Finite Group Databasebeta

← C2×#20248633 #26386672

Subgroups — C2×#20248633 #26386672

Order 12032.

2614 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248633C2116yesmaximal, direct product factor
2C2×#15689065C211yesmaximal, characteristic, complemented
3C2×#15689039C211yesmaximal, characteristic
4C2×#15689034C211yesmaximal, characteristic, complemented
5C2×#15689030C211yesmaximal, characteristic, complemented
6C2×#15689017C211yesmaximal, characteristic, complemented
7C2×#15689012C211yesmaximal, characteristic, complemented
8C2×#15689000C211yesmaximal, characteristic
9C2×#15688999C211yesmaximal, characteristic
10C2×#15688990C211yesmaximal, characteristic, complemented
11C2×#15688990C211yesmaximal, characteristic, complemented
12C2×#15688985C211yesmaximal, characteristic, complemented
13C2×#15688984C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#393C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×C4×Dic47C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32#15689065C2218yescomplemented
33#15689039C2218yes—
34#15689034C2218yescomplemented
35#15689030C2218yescomplemented
36#15689017C2218yescomplemented
37#15689012C2218yescomplemented
38#15689000C2218yes—
39#15688999C2218yes—
40#15688990C2218yescomplemented
41#15688990C2218yescomplemented
42#15688985C2218yescomplemented
43#15688984C2218yescomplemented
44C22⋊C4×Dic47C2218yescomplemented
45#15688970C2218yescomplemented
46C2×C47⋊#95C2211yescharacteristic
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×Q8×C47C2211yescharacteristic
60C22×C22⋊C4×C47C2211yescharacteristic
61C22×C22⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C47×#393C2218yescomplemented
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C24×D47C2311yescharacteristic
68C22×C22⋊D47—24no—
69C22×C22⋊D47—24no—
70C22×C22⋊D47—42no—
71C22×C22⋊D47C2314yes—
72C23×Dic47—24no—
73C23×Dic47—24no—
74C23×Dic47—42no—
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2314yes—
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C22×C4×D47—24no—
84C22×C4×D47—24no—
85C22×C4×D47—42no—
86C22×C4×D47C2314yes—
87C2×C4⋊Dic47—42no—
88C2×C4⋊Dic47C2314yes—
89C2×Dic47⋊C4—42no—
90C2×Dic47⋊C4C2314yes—
91C2×C22⋊Dic47—24no—
92C2×C22⋊Dic47—24no—
93C2×C22⋊Dic47C2314yes—
94C2×C22⋊Dic47C2314yes—
95C2×(C2×D47)⋊C4—24no—
96C2×(C2×D47)⋊C4—24no—
97C2×(C2×D47)⋊C4—24no—
98C2×(C2×D47)⋊C4—42no—
99C2×(C2×D47)⋊C4—42no—
100C2×(C2×D47)⋊C4C2314yes—
101C2×(C2×D47)⋊C4C2314yes—
102C2×(C2×D47)⋊C4C2314yes—
103C2×(C2×D47)⋊C4C2314yes—
104C2×(C2×D47)⋊C4C2314yes—
105C2×C4×Dic47—24no—
106C2×C4×Dic47—24no—
107C2×C4×Dic47—42no—
108C2×C4×Dic47C2314yes—
109C2×C4×Dic47C2314yes—
110C2×C4×Dic47C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C25×C47C2311yescharacteristic
125C22×Q8×C47—24no—
126C22×Q8×C47—42no—
127C22×Q8×C47—42no—
128C22×Q8×C47C2314yes—
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C2×C22⋊C4×C47—24no—
136C2×C22⋊C4×C47—42no—
137C2×C22⋊C4×C47—42no—
138C2×C22⋊C4×C47C2314yes—
139C2×C22⋊C4×C47C2314yes—
140C2×C22⋊C4×C47C2314yes—
141#95×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#4114yes—
151C24×C47C2412yes—
152C24×C47C2411yescharacteristic
153C23×D47—22no—
154C23×D47—22no—
155C23×D47—22no—
156C23×D47—22no—
157C23×D47—22no—
158C23×D47—22no—
159C23×D47#4114yes—
160C23×D47C2412yes—
161C2×Q8×C47—28no—
162C2×Q8×C47—44no—
163C2×Q8×C47—44no—
164C2×Q8×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—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47#4114yes—
183C22×C4×C47C2412yes—
184C22×C4×C47C2412yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2412yes—
189C2×C22⋊D47—28no—
190C2×C22⋊D47—28no—
191C2×C22⋊D47—44no—
192C2×C22⋊D47—416no—
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—28no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—28no—
214C22×Dic47—44no—
215C22×Dic47—416no—
216C22×Dic47#4114yes—
217C22×Dic47#4114yes—
218C22×Dic47C2412yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C2×C4×D47—28no—
226C2×C4×D47—28no—
227C2×C4×D47—44no—
228C2×C4×D47—416no—
229C22⋊C4×C47—28no—
230C22⋊C4×C47—44no—
231C22⋊C4×C47—44no—
232C22⋊Dic47—28no—
233C22⋊Dic47—28no—
234(C2×D47)⋊C4—28no—
235(C2×D47)⋊C4—28no—
236(C2×D47)⋊C4—28no—
237(C2×D47)⋊C4—44no—
238(C2×D47)⋊C4—44no—
239C4⋊Dic47—44no—
240Dic47⋊C4—44no—
241C4×Dic47—28no—
242C4×Dic47—28no—
243C4×Dic47—44no—
244C23×C47—28no—
245C23×C47—28no—
246C23×C47—28no—
247C23×C47—22no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—44no—
254C23×C47—44no—
255C23×C47—44no—
256C23×C47—44no—
257C23×C47C2×#4112yes—
258C23×C47C2×#4112yes—
259C23×C47C2×#4112yes—
260C23×C47C2×#4112yes—
261C23×C47C2×#4114yes—
262C23×C47C2×#4112yes—
263C23×C47H(5,𝔽2)12yes—
264C23×C47H(5,𝔽2)12yes—
265C23×C47C2511yescharacteristic
266C22×D47—28no—
267C22×D47—28no—
268C22×D47—28no—
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—44no—
276C22×D47—44no—
277C22×D47—44no—
278C22×D47—44no—
279C22×D47C2×#4114yes—
280Q8×C47—416no—
281C2×C4×C47—28no—
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—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—44no—
300C2×C4×C47—44no—
301C2×C4×C47—44no—
302C2×C4×C47—44no—
303C2×C4×C47—44no—
304C2×C4×C47C2×#4114yes—
305C22⋊D47—416no—
306C2×Dic47—28no—
307C2×Dic47—28no—
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—22no—
326C2×Dic47—22no—
327C2×Dic47—416no—
328C2×Dic47—44no—
329C2×Dic47—44no—
330C2×Dic47—44no—
331C2×Dic47—44no—
332C2×Dic47—44no—
333C2×Dic47C2×#4114yes—
334C2×Dic47C2×#4114yes—
335C4×D47—416no—
336C2×#2572—471nomaximal, Sylow
337C22×C47—24no—
338C22×C47—24no—
339C22×C47—24no—
340C22×C47—416no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47#52914yes—
346C22×C47#52914yes—
347C22×C47#53814yes—
348C22×C47#55114yes—
349C22×C47#55114yes—
350C22×C47#55114yes—
351C22×C47#55514yes—
352C22×C47C22×#4111yescharacteristic
353C22×C47C22×#4111yescharacteristic
354C22×C47C22×#4111yescharacteristic
355C22×C47C22×#4111yescharacteristic
356C22×C47C22×#4111yescharacteristic
357C22×C47C2×H(5,𝔽2)11yescharacteristic
358C22×C47C2×H(5,𝔽2)11yescharacteristic
359C2×D47—24no—
360C2×D47—24no—
361C2×D47—24no—
362C2×D47—416no—
363C2×D47—42no—
364C2×D47—42no—
365C2×D47—42no—
366C2×D47—42no—
367C4×C47—24no—
368C4×C47—42no—
369C4×C47—42no—
370C4×C47—42no—
371C4×C47—42no—
372C4×C47—42no—
373Dic47—24no—
374Dic47—24no—
375Dic47—42no—
376Dic47—42no—
377Dic47—42no—
378Dic47—42no—
379Dic47—42no—
380#2572—4716no—
381C2×#400—471no—
382C2×#394—471no—
383C2×#393—471no—
384C2×#393D4711yescharacteristic, complemented
385C2×#391—471no—
386C2×#388—471no—
387C2×#388—471no—
388C2×#386—471no—
389C2×#386—471no—
390C2×#383—471no—
391C2×#383—471no—
392C2×#381—471no—
393C2×#381—471no—
394C2×C4×C22⋊C4—471no—
395C2×C4×C22⋊C4—471no—
396C2×C47—44no—
397C2×C47#257218yescomplemented
398C2×C47C2×#52911yescharacteristic
399C2×C47C2×#52911yescharacteristic
400C2×C47C2×#53811yescharacteristic
401C2×C47C2×#55111yescharacteristic
402C2×C47C2×#55111yescharacteristic
403C2×C47C2×#55111yescharacteristic
404C2×C47C2×#55511yescharacteristic
405D47—44no—
406C23×Q8C2×D4711yescharacteristic
407C23×D4—471no—
408C24×C4—471no—
409C24×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#394—478no—
427#393—478no—
428#393C2×D4718yescomplemented
429#391—478no—
430#388—478no—
431#388—478no—
432#386—478no—
433#386—478no—
434#383—478no—
435#383—478no—
436#381—478no—
437#381—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×#95—471no—
453C2×#95C2×D4711yescharacteristic
454C2×#95C2×D4711yescharacteristic
455C2×#95C2×D4711yescharacteristic
456C47C2×#257211yescharacteristic, complemented, Sylow
457C25—471no—
458C25C22×D4711yescharacteristic
459C22×Q8—24no—
460C22×Q8—42no—
461C22×Q8—42no—
462C22×Q8C22×D4714yes—
463C22×D4—474no—
464C22×D4—944no—
465C22×D4—944no—
466C22×D4—1882no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4—471no—
474C23×C4—474no—
475C23×C4—474no—
476C23×C4—944no—
477C23×C4—944no—
478C23×C4—944no—
479C23×C4—944no—
480C23×C4—1882no—
481C23×C4—1882no—
482C23×C4C22×D4711yescharacteristic
483C23×C4C22×D4711yescharacteristic
484C23×C4C22×D4711yescharacteristic
485C23×C4C22×D4711yescharacteristic
486C23×C4C22×D4711yescharacteristic
487C23×C4C22×D4711yescharacteristic
488C2×C4⋊C4—474no—
489C2×C4⋊C4—474no—
490C2×C4⋊C4—1882no—
491C2×C4⋊C4—1882no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
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—944no—
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#95—474no—
531#95C22×D4714yes—
532#95C22×D4714yes—
533#95C22×D4714yes—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—474no—
541C24—472no—
542C24—942no—
543C24—942no—
544C24—942no—
545C24—942no—
546C24—942no—
547C24—942no—
548C24#1062535414yes—
549C24C23×D4712yes—
550C24C23×D4711yescharacteristic
551C2×Q8—28no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—416no—
555C2×D4—948no—
556C2×D4—948no—
557C2×D4—1884no—
558C2×D4—18816no—
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—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—474no—
577C22×C4—474no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—472no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—472no—
585C22×C4—948no—
586C22×C4—948no—
587C22×C4—948no—
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—948no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—1884no—
609C22×C4—18816no—
610C22×C4—1884no—
611C22×C4—18816no—
612C22×C4#1062535214yes—
613C22×C4C23×D4712yes—
614C22×C4C23×D4712yes—
615C22×C4C23×D4712yes—
616C22×C4C23×D4712yes—
617C22×C4C23×D4712yes—
618C22×C4C23×D4712yes—
619C4⋊C4—1884no—
620C4⋊C4—1884no—
621C22⋊C4—28no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—948no—
625C22⋊C4—948no—
626C22⋊C4—948no—
627C22⋊C4—948no—
628C22⋊C4—948no—
629C22⋊C4—1884no—
630C22⋊C4—1884no—
631C42—948no—
632C42—948no—
633C42—1884no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—474no—
648C23—948no—
649C23—948no—
650C23—948no—
651C23—942no—
652C23—942no—
653C23—942no—
654C23—942no—
655C23—942no—
656C23—942no—
657C23—1884no—
658C23—1884no—
659C23—1884no—
660C23—1884no—
661C23#41×D4712yes—
662C23#41×D4712yes—
663C23#41×D4712yes—
664C23C2×#1062535212yes—
665C23C2×#1062535414yes—
666C23C2×#1062535412yes—
667C23#1309406912yes—
668C23#1309406912yes—
669C23C24×D4711yescharacteristic
670Q8—416no—
671D4—18816no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—28no—
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—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—474no—
696C2×C4—474no—
697C2×C4—948no—
698C2×C4—948no—
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—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—18816no—
719C2×C4—18816no—
720C2×C4—1884no—
721C2×C4—1884no—
722C2×C4—1884no—
723C2×C4—1884no—
724C2×C4—1884no—
725C2×C4C2×#1062535214yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—416no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—944no—
735C22—944no—
736C22—944no—
737C22—18816no—
738C22—1882no—
739C22—1882no—
740C22—1882no—
741C22—1882no—
742C22#1568965214yes—
743C22#1568965914yes—
744C22#1568970814yes—
745C22#1568980014yes—
746C22#1568980014yes—
747C22#1568980314yes—
748C22#1568983514yes—
749C22C2×#41×D4711yescharacteristic
750C22C2×#41×D4711yescharacteristic
751C22C2×#41×D4711yescharacteristic
752C22C22×#1062535211yescharacteristic
753C22C22×#1062535411yescharacteristic
754C22C2×#1309406911yescharacteristic
755C22C2×#1309406911yescharacteristic
756C4—24no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—944no—
763C4—944no—
764C4—1882no—
765C4—1882no—
766C4—1882no—
767C4—1882no—
768C4—1882no—
769C2—44no—
770C2—1884no—
771C2#2024863318yesdirect product factor
772C2C2×#1568965211yescharacteristic
773C2C2×#1568965911yescharacteristic
774C2C2×#1568970811yescharacteristic
775C2C2×#1568980011yescharacteristic
776C2C2×#1568980011yescharacteristic
777C2C2×#1568980311yescharacteristic
778C2C2×#1568983511yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#393C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×#393D47
hypocenterC47C2×#2572
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. #20248633C2direct (N × H)
2. C2×#15689065C2semidirect
4. C2×#15689034C2semidirect
5. C2×#15689030C2semidirect
6. C2×#15689017C2semidirect
7. C2×#15689012C2semidirect
10. C2×#15688990C2semidirect
11. C2×#15688990C2semidirect
12. C2×#15688985C2semidirect
13. C2×#15688984C2semidirect
14. C2×C22⋊C4×Dic47C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#393C2semidirect
32. #15689065C22semidirect
34. #15689034C22semidirect
35. #15689030C22semidirect
36. #15689017C22semidirect
37. #15689012C22semidirect
40. #15688990C22semidirect
41. #15688990C22semidirect
42. #15688985C22semidirect
43. #15688984C22semidirect
44. C22⋊C4×Dic47C22semidirect
45. #15688970C22semidirect
63. C47×#393C22semidirect
384. C2×#393D47semidirect
397. C2×C47#2572semidirect
428. #393C2×D47semidirect
456. C47C2×#2572semidirect
771. C2#20248633direct (N × H)

Maximal subgroups

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

subgroupindex
#202486332
C2×#156890652
C2×#156890392
C2×#156890342
C2×#156890302
C2×#156890172
C2×#156890122
C2×#156890002
C2×#156889992
C2×#156889902
C2×#156889852
C2×#156889842
C2×C22⋊C4×Dic472
C2×#156889702
C2×C47×#3932
C2×#257247