Finite Group Databasebeta

← C47×#22036 #26061734

Subgroups — C47×#22036 #26061734

Order 12032.

1162 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×#435C211yesmaximal, characteristic, complemented
2C2×C47×#407C211yesmaximal, characteristic, complemented
3C4×#120×C47C211yesmaximal, characteristic
4C47×#1955C211yesmaximal, characteristic, complemented
5C47×#1954C211yesmaximal, characteristic, complemented
6C47×#1924C211yesmaximal, characteristic, complemented
7C47×#1924C211yesmaximal, characteristic, complemented
8C47×#1924C211yesmaximal, characteristic, complemented
9C47×#1923C211yesmaximal, characteristic, complemented
10C47×#1870C211yesmaximal, characteristic, complemented
11C47×#1869C211yesmaximal, characteristic, complemented
12C47×#1869C211yesmaximal, characteristic, complemented
13C47×#1851C211yesmaximal, characteristic, complemented
14C47×#1779C211yesmaximal, characteristic, complemented
15C47×#1753C211yesmaximal, characteristic, complemented
16C24×C4×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic, complemented
20C2×#120×C47C411yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C47×#435—24no—
25C2×C4⋊C8×C47C2211yescharacteristic, complemented
26C2×C4⋊C8×C47C2211yescharacteristic, complemented
27C2×C4⋊C8×C47C2211yescharacteristic, complemented
28C47×#407—24no—
29C2×C22⋊C8×C47C2211yescharacteristic
30C2×C22⋊C8×C47C2211yescharacteristic
31C2×C22⋊C8×C47C2211yescharacteristic
32C2×C22⋊C8×C47C2211yescharacteristic
33C2×C22⋊C8×C47C2211yescharacteristic
34C2×C22⋊C8×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C2×C22⋊C8×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic, complemented
40C2×C22⋊C8×C47C2211yescharacteristic, complemented
41C2×C22⋊C8×C47C2211yescharacteristic, complemented
42C2×#97×C47C2211yescharacteristic, complemented
43C2×#97×C47C2211yescharacteristic, complemented
44C2×C4×C8×C47C2211yescharacteristic, complemented
45C47×#386C411yescharacteristic
46C47×#386C411yescharacteristic
47C47×#386C411yescharacteristic
48C47×#385C411yescharacteristic
49C47×#385C411yescharacteristic
50C47×#385C411yescharacteristic
51C47×#379C411yescharacteristic
52C4×C22⋊C4×C47C2211yescharacteristic
53C4×C22⋊C4×C47C2211yescharacteristic
54C4×C22⋊C4×C47C2211yescharacteristic
55C47×#336C2211yescharacteristic, complemented
56C47×#336C2211yescharacteristic, complemented
57C47×#336C2211yescharacteristic, complemented
58C47×#336C2211yescharacteristic, complemented
59C47×#336C2211yescharacteristic, complemented
60C47×#336C2211yescharacteristic, complemented
61C25×C47C2×C411yescharacteristic
62C22×D4×C47C2×C411yescharacteristic
63C22×D4×C47C2×C411yescharacteristic
64C22×D4×C47C2×C411yescharacteristic
65C23×C4×C47—22no—
66C23×C4×C47—22no—
67C23×C4×C47—41no—
68C23×C4×C47—41no—
69C23×C4×C47—41no—
70C23×C4×C47—41no—
71C23×C4×C47C2×C411yescharacteristic
72C23×C4×C47C2×C411yescharacteristic
73C23×C4×C47C2×C411yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C2×M16×C47—22no—
79C2×M16×C47—41no—
80C2×M16×C47—41no—
81C2×M16×C47—41no—
82C2×M16×C47—41no—
83C2×M16×C47D414yescomplemented
84C22×C8×C47—22no—
85C22×C8×C47—41no—
86C22×C8×C47—41no—
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C22×C8×C47C2311yescharacteristic
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95#120×C47—24no—
96C4×D4×C47—22no—
97C4×D4×C47—22no—
98C4×D4×C47—41no—
99C4×D4×C47—41no—
100C4×D4×C47—41no—
101C4×D4×C47—41no—
102C2×C4⋊C4×C47C2×C411yescharacteristic
103C2×C4⋊C4×C47C2×C411yescharacteristic
104C2×C4⋊C4×C47C2×C411yescharacteristic
105C2×C22⋊C4×C47C2×C411yescharacteristic
106C2×C22⋊C4×C47C2×C411yescharacteristic
107C2×C22⋊C4×C47C2×C411yescharacteristic
108C2×C22⋊C4×C47C2×C411yescharacteristic
109C2×C22⋊C4×C47C2×C411yescharacteristic
110C2×C22⋊C4×C47C2×C411yescharacteristic
111C2×C22⋊C4×C47C2×C411yescharacteristic
112C2×C22⋊C4×C47C2×C411yescharacteristic
113C2×C22⋊C4×C47C2×C411yescharacteristic
114C2×C22⋊C4×C47C2×C411yescharacteristic
115C2×C22⋊C4×C47C2×C411yescharacteristic
116C2×C22⋊C4×C47C2×C411yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C4⋊C8×C47—22no—
121C4⋊C8×C47—41no—
122C4⋊C8×C47—41no—
123C22⋊C8×C47—22no—
124C22⋊C8×C47—22no—
125C22⋊C8×C47—22no—
126C22⋊C8×C47—22no—
127C22⋊C8×C47—22no—
128C22⋊C8×C47—22no—
129C22⋊C8×C47—22no—
130C22⋊C8×C47—41no—
131C22⋊C8×C47—41no—
132C22⋊C8×C47—41no—
133C22⋊C8×C47—41no—
134C22⋊C8×C47—41no—
135C22⋊C8×C47—41no—
136#97×C47—22no—
137#97×C47—41no—
138C4×C8×C47—41no—
139#95×C47C2×C411yescharacteristic
140#95×C47C2×C411yescharacteristic
141#95×C47C2×C411yescharacteristic
142#95×C47C2×C411yescharacteristic
143#95×C47C2×C411yescharacteristic
144#95×C47C2×C411yescharacteristic
145C24×C47—22no—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—41no—
149C24×C47—41no—
150C24×C47—41no—
151C24×C47—41no—
152C24×C47C22×C411yescharacteristic
153C24×C47C22×C411yescharacteristic
154C24×C47C22×C411yescharacteristic
155C24×C47C22×C411yescharacteristic
156C2×D4×C47—22no—
157C2×D4×C47—22no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—41no—
161C2×D4×C47—41no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47M1614yescomplemented
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
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—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—41no—
191C22×C4×C47—41no—
192C22×C4×C47—41no—
193C22×C4×C47—41no—
194C22×C4×C47—41no—
195C22×C4×C47—41no—
196C22×C4×C47—44no—
197C22×C4×C47—44no—
198C22×C4×C47—44no—
199C22×C4×C47—44no—
200C22×C4×C47C22×C411yescharacteristic
201C22×C4×C47C22×C411yescharacteristic
202C22×C4×C47C22×C411yescharacteristic
203C22×C4×C47C22×C411yescharacteristic
204C22×C4×C47C22×C411yescharacteristic
205C22×C4×C47C22×C411yescharacteristic
206C22×C4×C47C22×C411yescharacteristic
207C22×C4×C47C22×C411yescharacteristic
208C22×C4×C47C22×C411yescharacteristic
209C22×C4×C47C22×C411yescharacteristic
210C22×C4×C47C2×D412yes—
211C22×C4×C47#4112yes—
212C22×C4×C47C2411yescharacteristic
213M16×C47—44no—
214M16×C47—44no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
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×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—44no—
238C2×C8×C47C2×D412yes—
239C2×C8×C47C2×D412yes—
240C4⋊C4×C47—22no—
241C4⋊C4×C47—41no—
242C4⋊C4×C47—41no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—22no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—41no—
250C22⋊C4×C47—41no—
251C22⋊C4×C47—41no—
252C22⋊C4×C47—41no—
253C22⋊C4×C47—41no—
254C22⋊C4×C47—41no—
255C42×C47—21no—
256C42×C47—21no—
257C42×C47—21no—
258C42×C47—21no—
259C42×C47—21no—
260C42×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×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—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—44no—
286C23×C47—44no—
287C23×C47—44no—
288C23×C47—44no—
289C23×C47—44no—
290C23×C47—44no—
291C23×C47—44no—
292C23×C47C4×D412yes—
293C23×C47C2×M1612yes—
294C23×C47C2×M1612yes—
295C23×C47#13112yes—
296C23×C47C23×C411yescharacteristic
297D4×C47—44no—
298D4×C47—44no—
299D4×C47—44no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
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—44no—
333C2×C4×C47—44no—
334C2×C4×C47—44no—
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×C47C4×D412yes—
348C2×C4×C47C2×M1612yes—
349C2×C4×C47C22×D411yescharacteristic
350C2×C4×C47C2×#4111yescharacteristic
351C2×C4×C47H(5,𝔽2)11yescharacteristic
352C2×C4×C47H(5,𝔽2)11yescharacteristic
353C2×C4×C47H(5,𝔽2)11yescharacteristic
354C2×C4×C47H(5,𝔽2)11yescharacteristic
355C8×C47—22no—
356C8×C47—22no—
357C8×C47—41no—
358C8×C47—41no—
359C8×C47—41no—
360C8×C47—41no—
361C8×C47—41no—
362C8×C47—41no—
363#22036C4711yesmaximal, characteristic, direct product factor, Sylow
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—22no—
373C22×C47—22no—
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—416no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—41no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—41no—
387C22×C47—41no—
388C22×C47—41no—
389C22×C47—41no—
390C22×C47—41no—
391C22×C47—41no—
392C22×C47—41no—
393C22×C47C2×C4×D411yescharacteristic
394C22×C47#51811yescharacteristic
395C22×C47#51811yescharacteristic
396C22×C47C22×M1611yescharacteristic
397C22×C47C2×#13111yescharacteristic
398C22×C47#56811yescharacteristic
399C22×C47#56811yescharacteristic
400C4×C47—22no—
401C4×C47—22no—
402C4×C47—41no—
403C4×C47—41no—
404C4×C47—41no—
405C4×C47—41no—
406C4×C47—41no—
407C4×C47—41no—
408C4×C47—41no—
409C4×C47—41no—
410C4×C47#53411yescharacteristic
411C4×C47#53511yescharacteristic
412C4×C47#53811yescharacteristic
413C4×C47#53811yescharacteristic
414C2×#435C2×C4711yescharacteristic, complemented
415C2×#407C2×C4711yescharacteristic, complemented
416C4×#120C2×C4711yescharacteristic
417#1955C2×C4711yescharacteristic, complemented
418#1954C2×C4711yescharacteristic, complemented
419#1924C2×C4711yescharacteristic, complemented
420#1924C2×C4711yescharacteristic, complemented
421#1924C2×C4711yescharacteristic, complemented
422#1923C2×C4711yescharacteristic, complemented
423#1870C2×C4711yescharacteristic, complemented
424#1869C2×C4711yescharacteristic, complemented
425#1869C2×C4711yescharacteristic, complemented
426#1851C2×C4711yescharacteristic, complemented
427#1779C2×C4711yescharacteristic, complemented
428#1753C2×C4711yescharacteristic, complemented
429C2×C47—42no—
430C2×C47—42no—
431C2×C47—42no—
432C2×C47—42no—
433C2×C47#232111yescharacteristic
434C2×C47#293311yescharacteristic
435C2×C47D4×M1611yescharacteristic
436C2×C47#297311yescharacteristic
437C2×C47#297411yescharacteristic
438C2×C47#297611yescharacteristic
439C2×C47#297811yescharacteristic
440C24×C4C22×C4711yescharacteristic
441C22×M16C22×C4711yescharacteristic
442C22×M16C22×C4711yescharacteristic
443C23×C8C22×C4711yescharacteristic, complemented
444C2×#120C4×C4711yescharacteristic
445C2×C4×D4C22×C4711yescharacteristic
446C2×C4×D4C22×C4711yescharacteristic
447C2×C4×D4C22×C4711yescharacteristic
448#435—24no—
449C2×C4⋊C8C22×C4711yescharacteristic, complemented
450C2×C4⋊C8C22×C4711yescharacteristic, complemented
451C2×C4⋊C8C22×C4711yescharacteristic, complemented
452#407—24no—
453C2×C22⋊C8C22×C4711yescharacteristic
454C2×C22⋊C8C22×C4711yescharacteristic
455C2×C22⋊C8C22×C4711yescharacteristic
456C2×C22⋊C8C22×C4711yescharacteristic
457C2×C22⋊C8C22×C4711yescharacteristic
458C2×C22⋊C8C22×C4711yescharacteristic
459C2×C22⋊C8C22×C4711yescharacteristic
460C2×C22⋊C8C22×C4711yescharacteristic
461C2×C22⋊C8C22×C4711yescharacteristic
462C2×C22⋊C8C22×C4711yescharacteristic
463C2×C22⋊C8C22×C4711yescharacteristic, complemented
464C2×C22⋊C8C22×C4711yescharacteristic, complemented
465C2×C22⋊C8C22×C4711yescharacteristic, complemented
466C2×#97C22×C4711yescharacteristic, complemented
467C2×#97C22×C4711yescharacteristic, complemented
468C2×C4×C8C22×C4711yescharacteristic, complemented
469#386C4×C4711yescharacteristic
470#386C4×C4711yescharacteristic
471#386C4×C4711yescharacteristic
472#385C4×C4711yescharacteristic
473#385C4×C4711yescharacteristic
474#385C4×C4711yescharacteristic
475#379C4×C4711yescharacteristic
476C4×C22⋊C4C22×C4711yescharacteristic
477C4×C22⋊C4C22×C4711yescharacteristic
478C4×C22⋊C4C22×C4711yescharacteristic
479#336C22×C4711yescharacteristic, complemented
480#336C22×C4711yescharacteristic, complemented
481#336C22×C4711yescharacteristic, complemented
482#336C22×C4711yescharacteristic, complemented
483#336C22×C4711yescharacteristic, complemented
484#336C22×C4711yescharacteristic, complemented
485C47#2203611yescharacteristic, direct product factor, Sylow
486C25C2×C4×C4711yescharacteristic
487C22×D4C2×C4×C4711yescharacteristic
488C22×D4C2×C4×C4711yescharacteristic
489C22×D4C2×C4×C4711yescharacteristic
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4C2×C4×C4711yescharacteristic
497C23×C4C2×C4×C4711yescharacteristic
498C23×C4C2×C4×C4711yescharacteristic
499C23×C4C23×C4711yescharacteristic
500C23×C4C23×C4711yescharacteristic
501C23×C4C23×C4711yescharacteristic
502C23×C4C23×C4711yescharacteristic
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16D4×C4714yescomplemented
509C22×C8—22no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8C23×C4711yescharacteristic
513C22×C8C23×C4711yescharacteristic
514C22×C8C23×C4711yescharacteristic
515C22×C8C23×C4711yescharacteristic
516C22×C8C23×C4711yescharacteristic
517C22×C8C23×C4711yescharacteristic
518C22×C8C23×C4711yescharacteristic
519C22×C8C23×C4711yescharacteristic
520#120—24no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—41no—
524C4×D4—41no—
525C4×D4—41no—
526C4×D4—41no—
527C2×C4⋊C4C2×C4×C4711yescharacteristic
528C2×C4⋊C4C2×C4×C4711yescharacteristic
529C2×C4⋊C4C2×C4×C4711yescharacteristic
530C2×C22⋊C4C2×C4×C4711yescharacteristic
531C2×C22⋊C4C2×C4×C4711yescharacteristic
532C2×C22⋊C4C2×C4×C4711yescharacteristic
533C2×C22⋊C4C2×C4×C4711yescharacteristic
534C2×C22⋊C4C2×C4×C4711yescharacteristic
535C2×C22⋊C4C2×C4×C4711yescharacteristic
536C2×C22⋊C4C2×C4×C4711yescharacteristic
537C2×C22⋊C4C2×C4×C4711yescharacteristic
538C2×C22⋊C4C2×C4×C4711yescharacteristic
539C2×C22⋊C4C2×C4×C4711yescharacteristic
540C2×C22⋊C4C2×C4×C4711yescharacteristic
541C2×C22⋊C4C2×C4×C4711yescharacteristic
542C2×C42C23×C4711yescharacteristic
543C2×C42C23×C4711yescharacteristic
544C2×C42C23×C4711yescharacteristic
545C4⋊C8—22no—
546C4⋊C8—41no—
547C4⋊C8—41no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557C22⋊C8—41no—
558C22⋊C8—41no—
559C22⋊C8—41no—
560C22⋊C8—41no—
561#97—22no—
562#97—41no—
563C4×C8—41no—
564#95C2×C4×C4711yescharacteristic
565#95C2×C4×C4711yescharacteristic
566#95C2×C4×C4711yescharacteristic
567#95C2×C4×C4711yescharacteristic
568#95C2×C4×C4711yescharacteristic
569#95C2×C4×C4711yescharacteristic
570C24—22no—
571C24—22no—
572C24—22no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24C22×C4×C4711yescharacteristic
578C24C22×C4×C4711yescharacteristic
579C24C22×C4×C4711yescharacteristic
580C24C22×C4×C4711yescharacteristic
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4M16×C4714yescomplemented
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4C22×C4×C4711yescharacteristic
626C22×C4C22×C4×C4711yescharacteristic
627C22×C4C22×C4×C4711yescharacteristic
628C22×C4C22×C4×C4711yescharacteristic
629C22×C4C22×C4×C4711yescharacteristic
630C22×C4C22×C4×C4711yescharacteristic
631C22×C4C22×C4×C4711yescharacteristic
632C22×C4C22×C4×C4711yescharacteristic
633C22×C4C22×C4×C4711yescharacteristic
634C22×C4C22×C4×C4711yescharacteristic
635C22×C4C2×D4×C4712yes—
636C22×C4#41×C4712yes—
637C22×C4C24×C4711yescharacteristic
638M16—44no—
639M16—44no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
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×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—44no—
663C2×C8C2×D4×C4712yes—
664C2×C8C2×D4×C4712yes—
665C4⋊C4—22no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23C4×D4×C4712yes—
718C23C2×M16×C4712yes—
719C23C2×M16×C4712yes—
720C23#131×C4712yes—
721C23C23×C4×C4711yescharacteristic
722D4—44no—
723D4—44no—
724D4—44no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
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—44no—
758C2×C4—44no—
759C2×C4—44no—
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×C4C4×D4×C4712yes—
773C2×C4C2×M16×C4712yes—
774C2×C4C22×D4×C4711yescharacteristic
775C2×C4C2×#41×C4711yescharacteristic
776C2×C4H(5,𝔽2)×C4711yescharacteristic
777C2×C4H(5,𝔽2)×C4711yescharacteristic
778C2×C4H(5,𝔽2)×C4711yescharacteristic
779C2×C4H(5,𝔽2)×C4711yescharacteristic
780C8—22no—
781C8—22no—
782C8—41no—
783C8—41no—
784C8—41no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—416no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22C2×C4×D4×C4711yescharacteristic
818C22C47×#51811yescharacteristic
819C22C47×#51811yescharacteristic
820C22C22×M16×C4711yescharacteristic
821C22C2×#131×C4711yescharacteristic
822C22C47×#56811yescharacteristic
823C22C47×#56811yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4C47×#53411yescharacteristic
835C4C47×#53511yescharacteristic
836C4C47×#53811yescharacteristic
837C4C47×#53811yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—42no—
842C2C47×#232111yescharacteristic
843C2C47×#293311yescharacteristic
844C2D4×M16×C4711yescharacteristic
845C2C47×#297311yescharacteristic
846C2C47×#297411yescharacteristic
847C2C47×#297611yescharacteristic
848C2C47×#297811yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC2×#120×C47C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#435C2semidirect
2. C2×C47×#407C2semidirect
4. C47×#1955C2semidirect
5. C47×#1954C2semidirect
6. C47×#1924C2semidirect
7. C47×#1924C2semidirect
8. C47×#1924C2semidirect
9. C47×#1923C2semidirect
10. C47×#1870C2semidirect
11. C47×#1869C2semidirect
12. C47×#1869C2semidirect
13. C47×#1851C2semidirect
14. C47×#1779C2semidirect
15. C47×#1753C2semidirect
19. C23×C8×C47C22semidirect
25. C2×C4⋊C8×C47C22semidirect
26. C2×C4⋊C8×C47C22semidirect
27. C2×C4⋊C8×C47C22semidirect
39. C2×C22⋊C8×C47C22semidirect
40. C2×C22⋊C8×C47C22semidirect
41. C2×C22⋊C8×C47C22semidirect
42. C2×#97×C47C22semidirect
43. C2×#97×C47C22semidirect
44. C2×C4×C8×C47C22semidirect
55. C47×#336C22semidirect
56. C47×#336C22semidirect
57. C47×#336C22semidirect
58. C47×#336C22semidirect
59. C47×#336C22semidirect
60. C47×#336C22semidirect
83. C2×M16×C47D4semidirect
164. C2×D4×C47M16semidirect
363. #22036C47direct (N × H)
414. C2×#435C2×C47semidirect
415. C2×#407C2×C47semidirect
417. #1955C2×C47semidirect
418. #1954C2×C47semidirect
419. #1924C2×C47semidirect
420. #1924C2×C47semidirect
421. #1924C2×C47semidirect
422. #1923C2×C47semidirect
423. #1870C2×C47semidirect
424. #1869C2×C47semidirect
425. #1869C2×C47semidirect
426. #1851C2×C47semidirect
427. #1779C2×C47semidirect
428. #1753C2×C47semidirect
443. C23×C8C22×C47semidirect
449. C2×C4⋊C8C22×C47semidirect
450. C2×C4⋊C8C22×C47semidirect
451. C2×C4⋊C8C22×C47semidirect
463. C2×C22⋊C8C22×C47semidirect
464. C2×C22⋊C8C22×C47semidirect
465. C2×C22⋊C8C22×C47semidirect
466. C2×#97C22×C47semidirect
467. C2×#97C22×C47semidirect
468. C2×C4×C8C22×C47semidirect
479. #336C22×C47semidirect
480. #336C22×C47semidirect
481. #336C22×C47semidirect
482. #336C22×C47semidirect
483. #336C22×C47semidirect
484. #336C22×C47semidirect
485. C47#22036direct (N × H)
508. C2×M16D4×C47semidirect
589. C2×D4M16×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4352
C2×C47×#4072
C4×#120×C472
C47×#19552
C47×#19542
C47×#19242
C47×#19232
C47×#18702
C47×#18692
C47×#18512
C47×#17792
C47×#17532
#2203647