—
440C2×Q16—41no—
441C2×M16—22no—
442C2×M16—22no—
443C2×M16—41no—
444C22×C8C23×C4711yescharacteristic
445C22×C8C23×C4711yescharacteristic
446C22×C8C23×C4711yescharacteristic
447C22×C8C23×C4711yescharacteristic
448#126—28no—
449#125—28no—
450#125—22no—
451#125—22no—
452#123—28no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456C22⋊Q8—22no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—41no—
460C22⋊Q8D4×C4714yes—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×D4—22no—
464C4×D4—22no—
465#117—28no—
466#117—22no—
467#117—22no—
468#117—22no—
469#117—41no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4D4×C4711yescharacteristic
481C2×C4⋊C4D4×C4714yes—
482C2×C4⋊C4C23×C4711yescharacteristic
483C2×C4⋊C4C23×C4711yescharacteristic
484C2×C4⋊C4C23×C4711yescharacteristic
485C2×C4⋊C4C23×C4711yescharacteristic
486C2×C4⋊C4C23×C4711yescharacteristic
487C2×C4⋊C4C23×C4711yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4D4×C4711yescharacteristic
496C2×C22⋊C4D4×C4711yescharacteristic
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42C23×C4711yescharacteristic
501#107—22no—
502#107—22no—
503#106—22no—
504#103—22no—
505#103—22no—
506#103—22no—
507#103—22no—
508#103—22no—
509#103—41no—
510C22⋊C8—22no—
511C22⋊C8—22no—
512C22⋊C8—41no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517C24C2×D4×C4711yescharacteristic
518C24C2×D4×C4711yescharacteristic
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8C2×D4×C4712yes—
531C2×D4—22no—
532C2×D4—41no—
533C2×D4—41no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4C2×D4×C4711yescharacteristic
556C22×C4C2×D4×C4711yescharacteristic
557C22×C4C2×D4×C4711yescharacteristic
558C22×C4C2×D4×C4711yescharacteristic
559C22×C4C2×D4×C4712yes—
560C22×C4C2×D4×C4712yes—
561C22×C4C24×C4711yescharacteristic
562Q16—44no—
563M16—44no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8#41×C4712yes—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4C2×D4×C4712yes—
595C4⋊C4C2×D4×C4712yes—
596C4⋊C4C2×D4×C4712yes—
597C4⋊C4#41×C4712yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C42—24no—
608C42—24no—
609C42—21no—
610C42—21no—
611C42—42no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23#120×C4712yes—
626C23C22×D4×C4711yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635D4—44no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—48no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4#120×C4712yes—
681C2×C4C22×D4×C4711yescharacteristic
682C2×C4C22×D4×C4711yescharacteristic
683C2×C4C2×#41×C4711yescharacteristic
684C2×C4C2×#41×C4711yescharacteristic
685C2×C4H(5,𝔽2)×C4711yescharacteristic
686C2×C42−1+4×C4711yescharacteristic
687C8—22no—
688C8—41no—
689C8—41no—
690C8—41no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22C2×#120×C4711yescharacteristic
706C22C47×#54611yescharacteristic
707C22C47×#54711yescharacteristic
708C22C47×#57511yescharacteristic
709C22C47×#57511yescharacteristic
710C22C47×#57811yescharacteristic
711C22C47×#57811yescharacteristic
712C4—22no—
713C4—42no—
714C4—41no—
715C4—42no—
716C4—41no—
717C4—42no—
718C4—42no—
719C4—41no—
720C4—42no—
721C4—81no—
722C4—81no—
723C4—81no—
724C4C47×#53211yescharacteristic
725C4C47×#53711yescharacteristic
726C4C47×#54611yescharacteristic
727C4C47×#54711yescharacteristic
728C2—42no—
729C2—81no—
730C2C47×#243011yescharacteristic
731C2C47×#300511yescharacteristic
732C2C47×#301111yescharacteristic
733C2C47×#331511yescharacteristic
734C2C47×#332711yescharacteristic
735C2C47×#334911yescharacteristic
736C2C47×#335211yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47D4
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
2. C2×C47×#484C2semidirect
3. C2×C47×#470C2semidirect
5. C47×#2059C2semidirect
6. C47×#2036C2semidirect
7. C47×#2026C2semidirect
8. C47×#2001C2semidirect
9. C47×#1878C2semidirect
10. C47×#1873C2semidirect
11. C47×#1873C2semidirect
13. C47×#1863C2semidirect
14. C47×#1854C2semidirect
15. C47×#1736C2semidirect
322. #25557C47direct (N × H)
361. C2×#484C2×C47semidirect
362. C2×#470C2×C47semidirect
364. #2059C2×C47semidirect
365. #2036C2×C47semidirect
366. #2026C2×C47semidirect
367. #2001C2×C47semidirect
368. #1878C2×C47semidirect
369. #1873C2×C47semidirect
370. #1873C2×C47semidirect
372. #1863C2×C47semidirect
373. #1854C2×C47semidirect
374. #1736C2×C47semidirect
431. C47#25557direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5522
C2×C47×#4842
C2×C47×#4702
C47×#24152
C47×#20592
C47×#20362
C47×#20262
C47×#20012
C47×#18782
C47×#18732
C47×#18702
C47×#18632
C47×#18542
C47×#17362
#2555747