Finite Group Databasebeta

← C2×C47×#2472 #26074356

Subgroups — C2×C47×#2472 #26074356

Order 12032.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C47C211yesmaximal, characteristic, complemented
2C22×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
3C22×#120×C47C211yesmaximal, characteristic
4C23×C22⋊C4×C47C211yesmaximal, characteristic, complemented
5C47×#2472C2116yesmaximal, direct product factor
6C2×C47×#397C211yesmaximal, characteristic, complemented
7C2×C47×#394C211yesmaximal, characteristic, complemented
8C2×C47×#394C211yesmaximal, characteristic, complemented
9C2×C47×#393C211yesmaximal, characteristic, complemented
10C2×C47×#390C211yesmaximal, characteristic, complemented
11C2×C47×#388C211yesmaximal, characteristic, complemented
12C2×C47×#388C211yesmaximal, characteristic, complemented
13C2×C47×#386C211yesmaximal, characteristic, complemented
14C2×C47×#386C211yesmaximal, characteristic, complemented
15C2×C47×#379C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
17C26×C47C2211yescharacteristic
18C23×Q8×C47C2211yescharacteristic, complemented
19C23×D4×C47C2211yescharacteristic
20C23×D4×C47C2211yescharacteristic
21C23×D4×C47C2211yescharacteristic
22C24×C4×C47C2211yescharacteristic
23C24×C4×C47C2211yescharacteristic
24C2×#124×C47—28no—
25C2×#124×C47C2218yescomplemented
26C2×C22⋊Q8×C47—28no—
27C2×C22⋊Q8×C47C2218yescomplemented
28C2×#120×C47—28no—
29C2×#120×C47C2218yes—
30C22×C4⋊C4×C47C2211yescharacteristic, complemented
31C22×C4⋊C4×C47C2211yescharacteristic, complemented
32C22×C4⋊C4×C47C2211yescharacteristic, complemented
33C22×C22⋊C4×C47—28no—
34C22×C22⋊C4×C47C2211yescharacteristic
35C22×C22⋊C4×C47C2211yescharacteristic
36C22×C22⋊C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C22×C22⋊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×C47C2218yescomplemented
48C22×C22⋊C4×C47C2211yescharacteristic, complemented
49C22×C22⋊C4×C47C2211yescharacteristic, complemented
50C22×C22⋊C4×C47C2211yescharacteristic, complemented
51C22×C22⋊C4×C47C2211yescharacteristic, complemented
52C22×C42×C47C2211yescharacteristic, complemented
53C22×C42×C47C2211yescharacteristic, complemented
54C47×#397C2218yescomplemented
55C47×#394C2218yescomplemented
56C47×#394C2218yescomplemented
57C47×#393C2218yescomplemented
58C47×#390C2218yescomplemented
59C47×#388C2218yescomplemented
60C47×#388C2218yescomplemented
61C47×#386C2218yescomplemented
62C47×#386C2218yescomplemented
63C47×#379C2218yescomplemented
64C4×C22⋊C4×C47C2218yescomplemented
65C2×#95×C47C2211yescharacteristic, complemented
66C2×#95×C47C2211yescharacteristic, complemented
67C2×#95×C47C2211yescharacteristic, complemented
68C2×#95×C47C2211yescharacteristic, complemented
69C2×#95×C47C2211yescharacteristic, complemented
70C2×#95×C47C2211yescharacteristic, complemented
71C25×C47—24no—
72C25×C47—24no—
73C25×C47—24no—
74C25×C47—24no—
75C25×C47—24no—
76C25×C47—42no—
77C25×C47—42no—
78C25×C47C2311yescharacteristic
79C25×C47C2311yescharacteristic
80C25×C47C2311yescharacteristic
81C25×C47C2314yes—
82C25×C47C2311yescharacteristic
83C22×Q8×C47—24no—
84C22×Q8×C47—24no—
85C22×Q8×C47—42no—
86C22×Q8×C47C2314yescomplemented
87C22×D4×C47—24no—
88C22×D4×C47—24no—
89C22×D4×C47—24no—
90C22×D4×C47—24no—
91C22×D4×C47—24no—
92C22×D4×C47—24no—
93C22×D4×C47—24no—
94C22×D4×C47—42no—
95C22×D4×C47—42no—
96C22×D4×C47C2314yes—
97C22×D4×C47C2314yes—
98C22×D4×C47C2314yes—
99C23×C4×C47—24no—
100C23×C4×C47—24no—
101C23×C4×C47—24no—
102C23×C4×C47—24no—
103C23×C4×C47—42no—
104C23×C4×C47—42no—
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108C23×C4×C47C2311yescharacteristic
109C23×C4×C47C2311yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C23×C4×C47C2311yescharacteristic
112C23×C4×C47C2314yes—
113C23×C4×C47C2314yes—
114C23×C4×C47C2311yescharacteristic
115C23×C4×C47C2311yescharacteristic
116C23×C4×C47C2311yescharacteristic
117C23×C4×C47C2311yescharacteristic
118#124×C47—232no—
119C22⋊Q8×C47—232no—
120#120×C47—232no—
121C2×C4⋊C4×C47—24no—
122C2×C4⋊C4×C47—24no—
123C2×C4⋊C4×C47—24no—
124C2×C4⋊C4×C47C2314yescomplemented
125C2×C4⋊C4×C47C2314yescomplemented
126C2×C4⋊C4×C47C2314yescomplemented
127C2×C22⋊C4×C47—24no—
128C2×C22⋊C4×C47—24no—
129C2×C22⋊C4×C47—24no—
130C2×C22⋊C4×C47—24no—
131C2×C22⋊C4×C47—24no—
132C2×C22⋊C4×C47—24no—
133C2×C22⋊C4×C47—24no—
134C2×C22⋊C4×C47—24no—
135C2×C22⋊C4×C47—24no—
136C2×C22⋊C4×C47—24no—
137C2×C22⋊C4×C47—24no—
138C2×C22⋊C4×C47—232no—
139C2×C22⋊C4×C47—42no—
140C2×C22⋊C4×C47—42no—
141C2×C22⋊C4×C47—42no—
142C2×C22⋊C4×C47—42no—
143C2×C22⋊C4×C47D418yes—
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×C22⋊C4×C47C2314yes—
157C2×C22⋊C4×C47C2314yes—
158C2×C22⋊C4×C47C2314yescomplemented
159C2×C22⋊C4×C47C2314yescomplemented
160C2×C22⋊C4×C47C2314yescomplemented
161C2×C22⋊C4×C47C2314yescomplemented
162C2×C42×C47—24no—
163C2×C42×C47—42no—
164C2×C42×C47C2314yescomplemented
165C2×C42×C47C2314yescomplemented
166#95×C47C2314yescomplemented
167#95×C47C2314yescomplemented
168#95×C47C2314yescomplemented
169#95×C47C2314yescomplemented
170#95×C47C2314yescomplemented
171#95×C47C2314yescomplemented
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—232no—
177C24×C47—28no—
178C24×C47—22no—
179C24×C47—22no—
180C24×C47—22no—
181C24×C47—28no—
182C24×C47—28no—
183C24×C47—22no—
184C24×C47—22no—
185C24×C47—22no—
186C24×C47—22no—
187C24×C47—22no—
188C24×C47—22no—
189C24×C47—22no—
190C24×C47—22no—
191C24×C47—22no—
192C24×C47—22no—
193C24×C47—28no—
194C24×C47—22no—
195C24×C47—22no—
196C24×C47—22no—
197C24×C47—22no—
198C24×C47—28no—
199C24×C47—22no—
200C24×C47—22no—
201C24×C47—44no—
202C24×C47—44no—
203C24×C47—416no—
204C24×C47—416no—
205C24×C47—416no—
206C24×C47—416no—
207C24×C47—416no—
208C24×C47—416no—
209C24×C47C2×D414yes—
210C24×C47C2×D414yes—
211C24×C47#4114yes—
212C24×C47#4114yes—
213C24×C47#4114yes—
214C24×C47C2412yes—
215C24×C47C2412yes—
216C24×C47C2412yes—
217C24×C47C2412yes—
218C24×C47C2411yescharacteristic
219C2×Q8×C47—28no—
220C2×Q8×C47—28no—
221C2×Q8×C47—44no—
222C2×Q8×C47—416no—
223C2×D4×C47—28no—
224C2×D4×C47—28no—
225C2×D4×C47—28no—
226C2×D4×C47—28no—
227C2×D4×C47—28no—
228C2×D4×C47—28no—
229C2×D4×C47—28no—
230C2×D4×C47—44no—
231C2×D4×C47—44no—
232C2×D4×C47—416no—
233C2×D4×C47—416no—
234C2×D4×C47—416no—
235C22×C4×C47—22no—
236C22×C4×C47—22no—
237C22×C4×C47—22no—
238C22×C4×C47—22no—
239C22×C4×C47—22no—
240C22×C4×C47—22no—
241C22×C4×C47—22no—
242C22×C4×C47—22no—
243C22×C4×C47—22no—
244C22×C4×C47—22no—
245C22×C4×C47—22no—
246C22×C4×C47—22no—
247C22×C4×C47—22no—
248C22×C4×C47—22no—
249C22×C4×C47—22no—
250C22×C4×C47—22no—
251C22×C4×C47—28no—
252C22×C4×C47—22no—
253C22×C4×C47—22no—
254C22×C4×C47—22no—
255C22×C4×C47—22no—
256C22×C4×C47—28no—
257C22×C4×C47—22no—
258C22×C4×C47—22no—
259C22×C4×C47—22no—
260C22×C4×C47—22no—
261C22×C4×C47—22no—
262C22×C4×C47—22no—
263C22×C4×C47—22no—
264C22×C4×C47—22no—
265C22×C4×C47—22no—
266C22×C4×C47—28no—
267C22×C4×C47—28no—
268C22×C4×C47—44no—
269C22×C4×C47—44no—
270C22×C4×C47—416no—
271C22×C4×C47—416no—
272C22×C4×C47C2×D414yes—
273C22×C4×C47C2×D414yes—
274C22×C4×C47C2×D414yes—
275C22×C4×C47C2×D414yes—
276C22×C4×C47C2412yes—
277C22×C4×C47C2412yes—
278C22×C4×C47C2412yes—
279C22×C4×C47C2412yes—
280C22×C4×C47C2412yes—
281C22×C4×C47C2412yes—
282C22×C4×C47C2412yes—
283C22×C4×C47C2412yes—
284C22×C4×C47C2412yes—
285C22×C4×C47C2412yes—
286C22×C4×C47C2412yes—
287C4⋊C4×C47—28no—
288C4⋊C4×C47—28no—
289C4⋊C4×C47—28no—
290C22⋊C4×C47—28no—
291C22⋊C4×C47—28no—
292C22⋊C4×C47—28no—
293C22⋊C4×C47—28no—
294C22⋊C4×C47—28no—
295C22⋊C4×C47—28no—
296C22⋊C4×C47—28no—
297C22⋊C4×C47—28no—
298C22⋊C4×C47—28no—
299C22⋊C4×C47—28no—
300C22⋊C4×C47—28no—
301C22⋊C4×C47—44no—
302C22⋊C4×C47—44no—
303C22⋊C4×C47—44no—
304C22⋊C4×C47—44no—
305C22⋊C4×C47C2×D4116yes—
306C22⋊C4×C47C2×D4116yescomplemented
307C42×C47—28no—
308C42×C47—44no—
309C23×C47—28no—
310C23×C47—28no—
311C23×C47—28no—
312C23×C47—28no—
313C23×C47—28no—
314C23×C47—28no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—232no—
320C23×C47—28no—
321C23×C47—28no—
322C23×C47—28no—
323C23×C47—28no—
324C23×C47—28no—
325C23×C47—28no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47—22no—
332C23×C47—22no—
333C23×C47—22no—
334C23×C47—22no—
335C23×C47—22no—
336C23×C47—22no—
337C23×C47—22no—
338C23×C47—22no—
339C23×C47—22no—
340C23×C47—22no—
341C23×C47—22no—
342C23×C47—22no—
343C23×C47—22no—
344C23×C47—22no—
345C23×C47—416no—
346C23×C47—416no—
347C23×C47—416no—
348C23×C47—416no—
349C23×C47—416no—
350C23×C47—4128no—
351C23×C47—44no—
352C23×C47—44no—
353C23×C47—416no—
354C23×C47—44no—
355C23×C47—44no—
356C23×C47—44no—
357C23×C47—44no—
358C23×C47—44no—
359C23×C47—44no—
360C23×C47—44no—
361C23×C47—44no—
362C23×C47—44no—
363C23×C47—44no—
364C23×C47—44no—
365C23×C47—44no—
366C23×C47—44no—
367C23×C47#124116yescomplemented
368C23×C47C22×D414yes—
369C23×C47C22×D414yes—
370C23×C47C22×D412yes—
371C23×C47C22×D412yes—
372C23×C47C2×#4114yes—
373C23×C47C2×#4114yes—
374C23×C47C2×#4114yes—
375C23×C47C2×#4112yes—
376C23×C47C2×#4112yes—
377C23×C47C2×#4112yes—
378C23×C47H(5,𝔽2)12yes—
379C23×C47H(5,𝔽2)12yes—
380C23×C47C2511yescharacteristic
381Q8×C47—416no—
382D4×C47—416no—
383D4×C47—416no—
384D4×C47—416no—
385C2×C4×C47—28no—
386C2×C4×C47—28no—
387C2×C4×C47—28no—
388C2×C4×C47—28no—
389C2×C4×C47—22no—
390C2×C4×C47—22no—
391C2×C4×C47—22no—
392C2×C4×C47—22no—
393C2×C4×C47—22no—
394C2×C4×C47—22no—
395C2×C4×C47—22no—
396C2×C4×C47—22no—
397C2×C4×C47—22no—
398C2×C4×C47—22no—
399C2×C4×C47—22no—
400C2×C4×C47—22no—
401C2×C4×C47—22no—
402C2×C4×C47—22no—
403C2×C4×C47—22no—
404C2×C4×C47—22no—
405C2×C4×C47—22no—
406C2×C4×C47—22no—
407C2×C4×C47—22no—
408C2×C4×C47—22no—
409C2×C4×C47—22no—
410C2×C4×C47—22no—
411C2×C4×C47—22no—
412C2×C4×C47—22no—
413C2×C4×C47—22no—
414C2×C4×C47—22no—
415C2×C4×C47—22no—
416C2×C4×C47—22no—
417C2×C4×C47—22no—
418C2×C4×C47—416no—
419C2×C4×C47—416no—
420C2×C4×C47—44no—
421C2×C4×C47—44no—
422C2×C4×C47—44no—
423C2×C4×C47—44no—
424C2×C4×C47—44no—
425C2×C4×C47—44no—
426C2×C4×C47—44no—
427C2×C4×C47C22×D414yes—
428C2×C4×C47C22×D414yes—
429C2×C4×C47C22×D414yes—
430C2×C4×C47C22×D414yes—
431C2×#2472C4711yesmaximal, characteristic, direct product factor, Sylow
432C22×C47—24no—
433C22×C47—24no—
434C22×C47—24no—
435C22×C47—24no—
436C22×C47—24no—
437C22×C47—24no—
438C22×C47—232no—
439C22×C47—24no—
440C22×C47—24no—
441C22×C47—24no—
442C22×C47—24no—
443C22×C47—24no—
444C22×C47—24no—
445C22×C47—464no—
446C22×C47—42no—
447C22×C47—42no—
448C22×C47—42no—
449C22×C47—42no—
450C22×C47—42no—
451C22×C47—42no—
452C22×C47—42no—
453C22×C47—42no—
454C22×C47—416no—
455C22×C47—416no—
456C22×C47—42no—
457C22×C47—42no—
458C22×C47—42no—
459C22×C47—42no—
460C22×C47—42no—
461C22×C47—42no—
462C22×C47—42no—
463C22×C47—88no—
464C22×C47#52514yes—
465C22×C47C2×#12414yes—
466C22×C47C2×#12418yescomplemented
467C22×C47#53814yes—
468C22×C47D4214yes—
469C22×C47#54614yes—
470C22×C47#54614yes—
471C22×C47#55114yes—
472C22×C47C23×D411yescharacteristic
473C22×C47C23×D411yescharacteristic
474C22×C47C22×#4111yescharacteristic
475C22×C47C22×#4111yescharacteristic
476C22×C47C22×#4111yescharacteristic
477C22×C47C2×H(5,𝔽2)11yescharacteristic
478C22×C47C2×H(5,𝔽2)11yescharacteristic
479C4×C47—24no—
480C4×C47—24no—
481C4×C47—24no—
482C4×C47—24no—
483C4×C47—42no—
484C4×C47—42no—
485C4×C47—42no—
486C4×C47—42no—
487C4×C47—42no—
488C4×C47—42no—
489C4×C47—42no—
490C22×#124C2×C4711yescharacteristic, complemented
491C22×C22⋊Q8C2×C4711yescharacteristic, complemented
492C22×#120C2×C4711yescharacteristic
493C23×C22⋊C4C2×C4711yescharacteristic, complemented
494#2472C2×C47116yesdirect product factor
495C2×#397C2×C4711yescharacteristic, complemented
496C2×#394C2×C4711yescharacteristic, complemented
497C2×#394C2×C4711yescharacteristic, complemented
498C2×#393C2×C4711yescharacteristic, complemented
499C2×#390C2×C4711yescharacteristic, complemented
500C2×#388C2×C4711yescharacteristic, complemented
501C2×#388C2×C4711yescharacteristic, complemented
502C2×#386C2×C4711yescharacteristic, complemented
503C2×#386C2×C4711yescharacteristic, complemented
504C2×#379C2×C4711yescharacteristic, complemented
505C2×C4×C22⋊C4C2×C4711yescharacteristic, complemented
506C2×C47—28no—
507C2×C47—44no—
508C2×C47—44no—
509C2×C47—82no—
510C2×C47#247218yesdirect product factor
511C2×C47C2×#52511yescharacteristic
512C2×C47C22×#12411yescharacteristic
513C2×C47C2×#53811yescharacteristic
514C2×C47C2×D4211yescharacteristic
515C2×C47C2×#54611yescharacteristic
516C2×C47C2×#54611yescharacteristic
517C2×C47C2×#55111yescharacteristic
518C26C22×C4711yescharacteristic
519C23×Q8C22×C4711yescharacteristic, complemented
520C23×D4C22×C4711yescharacteristic
521C23×D4C22×C4711yescharacteristic
522C23×D4C22×C4711yescharacteristic
523C24×C4C22×C4711yescharacteristic
524C24×C4C22×C4711yescharacteristic
525C2×#124—28no—
526C2×#124C22×C4718yescomplemented
527C2×C22⋊Q8—28no—
528C2×C22⋊Q8C22×C4718yescomplemented
529C2×#120—28no—
530C2×#120C22×C4718yes—
531C22×C4⋊C4C22×C4711yescharacteristic, complemented
532C22×C4⋊C4C22×C4711yescharacteristic, complemented
533C22×C4⋊C4C22×C4711yescharacteristic, complemented
534C22×C22⋊C4—28no—
535C22×C22⋊C4C22×C4711yescharacteristic
536C22×C22⋊C4C22×C4711yescharacteristic
537C22×C22⋊C4C22×C4711yescharacteristic
538C22×C22⋊C4C22×C4711yescharacteristic
539C22×C22⋊C4C22×C4711yescharacteristic
540C22×C22⋊C4C22×C4711yescharacteristic
541C22×C22⋊C4C22×C4711yescharacteristic
542C22×C22⋊C4C22×C4711yescharacteristic
543C22×C22⋊C4C22×C4711yescharacteristic
544C22×C22⋊C4C22×C4711yescharacteristic
545C22×C22⋊C4C22×C4711yescharacteristic
546C22×C22⋊C4C22×C4711yescharacteristic
547C22×C22⋊C4C22×C4711yescharacteristic
548C22×C22⋊C4C22×C4718yescomplemented
549C22×C22⋊C4C22×C4711yescharacteristic, complemented
550C22×C22⋊C4C22×C4711yescharacteristic, complemented
551C22×C22⋊C4C22×C4711yescharacteristic, complemented
552C22×C22⋊C4C22×C4711yescharacteristic, complemented
553C22×C42C22×C4711yescharacteristic, complemented
554C22×C42C22×C4711yescharacteristic, complemented
555#397C22×C4718yescomplemented
556#394C22×C4718yescomplemented
557#394C22×C4718yescomplemented
558#393C22×C4718yescomplemented
559#390C22×C4718yescomplemented
560#388C22×C4718yescomplemented
561#388C22×C4718yescomplemented
562#386C22×C4718yescomplemented
563#386C22×C4718yescomplemented
564#379C22×C4718yescomplemented
565C4×C22⋊C4C22×C4718yescomplemented
566C2×#95C22×C4711yescharacteristic, complemented
567C2×#95C22×C4711yescharacteristic, complemented
568C2×#95C22×C4711yescharacteristic, complemented
569C2×#95C22×C4711yescharacteristic, complemented
570C2×#95C22×C4711yescharacteristic, complemented
571C2×#95C22×C4711yescharacteristic, complemented
572C47C2×#247211yescharacteristic, direct product factor, Sylow
573C25—24no—
574C25—24no—
575C25—24no—
576C25—24no—
577C25—24no—
578C25—42no—
579C25—42no—
580C25C23×C4711yescharacteristic
581C25C23×C4711yescharacteristic
582C25C23×C4711yescharacteristic
583C25C23×C4714yes—
584C25C23×C4711yescharacteristic
585C22×Q8—24no—
586C22×Q8—24no—
587C22×Q8—42no—
588C22×Q8C23×C4714yescomplemented
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—24no—
592C22×D4—24no—
593C22×D4—24no—
594C22×D4—24no—
595C22×D4—24no—
596C22×D4—42no—
597C22×D4—42no—
598C22×D4C23×C4714yes—
599C22×D4C23×C4714yes—
600C22×D4C23×C4714yes—
601C23×C4—24no—
602C23×C4—24no—
603C23×C4—24no—
604C23×C4—24no—
605C23×C4—42no—
606C23×C4—42no—
607C23×C4C23×C4711yescharacteristic
608C23×C4C23×C4711yescharacteristic
609C23×C4C23×C4711yescharacteristic
610C23×C4C23×C4711yescharacteristic
611C23×C4C23×C4711yescharacteristic
612C23×C4C23×C4711yescharacteristic
613C23×C4C23×C4711yescharacteristic
614C23×C4C23×C4714yes—
615C23×C4C23×C4714yes—
616C23×C4C23×C4711yescharacteristic
617C23×C4C23×C4711yescharacteristic
618C23×C4C23×C4711yescharacteristic
619C23×C4C23×C4711yescharacteristic
620#124—232no—
621C22⋊Q8—232no—
622#120—232no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4C23×C4714yescomplemented
627C2×C4⋊C4C23×C4714yescomplemented
628C2×C4⋊C4C23×C4714yescomplemented
629C2×C22⋊C4—24no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—232no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4—42no—
644C2×C22⋊C4—42no—
645C2×C22⋊C4D4×C4718yes—
646C2×C22⋊C4D4×C4718yescomplemented
647C2×C22⋊C4C23×C4714yes—
648C2×C22⋊C4C23×C4714yes—
649C2×C22⋊C4C23×C4714yes—
650C2×C22⋊C4C23×C4714yes—
651C2×C22⋊C4C23×C4714yes—
652C2×C22⋊C4C23×C4714yes—
653C2×C22⋊C4C23×C4714yes—
654C2×C22⋊C4C23×C4714yes—
655C2×C22⋊C4C23×C4714yes—
656C2×C22⋊C4C23×C4714yes—
657C2×C22⋊C4C23×C4714yes—
658C2×C22⋊C4C23×C4714yes—
659C2×C22⋊C4C23×C4714yes—
660C2×C22⋊C4C23×C4714yescomplemented
661C2×C22⋊C4C23×C4714yescomplemented
662C2×C22⋊C4C23×C4714yescomplemented
663C2×C22⋊C4C23×C4714yescomplemented
664C2×C42—24no—
665C2×C42—42no—
666C2×C42C23×C4714yescomplemented
667C2×C42C23×C4714yescomplemented
668#95C23×C4714yescomplemented
669#95C23×C4714yescomplemented
670#95C23×C4714yescomplemented
671#95C23×C4714yescomplemented
672#95C23×C4714yescomplemented
673#95C23×C4714yescomplemented
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—232no—
679C24—28no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—28no—
684C24—28no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—28no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—28no—
701C24—22no—
702C24—22no—
703C24—44no—
704C24—44no—
705C24—416no—
706C24—416no—
707C24—416no—
708C24—416no—
709C24—416no—
710C24—416no—
711C24C2×D4×C4714yes—
712C24C2×D4×C4714yes—
713C24#41×C4714yes—
714C24#41×C4714yes—
715C24#41×C4714yes—
716C24C24×C4712yes—
717C24C24×C4712yes—
718C24C24×C4712yes—
719C24C24×C4712yes—
720C24C24×C4711yescharacteristic
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—44no—
724C2×Q8—416no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—416no—
735C2×D4—416no—
736C2×D4—416no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—28no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—28no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—416no—
773C22×C4—416no—
774C22×C4C2×D4×C4714yes—
775C22×C4C2×D4×C4714yes—
776C22×C4C2×D4×C4714yes—
777C22×C4C2×D4×C4714yes—
778C22×C4C24×C4712yes—
779C22×C4C24×C4712yes—
780C22×C4C24×C4712yes—
781C22×C4C24×C4712yes—
782C22×C4C24×C4712yes—
783C22×C4C24×C4712yes—
784C22×C4C24×C4712yes—
785C22×C4C24×C4712yes—
786C22×C4C24×C4712yes—
787C22×C4C24×C4712yes—
788C22×C4C24×C4712yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4C2×D4×C47116yes—
808C22⋊C4C2×D4×C47116yescomplemented
809C42—28no—
810C42—44no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—232no—
822C23—28no—
823C23—28no—
824C23—28no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—416no—
848C23—416no—
849C23—416no—
850C23—416no—
851C23—416no—
852C23—4128no—
853C23—44no—
854C23—44no—
855C23—416no—
856C23—44no—
857C23—44no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23—44no—
869C23#124×C47116yescomplemented
870C23C22×D4×C4714yes—
871C23C22×D4×C4714yes—
872C23C22×D4×C4712yes—
873C23C22×D4×C4712yes—
874C23C2×#41×C4714yes—
875C23C2×#41×C4714yes—
876C23C2×#41×C4714yes—
877C23C2×#41×C4712yes—
878C23C2×#41×C4712yes—
879C23C2×#41×C4712yes—
880C23H(5,𝔽2)×C4712yes—
881C23H(5,𝔽2)×C4712yes—
882C23C25×C4711yescharacteristic
883Q8—416no—
884D4—416no—
885D4—416no—
886D4—416no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—28no—
890C2×C4—28no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—416no—
921C2×C4—416no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4C22×D4×C4714yes—
930C2×C4C22×D4×C4714yes—
931C2×C4C22×D4×C4714yes—
932C2×C4C22×D4×C4714yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—232no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—464no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—416no—
956C22—416no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—88no—
965C22C47×#52514yes—
966C22C2×#124×C4714yes—
967C22C2×#124×C4718yescomplemented
968C22C47×#53814yes—
969C22D42×C4714yes—
970C22C47×#54614yes—
971C22C47×#54614yes—
972C22C47×#55114yes—
973C22C23×D4×C4711yescharacteristic
974C22C23×D4×C4711yescharacteristic
975C22C22×#41×C4711yescharacteristic
976C22C22×#41×C4711yescharacteristic
977C22C22×#41×C4711yescharacteristic
978C22C2×H(5,𝔽2)×C4711yescharacteristic
979C22C2×H(5,𝔽2)×C4711yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—24no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C2—28no—
992C2—44no—
993C2—44no—
994C2—82no—
995C2C47×#247218yesdirect product factor
996C2C2×C47×#52511yescharacteristic
997C2C22×#124×C4711yescharacteristic
998C2C2×C47×#53811yescharacteristic
999C2C2×D42×C4711yescharacteristic
1000C2C2×C47×#54611yescharacteristic
1001C2C2×C47×#54611yescharacteristic
1002C2C2×C47×#55111yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC23C25×C47
prime radicalC22×#120×C47C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#124×C47C2semidirect
2. C22×C22⋊Q8×C47C2semidirect
4. C23×C22⋊C4×C47C2semidirect
5. C47×#2472C2direct (N × H)
6. C2×C47×#397C2semidirect
7. C2×C47×#394C2semidirect
8. C2×C47×#394C2semidirect
9. C2×C47×#393C2semidirect
10. C2×C47×#390C2semidirect
11. C2×C47×#388C2semidirect
12. C2×C47×#388C2semidirect
13. C2×C47×#386C2semidirect
14. C2×C47×#386C2semidirect
15. C2×C47×#379C2semidirect
16. C2×C4×C22⋊C4×C47C2semidirect
18. C23×Q8×C47C22semidirect
25. C2×#124×C47C22semidirect
27. C2×C22⋊Q8×C47C22semidirect
30. C22×C4⋊C4×C47C22semidirect
31. C22×C4⋊C4×C47C22semidirect
32. C22×C4⋊C4×C47C22semidirect
47. C22×C22⋊C4×C47C22semidirect
48. C22×C22⋊C4×C47C22semidirect
49. C22×C22⋊C4×C47C22semidirect
50. C22×C22⋊C4×C47C22semidirect
51. C22×C22⋊C4×C47C22semidirect
52. C22×C42×C47C22semidirect
53. C22×C42×C47C22semidirect
54. C47×#397C22semidirect
55. C47×#394C22semidirect
56. C47×#394C22semidirect
57. C47×#393C22semidirect
58. C47×#390C22semidirect
59. C47×#388C22semidirect
60. C47×#388C22semidirect
61. C47×#386C22semidirect
62. C47×#386C22semidirect
63. C47×#379C22semidirect
64. C4×C22⋊C4×C47C22semidirect
65. C2×#95×C47C22semidirect
66. C2×#95×C47C22semidirect
67. C2×#95×C47C22semidirect
68. C2×#95×C47C22semidirect
69. C2×#95×C47C22semidirect
70. C2×#95×C47C22semidirect
86. C22×Q8×C47C23semidirect
124. C2×C4⋊C4×C47C23semidirect
125. C2×C4⋊C4×C47C23semidirect
126. C2×C4⋊C4×C47C23semidirect
144. C2×C22⋊C4×C47D4semidirect
158. C2×C22⋊C4×C47C23semidirect
159. C2×C22⋊C4×C47C23semidirect
160. C2×C22⋊C4×C47C23semidirect
161. C2×C22⋊C4×C47C23semidirect
164. C2×C42×C47C23semidirect
165. C2×C42×C47C23semidirect
166. #95×C47C23semidirect
167. #95×C47C23semidirect
168. #95×C47C23semidirect
169. #95×C47C23semidirect
170. #95×C47C23semidirect
171. #95×C47C23semidirect
306. C22⋊C4×C47C2×D4semidirect
367. C23×C47#124semidirect
431. C2×#2472C47direct (N × H)
466. C22×C47C2×#124semidirect
490. C22×#124C2×C47semidirect
491. C22×C22⋊Q8C2×C47semidirect
493. C23×C22⋊C4C2×C47semidirect
494. #2472C2×C47direct (N × H)
495. C2×#397C2×C47semidirect
496. C2×#394C2×C47semidirect
497. C2×#394C2×C47semidirect
498. C2×#393C2×C47semidirect
499. C2×#390C2×C47semidirect
500. C2×#388C2×C47semidirect
501. C2×#388C2×C47semidirect
502. C2×#386C2×C47semidirect
503. C2×#386C2×C47semidirect
504. C2×#379C2×C47semidirect
505. C2×C4×C22⋊C4C2×C47semidirect
510. C2×C47#2472direct (N × H)
519. C23×Q8C22×C47semidirect
526. C2×#124C22×C47semidirect
528. C2×C22⋊Q8C22×C47semidirect
531. C22×C4⋊C4C22×C47semidirect
532. C22×C4⋊C4C22×C47semidirect
533. C22×C4⋊C4C22×C47semidirect
548. C22×C22⋊C4C22×C47semidirect
549. C22×C22⋊C4C22×C47semidirect
550. C22×C22⋊C4C22×C47semidirect
551. C22×C22⋊C4C22×C47semidirect
552. C22×C22⋊C4C22×C47semidirect
553. C22×C42C22×C47semidirect
554. C22×C42C22×C47semidirect
555. #397C22×C47semidirect
556. #394C22×C47semidirect
557. #394C22×C47semidirect
558. #393C22×C47semidirect
559. #390C22×C47semidirect
560. #388C22×C47semidirect
561. #388C22×C47semidirect
562. #386C22×C47semidirect
563. #386C22×C47semidirect
564. #379C22×C47semidirect
565. C4×C22⋊C4C22×C47semidirect
566. C2×#95C22×C47semidirect
567. C2×#95C22×C47semidirect
568. C2×#95C22×C47semidirect
569. C2×#95C22×C47semidirect
570. C2×#95C22×C47semidirect
571. C2×#95C22×C47semidirect
572. C47C2×#2472direct (N × H)
588. C22×Q8C23×C47semidirect
626. C2×C4⋊C4C23×C47semidirect
627. C2×C4⋊C4C23×C47semidirect
628. C2×C4⋊C4C23×C47semidirect
646. C2×C22⋊C4D4×C47semidirect
660. C2×C22⋊C4C23×C47semidirect
661. C2×C22⋊C4C23×C47semidirect
662. C2×C22⋊C4C23×C47semidirect
663. C2×C22⋊C4C23×C47semidirect
666. C2×C42C23×C47semidirect
667. C2×C42C23×C47semidirect
668. #95C23×C47semidirect
669. #95C23×C47semidirect
670. #95C23×C47semidirect
671. #95C23×C47semidirect
672. #95C23×C47semidirect
673. #95C23×C47semidirect
808. C22⋊C4C2×D4×C47semidirect
869. C23#124×C47semidirect
967. C22C2×#124×C47semidirect
995. C2C47×#2472direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#124×C472
C22×C22⋊Q8×C472
C22×#120×C472
C23×C22⋊C4×C472
C47×#24722
C2×C47×#3972
C2×C47×#3942
C2×C47×#3932
C2×C47×#3902
C2×C47×#3882
C2×C47×#3862
C2×C47×#3792
C2×C4×C22⋊C4×C472
C2×#247247