Finite Group Databasebeta

← C2×#20243872 #26218157

Subgroups — C2×#20243872 #26218157

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×#13094049C211yesmaximal, characteristic
2C2×#15689597C211yesmaximal, characteristic, complemented
3C2×#15689129C211yesmaximal, characteristic, complemented
4C2×#15689097C211yesmaximal, characteristic, complemented
5#20243872C218yesmaximal, direct product factor
6C2×#15688895C211yesmaximal, characteristic, complemented
7C2×#15688879C211yesmaximal, characteristic, complemented
8C2×C47×#421C211yesmaximal, characteristic, complemented
9C23×D188C2211yescharacteristic
10C2×#13094049—22no—
11C2×#13094049—22no—
12C2×#13094049—22no—
13C2×#13094049—22no—
14C2×#13094049C414yescomplemented
15C2×#13094049C2214yes—
16C22×#10625336C412yescomplemented
17C22×#10625334C412yescomplemented
18C22×#10625329C2211yescharacteristic
19#15689597—22no—
20#15689597—22no—
21#15689597—22no—
22#15689597C2214yescomplemented
23C2×C4×D188—22no—
24C2×#13093986—22no—
25C2×#13093983C2211yescharacteristic
26C2×#13093983C2211yescharacteristic
27C2×C22⋊C4×D47—22no—
28#15689129—22no—
29#15689129C2214yescomplemented
30C2×#13093946—22no—
31#15689097—22no—
32#15689097C2214yescomplemented
33C2×#13093939—22no—
34#15688895C2214yescomplemented
35#15688879C2214yescomplemented
36C22×#41×C47C2211yescharacteristic
37C22×M16×C47C2211yescharacteristic
38C2×#117×C47C2211yescharacteristic
39C47×#421—22no—
40C47×#421C2214yescomplemented
41C2×#104×C47—22no—
42C24×D47—21no—
43C22×D188—21no—
44C22×D188—21no—
45C22×D188—21no—
46C22×D188—21no—
47C22×D188—21no—
48C22×D188—21no—
49C22×D188—21no—
50C22×D188C2×C412yes—
51C22×D188C2×C412yes—
52C22×D188D412yes—
53C22×D188D412yes—
54C22×D188D412yes—
55C22×D188D412yes—
56C22×D188C2312yes—
57C22×C4×D47—24no—
58#13094049—28no—
59#13094049—28no—
60#13094049—28no—
61#13094049—28no—
62C2×#10625336—24no—
63C2×#10625336—24no—
64C2×#10625336C2×C418yescomplemented
65C2×#10625334—24no—
66C2×#10625334—24no—
67C2×#10625334C2×C418yescomplemented
68C2×#10625329—21no—
69C2×#10625329—21no—
70C2×#10625329—21no—
71C2×#10625329—21no—
72C2×#10625329C2×C412yescomplemented
73C2×#10625329C2312yes—
74C22×C47⋊C8C2×C412yescomplemented
75C4×D188—28no—
76C4×D188—28no—
77#13093986—28no—
78#13093986—28no—
79#13093983—21no—
80#13093983—21no—
81#13093983—21no—
82#13093983—21no—
83#13093983—21no—
84#13093983D412yes—
85#13093983C2312yes—
86#13093983C2312yes—
87C2×C4⋊Dic47—21no—
88C2×C4⋊Dic47—21no—
89C2×C22⋊Dic47—21no—
90C2×C22⋊Dic47D412yes—
91C2×(C2×D47)⋊C4—24no—
92C22⋊C4×D47—28no—
93C22⋊C4×D47—28no—
94C2×C4×Dic47—21no—
95C2×C4×Dic47—21no—
96#13093946—28no—
97#13093939—28no—
98C2×#41×C47—21no—
99C2×#41×C47—21no—
100C2×#41×C47—21no—
101C2×#41×C47—21no—
102C2×#41×C47—21no—
103C2×#41×C47—21no—
104C2×#41×C47—21no—
105C2×#41×C47—21no—
106C2×#41×C47—21no—
107C2×#41×C47—21no—
108C2×#41×C47C2×C412yescomplemented
109C2×#41×C47C2312yes—
110C22×Q8×C47C2×C411yescharacteristic, complemented
111C22×D4×C47—21no—
112C22×D4×C47C2×C411yescharacteristic, complemented
113C23×C4×C47—21no—
114C23×C4×C47C2311yescharacteristic
115C2×M16×C47—21no—
116C2×M16×C47—21no—
117C2×M16×C47—21no—
118C2×M16×C47—21no—
119C2×M16×C47—21no—
120C2×M16×C47C2312yes—
121C22×C8×C47—21no—
122#117×C47—21no—
123#117×C47—21no—
124#117×C47D412yes—
125#117×C47C2312yes—
126C2×C4⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C42×C47D412yes—
129#104×C47—28no—
130C24×C47—21no—
131C24×C47C2×D411yescharacteristic
132C23×D47—22no—
133C23×D47—22no—
134C23×D47—22no—
135C23×D47—22no—
136C23×D47—22no—
137C23×D47—22no—
138C23×D47—22no—
139C23×D47—84no—
140#41×C47—22no—
141#41×C47—22no—
142#41×C47—22no—
143#41×C47—22no—
144#41×C47—22no—
145#41×C47—22no—
146#41×C47—22no—
147#41×C47—22no—
148#41×C47—41no—
149#41×C47—41no—
150#41×C47—41no—
151#41×C47—41no—
152#41×C47—41no—
153#41×C47—41no—
154#41×C47—41no—
155#41×C47—41no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47C22×C412yescomplemented
162C2×D4×C47—22no—
163C2×D4×C47—22no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—41no—
170C2×D4×C47—41no—
171C2×D4×C47—41no—
172C2×D4×C47—41no—
173C2×D4×C47C22×C412yescomplemented
174C22×C4×C47—21no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—41no—
179C22×C4×C47—41no—
180C22×C4×C47—41no—
181C22×C4×C47—41no—
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47#4111yescharacteristic
192C22×C4×C47#4111yescharacteristic
193C22×C4×C47#4111yescharacteristic
194C22×C4×C47#4111yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C22×Dic47—22no—
197C22×Dic47—41no—
198C2×D188—22no—
199C2×D188—22no—
200C2×D188—22no—
201C2×D188—22no—
202C2×D188—22no—
203C2×D188—22no—
204C2×D188—22no—
205C2×D188—22no—
206C2×D188—22no—
207C2×D188—22no—
208C2×D188—22no—
209C2×D188—22no—
210C2×D188—22no—
211C2×D188—22no—
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—22no—
219C2×D188C22⋊C414yes—
220C2×D188C22⋊C414yes—
221C2×D188C22⋊C414yes—
222C2×D188C22⋊C414yes—
223C2×D188C22×C414yes—
224C2×D188C2×D414yes—
225C2×D188C2×D414yes—
226C2×C4×D47—216no—
227C2×C4×D47—88no—
228M16×C47—22no—
229M16×C47—22no—
230M16×C47—41no—
231M16×C47—41no—
232C2×C8×C47—22no—
233C2×C8×C47—41no—
234C2×C8×C47—41no—
235C4⋊C4×C47—22no—
236C4⋊C4×C47—22no—
237C22⋊C4×C47—22no—
238C22⋊C4×C47—22no—
239C42×C47—22no—
240C42×C47C2×D414yes—
241C22⋊Dic47—22no—
242C22⋊Dic47—22no—
243C22⋊Dic47—41no—
244C22⋊Dic47C2×D414yes—
245#10625336—216no—
246#10625334—216no—
247(C2×D47)⋊C4—216no—
248C4⋊Dic47—22no—
249C4⋊Dic47—22no—
250C4⋊Dic47—22no—
251C4⋊Dic47—41no—
252C4×Dic47—22no—
253C4×Dic47—22no—
254C4×Dic47—22no—
255C4×Dic47—41no—
256#10625329—22no—
257#10625329—22no—
258#10625329—22no—
259#10625329—22no—
260C2×C47⋊C8—22no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8C22×C414yescomplemented
263C23×C47—22no—
264C23×C47—42no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—82no—
268C23×C47C4×D411yescharacteristic
269C23×C47C4×D411yescharacteristic
270C23×C47#12011yescharacteristic
271C23×C47#12011yescharacteristic
272C23×C47#12111yescharacteristic
273C23×C47#12111yescharacteristic
274C23×C47C22×D411yescharacteristic
275C22×D47—24no—
276C22×D47—24no—
277C22×D47—24no—
278C22×D47—24no—
279C22×D47—24no—
280C22×D47—24no—
281C22×D47—24no—
282C22×D47—48no—
283C22×D47—84no—
284C22×D47—84no—
285C22×D47—84no—
286C22×D47—84no—
287C22×D47—84no—
288C22×D47—84no—
289Q8×C47—22no—
290Q8×C47—22no—
291Q8×C47—41no—
292Q8×C47—41no—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—42no—
296D4×C47—42no—
297D4×C47—42no—
298D4×C47—42no—
299D4×C47—41no—
300D4×C47—41no—
301C2×C4×C47—22no—
302C2×C4×C47—24no—
303C2×C4×C47—44no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47C2×C22⋊C411yescharacteristic
311C2×C4×C47C2×C22⋊C411yescharacteristic
312C2×C4×C47C2×C22⋊C411yescharacteristic
313C2×C4×C47C2×C22⋊C411yescharacteristic
314C2×C4×C47C4×D411yescharacteristic
315C2×C4×C47C4×D411yescharacteristic
316C2×C4×C47C4×D411yescharacteristic
317C2×C4×C47C4×D411yescharacteristic
318C2×C4×C47C4×D411yescharacteristic
319C2×C4×C47C4×D411yescharacteristic
320C2×C4×C47#12011yescharacteristic
321C2×C4×C47#12011yescharacteristic
322C2×C4×C47#12111yescharacteristic
323C2×C4×C47#12111yescharacteristic
324C2×C4×C47#12111yescharacteristic
325C2×C4×C47#12111yescharacteristic
326C2×C4×C47#12111yescharacteristic
327C2×C4×C47#12111yescharacteristic
328C2×C4×C47#12311yescharacteristic
329C2×C4×C47#12311yescharacteristic
330C2×C4×C47#12311yescharacteristic
331C2×C4×C47#12311yescharacteristic
332C2×C4×C47C23×C411yescharacteristic
333C2×C4×C47C22×D411yescharacteristic
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47C2×#4111yescharacteristic
337C2×C4×C47C2×#4111yescharacteristic
338C2×Dic47—24no—
339C2×Dic47—44no—
340C2×Dic47—42no—
341C2×Dic47—82no—
342D188—24no—
343D188—24no—
344D188—24no—
345D188—24no—
346D188—24no—
347D188—24no—
348D188—24no—
349D188C2×C22⋊C418yes—
350C4×D47—816no—
351C8×C47—42no—
352C47⋊C8—24no—
353C2×#1904—471nomaximal, Sylow
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—42no—
362C22×C47—82no—
363C22×C47—82no—
364C22×C47—82no—
365C22×C47#38611yescharacteristic
366C22×C47#38611yescharacteristic
367C22×C47#38611yescharacteristic
368C22×C47#38611yescharacteristic
369C22×C47C2×C4×D411yescharacteristic
370C22×C47C2×#12011yescharacteristic
371C22×C47C2×#12111yescharacteristic
372C2×D47—28no—
373C2×D47—48no—
374C2×D47—48no—
375C2×D47—48no—
376C2×D47—84no—
377C2×D47—84no—
378C2×D47—84no—
379C2×D47—84no—
380C4×C47—44no—
381C4×C47—42no—
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—44no—
391Dic47—82no—
392C22×AGL(1,ℤ/8)—471no—
393C2×#518—471no—
394C2×#421D4711yescharacteristic, complemented
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—82no—
407C2×C47#190412yescomplemented
408C2×C47C2×#38611yescharacteristic
409D47—48no—
410C22×#41C2×D4711yescharacteristic
411C23×D4—471no—
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×M16C2×D4711yescharacteristic
422#518—474no—
423#518—942no—
424#518—942no—
425#518—942no—
426C2×C4×D4—942no—
427C2×C4×D4—942no—
428C2×#117—471no—
429C2×#117—471no—
430C2×#117C2×D4711yescharacteristic
431C22×C22⋊C4—942no—
432#421—22no—
433#421C2×D4714yescomplemented
434C2×#104—22no—
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—941no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41C4×D4712yescomplemented
456C2×#41C22×D4712yes—
457C22×Q8C4×D4711yescharacteristic, complemented
458C22×D4—21no—
459C22×D4—472no—
460C22×D4—472no—
461C22×D4—472no—
462C22×D4—472no—
463C22×D4—472no—
464C22×D4—472no—
465C22×D4—472no—
466C22×D4—941no—
467C22×D4—941no—
468C22×D4—941no—
469C22×D4—941no—
470C22×D4—941no—
471C22×D4—941no—
472C22×D4—941no—
473C22×D4C4×D4711yescharacteristic, complemented
474C23×C4—21no—
475C23×C4—944no—
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—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—472no—
493C2×M16—472no—
494C2×M16—941no—
495C2×M16—941no—
496C2×M16—941no—
497C2×M16—941no—
498C2×M16C22×D4712yes—
499C22×C8—21no—
500C22×C8—472no—
501C4×D4—948no—
502C4×D4—948no—
503C4×D4—948no—
504C4×D4—948no—
505#117—21no—
506#117—21no—
507#117—472no—
508#117—472no—
509#117—472no—
510#117—941no—
511#117—941no—
512#117—941no—
513#117—941no—
514#117—941no—
515#117C22⋊D4712yes—
516#117C22×D4712yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—472no—
522C2×C22⋊C4—948no—
523C2×C22⋊C4—948no—
524C2×C22⋊C4—944no—
525C2×C22⋊C4—941no—
526C2×C42—941no—
527C2×C42—941no—
528C2×C42C22⋊D4712yes—
529#104—28no—
530#102—948no—
531#99—948no—
532C24—21no—
533C24—942no—
534C24—942no—
535C24—942no—
536C24—942no—
537C24—942no—
538C24—942no—
539C24—942no—
540C24—3764no—
541C24D4×D4711yescharacteristic
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8C2×C4×D4712yescomplemented
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—474no—
576C2×D4—474no—
577C2×D4—474no—
578C2×D4—474no—
579C2×D4—474no—
580C2×D4—474no—
581C2×D4—474no—
582C2×D4—942no—
583C2×D4—942no—
584C2×D4—942no—
585C2×D4—942no—
586C2×D4—942no—
587C2×D4—942no—
588C2×D4—942no—
589C2×D4—942no—
590C2×D4—942no—
591C2×D4—942no—
592C2×D4—942no—
593C2×D4—942no—
594C2×D4—942no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—942no—
600C2×D4—942no—
601C2×D4—942no—
602C2×D4—942no—
603C2×D4C2×C4×D4712yescomplemented
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—9416no—
613C22×C4—942no—
614C22×C4—3768no—
615C22×C4—1881no—
616C22×C4C2×C4×D4711yescharacteristic
617C22×C4C2×C4×D4711yescharacteristic
618C22×C4#1062535011yescharacteristic
619C22×C4#1062535011yescharacteristic
620C22×C4D4×D4711yescharacteristic
621C22×C4D4×D4711yescharacteristic
622C22×C4D4×D4711yescharacteristic
623C22×C4D4×D4711yescharacteristic
624C22×C4D4×D4711yescharacteristic
625C22×C4#1062535211yescharacteristic
626C22×C4#1062535211yescharacteristic
627C22×C4C2×C22⋊D4711yescharacteristic
628C22×C4C2×C22⋊D4711yescharacteristic
629C22×C4C23×D4711yescharacteristic
630SD16—9416no—
631D8—9416no—
632M16—22no—
633M16—22no—
634M16—41no—
635M16—41no—
636M16—942no—
637M16—942no—
638M16—942no—
639M16—942no—
640C2×C8—22no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—474no—
644C2×C8—942no—
645C2×C8—942no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—942no—
649C4⋊C4—942no—
650C4⋊C4—942no—
651C4⋊C4—1881no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—474no—
655C22⋊C4—9416no—
656C22⋊C4—942no—
657C22⋊C4—942no—
658C22⋊C4—1881no—
659C42—22no—
660C42—942no—
661C42—942no—
662C42—942no—
663C42—1881no—
664C42C2×C22⋊D4714yes—
665C23—22no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—82no—
670C23—944no—
671C23—944no—
672C23—944no—
673C23—944no—
674C23—944no—
675C23—944no—
676C23—944no—
677C23—3764no—
678C23—3764no—
679C23—3764no—
680C23—3764no—
681C23—3764no—
682C23—3764no—
683C23—1888no—
684C23(C22⋊D47)⋊C411yescharacteristic
685C23(C22⋊D47)⋊C411yescharacteristic
686C23#1309399211yescharacteristic
687C23#1309399211yescharacteristic
688C23#1309399711yescharacteristic
689C23#1309399711yescharacteristic
690C23C2×D4×D4711yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695D4—22no—
696D4—22no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—478no—
704D4—944no—
705D4—944no—
706D4—944no—
707D4—944no—
708D4—944no—
709D4—944no—
710D4—944no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—44no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—944no—
721C2×C4—37616no—
722C2×C4—3762no—
723C2×C4—1882no—
724C2×C4—1884no—
725C2×C4C22⋊C4×D4711yescharacteristic
726C2×C4C22⋊C4×D4711yescharacteristic
727C2×C4C22⋊C4×D4711yescharacteristic
728C2×C4C22⋊C4×D4711yescharacteristic
729C2×C4(C22⋊D47)⋊C411yescharacteristic
730C2×C4(C22⋊D47)⋊C411yescharacteristic
731C2×C4C4×C22⋊D4711yescharacteristic
732C2×C4C4×C22⋊D4711yescharacteristic
733C2×C4C4×C22⋊D4711yescharacteristic
734C2×C4C4×C22⋊D4711yescharacteristic
735C2×C4#1309399211yescharacteristic
736C2×C4#1309399211yescharacteristic
737C2×C4#1309399511yescharacteristic
738C2×C4#1309399511yescharacteristic
739C2×C4#1309399511yescharacteristic
740C2×C4#1309399511yescharacteristic
741C2×C4#1309399711yescharacteristic
742C2×C4#1309399711yescharacteristic
743C2×C4#1309400611yescharacteristic
744C2×C4#1309400611yescharacteristic
745C2×C4#1309400611yescharacteristic
746C2×C4#1309400611yescharacteristic
747C2×C4C22×C4×D4711yescharacteristic
748C2×C4C2×D4×D4711yescharacteristic
749C2×C4C2×D4×D4711yescharacteristic
750C2×C4C22×C22⋊D4711yescharacteristic
751C2×C4C2×#1062535211yescharacteristic
752C2×C4C2×#1062535011yescharacteristic
753C8—42no—
754C8—944no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—948no—
767C22—3764no—
768C22—3764no—
769C22—3764no—
770C22—3764no—
771C22—1888no—
772C22—1888no—
773C22—1888no—
774C22#1568899911yescharacteristic
775C22#1568899911yescharacteristic
776C22#1568899911yescharacteristic
777C22#1568899911yescharacteristic
778C22C2×(C22⋊D47)⋊C411yescharacteristic
779C22C2×#1309399211yescharacteristic
780C22C2×#1309399711yescharacteristic
781C4—44no—
782C4—42no—
783C4—3762no—
784C4—1884no—
785C4#1568899911yescharacteristic
786C4#1568899911yescharacteristic
787C4#1568899911yescharacteristic
788C4#1568899911yescharacteristic
789C4C2×C22⋊C4×D4711yescharacteristic
790C4C2×C4×C22⋊D4711yescharacteristic
791C4C2×#1309399511yescharacteristic
792C4C2×#1309400611yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—82no—
800C2—1888no—
801C2#2024387212yesdirect product factor
802C2C2×#1568899911yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#421C2
socleC22×C47#386
prime radicalC22×#13094049C2
cosocleC22×C4×C47C24
hypercenterC2×#421D47
hypocenterC47C2×#1904
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#15689597C2semidirect
3. C2×#15689129C2semidirect
4. C2×#15689097C2semidirect
5. #20243872C2direct (N × H)
6. C2×#15688895C2semidirect
7. C2×#15688879C2semidirect
8. C2×C47×#421C2semidirect
14. C2×#13094049C4semidirect
16. C22×#10625336C4semidirect
17. C22×#10625334C4semidirect
22. #15689597C22semidirect
29. #15689129C22semidirect
32. #15689097C22semidirect
34. #15688895C22semidirect
35. #15688879C22semidirect
40. C47×#421C22semidirect
64. C2×#10625336C2×C4semidirect
67. C2×#10625334C2×C4semidirect
72. C2×#10625329C2×C4semidirect
74. C22×C47⋊C8C2×C4semidirect
108. C2×#41×C47C2×C4semidirect
110. C22×Q8×C47C2×C4semidirect
112. C22×D4×C47C2×C4semidirect
161. C2×Q8×C47C22×C4semidirect
173. C2×D4×C47C22×C4semidirect
262. C2×C47⋊C8C22×C4semidirect
394. C2×#421D47semidirect
407. C2×C47#1904semidirect
433. #421C2×D47semidirect
443. C47C2×#1904semidirect
455. C2×#41C4×D47semidirect
457. C22×Q8C4×D47semidirect
473. C22×D4C4×D47semidirect
563. C2×Q8C2×C4×D47semidirect
603. C2×D4C2×C4×D47semidirect
801. C2#20243872direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940492
C2×#156895972
C2×#156891292
C2×#156890972
#202438722
C2×#156888952
C2×#156888792
C2×C47×#4212
C2×#190447