Finite Group Databasebeta

← C47×#22039 #26061737

Subgroups — C47×#22039 #26061737

Order 12032.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#436C211yesmaximal, characteristic, complemented
2C2×C47×#408C211yesmaximal, characteristic, complemented
3C47×#2388C211yesmaximal, characteristic
4C47×#1955C211yesmaximal, characteristic, complemented
5C47×#1954C211yesmaximal, characteristic, complemented
6C47×#1924C211yesmaximal, characteristic, complemented
7C47×#1923C211yesmaximal, characteristic, complemented
8C47×#1923C211yesmaximal, characteristic, complemented
9C47×#1923C211yesmaximal, characteristic, complemented
10C47×#1870C211yesmaximal, characteristic, complemented
11C47×#1870C211yesmaximal, characteristic, complemented
12C47×#1869C211yesmaximal, characteristic, complemented
13C47×#1850C211yesmaximal, characteristic, complemented
14C47×#1780C211yesmaximal, characteristic, complemented
15C47×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C47×#436—24no—
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×C4⋊C8×C47C2211yescharacteristic
27C47×#408—24no—
28C2×C22⋊C8×C47C2211yescharacteristic
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
40C2×C22⋊C8×C47C2211yescharacteristic
41C2×#97×C47C2211yescharacteristic
42C2×C4×C8×C47C2211yescharacteristic
43C2×C4×C8×C47C2211yescharacteristic
44C47×#395C411yescharacteristic
45C47×#394C411yescharacteristic
46C47×#394C411yescharacteristic
47C47×#394C411yescharacteristic
48C47×#393C411yescharacteristic
49C47×#392C411yescharacteristic
50C47×#392C411yescharacteristic
51C47×#392C411yescharacteristic
52C4×C22⋊C4×C47C2211yescharacteristic
53C4×C22⋊C4×C47C2211yescharacteristic
54C4×C22⋊C4×C47C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C2×#41×C47—22no—
62C2×#41×C47—22no—
63C2×#41×C47—41no—
64C2×#41×C47—41no—
65C2×#41×C47—41no—
66C2×#41×C47—41no—
67C22×Q8×C47C2×C411yescharacteristic
68C22×D4×C47C2×C411yescharacteristic
69C22×D4×C47C2×C411yescharacteristic
70C22×D4×C47C2×C411yescharacteristic
71C22×D4×C47C2×C411yescharacteristic
72C22×D4×C47C2×C411yescharacteristic
73C22×D4×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
95C4×D4×C47—22no—
96C4×D4×C47—22no—
97C4×D4×C47—41no—
98C4×D4×C47—41no—
99C4×D4×C47—41no—
100C4×D4×C47—41no—
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
119C4⋊C8×C47—22no—
120C4⋊C8×C47—41no—
121C4⋊C8×C47—41no—
122C22⋊C8×C47—22no—
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—41no—
130C22⋊C8×C47—41no—
131C22⋊C8×C47—41no—
132C22⋊C8×C47—41no—
133C22⋊C8×C47—41no—
134C22⋊C8×C47—41no—
135#97×C47—41no—
136C4×C8×C47—22no—
137C4×C8×C47—41no—
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
147C24×C47C22×C411yescharacteristic
148#41×C47—44no—
149#41×C47—44no—
150#41×C47—44no—
151#41×C47—44no—
152C2×Q8×C47—22no—
153C2×Q8×C47—41no—
154C2×Q8×C47—41no—
155C2×D4×C47—22no—
156C2×D4×C47—22no—
157C2×D4×C47—22no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—22no—
161C2×D4×C47—41no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47—41no—
165C2×D4×C47—41no—
166C2×D4×C47—41no—
167C2×D4×C47—41no—
168C2×D4×C47—41no—
169C2×D4×C47—41no—
170C2×D4×C47—41no—
171C2×D4×C47—41no—
172C2×D4×C47—41no—
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—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47C22×C411yescharacteristic
196C22×C4×C47C22×C411yescharacteristic
197C22×C4×C47C22×C411yescharacteristic
198C22×C4×C47C22×C411yescharacteristic
199C22×C4×C47C22×C411yescharacteristic
200C22×C4×C47C22×C411yescharacteristic
201C22×C4×C47C22×C411yescharacteristic
202C22×C4×C47C22×C411yescharacteristic
203C22×C4×C47C22×C411yescharacteristic
204C22×C4×C47C22×C411yescharacteristic
205C22×C4×C47C2×D412yes—
206C22×C4×C47#4112yes—
207C22×C4×C47C2411yescharacteristic
208M16×C47—44no—
209M16×C47—44no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
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—44no—
233C2×C8×C47C2×D412yes—
234C2×C8×C47C2×D412yes—
235C4⋊C4×C47—22no—
236C4⋊C4×C47—41no—
237C4⋊C4×C47—41no—
238C22⋊C4×C47—22no—
239C22⋊C4×C47—22no—
240C22⋊C4×C47—22no—
241C22⋊C4×C47—22no—
242C22⋊C4×C47—22no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—41no—
245C22⋊C4×C47—41no—
246C22⋊C4×C47—41no—
247C22⋊C4×C47—41no—
248C22⋊C4×C47—41no—
249C22⋊C4×C47—41no—
250C42×C47—21no—
251C42×C47—21no—
252C42×C47—21no—
253C42×C47—21no—
254C42×C47—21no—
255C42×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×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×C47C4×D412yes—
284C23×C47C23×C411yescharacteristic
285Q8×C47—44no—
286D4×C47—44no—
287D4×C47—44no—
288D4×C47—44no—
289D4×C47—44no—
290D4×C47—44no—
291D4×C47—44no—
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—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
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—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
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×C47C4×D412yes—
336C2×C4×C47#13112yes—
337C2×C4×C47#13112yes—
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C2×#4111yescharacteristic
340C2×C4×C47H(5,𝔽2)11yescharacteristic
341C2×C4×C47H(5,𝔽2)11yescharacteristic
342C2×C4×C47H(5,𝔽2)11yescharacteristic
343C2×C4×C47H(5,𝔽2)11yescharacteristic
344C8×C47—22no—
345C8×C47—22no—
346C8×C47—41no—
347C8×C47—41no—
348C8×C47—41no—
349C8×C47—41no—
350C8×C47—41no—
351C8×C47—41no—
352#22039C4711yesmaximal, characteristic, direct product factor, Sylow
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47C2×C4×D411yescharacteristic
382C22×C47#51811yescharacteristic
383C22×C47#51811yescharacteristic
384C22×C47C2×#13111yescharacteristic
385C22×C47C2×#13111yescharacteristic
386C22×C47#56811yescharacteristic
387C22×C47#56811yescharacteristic
388C4×C47—22no—
389C4×C47—22no—
390C4×C47—22no—
391C4×C47—41no—
392C4×C47—41no—
393C4×C47—41no—
394C4×C47—41no—
395C4×C47—41no—
396C4×C47—41no—
397C4×C47—41no—
398C4×C47#53411yescharacteristic
399C4×C47#53511yescharacteristic
400C4×C47#53811yescharacteristic
401C4×C47#53811yescharacteristic
402C2×#436C2×C4711yescharacteristic, complemented
403C2×#408C2×C4711yescharacteristic, complemented
404#2388C2×C4711yescharacteristic
405#1955C2×C4711yescharacteristic, complemented
406#1954C2×C4711yescharacteristic, complemented
407#1924C2×C4711yescharacteristic, complemented
408#1923C2×C4711yescharacteristic, complemented
409#1923C2×C4711yescharacteristic, complemented
410#1923C2×C4711yescharacteristic, complemented
411#1870C2×C4711yescharacteristic, complemented
412#1870C2×C4711yescharacteristic, complemented
413#1869C2×C4711yescharacteristic, complemented
414#1850C2×C4711yescharacteristic, complemented
415#1780C2×C4711yescharacteristic, complemented
416#1753C2×C4711yescharacteristic, complemented
417C2×C47—42no—
418C2×C47—81no—
419C2×C47—81no—
420C2×C47—81no—
421C2×C47#232111yescharacteristic
422C2×C47#293311yescharacteristic
423C2×C47#293511yescharacteristic
424C2×C47#297611yescharacteristic
425C2×C47#297811yescharacteristic
426C2×C47#297911yescharacteristic
427C2×C47#298111yescharacteristic
428C22×#41C22×C4711yescharacteristic
429C22×M16C22×C4711yescharacteristic
430C22×M16C22×C4711yescharacteristic
431C23×C8C22×C4711yescharacteristic
432C2×C4×D4C22×C4711yescharacteristic
433C2×C4×D4C22×C4711yescharacteristic
434C2×C4×D4C22×C4711yescharacteristic
435#436—24no—
436C2×C4⋊C8C22×C4711yescharacteristic
437C2×C4⋊C8C22×C4711yescharacteristic
438C2×C4⋊C8C22×C4711yescharacteristic
439#408—24no—
440C2×C22⋊C8C22×C4711yescharacteristic
441C2×C22⋊C8C22×C4711yescharacteristic
442C2×C22⋊C8C22×C4711yescharacteristic
443C2×C22⋊C8C22×C4711yescharacteristic
444C2×C22⋊C8C22×C4711yescharacteristic
445C2×C22⋊C8C22×C4711yescharacteristic
446C2×C22⋊C8C22×C4711yescharacteristic
447C2×C22⋊C8C22×C4711yescharacteristic
448C2×C22⋊C8C22×C4711yescharacteristic
449C2×C22⋊C8C22×C4711yescharacteristic
450C2×C22⋊C8C22×C4711yescharacteristic
451C2×C22⋊C8C22×C4711yescharacteristic
452C2×C22⋊C8C22×C4711yescharacteristic
453C2×#97C22×C4711yescharacteristic
454C2×C4×C8C22×C4711yescharacteristic
455C2×C4×C8C22×C4711yescharacteristic
456#395C4×C4711yescharacteristic
457#394C4×C4711yescharacteristic
458#394C4×C4711yescharacteristic
459#394C4×C4711yescharacteristic
460#393C4×C4711yescharacteristic
461#392C4×C4711yescharacteristic
462#392C4×C4711yescharacteristic
463#392C4×C4711yescharacteristic
464C4×C22⋊C4C22×C4711yescharacteristic
465C4×C22⋊C4C22×C4711yescharacteristic
466C4×C22⋊C4C22×C4711yescharacteristic
467#336C22×C4711yescharacteristic
468#336C22×C4711yescharacteristic
469#336C22×C4711yescharacteristic
470#336C22×C4711yescharacteristic
471#336C22×C4711yescharacteristic
472#336C22×C4711yescharacteristic
473C47#2203911yescharacteristic, direct product factor, Sylow
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8C2×C4×C4711yescharacteristic
481C22×D4C2×C4×C4711yescharacteristic
482C22×D4C2×C4×C4711yescharacteristic
483C22×D4C2×C4×C4711yescharacteristic
484C22×D4C2×C4×C4711yescharacteristic
485C22×D4C2×C4×C4711yescharacteristic
486C22×D4C2×C4×C4711yescharacteristic
487C23×C4C23×C4711yescharacteristic
488C23×C4C23×C4711yescharacteristic
489C23×C4C23×C4711yescharacteristic
490C23×C4C23×C4711yescharacteristic
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—41no—
495C2×M16—41no—
496C2×M16D4×C4714yescomplemented
497C22×C8—22no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8C23×C4711yescharacteristic
501C22×C8C23×C4711yescharacteristic
502C22×C8C23×C4711yescharacteristic
503C22×C8C23×C4711yescharacteristic
504C22×C8C23×C4711yescharacteristic
505C22×C8C23×C4711yescharacteristic
506C22×C8C23×C4711yescharacteristic
507C22×C8C23×C4711yescharacteristic
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513C4×D4—41no—
514C2×C4⋊C4C2×C4×C4711yescharacteristic
515C2×C4⋊C4C2×C4×C4711yescharacteristic
516C2×C4⋊C4C2×C4×C4711yescharacteristic
517C2×C22⋊C4C2×C4×C4711yescharacteristic
518C2×C22⋊C4C2×C4×C4711yescharacteristic
519C2×C22⋊C4C2×C4×C4711yescharacteristic
520C2×C22⋊C4C2×C4×C4711yescharacteristic
521C2×C22⋊C4C2×C4×C4711yescharacteristic
522C2×C22⋊C4C2×C4×C4711yescharacteristic
523C2×C22⋊C4C2×C4×C4711yescharacteristic
524C2×C22⋊C4C2×C4×C4711yescharacteristic
525C2×C22⋊C4C2×C4×C4711yescharacteristic
526C2×C22⋊C4C2×C4×C4711yescharacteristic
527C2×C22⋊C4C2×C4×C4711yescharacteristic
528C2×C22⋊C4C2×C4×C4711yescharacteristic
529C2×C42C23×C4711yescharacteristic
530C2×C42C23×C4711yescharacteristic
531C2×C42C23×C4711yescharacteristic
532C4⋊C8—22no—
533C4⋊C8—41no—
534C4⋊C8—41no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—41no—
543C22⋊C8—41no—
544C22⋊C8—41no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547C22⋊C8—41no—
548#97—41no—
549C4×C8—22no—
550C4×C8—41no—
551#95C2×C4×C4711yescharacteristic
552#95C2×C4×C4711yescharacteristic
553#95C2×C4×C4711yescharacteristic
554#95C2×C4×C4711yescharacteristic
555#95C2×C4×C4711yescharacteristic
556#95C2×C4×C4711yescharacteristic
557C24C22×C4×C4711yescharacteristic
558C24C22×C4×C4711yescharacteristic
559C24C22×C4×C4711yescharacteristic
560C24C22×C4×C4711yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
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×C4C22×C4×C4711yescharacteristic
609C22×C4C22×C4×C4711yescharacteristic
610C22×C4C22×C4×C4711yescharacteristic
611C22×C4C22×C4×C4711yescharacteristic
612C22×C4C22×C4×C4711yescharacteristic
613C22×C4C22×C4×C4711yescharacteristic
614C22×C4C22×C4×C4711yescharacteristic
615C22×C4C22×C4×C4711yescharacteristic
616C22×C4C22×C4×C4711yescharacteristic
617C22×C4C22×C4×C4711yescharacteristic
618C22×C4C2×D4×C4712yes—
619C22×C4#41×C4712yes—
620C22×C4C24×C4711yescharacteristic
621M16—44no—
622M16—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—44no—
646C2×C8C2×D4×C4712yes—
647C2×C8C2×D4×C4712yes—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23C4×D4×C4712yes—
697C23C23×C4×C4711yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—44no—
704D4—44no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4C4×D4×C4712yes—
749C2×C4#131×C4712yes—
750C2×C4#131×C4712yes—
751C2×C4C22×D4×C4711yescharacteristic
752C2×C4C2×#41×C4711yescharacteristic
753C2×C4H(5,𝔽2)×C4711yescharacteristic
754C2×C4H(5,𝔽2)×C4711yescharacteristic
755C2×C4H(5,𝔽2)×C4711yescharacteristic
756C2×C4H(5,𝔽2)×C4711yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—41no—
762C8—41no—
763C8—41no—
764C8—41no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22C2×C4×D4×C4711yescharacteristic
794C22C47×#51811yescharacteristic
795C22C47×#51811yescharacteristic
796C22C2×#131×C4711yescharacteristic
797C22C2×#131×C4711yescharacteristic
798C22C47×#56811yescharacteristic
799C22C47×#56811yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4C47×#53411yescharacteristic
811C4C47×#53511yescharacteristic
812C4C47×#53811yescharacteristic
813C4C47×#53811yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2C47×#232111yescharacteristic
819C2C47×#293311yescharacteristic
820C2C47×#293511yescharacteristic
821C2C47×#297611yescharacteristic
822C2C47×#297811yescharacteristic
823C2C47×#297911yescharacteristic
824C2C47×#298111yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC47×#2388C2
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×#436C2semidirect
2. C2×C47×#408C2semidirect
4. C47×#1955C2semidirect
5. C47×#1954C2semidirect
6. C47×#1924C2semidirect
7. C47×#1923C2semidirect
8. C47×#1923C2semidirect
9. C47×#1923C2semidirect
10. C47×#1870C2semidirect
11. C47×#1870C2semidirect
12. C47×#1869C2semidirect
13. C47×#1850C2semidirect
14. C47×#1780C2semidirect
15. C47×#1753C2semidirect
83. C2×M16×C47D4semidirect
352. #22039C47direct (N × H)
402. C2×#436C2×C47semidirect
403. C2×#408C2×C47semidirect
405. #1955C2×C47semidirect
406. #1954C2×C47semidirect
407. #1924C2×C47semidirect
408. #1923C2×C47semidirect
409. #1923C2×C47semidirect
410. #1923C2×C47semidirect
411. #1870C2×C47semidirect
412. #1870C2×C47semidirect
413. #1869C2×C47semidirect
414. #1850C2×C47semidirect
415. #1780C2×C47semidirect
416. #1753C2×C47semidirect
473. C47#22039direct (N × H)
496. C2×M16D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4362
C2×C47×#4082
C47×#23882
C47×#19552
C47×#19542
C47×#19242
C47×#19232
C47×#18702
C47×#18692
C47×#18502
C47×#17802
C47×#17532
#2203947