Finite Group Databasebeta

← C2×#20247651 #26383908

Subgroups — C2×#20247651 #26383908

Order 12032.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094017C211yesmaximal, characteristic, complemented
2C23×Dic47⋊C4C211yesmaximal, characteristic, complemented
3#20247651C2116yesmaximal, direct product factor
4C2×#15689065C211yesmaximal, characteristic, complemented
5C2×#15689064C211yesmaximal, characteristic, complemented
6C2×#15689051C211yesmaximal, characteristic, complemented
7C2×#15689046C211yesmaximal, characteristic, complemented
8C2×#15689017C211yesmaximal, characteristic, complemented
9C2×#15689008C211yesmaximal, characteristic, complemented
10C2×#15689005C211yesmaximal, characteristic, complemented
11C2×#15689003C211yesmaximal, characteristic
12C2×#15689003C211yesmaximal, characteristic
13C2×#15688998C211yesmaximal, characteristic, complemented
14C2×#15688981C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#386C211yesmaximal, characteristic
17C24×Dic47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C2×#13094017—28no—
20C2×#13094017C2218yescomplemented
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2211yescharacteristic
23C22×Dic47⋊C4—28no—
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2218yescomplemented
31C22×C22⋊Dic47C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×C22⋊Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39#15689065C2218yescomplemented
40#15689064C2218yescomplemented
41#15689051C2218yescomplemented
42#15689046C2218yescomplemented
43#15689017C2218yescomplemented
44#15689008C2218yescomplemented
45#15689005C2218yescomplemented
46#15689003C2218yes—
47#15689003C2218yes—
48#15688998C2218yescomplemented
49#15688981C2218yescomplemented
50C4×C22⋊Dic47C2218yescomplemented
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C23×D4×C47C2211yescharacteristic
62C24×C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C47×#386C2218yes—
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C23×Dic47—24no—
70C23×Dic47—24no—
71C23×Dic47—24no—
72C23×Dic47—24no—
73C23×Dic47—24no—
74C23×Dic47—42no—
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2314yes—
81C23×Dic47C2314yes—
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85#13094017—232no—
86C2×C4⋊Dic47—24no—
87C2×C4⋊Dic47—24no—
88C2×C4⋊Dic47C2314yes—
89C2×C4⋊Dic47C2314yes—
90C2×Dic47⋊C4—24no—
91C2×Dic47⋊C4—24no—
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4—232no—
95C2×Dic47⋊C4—42no—
96C2×Dic47⋊C4D418yescomplemented
97C2×Dic47⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×C22⋊Dic47—24no—
104C2×C22⋊Dic47—24no—
105C2×C22⋊Dic47—24no—
106C2×C22⋊Dic47—24no—
107C2×C22⋊Dic47—24no—
108C2×C22⋊Dic47—42no—
109C2×C22⋊Dic47C2314yes—
110C2×C22⋊Dic47C2314yes—
111C2×C22⋊Dic47C2314yes—
112C2×C22⋊Dic47C2314yes—
113C2×C22⋊Dic47C2314yes—
114C2×C22⋊Dic47C2314yes—
115C2×C4×Dic47—24no—
116C2×C4×Dic47—42no—
117C2×C4×Dic47C2314yes—
118C2×C4×Dic47C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C25×C47C2311yescharacteristic
130C25×C47C2311yescharacteristic
131C22×D4×C47—24no—
132C22×D4×C47—24no—
133C22×D4×C47—24no—
134C22×D4×C47C2314yes—
135C23×C4×C47—24no—
136C23×C4×C47—24no—
137C23×C4×C47—42no—
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2314yes—
143C23×C4×C47C2311yescharacteristic
144C2×C22⋊C4×C47—24no—
145C2×C22⋊C4×C47—24no—
146C2×C22⋊C4×C47—42no—
147C2×C22⋊C4×C47C2314yes—
148C2×C22⋊C4×C47C2314yes—
149C2×C22⋊C4×C47C2314yes—
150#95×C47C2314yes—
151#95×C47C2314yes—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47—22no—
157C24×C47—22no—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47#4114yes—
164C24×C47#4114yes—
165C24×C47#4114yes—
166C24×C47C2412yes—
167C24×C47C2412yes—
168C24×C47C2411yescharacteristic
169C2×D4×C47—28no—
170C2×D4×C47—28no—
171C2×D4×C47—28no—
172C2×D4×C47—416no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—28no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—28no—
189C22×C4×C47—44no—
190C22×C4×C47—416no—
191C22×C4×C47C2×D414yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×Dic47—232no—
198C22×Dic47—22no—
199C22×Dic47—28no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—28no—
206C22×Dic47—28no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—28no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—28no—
224C22×Dic47—44no—
225C22×Dic47—416no—
226C22×Dic47C2×D414yes—
227C22×Dic47C2×D414yes—
228C22×Dic47#4114yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C22×Dic47C2412yes—
236C22×Dic47C2412yes—
237C22⋊C4×C47—28no—
238C22⋊C4×C47—28no—
239C22⋊C4×C47—44no—
240C22⋊Dic47—28no—
241C22⋊Dic47—28no—
242C22⋊Dic47—28no—
243C22⋊Dic47—28no—
244C22⋊Dic47—28no—
245C22⋊Dic47—44no—
246C4⋊Dic47—28no—
247C4⋊Dic47—28no—
248Dic47⋊C4—28no—
249Dic47⋊C4—28no—
250Dic47⋊C4—28no—
251Dic47⋊C4—28no—
252Dic47⋊C4—44no—
253Dic47⋊C4C2×D4116yescomplemented
254C4×Dic47—28no—
255C4×Dic47—44no—
256C23×C47—28no—
257C23×C47—28no—
258C23×C47—28no—
259C23×C47—28no—
260C23×C47—28no—
261C23×C47—28no—
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—22no—
273C23×C47—44no—
274C23×C47—44no—
275C23×C47—44no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47—44no—
280C23×C47#126116yescomplemented
281C23×C47C22×D412yes—
282C23×C47C2×#4112yes—
283C23×C47C2×#4114yes—
284C23×C47C2×#4114yes—
285C23×C47C2×#4112yes—
286C23×C47C2×#4112yes—
287C23×C47C2×#4114yes—
288C23×C47C2×#4112yes—
289C23×C47H(5,𝔽2)12yes—
290C23×C472−1+412yes—
291C23×C47C2511yescharacteristic
292D4×C47—416no—
293C2×C4×C47—28no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—416no—
309C2×C4×C47—44no—
310C2×C4×C47—44no—
311C2×C4×C47—44no—
312C2×C4×C47—44no—
313C2×C4×C47C22×D414yes—
314C2×Dic47—232no—
315C2×Dic47—28no—
316C2×Dic47—28no—
317C2×Dic47—28no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—416no—
340C2×Dic47—44no—
341C2×Dic47—44no—
342C2×Dic47—44no—
343C2×Dic47—44no—
344C2×Dic47—44no—
345C2×Dic47C22×D414yes—
346C2×Dic47C22×D414yes—
347C2×Dic47C2×#4114yes—
348C2×#2481—471nomaximal, Sylow
349C22×C47—24no—
350C22×C47—24no—
351C22×C47—24no—
352C22×C47—24no—
353C22×C47—24no—
354C22×C47—24no—
355C22×C47—232no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—88no—
364C22×C47#52514yes—
365C22×C47C2×#12614yes—
366C22×C47C2×#12618yescomplemented
367C22×C47#53914yes—
368C22×C47#54614yes—
369C22×C47#54814yes—
370C22×C47#55214yes—
371C22×C47#55314yes—
372C22×C47C23×D411yescharacteristic
373C22×C47C22×#4111yescharacteristic
374C22×C47C22×#4111yescharacteristic
375C22×C47C22×#4111yescharacteristic
376C22×C47C22×#4111yescharacteristic
377C22×C47C2×H(5,𝔽2)11yescharacteristic
378C22×C47C2×2−1+411yescharacteristic
379C4×C47—24no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47—42no—
383C4×C47—42no—
384Dic47—24no—
385Dic47—24no—
386Dic47—24no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390Dic47—42no—
391Dic47—42no—
392C22×#126—471no—
393C23×C4⋊C4—471no—
394#2481—4716no—
395C2×#400—471no—
396C2×#400—471no—
397C2×#397—471no—
398C2×#396—471no—
399C2×#388—471no—
400C2×#387—471no—
401C2×#387—471no—
402C2×#386—471no—
403C2×#386—471no—
404C2×#386D4711yescharacteristic
405C2×#385—471no—
406C2×#380—471no—
407C2×C4×C22⋊C4—471no—
408C2×C47—28no—
409C2×C47—82no—
410C2×C47#248118yescomplemented
411C2×C47C2×#52511yescharacteristic
412C2×C47C22×#12611yescharacteristic
413C2×C47C2×#53911yescharacteristic
414C2×C47C2×#54611yescharacteristic
415C2×C47C2×#54811yescharacteristic
416C2×C47C2×#55211yescharacteristic
417C2×C47C2×#55311yescharacteristic
418C23×D4C2×D4711yescharacteristic
419C24×C4—471no—
420C24×C4—471no—
421C24×C4C2×D4711yescharacteristic
422C2×#126—478no—
423C2×#126—948no—
424C22×C4⋊C4—471no—
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4—471no—
428C22×C4⋊C4—471no—
429C22×C4⋊C4—471no—
430C22×C4⋊C4—471no—
431C22×C4⋊C4—478no—
432C22×C4⋊C4—471no—
433C22×C4⋊C4—948no—
434C22×C22⋊C4—471no—
435C22×C22⋊C4—471no—
436C22×C22⋊C4—471no—
437C22×C22⋊C4—471no—
438C22×C22⋊C4—471no—
439C22×C22⋊C4—471no—
440C22×C22⋊C4C2×D4711yescharacteristic
441C22×C22⋊C4C2×D4711yescharacteristic
442C22×C22⋊C4C2×D4711yescharacteristic
443C22×C42—471no—
444C22×C42—471no—
445#400—478no—
446#400—478no—
447#397—478no—
448#396—478no—
449#388—478no—
450#387—478no—
451#387—478no—
452#386—478no—
453#386—478no—
454#386C2×D4718yes—
455#385—478no—
456#380—478no—
457C4×C22⋊C4—478no—
458C2×#95—471no—
459C2×#95—471no—
460C2×#95—471no—
461C2×#95—471no—
462C2×#95—471no—
463C2×#95—471no—
464C2×#95—471no—
465C2×#95—471no—
466C2×#95—471no—
467C2×#95—471no—
468C2×#95C2×D4711yescharacteristic
469C2×#95C2×D4711yescharacteristic
470C47C2×#248111yescharacteristic, complemented, Sylow
471C25C22×D4711yescharacteristic
472C25C22×D4711yescharacteristic
473C22×D4—24no—
474C22×D4—24no—
475C22×D4—24no—
476C22×D4C22×D4714yes—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—471no—
481C23×C4—471no—
482C23×C4—471no—
483C23×C4—474no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—471no—
487C23×C4—471no—
488C23×C4—471no—
489C23×C4—474no—
490C23×C4—944no—
491C23×C4—944no—
492C23×C4—944no—
493C23×C4—944no—
494C23×C4—944no—
495C23×C4—1882no—
496C23×C4C22×D4711yescharacteristic
497C23×C4C22×D4711yescharacteristic
498C23×C4C22×D4711yescharacteristic
499C23×C4C22×D4711yescharacteristic
500C23×C4C22×D4714yes—
501C23×C4C22×D4711yescharacteristic
502#126—9432no—
503C2×C4⋊C4—478no—
504C2×C4⋊C4—474no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—474no—
508C2×C4⋊C4—474no—
509C2×C4⋊C4—474no—
510C2×C4⋊C4—474no—
511C2×C4⋊C4—474no—
512C2×C4⋊C4—9432no—
513C2×C4⋊C4—944no—
514C2×C4⋊C4—944no—
515C2×C4⋊C4—944no—
516C2×C4⋊C4—944no—
517C2×C4⋊C4—944no—
518C2×C4⋊C4—944no—
519C2×C4⋊C4—1882no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—474no—
524C2×C22⋊C4—474no—
525C2×C22⋊C4—474no—
526C2×C22⋊C4—474no—
527C2×C22⋊C4—474no—
528C2×C22⋊C4—474no—
529C2×C22⋊C4—944no—
530C2×C22⋊C4—944no—
531C2×C22⋊C4—944no—
532C2×C22⋊C4—944no—
533C2×C22⋊C4—944no—
534C2×C22⋊C4—1882no—
535C2×C22⋊C4C22×D4714yes—
536C2×C22⋊C4C22×D4714yes—
537C2×C22⋊C4C22×D4714yes—
538C2×C42—474no—
539C2×C42—474no—
540C2×C42—944no—
541C2×C42—1882no—
542#95—474no—
543#95—474no—
544#95—474no—
545#95—474no—
546#95—474no—
547#95—474no—
548#95—474no—
549#95—474no—
550#95—474no—
551#95—474no—
552#95C22×D4714yes—
553#95C22×D4714yes—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24#1062535014yes—
566C24#1062535214yes—
567C24#1062535214yes—
568C24C23×D4712yes—
569C24C23×D4712yes—
570C24C23×D4711yescharacteristic
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—416no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—28no—
591C22×C4—44no—
592C22×C4—416no—
593C22×C4—474no—
594C22×C4—474no—
595C22×C4—474no—
596C22×C4—472no—
597C22×C4—472no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—472no—
604C22×C4—948no—
605C22×C4—948no—
606C22×C4—948no—
607C22×C4—9432no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—948no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—948no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—1884no—
632C22×C4—18816no—
633C22×C4D4×D4714yes—
634C22×C4C23×D4712yes—
635C22×C4C23×D4712yes—
636C22×C4C23×D4712yes—
637C22×C4C23×D4712yes—
638C22×C4C23×D4712yes—
639C4⋊C4—4716no—
640C4⋊C4—948no—
641C4⋊C4—948no—
642C4⋊C4—948no—
643C4⋊C4—948no—
644C4⋊C4—948no—
645C4⋊C4—948no—
646C4⋊C4—1884no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—44no—
650C22⋊C4—948no—
651C22⋊C4—948no—
652C22⋊C4—948no—
653C22⋊C4—948no—
654C22⋊C4—948no—
655C22⋊C4—1884no—
656C42—948no—
657C42—1884no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—28no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23#13094017116yescomplemented
683C23C2×D4×D4712yes—
684C23#41×D4712yes—
685C23C2×#1062535214yes—
686C23C2×#1062535214yes—
687C23C2×#1062535212yes—
688C23C2×#1062535212yes—
689C23C2×#1062535014yes—
690C23C2×#1062535012yes—
691C23#1309406912yes—
692C23#1309407112yes—
693C23C24×D4711yescharacteristic
694D4—416no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—416no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—474no—
716C2×C4—474no—
717C2×C4—474no—
718C2×C4—9432no—
719C2×C4—948no—
720C2×C4—948no—
721C2×C4—948no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—18816no—
744C2×C4—1884no—
745C2×C4—1884no—
746C2×C4—1884no—
747C2×C4—1884no—
748C2×C4—1884no—
749C2×C4C2×D4×D4714yes—
750C22—24no—
751C22—24no—
752C22—232no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—88no—
765C22#1568963214yes—
766C22C2×#1309401714yes—
767C22C2×#1309401718yescomplemented
768C22#1568971514yes—
769C22#1568976014yes—
770C22#1568977914yes—
771C22#1568981014yes—
772C22#1568981614yes—
773C22C22×D4×D4711yescharacteristic
774C22C2×#41×D4711yescharacteristic
775C22C22×#1062535211yescharacteristic
776C22C22×#1062535211yescharacteristic
777C22C22×#1062535011yescharacteristic
778C22C2×#1309406911yescharacteristic
779C22C2×#1309407111yescharacteristic
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—944no—
786C4—944no—
787C4—944no—
788C4—1882no—
789C4—1882no—
790C4—1882no—
791C4—1882no—
792C4—1882no—
793C2—28no—
794C2—82no—
795C2#2024765118yesdirect product factor
796C2C2×#1568963211yescharacteristic
797C2C22×#1309401711yescharacteristic
798C2C2×#1568971511yescharacteristic
799C2C2×#1568976011yescharacteristic
800C2C2×#1568977911yescharacteristic
801C2C2×#1568981011yescharacteristic
802C2C2×#1568981611yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#386C2
socleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC2×#386D47
hypocenterC47C2×#2481
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#13094017C2semidirect
2. C23×Dic47⋊C4C2semidirect
3. #20247651C2direct (N × H)
4. C2×#15689065C2semidirect
5. C2×#15689064C2semidirect
6. C2×#15689051C2semidirect
7. C2×#15689046C2semidirect
8. C2×#15689017C2semidirect
9. C2×#15689008C2semidirect
10. C2×#15689005C2semidirect
13. C2×#15688998C2semidirect
14. C2×#15688981C2semidirect
15. C2×C4×C22⋊Dic47C2semidirect
20. C2×#13094017C22semidirect
30. C22×Dic47⋊C4C22semidirect
39. #15689065C22semidirect
40. #15689064C22semidirect
41. #15689051C22semidirect
42. #15689046C22semidirect
43. #15689017C22semidirect
44. #15689008C22semidirect
45. #15689005C22semidirect
48. #15688998C22semidirect
49. #15688981C22semidirect
50. C4×C22⋊Dic47C22semidirect
96. C2×Dic47⋊C4D4semidirect
253. Dic47⋊C4C2×D4semidirect
280. C23×C47#126semidirect
366. C22×C47C2×#126semidirect
410. C2×C47#2481semidirect
470. C47C2×#2481semidirect
682. C23#13094017semidirect
767. C22C2×#13094017semidirect
795. C2#20247651direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940172
C23×Dic47⋊C42
#202476512
C2×#156890652
C2×#156890642
C2×#156890512
C2×#156890462
C2×#156890172
C2×#156890082
C2×#156890052
C2×#156890032
C2×#156889982
C2×#156889812
C2×C4×C22⋊Dic472
C2×C47×#3862
C2×#248147