Finite Group Databasebeta

← C47×#21599 #26061297

Subgroups — C47×#21599 #26061297

Order 12032.

898 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#446C211yesmaximal, characteristic, complemented
2C22×#97×C47C211yesmaximal, characteristic
3C4×C22⋊Q8×C47C211yesmaximal, characteristic
4C47×#1985C211yesmaximal, characteristic, complemented
5C47×#1940C211yesmaximal, characteristic, complemented
6C47×#1917C211yesmaximal, characteristic, complemented
7C47×#1917C211yesmaximal, characteristic, complemented
8C47×#1850C211yesmaximal, characteristic
9C47×#1850C211yesmaximal, characteristic
10C47×#1797C211yesmaximal, characteristic
11C47×#1771C211yesmaximal, characteristic, complemented
12C47×#1771C211yesmaximal, characteristic, complemented
13C47×#1770C211yesmaximal, characteristic, complemented
14C47×#1752C211yesmaximal, characteristic
15C8×C22⋊C4×C47C211yesmaximal, characteristic
16C23×C8×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C2×C22⋊Q8×C47C411yescharacteristic
19C2×C4×Q8×C47C2211yescharacteristic
20C22×C42×C47C2211yescharacteristic
21C47×#446—24no—
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×C22⋊C8×C47C2211yescharacteristic
29C2×C22⋊C8×C47C2211yescharacteristic
30C2×#97×C47—24no—
31C2×#97×C47C2211yescharacteristic
32C2×#97×C47C2211yescharacteristic
33C2×#97×C47C2211yescharacteristic
34C2×#97×C47C2211yescharacteristic
35C2×#97×C47C2211yescharacteristic
36C2×#97×C47C2211yescharacteristic
37C2×C4×C8×C47C2211yescharacteristic
38C2×C4×C8×C47C2211yescharacteristic
39C47×#391C411yescharacteristic
40C47×#389C411yescharacteristic
41C47×#387C411yescharacteristic
42C47×#387C411yescharacteristic
43C47×#385C411yescharacteristic
44C47×#385C411yescharacteristic
45C47×#380C411yescharacteristic
46C4×C4⋊C4×C47C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C4×C4⋊C4×C47C2211yescharacteristic
49C4×C22⋊C4×C47C2211yescharacteristic
50C4×C22⋊C4×C47C2211yescharacteristic
51C47×#336C2211yescharacteristic
52C47×#336C2211yescharacteristic
53C47×#336C2211yescharacteristic
54C47×#336C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×Q8×C47C2×C411yescharacteristic
62C23×C4×C47C2×C411yescharacteristic
63C23×C4×C47C2×C411yescharacteristic
64C23×C4×C47C2311yescharacteristic
65C22×C8×C47—22no—
66C22×C8×C47—22no—
67C22×C8×C47—22no—
68C22×C8×C47—22no—
69C22×C8×C47—22no—
70C22×C8×C47Q814yescomplemented
71C22×C8×C47C2311yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22⋊Q8×C47—24no—
80C4×Q8×C47—22no—
81C4×Q8×C47—22no—
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×C4⋊C4×C47C2×C411yescharacteristic
91C2×C22⋊C4×C47C2×C411yescharacteristic
92C2×C22⋊C4×C47C2×C411yescharacteristic
93C2×C22⋊C4×C47C2×C411yescharacteristic
94C2×C22⋊C4×C47C2×C411yescharacteristic
95C2×C42×C47—22no—
96C2×C42×C47—22no—
97C2×C42×C47C2×C411yescharacteristic
98C2×C42×C47C2×C411yescharacteristic
99C2×C42×C47C2311yescharacteristic
100C2×C42×C47C2311yescharacteristic
101C2×C42×C47C2311yescharacteristic
102C2×C42×C47C2311yescharacteristic
103C2×C42×C47C2311yescharacteristic
104C2×C42×C47C2311yescharacteristic
105C4⋊C8×C47—22no—
106C4⋊C8×C47—22no—
107C4⋊C8×C47—22no—
108C4⋊C8×C47—22no—
109C4⋊C8×C47—22no—
110C4⋊C8×C47—22no—
111C22⋊C8×C47—22no—
112C22⋊C8×C47—22no—
113#97×C47—22no—
114#97×C47—22no—
115#97×C47—22no—
116#97×C47—22no—
117#97×C47—22no—
118#97×C47D414yes—
119C4×C8×C47—22no—
120C4×C8×C47—22no—
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
130#95×C47C2×C411yescharacteristic
131C24×C47C22×C411yescharacteristic
132C2×Q8×C47—22no—
133C2×Q8×C47—22no—
134C2×Q8×C47—41no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—41no—
144C22×C4×C47—41no—
145C22×C4×C47C22×C411yescharacteristic
146C22×C4×C47C22×C411yescharacteristic
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C22×C411yescharacteristic
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C22×C411yescharacteristic
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C22×C411yescharacteristic
158C22×C4×C47C2×Q812yes—
159C22×C4×C47#4112yes—
160C22×C4×C47C2411yescharacteristic
161C2×C8×C47—28no—
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—28no—
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—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47C2×D412yes—
182C2×C8×C47C2×D412yes—
183C2×C8×C47C2×Q812yes—
184C2×C8×C47C2×Q812yes—
185C2×C8×C47#4112yes—
186C2×C8×C47#4112yes—
187C4⋊C4×C47—22no—
188C4⋊C4×C47—22no—
189C4⋊C4×C47—22no—
190C4⋊C4×C47—22no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—41no—
194C4⋊C4×C47—41no—
195C4⋊C4×C47—41no—
196C22⋊C4×C47—22no—
197C22⋊C4×C47—22no—
198C22⋊C4×C47—22no—
199C22⋊C4×C47M1614yes—
200C42×C47—22no—
201C42×C47—22no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47—21no—
205C42×C47—21no—
206C42×C47—21no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47—21no—
212C42×C47C2×D412yes—
213C42×C47#4112yes—
214C23×C47—21no—
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47C4×Q812yes—
219C23×C47C2×M1612yes—
220C23×C47#13112yes—
221C23×C47C23×C411yescharacteristic
222Q8×C47—44no—
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—22no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
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×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—44no—
262C2×C4×C47—44no—
263C2×C4×C47C4×D412yes—
264C2×C4×C47C4×D412yes—
265C2×C4×C47C4×Q812yes—
266C2×C4×C47C2×M1612yes—
267C2×C4×C47C2×M1612yes—
268C2×C4×C47C22×D411yescharacteristic
269C2×C4×C47C22×Q811yescharacteristic
270C2×C4×C47C2×#4111yescharacteristic
271C2×C4×C47C2×#4111yescharacteristic
272C2×C4×C47C2×#4111yescharacteristic
273C2×C4×C47C2×#4111yescharacteristic
274C8×C47—22no—
275C8×C47—22no—
276C8×C47—22no—
277C8×C47—41no—
278C8×C47—41no—
279C8×C47—41no—
280C8×C47—41no—
281C8×C47C22⋊Q814yescomplemented
282#21599C4711yesmaximal, characteristic, direct product factor, Sylow
283C22×C47—22no—
284C22×C47—22no—
285C22×C47—22no—
286C22×C47—22no—
287C22×C47—22no—
288C22×C47—22no—
289C22×C47#44614yescomplemented
290C22×C47C2×C4×D411yescharacteristic
291C22×C47C2×C4×Q811yescharacteristic
292C22×C47C4×#4111yescharacteristic
293C22×C47C22×M1611yescharacteristic
294C22×C47C2×#13111yescharacteristic
295C22×C47#56811yescharacteristic
296C22×C47#56811yescharacteristic
297C4×C47—22no—
298C4×C47—22no—
299C4×C47—22no—
300C4×C47—22no—
301C4×C47—22no—
302C4×C47—41no—
303C4×C47—41no—
304C4×C47—41no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47—41no—
308C4×C47—41no—
309C4×C47—41no—
310C4×C47C2×C22⋊Q811yescharacteristic
311C4×C47#52511yescharacteristic
312C4×C47#52911yescharacteristic
313C4×C47#53311yescharacteristic
314C2×#446C2×C4711yescharacteristic, complemented
315C22×#97C2×C4711yescharacteristic
316C4×C22⋊Q8C2×C4711yescharacteristic
317#1985C2×C4711yescharacteristic, complemented
318#1940C2×C4711yescharacteristic, complemented
319#1917C2×C4711yescharacteristic, complemented
320#1917C2×C4711yescharacteristic, complemented
321#1850C2×C4711yescharacteristic
322#1850C2×C4711yescharacteristic
323#1797C2×C4711yescharacteristic
324#1771C2×C4711yescharacteristic, complemented
325#1771C2×C4711yescharacteristic, complemented
326#1770C2×C4711yescharacteristic, complemented
327#1752C2×C4711yescharacteristic
328C8×C22⋊C4C2×C4711yescharacteristic
329C2×C47—24no—
330C2×C47C4×C22⋊Q811yescharacteristic
331C2×C47#293311yescharacteristic
332C2×C47D4×M1611yescharacteristic
333C2×C47C2×#44611yescharacteristic
334C2×C47#296111yescharacteristic
335C2×C47#296811yescharacteristic
336C2×C47#297011yescharacteristic
337C23×C8C22×C4711yescharacteristic
338C23×C8C22×C4711yescharacteristic
339C2×C22⋊Q8C4×C4711yescharacteristic
340C2×C4×Q8C22×C4711yescharacteristic
341C22×C42C22×C4711yescharacteristic
342#446—24no—
343C2×C4⋊C8C22×C4711yescharacteristic
344C2×C4⋊C8C22×C4711yescharacteristic
345C2×C4⋊C8C22×C4711yescharacteristic
346C2×C4⋊C8C22×C4711yescharacteristic
347C2×C4⋊C8C22×C4711yescharacteristic
348C2×C4⋊C8C22×C4711yescharacteristic
349C2×C22⋊C8C22×C4711yescharacteristic
350C2×C22⋊C8C22×C4711yescharacteristic
351C2×#97—24no—
352C2×#97C22×C4711yescharacteristic
353C2×#97C22×C4711yescharacteristic
354C2×#97C22×C4711yescharacteristic
355C2×#97C22×C4711yescharacteristic
356C2×#97C22×C4711yescharacteristic
357C2×#97C22×C4711yescharacteristic
358C2×C4×C8C22×C4711yescharacteristic
359C2×C4×C8C22×C4711yescharacteristic
360#391C4×C4711yescharacteristic
361#389C4×C4711yescharacteristic
362#387C4×C4711yescharacteristic
363#387C4×C4711yescharacteristic
364#385C4×C4711yescharacteristic
365#385C4×C4711yescharacteristic
366#380C4×C4711yescharacteristic
367C4×C4⋊C4C22×C4711yescharacteristic
368C4×C4⋊C4C22×C4711yescharacteristic
369C4×C4⋊C4C22×C4711yescharacteristic
370C4×C22⋊C4C22×C4711yescharacteristic
371C4×C22⋊C4C22×C4711yescharacteristic
372#336C22×C4711yescharacteristic
373#336C22×C4711yescharacteristic
374#336C22×C4711yescharacteristic
375#336C22×C4711yescharacteristic
376#336C22×C4711yescharacteristic
377#336C22×C4711yescharacteristic
378#336C22×C4711yescharacteristic
379#336C22×C4711yescharacteristic
380#336C22×C4711yescharacteristic
381#336C22×C4711yescharacteristic
382C47#2159911yescharacteristic, direct product factor, Sylow
383C22×Q8C2×C4×C4711yescharacteristic
384C23×C4C2×C4×C4711yescharacteristic
385C23×C4C2×C4×C4711yescharacteristic
386C23×C4C23×C4711yescharacteristic
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8Q8×C4714yescomplemented
393C22×C8C23×C4711yescharacteristic
394C22×C8C23×C4711yescharacteristic
395C22×C8C23×C4711yescharacteristic
396C22×C8C23×C4711yescharacteristic
397C22×C8C23×C4711yescharacteristic
398C22×C8C23×C4711yescharacteristic
399C22×C8C23×C4711yescharacteristic
400C22×C8C23×C4711yescharacteristic
401C22⋊Q8—24no—
402C4×Q8—22no—
403C4×Q8—22no—
404C2×C4⋊C4C2×C4×C4711yescharacteristic
405C2×C4⋊C4C2×C4×C4711yescharacteristic
406C2×C4⋊C4C2×C4×C4711yescharacteristic
407C2×C4⋊C4C2×C4×C4711yescharacteristic
408C2×C4⋊C4C2×C4×C4711yescharacteristic
409C2×C4⋊C4C2×C4×C4711yescharacteristic
410C2×C4⋊C4C2×C4×C4711yescharacteristic
411C2×C4⋊C4C2×C4×C4711yescharacteristic
412C2×C4⋊C4C2×C4×C4711yescharacteristic
413C2×C22⋊C4C2×C4×C4711yescharacteristic
414C2×C22⋊C4C2×C4×C4711yescharacteristic
415C2×C22⋊C4C2×C4×C4711yescharacteristic
416C2×C22⋊C4C2×C4×C4711yescharacteristic
417C2×C42—22no—
418C2×C42—22no—
419C2×C42C2×C4×C4711yescharacteristic
420C2×C42C2×C4×C4711yescharacteristic
421C2×C42C23×C4711yescharacteristic
422C2×C42C23×C4711yescharacteristic
423C2×C42C23×C4711yescharacteristic
424C2×C42C23×C4711yescharacteristic
425C2×C42C23×C4711yescharacteristic
426C2×C42C23×C4711yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—22no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433C22⋊C8—22no—
434C22⋊C8—22no—
435#97—22no—
436#97—22no—
437#97—22no—
438#97—22no—
439#97—22no—
440#97D4×C4714yes—
441C4×C8—22no—
442C4×C8—22no—
443#95C2×C4×C4711yescharacteristic
444#95C2×C4×C4711yescharacteristic
445#95C2×C4×C4711yescharacteristic
446#95C2×C4×C4711yescharacteristic
447#95C2×C4×C4711yescharacteristic
448#95C2×C4×C4711yescharacteristic
449#95C2×C4×C4711yescharacteristic
450#95C2×C4×C4711yescharacteristic
451#95C2×C4×C4711yescharacteristic
452#95C2×C4×C4711yescharacteristic
453C24C22×C4×C4711yescharacteristic
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—41no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4C22×C4×C4711yescharacteristic
468C22×C4C22×C4×C4711yescharacteristic
469C22×C4C22×C4×C4711yescharacteristic
470C22×C4C22×C4×C4711yescharacteristic
471C22×C4C22×C4×C4711yescharacteristic
472C22×C4C22×C4×C4711yescharacteristic
473C22×C4C22×C4×C4711yescharacteristic
474C22×C4C22×C4×C4711yescharacteristic
475C22×C4C22×C4×C4711yescharacteristic
476C22×C4C22×C4×C4711yescharacteristic
477C22×C4C22×C4×C4711yescharacteristic
478C22×C4C22×C4×C4711yescharacteristic
479C22×C4C22×C4×C4711yescharacteristic
480C22×C4C2×Q8×C4712yes—
481C22×C4#41×C4712yes—
482C22×C4C24×C4711yescharacteristic
483C2×C8—28no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—28no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8C2×D4×C4712yes—
504C2×C8C2×D4×C4712yes—
505C2×C8C2×Q8×C4712yes—
506C2×C8C2×Q8×C4712yes—
507C2×C8#41×C4712yes—
508C2×C8#41×C4712yes—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4M16×C4714yes—
522C42—22no—
523C42—22no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42C2×D4×C4712yes—
535C42#41×C4712yes—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23C4×Q8×C4712yes—
541C23C2×M16×C4712yes—
542C23#131×C4712yes—
543C23C23×C4×C4711yescharacteristic
544Q8—44no—
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—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4C4×D4×C4712yes—
586C2×C4C4×D4×C4712yes—
587C2×C4C4×Q8×C4712yes—
588C2×C4C2×M16×C4712yes—
589C2×C4C2×M16×C4712yes—
590C2×C4C22×D4×C4711yescharacteristic
591C2×C4C22×Q8×C4711yescharacteristic
592C2×C4C2×#41×C4711yescharacteristic
593C2×C4C2×#41×C4711yescharacteristic
594C2×C4C2×#41×C4711yescharacteristic
595C2×C4C2×#41×C4711yescharacteristic
596C8—22no—
597C8—22no—
598C8—22no—
599C8—41no—
600C8—41no—
601C8—41no—
602C8—41no—
603C8C22⋊Q8×C4714yescomplemented
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22C47×#44614yescomplemented
611C22C2×C4×D4×C4711yescharacteristic
612C22C2×C4×Q8×C4711yescharacteristic
613C22C4×#41×C4711yescharacteristic
614C22C22×M16×C4711yescharacteristic
615C22C2×#131×C4711yescharacteristic
616C22C47×#56811yescharacteristic
617C22C47×#56811yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—22no—
622C4—22no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4C2×C22⋊Q8×C4711yescharacteristic
632C4C47×#52511yescharacteristic
633C4C47×#52911yescharacteristic
634C4C47×#53311yescharacteristic
635C2—24no—
636C2C4×C22⋊Q8×C4711yescharacteristic
637C2C47×#293311yescharacteristic
638C2D4×M16×C4711yescharacteristic
639C2C2×C47×#44611yescharacteristic
640C2C47×#296111yescharacteristic
641C2C47×#296811yescharacteristic
642C2C47×#297011yescharacteristic
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
1. C2×C47×#446C2semidirect
4. C47×#1985C2semidirect
5. C47×#1940C2semidirect
6. C47×#1917C2semidirect
7. C47×#1917C2semidirect
11. C47×#1771C2semidirect
12. C47×#1771C2semidirect
13. C47×#1770C2semidirect
70. C22×C8×C47Q8semidirect
281. C8×C47C22⋊Q8semidirect
282. #21599C47direct (N × H)
289. C22×C47#446semidirect
314. C2×#446C2×C47semidirect
317. #1985C2×C47semidirect
318. #1940C2×C47semidirect
319. #1917C2×C47semidirect
320. #1917C2×C47semidirect
324. #1771C2×C47semidirect
325. #1771C2×C47semidirect
326. #1770C2×C47semidirect
382. C47#21599direct (N × H)
392. C22×C8Q8×C47semidirect
603. C8C22⋊Q8×C47semidirect
610. C22C47×#446semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4462
C22×#97×C472
C4×C22⋊Q8×C472
C47×#19852
C47×#19402
C47×#19172
C47×#18502
C47×#17972
C47×#17712
C47×#17702
C47×#17522
C8×C22⋊C4×C472
#2159947