Finite Group Databasebeta

← C47×#24741 #26064439

Subgroups — C47×#24741 #26064439

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#464C211yesmaximal, characteristic
2C2×C47×#464C211yesmaximal, characteristic
3C2×C47×#462C211yesmaximal, characteristic, complemented
4C2×C47×#441C211yesmaximal, characteristic, complemented
5C47×#2545C211yesmaximal, characteristic
6Q8×C4⋊C4×C47C211yesmaximal, characteristic, complemented
7C47×#2066C211yesmaximal, characteristic, complemented
8C47×#2065C211yesmaximal, characteristic
9C47×#2043C211yesmaximal, characteristic, complemented
10C47×#2042C211yesmaximal, characteristic
11C47×#1959C211yesmaximal, characteristic
12C47×#1940C211yesmaximal, characteristic, complemented
13C47×#1880C211yesmaximal, characteristic
14C47×#1878C211yesmaximal, characteristic, complemented
15C47×#1803C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×Q16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C2×C4⋊Q8×C47C2211yescharacteristic
20C2×#124×C47C2211yescharacteristic
21C2×#124×C47C2211yescharacteristic
22C2×C4×Q8×C47C2211yescharacteristic
23C2×C4×Q8×C47C2211yescharacteristic
24C2×C4×Q8×C47C2211yescharacteristic
25C2×C4×Q8×C47C2211yescharacteristic
26C47×#464—24no—
27C47×#464—24no—
28C47×#462—24no—
29C47×#441—24no—
30C2×#106×C47C2211yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×#103×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#97×C47C2211yescharacteristic
45C47×#396—21no—
46C47×#396—21no—
47C47×#391C2211yescharacteristic
48C47×#390C2211yescharacteristic
49C47×#389—21no—
50C47×#389—21no—
51C47×#389C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#388—21no—
54C47×#388—21no—
55C47×#384—21no—
56C47×#384C2211yescharacteristic
57C4×C4⋊C4×C47—21no—
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×Q8×C47C2311yescharacteristic
65C22×Q8×C47C2311yescharacteristic
66C22×D4×C47C2311yescharacteristic
67C2×Q16×C47—22no—
68C2×Q16×C47—22no—
69C2×Q16×C47—22no—
70C2×Q16×C47—22no—
71C2×Q16×C47—22no—
72C2×Q16×C47D414yes—
73C2×SD16×C47—22no—
74C2×SD16×C47—22no—
75C2×SD16×C47—22no—
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C4⋊Q8×C47—22no—
81C4⋊Q8×C47—41no—
82#124×C47—22no—
83#124×C47—22no—
84#124×C47—22no—
85#124×C47—41no—
86C4×Q8×C47—22no—
87C4×Q8×C47—22no—
88C4×Q8×C47—22no—
89C4×Q8×C47—22no—
90C4×Q8×C47—22no—
91C4×Q8×C47—41no—
92C4×Q8×C47—41no—
93C4×Q8×C47D414yes—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47D411yescharacteristic
105C2×C4⋊C4×C47D411yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C42×C47—21no—
117C2×C42×C47—21no—
118C2×C42×C47—21no—
119C2×C42×C47—21no—
120C2×C42×C47C2311yescharacteristic
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123#106×C47—22no—
124C4⋊C8×C47—22no—
125C4⋊C8×C47—22no—
126C4⋊C8×C47—22no—
127#103×C47—22no—
128#103×C47—22no—
129#103×C47—22no—
130#103×C47—22no—
131#103×C47—22no—
132#103×C47—22no—
133#103×C47—41no—
134#102×C47—22no—
135#102×C47—22no—
136#102×C47—41no—
137#97×C47—22no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47D411yescharacteristic
143#95×C47D411yescharacteristic
144C24×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
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×C47C2×D412yes—
160C2×Q8×C47C2×D412yes—
161C2×Q8×C47C2×D412yes—
162C2×Q8×C47#4112yes—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C22×C4×C47—21no—
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×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2411yescharacteristic
183Q16×C47—28no—
184Q16×C47—44no—
185SD16×C47—44no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47C2×D412yes—
198C4⋊C4×C47—24no—
199C4⋊C4×C47—22no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—41no—
208C4⋊C4×C47—42no—
209C4⋊C4×C47—42no—
210C4⋊C4×C47—42no—
211C4⋊C4×C47—42no—
212C4⋊C4×C47—42no—
213C4⋊C4×C47—42no—
214C4⋊C4×C47—81no—
215C4⋊C4×C47—81no—
216C4⋊C4×C47—81no—
217C4⋊C4×C47C2×D412yes—
218C22⋊C4×C47—42no—
219C22⋊C4×C47—42no—
220C22⋊C4×C47—42no—
221C22⋊C4×C47—42no—
222C22⋊C4×C47—42no—
223C22⋊C4×C47—42no—
224C42×C47—24no—
225C42×C47—21no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—42no—
230C42×C47—42no—
231C42×C47—42no—
232C42×C47C2×D412yes—
233C42×C47#4112yes—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47C22×D411yescharacteristic
242Q8×C47—22no—
243Q8×C47—22no—
244Q8×C47—22no—
245Q8×C47—22no—
246Q8×C47—22no—
247Q8×C47—41no—
248Q8×C47—41no—
249Q8×C47—41no—
250Q8×C47—41no—
251Q8×C47—41no—
252Q8×C47—41no—
253Q8×C47#12114yes—
254D4×C47—41no—
255D4×C47—41no—
256D4×C47—41no—
257D4×C47—41no—
258C2×C4×C47—22no—
259C2×C4×C47—21no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—22no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—22no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
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#12112yes—
295C2×C4×C47#12112yes—
296C2×C4×C47#13712yes—
297C2×C4×C47C22×D411yescharacteristic
298C2×C4×C47C22×D411yescharacteristic
299C2×C4×C47C2×#4111yescharacteristic
300C2×C4×C47C2×#4111yescharacteristic
301C2×C4×C47H(5,𝔽2)11yescharacteristic
302C2×C4×C472−1+411yescharacteristic
303C8×C47—22no—
304C8×C47—41no—
305C8×C47—41no—
306C8×C47—41no—
307#24741C4711yesmaximal, characteristic, direct product factor, Sylow
308C22×C47—81no—
309C22×C47—81no—
310C22×C47—81no—
311C22×C47—81no—
312C22×C47—81no—
313C22×C47—81no—
314C22×C47—81no—
315C22×C47C2×#12111yescharacteristic
316C22×C47D4211yescharacteristic
317C22×C47#54811yescharacteristic
318C22×C47C2×#13711yescharacteristic
319C22×C47#57511yescharacteristic
320C22×C47#57711yescharacteristic
321C22×C47#57811yescharacteristic
322C4×C47—24no—
323C4×C47—22no—
324C4×C47—22no—
325C4×C47—22no—
326C4×C47—42no—
327C4×C47—41no—
328C4×C47—41no—
329C4×C47—41no—
330C4×C47—42no—
331C4×C47—81no—
332C4×C47—81no—
333C4×C47—81no—
334C4×C47—81no—
335C4×C47C2×#12111yescharacteristic
336C4×C47#53711yescharacteristic
337C4×C47#54711yescharacteristic
338C4×C47#55311yescharacteristic
339C2×#464C2×C4711yescharacteristic
340C2×#464C2×C4711yescharacteristic
341C2×#462C2×C4711yescharacteristic, complemented
342C2×#441C2×C4711yescharacteristic, complemented
343#2545C2×C4711yescharacteristic
344Q8×C4⋊C4C2×C4711yescharacteristic, complemented
345#2066C2×C4711yescharacteristic, complemented
346#2065C2×C4711yescharacteristic
347#2043C2×C4711yescharacteristic, complemented
348#2042C2×C4711yescharacteristic
349#1959C2×C4711yescharacteristic
350#1940C2×C4711yescharacteristic, complemented
351#1880C2×C4711yescharacteristic
352#1878C2×C4711yescharacteristic, complemented
353#1803C2×C4711yescharacteristic, complemented
354C2×C47—161no—
355C2×C47#241611yescharacteristic
356C2×C47#303711yescharacteristic
357C2×C47#304611yescharacteristic
358C2×C47#327011yescharacteristic
359C2×C47#327111yescharacteristic
360C2×C47#336911yescharacteristic
361C2×C47#337711yescharacteristic
362C22×Q16C22×C4711yescharacteristic
363C22×Q16C22×C4711yescharacteristic
364C22×SD16C22×C4711yescharacteristic
365C2×C4⋊Q8C22×C4711yescharacteristic
366C2×#124C22×C4711yescharacteristic
367C2×#124C22×C4711yescharacteristic
368C2×C4×Q8C22×C4711yescharacteristic
369C2×C4×Q8C22×C4711yescharacteristic
370C2×C4×Q8C22×C4711yescharacteristic
371C2×C4×Q8C22×C4711yescharacteristic
372#464—24no—
373#464—24no—
374#462—24no—
375#441—24no—
376C2×#106C22×C4711yescharacteristic
377C2×C4⋊C8C22×C4711yescharacteristic
378C2×C4⋊C8C22×C4711yescharacteristic
379C2×C4⋊C8C22×C4711yescharacteristic
380C2×#103C22×C4711yescharacteristic
381C2×#103C22×C4711yescharacteristic
382C2×#103C22×C4711yescharacteristic
383C2×#103C22×C4711yescharacteristic
384C2×#103C22×C4711yescharacteristic
385C2×#103C22×C4711yescharacteristic
386C2×#103C22×C4711yescharacteristic
387C2×#102C22×C4711yescharacteristic
388C2×#102C22×C4711yescharacteristic
389C2×#102C22×C4711yescharacteristic
390C2×#97C22×C4711yescharacteristic
391#396—21no—
392#396—21no—
393#391C22×C4711yescharacteristic
394#390C22×C4711yescharacteristic
395#389—21no—
396#389—21no—
397#389C22×C4711yescharacteristic
398#389C22×C4711yescharacteristic
399#388—21no—
400#388—21no—
401#384—21no—
402#384C22×C4711yescharacteristic
403C4×C4⋊C4—21no—
404C4×C4⋊C4C22×C4711yescharacteristic
405#340C22×C4711yescharacteristic
406#340C22×C4711yescharacteristic
407#336C22×C4711yescharacteristic
408#336C22×C4711yescharacteristic
409C47#2474111yescharacteristic, direct product factor, Sylow
410C22×Q8C23×C4711yescharacteristic
411C22×Q8C23×C4711yescharacteristic
412C22×Q8C23×C4711yescharacteristic
413C22×D4C23×C4711yescharacteristic
414C2×Q16—22no—
415C2×Q16—22no—
416C2×Q16—22no—
417C2×Q16—22no—
418C2×Q16—22no—
419C2×Q16D4×C4714yes—
420C2×SD16—22no—
421C2×SD16—22no—
422C2×SD16—22no—
423C22×C8C23×C4711yescharacteristic
424C22×C8C23×C4711yescharacteristic
425C22×C8C23×C4711yescharacteristic
426C22×C8C23×C4711yescharacteristic
427C4⋊Q8—22no—
428C4⋊Q8—41no—
429#124—22no—
430#124—22no—
431#124—22no—
432#124—41no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×Q8—22no—
436C4×Q8—22no—
437C4×Q8—22no—
438C4×Q8—41no—
439C4×Q8—41no—
440C4×Q8D4×C4714yes—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4D4×C4711yescharacteristic
452C2×C4⋊C4D4×C4711yescharacteristic
453C2×C4⋊C4C23×C4711yescharacteristic
454C2×C4⋊C4C23×C4711yescharacteristic
455C2×C4⋊C4C23×C4711yescharacteristic
456C2×C4⋊C4C23×C4711yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42C23×C4711yescharacteristic
468C2×C42C23×C4711yescharacteristic
469C2×C42C23×C4711yescharacteristic
470#106—22no—
471C4⋊C8—22no—
472C4⋊C8—22no—
473C4⋊C8—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477#103—22no—
478#103—22no—
479#103—22no—
480#103—41no—
481#102—22no—
482#102—22no—
483#102—41no—
484#97—22no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95D4×C4711yescharacteristic
490#95D4×C4711yescharacteristic
491C24—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8C2×D4×C4712yes—
507C2×Q8C2×D4×C4712yes—
508C2×Q8C2×D4×C4712yes—
509C2×Q8#41×C4712yes—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4C2×D4×C4711yescharacteristic
524C22×C4C2×D4×C4711yescharacteristic
525C22×C4C2×D4×C4711yescharacteristic
526C22×C4C2×D4×C4711yescharacteristic
527C22×C4C2×D4×C4711yescharacteristic
528C22×C4C2×D4×C4711yescharacteristic
529C22×C4C24×C4711yescharacteristic
530Q16—28no—
531Q16—44no—
532SD16—44no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8C2×D4×C4712yes—
545C4⋊C4—24no—
546C4⋊C4—22no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—41no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4—81no—
564C4⋊C4C2×D4×C4712yes—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C42—24no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—42no—
578C42—42no—
579C42C2×D4×C4712yes—
580C42#41×C4712yes—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C22×D4×C4711yescharacteristic
589Q8—22no—
590Q8—22no—
591Q8—22no—
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—41no—
597Q8—41no—
598Q8—41no—
599Q8—41no—
600Q8#121×C4714yes—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4#121×C4712yes—
642C2×C4#121×C4712yes—
643C2×C4#137×C4712yes—
644C2×C4C22×D4×C4711yescharacteristic
645C2×C4C22×D4×C4711yescharacteristic
646C2×C4C2×#41×C4711yescharacteristic
647C2×C4C2×#41×C4711yescharacteristic
648C2×C4H(5,𝔽2)×C4711yescharacteristic
649C2×C42−1+4×C4711yescharacteristic
650C8—22no—
651C8—41no—
652C8—41no—
653C8—41no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×#121×C4711yescharacteristic
662C22D42×C4711yescharacteristic
663C22C47×#54811yescharacteristic
664C22C2×#137×C4711yescharacteristic
665C22C47×#57511yescharacteristic
666C22C47×#57711yescharacteristic
667C22C47×#57811yescharacteristic
668C4—22no—
669C4—22no—
670C4—24no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—41no—
675C4—41no—
676C4—41no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4C2×#121×C4711yescharacteristic
682C4C47×#53711yescharacteristic
683C4C47×#54711yescharacteristic
684C4C47×#55311yescharacteristic
685C2—161no—
686C2C47×#241611yescharacteristic
687C2C47×#303711yescharacteristic
688C2C47×#304611yescharacteristic
689C2C47×#327011yescharacteristic
690C2C47×#327111yescharacteristic
691C2C47×#336911yescharacteristic
692C2C47×#337711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C4⋊C4×C47 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C47×#462C2semidirect
4. C2×C47×#441C2semidirect
6. Q8×C4⋊C4×C47C2semidirect
7. C47×#2066C2semidirect
9. C47×#2043C2semidirect
12. C47×#1940C2semidirect
14. C47×#1878C2semidirect
15. C47×#1803C2semidirect
307. #24741C47direct (N × H)
341. C2×#462C2×C47semidirect
342. C2×#441C2×C47semidirect
344. Q8×C4⋊C4C2×C47semidirect
345. #2066C2×C47semidirect
347. #2043C2×C47semidirect
350. #1940C2×C47semidirect
352. #1878C2×C47semidirect
353. #1803C2×C47semidirect
409. C47#24741direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4642
C2×C47×#4622
C2×C47×#4412
C47×#25452
Q8×C4⋊C4×C472
C47×#20662
C47×#20652
C47×#20432
C47×#20422
C47×#19592
C47×#19402
C47×#18802
C47×#18782
C47×#18032
#2474147