Finite Group Databasebeta

← C47×#21980 #26061678

Subgroups — C47×#21980 #26061678

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#433C211yesmaximal, characteristic
2C2×C47×#424C211yesmaximal, characteristic
3C47×#2298C211yesmaximal, characteristic
4C47×#1940C211yesmaximal, characteristic, complemented
5C47×#1940C211yesmaximal, characteristic, complemented
6C47×#1939C211yesmaximal, characteristic, complemented
7C47×#1939C211yesmaximal, characteristic, complemented
8C47×#1851C211yesmaximal, characteristic
9C47×#1851C211yesmaximal, characteristic
10C47×#1850C211yesmaximal, characteristic
11C47×#1850C211yesmaximal, characteristic
12C47×#1843C211yesmaximal, characteristic, complemented
13C47×#1842C211yesmaximal, characteristic, complemented
14C47×#1832C211yesmaximal, characteristic, complemented
15C47×#1831C211yesmaximal, characteristic, complemented
16C22×M16×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C2×#117×C47C2211yescharacteristic
19C47×#433—24no—
20C47×#424—24no—
21C2×C4⋊C8×C47C2211yescharacteristic
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
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×C4⋊C8×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C2×C22⋊C8×C47C2211yescharacteristic
37C2×#97×C47C2211yescharacteristic
38C2×C4×C8×C47C2211yescharacteristic
39C47×#388C411yescharacteristic
40C47×#388C411yescharacteristic
41C47×#388C411yescharacteristic
42C47×#388C411yescharacteristic
43C47×#387C411yescharacteristic
44C47×#387C411yescharacteristic
45C47×#387C411yescharacteristic
46C47×#387C411yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C4×C4⋊C4×C47C2211yescharacteristic
49C4×C22⋊C4×C47C2211yescharacteristic
50C4×C22⋊C4×C47C2211yescharacteristic
51C47×#376C2211yescharacteristic
52C43×C47C2211yescharacteristic
53C47×#336C2211yescharacteristic
54C47×#336C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C23×C4×C47C2311yescharacteristic
62C2×M16×C47—22no—
63C2×M16×C47—41no—
64C2×M16×C47—41no—
65C22×C8×C47—22no—
66C22×C8×C47—41no—
67C22×C8×C47—41no—
68C22×C8×C47C2311yescharacteristic
69C22×C8×C47C2311yescharacteristic
70C22×C8×C47C2311yescharacteristic
71C22×C8×C47C2311yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75C22×C8×C47C2311yescharacteristic
76#117×C47D414yes—
77#117×C47Q814yes—
78C2×C4⋊C4×C47C2×C411yescharacteristic
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×C22⋊C4×C47C2×C411yescharacteristic
85C2×C22⋊C4×C47C2×C411yescharacteristic
86C2×C22⋊C4×C47C2×C411yescharacteristic
87C2×C22⋊C4×C47C2×C411yescharacteristic
88C2×C22⋊C4×C47C2×C411yescharacteristic
89C2×C22⋊C4×C47C2×C411yescharacteristic
90C2×C42×C47C2×C411yescharacteristic
91C2×C42×C47C2×C411yescharacteristic
92C2×C42×C47C2×C411yescharacteristic
93C2×C42×C47C2×C411yescharacteristic
94C2×C42×C47C2311yescharacteristic
95C2×C42×C47C2311yescharacteristic
96C2×C42×C47C2311yescharacteristic
97C2×C42×C47C2311yescharacteristic
98C2×C42×C47C2311yescharacteristic
99C2×C42×C47C2311yescharacteristic
100C4⋊C8×C47—22no—
101C4⋊C8×C47—22no—
102C4⋊C8×C47—22no—
103C4⋊C8×C47—22no—
104C4⋊C8×C47—22no—
105C4⋊C8×C47—22no—
106C4⋊C8×C47—41no—
107C4⋊C8×C47—41no—
108C4⋊C8×C47—41no—
109C4⋊C8×C47—41no—
110C4⋊C8×C47—41no—
111C4⋊C8×C47—41no—
112C4⋊C8×C47—41no—
113C4⋊C8×C47—41no—
114C22⋊C8×C47—22no—
115C22⋊C8×C47—22no—
116#97×C47—22no—
117C4×C8×C47—22no—
118#95×C47C2×C411yescharacteristic
119#95×C47C2×C411yescharacteristic
120#95×C47C2×C411yescharacteristic
121#95×C47C2×C411yescharacteristic
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
130C24×C47C22×C411yescharacteristic
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
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×C47C22×C411yescharacteristic
146C22×C4×C47C22×C411yescharacteristic
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×Q812yes—
150C22×C4×C47C2411yescharacteristic
151M16×C47—44no—
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—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—44no—
177C4⋊C4×C47—22no—
178C4⋊C4×C47—22no—
179C4⋊C4×C47—41no—
180C4⋊C4×C47—41no—
181C4⋊C4×C47C4⋊C414yes—
182C4⋊C4×C47C4⋊C414yes—
183C22⋊C4×C47—22no—
184C22⋊C4×C47—22no—
185C22⋊C4×C47—41no—
186C22⋊C4×C47—41no—
187C22⋊C4×C47C4⋊C414yes—
188C22⋊C4×C47C4⋊C414yes—
189C42×C47—22no—
190C42×C47—22no—
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—41no—
200C42×C47—41no—
201C42×C47C2×D412yes—
202C42×C47C2×D412yes—
203C42×C47C2×Q812yes—
204C42×C47C2×Q812yes—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47C2×C4⋊C412yes—
212C23×C47C23×C411yescharacteristic
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
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×C47C2×C4⋊C412yes—
250C2×C4×C47C2×C4⋊C412yes—
251C2×C4×C47C2×C4⋊C412yes—
252C2×C4×C47C2×C4⋊C412yes—
253C2×C4×C47C2×C4⋊C412yes—
254C2×C4×C47#13112yes—
255C2×C4×C47#13112yes—
256C2×C4×C47C22×D411yescharacteristic
257C2×C4×C47C22×Q811yescharacteristic
258C2×C4×C47H(5,𝔽2)11yescharacteristic
259C2×C4×C47H(5,𝔽2)11yescharacteristic
260C2×C4×C472−1+411yescharacteristic
261C2×C4×C472−1+411yescharacteristic
262C8×C47—41no—
263C8×C47—41no—
264C8×C47—41no—
265C8×C47—41no—
266C8×C47—41no—
267C8×C47—41no—
268C8×C47—41no—
269C8×C47—41no—
270#21980C4711yesmaximal, characteristic, direct product factor, Sylow
271C22×C47—22no—
272C22×C47—22no—
273C22×C47—22no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47C22×C4⋊C411yescharacteristic
279C22×C47#52011yescharacteristic
280C22×C47#52011yescharacteristic
281C22×C47C2×#13111yescharacteristic
282C22×C47C2×#13111yescharacteristic
283C22×C47#56811yescharacteristic
284C22×C47#56811yescharacteristic
285C4×C47—22no—
286C4×C47—22no—
287C4×C47—22no—
288C4×C47—22no—
289C4×C47—22no—
290C4×C47—22no—
291C4×C47—22no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—41no—
297C4×C47—41no—
298C4×C47#53511yescharacteristic
299C4×C47#53611yescharacteristic
300C4×C47#54411yescharacteristic
301C4×C47#54411yescharacteristic
302C2×#433C2×C4711yescharacteristic
303C2×#424C2×C4711yescharacteristic
304#2298C2×C4711yescharacteristic
305#1940C2×C4711yescharacteristic, complemented
306#1940C2×C4711yescharacteristic, complemented
307#1939C2×C4711yescharacteristic, complemented
308#1939C2×C4711yescharacteristic, complemented
309#1851C2×C4711yescharacteristic
310#1851C2×C4711yescharacteristic
311#1850C2×C4711yescharacteristic
312#1850C2×C4711yescharacteristic
313#1843C2×C4711yescharacteristic, complemented
314#1842C2×C4711yescharacteristic, complemented
315#1832C2×C4711yescharacteristic, complemented
316#1831C2×C4711yescharacteristic, complemented
317C2×C47—42no—
318C2×C47#231711yescharacteristic
319C2×C47#290611yescharacteristic
320C2×C47#290611yescharacteristic
321C2×C47#299211yescharacteristic
322C2×C47#299311yescharacteristic
323C2×C47#299411yescharacteristic
324C2×C47#299511yescharacteristic
325C22×M16C22×C4711yescharacteristic
326C23×C8C22×C4711yescharacteristic
327C2×#117C22×C4711yescharacteristic
328#433—24no—
329#424—24no—
330C2×C4⋊C8C22×C4711yescharacteristic
331C2×C4⋊C8C22×C4711yescharacteristic
332C2×C4⋊C8C22×C4711yescharacteristic
333C2×C4⋊C8C22×C4711yescharacteristic
334C2×C4⋊C8C22×C4711yescharacteristic
335C2×C4⋊C8C22×C4711yescharacteristic
336C2×C4⋊C8C22×C4711yescharacteristic
337C2×C4⋊C8C22×C4711yescharacteristic
338C2×C4⋊C8C22×C4711yescharacteristic
339C2×C4⋊C8C22×C4711yescharacteristic
340C2×C4⋊C8C22×C4711yescharacteristic
341C2×C4⋊C8C22×C4711yescharacteristic
342C2×C4⋊C8C22×C4711yescharacteristic
343C2×C4⋊C8C22×C4711yescharacteristic
344C2×C22⋊C8C22×C4711yescharacteristic
345C2×C22⋊C8C22×C4711yescharacteristic
346C2×#97C22×C4711yescharacteristic
347C2×C4×C8C22×C4711yescharacteristic
348#388C4×C4711yescharacteristic
349#388C4×C4711yescharacteristic
350#388C4×C4711yescharacteristic
351#388C4×C4711yescharacteristic
352#387C4×C4711yescharacteristic
353#387C4×C4711yescharacteristic
354#387C4×C4711yescharacteristic
355#387C4×C4711yescharacteristic
356C4×C4⋊C4C22×C4711yescharacteristic
357C4×C4⋊C4C22×C4711yescharacteristic
358C4×C22⋊C4C22×C4711yescharacteristic
359C4×C22⋊C4C22×C4711yescharacteristic
360#376C22×C4711yescharacteristic
361C43C22×C4711yescharacteristic
362#336C22×C4711yescharacteristic
363#336C22×C4711yescharacteristic
364#336C22×C4711yescharacteristic
365#336C22×C4711yescharacteristic
366#336C22×C4711yescharacteristic
367#336C22×C4711yescharacteristic
368#336C22×C4711yescharacteristic
369#336C22×C4711yescharacteristic
370C47#2198011yescharacteristic, direct product factor, Sylow
371C23×C4C23×C4711yescharacteristic
372C2×M16—22no—
373C2×M16—41no—
374C2×M16—41no—
375C22×C8—22no—
376C22×C8—41no—
377C22×C8—41no—
378C22×C8C23×C4711yescharacteristic
379C22×C8C23×C4711yescharacteristic
380C22×C8C23×C4711yescharacteristic
381C22×C8C23×C4711yescharacteristic
382C22×C8C23×C4711yescharacteristic
383C22×C8C23×C4711yescharacteristic
384C22×C8C23×C4711yescharacteristic
385C22×C8C23×C4711yescharacteristic
386#117D4×C4714yes—
387#117Q8×C4714yes—
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×C22⋊C4C2×C4×C4711yescharacteristic
395C2×C22⋊C4C2×C4×C4711yescharacteristic
396C2×C22⋊C4C2×C4×C4711yescharacteristic
397C2×C22⋊C4C2×C4×C4711yescharacteristic
398C2×C22⋊C4C2×C4×C4711yescharacteristic
399C2×C22⋊C4C2×C4×C4711yescharacteristic
400C2×C42C2×C4×C4711yescharacteristic
401C2×C42C2×C4×C4711yescharacteristic
402C2×C42C2×C4×C4711yescharacteristic
403C2×C42C2×C4×C4711yescharacteristic
404C2×C42C23×C4711yescharacteristic
405C2×C42C23×C4711yescharacteristic
406C2×C42C23×C4711yescharacteristic
407C2×C42C23×C4711yescharacteristic
408C2×C42C23×C4711yescharacteristic
409C2×C42C23×C4711yescharacteristic
410C4⋊C8—22no—
411C4⋊C8—22no—
412C4⋊C8—22no—
413C4⋊C8—22no—
414C4⋊C8—22no—
415C4⋊C8—22no—
416C4⋊C8—41no—
417C4⋊C8—41no—
418C4⋊C8—41no—
419C4⋊C8—41no—
420C4⋊C8—41no—
421C4⋊C8—41no—
422C4⋊C8—41no—
423C4⋊C8—41no—
424C22⋊C8—22no—
425C22⋊C8—22no—
426#97—22no—
427C4×C8—22no—
428#95C2×C4×C4711yescharacteristic
429#95C2×C4×C4711yescharacteristic
430#95C2×C4×C4711yescharacteristic
431#95C2×C4×C4711yescharacteristic
432#95C2×C4×C4711yescharacteristic
433#95C2×C4×C4711yescharacteristic
434#95C2×C4×C4711yescharacteristic
435#95C2×C4×C4711yescharacteristic
436#95C2×C4×C4711yescharacteristic
437#95C2×C4×C4711yescharacteristic
438#95C2×C4×C4711yescharacteristic
439#95C2×C4×C4711yescharacteristic
440C24C22×C4×C4711yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
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×C4C22×C4×C4711yescharacteristic
455C22×C4C22×C4×C4711yescharacteristic
456C22×C4C22×C4×C4711yescharacteristic
457C22×C4C22×C4×C4711yescharacteristic
458C22×C4C2×D4×C4712yes—
459C22×C4C2×Q8×C4712yes—
460C22×C4C24×C4711yescharacteristic
461M16—44no—
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—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—44no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C4⋊C4×C4714yes—
492C4⋊C4C4⋊C4×C4714yes—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4C4⋊C4×C4714yes—
498C22⋊C4C4⋊C4×C4714yes—
499C42—22no—
500C42—22no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—41no—
510C42—41no—
511C42C2×D4×C4712yes—
512C42C2×D4×C4712yes—
513C42C2×Q8×C4712yes—
514C42C2×Q8×C4712yes—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23C2×C4⋊C4×C4712yes—
522C23C23×C4×C4711yescharacteristic
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
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×C4C2×C4⋊C4×C4712yes—
560C2×C4C2×C4⋊C4×C4712yes—
561C2×C4C2×C4⋊C4×C4712yes—
562C2×C4C2×C4⋊C4×C4712yes—
563C2×C4C2×C4⋊C4×C4712yes—
564C2×C4#131×C4712yes—
565C2×C4#131×C4712yes—
566C2×C4C22×D4×C4711yescharacteristic
567C2×C4C22×Q8×C4711yescharacteristic
568C2×C4H(5,𝔽2)×C4711yescharacteristic
569C2×C4H(5,𝔽2)×C4711yescharacteristic
570C2×C42−1+4×C4711yescharacteristic
571C2×C42−1+4×C4711yescharacteristic
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8—41no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C22×C4⋊C4×C4711yescharacteristic
588C22C47×#52011yescharacteristic
589C22C47×#52011yescharacteristic
590C22C2×#131×C4711yescharacteristic
591C22C2×#131×C4711yescharacteristic
592C22C47×#56811yescharacteristic
593C22C47×#56811yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—22no—
599C4—22no—
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4C47×#53511yescharacteristic
608C4C47×#53611yescharacteristic
609C4C47×#54411yescharacteristic
610C4C47×#54411yescharacteristic
611C2—42no—
612C2C47×#231711yescharacteristic
613C2C47×#290611yescharacteristic
614C2C47×#290611yescharacteristic
615C2C47×#299211yescharacteristic
616C2C47×#299311yescharacteristic
617C2C47×#299411yescharacteristic
618C2C47×#299511yescharacteristic
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
4. C47×#1940C2semidirect
5. C47×#1940C2semidirect
6. C47×#1939C2semidirect
7. C47×#1939C2semidirect
12. C47×#1843C2semidirect
13. C47×#1842C2semidirect
14. C47×#1832C2semidirect
15. C47×#1831C2semidirect
270. #21980C47direct (N × H)
305. #1940C2×C47semidirect
306. #1940C2×C47semidirect
307. #1939C2×C47semidirect
308. #1939C2×C47semidirect
313. #1843C2×C47semidirect
314. #1842C2×C47semidirect
315. #1832C2×C47semidirect
316. #1831C2×C47semidirect
370. C47#21980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4332
C2×C47×#4242
C47×#22982
C47×#19402
C47×#19392
C47×#18512
C47×#18502
C47×#18432
C47×#18422
C47×#18322
C47×#18312
#2198047