Finite Group Databasebeta

← C47×#25174 #26064872

Subgroups — C47×#25174 #26064872

Order 12032.

1234 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#459C211yesmaximal, characteristic, complemented
2C2×C47×#449C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic, complemented
4C2×C47×#442C211yesmaximal, characteristic, complemented
5C47×#2428C211yesmaximal, characteristic, complemented
6C47×#2339C211yesmaximal, characteristic, complemented
7C47×#2066C211yesmaximal, characteristic, complemented
8C47×#2034C211yesmaximal, characteristic, complemented
9C47×#2033C211yesmaximal, characteristic, complemented
10C47×#2014C211yesmaximal, characteristic, complemented
11C47×#1973C211yesmaximal, characteristic, complemented
12C47×#1924C211yesmaximal, characteristic, complemented
13C47×#1879C211yesmaximal, characteristic, complemented
14C47×#1877C211yesmaximal, characteristic, complemented
15C47×#1862C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C22×D8×C47C2211yescharacteristic
21C2×#127×C47C2211yescharacteristic
22C2×#121×C47—21no—
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×C4×D4×C47C2211yescharacteristic
26C2×C4×D4×C47C2211yescharacteristic
27C2×C4×D4×C47C2211yescharacteristic
28C47×#459—24no—
29C47×#449—24no—
30C47×#449—24no—
31C47×#442—24no—
32C2×#107×C47C2211yescharacteristic
33C2×#106×C47C2211yescharacteristic
34C2×C4⋊C8×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×#97×C47C2211yescharacteristic
46C47×#394—21no—
47C47×#392—21no—
48C47×#391C2211yescharacteristic
49C47×#391C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#386—21no—
53C47×#386—21no—
54C47×#386—21no—
55C47×#381—21no—
56C47×#380C2211yescharacteristic
57C4×C22⋊C4×C47C2211yescharacteristic
58C2×#95×C47—21no—
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C2×#41×C47—22no—
64C2×#41×C47—22no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—41no—
68C2×#41×C47—41no—
69C22×Q8×C47C2311yescharacteristic
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47C2311yescharacteristic
76C22×D4×C47C2311yescharacteristic
77C22×D4×C47C2311yescharacteristic
78C23×C4×C47—21no—
79C23×C4×C47—21no—
80C23×C4×C47—21no—
81C23×C4×C47—21no—
82C23×C4×C47C2311yescharacteristic
83C2×SD16×C47—22no—
84C2×SD16×C47—22no—
85C2×SD16×C47—22no—
86C2×SD16×C47—22no—
87C2×SD16×C47—41no—
88C2×SD16×C47—41no—
89C2×D8×C47—22no—
90C2×D8×C47—22no—
91C2×D8×C47—22no—
92C2×D8×C47—22no—
93C2×D8×C47—22no—
94C2×D8×C47D414yescomplemented
95C22×C8×C47C2311yescharacteristic
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98C22×C8×C47C2311yescharacteristic
99#127×C47—22no—
100#127×C47—41no—
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—44no—
104#121×C47—41no—
105#121×C47—41no—
106C4×D4×C47—22no—
107C4×D4×C47—22no—
108C4×D4×C47—22no—
109C4×D4×C47—41no—
110C4×D4×C47—41no—
111C4×D4×C47—41no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
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×C47D411yescharacteristic
126C2×C22⋊C4×C47D411yescharacteristic
127C2×C42×C47C2311yescharacteristic
128C2×C42×C47C2311yescharacteristic
129#107×C47—41no—
130#106×C47—22no—
131C4⋊C8×C47—22no—
132#103×C47—22no—
133#103×C47—22no—
134#102×C47—22no—
135#102×C47—22no—
136#102×C47—22no—
137#102×C47—22no—
138#102×C47—41no—
139#102×C47D414yescomplemented
140C22⋊C8×C47—22no—
141C22⋊C8×C47—22no—
142#97×C47—22no—
143#95×C47—21no—
144#95×C47—21no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47D411yescharacteristic
150#95×C47D411yescharacteristic
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47C2×D411yescharacteristic
155#41×C47—44no—
156#41×C47—44no—
157#41×C47—44no—
158#41×C47—44no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47#4112yes—
165C2×D4×C47—24no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—42no—
181C2×D4×C47—42no—
182C2×D4×C47—42no—
183C2×D4×C47—42no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
186C2×D4×C47—42no—
187C2×D4×C47—42no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—81no—
191C2×D4×C47—81no—
192C2×D4×C47—81no—
193C2×D4×C47—81no—
194C2×D4×C47C2×D412yes—
195C2×D4×C47C2×D412yes—
196C2×D4×C47C2×D412yes—
197C2×D4×C47#4112yes—
198C22×C4×C47—24no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—42no—
211C22×C4×C47—42no—
212C22×C4×C47—42no—
213C22×C4×C47—42no—
214C22×C4×C47—42no—
215C22×C4×C47—42no—
216C22×C4×C47—42no—
217C22×C4×C47—42no—
218C22×C4×C47—81no—
219C22×C4×C47—81no—
220C22×C4×C47—81no—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2411yescharacteristic
227SD16×C47—44no—
228SD16×C47—44no—
229D8×C47—28no—
230D8×C47—44no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47C2×D412yes—
242C2×C8×C47C2×D412yes—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—42no—
251C4⋊C4×C47C2×D412yes—
252C22⋊C4×C47—22no—
253C22⋊C4×C47—41no—
254C22⋊C4×C47—42no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—42no—
257C22⋊C4×C47—42no—
258C22⋊C4×C47—42no—
259C22⋊C4×C47—42no—
260C22⋊C4×C47—81no—
261C22⋊C4×C47—81no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47—21no—
265C42×C47—21no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—21no—
270C23×C47—22no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47C22×D411yescharacteristic
295Q8×C47—22no—
296Q8×C47—22no—
297Q8×C47—41no—
298Q8×C47—41no—
299D4×C47—22no—
300D4×C47—22no—
301D4×C47—22no—
302D4×C47—22no—
303D4×C47—22no—
304D4×C47—48no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—84no—
312D4×C47—84no—
313D4×C47—84no—
314D4×C47—84no—
315D4×C47#12114yescomplemented
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—22no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—22no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—48no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—84no—
351C2×C4×C47—84no—
352C2×C4×C47—84no—
353C2×C4×C47AGL(1,ℤ/8)12yes—
354C2×C4×C47C22×D411yescharacteristic
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C2×#4111yescharacteristic
357C2×C4×C47C2×#4111yescharacteristic
358C2×C4×C47H(5,𝔽2)11yescharacteristic
359C2×C4×C47H(5,𝔽2)11yescharacteristic
360C8×C47—22no—
361C8×C47—22no—
362C8×C47—41no—
363C8×C47—41no—
364#25174C4711yesmaximal, characteristic, direct product factor, Sylow
365C22×C47—24no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—42no—
376C22×C47—41no—
377C22×C47—42no—
378C22×C47—42no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—81no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47—81no—
386C22×C47—81no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47#52511yescharacteristic
394C22×C47D4211yescharacteristic
395C22×C47D4211yescharacteristic
396C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
397C22×C47#57511yescharacteristic
398C22×C47#57611yescharacteristic
399C22×C47#57711yescharacteristic
400C4×C47—22no—
401C4×C47—41no—
402C4×C47—42no—
403C4×C47—41no—
404C4×C47—41no—
405C4×C47—41no—
406C4×C47—42no—
407C4×C47—81no—
408C4×C47—81no—
409C4×C47—81no—
410C4×C47C2×#12111yescharacteristic
411C4×C47#53811yescharacteristic
412C4×C47#54611yescharacteristic
413C4×C47#54611yescharacteristic
414C2×#459C2×C4711yescharacteristic, complemented
415C2×#449C2×C4711yescharacteristic, complemented
416C2×#449C2×C4711yescharacteristic, complemented
417C2×#442C2×C4711yescharacteristic, complemented
418#2428C2×C4711yescharacteristic, complemented
419#2339C2×C4711yescharacteristic, complemented
420#2066C2×C4711yescharacteristic, complemented
421#2034C2×C4711yescharacteristic, complemented
422#2033C2×C4711yescharacteristic, complemented
423#2014C2×C4711yescharacteristic, complemented
424#1973C2×C4711yescharacteristic, complemented
425#1924C2×C4711yescharacteristic, complemented
426#1879C2×C4711yescharacteristic, complemented
427#1877C2×C4711yescharacteristic, complemented
428#1862C2×C4711yescharacteristic, complemented
429C2×C47—44no—
430C2×C47—81no—
431C2×C47—82no—
432C2×C47—161no—
433C2×C47#242411yescharacteristic
434C2×C47#311511yescharacteristic
435C2×C47#311911yescharacteristic
436C2×C47#326411yescharacteristic
437C2×C47#326711yescharacteristic
438C2×C47#326811yescharacteristic
439C2×C47#327211yescharacteristic
440C22×#41C22×C4711yescharacteristic
441C22×SD16C22×C4711yescharacteristic
442C22×SD16C22×C4711yescharacteristic
443C22×D8C22×C4711yescharacteristic
444C22×D8C22×C4711yescharacteristic
445C2×#127C22×C4711yescharacteristic
446C2×#121—21no—
447C2×#121C22×C4711yescharacteristic
448C2×#121C22×C4711yescharacteristic
449C2×C4×D4C22×C4711yescharacteristic
450C2×C4×D4C22×C4711yescharacteristic
451C2×C4×D4C22×C4711yescharacteristic
452#459—24no—
453#449—24no—
454#449—24no—
455#442—24no—
456C2×#107C22×C4711yescharacteristic
457C2×#106C22×C4711yescharacteristic
458C2×C4⋊C8C22×C4711yescharacteristic
459C2×#103C22×C4711yescharacteristic
460C2×#103C22×C4711yescharacteristic
461C2×#102C22×C4711yescharacteristic
462C2×#102C22×C4711yescharacteristic
463C2×#102C22×C4711yescharacteristic
464C2×#102C22×C4711yescharacteristic
465C2×#102C22×C4711yescharacteristic
466C2×#102C22×C4711yescharacteristic
467C2×C22⋊C8C22×C4711yescharacteristic
468C2×C22⋊C8C22×C4711yescharacteristic
469C2×#97C22×C4711yescharacteristic
470#394—21no—
471#392—21no—
472#391C22×C4711yescharacteristic
473#391C22×C4711yescharacteristic
474#390C22×C4711yescharacteristic
475#389C22×C4711yescharacteristic
476#386—21no—
477#386—21no—
478#386—21no—
479#381—21no—
480#380C22×C4711yescharacteristic
481C4×C22⋊C4C22×C4711yescharacteristic
482C2×#95—21no—
483#340C22×C4711yescharacteristic
484#340C22×C4711yescharacteristic
485#336C22×C4711yescharacteristic
486#336C22×C4711yescharacteristic
487C47#2517411yescharacteristic, direct product factor, Sylow
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C23×C4711yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C4711yescharacteristic
501C22×D4C23×C4711yescharacteristic
502C22×D4C23×C4711yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C4711yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8D4×C4714yescomplemented
520C22×C8C23×C4711yescharacteristic
521C22×C8C23×C4711yescharacteristic
522C22×C8C23×C4711yescharacteristic
523C22×C8C23×C4711yescharacteristic
524#127—22no—
525#127—41no—
526#121—22no—
527#121—22no—
528#121—44no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C4711yescharacteristic
539C2×C4⋊C4C23×C4711yescharacteristic
540C2×C4⋊C4C23×C4711yescharacteristic
541C2×C4⋊C4C23×C4711yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C4711yescharacteristic
551C2×C22⋊C4D4×C4711yescharacteristic
552C2×C42C23×C4711yescharacteristic
553C2×C42C23×C4711yescharacteristic
554#107—41no—
555#106—22no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C4714yescomplemented
565C22⋊C8—22no—
566C22⋊C8—22no—
567#97—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C4711yescharacteristic
575#95D4×C4711yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C4711yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C4712yes—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C4712yes—
620C2×D4C2×D4×C4712yes—
621C2×D4C2×D4×C4712yes—
622C2×D4#41×C4712yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C4711yescharacteristic
647C22×C4C2×D4×C4711yescharacteristic
648C22×C4C2×D4×C4711yescharacteristic
649C22×C4C2×D4×C4711yescharacteristic
650C22×C4C2×D4×C4711yescharacteristic
651C22×C4C24×C4711yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C4712yes—
667C2×C8C2×D4×C4712yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C4712yes—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23C22×D4×C4711yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4#121×C4714yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4AGL(1,ℤ/8)×C4712yes—
779C2×C4C22×D4×C4711yescharacteristic
780C2×C4C22×D4×C4711yescharacteristic
781C2×C4C2×#41×C4711yescharacteristic
782C2×C4C2×#41×C4711yescharacteristic
783C2×C4H(5,𝔽2)×C4711yescharacteristic
784C2×C4H(5,𝔽2)×C4711yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—42no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22C47×#52511yescharacteristic
818C22D42×C4711yescharacteristic
819C22D42×C4711yescharacteristic
820C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
821C22C47×#57511yescharacteristic
822C22C47×#57611yescharacteristic
823C22C47×#57711yescharacteristic
824C4—22no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#121×C4711yescharacteristic
835C4C47×#53811yescharacteristic
836C4C47×#54611yescharacteristic
837C4C47×#54611yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C47×#242411yescharacteristic
843C2C47×#311511yescharacteristic
844C2C47×#311911yescharacteristic
845C2C47×#326411yescharacteristic
846C2C47×#326711yescharacteristic
847C2C47×#326811yescharacteristic
848C2C47×#327211yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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
1. C2×C47×#459C2semidirect
2. C2×C47×#449C2semidirect
3. C2×C47×#449C2semidirect
4. C2×C47×#442C2semidirect
5. C47×#2428C2semidirect
6. C47×#2339C2semidirect
7. C47×#2066C2semidirect
8. C47×#2034C2semidirect
9. C47×#2033C2semidirect
10. C47×#2014C2semidirect
11. C47×#1973C2semidirect
12. C47×#1924C2semidirect
13. C47×#1879C2semidirect
14. C47×#1877C2semidirect
15. C47×#1862C2semidirect
94. C2×D8×C47D4semidirect
139. #102×C47D4semidirect
315. D4×C47#121semidirect
364. #25174C47direct (N × H)
414. C2×#459C2×C47semidirect
415. C2×#449C2×C47semidirect
416. C2×#449C2×C47semidirect
417. C2×#442C2×C47semidirect
418. #2428C2×C47semidirect
419. #2339C2×C47semidirect
420. #2066C2×C47semidirect
421. #2034C2×C47semidirect
422. #2033C2×C47semidirect
423. #2014C2×C47semidirect
424. #1973C2×C47semidirect
425. #1924C2×C47semidirect
426. #1879C2×C47semidirect
427. #1877C2×C47semidirect
428. #1862C2×C47semidirect
487. C47#25174direct (N × H)
519. C2×D8D4×C47semidirect
564. #102D4×C47semidirect
740. D4#121×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4592
C2×C47×#4492
C2×C47×#4422
C47×#24282
C47×#23392
C47×#20662
C47×#20342
C47×#20332
C47×#20142
C47×#19732
C47×#19242
C47×#18792
C47×#18772
C47×#18622
#2517447