Finite Group Databasebeta

← C47×#22333 #26062031

Subgroups — C47×#22333 #26062031

Order 12032.

884 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C47C211yesmaximal, characteristic
2C47×#1955C211yesmaximal, characteristic, complemented
3C47×#1954C211yesmaximal, characteristic, complemented
4C47×#1923C211yesmaximal, characteristic, complemented
5C47×#1923C211yesmaximal, characteristic, complemented
6C47×#1917C211yesmaximal, characteristic, complemented
7C47×#1916C211yesmaximal, characteristic, complemented
8C47×#1870C211yesmaximal, characteristic, complemented
9C47×#1870C211yesmaximal, characteristic, complemented
10C47×#1869C211yesmaximal, characteristic, complemented
11C47×#1869C211yesmaximal, characteristic, complemented
12C47×#1817C211yesmaximal, characteristic, complemented
13C47×#1753C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C47C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C47C211yesmaximal, characteristic, complemented
16C22×M16×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C2×#121×C47C411yescharacteristic
19C2×C4×D4×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C22×C42×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
30C2×C22⋊C8×C47C2211yescharacteristic
31C2×C22⋊C8×C47C2211yescharacteristic
32C2×C22⋊C8×C47C2211yescharacteristic
33C2×C22⋊C8×C47C2211yescharacteristic
34C2×C22⋊C8×C47C2211yescharacteristic
35C2×#97×C47C2211yescharacteristic
36C2×C4×C8×C47C2211yescharacteristic
37C2×C4×C8×C47C2211yescharacteristic
38C2×C4×C8×C47C2211yescharacteristic
39C47×#390C411yescharacteristic
40C47×#389C411yescharacteristic
41C47×#388C411yescharacteristic
42C47×#388C411yescharacteristic
43C47×#386C411yescharacteristic
44C47×#386C411yescharacteristic
45C47×#380C411yescharacteristic
46C4×C4⋊C4×C47C2211yescharacteristic
47C4×C22⋊C4×C47C2211yescharacteristic
48C4×C22⋊C4×C47C2211yescharacteristic
49C47×#336C2211yescharacteristic
50C47×#336C2211yescharacteristic
51C47×#336C2211yescharacteristic
52C47×#336C2211yescharacteristic
53C47×#336C2211yescharacteristic
54C47×#336C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×D4×C47C2×C411yescharacteristic
60C22×D4×C47C2×C411yescharacteristic
61C22×D4×C47C2×C411yescharacteristic
62C23×C4×C47C2×C411yescharacteristic
63C23×C4×C47C2×C411yescharacteristic
64C23×C4×C47C2311yescharacteristic
65C23×C4×C47C2311yescharacteristic
66C23×C4×C47C2311yescharacteristic
67C2×M16×C47—22no—
68C2×M16×C47—41no—
69C2×M16×C47—41no—
70C22×C8×C47—22no—
71C22×C8×C47—41no—
72C22×C8×C47—41no—
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81#121×C47—24no—
82C4×D4×C47—41no—
83C4×D4×C47—41no—
84C4×D4×C47—41no—
85C4×D4×C47—41no—
86C4×D4×C47—41no—
87C4×D4×C47—41no—
88C2×C4⋊C4×C47C2×C411yescharacteristic
89C2×C4⋊C4×C47C2×C411yescharacteristic
90C2×C4⋊C4×C47C2×C411yescharacteristic
91C2×C4⋊C4×C47C2×C411yescharacteristic
92C2×C4⋊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×C22⋊C4×C47C2×C411yescharacteristic
103C2×C42×C47—41no—
104C2×C42×C47—41no—
105C2×C42×C47C2×C411yescharacteristic
106C2×C42×C47C2×C411yescharacteristic
107C2×C42×C47C2311yescharacteristic
108C2×C42×C47C2311yescharacteristic
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111C4⋊C8×C47—41no—
112C4⋊C8×C47—41no—
113C22⋊C8×C47—22no—
114C22⋊C8×C47—22no—
115C22⋊C8×C47—22no—
116C22⋊C8×C47—22no—
117C22⋊C8×C47—41no—
118C22⋊C8×C47—41no—
119C22⋊C8×C47—41no—
120C22⋊C8×C47—41no—
121C22⋊C8×C47—41no—
122C22⋊C8×C47—41no—
123#97×C47—41no—
124C4×C8×C47—41no—
125C4×C8×C47—41no—
126C4×C8×C47—41no—
127#95×C47C2×C411yescharacteristic
128#95×C47C2×C411yescharacteristic
129#95×C47C2×C411yescharacteristic
130#95×C47C2×C411yescharacteristic
131#95×C47C2×C411yescharacteristic
132#95×C47C2×C411yescharacteristic
133C24×C47C22×C411yescharacteristic
134C24×C47C22×C411yescharacteristic
135C24×C47C22×C411yescharacteristic
136C2×D4×C47—22no—
137C2×D4×C47—22no—
138C2×D4×C47—22no—
139C2×D4×C47—22no—
140C2×D4×C47—22no—
141C2×D4×C47—22no—
142C2×D4×C47—41no—
143C2×D4×C47—41no—
144C2×D4×C47—41no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
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—41no—
168C22×C4×C47—41no—
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C22×C411yescharacteristic
171C22×C4×C47C22×C411yescharacteristic
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×C47C2411yescharacteristic
181M16×C47—44no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
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—44no—
205C2×C8×C47#4112yes—
206C2×C8×C47#4112yes—
207C4⋊C4×C47—22no—
208C4⋊C4×C47—22no—
209C4⋊C4×C47—41no—
210C4⋊C4×C47—41no—
211C4⋊C4×C47—41no—
212C22⋊C4×C47—22no—
213C22⋊C4×C47—22no—
214C22⋊C4×C47—22no—
215C22⋊C4×C47—41no—
216C22⋊C4×C47—41no—
217C22⋊C4×C47—41no—
218C22⋊C4×C47—41no—
219C22⋊C4×C47—41no—
220C22⋊C4×C47—41no—
221C22⋊C4×C47M1614yescomplemented
222C42×C47—21no—
223C42×C47—21no—
224C42×C47—21no—
225C42×C47—21no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47—41no—
231C42×C47—41no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
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×C47C2×M1612yes—
252C23×C47#13112yes—
253C23×C47C23×C411yescharacteristic
254D4×C47—44no—
255D4×C47—44no—
256D4×C47—44no—
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—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
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—44no—
287C2×C4×C47—44no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47C2×M1612yes—
301C2×C4×C47C2×M1612yes—
302C2×C4×C47#13112yes—
303C2×C4×C47#13112yes—
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C2×C4×C47H(5,𝔽2)11yescharacteristic
307C2×C4×C47H(5,𝔽2)11yescharacteristic
308C2×C4×C47H(5,𝔽2)11yescharacteristic
309C2×C4×C47H(5,𝔽2)11yescharacteristic
310C8×C47—22no—
311C8×C47—22no—
312C8×C47—41no—
313C8×C47—41no—
314C8×C47—41no—
315C8×C47—41no—
316C8×C47—41no—
317C8×C47—41no—
318#22333C4711yesmaximal, characteristic, direct product factor, Sylow
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—22no—
322C22×C47—22no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
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×C47C4×#4111yescharacteristic
341C22×C47#51811yescharacteristic
342C22×C47#51811yescharacteristic
343C22×C47C22×M1611yescharacteristic
344C22×C47C2×#13111yescharacteristic
345C22×C47C2×#13111yescharacteristic
346C22×C47C2×#13111yescharacteristic
347C4×C47—22no—
348C4×C47—22no—
349C4×C47—22no—
350C4×C47—22no—
351C4×C47—41no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—41no—
355C4×C47—41no—
356C4×C47—41no—
357C4×C47—41no—
358C4×C47#53811yescharacteristic
359C4×C47#53811yescharacteristic
360C4×C47#54011yescharacteristic
361C4×C47#54011yescharacteristic
362C4×#121C2×C4711yescharacteristic
363#1955C2×C4711yescharacteristic, complemented
364#1954C2×C4711yescharacteristic, complemented
365#1923C2×C4711yescharacteristic, complemented
366#1923C2×C4711yescharacteristic, complemented
367#1917C2×C4711yescharacteristic, complemented
368#1916C2×C4711yescharacteristic, complemented
369#1870C2×C4711yescharacteristic, complemented
370#1870C2×C4711yescharacteristic, complemented
371#1869C2×C4711yescharacteristic, complemented
372#1869C2×C4711yescharacteristic, complemented
373#1817C2×C4711yescharacteristic, complemented
374#1753C2×C4711yescharacteristic, complemented
375C8×C22⋊C4C2×C4711yescharacteristic, complemented
376C4×C22⋊C8C2×C4711yescharacteristic, complemented
377C2×C47—42no—
378C2×C47—42no—
379C2×C47—81no—
380C2×C47#233311yescharacteristic
381C2×C47#296511yescharacteristic
382C2×C47#296611yescharacteristic
383C2×C47#297411yescharacteristic
384C2×C47#297411yescharacteristic
385C2×C47#297711yescharacteristic
386C2×C47#297911yescharacteristic
387C22×M16C22×C4711yescharacteristic
388C23×C8C22×C4711yescharacteristic
389C2×#121C4×C4711yescharacteristic
390C2×C4×D4C22×C4711yescharacteristic
391C2×C4×D4C22×C4711yescharacteristic
392C2×C4×D4C22×C4711yescharacteristic
393C22×C42C22×C4711yescharacteristic
394C2×C4⋊C8C22×C4711yescharacteristic
395C2×C4⋊C8C22×C4711yescharacteristic
396C2×C22⋊C8C22×C4711yescharacteristic
397C2×C22⋊C8C22×C4711yescharacteristic
398C2×C22⋊C8C22×C4711yescharacteristic
399C2×C22⋊C8C22×C4711yescharacteristic
400C2×C22⋊C8C22×C4711yescharacteristic
401C2×C22⋊C8C22×C4711yescharacteristic
402C2×C22⋊C8C22×C4711yescharacteristic
403C2×C22⋊C8C22×C4711yescharacteristic
404C2×C22⋊C8C22×C4711yescharacteristic
405C2×C22⋊C8C22×C4711yescharacteristic
406C2×#97C22×C4711yescharacteristic
407C2×C4×C8C22×C4711yescharacteristic
408C2×C4×C8C22×C4711yescharacteristic
409C2×C4×C8C22×C4711yescharacteristic
410#390C4×C4711yescharacteristic
411#389C4×C4711yescharacteristic
412#388C4×C4711yescharacteristic
413#388C4×C4711yescharacteristic
414#386C4×C4711yescharacteristic
415#386C4×C4711yescharacteristic
416#380C4×C4711yescharacteristic
417C4×C4⋊C4C22×C4711yescharacteristic
418C4×C22⋊C4C22×C4711yescharacteristic
419C4×C22⋊C4C22×C4711yescharacteristic
420#336C22×C4711yescharacteristic
421#336C22×C4711yescharacteristic
422#336C22×C4711yescharacteristic
423#336C22×C4711yescharacteristic
424#336C22×C4711yescharacteristic
425#336C22×C4711yescharacteristic
426#336C22×C4711yescharacteristic
427#336C22×C4711yescharacteristic
428#336C22×C4711yescharacteristic
429#336C22×C4711yescharacteristic
430C47#2233311yescharacteristic, direct product factor, Sylow
431C22×D4C2×C4×C4711yescharacteristic
432C22×D4C2×C4×C4711yescharacteristic
433C22×D4C2×C4×C4711yescharacteristic
434C23×C4C2×C4×C4711yescharacteristic
435C23×C4C2×C4×C4711yescharacteristic
436C23×C4C23×C4711yescharacteristic
437C23×C4C23×C4711yescharacteristic
438C23×C4C23×C4711yescharacteristic
439C2×M16—22no—
440C2×M16—41no—
441C2×M16—41no—
442C22×C8—22no—
443C22×C8—41no—
444C22×C8—41no—
445C22×C8C23×C4711yescharacteristic
446C22×C8C23×C4711yescharacteristic
447C22×C8C23×C4711yescharacteristic
448C22×C8C23×C4711yescharacteristic
449C22×C8C23×C4711yescharacteristic
450C22×C8C23×C4711yescharacteristic
451C22×C8C23×C4711yescharacteristic
452C22×C8C23×C4711yescharacteristic
453#121—24no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458C4×D4—41no—
459C4×D4—41no—
460C2×C4⋊C4C2×C4×C4711yescharacteristic
461C2×C4⋊C4C2×C4×C4711yescharacteristic
462C2×C4⋊C4C2×C4×C4711yescharacteristic
463C2×C4⋊C4C2×C4×C4711yescharacteristic
464C2×C4⋊C4C2×C4×C4711yescharacteristic
465C2×C22⋊C4C2×C4×C4711yescharacteristic
466C2×C22⋊C4C2×C4×C4711yescharacteristic
467C2×C22⋊C4C2×C4×C4711yescharacteristic
468C2×C22⋊C4C2×C4×C4711yescharacteristic
469C2×C22⋊C4C2×C4×C4711yescharacteristic
470C2×C22⋊C4C2×C4×C4711yescharacteristic
471C2×C22⋊C4C2×C4×C4711yescharacteristic
472C2×C22⋊C4C2×C4×C4711yescharacteristic
473C2×C22⋊C4C2×C4×C4711yescharacteristic
474C2×C22⋊C4C2×C4×C4711yescharacteristic
475C2×C42—41no—
476C2×C42—41no—
477C2×C42C2×C4×C4711yescharacteristic
478C2×C42C2×C4×C4711yescharacteristic
479C2×C42C23×C4711yescharacteristic
480C2×C42C23×C4711yescharacteristic
481C2×C42C23×C4711yescharacteristic
482C2×C42C23×C4711yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—41no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492C22⋊C8—41no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495#97—41no—
496C4×C8—41no—
497C4×C8—41no—
498C4×C8—41no—
499#95C2×C4×C4711yescharacteristic
500#95C2×C4×C4711yescharacteristic
501#95C2×C4×C4711yescharacteristic
502#95C2×C4×C4711yescharacteristic
503#95C2×C4×C4711yescharacteristic
504#95C2×C4×C4711yescharacteristic
505C24C22×C4×C4711yescharacteristic
506C24C22×C4×C4711yescharacteristic
507C24C22×C4×C4711yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4C22×C4×C4711yescharacteristic
542C22×C4C22×C4×C4711yescharacteristic
543C22×C4C22×C4×C4711yescharacteristic
544C22×C4C22×C4×C4711yescharacteristic
545C22×C4C22×C4×C4711yescharacteristic
546C22×C4C22×C4×C4711yescharacteristic
547C22×C4C22×C4×C4711yescharacteristic
548C22×C4C22×C4×C4711yescharacteristic
549C22×C4C22×C4×C4711yescharacteristic
550C22×C4C22×C4×C4711yescharacteristic
551C22×C4C22×C4×C4711yescharacteristic
552C22×C4C24×C4711yescharacteristic
553M16—44no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
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—44no—
577C2×C8#41×C4712yes—
578C2×C8#41×C4712yes—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4M16×C4714yescomplemented
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—41no—
603C42—41no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×M16×C4712yes—
624C23#131×C4712yes—
625C23C23×C4×C4711yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4C2×M16×C4712yes—
673C2×C4C2×M16×C4712yes—
674C2×C4#131×C4712yes—
675C2×C4#131×C4712yes—
676C2×C4C2×#41×C4711yescharacteristic
677C2×C4C2×#41×C4711yescharacteristic
678C2×C4H(5,𝔽2)×C4711yescharacteristic
679C2×C4H(5,𝔽2)×C4711yescharacteristic
680C2×C4H(5,𝔽2)×C4711yescharacteristic
681C2×C4H(5,𝔽2)×C4711yescharacteristic
682C8—22no—
683C8—22no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22C4×#41×C4711yescharacteristic
712C22C47×#51811yescharacteristic
713C22C47×#51811yescharacteristic
714C22C22×M16×C4711yescharacteristic
715C22C2×#131×C4711yescharacteristic
716C22C2×#131×C4711yescharacteristic
717C22C2×#131×C4711yescharacteristic
718C4—22no—
719C4—22no—
720C4—22no—
721C4—22no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4C47×#53811yescharacteristic
730C4C47×#53811yescharacteristic
731C4C47×#54011yescharacteristic
732C4C47×#54011yescharacteristic
733C2—42no—
734C2—42no—
735C2—81no—
736C2C47×#233311yescharacteristic
737C2C47×#296511yescharacteristic
738C2C47×#296611yescharacteristic
739C2C47×#297411yescharacteristic
740C2C47×#297411yescharacteristic
741C2C47×#297711yescharacteristic
742C2C47×#297911yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC2×#121×C47C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1955C2semidirect
3. C47×#1954C2semidirect
4. C47×#1923C2semidirect
5. C47×#1923C2semidirect
6. C47×#1917C2semidirect
7. C47×#1916C2semidirect
8. C47×#1870C2semidirect
9. C47×#1870C2semidirect
10. C47×#1869C2semidirect
11. C47×#1869C2semidirect
12. C47×#1817C2semidirect
13. C47×#1753C2semidirect
14. C8×C22⋊C4×C47C2semidirect
15. C4×C22⋊C8×C47C2semidirect
221. C22⋊C4×C47M16semidirect
318. #22333C47direct (N × H)
363. #1955C2×C47semidirect
364. #1954C2×C47semidirect
365. #1923C2×C47semidirect
366. #1923C2×C47semidirect
367. #1917C2×C47semidirect
368. #1916C2×C47semidirect
369. #1870C2×C47semidirect
370. #1870C2×C47semidirect
371. #1869C2×C47semidirect
372. #1869C2×C47semidirect
373. #1817C2×C47semidirect
374. #1753C2×C47semidirect
375. C8×C22⋊C4C2×C47semidirect
376. C4×C22⋊C8C2×C47semidirect
430. C47#22333direct (N × H)
593. C22⋊C4M16×C47semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C472
C47×#19552
C47×#19542
C47×#19232
C47×#19172
C47×#19162
C47×#18702
C47×#18692
C47×#18172
C47×#17532
C8×C22⋊C4×C472
C4×C22⋊C8×C472
#2233347