Finite Group Databasebeta

← C2×#20248719 #26386756

Subgroups — C2×#20248719 #26386756

Order 12032.

2550 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248719C2116yesmaximal, direct product factor
2C2×#15689064C211yesmaximal, characteristic, complemented
3C2×#15689051C211yesmaximal, characteristic, complemented
4C2×#15689048C211yesmaximal, characteristic, complemented
5C2×#15689037C211yesmaximal, characteristic
6C2×#15689017C211yesmaximal, characteristic, complemented
7C2×#15689016C211yesmaximal, characteristic, complemented
8C2×#15689010C211yesmaximal, characteristic, complemented
9C2×#15689005C211yesmaximal, characteristic, complemented
10C2×#15689003C211yesmaximal, characteristic
11C2×#15688996C211yesmaximal, characteristic, complemented
12C2×#15688990C211yesmaximal, characteristic, complemented
13C2×#15688981C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#386C211yesmaximal, characteristic
17C24×Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33#15689064C2218yescomplemented
34#15689051C2218yescomplemented
35#15689048C2218yescomplemented
36#15689037C2218yes—
37#15689017C2218yescomplemented
38#15689016C2218yescomplemented
39#15689010C2218yescomplemented
40#15689005C2218yescomplemented
41#15689003C2218yes—
42#15688996C2218yescomplemented
43#15688990C2218yescomplemented
44#15688981C2218yescomplemented
45C22⋊C4×Dic47C2218yescomplemented
46C4×C22⋊Dic47C2218yescomplemented
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C23×D4×C47C2211yescharacteristic
60C24×C4×C47C2211yescharacteristic
61C22×C22⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C47×#386C2218yes—
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C23×Dic47—24no—
68C23×Dic47—24no—
69C23×Dic47—42no—
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2314yes—
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C2×C4⋊Dic47—42no—
80C2×C4⋊Dic47C2314yes—
81C2×Dic47⋊C4—24no—
82C2×Dic47⋊C4—24no—
83C2×Dic47⋊C4—42no—
84C2×Dic47⋊C4—42no—
85C2×Dic47⋊C4C2314yes—
86C2×Dic47⋊C4C2314yes—
87C2×Dic47⋊C4C2314yes—
88C2×Dic47⋊C4C2314yes—
89C2×C22⋊Dic47—24no—
90C2×C22⋊Dic47—24no—
91C2×C22⋊Dic47—24no—
92C2×C22⋊Dic47—24no—
93C2×C22⋊Dic47—24no—
94C2×C22⋊Dic47—42no—
95C2×C22⋊Dic47—42no—
96C2×C22⋊Dic47C2314yes—
97C2×C22⋊Dic47C2314yes—
98C2×C22⋊Dic47C2314yes—
99C2×C22⋊Dic47C2314yes—
100C2×C22⋊Dic47C2314yes—
101C2×C22⋊Dic47C2314yes—
102C2×C22⋊Dic47C2314yes—
103C2×C4×Dic47—24no—
104C2×C4×Dic47—42no—
105C2×C4×Dic47—42no—
106C2×C4×Dic47C2314yes—
107C2×C4×Dic47C2314yes—
108C2×C4×Dic47C2314yes—
109C47⋊#95C2314yes—
110C47⋊#95C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C25×C47C2311yescharacteristic
122C25×C47C2311yescharacteristic
123C22×D4×C47—24no—
124C22×D4×C47—24no—
125C22×D4×C47—42no—
126C22×D4×C47C2314yes—
127C23×C4×C47—24no—
128C23×C4×C47—42no—
129C23×C4×C47—42no—
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2314yes—
136C2×C22⋊C4×C47—24no—
137C2×C22⋊C4×C47—24no—
138C2×C22⋊C4×C47—42no—
139C2×C22⋊C4×C47C2314yes—
140C2×C22⋊C4×C47C2314yes—
141C2×C22⋊C4×C47C2314yes—
142#95×C47C2314yes—
143#95×C47C2314yes—
144C24×C47—22no—
145C24×C47—22no—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—22no—
149C24×C47—22no—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47#4114yes—
157C24×C47#4114yes—
158C24×C47C2412yes—
159C24×C47C2412yes—
160C24×C47C2411yescharacteristic
161C2×D4×C47—28no—
162C2×D4×C47—28no—
163C2×D4×C47—44no—
164C2×D4×C47—416no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
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—44no—
181C22×C4×C47—44no—
182C22×C4×C47—416no—
183C22×C4×C47#4114yes—
184C22×C4×C47C2412yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2412yes—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—28no—
212C22×Dic47—28no—
213C22×Dic47—44no—
214C22×Dic47—416no—
215C22×Dic47#4114yes—
216C22×Dic47#4114yes—
217C22×Dic47C2412yes—
218C22×Dic47C2412yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22⋊C4×C47—28no—
226C22⋊C4×C47—28no—
227C22⋊C4×C47—44no—
228C22⋊Dic47—28no—
229C22⋊Dic47—28no—
230C22⋊Dic47—28no—
231C22⋊Dic47—28no—
232C22⋊Dic47—28no—
233C22⋊Dic47—44no—
234C22⋊Dic47—44no—
235C4⋊Dic47—44no—
236Dic47⋊C4—28no—
237Dic47⋊C4—28no—
238Dic47⋊C4—44no—
239Dic47⋊C4—44no—
240C4×Dic47—28no—
241C4×Dic47—44no—
242C4×Dic47—44no—
243C23×C47—28no—
244C23×C47—28no—
245C23×C47—28no—
246C23×C47—28no—
247C23×C47—28no—
248C23×C47—28no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—44no—
262C23×C47—44no—
263C23×C47—44no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47—44no—
267C23×C47—44no—
268C23×C47—44no—
269C23×C47C2×#4112yes—
270C23×C47C2×#4112yes—
271C23×C47C2×#4114yes—
272C23×C47C2×#4112yes—
273C23×C47C2×#4112yes—
274C23×C47C2×#4114yes—
275C23×C47C2×#4112yes—
276C23×C47H(5,𝔽2)12yes—
277C23×C47H(5,𝔽2)12yes—
278C23×C47C2511yescharacteristic
279D4×C47—416no—
280C2×C4×C47—28no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—416no—
296C2×C4×C47—44no—
297C2×C4×C47—44no—
298C2×C4×C47—44no—
299C2×C4×C47—44no—
300C2×C4×C47C2×#4114yes—
301C2×Dic47—28no—
302C2×Dic47—28no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—416no—
326C2×Dic47—44no—
327C2×Dic47—44no—
328C2×Dic47—44no—
329C2×Dic47—44no—
330C2×Dic47—44no—
331C2×Dic47—44no—
332C2×Dic47C2×#4114yes—
333C2×Dic47C2×#4114yes—
334C2×#2578—471nomaximal, Sylow
335C22×C47—24no—
336C22×C47—24no—
337C22×C47—24no—
338C22×C47—24no—
339C22×C47—24no—
340C22×C47—24no—
341C22×C47—416no—
342C22×C47—416no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47#52914yes—
352C22×C47#52914yes—
353C22×C47#53814yes—
354C22×C47#55114yes—
355C22×C47#55114yes—
356C22×C47#55314yes—
357C22×C47#55314yes—
358C22×C47C22×#4111yescharacteristic
359C22×C47C22×#4111yescharacteristic
360C22×C47C22×#4111yescharacteristic
361C22×C47C22×#4111yescharacteristic
362C22×C47C22×#4111yescharacteristic
363C22×C47C2×H(5,𝔽2)11yescharacteristic
364C22×C47C2×H(5,𝔽2)11yescharacteristic
365C4×C47—24no—
366C4×C47—42no—
367C4×C47—42no—
368C4×C47—42no—
369C4×C47—42no—
370Dic47—24no—
371Dic47—24no—
372Dic47—42no—
373Dic47—42no—
374Dic47—42no—
375Dic47—42no—
376Dic47—42no—
377Dic47—42no—
378#2578—4716no—
379C2×#400—471no—
380C2×#397—471no—
381C2×#397—471no—
382C2×#394—471no—
383C2×#388—471no—
384C2×#388—471no—
385C2×#387—471no—
386C2×#387—471no—
387C2×#386—471no—
388C2×#386D4711yescharacteristic
389C2×#385—471no—
390C2×#383—471no—
391C2×#380—471no—
392C2×C4×C22⋊C4—471no—
393C2×C4×C22⋊C4—471no—
394C2×C47—44no—
395C2×C47—44no—
396C2×C47#257818yescomplemented
397C2×C47C2×#52911yescharacteristic
398C2×C47C2×#52911yescharacteristic
399C2×C47C2×#53811yescharacteristic
400C2×C47C2×#55111yescharacteristic
401C2×C47C2×#55111yescharacteristic
402C2×C47C2×#55311yescharacteristic
403C2×C47C2×#55311yescharacteristic
404C23×D4C2×D4711yescharacteristic
405C24×C4—471no—
406C24×C4C2×D4711yescharacteristic
407C22×C4⋊C4—471no—
408C22×C4⋊C4—471no—
409C22×C4⋊C4—471no—
410C22×C4⋊C4—471no—
411C22×C4⋊C4—471no—
412C22×C22⋊C4—471no—
413C22×C22⋊C4—471no—
414C22×C22⋊C4—471no—
415C22×C22⋊C4—471no—
416C22×C22⋊C4—471no—
417C22×C22⋊C4—471no—
418C22×C22⋊C4—471no—
419C22×C22⋊C4C2×D4711yescharacteristic
420C22×C22⋊C4C2×D4711yescharacteristic
421C22×C22⋊C4C2×D4711yescharacteristic
422C22×C42—471no—
423C22×C42—471no—
424C22×C42—471no—
425#400—478no—
426#397—478no—
427#397—478no—
428#394—478no—
429#388—478no—
430#388—478no—
431#387—478no—
432#387—478no—
433#386—478no—
434#386C2×D4718yes—
435#385—478no—
436#383—478no—
437#380—478no—
438C4×C22⋊C4—478no—
439C4×C22⋊C4—478no—
440C2×#95—471no—
441C2×#95—471no—
442C2×#95—471no—
443C2×#95—471no—
444C2×#95—471no—
445C2×#95—471no—
446C2×#95—471no—
447C2×#95—471no—
448C2×#95—471no—
449C2×#95—471no—
450C2×#95—471no—
451C2×#95—471no—
452C2×#95C2×D4711yescharacteristic
453C2×#95C2×D4711yescharacteristic
454C47C2×#257811yescharacteristic, complemented, Sylow
455C25C22×D4711yescharacteristic
456C25C22×D4711yescharacteristic
457C22×D4—24no—
458C22×D4—24no—
459C22×D4—42no—
460C22×D4C22×D4714yes—
461C23×C4—24no—
462C23×C4—42no—
463C23×C4—42no—
464C23×C4—471no—
465C23×C4—471no—
466C23×C4—471no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4—474no—
473C23×C4—944no—
474C23×C4—944no—
475C23×C4—1882no—
476C23×C4C22×D4711yescharacteristic
477C23×C4C22×D4711yescharacteristic
478C23×C4C22×D4711yescharacteristic
479C23×C4C22×D4711yescharacteristic
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4714yes—
482C2×C4⋊C4—474no—
483C2×C4⋊C4—474no—
484C2×C4⋊C4—474no—
485C2×C4⋊C4—474no—
486C2×C4⋊C4—474no—
487C2×C4⋊C4—944no—
488C2×C4⋊C4—944no—
489C2×C4⋊C4—1882no—
490C2×C4⋊C4—1882no—
491C2×C4⋊C4—1882no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—474no—
496C2×C22⋊C4—474no—
497C2×C22⋊C4—474no—
498C2×C22⋊C4—474no—
499C2×C22⋊C4—474no—
500C2×C22⋊C4—474no—
501C2×C22⋊C4—474no—
502C2×C22⋊C4—944no—
503C2×C22⋊C4—944no—
504C2×C22⋊C4—944no—
505C2×C22⋊C4—944no—
506C2×C22⋊C4—944no—
507C2×C22⋊C4—1882no—
508C2×C22⋊C4—1882no—
509C2×C22⋊C4C22×D4714yes—
510C2×C22⋊C4C22×D4714yes—
511C2×C22⋊C4C22×D4714yes—
512C2×C42—474no—
513C2×C42—474no—
514C2×C42—474no—
515C2×C42—944no—
516C2×C42—1882no—
517C2×C42—1882no—
518#95—474no—
519#95—474no—
520#95—474no—
521#95—474no—
522#95—474no—
523#95—474no—
524#95—474no—
525#95—474no—
526#95—474no—
527#95—474no—
528#95—474no—
529#95—474no—
530#95C22×D4714yes—
531#95C22×D4714yes—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24#1062535014yes—
545C24#1062535214yes—
546C24C23×D4712yes—
547C24C23×D4712yes—
548C24C23×D4711yescharacteristic
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—44no—
552C2×D4—416no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—416no—
571C22×C4—474no—
572C22×C4—474no—
573C22×C4—472no—
574C22×C4—472no—
575C22×C4—472no—
576C22×C4—472no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—948no—
582C22×C4—948no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—942no—
594C22×C4—942no—
595C22×C4—942no—
596C22×C4—942no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—1884no—
606C22×C4—18816no—
607C22×C4#1062535214yes—
608C22×C4C23×D4712yes—
609C22×C4C23×D4712yes—
610C22×C4C23×D4712yes—
611C22×C4C23×D4712yes—
612C22×C4C23×D4712yes—
613C4⋊C4—948no—
614C4⋊C4—948no—
615C4⋊C4—1884no—
616C4⋊C4—1884no—
617C4⋊C4—1884no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—44no—
621C22⋊C4—948no—
622C22⋊C4—948no—
623C22⋊C4—948no—
624C22⋊C4—948no—
625C22⋊C4—948no—
626C22⋊C4—1884no—
627C22⋊C4—1884no—
628C42—948no—
629C42—1884no—
630C42—1884no—
631C23—28no—
632C23—28no—
633C23—28no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23#41×D4712yes—
658C23#41×D4712yes—
659C23C2×#1062535214yes—
660C23C2×#1062535212yes—
661C23C2×#1062535212yes—
662C23C2×#1062535014yes—
663C23C2×#1062535012yes—
664C23#1309406912yes—
665C23#1309406912yes—
666C23C24×D4711yescharacteristic
667D4—416no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—416no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—474no—
689C2×C4—474no—
690C2×C4—948no—
691C2×C4—948no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—18816no—
715C2×C4—1884no—
716C2×C4—1884no—
717C2×C4—1884no—
718C2×C4—1884no—
719C2×C4—1884no—
720C2×C4—1884no—
721C2×C4C2×#1062535214yes—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—416no—
735C22—416no—
736C22—42no—
737C22—42no—
738C22#1568965314yes—
739C22#1568965414yes—
740C22#1568970814yes—
741C22#1568979914yes—
742C22#1568980114yes—
743C22#1568981614yes—
744C22#1568982214yes—
745C22C2×#41×D4711yescharacteristic
746C22C2×#41×D4711yescharacteristic
747C22C22×#1062535211yescharacteristic
748C22C22×#1062535211yescharacteristic
749C22C22×#1062535011yescharacteristic
750C22C2×#1309406911yescharacteristic
751C22C2×#1309406911yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—944no—
758C4—944no—
759C4—1882no—
760C4—1882no—
761C4—1882no—
762C4—1882no—
763C4—1882no—
764C4—1882no—
765C2—44no—
766C2—44no—
767C2#2024871918yesdirect product factor
768C2C2×#1568965311yescharacteristic
769C2C2×#1568965411yescharacteristic
770C2C2×#1568970811yescharacteristic
771C2C2×#1568979911yescharacteristic
772C2C2×#1568980111yescharacteristic
773C2C2×#1568981611yescharacteristic
774C2C2×#1568982211yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#386C2
socleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC2×#386D47
hypocenterC47C2×#2578
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. #20248719C2direct (N × H)
2. C2×#15689064C2semidirect
3. C2×#15689051C2semidirect
4. C2×#15689048C2semidirect
6. C2×#15689017C2semidirect
7. C2×#15689016C2semidirect
8. C2×#15689010C2semidirect
9. C2×#15689005C2semidirect
11. C2×#15688996C2semidirect
12. C2×#15688990C2semidirect
13. C2×#15688981C2semidirect
14. C2×C22⋊C4×Dic47C2semidirect
15. C2×C4×C22⋊Dic47C2semidirect
33. #15689064C22semidirect
34. #15689051C22semidirect
35. #15689048C22semidirect
37. #15689017C22semidirect
38. #15689016C22semidirect
39. #15689010C22semidirect
40. #15689005C22semidirect
42. #15688996C22semidirect
43. #15688990C22semidirect
44. #15688981C22semidirect
45. C22⋊C4×Dic47C22semidirect
46. C4×C22⋊Dic47C22semidirect
396. C2×C47#2578semidirect
454. C47C2×#2578semidirect
767. C2#20248719direct (N × H)

Maximal subgroups

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

subgroupindex
#202487192
C2×#156890642
C2×#156890512
C2×#156890482
C2×#156890372
C2×#156890172
C2×#156890162
C2×#156890102
C2×#156890052
C2×#156890032
C2×#156889962
C2×#156889902
C2×#156889812
C2×C22⋊C4×Dic472
C2×C4×C22⋊Dic472
C2×C47×#3862
C2×#257847