Finite Group Databasebeta

← C47×#21571 #26061269

Subgroups — C47×#21571 #26061269

Order 12032.

872 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#436C211yesmaximal, characteristic
2C2×C47×#405C211yesmaximal, characteristic, complemented
3C47×#2395C211yesmaximal, characteristic
4C47×#1924C211yesmaximal, characteristic, complemented
5C47×#1923C211yesmaximal, characteristic, complemented
6C47×#1917C211yesmaximal, characteristic, complemented
7C47×#1916C211yesmaximal, characteristic, complemented
8C47×#1869C211yesmaximal, characteristic
9C47×#1850C211yesmaximal, characteristic, complemented
10C47×#1818C211yesmaximal, characteristic, complemented
11C47×#1771C211yesmaximal, characteristic, complemented
12C8×C4⋊C4×C47C211yesmaximal, characteristic, complemented
13C47×#1753C211yesmaximal, characteristic, complemented
14C47×#1753C211yesmaximal, characteristic, complemented
15C47×#1753C211yesmaximal, characteristic, complemented
16C22×M16×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C2×C4×D4×C47C2211yescharacteristic
20C2×#117×C47C2211yescharacteristic
21C47×#436—24no—
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C22⋊C8×C47C2211yescharacteristic
26C2×C22⋊C8×C47C2211yescharacteristic
27C2×C22⋊C8×C47C2211yescharacteristic
28C2×C22⋊C8×C47C2211yescharacteristic
29C2×C22⋊C8×C47C2211yescharacteristic
30C47×#405—24no—
31C2×#97×C47C2211yescharacteristic
32C2×#97×C47C2211yescharacteristic
33C2×#97×C47C2211yescharacteristic
34C2×C4×C8×C47C2211yescharacteristic
35C2×C4×C8×C47C2211yescharacteristic
36C2×C4×C8×C47C2211yescharacteristic
37C2×C4×C8×C47C2211yescharacteristic
38C47×#400C411yescharacteristic
39C47×#399C411yescharacteristic
40C47×#398C411yescharacteristic
41C47×#397C411yescharacteristic
42C47×#397C411yescharacteristic
43C47×#397C411yescharacteristic
44C47×#394C411yescharacteristic
45C47×#394C411yescharacteristic
46C4×C4⋊C4×C47C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C4×C22⋊C4×C47C2211yescharacteristic
49C4×C22⋊C4×C47C2211yescharacteristic
50C4×C22⋊C4×C47C2211yescharacteristic
51C47×#336C2211yescharacteristic
52C47×#336C2211yescharacteristic
53C47×#336C2211yescharacteristic
54C47×#336C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×D4×C47C2×C411yescharacteristic
62C23×C4×C47C2311yescharacteristic
63C23×C4×C47C2311yescharacteristic
64C2×M16×C47—22no—
65C2×M16×C47—22no—
66C2×M16×C47—22no—
67C2×M16×C47—22no—
68C2×M16×C47—22no—
69C2×M16×C47D414yes—
70C22×C8×C47—22no—
71C22×C8×C47—22no—
72C22×C8×C47—22no—
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C4×D4×C47—22no—
82C4×D4×C47—22no—
83#117×C47—22no—
84#117×C47—22no—
85C2×C4⋊C4×C47C2×C411yescharacteristic
86C2×C4⋊C4×C47C2×C411yescharacteristic
87C2×C4⋊C4×C47C2×C411yescharacteristic
88C2×C4⋊C4×C47C2×C411yescharacteristic
89C2×C4⋊C4×C47C2×C411yescharacteristic
90C2×C4⋊C4×C47C2×C411yescharacteristic
91C2×C4⋊C4×C47C2×C411yescharacteristic
92C2×C22⋊C4×C47C2×C411yescharacteristic
93C2×C22⋊C4×C47C2×C411yescharacteristic
94C2×C22⋊C4×C47C2×C411yescharacteristic
95C2×C22⋊C4×C47C2×C411yescharacteristic
96C2×C22⋊C4×C47C2×C411yescharacteristic
97C2×C22⋊C4×C47C2×C411yescharacteristic
98C2×C22⋊C4×C47C2×C411yescharacteristic
99C2×C22⋊C4×C47C2×C411yescharacteristic
100C2×C22⋊C4×C47C2×C411yescharacteristic
101C2×C22⋊C4×C47C2×C411yescharacteristic
102C2×C42×C47C2311yescharacteristic
103C2×C42×C47C2311yescharacteristic
104C2×C42×C47C2311yescharacteristic
105C2×C42×C47C2311yescharacteristic
106C2×C42×C47C2311yescharacteristic
107C4⋊C8×C47—22no—
108C4⋊C8×C47—22no—
109C4⋊C8×C47—22no—
110C22⋊C8×C47—22no—
111C22⋊C8×C47—22no—
112C22⋊C8×C47—22no—
113C22⋊C8×C47—22no—
114C22⋊C8×C47—22no—
115#97×C47—22no—
116#97×C47—22no—
117#97×C47—22no—
118C4×C8×C47—22no—
119C4×C8×C47—22no—
120C4×C8×C47—22no—
121C4×C8×C47—22no—
122#95×C47C2×C411yescharacteristic
123#95×C47C2×C411yescharacteristic
124#95×C47C2×C411yescharacteristic
125#95×C47C2×C411yescharacteristic
126#95×C47C2×C411yescharacteristic
127#95×C47C2×C411yescharacteristic
128#95×C47C2×C411yescharacteristic
129#95×C47C2×C411yescharacteristic
130#95×C47C2×C411yescharacteristic
131#95×C47C2×C411yescharacteristic
132C24×C47C22×C411yescharacteristic
133C24×C47C22×C411yescharacteristic
134C2×D4×C47—22no—
135C2×D4×C47—22no—
136C2×D4×C47—41no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C22×C411yescharacteristic
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C22×C411yescharacteristic
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C22×C411yescharacteristic
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47C2×D412yes—
160C22×C4×C47#4112yes—
161C22×C4×C47C2411yescharacteristic
162M16×C47—28no—
163M16×C47—44no—
164C2×C8×C47—28no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47C2×D412yes—
184C2×C8×C47C2×D412yes—
185C2×C8×C47#4112yes—
186C2×C8×C47#4112yes—
187C2×C8×C47#4112yes—
188C2×C8×C47#4112yes—
189C4⋊C4×C47—22no—
190C4⋊C4×C47—22no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—22no—
194C4⋊C4×C47—22no—
195C4⋊C4×C47—41no—
196C22⋊C4×C47—22no—
197C22⋊C4×C47—22no—
198C22⋊C4×C47—22no—
199C22⋊C4×C47—22no—
200C22⋊C4×C47—22no—
201C22⋊C4×C47—22no—
202C22⋊C4×C47—41no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C42×C47—21no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47—21no—
212C42×C47—21no—
213C42×C47—21no—
214C42×C47—21no—
215C42×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—21no—
220C23×C47—21no—
221C23×C47—21no—
222C23×C47—21no—
223C23×C47—21no—
224C23×C47—21no—
225C23×C47—21no—
226C23×C47—21no—
227C23×C47—21no—
228C23×C47—21no—
229C23×C47C4×D412yes—
230C23×C47C23×C411yescharacteristic
231D4×C47—44no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—22no—
239C2×C4×C47—22no—
240C2×C4×C47—22no—
241C2×C4×C47—22no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47C4×D412yes—
274C2×C4×C47#13112yes—
275C2×C4×C47#13112yes—
276C2×C4×C47C22×D411yescharacteristic
277C2×C4×C47C2×#4111yescharacteristic
278C2×C4×C47C2×#4111yescharacteristic
279C2×C4×C47C2×#4111yescharacteristic
280C2×C4×C47C2×#4111yescharacteristic
281C2×C4×C47C2×#4111yescharacteristic
282C8×C47—22no—
283C8×C47—22no—
284C8×C47—22no—
285C8×C47—41no—
286C8×C47—41no—
287C8×C47—41no—
288C8×C47—41no—
289C8×C47#12314yes—
290#21571C4711yesmaximal, characteristic, direct product factor, Sylow
291C22×C47—22no—
292C22×C47—22no—
293C22×C47—22no—
294C22×C47—41no—
295C22×C47—41no—
296C22×C47—41no—
297C22×C47—41no—
298C22×C47—41no—
299C22×C47—41no—
300C22×C47—41no—
301C22×C47—41no—
302C22×C47—41no—
303C22×C47—41no—
304C22×C47—41no—
305C22×C47C2×C4×D411yescharacteristic
306C22×C47C4×#4111yescharacteristic
307C22×C47C4×#4111yescharacteristic
308C22×C47C2×#13111yescharacteristic
309C22×C47C2×#13111yescharacteristic
310C22×C47#56811yescharacteristic
311C22×C47#56811yescharacteristic
312C4×C47—22no—
313C4×C47—22no—
314C4×C47—22no—
315C4×C47—41no—
316C4×C47—41no—
317C4×C47—41no—
318C4×C47—41no—
319C4×C47—41no—
320C4×C47—41no—
321C4×C47—41no—
322C4×C47—41no—
323C4×C47—41no—
324C4×C47C2×#12311yescharacteristic
325C4×C47#52511yescharacteristic
326C4×C47#52911yescharacteristic
327C4×C47#52911yescharacteristic
328C2×#436C2×C4711yescharacteristic
329C2×#405C2×C4711yescharacteristic, complemented
330#2395C2×C4711yescharacteristic
331#1924C2×C4711yescharacteristic, complemented
332#1923C2×C4711yescharacteristic, complemented
333#1917C2×C4711yescharacteristic, complemented
334#1916C2×C4711yescharacteristic, complemented
335#1869C2×C4711yescharacteristic
336#1850C2×C4711yescharacteristic, complemented
337#1818C2×C4711yescharacteristic, complemented
338#1771C2×C4711yescharacteristic, complemented
339C8×C4⋊C4C2×C4711yescharacteristic, complemented
340#1753C2×C4711yescharacteristic, complemented
341#1753C2×C4711yescharacteristic, complemented
342#1753C2×C4711yescharacteristic, complemented
343C2×C47—42no—
344C2×C47—81no—
345C2×C47C4×#12311yescharacteristic
346C2×C47#293311yescharacteristic
347C2×C47#293511yescharacteristic
348C2×C47#296611yescharacteristic
349C2×C47#296711yescharacteristic
350C2×C47#296911yescharacteristic
351C2×C47#296911yescharacteristic
352C22×M16C22×C4711yescharacteristic
353C22×M16C22×C4711yescharacteristic
354C23×C8C22×C4711yescharacteristic
355C2×C4×D4C22×C4711yescharacteristic
356C2×#117C22×C4711yescharacteristic
357#436—24no—
358C2×C4⋊C8C22×C4711yescharacteristic
359C2×C4⋊C8C22×C4711yescharacteristic
360C2×C4⋊C8C22×C4711yescharacteristic
361C2×C22⋊C8C22×C4711yescharacteristic
362C2×C22⋊C8C22×C4711yescharacteristic
363C2×C22⋊C8C22×C4711yescharacteristic
364C2×C22⋊C8C22×C4711yescharacteristic
365C2×C22⋊C8C22×C4711yescharacteristic
366#405—24no—
367C2×#97C22×C4711yescharacteristic
368C2×#97C22×C4711yescharacteristic
369C2×#97C22×C4711yescharacteristic
370C2×C4×C8C22×C4711yescharacteristic
371C2×C4×C8C22×C4711yescharacteristic
372C2×C4×C8C22×C4711yescharacteristic
373C2×C4×C8C22×C4711yescharacteristic
374#400C4×C4711yescharacteristic
375#399C4×C4711yescharacteristic
376#398C4×C4711yescharacteristic
377#397C4×C4711yescharacteristic
378#397C4×C4711yescharacteristic
379#397C4×C4711yescharacteristic
380#394C4×C4711yescharacteristic
381#394C4×C4711yescharacteristic
382C4×C4⋊C4C22×C4711yescharacteristic
383C4×C4⋊C4C22×C4711yescharacteristic
384C4×C22⋊C4C22×C4711yescharacteristic
385C4×C22⋊C4C22×C4711yescharacteristic
386C4×C22⋊C4C22×C4711yescharacteristic
387#336C22×C4711yescharacteristic
388#336C22×C4711yescharacteristic
389#336C22×C4711yescharacteristic
390#336C22×C4711yescharacteristic
391#336C22×C4711yescharacteristic
392#336C22×C4711yescharacteristic
393#336C22×C4711yescharacteristic
394#336C22×C4711yescharacteristic
395#336C22×C4711yescharacteristic
396#336C22×C4711yescharacteristic
397C47#2157111yescharacteristic, direct product factor, Sylow
398C22×D4C2×C4×C4711yescharacteristic
399C23×C4C23×C4711yescharacteristic
400C23×C4C23×C4711yescharacteristic
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—22no—
406C2×M16D4×C4714yes—
407C22×C8—22no—
408C22×C8—22no—
409C22×C8—22no—
410C22×C8C23×C4711yescharacteristic
411C22×C8C23×C4711yescharacteristic
412C22×C8C23×C4711yescharacteristic
413C22×C8C23×C4711yescharacteristic
414C22×C8C23×C4711yescharacteristic
415C22×C8C23×C4711yescharacteristic
416C22×C8C23×C4711yescharacteristic
417C22×C8C23×C4711yescharacteristic
418C4×D4—22no—
419C4×D4—22no—
420#117—22no—
421#117—22no—
422C2×C4⋊C4C2×C4×C4711yescharacteristic
423C2×C4⋊C4C2×C4×C4711yescharacteristic
424C2×C4⋊C4C2×C4×C4711yescharacteristic
425C2×C4⋊C4C2×C4×C4711yescharacteristic
426C2×C4⋊C4C2×C4×C4711yescharacteristic
427C2×C4⋊C4C2×C4×C4711yescharacteristic
428C2×C4⋊C4C2×C4×C4711yescharacteristic
429C2×C22⋊C4C2×C4×C4711yescharacteristic
430C2×C22⋊C4C2×C4×C4711yescharacteristic
431C2×C22⋊C4C2×C4×C4711yescharacteristic
432C2×C22⋊C4C2×C4×C4711yescharacteristic
433C2×C22⋊C4C2×C4×C4711yescharacteristic
434C2×C22⋊C4C2×C4×C4711yescharacteristic
435C2×C22⋊C4C2×C4×C4711yescharacteristic
436C2×C22⋊C4C2×C4×C4711yescharacteristic
437C2×C22⋊C4C2×C4×C4711yescharacteristic
438C2×C22⋊C4C2×C4×C4711yescharacteristic
439C2×C42C23×C4711yescharacteristic
440C2×C42C23×C4711yescharacteristic
441C2×C42C23×C4711yescharacteristic
442C2×C42C23×C4711yescharacteristic
443C2×C42C23×C4711yescharacteristic
444C4⋊C8—22no—
445C4⋊C8—22no—
446C4⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—22no—
452#97—22no—
453#97—22no—
454#97—22no—
455C4×C8—22no—
456C4×C8—22no—
457C4×C8—22no—
458C4×C8—22no—
459#95C2×C4×C4711yescharacteristic
460#95C2×C4×C4711yescharacteristic
461#95C2×C4×C4711yescharacteristic
462#95C2×C4×C4711yescharacteristic
463#95C2×C4×C4711yescharacteristic
464#95C2×C4×C4711yescharacteristic
465#95C2×C4×C4711yescharacteristic
466#95C2×C4×C4711yescharacteristic
467#95C2×C4×C4711yescharacteristic
468#95C2×C4×C4711yescharacteristic
469C24C22×C4×C4711yescharacteristic
470C24C22×C4×C4711yescharacteristic
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—41no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4C22×C4×C4711yescharacteristic
485C22×C4C22×C4×C4711yescharacteristic
486C22×C4C22×C4×C4711yescharacteristic
487C22×C4C22×C4×C4711yescharacteristic
488C22×C4C22×C4×C4711yescharacteristic
489C22×C4C22×C4×C4711yescharacteristic
490C22×C4C22×C4×C4711yescharacteristic
491C22×C4C22×C4×C4711yescharacteristic
492C22×C4C22×C4×C4711yescharacteristic
493C22×C4C22×C4×C4711yescharacteristic
494C22×C4C22×C4×C4711yescharacteristic
495C22×C4C22×C4×C4711yescharacteristic
496C22×C4C2×D4×C4712yes—
497C22×C4#41×C4712yes—
498C22×C4C24×C4711yescharacteristic
499M16—28no—
500M16—44no—
501C2×C8—28no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8C2×D4×C4712yes—
521C2×C8C2×D4×C4712yes—
522C2×C8#41×C4712yes—
523C2×C8#41×C4712yes—
524C2×C8#41×C4712yes—
525C2×C8#41×C4712yes—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—41no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C4×D4×C4712yes—
567C23C23×C4×C4711yescharacteristic
568D4—44no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4C4×D4×C4712yes—
611C2×C4#131×C4712yes—
612C2×C4#131×C4712yes—
613C2×C4C22×D4×C4711yescharacteristic
614C2×C4C2×#41×C4711yescharacteristic
615C2×C4C2×#41×C4711yescharacteristic
616C2×C4C2×#41×C4711yescharacteristic
617C2×C4C2×#41×C4711yescharacteristic
618C2×C4C2×#41×C4711yescharacteristic
619C8—22no—
620C8—22no—
621C8—22no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8#123×C4714yes—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×C4×D4×C4711yescharacteristic
642C22C4×#41×C4711yescharacteristic
643C22C4×#41×C4711yescharacteristic
644C22C2×#131×C4711yescharacteristic
645C22C2×#131×C4711yescharacteristic
646C22C47×#56811yescharacteristic
647C22C47×#56811yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4C2×#123×C4711yescharacteristic
661C4C47×#52511yescharacteristic
662C4C47×#52911yescharacteristic
663C4C47×#52911yescharacteristic
664C2—42no—
665C2—81no—
666C2C4×#123×C4711yescharacteristic
667C2C47×#293311yescharacteristic
668C2C47×#293511yescharacteristic
669C2C47×#296611yescharacteristic
670C2C47×#296711yescharacteristic
671C2C47×#296911yescharacteristic
672C2C47×#296911yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC22×D4×C47C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#405C2semidirect
4. C47×#1924C2semidirect
5. C47×#1923C2semidirect
6. C47×#1917C2semidirect
7. C47×#1916C2semidirect
9. C47×#1850C2semidirect
10. C47×#1818C2semidirect
11. C47×#1771C2semidirect
12. C8×C4⋊C4×C47C2semidirect
13. C47×#1753C2semidirect
14. C47×#1753C2semidirect
15. C47×#1753C2semidirect
290. #21571C47direct (N × H)
329. C2×#405C2×C47semidirect
331. #1924C2×C47semidirect
332. #1923C2×C47semidirect
333. #1917C2×C47semidirect
334. #1916C2×C47semidirect
336. #1850C2×C47semidirect
337. #1818C2×C47semidirect
338. #1771C2×C47semidirect
339. C8×C4⋊C4C2×C47semidirect
340. #1753C2×C47semidirect
341. #1753C2×C47semidirect
342. #1753C2×C47semidirect
397. C47#21571direct (N × H)

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×#4052
C47×#23952
C47×#19242
C47×#19232
C47×#19172
C47×#19162
C47×#18692
C47×#18502
C47×#18182
C47×#17712
C8×C4⋊C4×C472
C47×#17532
#2157147