Finite Group Databasebeta

← C47×#24922 #26064620

Subgroups — C47×#24922 #26064620

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#451C211yesmaximal, characteristic
2C2×C47×#441C211yesmaximal, characteristic, complemented
3C47×#2421C211yesmaximal, characteristic
4Q8×C22⋊C4×C47C211yesmaximal, characteristic
5C47×#2097C211yesmaximal, characteristic, complemented
6C47×#2077C211yesmaximal, characteristic
7C47×#2056C211yesmaximal, characteristic, complemented
8C47×#2036C211yesmaximal, characteristic
9C47×#1935C211yesmaximal, characteristic, complemented
10C47×#1924C211yesmaximal, characteristic
11C47×#1878C211yesmaximal, characteristic, complemented
12C47×#1878C211yesmaximal, characteristic, complemented
13C47×#1863C211yesmaximal, characteristic, complemented
14C47×#1805C211yesmaximal, characteristic, complemented
15C47×#1787C211yesmaximal, characteristic
16C23×Q8×C47C2211yescharacteristic
17C22×Q16×C47C2211yescharacteristic
18C22×Q16×C47C2211yescharacteristic
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×C4×Q8×C47C2211yescharacteristic
21C2×C4×Q8×C47C2211yescharacteristic
22C2×C4×Q8×C47C2211yescharacteristic
23C47×#451—24no—
24C47×#441—24no—
25C2×#107×C47C2211yescharacteristic
26C2×#106×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C2×#103×C47C2211yescharacteristic
29C2×#103×C47C2211yescharacteristic
30C2×#103×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×#103×C47C2211yescharacteristic
33C2×#103×C47C2211yescharacteristic
34C2×#103×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×C22⋊C8×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×#97×C47C2211yescharacteristic
39C47×#400—21no—
40C47×#397—21no—
41C47×#391—21no—
42C47×#391—21no—
43C47×#391C2211yescharacteristic
44C47×#391C2211yescharacteristic
45C47×#391C2211yescharacteristic
46C47×#389C2211yescharacteristic
47C47×#388—21no—
48C47×#387—21no—
49C47×#382C2211yescharacteristic
50C47×#380—21no—
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C4×C22⋊C4×C47—21no—
54C4×C22⋊C4×C47C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×Q8×C47—22no—
62C22×Q8×C47—22no—
63C22×Q8×C47—21no—
64C22×Q8×C47—22no—
65C22×Q8×C47—22no—
66C22×Q8×C47—41no—
67C22×Q8×C47—41no—
68C22×Q8×C47C2311yescharacteristic
69C22×Q8×C47C2311yescharacteristic
70C22×Q8×C47C2311yescharacteristic
71C23×C4×C47—21no—
72C23×C4×C47C2311yescharacteristic
73C2×Q16×C47—22no—
74C2×Q16×C47—22no—
75C2×Q16×C47—22no—
76C2×Q16×C47—22no—
77C2×Q16×C47—41no—
78C2×Q16×C47D414yes—
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22⋊Q8×C47—22no—
84C22⋊Q8×C47—41no—
85C4×Q8×C47—22no—
86C4×Q8×C47—22no—
87C4×Q8×C47—22no—
88C4×Q8×C47—41no—
89C4×Q8×C47—41no—
90C4×Q8×C47—41no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47D411yescharacteristic
105C2×C22⋊C4×C47D411yescharacteristic
106C2×C42×C47—21no—
107C2×C42×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111#107×C47—41no—
112#106×C47—22no—
113C4⋊C8×C47—41no—
114#103×C47—22no—
115#103×C47—22no—
116#103×C47—22no—
117#103×C47—22no—
118#103×C47—22no—
119#103×C47—22no—
120#103×C47—41no—
121#103×C47—41no—
122C22⋊C8×C47—22no—
123C22⋊C8×C47—41no—
124#97×C47—22no—
125#95×C47—21no—
126#95×C47—21no—
127#95×C47—21no—
128#95×C47—21no—
129#95×C47—21no—
130#95×C47—21no—
131#95×C47—21no—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47D411yescharacteristic
137#95×C47D411yescharacteristic
138C24×C47C2×D411yescharacteristic
139C2×Q8×C47—24no—
140C2×Q8×C47—21no—
141C2×Q8×C47—21no—
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×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—42no—
154C2×Q8×C47—42no—
155C2×Q8×C47—44no—
156C2×Q8×C47—44no—
157C2×Q8×C47—44no—
158C2×Q8×C47—44no—
159C2×Q8×C47C2×D412yes—
160C2×Q8×C47C2×D412yes—
161C2×Q8×C47#4112yes—
162C2×Q8×C47#4112yes—
163C2×Q8×C47#4112yes—
164C22×C4×C47—21no—
165C22×C4×C47—24no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×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×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—42no—
180C22×C4×C47—42no—
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2411yescharacteristic
187Q16×C47—28no—
188Q16×C47—44no—
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×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47C2×D412yes—
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—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—42no—
212C4⋊C4×C47—42no—
213C4⋊C4×C47—42no—
214C4⋊C4×C47—42no—
215C4⋊C4×C47—42no—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—41no—
218C22⋊C4×C47—42no—
219C22⋊C4×C47—42no—
220C22⋊C4×C47—42no—
221C42×C47—21no—
222C42×C47—21no—
223C42×C47—21no—
224C42×C47—21no—
225C42×C47—42no—
226C42×C47—42no—
227C42×C47—42no—
228C23×C47—21no—
229C23×C47—21no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47#13712yes—
235C23×C47C22×D411yescharacteristic
236Q8×C47—22no—
237Q8×C47—22no—
238Q8×C47—22no—
239Q8×C47—22no—
240Q8×C47—22no—
241Q8×C47—22no—
242Q8×C47—22no—
243Q8×C47—48no—
244Q8×C47—41no—
245Q8×C47—41no—
246Q8×C47—41no—
247Q8×C47—41no—
248Q8×C47#12314yes—
249C2×C4×C47—22no—
250C2×C4×C47—22no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—22no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—48no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
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×C47C22×D411yescharacteristic
294C2×C4×C47C2×#4111yescharacteristic
295C2×C4×C47C2×#4111yescharacteristic
296C2×C4×C47C2×#4111yescharacteristic
297C2×C4×C47H(5,𝔽2)11yescharacteristic
298C2×C4×C47H(5,𝔽2)11yescharacteristic
299C8×C47—22no—
300C8×C47—41no—
301C8×C47—41no—
302C8×C47—41no—
303#24922C4711yesmaximal, characteristic, direct product factor, Sylow
304C22×C47—22no—
305C22×C47—22no—
306C22×C47—22no—
307C22×C47—41no—
308C22×C47—41no—
309C22×C47—41no—
310C22×C47—41no—
311C22×C47#52511yescharacteristic
312C22×C47D4211yescharacteristic
313C22×C47#54611yescharacteristic
314C22×C47C2×#13711yescharacteristic
315C22×C47#57511yescharacteristic
316C22×C47#57811yescharacteristic
317C22×C47#57811yescharacteristic
318C4×C47—24no—
319C4×C47—41no—
320C4×C47—42no—
321C4×C47—42no—
322C4×C47—41no—
323C4×C47—41no—
324C4×C47—41no—
325C4×C47—41no—
326C4×C47—81no—
327C4×C47—81no—
328C4×C47—81no—
329C4×C47—81no—
330C4×C47—81no—
331C4×C47C2×#12311yescharacteristic
332C4×C47#53811yescharacteristic
333C4×C47#54611yescharacteristic
334C4×C47#55111yescharacteristic
335C2×#451C2×C4711yescharacteristic
336C2×#441C2×C4711yescharacteristic, complemented
337#2421C2×C4711yescharacteristic
338Q8×C22⋊C4C2×C4711yescharacteristic
339#2097C2×C4711yescharacteristic, complemented
340#2077C2×C4711yescharacteristic
341#2056C2×C4711yescharacteristic, complemented
342#2036C2×C4711yescharacteristic
343#1935C2×C4711yescharacteristic, complemented
344#1924C2×C4711yescharacteristic
345#1878C2×C4711yescharacteristic, complemented
346#1878C2×C4711yescharacteristic, complemented
347#1863C2×C4711yescharacteristic, complemented
348#1805C2×C4711yescharacteristic, complemented
349#1787C2×C4711yescharacteristic
350C2×C47—42no—
351C2×C47#241811yescharacteristic
352C2×C47#311711yescharacteristic
353C2×C47#312711yescharacteristic
354C2×C47#327011yescharacteristic
355C2×C47#327711yescharacteristic
356C2×C47#331211yescharacteristic
357C2×C47#331311yescharacteristic
358C23×Q8C22×C4711yescharacteristic
359C22×Q16C22×C4711yescharacteristic
360C22×Q16C22×C4711yescharacteristic
361C2×C22⋊Q8C22×C4711yescharacteristic
362C2×C4×Q8C22×C4711yescharacteristic
363C2×C4×Q8C22×C4711yescharacteristic
364C2×C4×Q8C22×C4711yescharacteristic
365#451—24no—
366#441—24no—
367C2×#107C22×C4711yescharacteristic
368C2×#106C22×C4711yescharacteristic
369C2×C4⋊C8C22×C4711yescharacteristic
370C2×#103C22×C4711yescharacteristic
371C2×#103C22×C4711yescharacteristic
372C2×#103C22×C4711yescharacteristic
373C2×#103C22×C4711yescharacteristic
374C2×#103C22×C4711yescharacteristic
375C2×#103C22×C4711yescharacteristic
376C2×#103C22×C4711yescharacteristic
377C2×#103C22×C4711yescharacteristic
378C2×C22⋊C8C22×C4711yescharacteristic
379C2×C22⋊C8C22×C4711yescharacteristic
380C2×#97C22×C4711yescharacteristic
381#400—21no—
382#397—21no—
383#391—21no—
384#391—21no—
385#391C22×C4711yescharacteristic
386#391C22×C4711yescharacteristic
387#391C22×C4711yescharacteristic
388#389C22×C4711yescharacteristic
389#388—21no—
390#387—21no—
391#382C22×C4711yescharacteristic
392#380—21no—
393#380C22×C4711yescharacteristic
394#380C22×C4711yescharacteristic
395C4×C22⋊C4—21no—
396C4×C22⋊C4C22×C4711yescharacteristic
397#340C22×C4711yescharacteristic
398#340C22×C4711yescharacteristic
399#340C22×C4711yescharacteristic
400#340C22×C4711yescharacteristic
401#336C22×C4711yescharacteristic
402#336C22×C4711yescharacteristic
403C47#2492211yescharacteristic, direct product factor, Sylow
404C22×Q8—22no—
405C22×Q8—22no—
406C22×Q8—21no—
407C22×Q8—22no—
408C22×Q8—22no—
409C22×Q8—41no—
410C22×Q8—41no—
411C22×Q8C23×C4711yescharacteristic
412C22×Q8C23×C4711yescharacteristic
413C22×Q8C23×C4711yescharacteristic
414C23×C4—21no—
415C23×C4C23×C4711yescharacteristic
416C2×Q16—22no—
417C2×Q16—22no—
418C2×Q16—22no—
419C2×Q16—22no—
420C2×Q16—41no—
421C2×Q16D4×C4714yes—
422C22×C8C23×C4711yescharacteristic
423C22×C8C23×C4711yescharacteristic
424C22×C8C23×C4711yescharacteristic
425C22×C8C23×C4711yescharacteristic
426C22⋊Q8—22no—
427C22⋊Q8—41no—
428C4×Q8—22no—
429C4×Q8—22no—
430C4×Q8—22no—
431C4×Q8—41no—
432C4×Q8—41no—
433C4×Q8—41no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4C23×C4711yescharacteristic
440C2×C4⋊C4C23×C4711yescharacteristic
441C2×C4⋊C4C23×C4711yescharacteristic
442C2×C4⋊C4C23×C4711yescharacteristic
443C2×C4⋊C4C23×C4711yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C4711yescharacteristic
448C2×C22⋊C4D4×C4711yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C23×C4711yescharacteristic
453C2×C42C23×C4711yescharacteristic
454#107—41no—
455#106—22no—
456C4⋊C8—41no—
457#103—22no—
458#103—22no—
459#103—22no—
460#103—22no—
461#103—22no—
462#103—22no—
463#103—41no—
464#103—41no—
465C22⋊C8—22no—
466C22⋊C8—41no—
467#97—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95D4×C4711yescharacteristic
480#95D4×C4711yescharacteristic
481C24C2×D4×C4711yescharacteristic
482C2×Q8—24no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8C2×D4×C4712yes—
503C2×Q8C2×D4×C4712yes—
504C2×Q8#41×C4712yes—
505C2×Q8#41×C4712yes—
506C2×Q8#41×C4712yes—
507C22×C4—21no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
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—
532C2×C8—21no—
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×C8C2×D4×C4712yes—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C22⋊C4—22no—
560C22⋊C4—41no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—42no—
569C42—42no—
570C42—42no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23#137×C4712yes—
578C23C22×D4×C4711yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—48no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8#123×C4714yes—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—48no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
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×C4C22×D4×C4711yescharacteristic
637C2×C4C2×#41×C4711yescharacteristic
638C2×C4C2×#41×C4711yescharacteristic
639C2×C4C2×#41×C4711yescharacteristic
640C2×C4H(5,𝔽2)×C4711yescharacteristic
641C2×C4H(5,𝔽2)×C4711yescharacteristic
642C8—22no—
643C8—41no—
644C8—41no—
645C8—41no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22C47×#52511yescharacteristic
654C22D42×C4711yescharacteristic
655C22C47×#54611yescharacteristic
656C22C2×#137×C4711yescharacteristic
657C22C47×#57511yescharacteristic
658C22C47×#57811yescharacteristic
659C22C47×#57811yescharacteristic
660C4—24no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—42no—
665C4—42no—
666C4—41no—
667C4—41no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4C2×#123×C4711yescharacteristic
674C4C47×#53811yescharacteristic
675C4C47×#54611yescharacteristic
676C4C47×#55111yescharacteristic
677C2—42no—
678C2C47×#241811yescharacteristic
679C2C47×#311711yescharacteristic
680C2C47×#312711yescharacteristic
681C2C47×#327011yescharacteristic
682C2C47×#327711yescharacteristic
683C2C47×#331211yescharacteristic
684C2C47×#331311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC24×C47C2×D4
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
2. C2×C47×#441C2semidirect
5. C47×#2097C2semidirect
7. C47×#2056C2semidirect
9. C47×#1935C2semidirect
11. C47×#1878C2semidirect
12. C47×#1878C2semidirect
13. C47×#1863C2semidirect
14. C47×#1805C2semidirect
303. #24922C47direct (N × H)
336. C2×#441C2×C47semidirect
339. #2097C2×C47semidirect
341. #2056C2×C47semidirect
343. #1935C2×C47semidirect
345. #1878C2×C47semidirect
346. #1878C2×C47semidirect
347. #1863C2×C47semidirect
348. #1805C2×C47semidirect
403. C47#24922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4512
C2×C47×#4412
C47×#24212
Q8×C22⋊C4×C472
C47×#20972
C47×#20772
C47×#20562
C47×#20362
C47×#19352
C47×#19242
C47×#18782
C47×#18632
C47×#18052
C47×#17872
#2492247