Finite Group Databasebeta

← C2×C47×#2425 #26074365

Subgroups — C2×C47×#2425 #26074365

Order 12032.

3938 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C47C211yesmaximal, characteristic, complemented
2C22×#123×C47C211yesmaximal, characteristic, complemented
3C22×#121×C47C211yesmaximal, characteristic
4C22×C4×D4×C47C211yesmaximal, characteristic, complemented
5C47×#2425C2116yesmaximal, direct product factor
6C2×C47×#398C211yesmaximal, characteristic, complemented
7C2×C47×#397C211yesmaximal, characteristic, complemented
8C2×C47×#396C211yesmaximal, characteristic, complemented
9C2×C47×#394C211yesmaximal, characteristic, complemented
10C2×C47×#389C211yesmaximal, characteristic, complemented
11C2×C47×#388C211yesmaximal, characteristic, complemented
12C2×C47×#386C211yesmaximal, characteristic, complemented
13C2×C47×#386C211yesmaximal, characteristic, complemented
14C2×C47×#385C211yesmaximal, characteristic, complemented
15C2×C47×#380C211yesmaximal, characteristic, complemented
16C22×#95×C47C211yesmaximal, characteristic, complemented
17C23×D4×C47C2211yescharacteristic
18C23×D4×C47C2211yescharacteristic
19C23×D4×C47C2211yescharacteristic
20C24×C4×C47C2211yescharacteristic
21C24×C4×C47C2211yescharacteristic
22C24×C4×C47C2211yescharacteristic
23C24×C4×C47C2211yescharacteristic
24C2×#123×C47—28no—
25C2×#123×C47—28no—
26C2×#123×C47C2218yescomplemented
27C2×#123×C47C2218yescomplemented
28C2×#121×C47—28no—
29C2×#121×C47C2218yes—
30C2×C4×D4×C47—28no—
31C2×C4×D4×C47C2218yescomplemented
32C22×C4⋊C4×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C22×C4⋊C4×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2211yescharacteristic
40C22×C22⋊C4×C47C2211yescharacteristic
41C22×C22⋊C4×C47C2211yescharacteristic
42C22×C22⋊C4×C47C2211yescharacteristic
43C22×C22⋊C4×C47C2211yescharacteristic
44C22×C22⋊C4×C47C2211yescharacteristic
45C22×C22⋊C4×C47C2211yescharacteristic
46C22×C22⋊C4×C47C2211yescharacteristic
47C22×C22⋊C4×C47C2211yescharacteristic
48C22×C22⋊C4×C47C2211yescharacteristic
49C22×C22⋊C4×C47C2211yescharacteristic
50C22×C22⋊C4×C47C2211yescharacteristic
51C22×C42×C47C2211yescharacteristic
52C47×#398C2218yescomplemented
53C47×#397C2218yescomplemented
54C47×#396C2218yescomplemented
55C47×#394C2218yescomplemented
56C47×#389C2218yescomplemented
57C47×#388C2218yescomplemented
58C47×#386C2218yescomplemented
59C47×#386C2218yescomplemented
60C47×#385C2218yescomplemented
61C47×#380C2218yescomplemented
62C2×#95×C47C2211yescharacteristic
63C2×#95×C47C2211yescharacteristic
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C2×#95×C47C2218yescomplemented
71C25×C47C2311yescharacteristic
72C25×C47C2311yescharacteristic
73C25×C47C2311yescharacteristic
74C22×D4×C47—24no—
75C22×D4×C47—24no—
76C22×D4×C47—24no—
77C22×D4×C47—24no—
78C22×D4×C47—24no—
79C22×D4×C47—24no—
80C22×D4×C47—24no—
81C22×D4×C47—42no—
82C22×D4×C47D418yes—
83C22×D4×C47C2314yes—
84C22×D4×C47C2314yes—
85C22×D4×C47C2314yes—
86C23×C4×C47—24no—
87C23×C4×C47—24no—
88C23×C4×C47—24no—
89C23×C4×C47—24no—
90C23×C4×C47—24no—
91C23×C4×C47—24no—
92C23×C4×C47—24no—
93C23×C4×C47—24no—
94C23×C4×C47—24no—
95C23×C4×C47—42no—
96C23×C4×C47—42no—
97C23×C4×C47—42no—
98C23×C4×C47C2314yes—
99C23×C4×C47C2311yescharacteristic
100C23×C4×C47C2311yescharacteristic
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2314yes—
107C23×C4×C47C2314yes—
108C23×C4×C47C2314yes—
109C23×C4×C47C2311yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C23×C4×C47C2311yescharacteristic
112C23×C4×C47C2311yescharacteristic
113C23×C4×C47C2311yescharacteristic
114#123×C47—232no—
115#123×C47—232no—
116#121×C47—232no—
117C4×D4×C47—232no—
118C2×C4⋊C4×C47—24no—
119C2×C4⋊C4×C47—24no—
120C2×C4⋊C4×C47—24no—
121C2×C4⋊C4×C47—24no—
122C2×C4⋊C4×C47—24no—
123C2×C4⋊C4×C47—24no—
124C2×C4⋊C4×C47—24no—
125C2×C4⋊C4×C47—42no—
126C2×C4⋊C4×C47C2314yes—
127C2×C4⋊C4×C47C2314yes—
128C2×C4⋊C4×C47C2314yes—
129C2×C4⋊C4×C47C2314yes—
130C2×C4⋊C4×C47C2314yes—
131C2×C4⋊C4×C47C2314yes—
132C2×C4⋊C4×C47C2314yes—
133C2×C4⋊C4×C47C2314yes—
134C2×C22⋊C4×C47—24no—
135C2×C22⋊C4×C47—24no—
136C2×C22⋊C4×C47—24no—
137C2×C22⋊C4×C47—24no—
138C2×C22⋊C4×C47—24no—
139C2×C22⋊C4×C47—24no—
140C2×C22⋊C4×C47—24no—
141C2×C22⋊C4×C47—24no—
142C2×C22⋊C4×C47—24no—
143C2×C22⋊C4×C47—42no—
144C2×C22⋊C4×C47D418yescomplemented
145C2×C22⋊C4×C47C2314yes—
146C2×C22⋊C4×C47C2314yes—
147C2×C22⋊C4×C47C2314yes—
148C2×C22⋊C4×C47C2314yes—
149C2×C22⋊C4×C47C2314yes—
150C2×C22⋊C4×C47C2314yes—
151C2×C22⋊C4×C47C2314yes—
152C2×C22⋊C4×C47C2314yes—
153C2×C22⋊C4×C47C2314yes—
154C2×C22⋊C4×C47C2314yes—
155C2×C22⋊C4×C47C2314yes—
156C2×C42×C47—24no—
157C2×C42×C47C2314yes—
158#95×C47C2314yes—
159#95×C47C2314yes—
160#95×C47C2314yes—
161#95×C47C2314yes—
162#95×C47C2314yes—
163#95×C47C2314yes—
164#95×C47C2314yes—
165#95×C47C2314yes—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47—22no—
171C24×C47—22no—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47—22no—
179C24×C47—22no—
180C24×C47—22no—
181C24×C47—22no—
182C24×C47—22no—
183C24×C47C2×D414yes—
184C24×C47C2×D414yes—
185C24×C47C2×D414yes—
186C24×C47#4114yes—
187C24×C47C2412yes—
188C24×C47C2412yes—
189C24×C47C2412yes—
190C24×C47C2411yescharacteristic
191C2×D4×C47—232no—
192C2×D4×C47—28no—
193C2×D4×C47—28no—
194C2×D4×C47—28no—
195C2×D4×C47—28no—
196C2×D4×C47—28no—
197C2×D4×C47—28no—
198C2×D4×C47—28no—
199C2×D4×C47—44no—
200C2×D4×C47—416no—
201C2×D4×C47—416no—
202C2×D4×C47C2×D4116yes—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
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—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—28no—
224C22×C4×C47—28no—
225C22×C4×C47—28no—
226C22×C4×C47—28no—
227C22×C4×C47—22no—
228C22×C4×C47—22no—
229C22×C4×C47—28no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47—22no—
235C22×C4×C47—22no—
236C22×C4×C47—22no—
237C22×C4×C47—22no—
238C22×C4×C47—22no—
239C22×C4×C47—28no—
240C22×C4×C47—28no—
241C22×C4×C47—28no—
242C22×C4×C47—28no—
243C22×C4×C47—44no—
244C22×C4×C47—44no—
245C22×C4×C47—44no—
246C22×C4×C47—416no—
247C22×C4×C47—416no—
248C22×C4×C47—416no—
249C22×C4×C47—416no—
250C22×C4×C47C2×D414yes—
251C22×C4×C47C2×D414yes—
252C22×C4×C47C2×D414yes—
253C22×C4×C47#4114yes—
254C22×C4×C47#4114yes—
255C22×C4×C47C2412yes—
256C22×C4×C47C2412yes—
257C22×C4×C47C2412yes—
258C22×C4×C47C2412yes—
259C22×C4×C47C2412yes—
260C22×C4×C47C2412yes—
261C22×C4×C47C2412yes—
262C22×C4×C47C2412yes—
263C22×C4×C47C2412yes—
264C22×C4×C47C2412yes—
265C22×C4×C47C2412yes—
266C22×C4×C47C2412yes—
267C4⋊C4×C47—28no—
268C4⋊C4×C47—28no—
269C4⋊C4×C47—28no—
270C4⋊C4×C47—28no—
271C4⋊C4×C47—28no—
272C4⋊C4×C47—28no—
273C4⋊C4×C47—28no—
274C4⋊C4×C47—44no—
275C22⋊C4×C47—28no—
276C22⋊C4×C47—28no—
277C22⋊C4×C47—28no—
278C22⋊C4×C47—28no—
279C22⋊C4×C47—28no—
280C22⋊C4×C47—28no—
281C22⋊C4×C47—28no—
282C22⋊C4×C47—28no—
283C22⋊C4×C47—28no—
284C22⋊C4×C47—44no—
285C22⋊C4×C47C2×D4116yescomplemented
286C42×C47—28no—
287C23×C47—28no—
288C23×C47—28no—
289C23×C47—28no—
290C23×C47—28no—
291C23×C47—28no—
292C23×C47—28no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—28no—
298C23×C47—28no—
299C23×C47—28no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—44no—
314C23×C47—44no—
315C23×C47—44no—
316C23×C47—44no—
317C23×C47—44no—
318C23×C47—44no—
319C23×C47—44no—
320C23×C47—44no—
321C23×C47—44no—
322C23×C47—44no—
323C23×C47—44no—
324C23×C47#121116yes—
325C23×C47C22×D414yes—
326C23×C47C22×D414yes—
327C23×C47C22×D414yes—
328C23×C47C22×D412yes—
329C23×C47C22×D412yes—
330C23×C47C2×#4114yes—
331C23×C47C2×#4112yes—
332C23×C47C2×#4112yes—
333C23×C47C2×#4112yes—
334C23×C47H(5,𝔽2)12yes—
335C23×C472−1+412yes—
336C23×C47C2511yescharacteristic
337D4×C47—232no—
338D4×C47—416no—
339D4×C47—416no—
340C2×C4×C47—28no—
341C2×C4×C47—28no—
342C2×C4×C47—28no—
343C2×C4×C47—28no—
344C2×C4×C47—28no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—416no—
377C2×C4×C47—416no—
378C2×C4×C47—416no—
379C2×C4×C47—416no—
380C2×C4×C47—44no—
381C2×C4×C47—44no—
382C2×C4×C47—44no—
383C2×C4×C47—44no—
384C2×C4×C47—44no—
385C2×C4×C47—44no—
386C2×C4×C47—44no—
387C2×C4×C47C22×D414yes—
388C2×C4×C47C22×D414yes—
389C2×C4×C47C22×D414yes—
390C2×C4×C47C2×#4114yes—
391C2×C4×C47C2×#4114yes—
392C2×#2425C4711yesmaximal, characteristic, direct product factor, Sylow
393C22×C47—24no—
394C22×C47—232no—
395C22×C47—24no—
396C22×C47—24no—
397C22×C47—24no—
398C22×C47—24no—
399C22×C47—24no—
400C22×C47—24no—
401C22×C47—24no—
402C22×C47—24no—
403C22×C47—42no—
404C22×C47—416no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—42no—
408C22×C47—42no—
409C22×C47—42no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47—42no—
413C22×C47—42no—
414C22×C47—42no—
415C22×C47—88no—
416C22×C47C2×#12118yes—
417C22×C47C2×#12114yes—
418C22×C47#52914yes—
419C22×C47#53914yes—
420C22×C47#54614yes—
421C22×C47#54614yes—
422C22×C47#54714yes—
423C22×C47#54714yes—
424C22×C47C23×D411yescharacteristic
425C22×C47C23×D411yescharacteristic
426C22×C47C22×#4111yescharacteristic
427C22×C47C22×#4111yescharacteristic
428C22×C47C22×#4111yescharacteristic
429C22×C47C2×H(5,𝔽2)11yescharacteristic
430C22×C47C2×2−1+411yescharacteristic
431C4×C47—24no—
432C4×C47—24no—
433C4×C47—24no—
434C4×C47—24no—
435C4×C47—24no—
436C4×C47—42no—
437C4×C47—42no—
438C4×C47—42no—
439C4×C47—42no—
440C4×C47—42no—
441C4×C47—42no—
442C4×C47—42no—
443C22×#123C2×C4711yescharacteristic, complemented
444C22×#123C2×C4711yescharacteristic, complemented
445C22×#121C2×C4711yescharacteristic
446C22×C4×D4C2×C4711yescharacteristic, complemented
447#2425C2×C47116yesdirect product factor
448C2×#398C2×C4711yescharacteristic, complemented
449C2×#397C2×C4711yescharacteristic, complemented
450C2×#396C2×C4711yescharacteristic, complemented
451C2×#394C2×C4711yescharacteristic, complemented
452C2×#389C2×C4711yescharacteristic, complemented
453C2×#388C2×C4711yescharacteristic, complemented
454C2×#386C2×C4711yescharacteristic, complemented
455C2×#386C2×C4711yescharacteristic, complemented
456C2×#385C2×C4711yescharacteristic, complemented
457C2×#380C2×C4711yescharacteristic, complemented
458C22×#95C2×C4711yescharacteristic, complemented
459C2×C47—28no—
460C2×C47—44no—
461C2×C47—82no—
462C2×C47#242518yesdirect product factor
463C2×C47C22×#12111yescharacteristic
464C2×C47C2×#52911yescharacteristic
465C2×C47C2×#53911yescharacteristic
466C2×C47C2×#54611yescharacteristic
467C2×C47C2×#54611yescharacteristic
468C2×C47C2×#54711yescharacteristic
469C2×C47C2×#54711yescharacteristic
470C23×D4C22×C4711yescharacteristic
471C23×D4C22×C4711yescharacteristic
472C23×D4C22×C4711yescharacteristic
473C24×C4C22×C4711yescharacteristic
474C24×C4C22×C4711yescharacteristic
475C24×C4C22×C4711yescharacteristic
476C24×C4C22×C4711yescharacteristic
477C2×#123—28no—
478C2×#123—28no—
479C2×#123C22×C4718yescomplemented
480C2×#123C22×C4718yescomplemented
481C2×#121—28no—
482C2×#121C22×C4718yes—
483C2×C4×D4—28no—
484C2×C4×D4C22×C4718yescomplemented
485C22×C4⋊C4C22×C4711yescharacteristic
486C22×C4⋊C4C22×C4711yescharacteristic
487C22×C4⋊C4C22×C4711yescharacteristic
488C22×C4⋊C4C22×C4711yescharacteristic
489C22×C4⋊C4C22×C4711yescharacteristic
490C22×C4⋊C4C22×C4711yescharacteristic
491C22×C4⋊C4C22×C4711yescharacteristic
492C22×C4⋊C4C22×C4711yescharacteristic
493C22×C22⋊C4C22×C4711yescharacteristic
494C22×C22⋊C4C22×C4711yescharacteristic
495C22×C22⋊C4C22×C4711yescharacteristic
496C22×C22⋊C4C22×C4711yescharacteristic
497C22×C22⋊C4C22×C4711yescharacteristic
498C22×C22⋊C4C22×C4711yescharacteristic
499C22×C22⋊C4C22×C4711yescharacteristic
500C22×C22⋊C4C22×C4711yescharacteristic
501C22×C22⋊C4C22×C4711yescharacteristic
502C22×C22⋊C4C22×C4711yescharacteristic
503C22×C22⋊C4C22×C4711yescharacteristic
504C22×C42C22×C4711yescharacteristic
505#398C22×C4718yescomplemented
506#397C22×C4718yescomplemented
507#396C22×C4718yescomplemented
508#394C22×C4718yescomplemented
509#389C22×C4718yescomplemented
510#388C22×C4718yescomplemented
511#386C22×C4718yescomplemented
512#386C22×C4718yescomplemented
513#385C22×C4718yescomplemented
514#380C22×C4718yescomplemented
515C2×#95C22×C4711yescharacteristic
516C2×#95C22×C4711yescharacteristic
517C2×#95C22×C4711yescharacteristic
518C2×#95C22×C4711yescharacteristic
519C2×#95C22×C4711yescharacteristic
520C2×#95C22×C4711yescharacteristic
521C2×#95C22×C4711yescharacteristic
522C2×#95C22×C4711yescharacteristic
523C2×#95C22×C4718yescomplemented
524C47C2×#242511yescharacteristic, direct product factor, Sylow
525C25C23×C4711yescharacteristic
526C25C23×C4711yescharacteristic
527C25C23×C4711yescharacteristic
528C22×D4—24no—
529C22×D4—24no—
530C22×D4—24no—
531C22×D4—24no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—24no—
535C22×D4—42no—
536C22×D4D4×C4718yes—
537C22×D4C23×C4714yes—
538C22×D4C23×C4714yes—
539C22×D4C23×C4714yes—
540C23×C4—24no—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—24no—
546C23×C4—24no—
547C23×C4—24no—
548C23×C4—24no—
549C23×C4—42no—
550C23×C4—42no—
551C23×C4—42no—
552C23×C4C23×C4711yescharacteristic
553C23×C4C23×C4711yescharacteristic
554C23×C4C23×C4711yescharacteristic
555C23×C4C23×C4711yescharacteristic
556C23×C4C23×C4711yescharacteristic
557C23×C4C23×C4711yescharacteristic
558C23×C4C23×C4711yescharacteristic
559C23×C4C23×C4714yes—
560C23×C4C23×C4714yes—
561C23×C4C23×C4714yes—
562C23×C4C23×C4714yes—
563C23×C4C23×C4711yescharacteristic
564C23×C4C23×C4711yescharacteristic
565C23×C4C23×C4711yescharacteristic
566C23×C4C23×C4711yescharacteristic
567C23×C4C23×C4711yescharacteristic
568#123—232no—
569#123—232no—
570#121—232no—
571C4×D4—232no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—42no—
580C2×C4⋊C4C23×C4714yes—
581C2×C4⋊C4C23×C4714yes—
582C2×C4⋊C4C23×C4714yes—
583C2×C4⋊C4C23×C4714yes—
584C2×C4⋊C4C23×C4714yes—
585C2×C4⋊C4C23×C4714yes—
586C2×C4⋊C4C23×C4714yes—
587C2×C4⋊C4C23×C4714yes—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4D4×C4718yescomplemented
599C2×C22⋊C4C23×C4714yes—
600C2×C22⋊C4C23×C4714yes—
601C2×C22⋊C4C23×C4714yes—
602C2×C22⋊C4C23×C4714yes—
603C2×C22⋊C4C23×C4714yes—
604C2×C22⋊C4C23×C4714yes—
605C2×C22⋊C4C23×C4714yes—
606C2×C22⋊C4C23×C4714yes—
607C2×C22⋊C4C23×C4714yes—
608C2×C22⋊C4C23×C4714yes—
609C2×C22⋊C4C23×C4714yes—
610C2×C42—24no—
611C2×C42C23×C4714yes—
612#95C23×C4714yes—
613#95C23×C4714yes—
614#95C23×C4714yes—
615#95C23×C4714yes—
616#95C23×C4714yes—
617#95C23×C4714yes—
618#95C23×C4714yes—
619#95C23×C4714yes—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24C2×D4×C4714yes—
638C24C2×D4×C4714yes—
639C24C2×D4×C4714yes—
640C24#41×C4714yes—
641C24C24×C4712yes—
642C24C24×C4712yes—
643C24C24×C4712yes—
644C24C24×C4711yescharacteristic
645C2×D4—232no—
646C2×D4—28no—
647C2×D4—28no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—44no—
654C2×D4—416no—
655C2×D4—416no—
656C2×D4C2×D4×C47116yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—28no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—28no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—416no—
701C22×C4—416no—
702C22×C4—416no—
703C22×C4—416no—
704C22×C4C2×D4×C4714yes—
705C22×C4C2×D4×C4714yes—
706C22×C4C2×D4×C4714yes—
707C22×C4#41×C4714yes—
708C22×C4#41×C4714yes—
709C22×C4C24×C4712yes—
710C22×C4C24×C4712yes—
711C22×C4C24×C4712yes—
712C22×C4C24×C4712yes—
713C22×C4C24×C4712yes—
714C22×C4C24×C4712yes—
715C22×C4C24×C4712yes—
716C22×C4C24×C4712yes—
717C22×C4C24×C4712yes—
718C22×C4C24×C4712yes—
719C22×C4C24×C4712yes—
720C22×C4C24×C4712yes—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—44no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—28no—
736C22⋊C4—28no—
737C22⋊C4—28no—
738C22⋊C4—44no—
739C22⋊C4C2×D4×C47116yescomplemented
740C42—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23#121×C47116yes—
779C23C22×D4×C4714yes—
780C23C22×D4×C4714yes—
781C23C22×D4×C4714yes—
782C23C22×D4×C4712yes—
783C23C22×D4×C4712yes—
784C23C2×#41×C4714yes—
785C23C2×#41×C4712yes—
786C23C2×#41×C4712yes—
787C23C2×#41×C4712yes—
788C23H(5,𝔽2)×C4712yes—
789C232−1+4×C4712yes—
790C23C25×C4711yescharacteristic
791D4—232no—
792D4—416no—
793D4—416no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—416no—
831C2×C4—416no—
832C2×C4—416no—
833C2×C4—416no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4C22×D4×C4714yes—
842C2×C4C22×D4×C4714yes—
843C2×C4C22×D4×C4714yes—
844C2×C4C2×#41×C4714yes—
845C2×C4C2×#41×C4714yes—
846C22—24no—
847C22—232no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—416no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—88no—
869C22C2×#121×C4718yes—
870C22C2×#121×C4714yes—
871C22C47×#52914yes—
872C22C47×#53914yes—
873C22C47×#54614yes—
874C22C47×#54614yes—
875C22C47×#54714yes—
876C22C47×#54714yes—
877C22C23×D4×C4711yescharacteristic
878C22C23×D4×C4711yescharacteristic
879C22C22×#41×C4711yescharacteristic
880C22C22×#41×C4711yescharacteristic
881C22C22×#41×C4711yescharacteristic
882C22C2×H(5,𝔽2)×C4711yescharacteristic
883C22C2×2−1+4×C4711yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—24no—
889C4—42no—
890C4—42no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—42no—
896C2—28no—
897C2—44no—
898C2—82no—
899C2C47×#242518yesdirect product factor
900C2C22×#121×C4711yescharacteristic
901C2C2×C47×#52911yescharacteristic
902C2C2×C47×#53911yescharacteristic
903C2C2×C47×#54611yescharacteristic
904C2C2×C47×#54611yescharacteristic
905C2C2×C47×#54711yescharacteristic
906C2C2×C47×#54711yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC23C25×C47
prime radicalC22×#121×C47C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#123×C47C2semidirect
2. C22×#123×C47C2semidirect
4. C22×C4×D4×C47C2semidirect
5. C47×#2425C2direct (N × H)
6. C2×C47×#398C2semidirect
7. C2×C47×#397C2semidirect
8. C2×C47×#396C2semidirect
9. C2×C47×#394C2semidirect
10. C2×C47×#389C2semidirect
11. C2×C47×#388C2semidirect
12. C2×C47×#386C2semidirect
13. C2×C47×#386C2semidirect
14. C2×C47×#385C2semidirect
15. C2×C47×#380C2semidirect
16. C22×#95×C47C2semidirect
26. C2×#123×C47C22semidirect
27. C2×#123×C47C22semidirect
31. C2×C4×D4×C47C22semidirect
52. C47×#398C22semidirect
53. C47×#397C22semidirect
54. C47×#396C22semidirect
55. C47×#394C22semidirect
56. C47×#389C22semidirect
57. C47×#388C22semidirect
58. C47×#386C22semidirect
59. C47×#386C22semidirect
60. C47×#385C22semidirect
61. C47×#380C22semidirect
70. C2×#95×C47C22semidirect
144. C2×C22⋊C4×C47D4semidirect
285. C22⋊C4×C47C2×D4semidirect
392. C2×#2425C47direct (N × H)
443. C22×#123C2×C47semidirect
444. C22×#123C2×C47semidirect
446. C22×C4×D4C2×C47semidirect
447. #2425C2×C47direct (N × H)
448. C2×#398C2×C47semidirect
449. C2×#397C2×C47semidirect
450. C2×#396C2×C47semidirect
451. C2×#394C2×C47semidirect
452. C2×#389C2×C47semidirect
453. C2×#388C2×C47semidirect
454. C2×#386C2×C47semidirect
455. C2×#386C2×C47semidirect
456. C2×#385C2×C47semidirect
457. C2×#380C2×C47semidirect
458. C22×#95C2×C47semidirect
462. C2×C47#2425direct (N × H)
479. C2×#123C22×C47semidirect
480. C2×#123C22×C47semidirect
484. C2×C4×D4C22×C47semidirect
505. #398C22×C47semidirect
506. #397C22×C47semidirect
507. #396C22×C47semidirect
508. #394C22×C47semidirect
509. #389C22×C47semidirect
510. #388C22×C47semidirect
511. #386C22×C47semidirect
512. #386C22×C47semidirect
513. #385C22×C47semidirect
514. #380C22×C47semidirect
523. C2×#95C22×C47semidirect
524. C47C2×#2425direct (N × H)
598. C2×C22⋊C4D4×C47semidirect
739. C22⋊C4C2×D4×C47semidirect
899. C2C47×#2425direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C472
C22×#121×C472
C22×C4×D4×C472
C47×#24252
C2×C47×#3982
C2×C47×#3972
C2×C47×#3962
C2×C47×#3942
C2×C47×#3892
C2×C47×#3882
C2×C47×#3862
C2×C47×#3852
C2×C47×#3802
C22×#95×C472
C2×#242547