Finite Group Databasebeta

← C47×#22292 #26061990

Subgroups — C47×#22292 #26061990

Order 12032.

702 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2396C211yesmaximal, characteristic
2C47×#1985C211yesmaximal, characteristic, complemented
3C47×#1984C211yesmaximal, characteristic, complemented
4C47×#1940C211yesmaximal, characteristic, complemented
5C47×#1939C211yesmaximal, characteristic, complemented
6C47×#1917C211yesmaximal, characteristic, complemented
7C47×#1917C211yesmaximal, characteristic, complemented
8C47×#1916C211yesmaximal, characteristic, complemented
9C47×#1916C211yesmaximal, characteristic, complemented
10C47×#1851C211yesmaximal, characteristic
11C47×#1851C211yesmaximal, characteristic
12C47×#1798C211yesmaximal, characteristic
13C47×#1752C211yesmaximal, characteristic
14C8×C22⋊C4×C47C211yesmaximal, characteristic
15C47×#1729C211yesmaximal, characteristic
16C22×M16×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C2×C4×Q8×C47C2211yescharacteristic
19C2×#117×C47C2211yescharacteristic
20C2×C4⋊C8×C47C2211yescharacteristic
21C2×C4⋊C8×C47C2211yescharacteristic
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×C22⋊C8×C47C2211yescharacteristic
27C2×C22⋊C8×C47C2211yescharacteristic
28C2×#97×C47C2211yescharacteristic
29C2×#97×C47C2211yescharacteristic
30C2×C4×C8×C47C2211yescharacteristic
31C2×C4×C8×C47C2211yescharacteristic
32C47×#400C411yescharacteristic
33C47×#399C411yescharacteristic
34C47×#398C411yescharacteristic
35C47×#398C411yescharacteristic
36C47×#396C411yescharacteristic
37C47×#396C411yescharacteristic
38C47×#395C411yescharacteristic
39C47×#393C411yescharacteristic
40C4×C4⋊C4×C47C2211yescharacteristic
41C4×C4⋊C4×C47C2211yescharacteristic
42C4×C4⋊C4×C47C2211yescharacteristic
43C4×C22⋊C4×C47C2211yescharacteristic
44C4×C22⋊C4×C47C2211yescharacteristic
45C47×#336C2211yescharacteristic
46C47×#336C2211yescharacteristic
47C47×#336C2211yescharacteristic
48C47×#336C2211yescharacteristic
49C47×#336C2211yescharacteristic
50C47×#336C2211yescharacteristic
51C47×#336C2211yescharacteristic
52C47×#336C2211yescharacteristic
53C47×#336C2211yescharacteristic
54C47×#336C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Q8×C47C2×C411yescharacteristic
60C23×C4×C47C2311yescharacteristic
61C2×M16×C47—22no—
62C2×M16×C47—41no—
63C2×M16×C47—41no—
64C22×C8×C47—41no—
65C22×C8×C47—41no—
66C22×C8×C47Q814yescomplemented
67C22×C8×C47C2311yescharacteristic
68C22×C8×C47C2311yescharacteristic
69C22×C8×C47C2311yescharacteristic
70C22×C8×C47C2311yescharacteristic
71C22×C8×C47C2311yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75C4×Q8×C47—41no—
76C4×Q8×C47—41no—
77#117×C47—41no—
78#117×C47—41no—
79C2×C4⋊C4×C47C2×C411yescharacteristic
80C2×C4⋊C4×C47C2×C411yescharacteristic
81C2×C4⋊C4×C47C2×C411yescharacteristic
82C2×C4⋊C4×C47C2×C411yescharacteristic
83C2×C4⋊C4×C47C2×C411yescharacteristic
84C2×C4⋊C4×C47C2×C411yescharacteristic
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×C22⋊C4×C47C2×C411yescharacteristic
91C2×C22⋊C4×C47C2×C411yescharacteristic
92C2×C22⋊C4×C47C2×C411yescharacteristic
93C2×C22⋊C4×C47C2×C411yescharacteristic
94C2×C22⋊C4×C47C2×C411yescharacteristic
95C2×C22⋊C4×C47C2×C411yescharacteristic
96C2×C42×C47C2311yescharacteristic
97C2×C42×C47C2311yescharacteristic
98C2×C42×C47C2311yescharacteristic
99C2×C42×C47C2311yescharacteristic
100C2×C42×C47C2311yescharacteristic
101C2×C42×C47C2311yescharacteristic
102C4⋊C8×C47—41no—
103C4⋊C8×C47—41no—
104C4⋊C8×C47—41no—
105C4⋊C8×C47—41no—
106C4⋊C8×C47—41no—
107C4⋊C8×C47—41no—
108C22⋊C8×C47—22no—
109C22⋊C8×C47—22no—
110#97×C47—41no—
111#97×C47—41no—
112C4×C8×C47—41no—
113C4×C8×C47—41no—
114#95×C47C2×C411yescharacteristic
115#95×C47C2×C411yescharacteristic
116#95×C47C2×C411yescharacteristic
117#95×C47C2×C411yescharacteristic
118#95×C47C2×C411yescharacteristic
119#95×C47C2×C411yescharacteristic
120#95×C47C2×C411yescharacteristic
121#95×C47C2×C411yescharacteristic
122#95×C47C2×C411yescharacteristic
123#95×C47C2×C411yescharacteristic
124C24×C47C22×C411yescharacteristic
125C2×Q8×C47—22no—
126C2×Q8×C47—41no—
127C2×Q8×C47—41no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C22×C411yescharacteristic
134C22×C4×C47C22×C411yescharacteristic
135C22×C4×C47C22×C411yescharacteristic
136C22×C4×C47C22×C411yescharacteristic
137C22×C4×C47C22×C411yescharacteristic
138C22×C4×C47C22×C411yescharacteristic
139C22×C4×C47C22×C411yescharacteristic
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C22×C411yescharacteristic
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×Q812yes—
146C22×C4×C47#4112yes—
147C22×C4×C47C2411yescharacteristic
148M16×C47—44no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
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—44no—
172C2×C8×C47C2×Q812yes—
173C2×C8×C47C2×Q812yes—
174C4⋊C4×C47—22no—
175C4⋊C4×C47—22no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47—41no—
178C4⋊C4×C47—41no—
179C4⋊C4×C47—41no—
180C4⋊C4×C47—41no—
181C4⋊C4×C47—41no—
182C4⋊C4×C47—41no—
183C4⋊C4×C47—41no—
184C4⋊C4×C47—41no—
185C22⋊C4×C47—22no—
186C22⋊C4×C47—22no—
187C22⋊C4×C47—41no—
188C22⋊C4×C47—41no—
189C22⋊C4×C47—41no—
190C22⋊C4×C47—41no—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C42×C47—21no—
196C42×C47—21no—
197C42×C47—21no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47C4×Q812yes—
210C23×C47C23×C411yescharacteristic
211Q8×C47—44no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
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—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
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×C47C4×Q812yes—
253C2×C4×C47#13112yes—
254C2×C4×C47#13112yes—
255C2×C4×C47C22×Q811yescharacteristic
256C2×C4×C47C2×#4111yescharacteristic
257C2×C4×C47H(5,𝔽2)11yescharacteristic
258C2×C4×C47H(5,𝔽2)11yescharacteristic
259C2×C4×C47H(5,𝔽2)11yescharacteristic
260C2×C4×C472−1+411yescharacteristic
261C8×C47—22no—
262C8×C47—22no—
263C8×C47—41no—
264C8×C47—41no—
265C8×C47—41no—
266C8×C47—41no—
267C8×C47—41no—
268C8×C47—41no—
269#22292C4711yesmaximal, characteristic, direct product factor, Sylow
270C22×C47—22no—
271C22×C47—22no—
272C22×C47—22no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47C2×C4×Q811yescharacteristic
278C22×C47#51811yescharacteristic
279C22×C47#52011yescharacteristic
280C22×C47C2×#13111yescharacteristic
281C22×C47C2×#13111yescharacteristic
282C22×C47#56811yescharacteristic
283C22×C47#56811yescharacteristic
284C4×C47—22no—
285C4×C47—22no—
286C4×C47—22no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—41no—
297C4×C47#53811yescharacteristic
298C4×C47#53911yescharacteristic
299C4×C47#54311yescharacteristic
300C4×C47#54411yescharacteristic
301#2396C2×C4711yescharacteristic
302#1985C2×C4711yescharacteristic, complemented
303#1984C2×C4711yescharacteristic, complemented
304#1940C2×C4711yescharacteristic, complemented
305#1939C2×C4711yescharacteristic, complemented
306#1917C2×C4711yescharacteristic, complemented
307#1917C2×C4711yescharacteristic, complemented
308#1916C2×C4711yescharacteristic, complemented
309#1916C2×C4711yescharacteristic, complemented
310#1851C2×C4711yescharacteristic
311#1851C2×C4711yescharacteristic
312#1798C2×C4711yescharacteristic
313#1752C2×C4711yescharacteristic
314C8×C22⋊C4C2×C4711yescharacteristic
315#1729C2×C4711yescharacteristic
316C2×C47—42no—
317C2×C47#232911yescharacteristic
318C2×C47#296011yescharacteristic
319C2×C47#296111yescharacteristic
320C2×C47#297611yescharacteristic
321C2×C47#298111yescharacteristic
322C2×C47#299211yescharacteristic
323C2×C47#299311yescharacteristic
324C22×M16C22×C4711yescharacteristic
325C23×C8C22×C4711yescharacteristic
326C2×C4×Q8C22×C4711yescharacteristic
327C2×#117C22×C4711yescharacteristic
328C2×C4⋊C8C22×C4711yescharacteristic
329C2×C4⋊C8C22×C4711yescharacteristic
330C2×C4⋊C8C22×C4711yescharacteristic
331C2×C4⋊C8C22×C4711yescharacteristic
332C2×C4⋊C8C22×C4711yescharacteristic
333C2×C4⋊C8C22×C4711yescharacteristic
334C2×C22⋊C8C22×C4711yescharacteristic
335C2×C22⋊C8C22×C4711yescharacteristic
336C2×#97C22×C4711yescharacteristic
337C2×#97C22×C4711yescharacteristic
338C2×C4×C8C22×C4711yescharacteristic
339C2×C4×C8C22×C4711yescharacteristic
340#400C4×C4711yescharacteristic
341#399C4×C4711yescharacteristic
342#398C4×C4711yescharacteristic
343#398C4×C4711yescharacteristic
344#396C4×C4711yescharacteristic
345#396C4×C4711yescharacteristic
346#395C4×C4711yescharacteristic
347#393C4×C4711yescharacteristic
348C4×C4⋊C4C22×C4711yescharacteristic
349C4×C4⋊C4C22×C4711yescharacteristic
350C4×C4⋊C4C22×C4711yescharacteristic
351C4×C22⋊C4C22×C4711yescharacteristic
352C4×C22⋊C4C22×C4711yescharacteristic
353#336C22×C4711yescharacteristic
354#336C22×C4711yescharacteristic
355#336C22×C4711yescharacteristic
356#336C22×C4711yescharacteristic
357#336C22×C4711yescharacteristic
358#336C22×C4711yescharacteristic
359#336C22×C4711yescharacteristic
360#336C22×C4711yescharacteristic
361#336C22×C4711yescharacteristic
362#336C22×C4711yescharacteristic
363#336C22×C4711yescharacteristic
364#336C22×C4711yescharacteristic
365#336C22×C4711yescharacteristic
366#336C22×C4711yescharacteristic
367C47#2229211yescharacteristic, direct product factor, Sylow
368C22×Q8C2×C4×C4711yescharacteristic
369C23×C4C23×C4711yescharacteristic
370C2×M16—22no—
371C2×M16—41no—
372C2×M16—41no—
373C22×C8—41no—
374C22×C8—41no—
375C22×C8Q8×C4714yescomplemented
376C22×C8C23×C4711yescharacteristic
377C22×C8C23×C4711yescharacteristic
378C22×C8C23×C4711yescharacteristic
379C22×C8C23×C4711yescharacteristic
380C22×C8C23×C4711yescharacteristic
381C22×C8C23×C4711yescharacteristic
382C22×C8C23×C4711yescharacteristic
383C22×C8C23×C4711yescharacteristic
384C4×Q8—41no—
385C4×Q8—41no—
386#117—41no—
387#117—41no—
388C2×C4⋊C4C2×C4×C4711yescharacteristic
389C2×C4⋊C4C2×C4×C4711yescharacteristic
390C2×C4⋊C4C2×C4×C4711yescharacteristic
391C2×C4⋊C4C2×C4×C4711yescharacteristic
392C2×C4⋊C4C2×C4×C4711yescharacteristic
393C2×C4⋊C4C2×C4×C4711yescharacteristic
394C2×C4⋊C4C2×C4×C4711yescharacteristic
395C2×C4⋊C4C2×C4×C4711yescharacteristic
396C2×C4⋊C4C2×C4×C4711yescharacteristic
397C2×C4⋊C4C2×C4×C4711yescharacteristic
398C2×C4⋊C4C2×C4×C4711yescharacteristic
399C2×C22⋊C4C2×C4×C4711yescharacteristic
400C2×C22⋊C4C2×C4×C4711yescharacteristic
401C2×C22⋊C4C2×C4×C4711yescharacteristic
402C2×C22⋊C4C2×C4×C4711yescharacteristic
403C2×C22⋊C4C2×C4×C4711yescharacteristic
404C2×C22⋊C4C2×C4×C4711yescharacteristic
405C2×C42C23×C4711yescharacteristic
406C2×C42C23×C4711yescharacteristic
407C2×C42C23×C4711yescharacteristic
408C2×C42C23×C4711yescharacteristic
409C2×C42C23×C4711yescharacteristic
410C2×C42C23×C4711yescharacteristic
411C4⋊C8—41no—
412C4⋊C8—41no—
413C4⋊C8—41no—
414C4⋊C8—41no—
415C4⋊C8—41no—
416C4⋊C8—41no—
417C22⋊C8—22no—
418C22⋊C8—22no—
419#97—41no—
420#97—41no—
421C4×C8—41no—
422C4×C8—41no—
423#95C2×C4×C4711yescharacteristic
424#95C2×C4×C4711yescharacteristic
425#95C2×C4×C4711yescharacteristic
426#95C2×C4×C4711yescharacteristic
427#95C2×C4×C4711yescharacteristic
428#95C2×C4×C4711yescharacteristic
429#95C2×C4×C4711yescharacteristic
430#95C2×C4×C4711yescharacteristic
431#95C2×C4×C4711yescharacteristic
432#95C2×C4×C4711yescharacteristic
433C24C22×C4×C4711yescharacteristic
434C2×Q8—22no—
435C2×Q8—41no—
436C2×Q8—41no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4C22×C4×C4711yescharacteristic
442C22×C4C22×C4×C4711yescharacteristic
443C22×C4C22×C4×C4711yescharacteristic
444C22×C4C22×C4×C4711yescharacteristic
445C22×C4C22×C4×C4711yescharacteristic
446C22×C4C22×C4×C4711yescharacteristic
447C22×C4C22×C4×C4711yescharacteristic
448C22×C4C22×C4×C4711yescharacteristic
449C22×C4C22×C4×C4711yescharacteristic
450C22×C4C22×C4×C4711yescharacteristic
451C22×C4C22×C4×C4711yescharacteristic
452C22×C4C22×C4×C4711yescharacteristic
453C22×C4C22×C4×C4711yescharacteristic
454C22×C4C2×Q8×C4712yes—
455C22×C4#41×C4712yes—
456C22×C4C24×C4711yescharacteristic
457M16—44no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—44no—
481C2×C8C2×Q8×C4712yes—
482C2×C8C2×Q8×C4712yes—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23C4×Q8×C4712yes—
519C23C23×C4×C4711yescharacteristic
520Q8—44no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4C4×Q8×C4712yes—
562C2×C4#131×C4712yes—
563C2×C4#131×C4712yes—
564C2×C4C22×Q8×C4711yescharacteristic
565C2×C4C2×#41×C4711yescharacteristic
566C2×C4H(5,𝔽2)×C4711yescharacteristic
567C2×C4H(5,𝔽2)×C4711yescharacteristic
568C2×C4H(5,𝔽2)×C4711yescharacteristic
569C2×C42−1+4×C4711yescharacteristic
570C8—22no—
571C8—22no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C4×Q8×C4711yescharacteristic
586C22C47×#51811yescharacteristic
587C22C47×#52011yescharacteristic
588C22C2×#131×C4711yescharacteristic
589C22C2×#131×C4711yescharacteristic
590C22C47×#56811yescharacteristic
591C22C47×#56811yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4C47×#53811yescharacteristic
606C4C47×#53911yescharacteristic
607C4C47×#54311yescharacteristic
608C4C47×#54411yescharacteristic
609C2—42no—
610C2C47×#232911yescharacteristic
611C2C47×#296011yescharacteristic
612C2C47×#296111yescharacteristic
613C2C47×#297611yescharacteristic
614C2C47×#298111yescharacteristic
615C2C47×#299211yescharacteristic
616C2C47×#299311yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC24×C47C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1985C2semidirect
3. C47×#1984C2semidirect
4. C47×#1940C2semidirect
5. C47×#1939C2semidirect
6. C47×#1917C2semidirect
7. C47×#1917C2semidirect
8. C47×#1916C2semidirect
9. C47×#1916C2semidirect
66. C22×C8×C47Q8semidirect
269. #22292C47direct (N × H)
302. #1985C2×C47semidirect
303. #1984C2×C47semidirect
304. #1940C2×C47semidirect
305. #1939C2×C47semidirect
306. #1917C2×C47semidirect
307. #1917C2×C47semidirect
308. #1916C2×C47semidirect
309. #1916C2×C47semidirect
367. C47#22292direct (N × H)
375. C22×C8Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#23962
C47×#19852
C47×#19842
C47×#19402
C47×#19392
C47×#19172
C47×#19162
C47×#18512
C47×#17982
C47×#17522
C8×C22⋊C4×C472
C47×#17292
#2229247