Finite Group Databasebeta

← C2×#20243875 #26218160

Subgroups — C2×#20243875 #26218160

Order 12032.

1894 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×#13094050C211yesmaximal, characteristic
2C2×#15689141C211yesmaximal, characteristic, complemented
3C2×#15689128C211yesmaximal, characteristic, complemented
4C2×#15689096C211yesmaximal, characteristic, complemented
5#20243875C218yesmaximal, direct product factor
6C2×#15688893C211yesmaximal, characteristic, complemented
7C2×#15688879C211yesmaximal, characteristic, complemented
8C2×C47×#518C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C2×#13094050—22no—
11C2×#13094050—22no—
12C2×#13094050—22no—
13C2×#13094050—22no—
14C2×#13094050C414yescomplemented
15C2×#13094050C2214yes—
16C22×#10625335C412yescomplemented
17C22×#10625334C412yescomplemented
18C22×#10625329C2211yescharacteristic
19C22×#10625329C2211yescharacteristic
20C2×#13093983C2211yescharacteristic
21#15689141—22no—
22#15689141C2214yescomplemented
23C2×#13093952—22no—
24#15689128—22no—
25#15689128C2214yescomplemented
26C2×#13093945—22no—
27#15689096—22no—
28#15689096C2214yescomplemented
29C2×#13093938—22no—
30#15688893C2214yescomplemented
31#15688879C2214yescomplemented
32C23×D4×C47C2211yescharacteristic
33C47×#518—22no—
34C47×#518—22no—
35C47×#518—22no—
36C47×#518C2214yescomplemented
37C2×C4×D4×C47—22no—
38C2×C4×D4×C47—22no—
39C2×#117×C47C2211yescharacteristic
40C2×#117×C47C2211yescharacteristic
41C22×C22⋊C4×C47—22no—
42C2×#10625350—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350C2×C412yescomplemented
53C2×#10625350C2312yes—
54C22×Dic94C2×C411yescharacteristic, complemented
55C22×D188C2×C411yescharacteristic, complemented
56C22×C22⋊D47—21no—
57C22×C4×D47—21no—
58#13094050—28no—
59#13094050—28no—
60#13094050—28no—
61#13094050—28no—
62C2×#10625335—24no—
63C2×#10625335—24no—
64C2×#10625335C2×C418yescomplemented
65C2×#10625334—24no—
66C2×#10625334—24no—
67C2×#10625334C2×C418yescomplemented
68C2×#10625329—21no—
69C2×#10625329—21no—
70C2×#10625329—21no—
71C2×#10625329—21no—
72C2×#10625329—21no—
73C2×#10625329—21no—
74C2×#10625329—21no—
75C2×#10625329—21no—
76C2×#10625329—21no—
77C2×#10625329C2×C412yescomplemented
78C2×#10625329C2312yes—
79C2×#10625329C2312yes—
80C22×C47⋊C8—21no—
81C22×C47⋊C8C2×C412yescomplemented
82#13093983—21no—
83#13093983—21no—
84#13093983—21no—
85#13093983C2312yes—
86C2×C4⋊Dic47—21no—
87C2×C22⋊Dic47—21no—
88C2×C4×Dic47—21no—
89#13093952—28no—
90#13093945—28no—
91#13093938—28no—
92C25×C47—21no—
93C22×D4×C47—21no—
94C22×D4×C47—21no—
95C22×D4×C47—21no—
96C22×D4×C47—21no—
97C22×D4×C47—21no—
98C22×D4×C47—21no—
99C22×D4×C47—21no—
100C22×D4×C47C2×C412yes—
101C22×D4×C47C2×C412yes—
102C22×D4×C47D412yes—
103C22×D4×C47D412yes—
104C22×D4×C47D412yes—
105C22×D4×C47D412yes—
106C22×D4×C47C2312yes—
107C23×C4×C47—24no—
108C23×C4×C47C2311yescharacteristic
109C4×D4×C47—28no—
110C4×D4×C47—28no—
111C4×D4×C47—28no—
112C4×D4×C47—28no—
113#117×C47—21no—
114#117×C47—21no—
115#117×C47—21no—
116#117×C47—21no—
117#117×C47D412yes—
118#117×C47D412yes—
119#117×C47C2312yes—
120#117×C47C2312yes—
121C2×C4⋊C4×C47—21no—
122C2×C4⋊C4×C47—21no—
123C2×C22⋊C4×C47—24no—
124C2×C22⋊C4×C47—28no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—28no—
127C2×C22⋊C4×C47D412yes—
128C2×C42×C47—21no—
129C2×C42×C47D412yes—
130C24×C47—22no—
131C24×C47—22no—
132C24×C47—22no—
133C24×C47—22no—
134C24×C47—22no—
135C24×C47—22no—
136C24×C47—22no—
137C24×C47—84no—
138C24×C47C2×D411yescharacteristic
139C23×D47—21no—
140C2×D4×C47—22no—
141C2×D4×C47—22no—
142C2×D4×C47—22no—
143C2×D4×C47—22no—
144C2×D4×C47—22no—
145C2×D4×C47—22no—
146C2×D4×C47—22no—
147C2×D4×C47—22no—
148C2×D4×C47—22no—
149C2×D4×C47—22no—
150C2×D4×C47—22no—
151C2×D4×C47—22no—
152C2×D4×C47—22no—
153C2×D4×C47—22no—
154C2×D4×C47—22no—
155C2×D4×C47—22no—
156C2×D4×C47—22no—
157C2×D4×C47—22no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—22no—
161C2×D4×C47C22⋊C414yes—
162C2×D4×C47C22⋊C414yes—
163C2×D4×C47C22⋊C414yes—
164C2×D4×C47C22⋊C414yes—
165C2×D4×C47C22×C414yes—
166C2×D4×C47C2×D414yes—
167C2×D4×C47C2×D414yes—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—216no—
171C22×C4×C47—88no—
172C22×C4×C47C22×C411yescharacteristic
173C22×C4×C47C22×C411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47#4111yescharacteristic
182C22×C4×C47#4111yescharacteristic
183C22×C4×C47#4111yescharacteristic
184C22×C4×C47#4111yescharacteristic
185C22×C4×C47C2411yescharacteristic
186C2×C22⋊D47—22no—
187C2×C22⋊D47—22no—
188C2×C22⋊D47—41no—
189C2×C22⋊D47—41no—
190C2×C22⋊D47—41no—
191C2×C22⋊D47—41no—
192C22×Dic47—21no—
193C22×Dic47—41no—
194#10625350—22no—
195#10625350—22no—
196#10625350—22no—
197#10625350—22no—
198#10625350—22no—
199#10625350—22no—
200#10625350—22no—
201#10625350—22no—
202#10625350—41no—
203#10625350—41no—
204#10625350—41no—
205#10625350—41no—
206#10625350—41no—
207#10625350—41no—
208#10625350—41no—
209#10625350—41no—
210C2×D188—21no—
211C2×D188—21no—
212C2×D188—21no—
213C2×D188—21no—
214C2×D188—21no—
215C2×D188C22×C412yescomplemented
216C2×C4×D47—22no—
217C2×C4×D47—22no—
218C2×C4×D47—41no—
219C2×C4×D47—41no—
220C2×C4×D47—41no—
221C2×C4×D47—41no—
222C2×Dic94—21no—
223C2×Dic94—21no—
224C2×Dic94—21no—
225C2×Dic94—21no—
226C2×Dic94—21no—
227C2×Dic94C22×C412yescomplemented
228C4⋊C4×C47—22no—
229C4⋊C4×C47—22no—
230C4⋊C4×C47—22no—
231C4⋊C4×C47—22no—
232C22⋊C4×C47—216no—
233C22⋊C4×C47—22no—
234C22⋊C4×C47—22no—
235C22⋊C4×C47—22no—
236C22⋊C4×C47C2×D414yes—
237C42×C47—22no—
238C42×C47—22no—
239C42×C47—22no—
240C42×C47C2×D414yes—
241C22⋊Dic47—22no—
242C22⋊Dic47—41no—
243#10625335—216no—
244#10625334—216no—
245C4⋊Dic47—22no—
246C4⋊Dic47—41no—
247C4×Dic47—22no—
248C4×Dic47—41no—
249#10625329—22no—
250#10625329—22no—
251#10625329—22no—
252#10625329—22no—
253#10625329—22no—
254#10625329—22no—
255#10625329—41no—
256#10625329—41no—
257C2×C47⋊C8—22no—
258C2×C47⋊C8—22no—
259C2×C47⋊C8—22no—
260C2×C47⋊C8—41no—
261C2×C47⋊C8—41no—
262C2×C47⋊C8C22×C414yescomplemented
263C23×C47—24no—
264C23×C47—24no—
265C23×C47—24no—
266C23×C47—24no—
267C23×C47—24no—
268C23×C47—24no—
269C23×C47—24no—
270C23×C47—42no—
271C23×C47—48no—
272C23×C47—84no—
273C23×C47—84no—
274C23×C47—84no—
275C23×C47—84no—
276C23×C47—84no—
277C23×C47—84no—
278C23×C47C4×D411yescharacteristic
279C23×C47C4×D411yescharacteristic
280C23×C47#12011yescharacteristic
281C23×C47#12011yescharacteristic
282C23×C47#12111yescharacteristic
283C23×C47#12111yescharacteristic
284C23×C47C22×D411yescharacteristic
285C22×D47—22no—
286C22×D47—41no—
287C22×D47—41no—
288C22×D47—82no—
289D4×C47—24no—
290D4×C47—24no—
291D4×C47—24no—
292D4×C47—24no—
293D4×C47—24no—
294D4×C47—24no—
295D4×C47—24no—
296D4×C47C2×C22⋊C418yes—
297C2×C4×C47—24no—
298C2×C4×C47—24no—
299C2×C4×C47—44no—
300C2×C4×C47—44no—
301C2×C4×C47—816no—
302C2×C4×C47C2×C22⋊C411yescharacteristic
303C2×C4×C47C2×C22⋊C411yescharacteristic
304C2×C4×C47C2×C22⋊C411yescharacteristic
305C2×C4×C47C2×C22⋊C411yescharacteristic
306C2×C4×C47C4×D411yescharacteristic
307C2×C4×C47C4×D411yescharacteristic
308C2×C4×C47C4×D411yescharacteristic
309C2×C4×C47C4×D411yescharacteristic
310C2×C4×C47C4×D411yescharacteristic
311C2×C4×C47C4×D411yescharacteristic
312C2×C4×C47#12011yescharacteristic
313C2×C4×C47#12011yescharacteristic
314C2×C4×C47#12111yescharacteristic
315C2×C4×C47#12111yescharacteristic
316C2×C4×C47#12111yescharacteristic
317C2×C4×C47#12111yescharacteristic
318C2×C4×C47#12111yescharacteristic
319C2×C4×C47#12111yescharacteristic
320C2×C4×C47#12311yescharacteristic
321C2×C4×C47#12311yescharacteristic
322C2×C4×C47#12311yescharacteristic
323C2×C4×C47#12311yescharacteristic
324C2×C4×C47C23×C411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C22×D411yescharacteristic
327C2×C4×C47C22×D411yescharacteristic
328C2×C4×C47C2×#4111yescharacteristic
329C2×C4×C47C2×#4111yescharacteristic
330C22⋊D47—42no—
331C22⋊D47—42no—
332C22⋊D47—42no—
333C22⋊D47—42no—
334C2×Dic47—22no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—42no—
338C2×Dic47—82no—
339D188—22no—
340D188—22no—
341D188—41no—
342D188—41no—
343C4×D47—42no—
344C4×D47—42no—
345C4×D47—42no—
346C4×D47—42no—
347Dic94—22no—
348Dic94—22no—
349Dic94—41no—
350Dic94—41no—
351C47⋊C8—24no—
352C47⋊C8—42no—
353C2×#1904—471nomaximal, Sylow
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—28no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—48no—
363C22×C47—48no—
364C22×C47—48no—
365C22×C47—84no—
366C22×C47—84no—
367C22×C47—84no—
368C22×C47—84no—
369C22×C47#38611yescharacteristic
370C22×C47#38611yescharacteristic
371C22×C47#38611yescharacteristic
372C22×C47#38611yescharacteristic
373C22×C47C2×C4×D411yescharacteristic
374C22×C47C2×#12011yescharacteristic
375C22×C47C2×#12111yescharacteristic
376C2×D47—42no—
377C2×D47—82no—
378C2×D47—82no—
379C2×D47—82no—
380C4×C47—44no—
381C4×C47—44no—
382C4×C47#38611yescharacteristic
383C4×C47#38611yescharacteristic
384C4×C47#38611yescharacteristic
385C4×C47#38611yescharacteristic
386C4×C47C22×C22⋊C411yescharacteristic
387C4×C47C2×C4×D411yescharacteristic
388C4×C47C2×#12111yescharacteristic
389C4×C47C2×#12311yescharacteristic
390Dic47—42no—
391Dic47—82no—
392C22×AGL(1,ℤ/8)—471no—
393C2×#518D4711yescharacteristic, complemented
394C2×#421—471no—
395C2×#418—471no—
396C2×#410—471no—
397#1904—478no—
398C2×#344—471no—
399C2×H(3,ℤ/4)—471no—
400C2×C47—21no—
401C2×C47—21no—
402C2×C47—21no—
403C2×C47—21no—
404C2×C47—21no—
405C2×C47—21no—
406C2×C47—48no—
407C2×C47#190412yescomplemented
408C2×C47C2×#38611yescharacteristic
409D47—82no—
410C22×#41—471no—
411C23×D4C2×D4711yescharacteristic
412C2×AGL(1,ℤ/8)—474no—
413C2×AGL(1,ℤ/8)—474no—
414C2×AGL(1,ℤ/8)—942no—
415C2×AGL(1,ℤ/8)—942no—
416C2×AGL(1,ℤ/8)—942no—
417C2×AGL(1,ℤ/8)—942no—
418C22×SD16—472no—
419C22×D8—472no—
420C22×M16—471no—
421C22×M16—471no—
422#518—22no—
423#518—22no—
424#518—22no—
425#518C2×D4714yescomplemented
426C2×C4×D4—22no—
427C2×C4×D4—22no—
428C2×#117—471no—
429C2×#117C2×D4711yescharacteristic
430C2×#117C2×D4711yescharacteristic
431C22×C22⋊C4—22no—
432#421—474no—
433#421—942no—
434C2×#104—942no—
435#418—474no—
436#418—942no—
437C2×#102—942no—
438#410—474no—
439#410—942no—
440C2×#99—942no—
441#344—474no—
442H(3,ℤ/4)—474no—
443C47C2×#190411yescharacteristic, complemented, Sylow
444C25—21no—
445C2×#41—472no—
446C2×#41—472no—
447C2×#41—941no—
448C2×#41—941no—
449C2×#41—941no—
450C2×#41—941no—
451C2×#41—941no—
452C2×#41—941no—
453C2×#41—941no—
454C2×#41—941no—
455C2×#41—941no—
456C2×#41—941no—
457C22×Q8—471no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—471no—
466C22×D4—941no—
467C22×D4C4×D4712yes—
468C22×D4C4×D4712yes—
469C22×D4D18812yes—
470C22×D4D18812yes—
471C22×D4C22⋊D4712yes—
472C22×D4C22⋊D4712yes—
473C22×D4C22×D4712yes—
474C23×C4—24no—
475C23×C4—941no—
476C23×C4C22×D4711yescharacteristic
477AGL(1,ℤ/8)—948no—
478AGL(1,ℤ/8)—948no—
479AGL(1,ℤ/8)—948no—
480AGL(1,ℤ/8)—948no—
481C2×SD16—478no—
482C2×SD16—944no—
483C2×SD16—944no—
484C2×D8—478no—
485C2×D8—944no—
486C2×D8—944no—
487C2×M16—472no—
488C2×M16—472no—
489C2×M16—472no—
490C2×M16—941no—
491C2×M16—941no—
492C2×M16—941no—
493C2×M16—941no—
494C2×M16—941no—
495C2×M16—941no—
496C2×M16—941no—
497C2×M16—941no—
498C2×M16—941no—
499C22×C8—472no—
500C22×C8—941no—
501C4×D4—28no—
502C4×D4—28no—
503C4×D4—28no—
504C4×D4—28no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—472no—
510#117—941no—
511#117—941no—
512#117—941no—
513#117C22⋊D4712yes—
514#117C22⋊D4712yes—
515#117C22×D4712yes—
516#117C22×D4712yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—941no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—28no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—28no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4C22⋊D4712yes—
526C2×C42—21no—
527C2×C42—941no—
528C2×C42C22⋊D4712yes—
529#104—948no—
530#102—948no—
531#99—948no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—84no—
540C24—941no—
541C24C2×C22⋊D4711yescharacteristic
542#41—942no—
543#41—942no—
544#41—942no—
545#41—942no—
546#41—942no—
547#41—942no—
548#41—942no—
549#41—942no—
550#41—1881no—
551#41—1881no—
552#41—1881no—
553#41—1881no—
554#41—1881no—
555#41—1881no—
556#41—1881no—
557#41—1881no—
558C2×Q8—472no—
559C2×Q8—941no—
560C2×Q8—941no—
561C2×Q8—941no—
562C2×Q8—941no—
563C2×Q8—941no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—472no—
586C2×D4—942no—
587C2×D4—942no—
588C2×D4—941no—
589C2×D4—941no—
590C2×D4—941no—
591C2×D4—941no—
592C2×D4—941no—
593C2×D4—1881no—
594C2×D4—1881no—
595C2×D4—1881no—
596C2×D4—1881no—
597C2×D4(C2×D47)⋊C414yes—
598C2×D4(C2×D47)⋊C414yes—
599C2×D4(C2×D47)⋊C414yes—
600C2×D4(C2×D47)⋊C414yes—
601C2×D4C2×C4×D4714yes—
602C2×D4C2×D18814yes—
603C2×D4C2×C22⋊D4714yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—216no—
607C22×C4—88no—
608C22×C4—941no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—1881no—
612C22×C4—1881no—
613C22×C4—1881no—
614C22×C4—1881no—
615C22×C4—1881no—
616C22×C4C2×C4×D4711yescharacteristic
617C22×C4C2×C4×D4711yescharacteristic
618C22×C4C2×D18811yescharacteristic
619C22×C4C2×D18811yescharacteristic
620C22×C4#1062535011yescharacteristic
621C22×C4#1062535011yescharacteristic
622C22×C4#1062535011yescharacteristic
623C22×C4#1062535011yescharacteristic
624C22×C4C2×C22⋊D4711yescharacteristic
625C22×C4C2×C22⋊D4711yescharacteristic
626C22×C4C2×C22⋊D4711yescharacteristic
627C22×C4C2×C22⋊D4711yescharacteristic
628C22×C4C2×C22⋊D4711yescharacteristic
629C22×C4C23×D4711yescharacteristic
630SD16—9416no—
631D8—9416no—
632M16—942no—
633M16—942no—
634M16—942no—
635M16—942no—
636M16—942no—
637M16—942no—
638M16—1881no—
639M16—1881no—
640C2×C8—474no—
641C2×C8—942no—
642C2×C8—942no—
643C2×C8—942no—
644C2×C8—1881no—
645C2×C8—1881no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—942no—
651C4⋊C4—1881no—
652C22⋊C4—216no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—942no—
657C22⋊C4—1881no—
658C22⋊C4C2×C22⋊D4714yes—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—942no—
663C42—1881no—
664C42C2×C22⋊D4714yes—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—42no—
673C23—48no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—942no—
681C23—3762no—
682C23—1881no—
683C23—1881no—
684C23C4×C22⋊D4711yescharacteristic
685C23C4×C22⋊D4711yescharacteristic
686C23#1309399311yescharacteristic
687C23#1309399311yescharacteristic
688C23#1309399811yescharacteristic
689C23#1309399811yescharacteristic
690C23C22×C22⋊D4711yescharacteristic
691Q8—942no—
692Q8—942no—
693Q8—1881no—
694Q8—1881no—
695D4—24no—
696D4—24no—
697D4—24no—
698D4—24no—
699D4—24no—
700D4—24no—
701D4—24no—
702D4—942no—
703D4—942no—
704D4—1882no—
705D4—1882no—
706D4—1882no—
707D4—1882no—
708D4—1881no—
709D4—1881no—
710D4C2×(C2×D47)⋊C418yes—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—816no—
716C2×C4—942no—
717C2×C4—3762no—
718C2×C4—1882no—
719C2×C4—1881no—
720C2×C4—1881no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4C2×(C2×D47)⋊C411yescharacteristic
726C2×C4C2×(C2×D47)⋊C411yescharacteristic
727C2×C4C2×(C2×D47)⋊C411yescharacteristic
728C2×C4C2×(C2×D47)⋊C411yescharacteristic
729C2×C4C4×C22⋊D4711yescharacteristic
730C2×C4C4×C22⋊D4711yescharacteristic
731C2×C4C4×C22⋊D4711yescharacteristic
732C2×C4C4×C22⋊D4711yescharacteristic
733C2×C4C4×C22⋊D4711yescharacteristic
734C2×C4C4×C22⋊D4711yescharacteristic
735C2×C4#1309399311yescharacteristic
736C2×C4#1309399311yescharacteristic
737C2×C4#1309399811yescharacteristic
738C2×C4#1309399811yescharacteristic
739C2×C4#1309399811yescharacteristic
740C2×C4#1309399811yescharacteristic
741C2×C4#1309399811yescharacteristic
742C2×C4#1309399811yescharacteristic
743C2×C4#1309400711yescharacteristic
744C2×C4#1309400711yescharacteristic
745C2×C4#1309400711yescharacteristic
746C2×C4#1309400711yescharacteristic
747C2×C4C22×C4×D4711yescharacteristic
748C2×C4C22×C22⋊D4711yescharacteristic
749C2×C4C22×C22⋊D4711yescharacteristic
750C2×C4C22×D18811yescharacteristic
751C2×C4C2×#1062535011yescharacteristic
752C2×C4C2×#1062535011yescharacteristic
753C8—944no—
754C8—1882no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—28no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—48no—
764C22—48no—
765C22—48no—
766C22—84no—
767C22—84no—
768C22—84no—
769C22—84no—
770C22—3762no—
771C22—3762no—
772C22—3762no—
773C22—1882no—
774C22#1568900211yescharacteristic
775C22#1568900211yescharacteristic
776C22#1568900211yescharacteristic
777C22#1568900211yescharacteristic
778C22C2×C4×C22⋊D4711yescharacteristic
779C22C2×#1309399311yescharacteristic
780C22C2×#1309399811yescharacteristic
781C4—44no—
782C4—44no—
783C4—3762no—
784C4—1882no—
785C4#1568900211yescharacteristic
786C4#1568900211yescharacteristic
787C4#1568900211yescharacteristic
788C4#1568900211yescharacteristic
789C4C22×(C2×D47)⋊C411yescharacteristic
790C4C2×C4×C22⋊D4711yescharacteristic
791C4C2×#1309399811yescharacteristic
792C4C2×#1309400711yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—48no—
800C2—3762no—
801C2#2024387512yesdirect product factor
802C2C2×#1568900211yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#518C2
socleC22×C47#386
prime radicalC22×#13094050C2
cosocleC22×C4×C47C24
hypercenterC2×#518D47
hypocenterC47C2×#1904
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C2×#15689141C2semidirect
3. C2×#15689128C2semidirect
4. C2×#15689096C2semidirect
5. #20243875C2direct (N × H)
6. C2×#15688893C2semidirect
7. C2×#15688879C2semidirect
8. C2×C47×#518C2semidirect
14. C2×#13094050C4semidirect
16. C22×#10625335C4semidirect
17. C22×#10625334C4semidirect
22. #15689141C22semidirect
25. #15689128C22semidirect
28. #15689096C22semidirect
30. #15688893C22semidirect
31. #15688879C22semidirect
36. C47×#518C22semidirect
52. C2×#10625350C2×C4semidirect
54. C22×Dic94C2×C4semidirect
55. C22×D188C2×C4semidirect
64. C2×#10625335C2×C4semidirect
67. C2×#10625334C2×C4semidirect
77. C2×#10625329C2×C4semidirect
81. C22×C47⋊C8C2×C4semidirect
215. C2×D188C22×C4semidirect
227. C2×Dic94C22×C4semidirect
262. C2×C47⋊C8C22×C4semidirect
393. C2×#518D47semidirect
407. C2×C47#1904semidirect
425. #518C2×D47semidirect
443. C47C2×#1904semidirect
801. C2#20243875direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940502
C2×#156891412
C2×#156891282
C2×#156890962
#202438752
C2×#156888932
C2×#156888792
C2×C47×#5182
C2×#190447