Finite Group Databasebeta

← C47×#15126 #26054824

Subgroups — C47×#15126 #26054824

Order 12032.

2506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C47C211yesmaximal, characteristic
2C2×C47×#394C212yesmaximal, complemented
3C2×C47×#390C211yesmaximal, characteristic, complemented
4C2×C47×#390C211yesmaximal, characteristic, complemented
5C2×C47×#389C211yesmaximal, characteristic, complemented
6C2×C47×#380C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
8C47×#1440C212yesmaximal, complemented
9C47×#1439C212yesmaximal, complemented
10C47×#1438C212yesmaximal, complemented
11C47×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C47C2211yescharacteristic
13C23×D4×C47C2212yes—
14C24×C4×C47C2211yescharacteristic
15C2×#121×C47—24no—
16C2×#121×C47—24no—
17C2×#121×C47—24no—
18C22×C4⋊C4×C47C2211yescharacteristic
19C22×C4⋊C4×C47C2212yes—
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C4⋊C4×C47C2211yescharacteristic
22C22×C22⋊C4×C47C2211yescharacteristic
23C22×C22⋊C4×C47C2212yes—
24C22×C22⋊C4×C47C2212yes—
25C22×C22⋊C4×C47C2212yes—
26C22×C22⋊C4×C47C2212yes—
27C22×C22⋊C4×C47C2212yes—
28C22×C22⋊C4×C47C2212yes—
29C22×C22⋊C4×C47C2211yescharacteristic
30C22×C42×C47C2211yescharacteristic
31C22×C42×C47C2211yescharacteristic
32C47×#394—28no—
33C47×#390—24no—
34C47×#390—24no—
35C47×#389—24no—
36C47×#380—24no—
37C4×C22⋊C4×C47—24no—
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2212yes—
41C2×#95×C47C2212yes—
42C2×#95×C47C2212yes—
43C2×#95×C47C2212yes—
44C25×C47C2312yes—
45C25×C47C2311yescharacteristic
46C22×D4×C47—24no—
47C22×D4×C47—24no—
48C22×D4×C47—24no—
49C22×D4×C47—24no—
50C22×D4×C47—24no—
51C22×D4×C47—22no—
52C22×D4×C47—22no—
53C22×D4×C47—22no—
54C22×D4×C47—22no—
55C22×D4×C47—22no—
56C22×D4×C47—22no—
57C22×D4×C47—42no—
58C22×D4×C47—42no—
59C22×D4×C47D414yes—
60C23×C4×C47—22no—
61C23×C4×C47—22no—
62C23×C4×C47—22no—
63C23×C4×C47—22no—
64C23×C4×C47—22no—
65C23×C4×C47—22no—
66C23×C4×C47D414yes—
67C23×C4×C47C2312yes—
68C23×C4×C47C2311yescharacteristic
69C23×C4×C47C2311yescharacteristic
70C23×C4×C47C2312yes—
71C23×C4×C47C2311yescharacteristic
72C23×C4×C47C2312yes—
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76#121×C47—232no—
77C2×C4⋊C4×C47—22no—
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47—22no—
80C2×C4⋊C4×C47—22no—
81C2×C4⋊C4×C47—22no—
82C2×C4⋊C4×C47—24no—
83C2×C4⋊C4×C47—22no—
84C2×C4⋊C4×C47—24no—
85C2×C4⋊C4×C47—22no—
86C2×C4⋊C4×C47—42no—
87C2×C4⋊C4×C47D414yes—
88C2×C4⋊C4×C47D414yescomplemented
89C2×C22⋊C4×C47—24no—
90C2×C22⋊C4×C47—22no—
91C2×C22⋊C4×C47—22no—
92C2×C22⋊C4×C47—22no—
93C2×C22⋊C4×C47—24no—
94C2×C22⋊C4×C47—24no—
95C2×C22⋊C4×C47—22no—
96C2×C22⋊C4×C47—22no—
97C2×C22⋊C4×C47—24no—
98C2×C22⋊C4×C47—24no—
99C2×C22⋊C4×C47—24no—
100C2×C22⋊C4×C47—24no—
101C2×C22⋊C4×C47—24no—
102C2×C22⋊C4×C47—24no—
103C2×C22⋊C4×C47—24no—
104C2×C22⋊C4×C47—24no—
105C2×C22⋊C4×C47—24no—
106C2×C22⋊C4×C47—24no—
107C2×C22⋊C4×C47—42no—
108C2×C22⋊C4×C47—42no—
109C2×C22⋊C4×C47—42no—
110C2×C22⋊C4×C47—42no—
111C2×C22⋊C4×C47—42no—
112C2×C22⋊C4×C47D414yescomplemented
113C2×C42×C47—22no—
114C2×C42×C47—22no—
115C2×C42×C47—22no—
116C2×C42×C47—22no—
117C2×C42×C47—22no—
118C2×C42×C47—22no—
119#95×C47—22no—
120#95×C47—22no—
121#95×C47—24no—
122#95×C47—24no—
123#95×C47—24no—
124#95×C47—42no—
125C24×C47—21no—
126C24×C47—21no—
127C24×C47—21no—
128C24×C47—21no—
129C24×C47—21no—
130C24×C47—21no—
131C24×C47—21no—
132C24×C47—21no—
133C24×C47—21no—
134C24×C47—21no—
135C24×C47—21no—
136C24×C47—21no—
137C24×C47—22no—
138C24×C47—22no—
139C24×C47—22no—
140C24×C47—22no—
141C24×C47—22no—
142C24×C47—22no—
143C24×C47—22no—
144C24×C47—22no—
145C24×C47—22no—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—22no—
149C24×C47—22no—
150C24×C47—22no—
151C24×C47C2×D414yes—
152C24×C47C2×D412yes—
153C24×C47C2×D412yes—
154C24×C47#4112yes—
155C24×C47C2411yescharacteristic
156C2×D4×C47—216no—
157C2×D4×C47—28no—
158C2×D4×C47—28no—
159C2×D4×C47—28no—
160C2×D4×C47—48no—
161C2×D4×C47—48no—
162C2×D4×C47—48no—
163C2×D4×C47—48no—
164C2×D4×C47—48no—
165C2×D4×C47—48no—
166C2×D4×C47—44no—
167C2×D4×C47—44no—
168C2×D4×C47—44no—
169C2×D4×C47—44no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—22no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—22no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—22no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—22no—
206C22×C4×C47—21no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—28no—
213C22×C4×C47—28no—
214C22×C4×C47—28no—
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—44no—
223C22×C4×C47—44no—
224C22×C4×C47—44no—
225C22×C4×C47—44no—
226C22×C4×C47C2×D414yes—
227C22×C4×C47C2×D412yes—
228C22×C4×C47C2×D412yes—
229C22×C4×C47C2×D412yes—
230C22×C4×C47C2×D414yes—
231C22×C4×C47C2×D412yes—
232C22×C4×C47C2×D412yes—
233C22×C4×C47C2×D412yes—
234C22×C4×C47C2×D412yes—
235C22×C4×C47#4112yes—
236C22×C4×C47#4112yes—
237C22×C4×C47#4112yes—
238C22×C4×C47#4112yes—
239C22×C4×C47#4112yes—
240C4⋊C4×C47—28no—
241C4⋊C4×C47—28no—
242C4⋊C4×C47—48no—
243C4⋊C4×C47—44no—
244C22⋊C4×C47—28no—
245C22⋊C4×C47—216no—
246C22⋊C4×C47—28no—
247C22⋊C4×C47—48no—
248C22⋊C4×C47—48no—
249C22⋊C4×C47—48no—
250C22⋊C4×C47—48no—
251C22⋊C4×C47—48no—
252C42×C47—44no—
253C42×C47—44no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—24no—
273C23×C47—24no—
274C23×C47—24no—
275C23×C47—24no—
276C23×C47—24no—
277C23×C47—24no—
278C23×C47—24no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—42no—
296C23×C47—42no—
297C23×C47—42no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47—42no—
303C23×C47—42no—
304C23×C47—42no—
305C23×C47—42no—
306C23×C47—42no—
307C23×C47—42no—
308C23×C47—42no—
309C23×C47—42no—
310C23×C47—42no—
311C23×C47—42no—
312C23×C47—42no—
313C23×C47—42no—
314C23×C47—42no—
315C23×C47—42no—
316C23×C47—42no—
317C23×C47—42no—
318C23×C47—42no—
319C23×C47—42no—
320C23×C47—42no—
321C23×C47—42no—
322C23×C47—42no—
323C23×C47#12114yes—
324C23×C47C22×D411yescharacteristic
325C23×C47C22×D411yescharacteristic
326C23×C47C22×D411yescharacteristic
327C23×C47C22×D411yescharacteristic
328C23×C47C22×D411yescharacteristic
329C23×C47C2×#4111yescharacteristic
330C23×C47C2×#4111yescharacteristic
331C23×C47C2×#4111yescharacteristic
332C23×C47C2×#4111yescharacteristic
333C23×C47C2×#4111yescharacteristic
334C23×C47C2×#4111yescharacteristic
335C23×C47H(5,𝔽2)11yescharacteristic
336C23×C47H(5,𝔽2)11yescharacteristic
337C23×C47H(5,𝔽2)11yescharacteristic
338C23×C472−1+411yescharacteristic
339D4×C47—432no—
340D4×C47—416no—
341C2×C4×C47—22no—
342C2×C4×C47—24no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—24no—
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—24no—
353C2×C4×C47—22no—
354C2×C4×C47—24no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—24no—
358C2×C4×C47—24no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—42no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—42no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—42no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—42no—
378C2×C4×C47—42no—
379C2×C4×C47—42no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—42no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—42no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—416no—
391C2×C4×C47—42no—
392C2×C4×C47—42no—
393C2×C4×C47—42no—
394C2×C4×C47—42no—
395C2×C4×C47—42no—
396C2×C4×C47—42no—
397C2×C4×C47—42no—
398C2×C4×C47#12014yes—
399C2×C4×C47#12114yes—
400C2×C4×C47#12114yes—
401C2×C4×C47#12114yes—
402C2×C4×C47#12314yes—
403C2×C4×C47#12314yes—
404C2×C4×C47#12414yes—
405#15126C4711yesmaximal, characteristic, direct product factor, Sylow
406C22×C47—24no—
407C22×C47—24no—
408C22×C47—24no—
409C22×C47—42no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47—42no—
413C22×C47—42no—
414C22×C47—42no—
415C22×C47—42no—
416C22×C47—42no—
417C22×C47—42no—
418C22×C47—42no—
419C22×C47—42no—
420C22×C47—42no—
421C22×C47—44no—
422C22×C47—44no—
423C22×C47—44no—
424C22×C47—44no—
425C22×C47—44no—
426C22×C47—44no—
427C22×C47—44no—
428C22×C47—82no—
429C22×C47—82no—
430C22×C47—82no—
431C22×C47—82no—
432C22×C47—82no—
433C22×C47—82no—
434C22×C47—82no—
435C22×C47—82no—
436C22×C47C2×#12011yescharacteristic
437C22×C47C2×#12111yescharacteristic
438C22×C47C2×#12111yescharacteristic
439C22×C47C2×#12111yescharacteristic
440C22×C47C2×#12111yescharacteristic
441C22×C47C2×#12311yescharacteristic
442C22×C47C2×#12311yescharacteristic
443C22×C47#52511yescharacteristic
444C22×C47C2×#12411yescharacteristic
445C22×C47#52911yescharacteristic
446C22×C47#52911yescharacteristic
447C22×C47#53211yescharacteristic
448C22×C47#53211yescharacteristic
449C22×C47#53511yescharacteristic
450C22×C47#53711yescharacteristic
451C22×C47#54011yescharacteristic
452C22×C47#54011yescharacteristic
453C22×C47#54211yescharacteristic
454C22×C47#54211yescharacteristic
455C22×C47D4211yescharacteristic
456C22×C47D4211yescharacteristic
457C22×C47D4211yescharacteristic
458C22×C47#54611yescharacteristic
459C22×C47#54611yescharacteristic
460C22×C47#54611yescharacteristic
461C22×C47#54611yescharacteristic
462C22×C47#54711yescharacteristic
463C22×C47#54711yescharacteristic
464C22×C47#54811yescharacteristic
465C22×C47#54811yescharacteristic
466C22×C47#55011yescharacteristic
467C22×C47#55011yescharacteristic
468C22×C47#55311yescharacteristic
469C22×C47#55311yescharacteristic
470C22×C47#55511yescharacteristic
471C4×C47—42no—
472C4×C47—42no—
473C4×C47—42no—
474C4×C47—44no—
475C4×C47—42no—
476C4×C47—42no—
477C4×C47—44no—
478C4×C47—82no—
479C4×C47#39418yescomplemented
480C22×#121C2×C4711yescharacteristic
481C2×#394C2×C4712yescomplemented
482C2×#390C2×C4711yescharacteristic, complemented
483C2×#390C2×C4711yescharacteristic, complemented
484C2×#389C2×C4711yescharacteristic, complemented
485C2×#380C2×C4711yescharacteristic, complemented
486C2×C4×C22⋊C4C2×C4711yescharacteristic, complemented
487#1440C2×C4712yescomplemented
488#1439C2×C4712yescomplemented
489#1438C2×C4712yescomplemented
490C4⋊#95C2×C4711yescharacteristic, complemented
491C2×C47—44no—
492C2×C47—84no—
493C2×C47C2×#39411yescharacteristic
494C2×C47#240711yescharacteristic
495C2×C47#240811yescharacteristic
496C2×C47#241411yescharacteristic
497C2×C47#241611yescharacteristic
498C2×C47#242011yescharacteristic
499C2×C47#242211yescharacteristic
500C2×C47#242611yescharacteristic
501C2×C47#242711yescharacteristic
502C2×C47#242811yescharacteristic
503C2×C47#242811yescharacteristic
504C2×C47#249011yescharacteristic
505C2×C47#249111yescharacteristic
506C2×C47#262411yescharacteristic
507C2×C47#285411yescharacteristic
508C23×D4C22×C4711yescharacteristic
509C23×D4C22×C4712yes—
510C24×C4C22×C4711yescharacteristic
511C2×#121—24no—
512C2×#121—24no—
513C2×#121—24no—
514C22×C4⋊C4C22×C4711yescharacteristic
515C22×C4⋊C4C22×C4712yes—
516C22×C4⋊C4C22×C4711yescharacteristic
517C22×C4⋊C4C22×C4711yescharacteristic
518C22×C22⋊C4C22×C4712yes—
519C22×C22⋊C4C22×C4711yescharacteristic
520C22×C22⋊C4C22×C4712yes—
521C22×C22⋊C4C22×C4712yes—
522C22×C22⋊C4C22×C4712yes—
523C22×C22⋊C4C22×C4712yes—
524C22×C22⋊C4C22×C4712yes—
525C22×C22⋊C4C22×C4711yescharacteristic
526C22×C42C22×C4711yescharacteristic
527C22×C42C22×C4711yescharacteristic
528#394—28no—
529#390—24no—
530#390—24no—
531#389—24no—
532#380—24no—
533C4×C22⋊C4—24no—
534C2×#95C22×C4712yes—
535C2×#95C22×C4712yes—
536C2×#95C22×C4711yescharacteristic
537C2×#95C22×C4712yes—
538C2×#95C22×C4711yescharacteristic
539C2×#95C22×C4712yes—
540C47#1512611yescharacteristic, direct product factor, Sylow
541C25C23×C4712yes—
542C25C23×C4711yescharacteristic
543C22×D4—24no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—22no—
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—22no—
554C22×D4—42no—
555C22×D4—42no—
556C22×D4D4×C4714yes—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4D4×C4714yes—
564C23×C4C23×C4712yes—
565C23×C4C23×C4712yes—
566C23×C4C23×C4711yescharacteristic
567C23×C4C23×C4711yescharacteristic
568C23×C4C23×C4711yescharacteristic
569C23×C4C23×C4712yes—
570C23×C4C23×C4711yescharacteristic
571C23×C4C23×C4711yescharacteristic
572C23×C4C23×C4711yescharacteristic
573#121—232no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—42no—
584C2×C4⋊C4D4×C4714yes—
585C2×C4⋊C4D4×C4714yescomplemented
586C2×C22⋊C4—24no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—42no—
605C2×C22⋊C4—42no—
606C2×C22⋊C4—42no—
607C2×C22⋊C4—42no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4D4×C4714yescomplemented
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—22no—
616#95—22no—
617#95—22no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—42no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24C2×D4×C4714yes—
649C24C2×D4×C4712yes—
650C24C2×D4×C4712yes—
651C24#41×C4712yes—
652C24C24×C4711yescharacteristic
653C2×D4—216no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—48no—
658C2×D4—48no—
659C2×D4—48no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—28no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4C2×D4×C4712yes—
724C22×C4C2×D4×C4712yes—
725C22×C4C2×D4×C4714yes—
726C22×C4C2×D4×C4714yes—
727C22×C4C2×D4×C4712yes—
728C22×C4C2×D4×C4712yes—
729C22×C4C2×D4×C4712yes—
730C22×C4C2×D4×C4712yes—
731C22×C4C2×D4×C4712yes—
732C22×C4#41×C4712yes—
733C22×C4#41×C4712yes—
734C22×C4#41×C4712yes—
735C22×C4#41×C4712yes—
736C22×C4#41×C4712yes—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—48no—
740C4⋊C4—44no—
741C22⋊C4—28no—
742C22⋊C4—216no—
743C22⋊C4—28no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C42—44no—
750C42—44no—
751C23—22no—
752C23—22no—
753C23—22no—
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—22no—
768C23—22no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23#121×C4714yes—
821C23C22×D4×C4711yescharacteristic
822C23C22×D4×C4711yescharacteristic
823C23C22×D4×C4711yescharacteristic
824C23C22×D4×C4711yescharacteristic
825C23C22×D4×C4711yescharacteristic
826C23C2×#41×C4711yescharacteristic
827C23C2×#41×C4711yescharacteristic
828C23C2×#41×C4711yescharacteristic
829C23C2×#41×C4711yescharacteristic
830C23C2×#41×C4711yescharacteristic
831C23C2×#41×C4711yescharacteristic
832C23H(5,𝔽2)×C4711yescharacteristic
833C23H(5,𝔽2)×C4711yescharacteristic
834C23H(5,𝔽2)×C4711yescharacteristic
835C232−1+4×C4711yescharacteristic
836D4—432no—
837D4—416no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—416no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4#120×C4714yes—
896C2×C4#121×C4714yes—
897C2×C4#121×C4714yes—
898C2×C4#121×C4714yes—
899C2×C4#123×C4714yes—
900C2×C4#123×C4714yes—
901C2×C4#124×C4714yes—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—82no—
932C22C2×#120×C4711yescharacteristic
933C22C2×#121×C4711yescharacteristic
934C22C2×#121×C4711yescharacteristic
935C22C2×#121×C4711yescharacteristic
936C22C2×#121×C4711yescharacteristic
937C22C2×#123×C4711yescharacteristic
938C22C2×#123×C4711yescharacteristic
939C22C47×#52511yescharacteristic
940C22C2×#124×C4711yescharacteristic
941C22C47×#52911yescharacteristic
942C22C47×#52911yescharacteristic
943C22C47×#53211yescharacteristic
944C22C47×#53211yescharacteristic
945C22C47×#53511yescharacteristic
946C22C47×#53711yescharacteristic
947C22C47×#54011yescharacteristic
948C22C47×#54011yescharacteristic
949C22C47×#54211yescharacteristic
950C22C47×#54211yescharacteristic
951C22D42×C4711yescharacteristic
952C22D42×C4711yescharacteristic
953C22D42×C4711yescharacteristic
954C22C47×#54611yescharacteristic
955C22C47×#54611yescharacteristic
956C22C47×#54611yescharacteristic
957C22C47×#54611yescharacteristic
958C22C47×#54711yescharacteristic
959C22C47×#54711yescharacteristic
960C22C47×#54811yescharacteristic
961C22C47×#54811yescharacteristic
962C22C47×#55011yescharacteristic
963C22C47×#55011yescharacteristic
964C22C47×#55311yescharacteristic
965C22C47×#55311yescharacteristic
966C22C47×#55511yescharacteristic
967C4—42no—
968C4—42no—
969C4—44no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—44no—
974C4—82no—
975C4C47×#39418yescomplemented
976C2—44no—
977C2—84no—
978C2C2×C47×#39411yescharacteristic
979C2C47×#240711yescharacteristic
980C2C47×#240811yescharacteristic
981C2C47×#241411yescharacteristic
982C2C47×#241611yescharacteristic
983C2C47×#242011yescharacteristic
984C2C47×#242211yescharacteristic
985C2C47×#242611yescharacteristic
986C2C47×#242711yescharacteristic
987C2C47×#242811yescharacteristic
988C2C47×#242811yescharacteristic
989C2C47×#249011yescharacteristic
990C2C47×#249111yescharacteristic
991C2C47×#262411yescharacteristic
992C2C47×#285411yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC24C24×C47
prime radicalC22×#121×C47C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#394C2semidirect
3. C2×C47×#390C2semidirect
4. C2×C47×#390C2semidirect
5. C2×C47×#389C2semidirect
6. C2×C47×#380C2semidirect
7. C2×C4×C22⋊C4×C47C2semidirect
8. C47×#1440C2semidirect
9. C47×#1439C2semidirect
10. C47×#1438C2semidirect
11. C47×C4⋊#95C2semidirect
88. C2×C4⋊C4×C47D4semidirect
112. C2×C22⋊C4×C47D4semidirect
405. #15126C47direct (N × H)
479. C4×C47#394semidirect
481. C2×#394C2×C47semidirect
482. C2×#390C2×C47semidirect
483. C2×#390C2×C47semidirect
484. C2×#389C2×C47semidirect
485. C2×#380C2×C47semidirect
486. C2×C4×C22⋊C4C2×C47semidirect
487. #1440C2×C47semidirect
488. #1439C2×C47semidirect
489. #1438C2×C47semidirect
490. C4⋊#95C2×C47semidirect
540. C47#15126direct (N × H)
585. C2×C4⋊C4D4×C47semidirect
609. C2×C22⋊C4D4×C47semidirect
975. C4C47×#394semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C472
C2×C47×#3942
C2×C47×#3902
C2×C47×#3892
C2×C47×#3802
C2×C4×C22⋊C4×C472
C47×#14402
C47×#14392
C47×#14382
C47×C4⋊#952
#1512647