Finite Group Databasebeta

← C47×#22142 #26061840

Subgroups — C47×#22142 #26061840

Order 12032.

882 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#435C211yesmaximal, characteristic, complemented
2C2×C47×#433C211yesmaximal, characteristic, complemented
3C47×#2392C211yesmaximal, characteristic
4C47×#1955C211yesmaximal, characteristic, complemented
5C47×#1954C211yesmaximal, characteristic, complemented
6C47×#1954C211yesmaximal, characteristic, complemented
7C47×#1939C211yesmaximal, characteristic, complemented
8C47×#1924C211yesmaximal, characteristic, complemented
9C47×#1923C211yesmaximal, characteristic, complemented
10C47×#1870C211yesmaximal, characteristic, complemented
11C47×#1869C211yesmaximal, characteristic, complemented
12C47×#1851C211yesmaximal, characteristic, complemented
13C47×#1850C211yesmaximal, characteristic, complemented
14C47×#1798C211yesmaximal, characteristic, complemented
15C47×#1771C211yesmaximal, characteristic, complemented
16C22×M16×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C2×C4×D4×C47C2211yescharacteristic
19C2×C4×D4×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic
21C2×#117×C47C2211yescharacteristic
22C47×#435—24no—
23C47×#433—24no—
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×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×#97×C47C2211yescharacteristic
41C2×#97×C47C2211yescharacteristic
42C2×C4×C8×C47C2211yescharacteristic
43C2×C4×C8×C47C2211yescharacteristic
44C47×#398C411yescharacteristic
45C47×#397C411yescharacteristic
46C47×#396C411yescharacteristic
47C47×#396C411yescharacteristic
48C47×#394C411yescharacteristic
49C47×#394C411yescharacteristic
50C47×#394C411yescharacteristic
51C47×#392C411yescharacteristic
52C4×C4⋊C4×C47C2211yescharacteristic
53C4×C22⋊C4×C47C2211yescharacteristic
54C4×C22⋊C4×C47C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×D4×C47C2×C411yescharacteristic
62C22×D4×C47C2×C411yescharacteristic
63C22×D4×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
81C4×D4×C47—22no—
82C4×D4×C47—22no—
83C4×D4×C47—41no—
84C4×D4×C47—41no—
85C4×D4×C47—41no—
86C4×D4×C47—41no—
87#117×C47—22no—
88#117×C47—22no—
89C2×C4⋊C4×C47C2×C411yescharacteristic
90C2×C4⋊C4×C47C2×C411yescharacteristic
91C2×C4⋊C4×C47C2×C411yescharacteristic
92C2×C4⋊C4×C47C2×C411yescharacteristic
93C2×C4⋊C4×C47C2×C411yescharacteristic
94C2×C4⋊C4×C47C2×C411yescharacteristic
95C2×C4⋊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×C22⋊C4×C47C2×C411yescharacteristic
104C2×C22⋊C4×C47C2×C411yescharacteristic
105C2×C22⋊C4×C47C2×C411yescharacteristic
106C2×C22⋊C4×C47C2×C411yescharacteristic
107C2×C22⋊C4×C47C2×C411yescharacteristic
108C2×C42×C47C2311yescharacteristic
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111C2×C42×C47C2311yescharacteristic
112C4⋊C8×C47—22no—
113C4⋊C8×C47—22no—
114C4⋊C8×C47—22no—
115C4⋊C8×C47—22no—
116C4⋊C8×C47—41no—
117C4⋊C8×C47—41no—
118C22⋊C8×C47—22no—
119C22⋊C8×C47—22no—
120C22⋊C8×C47—22no—
121C22⋊C8×C47—22no—
122C22⋊C8×C47—41no—
123C22⋊C8×C47—41no—
124C22⋊C8×C47—41no—
125C22⋊C8×C47—41no—
126C22⋊C8×C47—41no—
127C22⋊C8×C47—41no—
128#97×C47—41no—
129#97×C47D414yescomplemented
130C4×C8×C47—22no—
131C4×C8×C47—41no—
132#95×C47C2×C411yescharacteristic
133#95×C47C2×C411yescharacteristic
134#95×C47C2×C411yescharacteristic
135#95×C47C2×C411yescharacteristic
136#95×C47C2×C411yescharacteristic
137#95×C47C2×C411yescharacteristic
138C24×C47C22×C411yescharacteristic
139C24×C47C22×C411yescharacteristic
140C24×C47C22×C411yescharacteristic
141C2×D4×C47—22no—
142C2×D4×C47—22no—
143C2×D4×C47—22no—
144C2×D4×C47—22no—
145C2×D4×C47—41no—
146C2×D4×C47—41no—
147C2×D4×C47—41no—
148C2×D4×C47—41no—
149C2×D4×C47—41no—
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—21no—
168C22×C4×C47C22×C411yescharacteristic
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×C47C2411yescharacteristic
180M16×C47—44no—
181C2×C8×C47—21no—
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—44no—
204C2×C8×C47C2×D412yes—
205C2×C8×C47C2×D412yes—
206C4⋊C4×C47—22no—
207C4⋊C4×C47—22no—
208C4⋊C4×C47—22no—
209C4⋊C4×C47—22no—
210C4⋊C4×C47—41no—
211C4⋊C4×C47—41no—
212C4⋊C4×C47—41no—
213C22⋊C4×C47—22no—
214C22⋊C4×C47—22no—
215C22⋊C4×C47—22no—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C22⋊C4×C47—41no—
220C22⋊C4×C47—41no—
221C22⋊C4×C47—41no—
222C22⋊C4×C47—41no—
223C22⋊C4×C47—41no—
224C22⋊C4×C47—41no—
225C42×C47—21no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47—21no—
231C42×C47C2×D412yes—
232C42×C47#4112yes—
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×C47—21no—
252C23×C47—21no—
253C23×C47#13112yes—
254C23×C47C23×C411yescharacteristic
255D4×C47—44no—
256D4×C47—44no—
257D4×C47—44no—
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—21no—
287C2×C4×C47—21no—
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×C47C4×D412yes—
301C2×C4×C47C4×D412yes—
302C2×C4×C47#13112yes—
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47H(5,𝔽2)11yescharacteristic
306C2×C4×C47H(5,𝔽2)11yescharacteristic
307C2×C4×C47H(5,𝔽2)11yescharacteristic
308C2×C4×C472−1+411yescharacteristic
309C8×C47—22no—
310C8×C47—22no—
311C8×C47—41no—
312C8×C47—41no—
313C8×C47—41no—
314C8×C47—41no—
315C8×C47—41no—
316C8×C47—41no—
317#22142C4711yesmaximal, characteristic, direct product factor, Sylow
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47—41no—
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×C47C2×C4×D411yescharacteristic
340C22×C47#51811yescharacteristic
341C22×C47#52011yescharacteristic
342C22×C47C2×#13111yescharacteristic
343C22×C47C2×#13111yescharacteristic
344C22×C47#56811yescharacteristic
345C22×C47#56811yescharacteristic
346C4×C47—22no—
347C4×C47—22no—
348C4×C47—22no—
349C4×C47—41no—
350C4×C47—41no—
351C4×C47—41no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—41no—
355C4×C47—41no—
356C4×C47—41no—
357C4×C47#53511yescharacteristic
358C4×C47#53711yescharacteristic
359C4×C47#54011yescharacteristic
360C4×C47#54211yescharacteristic
361C2×#435C2×C4711yescharacteristic, complemented
362C2×#433C2×C4711yescharacteristic, complemented
363#2392C2×C4711yescharacteristic
364#1955C2×C4711yescharacteristic, complemented
365#1954C2×C4711yescharacteristic, complemented
366#1954C2×C4711yescharacteristic, complemented
367#1939C2×C4711yescharacteristic, complemented
368#1924C2×C4711yescharacteristic, complemented
369#1923C2×C4711yescharacteristic, complemented
370#1870C2×C4711yescharacteristic, complemented
371#1869C2×C4711yescharacteristic, complemented
372#1851C2×C4711yescharacteristic, complemented
373#1850C2×C4711yescharacteristic, complemented
374#1798C2×C4711yescharacteristic, complemented
375#1771C2×C4711yescharacteristic, complemented
376C2×C47—42no—
377C2×C47—81no—
378C2×C47—81no—
379C2×C47#232411yescharacteristic
380C2×C47#293311yescharacteristic
381C2×C47#293511yescharacteristic
382C2×C47#297611yescharacteristic
383C2×C47#297611yescharacteristic
384C2×C47#299411yescharacteristic
385C2×C47#299511yescharacteristic
386C22×M16C22×C4711yescharacteristic
387C23×C8C22×C4711yescharacteristic
388C2×C4×D4C22×C4711yescharacteristic
389C2×C4×D4C22×C4711yescharacteristic
390C2×C4×D4C22×C4711yescharacteristic
391C2×#117C22×C4711yescharacteristic
392#435—24no—
393#433—24no—
394C2×C4⋊C8C22×C4711yescharacteristic
395C2×C4⋊C8C22×C4711yescharacteristic
396C2×C4⋊C8C22×C4711yescharacteristic
397C2×C4⋊C8C22×C4711yescharacteristic
398C2×C4⋊C8C22×C4711yescharacteristic
399C2×C4⋊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×C22⋊C8C22×C4711yescharacteristic
407C2×C22⋊C8C22×C4711yescharacteristic
408C2×C22⋊C8C22×C4711yescharacteristic
409C2×C22⋊C8C22×C4711yescharacteristic
410C2×#97C22×C4711yescharacteristic
411C2×#97C22×C4711yescharacteristic
412C2×C4×C8C22×C4711yescharacteristic
413C2×C4×C8C22×C4711yescharacteristic
414#398C4×C4711yescharacteristic
415#397C4×C4711yescharacteristic
416#396C4×C4711yescharacteristic
417#396C4×C4711yescharacteristic
418#394C4×C4711yescharacteristic
419#394C4×C4711yescharacteristic
420#394C4×C4711yescharacteristic
421#392C4×C4711yescharacteristic
422C4×C4⋊C4C22×C4711yescharacteristic
423C4×C22⋊C4C22×C4711yescharacteristic
424C4×C22⋊C4C22×C4711yescharacteristic
425#336C22×C4711yescharacteristic
426#336C22×C4711yescharacteristic
427#336C22×C4711yescharacteristic
428#336C22×C4711yescharacteristic
429#336C22×C4711yescharacteristic
430#336C22×C4711yescharacteristic
431C47#2214211yescharacteristic, direct product factor, Sylow
432C22×D4C2×C4×C4711yescharacteristic
433C22×D4C2×C4×C4711yescharacteristic
434C22×D4C2×C4×C4711yescharacteristic
435C23×C4C23×C4711yescharacteristic
436C23×C4C23×C4711yescharacteristic
437C23×C4C23×C4711yescharacteristic
438C2×M16—22no—
439C2×M16—41no—
440C2×M16—41no—
441C22×C8—22no—
442C22×C8—41no—
443C22×C8—41no—
444C22×C8C23×C4711yescharacteristic
445C22×C8C23×C4711yescharacteristic
446C22×C8C23×C4711yescharacteristic
447C22×C8C23×C4711yescharacteristic
448C22×C8C23×C4711yescharacteristic
449C22×C8C23×C4711yescharacteristic
450C22×C8C23×C4711yescharacteristic
451C22×C8C23×C4711yescharacteristic
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458#117—22no—
459#117—22no—
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×C4⋊C4C2×C4×C4711yescharacteristic
466C2×C4⋊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×C22⋊C4C2×C4×C4711yescharacteristic
476C2×C22⋊C4C2×C4×C4711yescharacteristic
477C2×C22⋊C4C2×C4×C4711yescharacteristic
478C2×C22⋊C4C2×C4×C4711yescharacteristic
479C2×C42C23×C4711yescharacteristic
480C2×C42C23×C4711yescharacteristic
481C2×C42C23×C4711yescharacteristic
482C2×C42C23×C4711yescharacteristic
483C4⋊C8—22no—
484C4⋊C8—22no—
485C4⋊C8—22no—
486C4⋊C8—22no—
487C4⋊C8—41no—
488C4⋊C8—41no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495C22⋊C8—41no—
496C22⋊C8—41no—
497C22⋊C8—41no—
498C22⋊C8—41no—
499#97—41no—
500#97D4×C4714yescomplemented
501C4×C8—22no—
502C4×C8—41no—
503#95C2×C4×C4711yescharacteristic
504#95C2×C4×C4711yescharacteristic
505#95C2×C4×C4711yescharacteristic
506#95C2×C4×C4711yescharacteristic
507#95C2×C4×C4711yescharacteristic
508#95C2×C4×C4711yescharacteristic
509C24C22×C4×C4711yescharacteristic
510C24C22×C4×C4711yescharacteristic
511C24C22×C4×C4711yescharacteristic
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
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×C4C22×C4×C4711yescharacteristic
540C22×C4C22×C4×C4711yescharacteristic
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×C4C24×C4711yescharacteristic
551M16—44no—
552C2×C8—21no—
553C2×C8—21no—
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—44no—
575C2×C8C2×D4×C4712yes—
576C2×C8C2×D4×C4712yes—
577C4⋊C4—22no—
578C4⋊C4—22no—
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—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42C2×D4×C4712yes—
603C42#41×C4712yes—
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—
623C23—21no—
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—21no—
659C2×C4—41no—
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×C4C4×D4×C4712yes—
672C2×C4C4×D4×C4712yes—
673C2×C4#131×C4712yes—
674C2×C4C22×D4×C4711yescharacteristic
675C2×C4C2×#41×C4711yescharacteristic
676C2×C4H(5,𝔽2)×C4711yescharacteristic
677C2×C4H(5,𝔽2)×C4711yescharacteristic
678C2×C4H(5,𝔽2)×C4711yescharacteristic
679C2×C42−1+4×C4711yescharacteristic
680C8—22no—
681C8—22no—
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
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—
709C22C2×C4×D4×C4711yescharacteristic
710C22C47×#51811yescharacteristic
711C22C47×#52011yescharacteristic
712C22C2×#131×C4711yescharacteristic
713C22C2×#131×C4711yescharacteristic
714C22C47×#56811yescharacteristic
715C22C47×#56811yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4C47×#53511yescharacteristic
728C4C47×#53711yescharacteristic
729C4C47×#54011yescharacteristic
730C4C47×#54211yescharacteristic
731C2—42no—
732C2—81no—
733C2—81no—
734C2C47×#232411yescharacteristic
735C2C47×#293311yescharacteristic
736C2C47×#293511yescharacteristic
737C2C47×#297611yescharacteristic
738C2C47×#297611yescharacteristic
739C2C47×#299411yescharacteristic
740C2C47×#299511yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC47×#392C4
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×#435C2semidirect
2. C2×C47×#433C2semidirect
4. C47×#1955C2semidirect
5. C47×#1954C2semidirect
6. C47×#1954C2semidirect
7. C47×#1939C2semidirect
8. C47×#1924C2semidirect
9. C47×#1923C2semidirect
10. C47×#1870C2semidirect
11. C47×#1869C2semidirect
12. C47×#1851C2semidirect
13. C47×#1850C2semidirect
14. C47×#1798C2semidirect
15. C47×#1771C2semidirect
129. #97×C47D4semidirect
317. #22142C47direct (N × H)
361. C2×#435C2×C47semidirect
362. C2×#433C2×C47semidirect
364. #1955C2×C47semidirect
365. #1954C2×C47semidirect
366. #1954C2×C47semidirect
367. #1939C2×C47semidirect
368. #1924C2×C47semidirect
369. #1923C2×C47semidirect
370. #1870C2×C47semidirect
371. #1869C2×C47semidirect
372. #1851C2×C47semidirect
373. #1850C2×C47semidirect
374. #1798C2×C47semidirect
375. #1771C2×C47semidirect
431. C47#22142direct (N × H)
500. #97D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4352
C2×C47×#4332
C47×#23922
C47×#19552
C47×#19542
C47×#19392
C47×#19242
C47×#19232
C47×#18702
C47×#18692
C47×#18512
C47×#18502
C47×#17982
C47×#17712
#2214247