Finite Group Databasebeta

← C2×#20255276 #27092686

Subgroups — C2×#20255276 #27092686

Order 12032.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689812C211yesmaximal, characteristic, complemented
2C2×#15689780C211yesmaximal, characteristic
3#20255276C2116yesmaximal, direct product factor
4C2×#15689476C211yesmaximal, characteristic, complemented
5C2×#15689464C211yesmaximal, characteristic, complemented
6C2×#15689435C211yesmaximal, characteristic, complemented
7C2×#15689432C211yesmaximal, characteristic, complemented
8C2×#15689364C211yesmaximal, characteristic, complemented
9C2×#15689351C211yesmaximal, characteristic, complemented
10C2×#15689344C211yesmaximal, characteristic, complemented
11C2×#15689285C211yesmaximal, characteristic, complemented
12C2×#15689280C211yesmaximal, characteristic, complemented
13C2×#15689215C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
15C2×#103×D47C211yesmaximal, characteristic, complemented
16C2×C47×#416C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×C8×D47C2211yescharacteristic
22#15689812—24no—
23#15689812C2218yescomplemented
24#15689780—24no—
25#15689780C2218yes—
26C2×#13094017—21no—
27C2×#13094016—21no—
28C2×#13094015C2211yescharacteristic
29C2×#13094011—21no—
30C2×#13094011C2211yescharacteristic
31C2×#13094006—21no—
32C2×#13094004C2211yescharacteristic
33C2×#13094003—21no—
34C2×#13094003C2211yescharacteristic
35C2×#13094003C2211yescharacteristic
36C2×#13093995—21no—
37C2×#13093995C2211yescharacteristic
38C2×Q8×Dic47C2211yescharacteristic
39C2×#13093989C2211yescharacteristic
40C2×C4×C22⋊D47—21no—
41C2×C4×C22⋊D47C2211yescharacteristic
42C2×#13093981—21no—
43C2×C4⋊C4×D47C2211yescharacteristic
44#15689476C2218yescomplemented
45#15689464C2218yescomplemented
46#15689435C2218yescomplemented
47#15689432C2218yescomplemented
48#15689364C2218yescomplemented
49#15689351C2218yescomplemented
50#15689344C2218yescomplemented
51#15689285C2218yescomplemented
52#15689280C2218yescomplemented
53#15689215C2218yescomplemented
54C8×C22⋊D47C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64#103×D47C2218yescomplemented
65C2×#13093945C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×#41×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×#117×C47C2211yescharacteristic
72C47×#416C2218yescomplemented
73C2×#103×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C2×Q8×D47—22no—
81C2×Q8×D47—24no—
82C2×Q8×D47—42no—
83C2×Q8×D47C2314yes—
84C22×C22⋊D47—21no—
85C22×C22⋊D47D411yescharacteristic
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47C2311yescharacteristic
89C2×Dic188—42no—
90C2×Dic188C2314yes—
91C2×#10625337—24no—
92C2×#10625337C2314yes—
93C2×#10625335—42no—
94C2×#10625335C2314yes—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97C2×C8×D47—42no—
98C2×C8×D47C2314yes—
99#13094017—28no—
100#13094016—28no—
101#13094015—22no—
102#13094015C2314yes—
103#13094011—28no—
104#13094011—22no—
105#13094011C2314yes—
106#13094006—28no—
107#13094004—22no—
108#13094004C2314yes—
109#13094003—22no—
110#13094003—22no—
111#13094003—28no—
112#13094003C2314yes—
113#13094003C2314yes—
114#13093995—28no—
115#13093995—22no—
116#13093995C2314yes—
117Q8×Dic47—22no—
118Q8×Dic47C2314yes—
119#13093989—22no—
120#13093989C2314yes—
121C4×C22⋊D47—28no—
122C4×C22⋊D47D414yes—
123C4×C22⋊D47C2314yes—
124#13093981—28no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4D411yescharacteristic
136C4⋊C4×D47—22no—
137C4⋊C4×D47C2314yes—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47—21no—
142C2×C22⋊Dic47—21no—
143C2×C22⋊Dic47D411yescharacteristic
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093958C2314yes—
150#13093957C2314yes—
151#13093955C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157#13093947C2314yes—
158#13093945C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160(C2×D47)⋊C8C2314yes—
161C8×Dic47C2314yes—
162C2×#41×C47—22no—
163C2×#41×C47—24no—
164C2×#41×C47—42no—
165C2×#41×C47C2314yes—
166C22×Q8×C47C2311yescharacteristic
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47C2311yescharacteristic
171C22×C8×C47—42no—
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2314yes—
175#117×C47—22no—
176#117×C47C2314yes—
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C22⋊C4×C47—21no—
180C2×C42×C47—21no—
181#103×C47C2314yes—
182#103×C47C2314yes—
183#102×C47C2314yes—
184#102×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47C2×D411yescharacteristic
188#41×C47—28no—
189#41×C47—44no—
190#41×C47—48no—
191C2×Q8×C47—21no—
192C2×Q8×C47—22no—
193C2×Q8×C47#4114yes—
194C2×Q8×C47C2412yes—
195C2×D4×C47—24no—
196C2×D4×C47—21no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47—44no—
200C2×D4×C47C2412yes—
201C22×C4×C47—21no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—24no—
207C22×C4×C47—44no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2411yescharacteristic
212C2×C22⋊D47—24no—
213C2×C22⋊D47—24no—
214C2×C22⋊D47—44no—
215C2×C22⋊D47C2×D414yes—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47C2×D411yescharacteristic
221C22×Dic47C2×D411yescharacteristic
222C22×Dic47C2×D411yescharacteristic
223Q8×D47—28no—
224Q8×D47—44no—
225Q8×D47—48no—
226C2×C4×D47—22no—
227C2×C4×D47—22no—
228C2×C4×D47—24no—
229C2×C4×D47—24no—
230C2×C4×D47—44no—
231C2×C4×D47—44no—
232C2×C4×D47C2×D412yes—
233C2×C4×D47C2412yes—
234C2×Dic94—22no—
235C2×Dic94—22no—
236C2×Dic94—22no—
237C2×Dic94—22no—
238C2×Dic94—21no—
239C2×Dic94—21no—
240C2×Dic94—24no—
241C2×Dic94—44no—
242C2×Dic94C2412yes—
243C2×Dic94C2412yes—
244C2×C8×C47—22no—
245C2×C8×C47—22no—
246C2×C8×C47—44no—
247C2×C8×C47C2412yes—
248C2×C8×C47C2412yes—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47C2412yes—
252C4⋊C4×C47C2412yes—
253C22⋊C4×C47—24no—
254C42×C47—24no—
255C22⋊Dic47—24no—
256C22⋊Dic47—24no—
257C22⋊Dic47—24no—
258C22⋊Dic47—24no—
259C22⋊Dic47—24no—
260C22⋊Dic47C2×D414yes—
261#10625337—28no—
262#10625335—44no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4C2×D414yes—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47—24no—
268C4⋊Dic47—24no—
269C4⋊Dic47—24no—
270C4⋊Dic47C2412yes—
271C4⋊Dic47C2412yes—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4C2×D414yes—
278C4×Dic47—24no—
279C4×Dic47—24no—
280C4×Dic47C2×D412yes—
281C4×Dic47C2412yes—
282C2×C47⋊C8—22no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8C2412yes—
285C2×C47⋊C8C2412yes—
286Dic188—44no—
287C8×D47—44no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47—42no—
295C23×C47C22×D412yes—
296C23×C47C22×D411yescharacteristic
297C22×D47—22no—
298C22×D47—22no—
299C22×D47#13514yes—
300C22×D47C22×D412yes—
301Q8×C47—24no—
302Q8×C47—22no—
303Q8×C47C2×#4114yes—
304D4×C47—22no—
305D4×C47—22no—
306D4×C47—48no—
307D4×C47—42no—
308C2×C4×C47—24no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—24no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—48no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47C22×D412yes—
320C2×C4×C47C22×D411yescharacteristic
321C2×C4×C47C2×#4112yes—
322C2×C4×C47H(5,𝔽2)12yes—
323C2×C4×C47C2511yescharacteristic
324C22⋊D47—28no—
325C22⋊D47—48no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47C22×D412yes—
338C2×Dic47C22×D412yes—
339C2×Dic47C22×D412yes—
340C4×D47—24no—
341C4×D47—22no—
342C4×D47—22no—
343C4×D47—48no—
344C4×D47—48no—
345Dic94—22no—
346Dic94—22no—
347Dic94—22no—
348Dic94—22no—
349Dic94—48no—
350Dic94—42no—
351Dic94—42no—
352C8×C47—22no—
353C8×C47—22no—
354C47⋊C8—22no—
355C47⋊C8—22no—
356C2×#3300—471nomaximal, Sylow
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—44no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—84no—
365C22×C47#54612yes—
366C22×C47C2×#13512yes—
367C22×C47#57812yes—
368C22×C47C23×D411yescharacteristic
369C2×D47—22no—
370C2×D47—28no—
371C2×D47—22no—
372C2×D47C2×#13514yes—
373C4×C47—24no—
374C4×C47—22no—
375C4×C47—42no—
376C4×C47—42no—
377C4×C47#54612yes—
378C4×C47C22×#4111yescharacteristic
379C4×C47C2×H(5,𝔽2)11yescharacteristic
380Dic47—22no—
381Dic47—22no—
382Dic47—22no—
383Dic47—42no—
384Dic47—42no—
385Dic47—42no—
386Dic47—42no—
387C2×#552—471no—
388C2×#548—471no—
389#3300—4716no—
390C2×#488—471no—
391C2×#485—471no—
392C2×#480—471no—
393C2×#479—471no—
394C2×#467—471no—
395C2×#465—471no—
396C2×#464—471no—
397C2×#452—471no—
398C2×#451—471no—
399C2×C4×Q16—471no—
400C2×C8×D4—471no—
401C2×#416D4711yescharacteristic, complemented
402C22×#103—471no—
403C2×C47—42no—
404C2×C47—82no—
405C2×C47#330014yescomplemented
406C2×C47C2×#54611yescharacteristic
407C2×C47C22×#13511yescharacteristic
408C2×C47C2×#57811yescharacteristic
409D47—24no—
410C22×#41C2×D4711yescharacteristic
411C23×Q8—471no—
412C22×Q16—471no—
413C22×Q16—471no—
414C22×SD16—471no—
415C23×C8—471no—
416C23×C8C2×D4711yescharacteristic
417#552—478no—
418#552—944no—
419#548—478no—
420#548—944no—
421C2×#126—941no—
422C2×#125—471no—
423C2×#125—941no—
424C2×#124—471no—
425C2×#124—941no—
426C2×#123—941no—
427C2×C22⋊Q8—471no—
428C2×C22⋊Q8—471no—
429C2×C22⋊Q8—471no—
430C2×C22⋊Q8—941no—
431C2×#121—471no—
432C2×#121—941no—
433C2×C4×Q8—471no—
434C2×C4×Q8—471no—
435C2×C4×D4—471no—
436C2×C4×D4—941no—
437C2×#117—941no—
438C2×#117C2×D4711yescharacteristic
439C22×C4⋊C4—471no—
440#488—478no—
441#485—478no—
442#480—478no—
443#479—478no—
444#467—478no—
445#465—478no—
446#464—478no—
447#452—478no—
448#451—478no—
449C4×Q16—478no—
450C8×D4—478no—
451C2×#107—471no—
452C2×#107—471no—
453C2×#106—471no—
454C2×C4⋊C8—471no—
455#416C2×D4718yescomplemented
456C2×#103—471no—
457C2×#103—471no—
458C2×#103—471no—
459C2×#103—471no—
460C2×#103—471no—
461C2×#103—478no—
462C2×#103C2×D4711yescharacteristic
463C2×#103C2×D4711yescharacteristic
464C2×#102—471no—
465C2×#102C2×D4711yescharacteristic
466C2×#102C2×D4711yescharacteristic
467C2×C22⋊C8—471no—
468C2×C22⋊C8—471no—
469C2×C4×C8—471no—
470C47C2×#330011yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41C22×D4714yes—
475C22×Q8—474no—
476C22×Q8—471no—
477C22×Q8—471no—
478C22×Q8—941no—
479C22×Q8—942no—
480C22×Q8—944no—
481C22×Q8—1882no—
482C22×Q8C22×D4711yescharacteristic
483C22×D4—21no—
484C22×D4—471no—
485C22×D4—941no—
486C22×D4C22×D4711yescharacteristic
487C23×C4—21no—
488C23×C4—471no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4C22×D4711yescharacteristic
492C2×Q16—474no—
493C2×Q16—474no—
494C2×Q16—944no—
495C2×Q16—1882no—
496C2×SD16—474no—
497C2×SD16—1882no—
498C22×C8—42no—
499C22×C8—471no—
500C22×C8—471no—
501C22×C8—474no—
502C22×C8—1882no—
503C22×C8C22×D4711yescharacteristic
504C22×C8C22×D4711yescharacteristic
505C22×C8C22×D4714yes—
506#126—948no—
507#125—474no—
508#125—948no—
509#125—942no—
510#124—474no—
511#124—942no—
512#124—948no—
513#123—948no—
514C22⋊Q8—474no—
515C22⋊Q8—474no—
516C22⋊Q8—474no—
517C22⋊Q8—942no—
518C22⋊Q8—948no—
519C22⋊Q8—942no—
520C22⋊Q8—942no—
521#121—474no—
522#121—942no—
523#121—948no—
524C4×Q8—474no—
525C4×Q8—474no—
526C4×Q8—942no—
527C4×Q8—942no—
528C4×D4—474no—
529C4×D4—474no—
530C4×D4—948no—
531#117—22no—
532#117—948no—
533#117C22×D4714yes—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—474no—
538C2×C4⋊C4—942no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C4⋊C4C22×D4711yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—471no—
551C2×C22⋊C4—471no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C42—21no—
559C2×C42—471no—
560C2×C42—941no—
561C2×C42—941no—
562#107—474no—
563#107—474no—
564#106—474no—
565C4⋊C8—474no—
566#103—474no—
567#103—474no—
568#103—474no—
569#103—474no—
570#103—474no—
571#103C22×D4714yes—
572#103C22×D4714yes—
573#102—474no—
574#102C22×D4714yes—
575#102C22×D4714yes—
576C22⋊C8—474no—
577C22⋊C8—474no—
578C4×C8—474no—
579C24—21no—
580C24—471no—
581C24D4×D4711yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—472no—
588C2×Q8—472no—
589C2×Q8—944no—
590C2×Q8—941no—
591C2×Q8—941no—
592C2×Q8—948no—
593C2×Q8—942no—
594C2×Q8—942no—
595C2×Q8—942no—
596C2×Q8—942no—
597C2×Q8—1884no—
598C2×Q8—1884no—
599C2×Q8—1888no—
600C2×Q8#1062535014yes—
601C2×Q8C23×D4712yes—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—44no—
607C2×D4—474no—
608C2×D4—944no—
609C2×D4—944no—
610C2×D4—1884no—
611C2×D4C23×D4712yes—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
618C22×C4—44no—
619C22×C4—471no—
620C22×C4—471no—
621C22×C4—471no—
622C22×C4—472no—
623C22×C4—472no—
624C22×C4—944no—
625C22×C4—944no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4—1884no—
633C22×C4—1884no—
634C22×C4D4×D4712yes—
635C22×C4D4×D4711yescharacteristic
636C22×C4C23×D4712yes—
637C22×C4C23×D4711yescharacteristic
638Q16—948no—
639Q16—1884no—
640SD16—1884no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—44no—
644C2×C8—472no—
645C2×C8—472no—
646C2×C8—942no—
647C2×C8—942no—
648C2×C8—1884no—
649C2×C8C23×D4712yes—
650C2×C8C23×D4712yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—474no—
654C4⋊C4—472no—
655C4⋊C4—472no—
656C4⋊C4—944no—
657C4⋊C4—944no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—944no—
662C4⋊C4—944no—
663C4⋊C4—944no—
664C4⋊C4—941no—
665C4⋊C4—941no—
666C4⋊C4C23×D4712yes—
667C4⋊C4C23×D4712yes—
668C22⋊C4—24no—
669C22⋊C4—474no—
670C22⋊C4—474no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C22⋊C4—944no—
674C22⋊C4—944no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C42—24no—
678C42—472no—
679C42—472no—
680C42—944no—
681C42—944no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—474no—
690C23—472no—
691C23—942no—
692C23—942no—
693C23C2×D4×D4712yes—
694C23C2×D4×D4711yescharacteristic
695Q8—24no—
696Q8—22no—
697Q8—942no—
698Q8—942no—
699Q8—942no—
700Q8—942no—
701Q8—1888no—
702Q8—1882no—
703Q8—1882no—
704Q8C2×#1062535014yes—
705D4—22no—
706D4—22no—
707D4—48no—
708D4—42no—
709D4—948no—
710D4—1888no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—48no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—472no—
723C2×C4—472no—
724C2×C4—472no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—944no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—1888no—
736C2×C4—1888no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4C2×D4×D4712yes—
742C2×C4C2×D4×D4711yescharacteristic
743C2×C4C2×#1062535012yes—
744C2×C4#1309406912yes—
745C2×C4C24×D4711yescharacteristic
746C8—22no—
747C8—22no—
748C8—942no—
749C8—942no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—474no—
759C22—948no—
760C22—942no—
761C22—942no—
762C22#1568976312yes—
763C22#135×D4712yes—
764C22#1568993712yes—
765C22C22×D4×D4711yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—942no—
771C4—942no—
772C4—942no—
773C4—1882no—
774C4—1882no—
775C4—1882no—
776C4—1882no—
777C4#1568976312yes—
778C4C22×#1062535011yescharacteristic
779C4C2×#1309406911yescharacteristic
780C2—42no—
781C2—82no—
782C2—944no—
783C2#2025527614yesdirect product factor
784C2C2×#1568976311yescharacteristic
785C2C2×#135×D4711yescharacteristic
786C2C2×#1568993711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#416C2
socleC23×C47C22×D4
prime radicalC2×#15689780C2
hypercenterC2×#416D47
hypocenterC47C2×#3300
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#15689812C2semidirect
3. #20255276C2direct (N × H)
4. C2×#15689476C2semidirect
5. C2×#15689464C2semidirect
6. C2×#15689435C2semidirect
7. C2×#15689432C2semidirect
8. C2×#15689364C2semidirect
9. C2×#15689351C2semidirect
10. C2×#15689344C2semidirect
11. C2×#15689285C2semidirect
12. C2×#15689280C2semidirect
13. C2×#15689215C2semidirect
14. C2×C8×C22⋊D47C2semidirect
15. C2×#103×D47C2semidirect
16. C2×C47×#416C2semidirect
23. #15689812C22semidirect
44. #15689476C22semidirect
45. #15689464C22semidirect
46. #15689435C22semidirect
47. #15689432C22semidirect
48. #15689364C22semidirect
49. #15689351C22semidirect
50. #15689344C22semidirect
51. #15689285C22semidirect
52. #15689280C22semidirect
53. #15689215C22semidirect
54. C8×C22⋊D47C22semidirect
64. #103×D47C22semidirect
72. C47×#416C22semidirect
401. C2×#416D47semidirect
405. C2×C47#3300semidirect
455. #416C2×D47semidirect
470. C47C2×#3300semidirect
783. C2#20255276direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898122
C2×#156897802
#202552762
C2×#156894762
C2×#156894642
C2×#156894352
C2×#156894322
C2×#156893642
C2×#156893512
C2×#156893442
C2×#156892852
C2×#156892802
C2×#156892152
C2×C8×C22⋊D472
C2×#103×D472
C2×C47×#4162
C2×#330047