Finite Group Databasebeta

← C47×#22993 #26062691

Subgroups — C47×#22993 #26062691

Order 12032.

998 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#435C211yesmaximal, characteristic, complemented
2C2×C47×#435C211yesmaximal, characteristic, complemented
3C2×C47×#435C211yesmaximal, characteristic, complemented
4C2×C47×#424C211yesmaximal, characteristic, complemented
5C47×#2392C211yesmaximal, characteristic
6C47×#1954C211yesmaximal, characteristic, complemented
7C47×#1940C211yesmaximal, characteristic, complemented
8C47×#1924C211yesmaximal, characteristic, complemented
9C47×#1924C211yesmaximal, characteristic, complemented
10C47×#1870C211yesmaximal, characteristic, complemented
11C47×#1869C211yesmaximal, characteristic, complemented
12C47×#1851C211yesmaximal, characteristic, complemented
13C47×#1850C211yesmaximal, characteristic, complemented
14C47×#1770C211yesmaximal, characteristic, complemented
15C47×#1750C211yesmaximal, characteristic, complemented
16C22×M16×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C2×#117×C47C2211yescharacteristic
24C47×#435—24no—
25C47×#435—24no—
26C47×#435—24no—
27C47×#424—24no—
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4⋊C8×C47C2211yescharacteristic
30C2×C4⋊C8×C47C2211yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊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
40C2×C22⋊C8×C47C2211yescharacteristic
41C2×C22⋊C8×C47C2211yescharacteristic
42C2×#97×C47C2211yescharacteristic
43C2×#97×C47C2211yescharacteristic
44C2×#97×C47C2211yescharacteristic
45C2×C4×C8×C47C2211yescharacteristic
46C47×#398C411yescharacteristic
47C47×#397C411yescharacteristic
48C47×#396C411yescharacteristic
49C47×#396C411yescharacteristic
50C47×#394C411yescharacteristic
51C47×#394C411yescharacteristic
52C47×#394C411yescharacteristic
53C47×#392C411yescharacteristic
54C4×C4⋊C4×C47C2211yescharacteristic
55C4×C22⋊C4×C47C2211yescharacteristic
56C4×C22⋊C4×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×D4×C47C2×C411yescharacteristic
64C22×D4×C47C2×C411yescharacteristic
65C22×D4×C47C2×C411yescharacteristic
66C23×C4×C47C2311yescharacteristic
67C23×C4×C47C2311yescharacteristic
68C23×C4×C47C2311yescharacteristic
69C2×M16×C47—22no—
70C2×M16×C47—22no—
71C2×M16×C47—22no—
72C2×M16×C47—22no—
73C2×M16×C47—41no—
74C2×M16×C47—41no—
75C22×C8×C47—22no—
76C22×C8×C47—22no—
77C22×C8×C47—22no—
78C22×C8×C47—22no—
79C22×C8×C47—41no—
80C22×C8×C47—41no—
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C4×D4×C47—22no—
90C4×D4×C47—22no—
91C4×D4×C47—22no—
92C4×D4×C47—22no—
93C4×D4×C47—22no—
94C4×D4×C47—22no—
95#117×C47—22no—
96#117×C47—22no—
97C2×C4⋊C4×C47C2×C411yescharacteristic
98C2×C4⋊C4×C47C2×C411yescharacteristic
99C2×C4⋊C4×C47C2×C411yescharacteristic
100C2×C4⋊C4×C47C2×C411yescharacteristic
101C2×C4⋊C4×C47C2×C411yescharacteristic
102C2×C4⋊C4×C47C2×C411yescharacteristic
103C2×C4⋊C4×C47C2×C411yescharacteristic
104C2×C22⋊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×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C4⋊C8×C47—22no—
121C4⋊C8×C47—22no—
122C4⋊C8×C47—22no—
123C4⋊C8×C47—22no—
124C4⋊C8×C47—22no—
125C4⋊C8×C47D414yescomplemented
126C22⋊C8×C47—22no—
127C22⋊C8×C47—22no—
128C22⋊C8×C47—22no—
129C22⋊C8×C47—22no—
130C22⋊C8×C47—22no—
131C22⋊C8×C47—41no—
132C22⋊C8×C47—41no—
133C22⋊C8×C47D414yescomplemented
134#97×C47—22no—
135#97×C47—22no—
136#97×C47—22no—
137C4×C8×C47—22no—
138#95×C47C2×C411yescharacteristic
139#95×C47C2×C411yescharacteristic
140#95×C47C2×C411yescharacteristic
141#95×C47C2×C411yescharacteristic
142#95×C47C2×C411yescharacteristic
143#95×C47C2×C411yescharacteristic
144C24×C47C22×C411yescharacteristic
145C24×C47C22×C411yescharacteristic
146C24×C47C22×C411yescharacteristic
147C2×D4×C47—22no—
148C2×D4×C47—22no—
149C2×D4×C47—22no—
150C2×D4×C47—22no—
151C2×D4×C47—22no—
152C2×D4×C47—41no—
153C2×D4×C47—41no—
154C2×D4×C47—41no—
155C2×D4×C47—41no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47C22×C411yescharacteristic
173C22×C4×C47C22×C411yescharacteristic
174C22×C4×C47C22×C411yescharacteristic
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C22×C411yescharacteristic
178C22×C4×C47C22×C411yescharacteristic
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C2×D412yes—
184C22×C4×C47#4112yes—
185C22×C4×C47C2411yescharacteristic
186M16×C47—44no—
187M16×C47—44no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—44no—
209C2×C8×C47—44no—
210C2×C8×C47C2×D412yes—
211C2×C8×C47C2×D412yes—
212C2×C8×C47C2×D412yes—
213C2×C8×C47C2×D412yes—
214C4⋊C4×C47—22no—
215C4⋊C4×C47—22no—
216C4⋊C4×C47—22no—
217C4⋊C4×C47—22no—
218C4⋊C4×C47—22no—
219C4⋊C4×C47—41no—
220C4⋊C4×C47—41no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—22no—
223C22⋊C4×C47—22no—
224C22⋊C4×C47—22no—
225C22⋊C4×C47—22no—
226C22⋊C4×C47—22no—
227C22⋊C4×C47—22no—
228C22⋊C4×C47—22no—
229C22⋊C4×C47—22no—
230C22⋊C4×C47—41no—
231C22⋊C4×C47—41no—
232C22⋊C4×C47—41no—
233C42×C47—21no—
234C42×C47—21no—
235C42×C47—21no—
236C42×C47—21no—
237C42×C47—21no—
238C42×C47—21no—
239C42×C47C2×D412yes—
240C42×C47#4112yes—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47C4×D412yes—
261C23×C47#13112yes—
262C23×C47C23×C411yescharacteristic
263D4×C47—44no—
264D4×C47—44no—
265D4×C47—44no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47C4×D412yes—
309C2×C4×C47C4×D412yes—
310C2×C4×C47C4×D412yes—
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C2×#4111yescharacteristic
314C2×C4×C47C2×#4111yescharacteristic
315C2×C4×C47H(5,𝔽2)11yescharacteristic
316C2×C4×C472−1+411yescharacteristic
317C8×C47—22no—
318C8×C47—22no—
319C8×C47—22no—
320C8×C47—22no—
321C8×C47—41no—
322C8×C47—41no—
323C8×C47—41no—
324C8×C47—41no—
325#22993C4711yesmaximal, characteristic, direct product factor, Sylow
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47C2×C4×D411yescharacteristic
348C22×C47C2×C4×D411yescharacteristic
349C22×C47#52011yescharacteristic
350C22×C47C2×#13111yescharacteristic
351C22×C47#56811yescharacteristic
352C22×C47#56811yescharacteristic
353C22×C47#56811yescharacteristic
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47—41no—
360C4×C47—41no—
361C4×C47—41no—
362C4×C47—41no—
363C4×C47—41no—
364C4×C47—41no—
365C4×C47D4211yescharacteristic
366C4×C47#54711yescharacteristic
367C4×C47#54811yescharacteristic
368C4×C47#55311yescharacteristic
369C2×#435C2×C4711yescharacteristic, complemented
370C2×#435C2×C4711yescharacteristic, complemented
371C2×#435C2×C4711yescharacteristic, complemented
372C2×#424C2×C4711yescharacteristic, complemented
373#2392C2×C4711yescharacteristic
374#1954C2×C4711yescharacteristic, complemented
375#1940C2×C4711yescharacteristic, complemented
376#1924C2×C4711yescharacteristic, complemented
377#1924C2×C4711yescharacteristic, complemented
378#1870C2×C4711yescharacteristic, complemented
379#1869C2×C4711yescharacteristic, complemented
380#1851C2×C4711yescharacteristic, complemented
381#1850C2×C4711yescharacteristic, complemented
382#1770C2×C4711yescharacteristic, complemented
383#1750C2×C4711yescharacteristic, complemented
384C2×C47—42no—
385C2×C47—42no—
386C2×C47—81no—
387C2×C47#236111yescharacteristic
388C2×C47#293011yescharacteristic
389C2×C47#293211yescharacteristic
390C2×C47#293311yescharacteristic
391C2×C47#293311yescharacteristic
392C2×C47#299211yescharacteristic
393C2×C47#299511yescharacteristic
394C22×M16C22×C4711yescharacteristic
395C22×M16C22×C4711yescharacteristic
396C23×C8C22×C4711yescharacteristic
397C23×C8C22×C4711yescharacteristic
398C2×C4×D4C22×C4711yescharacteristic
399C2×C4×D4C22×C4711yescharacteristic
400C2×C4×D4C22×C4711yescharacteristic
401C2×#117C22×C4711yescharacteristic
402#435—24no—
403#435—24no—
404#435—24no—
405#424—24no—
406C2×C4⋊C8C22×C4711yescharacteristic
407C2×C4⋊C8C22×C4711yescharacteristic
408C2×C4⋊C8C22×C4711yescharacteristic
409C2×C4⋊C8C22×C4711yescharacteristic
410C2×C4⋊C8C22×C4711yescharacteristic
411C2×C4⋊C8C22×C4711yescharacteristic
412C2×C22⋊C8C22×C4711yescharacteristic
413C2×C22⋊C8C22×C4711yescharacteristic
414C2×C22⋊C8C22×C4711yescharacteristic
415C2×C22⋊C8C22×C4711yescharacteristic
416C2×C22⋊C8C22×C4711yescharacteristic
417C2×C22⋊C8C22×C4711yescharacteristic
418C2×C22⋊C8C22×C4711yescharacteristic
419C2×C22⋊C8C22×C4711yescharacteristic
420C2×#97C22×C4711yescharacteristic
421C2×#97C22×C4711yescharacteristic
422C2×#97C22×C4711yescharacteristic
423C2×C4×C8C22×C4711yescharacteristic
424#398C4×C4711yescharacteristic
425#397C4×C4711yescharacteristic
426#396C4×C4711yescharacteristic
427#396C4×C4711yescharacteristic
428#394C4×C4711yescharacteristic
429#394C4×C4711yescharacteristic
430#394C4×C4711yescharacteristic
431#392C4×C4711yescharacteristic
432C4×C4⋊C4C22×C4711yescharacteristic
433C4×C22⋊C4C22×C4711yescharacteristic
434C4×C22⋊C4C22×C4711yescharacteristic
435#336C22×C4711yescharacteristic
436#336C22×C4711yescharacteristic
437#336C22×C4711yescharacteristic
438#336C22×C4711yescharacteristic
439#336C22×C4711yescharacteristic
440#336C22×C4711yescharacteristic
441C47#2299311yescharacteristic, direct product factor, Sylow
442C22×D4C2×C4×C4711yescharacteristic
443C22×D4C2×C4×C4711yescharacteristic
444C22×D4C2×C4×C4711yescharacteristic
445C23×C4C23×C4711yescharacteristic
446C23×C4C23×C4711yescharacteristic
447C23×C4C23×C4711yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—41no—
453C2×M16—41no—
454C22×C8—22no—
455C22×C8—22no—
456C22×C8—22no—
457C22×C8—22no—
458C22×C8—41no—
459C22×C8—41no—
460C22×C8C23×C4711yescharacteristic
461C22×C8C23×C4711yescharacteristic
462C22×C8C23×C4711yescharacteristic
463C22×C8C23×C4711yescharacteristic
464C22×C8C23×C4711yescharacteristic
465C22×C8C23×C4711yescharacteristic
466C22×C8C23×C4711yescharacteristic
467C22×C8C23×C4711yescharacteristic
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4C2×C4×C4711yescharacteristic
477C2×C4⋊C4C2×C4×C4711yescharacteristic
478C2×C4⋊C4C2×C4×C4711yescharacteristic
479C2×C4⋊C4C2×C4×C4711yescharacteristic
480C2×C4⋊C4C2×C4×C4711yescharacteristic
481C2×C4⋊C4C2×C4×C4711yescharacteristic
482C2×C4⋊C4C2×C4×C4711yescharacteristic
483C2×C22⋊C4C2×C4×C4711yescharacteristic
484C2×C22⋊C4C2×C4×C4711yescharacteristic
485C2×C22⋊C4C2×C4×C4711yescharacteristic
486C2×C22⋊C4C2×C4×C4711yescharacteristic
487C2×C22⋊C4C2×C4×C4711yescharacteristic
488C2×C22⋊C4C2×C4×C4711yescharacteristic
489C2×C22⋊C4C2×C4×C4711yescharacteristic
490C2×C22⋊C4C2×C4×C4711yescharacteristic
491C2×C22⋊C4C2×C4×C4711yescharacteristic
492C2×C22⋊C4C2×C4×C4711yescharacteristic
493C2×C22⋊C4C2×C4×C4711yescharacteristic
494C2×C22⋊C4C2×C4×C4711yescharacteristic
495C2×C42C23×C4711yescharacteristic
496C2×C42C23×C4711yescharacteristic
497C2×C42C23×C4711yescharacteristic
498C2×C42C23×C4711yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8D4×C4714yescomplemented
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—41no—
511C22⋊C8—41no—
512C22⋊C8D4×C4714yescomplemented
513#97—22no—
514#97—22no—
515#97—22no—
516C4×C8—22no—
517#95C2×C4×C4711yescharacteristic
518#95C2×C4×C4711yescharacteristic
519#95C2×C4×C4711yescharacteristic
520#95C2×C4×C4711yescharacteristic
521#95C2×C4×C4711yescharacteristic
522#95C2×C4×C4711yescharacteristic
523C24C22×C4×C4711yescharacteristic
524C24C22×C4×C4711yescharacteristic
525C24C22×C4×C4711yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4C22×C4×C4711yescharacteristic
552C22×C4C22×C4×C4711yescharacteristic
553C22×C4C22×C4×C4711yescharacteristic
554C22×C4C22×C4×C4711yescharacteristic
555C22×C4C22×C4×C4711yescharacteristic
556C22×C4C22×C4×C4711yescharacteristic
557C22×C4C22×C4×C4711yescharacteristic
558C22×C4C22×C4×C4711yescharacteristic
559C22×C4C22×C4×C4711yescharacteristic
560C22×C4C22×C4×C4711yescharacteristic
561C22×C4C22×C4×C4711yescharacteristic
562C22×C4C2×D4×C4712yes—
563C22×C4#41×C4712yes—
564C22×C4C24×C4711yescharacteristic
565M16—44no—
566M16—44no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—44no—
588C2×C8—44no—
589C2×C8C2×D4×C4712yes—
590C2×C8C2×D4×C4712yes—
591C2×C8C2×D4×C4712yes—
592C2×C8C2×D4×C4712yes—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42C2×D4×C4712yes—
619C42#41×C4712yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23C4×D4×C4712yes—
640C23#131×C4712yes—
641C23C23×C4×C4711yescharacteristic
642D4—44no—
643D4—44no—
644D4—44no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4C4×D4×C4712yes—
688C2×C4C4×D4×C4712yes—
689C2×C4C4×D4×C4712yes—
690C2×C4C22×D4×C4711yescharacteristic
691C2×C4C22×D4×C4711yescharacteristic
692C2×C4C2×#41×C4711yescharacteristic
693C2×C4C2×#41×C4711yescharacteristic
694C2×C4H(5,𝔽2)×C4711yescharacteristic
695C2×C42−1+4×C4711yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22C2×C4×D4×C4711yescharacteristic
726C22C2×C4×D4×C4711yescharacteristic
727C22C47×#52011yescharacteristic
728C22C2×#131×C4711yescharacteristic
729C22C47×#56811yescharacteristic
730C22C47×#56811yescharacteristic
731C22C47×#56811yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4D42×C4711yescharacteristic
744C4C47×#54711yescharacteristic
745C4C47×#54811yescharacteristic
746C4C47×#55311yescharacteristic
747C2—42no—
748C2—42no—
749C2—81no—
750C2C47×#236111yescharacteristic
751C2C47×#293011yescharacteristic
752C2C47×#293211yescharacteristic
753C2C47×#293311yescharacteristic
754C2C47×#293311yescharacteristic
755C2C47×#299211yescharacteristic
756C2C47×#299511yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC47×#392C4
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×#435C2semidirect
3. C2×C47×#435C2semidirect
4. C2×C47×#424C2semidirect
6. C47×#1954C2semidirect
7. C47×#1940C2semidirect
8. C47×#1924C2semidirect
9. C47×#1924C2semidirect
10. C47×#1870C2semidirect
11. C47×#1869C2semidirect
12. C47×#1851C2semidirect
13. C47×#1850C2semidirect
14. C47×#1770C2semidirect
15. C47×#1750C2semidirect
125. C4⋊C8×C47D4semidirect
133. C22⋊C8×C47D4semidirect
325. #22993C47direct (N × H)
369. C2×#435C2×C47semidirect
370. C2×#435C2×C47semidirect
371. C2×#435C2×C47semidirect
372. C2×#424C2×C47semidirect
374. #1954C2×C47semidirect
375. #1940C2×C47semidirect
376. #1924C2×C47semidirect
377. #1924C2×C47semidirect
378. #1870C2×C47semidirect
379. #1869C2×C47semidirect
380. #1851C2×C47semidirect
381. #1850C2×C47semidirect
382. #1770C2×C47semidirect
383. #1750C2×C47semidirect
441. C47#22993direct (N × H)
504. C4⋊C8D4×C47semidirect
512. 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×#4352
C2×C47×#4242
C47×#23922
C47×#19542
C47×#19402
C47×#19242
C47×#18702
C47×#18692
C47×#18512
C47×#18502
C47×#17702
C47×#17502
#2299347