Finite Group Databasebeta

← C47×#24427 #26064125

Subgroups — C47×#24427 #26064125

Order 12032.

1500 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#550C211yesmaximal, characteristic
2C2×C47×#465C211yesmaximal, characteristic, complemented
3C2×C47×#452C211yesmaximal, characteristic, complemented
4C2×C47×#452C211yesmaximal, characteristic, complemented
5C2×C47×#416C211yesmaximal, characteristic, complemented
6C47×#2415C211yesmaximal, characteristic, complemented
7C47×#2041C211yesmaximal, characteristic, complemented
8C47×#2034C211yesmaximal, characteristic, complemented
9C47×#2014C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1878C211yesmaximal, characteristic, complemented
12C47×#1875C211yesmaximal, characteristic, complemented
13C47×#1869C211yesmaximal, characteristic, complemented
14C47×#1865C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C22×Q16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C22×SD16×C47C2211yescharacteristic
21C23×C8×C47C2211yescharacteristic
22C47×#550—24no—
23C47×#550—24no—
24C2×#127×C47—21no—
25C2×#127×C47C2211yescharacteristic
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×#121×C47—21no—
29C2×#121×C47—21no—
30C2×#121×C47C2211yescharacteristic
31C2×#121×C47C2211yescharacteristic
32C2×C4×Q8×C47C2211yescharacteristic
33C2×C4×D4×C47—21no—
34C2×C4×D4×C47C2211yescharacteristic
35C2×#117×C47C2211yescharacteristic
36C47×#465—24no—
37C47×#452—24no—
38C47×#452—24no—
39C2×#106×C47C2211yescharacteristic
40C47×#416—24no—
41C2×#103×C47C2211yescharacteristic
42C2×#103×C47C2211yescharacteristic
43C2×#103×C47C2211yescharacteristic
44C2×#103×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C2×#102×C47C2211yescharacteristic
48C2×#102×C47C2211yescharacteristic
49C2×#102×C47C2211yescharacteristic
50C2×#102×C47C2211yescharacteristic
51C2×C22⋊C8×C47C2211yescharacteristic
52C2×C22⋊C8×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic
54C47×#397—21no—
55C47×#394—21no—
56C47×#391C2211yescharacteristic
57C47×#389—21no—
58C47×#389C2211yescharacteristic
59C47×#388—21no—
60C47×#380C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#336C2211yescharacteristic
64C47×#336C2211yescharacteristic
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—22no—
70C2×#41×C47—22no—
71C2×#41×C47—22no—
72C2×#41×C47—41no—
73C2×#41×C47—41no—
74C2×#41×C47—41no—
75C2×#41×C47—41no—
76C2×#41×C47D414yes—
77C22×Q8×C47C2311yescharacteristic
78C22×Q8×C47C2311yescharacteristic
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47—21no—
83C22×D4×C47—21no—
84C22×D4×C47—21no—
85C22×D4×C47D411yescharacteristic
86C22×D4×C47C2311yescharacteristic
87C22×D4×C47C2311yescharacteristic
88C23×C4×C47—21no—
89C23×C4×C47—21no—
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C2×Q16×C47—22no—
93C2×Q16×C47—22no—
94C2×Q16×C47—22no—
95C2×SD16×C47—22no—
96C2×SD16×C47—22no—
97C2×SD16×C47—22no—
98C2×SD16×C47—41no—
99C2×SD16×C47—41no—
100C2×SD16×C47—41no—
101C22×C8×C47—22no—
102C22×C8×C47—22no—
103C22×C8×C47—41no—
104C22×C8×C47C2311yescharacteristic
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108#127×C47—28no—
109#127×C47—22no—
110#127×C47—22no—
111C22⋊Q8×C47—22no—
112C22⋊Q8×C47—22no—
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47—41no—
115#121×C47—28no—
116#121×C47—28no—
117#121×C47—22no—
118#121×C47—22no—
119#121×C47—22no—
120#121×C47D414yes—
121C4×Q8×C47—22no—
122C4×Q8×C47—22no—
123C4×D4×C47—28no—
124C4×D4×C47—22no—
125C4×D4×C47—22no—
126#117×C47—22no—
127#117×C47—41no—
128C2×C4⋊C4×C47—21no—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47D411yescharacteristic
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C22⋊C4×C47—21no—
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47—21no—
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47—21no—
143C2×C22⋊C4×C47D411yescharacteristic
144C2×C22⋊C4×C47D411yescharacteristic
145C2×C42×C47—21no—
146C2×C42×C47—21no—
147C2×C42×C47C2311yescharacteristic
148#106×C47—22no—
149#103×C47—22no—
150#103×C47—22no—
151#103×C47—22no—
152#103×C47D414yescomplemented
153#102×C47—22no—
154#102×C47—22no—
155#102×C47—22no—
156#102×C47—22no—
157#102×C47—22no—
158#102×C47—41no—
159C22⋊C8×C47—22no—
160C22⋊C8×C47—22no—
161C22⋊C8×C47—41no—
162#95×C47—21no—
163#95×C47—21no—
164#95×C47—21no—
165#95×C47—21no—
166C24×C47—21no—
167C24×C47—21no—
168C24×C47C2×D411yescharacteristic
169C24×C47C2×D411yescharacteristic
170#41×C47—28no—
171#41×C47—44no—
172#41×C47—44no—
173#41×C47—44no—
174#41×C47—44no—
175#41×C47—44no—
176#41×C47—44no—
177#41×C47—44no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47C2×D412yes—
188C2×Q8×C47C2×D412yes—
189C2×Q8×C47#4112yes—
190C2×D4×C47—24no—
191C2×D4×C47—24no—
192C2×D4×C47—22no—
193C2×D4×C47—24no—
194C2×D4×C47—24no—
195C2×D4×C47—24no—
196C2×D4×C47—24no—
197C2×D4×C47—22no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—41no—
209C2×D4×C47—42no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—42no—
215C2×D4×C47—81no—
216C2×D4×C47—81no—
217C2×D4×C47—81no—
218C2×D4×C47—81no—
219C2×D4×C47—81no—
220C2×D4×C47—81no—
221C2×D4×C47C2×D412yes—
222C2×D4×C47C2×D412yes—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—24no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—24no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—21no—
241C22×C4×C47—42no—
242C22×C4×C47—42no—
243C22×C4×C47—42no—
244C22×C4×C47—42no—
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D412yes—
249C22×C4×C47C2×D412yes—
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2411yescharacteristic
252Q16×C47—44no—
253SD16×C47—44no—
254SD16×C47—44no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C2×C8×C47—21no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—21no—
266C2×C8×C47—44no—
267C2×C8×C47C2×D412yes—
268C4⋊C4×C47—24no—
269C4⋊C4×C47—22no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—42no—
277C4⋊C4×C47—42no—
278C4⋊C4×C47—42no—
279C4⋊C4×C47C2×D412yes—
280C4⋊C4×C47C2×D412yes—
281C22⋊C4×C47—24no—
282C22⋊C4×C47—22no—
283C22⋊C4×C47—24no—
284C22⋊C4×C47—22no—
285C22⋊C4×C47—42no—
286C22⋊C4×C47—42no—
287C22⋊C4×C47—42no—
288C22⋊C4×C47—42no—
289C42×C47—24no—
290C42×C47—21no—
291C42×C47—21no—
292C42×C47—42no—
293C23×C47—21no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—21no—
297C23×C47—21no—
298C23×C47—21no—
299C23×C47—21no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—21no—
303C23×C47—21no—
304C23×C47—21no—
305C23×C47—21no—
306C23×C47—21no—
307C23×C47—21no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—41no—
319C23×C47—41no—
320C23×C47#12012yes—
321C23×C47C22×D411yescharacteristic
322Q8×C47—22no—
323Q8×C47—22no—
324Q8×C47—22no—
325Q8×C47—41no—
326Q8×C47—41no—
327Q8×C47—41no—
328Q8×C47—41no—
329Q8×C47#12114yes—
330D4×C47—22no—
331D4×C47—22no—
332D4×C47—22no—
333D4×C47—22no—
334D4×C47—44no—
335D4×C47—48no—
336D4×C47—48no—
337D4×C47—48no—
338D4×C47—41no—
339D4×C47—41no—
340D4×C47—41no—
341D4×C47—41no—
342D4×C47—84no—
343D4×C47—84no—
344D4×C47—84no—
345C2×C4×C47—21no—
346C2×C4×C47—22no—
347C2×C4×C47—21no—
348C2×C4×C47—22no—
349C2×C4×C47—21no—
350C2×C4×C47—22no—
351C2×C4×C47—21no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—21no—
357C2×C4×C47—22no—
358C2×C4×C47—21no—
359C2×C4×C47—22no—
360C2×C4×C47—21no—
361C2×C4×C47—21no—
362C2×C4×C47—21no—
363C2×C4×C47—21no—
364C2×C4×C47—48no—
365C2×C4×C47—48no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47#12012yes—
384C2×C4×C47#13512yes—
385C2×C4×C47C22×D411yescharacteristic
386C2×C4×C47C22×D411yescharacteristic
387C2×C4×C47C22×D411yescharacteristic
388C2×C4×C47C2×#4111yescharacteristic
389C2×C4×C47H(5,𝔽2)11yescharacteristic
390C2×C4×C47H(5,𝔽2)11yescharacteristic
391C8×C47—22no—
392C8×C47—41no—
393C8×C47—41no—
394C8×C47—41no—
395#24427C4711yesmaximal, characteristic, direct product factor, Sylow
396C22×C47—22no—
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—41no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—41no—
403C22×C47—42no—
404C22×C47—42no—
405C22×C47—41no—
406C22×C47—41no—
407C22×C47—42no—
408C22×C47—42no—
409C22×C47—41no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47—41no—
413C22×C47—41no—
414C22×C47—41no—
415C22×C47—41no—
416C22×C47—81no—
417C22×C47—81no—
418C22×C47—81no—
419C22×C47—81no—
420C22×C47—81no—
421C22×C47—81no—
422C22×C47—81no—
423C22×C47—81no—
424C22×C47C2×#12011yescharacteristic
425C22×C47D4211yescharacteristic
426C22×C47#54611yescharacteristic
427C22×C47C2×#13511yescharacteristic
428C22×C47#57511yescharacteristic
429C22×C47#57711yescharacteristic
430C22×C47#57711yescharacteristic
431C4×C47—22no—
432C4×C47—24no—
433C4×C47—22no—
434C4×C47—41no—
435C4×C47—41no—
436C4×C47—42no—
437C4×C47—42no—
438C4×C47—81no—
439C4×C47—81no—
440C4×C47—81no—
441C4×C47C2×#12111yescharacteristic
442C4×C47#53411yescharacteristic
443C4×C47D4211yescharacteristic
444C4×C47#54611yescharacteristic
445C2×#550C2×C4711yescharacteristic
446C2×#465C2×C4711yescharacteristic, complemented
447C2×#452C2×C4711yescharacteristic, complemented
448C2×#452C2×C4711yescharacteristic, complemented
449C2×#416C2×C4711yescharacteristic, complemented
450#2415C2×C4711yescharacteristic, complemented
451#2041C2×C4711yescharacteristic, complemented
452#2034C2×C4711yescharacteristic, complemented
453#2014C2×C4711yescharacteristic, complemented
454#2000C2×C4711yescharacteristic, complemented
455#1878C2×C4711yescharacteristic, complemented
456#1875C2×C4711yescharacteristic, complemented
457#1869C2×C4711yescharacteristic, complemented
458#1865C2×C4711yescharacteristic, complemented
459#1788C2×C4711yescharacteristic, complemented
460C2×C47—42no—
461C2×C47—81no—
462C2×C47—82no—
463C2×C47—82no—
464C2×C47#241011yescharacteristic
465C2×C47#300211yescharacteristic
466C2×C47#300911yescharacteristic
467C2×C47#327111yescharacteristic
468C2×C47#328411yescharacteristic
469C2×C47#330411yescharacteristic
470C2×C47#331711yescharacteristic
471C22×#41C22×C4711yescharacteristic
472C22×#41C22×C4711yescharacteristic
473C22×Q16C22×C4711yescharacteristic
474C22×SD16C22×C4711yescharacteristic
475C22×SD16C22×C4711yescharacteristic
476C23×C8C22×C4711yescharacteristic
477#550—24no—
478#550—24no—
479C2×#127—21no—
480C2×#127C22×C4711yescharacteristic
481C2×C22⋊Q8C22×C4711yescharacteristic
482C2×C22⋊Q8C22×C4711yescharacteristic
483C2×#121—21no—
484C2×#121—21no—
485C2×#121C22×C4711yescharacteristic
486C2×#121C22×C4711yescharacteristic
487C2×C4×Q8C22×C4711yescharacteristic
488C2×C4×D4—21no—
489C2×C4×D4C22×C4711yescharacteristic
490C2×#117C22×C4711yescharacteristic
491#465—24no—
492#452—24no—
493#452—24no—
494C2×#106C22×C4711yescharacteristic
495#416—24no—
496C2×#103C22×C4711yescharacteristic
497C2×#103C22×C4711yescharacteristic
498C2×#103C22×C4711yescharacteristic
499C2×#103C22×C4711yescharacteristic
500C2×#102C22×C4711yescharacteristic
501C2×#102C22×C4711yescharacteristic
502C2×#102C22×C4711yescharacteristic
503C2×#102C22×C4711yescharacteristic
504C2×#102C22×C4711yescharacteristic
505C2×#102C22×C4711yescharacteristic
506C2×C22⋊C8C22×C4711yescharacteristic
507C2×C22⋊C8C22×C4711yescharacteristic
508C2×C22⋊C8C22×C4711yescharacteristic
509#397—21no—
510#394—21no—
511#391C22×C4711yescharacteristic
512#389—21no—
513#389C22×C4711yescharacteristic
514#388—21no—
515#380C22×C4711yescharacteristic
516#340C22×C4711yescharacteristic
517#340C22×C4711yescharacteristic
518#336C22×C4711yescharacteristic
519#336C22×C4711yescharacteristic
520C47#2442711yescharacteristic, direct product factor, Sylow
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41D4×C4714yes—
533C22×Q8C23×C4711yescharacteristic
534C22×Q8C23×C4711yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4D4×C4711yescharacteristic
542C22×D4C23×C4711yescharacteristic
543C22×D4C23×C4711yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C4711yescharacteristic
547C23×C4C23×C4711yescharacteristic
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8C23×C4711yescharacteristic
561C22×C8C23×C4711yescharacteristic
562C22×C8C23×C4711yescharacteristic
563C22×C8C23×C4711yescharacteristic
564#127—28no—
565#127—22no—
566#127—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571#121—28no—
572#121—28no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121D4×C4714yes—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582#117—22no—
583#117—41no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C4711yescharacteristic
589C2×C4⋊C4C23×C4711yescharacteristic
590C2×C4⋊C4C23×C4711yescharacteristic
591C2×C4⋊C4C23×C4711yescharacteristic
592C2×C4⋊C4C23×C4711yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4D4×C4711yescharacteristic
600C2×C22⋊C4D4×C4711yescharacteristic
601C2×C42—21no—
602C2×C42—21no—
603C2×C42C23×C4711yescharacteristic
604#106—22no—
605#103—22no—
606#103—22no—
607#103—22no—
608#103D4×C4714yescomplemented
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—41no—
615C22⋊C8—22no—
616C22⋊C8—22no—
617C22⋊C8—41no—
618#95—21no—
619#95—21no—
620#95—21no—
621#95—21no—
622C24—21no—
623C24—21no—
624C24C2×D4×C4711yescharacteristic
625C24C2×D4×C4711yescharacteristic
626#41—28no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C4712yes—
644C2×Q8C2×D4×C4712yes—
645C2×Q8#41×C4712yes—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C4712yes—
678C2×D4C2×D4×C4712yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4C2×D4×C4711yescharacteristic
702C22×C4C2×D4×C4711yescharacteristic
703C22×C4C2×D4×C4711yescharacteristic
704C22×C4C2×D4×C4712yes—
705C22×C4C2×D4×C4712yes—
706C22×C4C2×D4×C4711yescharacteristic
707C22×C4C24×C4711yescharacteristic
708Q16—44no—
709SD16—44no—
710SD16—44no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C4712yes—
724C4⋊C4—24no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4C2×D4×C4712yes—
736C4⋊C4C2×D4×C4712yes—
737C22⋊C4—24no—
738C22⋊C4—22no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C42—24no—
746C42—21no—
747C42—21no—
748C42—42no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—22no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23#120×C4712yes—
777C23C22×D4×C4711yescharacteristic
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8#121×C4714yes—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—84no—
799D4—84no—
800D4—84no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4#120×C4712yes—
840C2×C4#135×C4712yes—
841C2×C4C22×D4×C4711yescharacteristic
842C2×C4C22×D4×C4711yescharacteristic
843C2×C4C22×D4×C4711yescharacteristic
844C2×C4C2×#41×C4711yescharacteristic
845C2×C4H(5,𝔽2)×C4711yescharacteristic
846C2×C4H(5,𝔽2)×C4711yescharacteristic
847C8—22no—
848C8—41no—
849C8—41no—
850C8—41no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—41no—
870C22—41no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22C2×#120×C4711yescharacteristic
880C22D42×C4711yescharacteristic
881C22C47×#54611yescharacteristic
882C22C2×#135×C4711yescharacteristic
883C22C47×#57511yescharacteristic
884C22C47×#57711yescharacteristic
885C22C47×#57711yescharacteristic
886C4—22no—
887C4—24no—
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4C2×#121×C4711yescharacteristic
897C4C47×#53411yescharacteristic
898C4D42×C4711yescharacteristic
899C4C47×#54611yescharacteristic
900C2—42no—
901C2—81no—
902C2—82no—
903C2—82no—
904C2C47×#241011yescharacteristic
905C2C47×#300211yescharacteristic
906C2C47×#300911yescharacteristic
907C2C47×#327111yescharacteristic
908C2C47×#328411yescharacteristic
909C2C47×#330411yescharacteristic
910C2C47×#331711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#550C2
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×#465C2semidirect
3. C2×C47×#452C2semidirect
4. C2×C47×#452C2semidirect
5. C2×C47×#416C2semidirect
6. C47×#2415C2semidirect
7. C47×#2041C2semidirect
8. C47×#2034C2semidirect
9. C47×#2014C2semidirect
10. C47×#2000C2semidirect
11. C47×#1878C2semidirect
12. C47×#1875C2semidirect
13. C47×#1869C2semidirect
14. C47×#1865C2semidirect
15. C47×#1788C2semidirect
152. #103×C47D4semidirect
395. #24427C47direct (N × H)
446. C2×#465C2×C47semidirect
447. C2×#452C2×C47semidirect
448. C2×#452C2×C47semidirect
449. C2×#416C2×C47semidirect
450. #2415C2×C47semidirect
451. #2041C2×C47semidirect
452. #2034C2×C47semidirect
453. #2014C2×C47semidirect
454. #2000C2×C47semidirect
455. #1878C2×C47semidirect
456. #1875C2×C47semidirect
457. #1869C2×C47semidirect
458. #1865C2×C47semidirect
459. #1788C2×C47semidirect
520. C47#24427direct (N × H)
608. #103D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5502
C2×C47×#4652
C2×C47×#4522
C2×C47×#4162
C47×#24152
C47×#20412
C47×#20342
C47×#20142
C47×#20002
C47×#18782
C47×#18752
C47×#18692
C47×#18652
C47×#17882
#2442747