Finite Group Databasebeta

← C47×#25139 #26064837

Subgroups — C47×#25139 #26064837

Order 12032.

1194 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#449C211yesmaximal, characteristic, complemented
3C2×C47×#436C211yesmaximal, characteristic, complemented
4C2×C47×#417C211yesmaximal, characteristic, complemented
5C47×#2416C211yesmaximal, characteristic, complemented
6C47×#2407C211yesmaximal, characteristic, complemented
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2055C211yesmaximal, characteristic, complemented
9C47×#2036C211yesmaximal, characteristic, complemented
10C47×#1999C211yesmaximal, characteristic, complemented
11C47×#1970C211yesmaximal, characteristic, complemented
12C47×#1933C211yesmaximal, characteristic, complemented
13C47×#1895C211yesmaximal, characteristic, complemented
14C47×#1895C211yesmaximal, characteristic, complemented
15C47×#1852C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C22×M16×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×#121×C47—21no—
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C2×C4×D4×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C47×#468—24no—
29C47×#449—24no—
30C47×#436—24no—
31C2×#107×C47C2211yescharacteristic
32C2×#107×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C47×#417—24no—
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×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×C4×C8×C47C2211yescharacteristic
46C47×#396—21no—
47C47×#394—21no—
48C47×#394—21no—
49C47×#392—21no—
50C47×#391C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#386—21no—
55C47×#386—21no—
56C47×#385—21no—
57C47×#380C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
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×C47D411yescharacteristic
75C22×D4×C47C2311yescharacteristic
76C22×D4×C47C2311yescharacteristic
77C23×C4×C47—21no—
78C23×C4×C47—21no—
79C23×C4×C47C2311yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C2×SD16×C47—22no—
82C2×SD16×C47—22no—
83C2×SD16×C47—41no—
84C2×D8×C47—22no—
85C2×D8×C47—22no—
86C2×D8×C47—41no—
87C2×M16×C47—22no—
88C2×M16×C47—22no—
89C2×M16×C47—22no—
90C2×M16×C47—22no—
91C2×M16×C47—41no—
92C2×M16×C47—41no—
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96C22×C8×C47C2311yescharacteristic
97C22⋊Q8×C47—22no—
98C22⋊Q8×C47—41no—
99#121×C47—22no—
100#121×C47—22no—
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—41no—
104#121×C47—41no—
105#121×C47—44no—
106C4×D4×C47—22no—
107C4×D4×C47—22no—
108C2×C4⋊C4×C47—22no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—41no—
113C2×C4⋊C4×C47D411yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47D411yescharacteristic
130C2×C22⋊C4×C47D411yescharacteristic
131C2×C42×C47C2311yescharacteristic
132#107×C47—22no—
133#107×C47—41no—
134C4⋊C8×C47—22no—
135#103×C47—22no—
136#103×C47—22no—
137#103×C47D414yescomplemented
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—41no—
143C22⋊C8×C47—22no—
144C22⋊C8×C47D414yescomplemented
145C4×C8×C47—22no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47—21no—
150#95×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47C2×D411yescharacteristic
154C24×C47C2×D411yescharacteristic
155#41×C47—28no—
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×C47C2×D412yes—
165C2×D4×C47—22no—
166C2×D4×C47—22no—
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—41no—
179C2×D4×C47—42no—
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—81no—
190C2×D4×C47—81no—
191C2×D4×C47#4112yes—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
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—42no—
209C22×C4×C47—42no—
210C22×C4×C47—42no—
211C22×C4×C47—42no—
212C22×C4×C47—42no—
213C22×C4×C47—81no—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D412yes—
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47#4112yes—
220C22×C4×C47C2411yescharacteristic
221SD16×C47—44no—
222D8×C47—44no—
223M16×C47—44no—
224M16×C47—44no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47C2×D412yes—
235C2×C8×C47C2×D412yes—
236C2×C8×C47C2×D412yes—
237C4⋊C4×C47—22no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—42no—
248C4⋊C4×C47—42no—
249C4⋊C4×C47—42no—
250C4⋊C4×C47C2×D412yes—
251C22⋊C4×C47—22no—
252C22⋊C4×C47—22no—
253C22⋊C4×C47—42no—
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—
262C22⋊C4×C47—81no—
263C42×C47—21no—
264C42×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—22no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
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#12112yes—
293C23×C47C22×D411yescharacteristic
294Q8×C47—22no—
295Q8×C47—22no—
296Q8×C47—41no—
297Q8×C47—41no—
298D4×C47—22no—
299D4×C47—22no—
300D4×C47—44no—
301D4×C47—48no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—84no—
309D4×C47—84no—
310D4×C47—84no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—48no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
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—84no—
349C2×C4×C47#12112yes—
350C2×C4×C47AGL(1,ℤ/8)12yes—
351C2×C4×C47C22×D411yescharacteristic
352C2×C4×C47C22×D411yescharacteristic
353C2×C4×C47C2×#4111yescharacteristic
354C2×C4×C47C2×#4111yescharacteristic
355C2×C4×C47H(5,𝔽2)11yescharacteristic
356C2×C4×C47H(5,𝔽2)11yescharacteristic
357C8×C47—22no—
358C8×C47—22no—
359C8×C47—22no—
360C8×C47—41no—
361#25139C4711yesmaximal, characteristic, direct product factor, Sylow
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—22no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—42no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
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×C47C2×#12111yescharacteristic
391C22×C47D4211yescharacteristic
392C22×C47#54611yescharacteristic
393C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C47#57511yescharacteristic
395C22×C47#57611yescharacteristic
396C22×C47#57811yescharacteristic
397C4×C47—22no—
398C4×C47—22no—
399C4×C47—41no—
400C4×C47—42no—
401C4×C47—42no—
402C4×C47—41no—
403C4×C47—81no—
404C4×C47—81no—
405C4×C47—81no—
406C4×C47—81no—
407C4×C47#52511yescharacteristic
408C4×C47#53811yescharacteristic
409C4×C47D4211yescharacteristic
410C4×C47#54611yescharacteristic
411C2×#468C2×C4711yescharacteristic, complemented
412C2×#449C2×C4711yescharacteristic, complemented
413C2×#436C2×C4711yescharacteristic, complemented
414C2×#417C2×C4711yescharacteristic, complemented
415#2416C2×C4711yescharacteristic, complemented
416#2407C2×C4711yescharacteristic, complemented
417#2067C2×C4711yescharacteristic, complemented
418#2055C2×C4711yescharacteristic, complemented
419#2036C2×C4711yescharacteristic, complemented
420#1999C2×C4711yescharacteristic, complemented
421#1970C2×C4711yescharacteristic, complemented
422#1933C2×C4711yescharacteristic, complemented
423#1895C2×C4711yescharacteristic, complemented
424#1895C2×C4711yescharacteristic, complemented
425#1852C2×C4711yescharacteristic, complemented
426C2×C47—42no—
427C2×C47—81no—
428C2×C47—82no—
429C2×C47—161no—
430C2×C47#242411yescharacteristic
431C2×C47#305511yescharacteristic
432C2×C47#306111yescharacteristic
433C2×C47#327411yescharacteristic
434C2×C47#327711yescharacteristic
435C2×C47#332211yescharacteristic
436C2×C47#333011yescharacteristic
437C22×#41C22×C4711yescharacteristic
438C22×SD16C22×C4711yescharacteristic
439C22×D8C22×C4711yescharacteristic
440C22×M16C22×C4711yescharacteristic
441C22×M16C22×C4711yescharacteristic
442C2×C22⋊Q8C22×C4711yescharacteristic
443C2×#121—21no—
444C2×#121C22×C4711yescharacteristic
445C2×#121C22×C4711yescharacteristic
446C2×#121C22×C4711yescharacteristic
447C2×C4×D4C22×C4711yescharacteristic
448C22×C4⋊C4C22×C4711yescharacteristic
449#468—24no—
450#449—24no—
451#436—24no—
452C2×#107C22×C4711yescharacteristic
453C2×#107C22×C4711yescharacteristic
454C2×C4⋊C8C22×C4711yescharacteristic
455#417—24no—
456C2×#103C22×C4711yescharacteristic
457C2×#103C22×C4711yescharacteristic
458C2×#103C22×C4711yescharacteristic
459C2×#102C22×C4711yescharacteristic
460C2×#102C22×C4711yescharacteristic
461C2×#102C22×C4711yescharacteristic
462C2×#102C22×C4711yescharacteristic
463C2×#102C22×C4711yescharacteristic
464C2×C22⋊C8C22×C4711yescharacteristic
465C2×C22⋊C8C22×C4711yescharacteristic
466C2×C4×C8C22×C4711yescharacteristic
467#396—21no—
468#394—21no—
469#394—21no—
470#392—21no—
471#391C22×C4711yescharacteristic
472#390C22×C4711yescharacteristic
473#390C22×C4711yescharacteristic
474#389C22×C4711yescharacteristic
475#386—21no—
476#386—21no—
477#385—21no—
478#380C22×C4711yescharacteristic
479#380C22×C4711yescharacteristic
480#340C22×C4711yescharacteristic
481#340C22×C4711yescharacteristic
482#340C22×C4711yescharacteristic
483#340C22×C4711yescharacteristic
484C47#2513911yescharacteristic, direct product factor, Sylow
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—41no—
490C2×#41—41no—
491C22×Q8C23×C4711yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4D4×C4711yescharacteristic
497C22×D4C23×C4711yescharacteristic
498C22×D4C23×C4711yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C23×C4711yescharacteristic
502C23×C4C23×C4711yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8C23×C4711yescharacteristic
516C22×C8C23×C4711yescharacteristic
517C22×C8C23×C4711yescharacteristic
518C22×C8C23×C4711yescharacteristic
519C22⋊Q8—22no—
520C22⋊Q8—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527#121—44no—
528C4×D4—22no—
529C4×D4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4D4×C4711yescharacteristic
536C2×C4⋊C4C23×C4711yescharacteristic
537C2×C4⋊C4C23×C4711yescharacteristic
538C2×C4⋊C4C23×C4711yescharacteristic
539C2×C4⋊C4C23×C4711yescharacteristic
540C2×C4⋊C4C23×C4711yescharacteristic
541C2×C22⋊C4—21no—
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⋊C4—21no—
551C2×C22⋊C4D4×C4711yescharacteristic
552C2×C22⋊C4D4×C4711yescharacteristic
553C2×C42C23×C4711yescharacteristic
554#107—22no—
555#107—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#103D4×C4714yescomplemented
560#102—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—41no—
565C22⋊C8—22no—
566C22⋊C8D4×C4714yescomplemented
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573C24—21no—
574C24—21no—
575C24C2×D4×C4711yescharacteristic
576C24C2×D4×C4711yescharacteristic
577#41—28no—
578#41—44no—
579#41—44no—
580#41—44no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C4712yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
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—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4#41×C4712yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4C2×D4×C4711yescharacteristic
637C22×C4C2×D4×C4711yescharacteristic
638C22×C4C2×D4×C4711yescharacteristic
639C22×C4C2×D4×C4712yes—
640C22×C4C2×D4×C4711yescharacteristic
641C22×C4#41×C4712yes—
642C22×C4C24×C4711yescharacteristic
643SD16—44no—
644D8—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8C2×D4×C4712yes—
657C2×C8C2×D4×C4712yes—
658C2×C8C2×D4×C4712yes—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C4712yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—41no—
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#121×C4712yes—
715C23C22×D4×C4711yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—41no—
719Q8—41no—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
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—84no—
771C2×C4#121×C4712yes—
772C2×C4AGL(1,ℤ/8)×C4712yes—
773C2×C4C22×D4×C4711yescharacteristic
774C2×C4C22×D4×C4711yescharacteristic
775C2×C4C2×#41×C4711yescharacteristic
776C2×C4C2×#41×C4711yescharacteristic
777C2×C4H(5,𝔽2)×C4711yescharacteristic
778C2×C4H(5,𝔽2)×C4711yescharacteristic
779C8—22no—
780C8—22no—
781C8—22no—
782C8—41no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—42no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22C2×#121×C4711yescharacteristic
812C22D42×C4711yescharacteristic
813C22C47×#54611yescharacteristic
814C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
815C22C47×#57511yescharacteristic
816C22C47×#57611yescharacteristic
817C22C47×#57811yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—42no—
823C4—42no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4C47×#52511yescharacteristic
829C4C47×#53811yescharacteristic
830C4D42×C4711yescharacteristic
831C4C47×#54611yescharacteristic
832C2—42no—
833C2—81no—
834C2—82no—
835C2—161no—
836C2C47×#242411yescharacteristic
837C2C47×#305511yescharacteristic
838C2C47×#306111yescharacteristic
839C2C47×#327411yescharacteristic
840C2C47×#327711yescharacteristic
841C2C47×#332211yescharacteristic
842C2C47×#333011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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
1. C2×C47×#468C2semidirect
2. C2×C47×#449C2semidirect
3. C2×C47×#436C2semidirect
4. C2×C47×#417C2semidirect
5. C47×#2416C2semidirect
6. C47×#2407C2semidirect
7. C47×#2067C2semidirect
8. C47×#2055C2semidirect
9. C47×#2036C2semidirect
10. C47×#1999C2semidirect
11. C47×#1970C2semidirect
12. C47×#1933C2semidirect
13. C47×#1895C2semidirect
14. C47×#1895C2semidirect
15. C47×#1852C2semidirect
137. #103×C47D4semidirect
144. C22⋊C8×C47D4semidirect
361. #25139C47direct (N × H)
411. C2×#468C2×C47semidirect
412. C2×#449C2×C47semidirect
413. C2×#436C2×C47semidirect
414. C2×#417C2×C47semidirect
415. #2416C2×C47semidirect
416. #2407C2×C47semidirect
417. #2067C2×C47semidirect
418. #2055C2×C47semidirect
419. #2036C2×C47semidirect
420. #1999C2×C47semidirect
421. #1970C2×C47semidirect
422. #1933C2×C47semidirect
423. #1895C2×C47semidirect
424. #1895C2×C47semidirect
425. #1852C2×C47semidirect
484. C47#25139direct (N × H)
559. #103D4×C47semidirect
566. C22⋊C8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4682
C2×C47×#4492
C2×C47×#4362
C2×C47×#4172
C47×#24162
C47×#24072
C47×#20672
C47×#20552
C47×#20362
C47×#19992
C47×#19702
C47×#19332
C47×#18952
C47×#18522
#2513947