Finite Group Databasebeta

← C47×#13899 #26053597

Subgroups — C47×#13899 #26053597

Order 12032.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C47C211yesmaximal, characteristic
2C2×C47×#386C212yesmaximal
3C2×C47×#385C212yesmaximal, complemented
4C2×C47×#380C211yesmaximal, characteristic, complemented
5C22×#95×C47C211yesmaximal, characteristic, complemented
6C47×#1441C212yesmaximal, complemented
7C47×#1439C212yesmaximal, complemented
8C47×C4⋊#95C211yesmaximal, characteristic, complemented
9C47×#1434C211yesmaximal, characteristic, complemented
10C47×C22⋊#95C211yesmaximal, characteristic, complemented
11C47×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C47C2211yescharacteristic
13C24×C4×C47C2212yes—
14C24×C4×C47C2211yescharacteristic
15C24×C4×C47C2211yescharacteristic
16C2×C4×D4×C47—28no—
17C2×C4×D4×C47C418yescomplemented
18C22×C4⋊C4×C47C2212yes—
19C22×C4⋊C4×C47C2212yes—
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C22⋊C4×C47C2212yes—
22C22×C22⋊C4×C47C2212yes—
23C22×C22⋊C4×C47C2212yes—
24C22×C22⋊C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47C2211yescharacteristic
26C22×C42×C47C2211yescharacteristic
27C47×#386—28no—
28C47×#385—28no—
29C47×#380—24no—
30C2×#95×C47—24no—
31C2×#95×C47C2211yescharacteristic
32C2×#95×C47C2212yes—
33C2×#95×C47C2211yescharacteristic
34C2×#95×C47C2212yes—
35C2×#95×C47C2212yes—
36C2×#95×C47C2212yes—
37C2×#95×C47C2212yes—
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2212yes—
40C2×#95×C47C2211yescharacteristic
41C25×C47C2311yescharacteristic
42C25×C47C2311yescharacteristic
43C22×D4×C47—24no—
44C22×D4×C47—24no—
45C22×D4×C47C2×C414yes—
46C22×D4×C47D414yes—
47C22×D4×C47Q814yes—
48C23×C4×C47—24no—
49C23×C4×C47—24no—
50C23×C4×C47—24no—
51C23×C4×C47—24no—
52C23×C4×C47—22no—
53C23×C4×C47—22no—
54C23×C4×C47—22no—
55C23×C4×C47—24no—
56C23×C4×C47—22no—
57C23×C4×C47—24no—
58C23×C4×C47—24no—
59C23×C4×C47—42no—
60C23×C4×C47—42no—
61C23×C4×C47—42no—
62C23×C4×C47—42no—
63C23×C4×C47C2×C414yes—
64C23×C4×C47C2×C414yescomplemented
65C23×C4×C47C2312yes—
66C23×C4×C47C2312yes—
67C23×C4×C47C2311yescharacteristic
68C23×C4×C47C2312yes—
69C23×C4×C47C2312yes—
70C23×C4×C47C2311yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C23×C4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C4×D4×C47—232no—
75C2×C4⋊C4×C47—24no—
76C2×C4⋊C4×C47—24no—
77C2×C4⋊C4×C47—24no—
78C2×C4⋊C4×C47—24no—
79C2×C4⋊C4×C47—24no—
80C2×C4⋊C4×C47—42no—
81C2×C4⋊C4×C47—42no—
82C2×C4⋊C4×C47C2×C414yescomplemented
83C2×C22⋊C4×C47—24no—
84C2×C22⋊C4×C47—24no—
85C2×C22⋊C4×C47—24no—
86C2×C22⋊C4×C47—24no—
87C2×C22⋊C4×C47—24no—
88C2×C22⋊C4×C47—24no—
89C2×C22⋊C4×C47—24no—
90C2×C22⋊C4×C47—24no—
91C2×C22⋊C4×C47—42no—
92C2×C22⋊C4×C47—42no—
93C2×C22⋊C4×C47C2×C414yes—
94C2×C22⋊C4×C47C2×C414yescomplemented
95C2×C22⋊C4×C47D418yes—
96C2×C42×C47—24no—
97C2×C42×C47C2×C414yescomplemented
98#95×C47—24no—
99#95×C47—22no—
100#95×C47—22no—
101#95×C47—24no—
102#95×C47—24no—
103#95×C47—24no—
104#95×C47—24no—
105#95×C47—22no—
106#95×C47—42no—
107#95×C47D414yescomplemented
108C24×C47—21no—
109C24×C47—21no—
110C24×C47—22no—
111C24×C47—22no—
112C24×C47—21no—
113C24×C47—21no—
114C24×C47—21no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47—21no—
118C24×C47—22no—
119C24×C47—21no—
120C24×C47—22no—
121C24×C47—21no—
122C24×C47C22×C412yes—
123C24×C47C22×C412yes—
124C24×C47C2×D412yes—
125C24×C47C2×D414yes—
126C24×C47C2×D412yes—
127C24×C47C2×Q812yes—
128C24×C47C2×Q812yes—
129C24×C47#4114yes—
130C24×C47C2411yescharacteristic
131C2×D4×C47—28no—
132C2×D4×C47—28no—
133C2×D4×C47—216no—
134C2×D4×C47—216no—
135C2×D4×C47C4⋊C4116yescomplemented
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—21no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—21no—
146C22×C4×C47—216no—
147C22×C4×C47—28no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—21no—
154C22×C4×C47—22no—
155C22×C4×C47—21no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—28no—
165C22×C4×C47—28no—
166C22×C4×C47—28no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—44no—
182C22×C4×C47—44no—
183C22×C4×C47—48no—
184C22×C4×C47—48no—
185C22×C4×C47—48no—
186C22×C4×C47—48no—
187C22×C4×C47—48no—
188C22×C4×C47—48no—
189C22×C4×C47—48no—
190C22×C4×C47—48no—
191C22×C4×C47—48no—
192C22×C4×C47—48no—
193C22×C4×C47C22×C412yes—
194C22×C4×C47C22×C412yes—
195C22×C4×C47C22×C412yes—
196C22×C4×C47C22×C412yes—
197C22×C4×C47C22×C412yes—
198C22×C4×C47C2×D414yes—
199C22×C4×C47C2×D414yes—
200C22×C4×C47C2×D414yes—
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2×Q812yes—
204C22×C4×C47#4114yes—
205C22×C4×C47#4112yes—
206C4⋊C4×C47—28no—
207C4⋊C4×C47—48no—
208C4⋊C4×C47—48no—
209C22⋊C4×C47—28no—
210C22⋊C4×C47—48no—
211C22⋊C4×C47—48no—
212C22⋊C4×C47—48no—
213C22⋊C4×C47C22⋊C4116yescomplemented
214C42×C47—28no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—24no—
220C23×C47—24no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—24no—
224C23×C47—22no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—24no—
228C23×C47—24no—
229C23×C47—22no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—24no—
233C23×C47—22no—
234C23×C47—22no—
235C23×C47—22no—
236C23×C47—22no—
237C23×C47—22no—
238C23×C47—22no—
239C23×C47—24no—
240C23×C47—24no—
241C23×C47—22no—
242C23×C47—24no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—24no—
247C23×C47—42no—
248C23×C47—42no—
249C23×C47—42no—
250C23×C47—42no—
251C23×C47—42no—
252C23×C47—42no—
253C23×C47—42no—
254C23×C47—42no—
255C23×C47C2×C22⋊C414yes—
256C23×C47C2×C4⋊C414yes—
257C23×C47C2×C4⋊C414yes—
258C23×C47#11714yes—
259C23×C47#12118yes—
260C23×C47C22⋊Q818yes—
261C23×C47C23×C411yescharacteristic
262C23×C47C22×D412yes—
263C23×C47C22×D411yescharacteristic
264C23×C47C22×D411yescharacteristic
265C23×C47C22×Q811yescharacteristic
266C23×C47C2×#4112yes—
267C23×C47C2×#4111yescharacteristic
268C23×C47C2×#4112yes—
269C23×C47H(5,𝔽2)12yes—
270C23×C47H(5,𝔽2)11yescharacteristic
271C23×C472−1+411yescharacteristic
272D4×C47—232no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—24no—
282C2×C4×C47—24no—
283C2×C4×C47—24no—
284C2×C4×C47—24no—
285C2×C4×C47—24no—
286C2×C4×C47—24no—
287C2×C4×C47—24no—
288C2×C4×C47—24no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—24no—
293C2×C4×C47—24no—
294C2×C4×C47—24no—
295C2×C4×C47—24no—
296C2×C4×C47—24no—
297C2×C4×C47—24no—
298C2×C4×C47—416no—
299C2×C4×C47—416no—
300C2×C4×C47—432no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47—42no—
325C2×C4×C47C2×C22⋊C414yes—
326C2×C4×C47C2×C22⋊C414yes—
327C2×C4×C47C2×C4⋊C414yes—
328C2×C4×C47C4×D414yes—
329#13899C4711yesmaximal, characteristic, direct product factor, Sylow
330C22×C47—24no—
331C22×C47—24no—
332C22×C47—24no—
333C22×C47—24no—
334C22×C47—24no—
335C22×C47—28no—
336C22×C47—28no—
337C22×C47—28no—
338C22×C47—28no—
339C22×C47—24no—
340C22×C47—24no—
341C22×C47—24no—
342C22×C47—24no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—44no—
347C22×C47—44no—
348C22×C47—44no—
349C22×C47—44no—
350C22×C47—42no—
351C22×C47#38018yescomplemented
352C22×C47C22×C22⋊C411yescharacteristic
353C22×C47C22×C4⋊C411yescharacteristic
354C22×C47C2×#11711yescharacteristic
355C22×C47C2×C4×D411yescharacteristic
356C22×C47C4×#4111yescharacteristic
357C22×C47#51811yescharacteristic
358C22×C47#52011yescharacteristic
359C22×C47C2×#12112yes—
360C22×C47C2×C22⋊Q812yes—
361C22×C47#52512yes—
362C22×C47#52912yes—
363C22×C47#53812yes—
364C22×C47#53912yes—
365C22×C47D4212yes—
366C22×C47D4211yescharacteristic
367C22×C47#54612yes—
368C22×C47#54612yes—
369C22×C47#54612yes—
370C22×C47#54712yes—
371C22×C47#54711yescharacteristic
372C22×C47D4×Q811yescharacteristic
373C22×C47#55411yescharacteristic
374C22×C47#55412yes—
375C4×C47—24no—
376C4×C47—24no—
377C4×C47—24no—
378C4×C47—24no—
379C4×C47—42no—
380C4×C47—44no—
381C4×C47—44no—
382C4×C47—82no—
383C4×C47—82no—
384C22×C4×D4C2×C4711yescharacteristic
385C2×#386C2×C4712yes—
386C2×#385C2×C4712yescomplemented
387C2×#380C2×C4711yescharacteristic, complemented
388C22×#95C2×C4711yescharacteristic, complemented
389#1441C2×C4712yescomplemented
390#1439C2×C4712yescomplemented
391C4⋊#95C2×C4711yescharacteristic, complemented
392#1434C2×C4711yescharacteristic, complemented
393C22⋊#95C2×C4711yescharacteristic, complemented
394C22⋊#95C2×C4711yescharacteristic, complemented
395C2×C47—28no—
396C2×C47—44no—
397C2×C47C2×#38011yescharacteristic
398C2×C47#229011yescharacteristic
399C2×C47#231811yescharacteristic
400C2×C47D4×C22⋊C411yescharacteristic
401C2×C47#233911yescharacteristic
402C2×C47D4×C4⋊C411yescharacteristic
403C2×C47#234911yescharacteristic
404C2×C47#242412yes—
405C2×C47#242512yes—
406C2×C47#244912yes—
407C2×C47#245012yes—
408C23×D4C22×C4711yescharacteristic
409C24×C4C22×C4712yes—
410C24×C4C22×C4711yescharacteristic
411C24×C4C22×C4711yescharacteristic
412C2×C4×D4—28no—
413C2×C4×D4C4×C4718yescomplemented
414C22×C4⋊C4C22×C4712yes—
415C22×C4⋊C4C22×C4712yes—
416C22×C4⋊C4C22×C4711yescharacteristic
417C22×C22⋊C4C22×C4712yes—
418C22×C22⋊C4C22×C4712yes—
419C22×C22⋊C4C22×C4712yes—
420C22×C22⋊C4C22×C4711yescharacteristic
421C22×C22⋊C4C22×C4711yescharacteristic
422C22×C42C22×C4711yescharacteristic
423#386—28no—
424#385—28no—
425#380—24no—
426C2×#95—24no—
427C2×#95C22×C4711yescharacteristic
428C2×#95C22×C4711yescharacteristic
429C2×#95C22×C4711yescharacteristic
430C2×#95C22×C4712yes—
431C2×#95C22×C4712yes—
432C2×#95C22×C4712yes—
433C2×#95C22×C4712yes—
434C2×#95C22×C4712yes—
435C2×#95C22×C4712yes—
436C2×#95C22×C4711yescharacteristic
437C47#1389911yescharacteristic, direct product factor, Sylow
438C25C23×C4711yescharacteristic
439C25C23×C4711yescharacteristic
440C22×D4—24no—
441C22×D4—24no—
442C22×D4C2×C4×C4714yes—
443C22×D4D4×C4714yes—
444C22×D4Q8×C4714yes—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—24no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—24no—
453C23×C4—22no—
454C23×C4—24no—
455C23×C4—24no—
456C23×C4—42no—
457C23×C4—42no—
458C23×C4—42no—
459C23×C4—42no—
460C23×C4C2×C4×C4714yes—
461C23×C4C2×C4×C4714yescomplemented
462C23×C4C23×C4712yes—
463C23×C4C23×C4712yes—
464C23×C4C23×C4711yescharacteristic
465C23×C4C23×C4712yes—
466C23×C4C23×C4712yes—
467C23×C4C23×C4711yescharacteristic
468C23×C4C23×C4711yescharacteristic
469C23×C4C23×C4711yescharacteristic
470C23×C4C23×C4711yescharacteristic
471C4×D4—232no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4C2×C4×C4714yescomplemented
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4C2×C4×C4714yes—
491C2×C22⋊C4C2×C4×C4714yescomplemented
492C2×C22⋊C4D4×C4718yes—
493C2×C42—24no—
494C2×C42C2×C4×C4714yescomplemented
495#95—24no—
496#95—22no—
497#95—22no—
498#95—24no—
499#95—24no—
500#95—24no—
501#95—24no—
502#95—22no—
503#95—42no—
504#95D4×C4714yescomplemented
505C24—21no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—21no—
515C24—22no—
516C24—21no—
517C24—22no—
518C24—21no—
519C24C22×C4×C4712yes—
520C24C22×C4×C4712yes—
521C24C2×D4×C4712yes—
522C24C2×D4×C4714yes—
523C24C2×D4×C4712yes—
524C24C2×Q8×C4712yes—
525C24C2×Q8×C4712yes—
526C24#41×C4714yes—
527C24C24×C4711yescharacteristic
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—216no—
531C2×D4—216no—
532C2×D4C4⋊C4×C47116yescomplemented
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—216no—
544C22×C4—28no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4C22×C4×C4712yes—
591C22×C4C22×C4×C4712yes—
592C22×C4C22×C4×C4712yes—
593C22×C4C22×C4×C4712yes—
594C22×C4C22×C4×C4712yes—
595C22×C4C2×D4×C4714yes—
596C22×C4C2×D4×C4714yes—
597C22×C4C2×D4×C4714yes—
598C22×C4C2×D4×C4712yes—
599C22×C4C2×D4×C4712yes—
600C22×C4C2×Q8×C4712yes—
601C22×C4#41×C4714yes—
602C22×C4#41×C4712yes—
603C4⋊C4—28no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C22⋊C4—28no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4C22⋊C4×C47116yescomplemented
611C42—28no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23C2×C22⋊C4×C4714yes—
653C23C2×C4⋊C4×C4714yes—
654C23C2×C4⋊C4×C4714yes—
655C23#117×C4714yes—
656C23#121×C4718yes—
657C23C22⋊Q8×C4718yes—
658C23C23×C4×C4711yescharacteristic
659C23C22×D4×C4712yes—
660C23C22×D4×C4711yescharacteristic
661C23C22×D4×C4711yescharacteristic
662C23C22×Q8×C4711yescharacteristic
663C23C2×#41×C4712yes—
664C23C2×#41×C4711yescharacteristic
665C23C2×#41×C4712yes—
666C23H(5,𝔽2)×C4712yes—
667C23H(5,𝔽2)×C4711yescharacteristic
668C232−1+4×C4711yescharacteristic
669D4—232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—416no—
696C2×C4—416no—
697C2×C4—432no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4C2×C22⋊C4×C4714yes—
723C2×C4C2×C22⋊C4×C4714yes—
724C2×C4C2×C4⋊C4×C4714yes—
725C2×C4C4×D4×C4714yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—28no—
733C22—28no—
734C22—28no—
735C22—28no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22C47×#38018yescomplemented
748C22C22×C22⋊C4×C4711yescharacteristic
749C22C22×C4⋊C4×C4711yescharacteristic
750C22C2×#117×C4711yescharacteristic
751C22C2×C4×D4×C4711yescharacteristic
752C22C4×#41×C4711yescharacteristic
753C22C47×#51811yescharacteristic
754C22C47×#52011yescharacteristic
755C22C2×#121×C4712yes—
756C22C2×C22⋊Q8×C4712yes—
757C22C47×#52512yes—
758C22C47×#52912yes—
759C22C47×#53812yes—
760C22C47×#53912yes—
761C22D42×C4712yes—
762C22D42×C4711yescharacteristic
763C22C47×#54612yes—
764C22C47×#54612yes—
765C22C47×#54612yes—
766C22C47×#54712yes—
767C22C47×#54711yescharacteristic
768C22D4×Q8×C4711yescharacteristic
769C22C47×#55411yescharacteristic
770C22C47×#55412yes—
771C4—24no—
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—44no—
777C4—44no—
778C4—82no—
779C4—82no—
780C2—28no—
781C2—44no—
782C2C2×C47×#38011yescharacteristic
783C2C47×#229011yescharacteristic
784C2C47×#231811yescharacteristic
785C2D4×C22⋊C4×C4711yescharacteristic
786C2C47×#233911yescharacteristic
787C2D4×C4⋊C4×C4711yescharacteristic
788C2C47×#234911yescharacteristic
789C2C47×#242412yes—
790C2C47×#242512yes—
791C2C47×#244912yes—
792C2C47×#245012yes—
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC23×D4×C47C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C47×#385C2semidirect
4. C2×C47×#380C2semidirect
5. C22×#95×C47C2semidirect
6. C47×#1441C2semidirect
7. C47×#1439C2semidirect
8. C47×C4⋊#95C2semidirect
9. C47×#1434C2semidirect
10. C47×C22⋊#95C2semidirect
11. C47×C22⋊#95C2semidirect
17. C2×C4×D4×C47C4semidirect
64. C23×C4×C47C2×C4semidirect
82. C2×C4⋊C4×C47C2×C4semidirect
94. C2×C22⋊C4×C47C2×C4semidirect
97. C2×C42×C47C2×C4semidirect
107. #95×C47D4semidirect
135. C2×D4×C47C4⋊C4semidirect
213. C22⋊C4×C47C22⋊C4semidirect
329. #13899C47direct (N × H)
351. C22×C47#380semidirect
386. C2×#385C2×C47semidirect
387. C2×#380C2×C47semidirect
388. C22×#95C2×C47semidirect
389. #1441C2×C47semidirect
390. #1439C2×C47semidirect
391. C4⋊#95C2×C47semidirect
392. #1434C2×C47semidirect
393. C22⋊#95C2×C47semidirect
394. C22⋊#95C2×C47semidirect
413. C2×C4×D4C4×C47semidirect
437. C47#13899direct (N × H)
461. C23×C4C2×C4×C47semidirect
479. C2×C4⋊C4C2×C4×C47semidirect
491. C2×C22⋊C4C2×C4×C47semidirect
494. C2×C42C2×C4×C47semidirect
504. #95D4×C47semidirect
532. C2×D4C4⋊C4×C47semidirect
610. C22⋊C4C22⋊C4×C47semidirect
747. C22C47×#380semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C472
C2×C47×#3862
C2×C47×#3852
C2×C47×#3802
C22×#95×C472
C47×#14412
C47×#14392
C47×C4⋊#952
C47×#14342
C47×C22⋊#952
#1389947