Finite Group Databasebeta

← C2×#20255477 #27092925

Subgroups — C2×#20255477 #27092925

Order 12032.

2126 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×#15689815C211yesmaximal, characteristic, complemented
2C2×#15689772C211yesmaximal, characteristic
3#20255477C2116yesmaximal, direct product factor
4C2×#15689490C211yesmaximal, characteristic, complemented
5C2×#15689459C211yesmaximal, characteristic, complemented
6C2×#15689463C211yesmaximal, characteristic, complemented
7C2×#15689421C211yesmaximal, characteristic, complemented
8C2×#15689379C211yesmaximal, characteristic, complemented
9C2×#15689361C211yesmaximal, characteristic, complemented
10C2×#15689331C211yesmaximal, characteristic, complemented
11C2×#15689282C211yesmaximal, characteristic, complemented
12C2×#15689224C211yesmaximal, characteristic, complemented
13C2×#15689197C211yesmaximal, characteristic, complemented
14C2×#15689124C211yesmaximal, characteristic, complemented
15C2×#15689116C211yesmaximal, characteristic, complemented
16C2×C47×#452C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625329C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689815—24no—
22#15689815C2218yescomplemented
23#15689772—24no—
24#15689772C2218yes—
25C2×#13094022C2211yescharacteristic
26C2×#13094019—21no—
27C2×#13094015—21no—
28C2×#13094015C2211yescharacteristic
29C2×#13094008—21no—
30C2×#13094007—21no—
31C2×#13094005—21no—
32C2×#13094003C2211yescharacteristic
33C2×#13094000C2211yescharacteristic
34C2×#13094000C2211yescharacteristic
35C2×#13093996—21no—
36C2×Q8×Dic47C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×#13093982C2211yescharacteristic
40C2×#13093980—21no—
41C22×C4⋊Dic47C2211yescharacteristic
42C22×Dic47⋊C4—21no—
43#15689490C2218yescomplemented
44#15689463C2218yescomplemented
45#15689459C2218yescomplemented
46#15689421C2218yescomplemented
47#15689379C2218yescomplemented
48#15689361C2218yescomplemented
49#15689331C2218yescomplemented
50#15689282C2218yescomplemented
51#15689224C2218yescomplemented
52#15689197C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57#15689124C2218yescomplemented
58#15689116C2218yescomplemented
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×#41×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C22×SD16×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#452C2218yescomplemented
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625352—24no—
78C2×#10625352—22no—
79C2×#10625352—42no—
80C2×#10625352C2314yes—
81C22×Dic94C2311yescharacteristic
82C22×C22⋊D47—21no—
83C22×C22⋊D47D411yescharacteristic
84C23×Dic47—21no—
85C23×Dic47—21no—
86C23×Dic47—21no—
87C22×C4×D47C2311yescharacteristic
88C2×#10625337—42no—
89C2×#10625337C2314yes—
90C2×#10625329—42no—
91C2×#10625329C2314yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C2×C8×D47—42no—
95C2×C8×D47C2314yes—
96#13094022—22no—
97#13094022C2314yes—
98#13094019—28no—
99#13094015—28no—
100#13094015—22no—
101#13094015C2314yes—
102#13094008—28no—
103#13094007—28no—
104#13094005—28no—
105#13094003—22no—
106#13094003C2314yes—
107#13094000—22no—
108#13094000—22no—
109#13094000C2314yes—
110#13094000C2314yes—
111#13093996—28no—
112Q8×Dic47—22no—
113Q8×Dic47C2314yes—
114D4×Dic47—22no—
115D4×Dic47C2314yes—
116C4×C22⋊D47D414yes—
117C4×C22⋊D47C2314yes—
118#13093982—22no—
119#13093982C2314yes—
120#13093980—28no—
121C2×C4⋊Dic47—22no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47C2314yes—
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—28no—
136C2×Dic47⋊C4D411yescharacteristic
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47D411yescharacteristic
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093958C2314yes—
148#13093958C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151#13093949C2314yes—
152#13093949C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157#13093945C2314yes—
158#13093945C2314yes—
159(C2×D47)⋊C8C2314yes—
160#13093934C2314yes—
161C2×#41×C47—22no—
162C2×#41×C47—24no—
163C2×#41×C47—42no—
164C2×#41×C47C2314yes—
165C22×Q8×C47C2311yescharacteristic
166C22×Q8×C47C2311yescharacteristic
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47C2311yescharacteristic
171C2×Q16×C47—42no—
172C2×Q16×C47C2314yes—
173C2×SD16×C47—24no—
174C2×SD16×C47C2314yes—
175C22×C8×C47C2311yescharacteristic
176C22×C8×C47C2311yescharacteristic
177C22⋊Q8×C47—22no—
178C22⋊Q8×C47C2314yes—
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182#103×C47C2314yes—
183#102×C47C2314yes—
184C22⋊C8×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—21no—
193C2×Q8×C47—22no—
194C2×Q8×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47—22no—
197C2×Q8×C47C2412yes—
198C2×Q8×C47C2412yes—
199C2×D4×C47—24no—
200C2×D4×C47—21no—
201C2×D4×C47—22no—
202C2×D4×C47—44no—
203C2×D4×C47#4114yes—
204C2×D4×C47C2412yes—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—24no—
211C22×C4×C47—44no—
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2411yescharacteristic
216C2×C22⋊D47—24no—
217C2×C22⋊D47—42no—
218C2×C22⋊D47—44no—
219C2×C22⋊D47C2×D414yes—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—24no—
225C22×Dic47—24no—
226C22×Dic47—24no—
227C22×Dic47—44no—
228C22×Dic47—44no—
229C22×Dic47—44no—
230C22×Dic47C2×D411yescharacteristic
231C22×Dic47C2×D411yescharacteristic
232C22×Dic47C2×D411yescharacteristic
233#10625352—28no—
234#10625352—44no—
235#10625352—48no—
236C2×C4×D47—22no—
237C2×C4×D47—22no—
238C2×C4×D47C2×D412yes—
239C2×C4×D47C2412yes—
240C2×Dic94—22no—
241C2×Dic94—22no—
242C2×Dic94—21no—
243C2×Dic94C2412yes—
244Q16×C47—44no—
245SD16×C47—28no—
246C2×C8×C47—22no—
247C2×C8×C47—22no—
248C2×C8×C47C2412yes—
249C2×C8×C47C2412yes—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47C2412yes—
253C22⋊C4×C47—24no—
254C22⋊Dic47—24no—
255C22⋊Dic47—24no—
256C22⋊Dic47C2×D414yes—
257#10625337—44no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4C2×D414yes—
262C4⋊Dic47—21no—
263C4⋊Dic47—21no—
264C4⋊Dic47—24no—
265C4⋊Dic47—21no—
266C4⋊Dic47—24no—
267C4⋊Dic47—24no—
268C4⋊Dic47C2412yes—
269C4⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271Dic47⋊C4—24no—
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—
282#10625329—44no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8—22no—
285C2×C47⋊C8C2412yes—
286C2×C47⋊C8C2412yes—
287C8×D47—44no—
288C23×C47—24no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—42no—
294C23×C47—42no—
295C23×C47C22×D412yes—
296C23×C47C22×D411yescharacteristic
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47C22×D412yes—
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47—42no—
306Q8×C47—42no—
307D4×C47—24no—
308D4×C47—22no—
309D4×C47—48no—
310D4×C47C2×#4114yes—
311C2×C4×C47—22no—
312C2×C4×C47—24no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—48no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47C22×D412yes—
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C2×#4112yes—
325C2×C4×C47H(5,𝔽2)12yes—
326C2×C4×C47C2511yescharacteristic
327C22⋊D47—44no—
328C22⋊D47—48no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—48no—
337C2×Dic47—48no—
338C2×Dic47—48no—
339C2×Dic47—42no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47C22×D412yes—
344C2×Dic47C22×D412yes—
345C2×Dic47C22×D412yes—
346C4×D47—24no—
347C4×D47—22no—
348C4×D47—22no—
349Dic94—22no—
350Dic94—22no—
351Dic94—42no—
352C8×C47—22no—
353C8×C47—22no—
354C47⋊C8—22no—
355C47⋊C8—22no—
356C2×#3315—471nomaximal, Sylow
357C22×C47—24no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—44no—
362C22×C47—48no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47#54612yes—
366C22×C47#57512yes—
367C22×C47#57812yes—
368C22×C47C23×D411yescharacteristic
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—22no—
372C2×D47—44no—
373C4×C47—22no—
374C4×C47—42no—
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×#547—471no—
389#3315—4716no—
390C2×#491—471no—
391C2×#484—471no—
392C2×#485—471no—
393C2×#478—471no—
394C2×#470—471no—
395C2×#467—471no—
396C2×#462—471no—
397C2×#452—471no—
398C2×#452D4711yescharacteristic, complemented
399C2×#440—471no—
400C2×#435—471no—
401C2×#417—471no—
402C2×#416—471no—
403C2×C47—42no—
404C2×C47—44no—
405C2×C47#331514yescomplemented
406C2×C47C2×#54611yescharacteristic
407C2×C47C2×#57511yescharacteristic
408C2×C47C2×#57811yescharacteristic
409D47—42no—
410C22×#41—471no—
411C22×#41C2×D4711yescharacteristic
412C22×Q16—471no—
413C22×Q16C2×D4711yescharacteristic
414C22×SD16C2×D4711yescharacteristic
415C22×M16—471no—
416C23×C8—471no—
417#552—478no—
418#552—944no—
419#547—478no—
420#547—944no—
421C2×C4⋊Q8—471no—
422C2×#126—941no—
423C2×#125—471no—
424C2×#125—941no—
425C2×#123—941no—
426C2×#123—941no—
427C2×#123—941no—
428C2×C22⋊Q8—471no—
429C2×C22⋊Q8—471no—
430C2×C22⋊Q8—471no—
431C2×C22⋊Q8C2×D4711yescharacteristic
432C2×#121—941no—
433C2×C4×Q8—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×#117—471no—
437C2×#117—941no—
438C22×C4⋊C4—471no—
439C22×C4⋊C4—941no—
440#491—478no—
441#485—478no—
442#484—478no—
443#478—478no—
444#470—478no—
445#467—478no—
446#462—478no—
447#452—478no—
448#452C2×D4718yescomplemented
449#440—478no—
450#435—478no—
451C2×#107—471no—
452C2×#107—471no—
453C2×#106—471no—
454C2×C4⋊C8—471no—
455#417—478no—
456#416—478no—
457C2×#103—471no—
458C2×#103—471no—
459C2×#103—471no—
460C2×#103—471no—
461C2×#103—471no—
462C2×#103—471no—
463C2×#103C2×D4711yescharacteristic
464C2×#102—471no—
465C2×#102—471no—
466C2×#102C2×D4711yescharacteristic
467C2×C22⋊C8—471no—
468C2×C22⋊C8C2×D4711yescharacteristic
469C2×#97—471no—
470C47C2×#331511yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41—474no—
475C2×#41—942no—
476C2×#41—944no—
477C2×#41—1882no—
478C2×#41C22×D4714yes—
479C22×Q8—471no—
480C22×Q8C22×D4711yescharacteristic
481C22×Q8C22×D4711yescharacteristic
482C22×D4—21no—
483C22×D4—471no—
484C22×D4—941no—
485C22×D4C22×D4711yescharacteristic
486C23×C4—21no—
487C23×C4—471no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4C22×D4711yescharacteristic
492C2×Q16—42no—
493C2×Q16—474no—
494C2×Q16—1882no—
495C2×Q16C22×D4714yes—
496C2×SD16—24no—
497C2×SD16C22×D4714yes—
498C2×M16—474no—
499C2×M16—1882no—
500C22×C8—471no—
501C22×C8—471no—
502C22×C8—474no—
503C22×C8—1882no—
504C22×C8C22×D4711yescharacteristic
505C22×C8C22×D4711yescharacteristic
506C4⋊Q8—474no—
507C4⋊Q8—942no—
508#126—948no—
509#125—474no—
510#125—942no—
511#125—948no—
512#123—948no—
513#123—948no—
514#123—948no—
515C22⋊Q8—22no—
516C22⋊Q8—474no—
517C22⋊Q8—474no—
518C22⋊Q8—474no—
519C22⋊Q8—942no—
520C22⋊Q8—942no—
521C22⋊Q8—942no—
522C22⋊Q8C22×D4714yes—
523#121—948no—
524C4×Q8—474no—
525C4×Q8—942no—
526C4×D4—474no—
527C4×D4—474no—
528C4×D4—474no—
529C4×D4—942no—
530#117—474no—
531#117—948no—
532#117—942no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—474no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—948no—
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⋊C4—941no—
548C2×C4⋊C4—942no—
549C2×C4⋊C4—941no—
550C2×C4⋊C4C22×D4711yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—471no—
553C2×C22⋊C4—471no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C22⋊C4—941no—
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#103—474no—
572#103C22×D4714yes—
573#102—474no—
574#102—474no—
575#102C22×D4714yes—
576C22⋊C8—474no—
577C22⋊C8C22×D4714yes—
578#97—474no—
579C24—21no—
580C24—471no—
581C24D4×D4711yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585#41—948no—
586#41—1884no—
587#41—1888no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—472no—
595C2×Q8—941no—
596C2×Q8—942no—
597C2×Q8—942no—
598C2×Q8C23×D4712yes—
599C2×Q8C23×D4712yes—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—44no—
604C2×D4—474no—
605C2×D4—944no—
606C2×D4—1882no—
607C2×D4—1884no—
608C2×D4#1062535214yes—
609C2×D4C23×D4712yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—471no—
618C22×C4—471no—
619C22×C4—471no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—944no—
623C22×C4—944no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—944no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—1884no—
632C22×C4—1884no—
633C22×C4—1884no—
634C22×C4D4×D4712yes—
635C22×C4D4×D4711yescharacteristic
636C22×C4C23×D4712yes—
637C22×C4C23×D4711yescharacteristic
638Q16—44no—
639Q16—1884no—
640SD16—28no—
641M16—1884no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—472no—
645C2×C8—472no—
646C2×C8—942no—
647C2×C8—942no—
648C2×C8—1884no—
649C2×C8C23×D4712yes—
650C2×C8C23×D4712yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—474no—
654C4⋊C4—472no—
655C4⋊C4—472no—
656C4⋊C4—472no—
657C4⋊C4—944no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—944no—
662C4⋊C4—944no—
663C4⋊C4—944no—
664C4⋊C4—944no—
665C4⋊C4—941no—
666C4⋊C4—941no—
667C4⋊C4—944no—
668C4⋊C4—941no—
669C4⋊C4C23×D4712yes—
670C22⋊C4—24no—
671C22⋊C4—474no—
672C22⋊C4—474no—
673C22⋊C4—944no—
674C22⋊C4—944no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C22⋊C4—944no—
678C42—472no—
679C42—472no—
680C42—944no—
681C42—944no—
682C23—22no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—472no—
690C23—942no—
691C23—942no—
692C23—942no—
693C23C2×D4×D4712yes—
694C23C2×D4×D4711yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—942no—
702Q8—942no—
703Q8—1882no—
704D4—24no—
705D4—22no—
706D4—48no—
707D4—1884no—
708D4—1888no—
709D4C2×#1062535214yes—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—472no—
722C2×C4—472no—
723C2×C4—472no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—944no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—1888no—
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×#1062535212yes—
744C2×C4#1309406912yes—
745C2×C4C24×D4711yescharacteristic
746C8—22no—
747C8—22no—
748C8—942no—
749C8—942no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—42no—
756C22—44no—
757C22—48no—
758C22—942no—
759C22—942no—
760C22—942no—
761C22—1884no—
762C22#1568976012yes—
763C22#1568992212yes—
764C22#1568993712yes—
765C22C22×D4×D4711yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—942no—
771C4—942no—
772C4—942no—
773C4—1882no—
774C4—1882no—
775C4—1882no—
776C4—1882no—
777C4#1568976012yes—
778C4C22×#1062535211yescharacteristic
779C4C2×#1309406911yescharacteristic
780C2—42no—
781C2—44no—
782C2—1882no—
783C2#2025547714yesdirect product factor
784C2C2×#1568976011yescharacteristic
785C2C2×#1568992211yescharacteristic
786C2C2×#1568993711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#452C2
socleC23×C47C22×D4
prime radicalC2×#15689772C2
hypercenterC2×#452D47
hypocenterC47C2×#3315
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#15689815C2semidirect
3. #20255477C2direct (N × H)
4. C2×#15689490C2semidirect
5. C2×#15689459C2semidirect
6. C2×#15689463C2semidirect
7. C2×#15689421C2semidirect
8. C2×#15689379C2semidirect
9. C2×#15689361C2semidirect
10. C2×#15689331C2semidirect
11. C2×#15689282C2semidirect
12. C2×#15689224C2semidirect
13. C2×#15689197C2semidirect
14. C2×#15689124C2semidirect
15. C2×#15689116C2semidirect
16. C2×C47×#452C2semidirect
22. #15689815C22semidirect
43. #15689490C22semidirect
44. #15689463C22semidirect
45. #15689459C22semidirect
46. #15689421C22semidirect
47. #15689379C22semidirect
48. #15689361C22semidirect
49. #15689331C22semidirect
50. #15689282C22semidirect
51. #15689224C22semidirect
52. #15689197C22semidirect
57. #15689124C22semidirect
58. #15689116C22semidirect
73. C47×#452C22semidirect
398. C2×#452D47semidirect
405. C2×C47#3315semidirect
448. #452C2×D47semidirect
470. C47C2×#3315semidirect
783. C2#20255477direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898152
C2×#156897722
#202554772
C2×#156894902
C2×#156894592
C2×#156894632
C2×#156894212
C2×#156893792
C2×#156893612
C2×#156893312
C2×#156892822
C2×#156892242
C2×#156891972
C2×#156891242
C2×#156891162
C2×C47×#4522
C2×#331547