Finite Group Databasebeta

← C47×#22141 #26061839

Subgroups — C47×#22141 #26061839

Order 12032.

940 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#435C211yesmaximal, characteristic, complemented
2C2×C47×#432C211yesmaximal, characteristic, complemented
3C4×#121×C47C211yesmaximal, characteristic
4C47×#1955C211yesmaximal, characteristic, complemented
5C47×#1955C211yesmaximal, characteristic, complemented
6C47×#1954C211yesmaximal, characteristic, complemented
7C47×#1940C211yesmaximal, 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×#1797C211yesmaximal, characteristic, complemented
15C47×#1771C211yesmaximal, 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
23C47×#435—24no—
24C47×#432—24no—
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×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×C22⋊C8×C47C2211yescharacteristic
41C2×#97×C47C2211yescharacteristic
42C2×#97×C47C2211yescharacteristic
43C2×#97×C47C2211yescharacteristic
44C2×C4×C8×C47C2211yescharacteristic
45C47×#390C411yescharacteristic
46C47×#389C411yescharacteristic
47C47×#388C411yescharacteristic
48C47×#388C411yescharacteristic
49C47×#386C411yescharacteristic
50C47×#386C411yescharacteristic
51C47×#380C411yescharacteristic
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×C47C2×C411yescharacteristic
65C23×C4×C47C2×C411yescharacteristic
66C23×C4×C47C2311yescharacteristic
67C23×C4×C47C2311yescharacteristic
68C23×C4×C47C2311yescharacteristic
69C2×M16×C47—22no—
70C2×M16×C47—41no—
71C2×M16×C47—41no—
72C22×C8×C47—22no—
73C22×C8×C47—41no—
74C22×C8×C47—41no—
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83#121×C47—24no—
84C4×D4×C47—22no—
85C4×D4×C47—22no—
86C4×D4×C47—41no—
87C4×D4×C47—41no—
88C4×D4×C47—41no—
89C4×D4×C47—41no—
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×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×C22⋊C4×C47C2×C411yescharacteristic
104C2×C22⋊C4×C47C2×C411yescharacteristic
105C2×C42×C47—22no—
106C2×C42×C47—22no—
107C2×C42×C47C2×C411yescharacteristic
108C2×C42×C47C2×C411yescharacteristic
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111C2×C42×C47C2311yescharacteristic
112C2×C42×C47C2311yescharacteristic
113C4⋊C8×C47—22no—
114C4⋊C8×C47—22no—
115C4⋊C8×C47—22no—
116C4⋊C8×C47—22no—
117C4⋊C8×C47—41no—
118C4⋊C8×C47—41no—
119C22⋊C8×C47—22no—
120C22⋊C8×C47—22no—
121C22⋊C8×C47—22no—
122C22⋊C8×C47—22no—
123C22⋊C8×C47—41no—
124C22⋊C8×C47—41no—
125C22⋊C8×C47—41no—
126C22⋊C8×C47—41no—
127C22⋊C8×C47—41no—
128C22⋊C8×C47—41no—
129#97×C47—22no—
130#97×C47—41no—
131#97×C47D414yescomplemented
132C4×C8×C47—41no—
133#95×C47C2×C411yescharacteristic
134#95×C47C2×C411yescharacteristic
135#95×C47C2×C411yescharacteristic
136#95×C47C2×C411yescharacteristic
137#95×C47C2×C411yescharacteristic
138#95×C47C2×C411yescharacteristic
139C24×C47C22×C411yescharacteristic
140C24×C47C22×C411yescharacteristic
141C24×C47C22×C411yescharacteristic
142C2×D4×C47—22no—
143C2×D4×C47—22no—
144C2×D4×C47—22no—
145C2×D4×C47—22no—
146C2×D4×C47—22no—
147C2×D4×C47—22no—
148C2×D4×C47—41no—
149C2×D4×C47—41no—
150C2×D4×C47—41no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
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×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—41no—
174C22×C4×C47—41no—
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C22×C411yescharacteristic
178C22×C4×C47C22×C411yescharacteristic
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C22×C411yescharacteristic
185C22×C4×C47C22×C411yescharacteristic
186C22×C4×C47C2411yescharacteristic
187M16×C47—44no—
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—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—44no—
211C2×C8×C47C2×D412yes—
212C2×C8×C47C2×D412yes—
213C4⋊C4×C47—22no—
214C4⋊C4×C47—22no—
215C4⋊C4×C47—41no—
216C4⋊C4×C47—41no—
217C4⋊C4×C47—41no—
218C22⋊C4×C47—22no—
219C22⋊C4×C47—22no—
220C22⋊C4×C47—22no—
221C22⋊C4×C47—41no—
222C22⋊C4×C47—41no—
223C22⋊C4×C47—41no—
224C22⋊C4×C47—41no—
225C22⋊C4×C47—41no—
226C22⋊C4×C47—41no—
227C22⋊C4×C47M1614yescomplemented
228C42×C47—22no—
229C42×C47—22no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47—21no—
233C42×C47—21no—
234C42×C47—21no—
235C42×C47—21no—
236C42×C47C2×D412yes—
237C42×C47#4112yes—
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—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47C2×M1612yes—
258C23×C47#13112yes—
259C23×C47C23×C411yescharacteristic
260D4×C47—44no—
261D4×C47—44no—
262D4×C47—44no—
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—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—44no—
293C2×C4×C47—44no—
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×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47C4×D412yes—
307C2×C4×C47C4×D412yes—
308C2×C4×C47C2×M1612yes—
309C2×C4×C47C2×M1612yes—
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C2×#4111yescharacteristic
312C2×C4×C47H(5,𝔽2)11yescharacteristic
313C2×C4×C47H(5,𝔽2)11yescharacteristic
314C2×C4×C47H(5,𝔽2)11yescharacteristic
315C2×C4×C472−1+411yescharacteristic
316C8×C47—22no—
317C8×C47—22no—
318C8×C47—41no—
319C8×C47—41no—
320C8×C47—41no—
321C8×C47—41no—
322C8×C47—41no—
323C8×C47—41no—
324#22141C4711yesmaximal, characteristic, direct product factor, Sylow
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—22no—
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×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47C2×C4×D411yescharacteristic
347C22×C47#51811yescharacteristic
348C22×C47#52011yescharacteristic
349C22×C47C22×M1611yescharacteristic
350C22×C47C2×#13111yescharacteristic
351C22×C47#56811yescharacteristic
352C22×C47#56811yescharacteristic
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47—41no—
360C4×C47—41no—
361C4×C47—41no—
362C4×C47—41no—
363C4×C47—41no—
364C4×C47#53511yescharacteristic
365C4×C47#53711yescharacteristic
366C4×C47#54011yescharacteristic
367C4×C47#54211yescharacteristic
368C2×#435C2×C4711yescharacteristic, complemented
369C2×#432C2×C4711yescharacteristic, complemented
370C4×#121C2×C4711yescharacteristic
371#1955C2×C4711yescharacteristic, complemented
372#1955C2×C4711yescharacteristic, complemented
373#1954C2×C4711yescharacteristic, complemented
374#1940C2×C4711yescharacteristic, complemented
375#1924C2×C4711yescharacteristic, complemented
376#1923C2×C4711yescharacteristic, complemented
377#1870C2×C4711yescharacteristic, complemented
378#1869C2×C4711yescharacteristic, complemented
379#1851C2×C4711yescharacteristic, complemented
380#1850C2×C4711yescharacteristic, complemented
381#1797C2×C4711yescharacteristic, complemented
382#1771C2×C4711yescharacteristic, complemented
383C2×C47—42no—
384C2×C47—42no—
385C2×C47—81no—
386C2×C47#232411yescharacteristic
387C2×C47#293311yescharacteristic
388C2×C47D4×M1611yescharacteristic
389C2×C47#297411yescharacteristic
390C2×C47#298011yescharacteristic
391C2×C47#298911yescharacteristic
392C2×C47#299211yescharacteristic
393C22×M16C22×C4711yescharacteristic
394C23×C8C22×C4711yescharacteristic
395C2×#121C4×C4711yescharacteristic
396C2×C4×D4C22×C4711yescharacteristic
397C2×C4×D4C22×C4711yescharacteristic
398C2×C4×D4C22×C4711yescharacteristic
399C22×C42C22×C4711yescharacteristic
400#435—24no—
401#432—24no—
402C2×C4⋊C8C22×C4711yescharacteristic
403C2×C4⋊C8C22×C4711yescharacteristic
404C2×C4⋊C8C22×C4711yescharacteristic
405C2×C4⋊C8C22×C4711yescharacteristic
406C2×C4⋊C8C22×C4711yescharacteristic
407C2×C4⋊C8C22×C4711yescharacteristic
408C2×C22⋊C8C22×C4711yescharacteristic
409C2×C22⋊C8C22×C4711yescharacteristic
410C2×C22⋊C8C22×C4711yescharacteristic
411C2×C22⋊C8C22×C4711yescharacteristic
412C2×C22⋊C8C22×C4711yescharacteristic
413C2×C22⋊C8C22×C4711yescharacteristic
414C2×C22⋊C8C22×C4711yescharacteristic
415C2×C22⋊C8C22×C4711yescharacteristic
416C2×C22⋊C8C22×C4711yescharacteristic
417C2×C22⋊C8C22×C4711yescharacteristic
418C2×#97C22×C4711yescharacteristic
419C2×#97C22×C4711yescharacteristic
420C2×#97C22×C4711yescharacteristic
421C2×C4×C8C22×C4711yescharacteristic
422#390C4×C4711yescharacteristic
423#389C4×C4711yescharacteristic
424#388C4×C4711yescharacteristic
425#388C4×C4711yescharacteristic
426#386C4×C4711yescharacteristic
427#386C4×C4711yescharacteristic
428#380C4×C4711yescharacteristic
429C4×C4⋊C4C22×C4711yescharacteristic
430C4×C22⋊C4C22×C4711yescharacteristic
431C4×C22⋊C4C22×C4711yescharacteristic
432#336C22×C4711yescharacteristic
433#336C22×C4711yescharacteristic
434#336C22×C4711yescharacteristic
435#336C22×C4711yescharacteristic
436#336C22×C4711yescharacteristic
437#336C22×C4711yescharacteristic
438C47#2214111yescharacteristic, direct product factor, Sylow
439C22×D4C2×C4×C4711yescharacteristic
440C22×D4C2×C4×C4711yescharacteristic
441C22×D4C2×C4×C4711yescharacteristic
442C23×C4C2×C4×C4711yescharacteristic
443C23×C4C2×C4×C4711yescharacteristic
444C23×C4C23×C4711yescharacteristic
445C23×C4C23×C4711yescharacteristic
446C23×C4C23×C4711yescharacteristic
447C2×M16—22no—
448C2×M16—41no—
449C2×M16—41no—
450C22×C8—22no—
451C22×C8—41no—
452C22×C8—41no—
453C22×C8C23×C4711yescharacteristic
454C22×C8C23×C4711yescharacteristic
455C22×C8C23×C4711yescharacteristic
456C22×C8C23×C4711yescharacteristic
457C22×C8C23×C4711yescharacteristic
458C22×C8C23×C4711yescharacteristic
459C22×C8C23×C4711yescharacteristic
460C22×C8C23×C4711yescharacteristic
461#121—24no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—41no—
465C4×D4—41no—
466C4×D4—41no—
467C4×D4—41no—
468C2×C4⋊C4C2×C4×C4711yescharacteristic
469C2×C4⋊C4C2×C4×C4711yescharacteristic
470C2×C4⋊C4C2×C4×C4711yescharacteristic
471C2×C4⋊C4C2×C4×C4711yescharacteristic
472C2×C4⋊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×C22⋊C4C2×C4×C4711yescharacteristic
480C2×C22⋊C4C2×C4×C4711yescharacteristic
481C2×C22⋊C4C2×C4×C4711yescharacteristic
482C2×C22⋊C4C2×C4×C4711yescharacteristic
483C2×C42—22no—
484C2×C42—22no—
485C2×C42C2×C4×C4711yescharacteristic
486C2×C42C2×C4×C4711yescharacteristic
487C2×C42C23×C4711yescharacteristic
488C2×C42C23×C4711yescharacteristic
489C2×C42C23×C4711yescharacteristic
490C2×C42C23×C4711yescharacteristic
491C4⋊C8—22no—
492C4⋊C8—22no—
493C4⋊C8—22no—
494C4⋊C8—22no—
495C4⋊C8—41no—
496C4⋊C8—41no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—41no—
502C22⋊C8—41no—
503C22⋊C8—41no—
504C22⋊C8—41no—
505C22⋊C8—41no—
506C22⋊C8—41no—
507#97—22no—
508#97—41no—
509#97D4×C4714yescomplemented
510C4×C8—41no—
511#95C2×C4×C4711yescharacteristic
512#95C2×C4×C4711yescharacteristic
513#95C2×C4×C4711yescharacteristic
514#95C2×C4×C4711yescharacteristic
515#95C2×C4×C4711yescharacteristic
516#95C2×C4×C4711yescharacteristic
517C24C22×C4×C4711yescharacteristic
518C24C22×C4×C4711yescharacteristic
519C24C22×C4×C4711yescharacteristic
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4C22×C4×C4711yescharacteristic
554C22×C4C22×C4×C4711yescharacteristic
555C22×C4C22×C4×C4711yescharacteristic
556C22×C4C22×C4×C4711yescharacteristic
557C22×C4C22×C4×C4711yescharacteristic
558C22×C4C22×C4×C4711yescharacteristic
559C22×C4C22×C4×C4711yescharacteristic
560C22×C4C22×C4×C4711yescharacteristic
561C22×C4C22×C4×C4711yescharacteristic
562C22×C4C22×C4×C4711yescharacteristic
563C22×C4C22×C4×C4711yescharacteristic
564C22×C4C24×C4711yescharacteristic
565M16—44no—
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—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—44no—
589C2×C8C2×D4×C4712yes—
590C2×C8C2×D4×C4712yes—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—41no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4M16×C4714yescomplemented
606C42—22no—
607C42—22no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42C2×D4×C4712yes—
615C42#41×C4712yes—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23C2×M16×C4712yes—
636C23#131×C4712yes—
637C23C23×C4×C4711yescharacteristic
638D4—44no—
639D4—44no—
640D4—44no—
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—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4C4×D4×C4712yes—
685C2×C4C4×D4×C4712yes—
686C2×C4C2×M16×C4712yes—
687C2×C4C2×M16×C4712yes—
688C2×C4C22×D4×C4711yescharacteristic
689C2×C4C2×#41×C4711yescharacteristic
690C2×C4H(5,𝔽2)×C4711yescharacteristic
691C2×C4H(5,𝔽2)×C4711yescharacteristic
692C2×C4H(5,𝔽2)×C4711yescharacteristic
693C2×C42−1+4×C4711yescharacteristic
694C8—22no—
695C8—22no—
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—41no—
701C8—41no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×C4×D4×C4711yescharacteristic
724C22C47×#51811yescharacteristic
725C22C47×#52011yescharacteristic
726C22C22×M16×C4711yescharacteristic
727C22C2×#131×C4711yescharacteristic
728C22C47×#56811yescharacteristic
729C22C47×#56811yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—22no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4C47×#53511yescharacteristic
742C4C47×#53711yescharacteristic
743C4C47×#54011yescharacteristic
744C4C47×#54211yescharacteristic
745C2—42no—
746C2—42no—
747C2—81no—
748C2C47×#232411yescharacteristic
749C2C47×#293311yescharacteristic
750C2D4×M16×C4711yescharacteristic
751C2C47×#297411yescharacteristic
752C2C47×#298011yescharacteristic
753C2C47×#298911yescharacteristic
754C2C47×#299211yescharacteristic
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
1. C2×C47×#435C2semidirect
2. C2×C47×#432C2semidirect
4. C47×#1955C2semidirect
5. C47×#1955C2semidirect
6. C47×#1954C2semidirect
7. C47×#1940C2semidirect
8. C47×#1924C2semidirect
9. C47×#1923C2semidirect
10. C47×#1870C2semidirect
11. C47×#1869C2semidirect
12. C47×#1851C2semidirect
13. C47×#1850C2semidirect
14. C47×#1797C2semidirect
15. C47×#1771C2semidirect
131. #97×C47D4semidirect
227. C22⋊C4×C47M16semidirect
324. #22141C47direct (N × H)
368. C2×#435C2×C47semidirect
369. C2×#432C2×C47semidirect
371. #1955C2×C47semidirect
372. #1955C2×C47semidirect
373. #1954C2×C47semidirect
374. #1940C2×C47semidirect
375. #1924C2×C47semidirect
376. #1923C2×C47semidirect
377. #1870C2×C47semidirect
378. #1869C2×C47semidirect
379. #1851C2×C47semidirect
380. #1850C2×C47semidirect
381. #1797C2×C47semidirect
382. #1771C2×C47semidirect
438. C47#22141direct (N × H)
509. #97D4×C47semidirect
605. C22⋊C4M16×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×#4322
C4×#121×C472
C47×#19552
C47×#19542
C47×#19402
C47×#19242
C47×#19232
C47×#18702
C47×#18692
C47×#18512
C47×#18502
C47×#17972
C47×#17712
#2214147