Finite Group Databasebeta

← C2×#20252924 #27083200

Subgroups — C2×#20252924 #27083200

Order 12032.

2934 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094051C211yesmaximal, characteristic, complemented
2C22×#13094045C211yesmaximal, characteristic, complemented
3C2×#15689686C211yesmaximal, characteristic, complemented
4C2×#15689605C211yesmaximal, characteristic, complemented
5#20252924C2116yesmaximal, direct product factor
6C2×#15689345C211yesmaximal, characteristic, complemented
7C2×#15689343C211yesmaximal, characteristic, complemented
8C2×#15689321C211yesmaximal, characteristic, complemented
9C2×#15689339C211yesmaximal, characteristic, complemented
10C2×#15689337C211yesmaximal, characteristic, complemented
11C2×#15689317C211yesmaximal, characteristic, complemented
12C2×#15689315C211yesmaximal, characteristic, complemented
13C2×#15689148C211yesmaximal, characteristic, complemented
14C2×#15689121C211yesmaximal, characteristic, complemented
15C2×#102×D47C211yesmaximal, characteristic, complemented
16C2×C47×#460C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625352C2211yescharacteristic
19C22×D4×D47C2211yescharacteristic
20C2×#13094051—28no—
21C2×#13094051C2218yescomplemented
22C2×#13094045—28no—
23C2×#13094045C2218yescomplemented
24C22×#10625337C2211yescharacteristic, complemented
25C22×#10625325C2211yescharacteristic, complemented
26C22×#10625336C2211yescharacteristic
27C22×D376C2211yescharacteristic
28C22×#10625334C2211yescharacteristic
29C22×#10625334C2211yescharacteristic, complemented
30C22×#10625324C2211yescharacteristic
31C22×C8×D47C2211yescharacteristic
32#15689686—24no—
33#15689686C2218yescomplemented
34C2×#13094020C2211yescharacteristic
35C2×#13094012C2211yescharacteristic
36C2×#13094011C2211yescharacteristic
37C2×#13093996—21no—
38C2×#13093996—21no—
39C2×#13093992—21no—
40C2×#13093992—21no—
41#15689605—24no—
42#15689605C2218yescomplemented
43C2×Q8×Dic47C2211yescharacteristic, complemented
44C2×C4×D188—21no—
45C2×C4×D188C2211yescharacteristic, complemented
46C2×#13093986—21no—
47C2×#13093986C2211yescharacteristic, complemented
48C2×#13093981—21no—
49C2×#13093981C2211yescharacteristic
50C2×C4⋊C4×D47—21no—
51C2×C4⋊C4×D47C2211yescharacteristic
52#15689345C2218yescomplemented
53#15689343C2218yescomplemented
54#15689339C2218yescomplemented
55#15689337C2218yescomplemented
56#15689321C2218yescomplemented
57#15689317C2218yescomplemented
58#15689315C2218yescomplemented
59#15689148C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
61C2×Dic47⋊C8C2211yescharacteristic, complemented
62C2×Dic47⋊C8C2211yescharacteristic, complemented
63#15689121C2218yescomplemented
64C2×#13093949C2211yescharacteristic, complemented
65C2×#13093947C2211yescharacteristic, complemented
66C2×#13093946C2211yescharacteristic
67C2×#13093945C2211yescharacteristic
68C2×#13093945C2211yescharacteristic, complemented
69C2×#13093944C2211yescharacteristic
70#102×D47C2218yescomplemented
71C22×SD16×C47C2211yescharacteristic
72C22×SD16×C47C2211yescharacteristic, complemented
73C2×#127×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic, complemented
75C47×#460C2218yescomplemented
76C2×C4⋊C8×C47C2211yescharacteristic, complemented
77C2×#102×C47C2211yescharacteristic
78C2×#102×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C2×#10625354—22no—
81C2×#10625354—24no—
82C2×#10625354D418yescomplemented
83C2×#10625354C2314yes—
84C2×#10625352—24no—
85C2×#10625352—22no—
86C2×#10625352—24no—
87C2×#10625352C2314yes—
88C22×Dic94C2311yescharacteristic
89C22×D188—21no—
90C22×D188C2311yescharacteristic
91C22×D188C2311yescharacteristic
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C22×C22⋊D47—21no—
96C2×D4×D47—24no—
97C2×D4×D47—22no—
98C2×D4×D47—24no—
99C2×D4×D47C2314yes—
100C23×Dic47—21no—
101C22×C4×D47—21no—
102C22×C4×D47—21no—
103C22×C4×D47—21no—
104C22×C4×D47—21no—
105C22×C4×D47C2311yescharacteristic
106#13094051—232no—
107#13094045—232no—
108C2×#10625337—24no—
109C2×#10625337C2314yescomplemented
110C2×#10625325—24no—
111C2×#10625325C2314yescomplemented
112C2×#10625336—24no—
113C2×#10625336C2314yes—
114C2×D376—24no—
115C2×D376C2314yes—
116C2×#10625334—24no—
117C2×#10625334—24no—
118C2×#10625334C2314yes—
119C2×#10625334C2314yescomplemented
120C2×#10625324—24no—
121C2×#10625324C2314yes—
122C22×C47⋊C8C2311yescharacteristic
123C22×C47⋊C8C2311yescharacteristic
124C2×C8×D47—24no—
125C2×C8×D47C2314yes—
126#13094020—22no—
127#13094020C2314yes—
128#13094012—22no—
129#13094012C2314yes—
130#13094011—22no—
131#13094011C2314yes—
132#13093996—28no—
133#13093996—28no—
134#13093992—28no—
135#13093992—28no—
136Q8×Dic47—22no—
137Q8×Dic47C2314yescomplemented
138C4×D188—22no—
139C4×D188—28no—
140C4×D188C2314yescomplemented
141#13093986—28no—
142#13093986—22no—
143#13093986C2314yescomplemented
144#13093981—28no—
145#13093981D414yes—
146#13093981C2314yes—
147C2×C4⋊Dic47—21no—
148C2×C4⋊Dic47C2311yescharacteristic
149C2×Dic47⋊C4—21no—
150C2×Dic47⋊C4D411yescharacteristic
151C2×Dic47⋊C4D411yescharacteristic
152C4⋊C4×D47—22no—
153C4⋊C4×D47—28no—
154C4⋊C4×D47C2314yes—
155C2×C22⋊Dic47—21no—
156C2×C22⋊Dic47—21no—
157C2×(C2×D47)⋊C4—21no—
158C2×(C2×D47)⋊C4—21no—
159C2×(C2×D47)⋊C4—21no—
160C2×(C2×D47)⋊C4—21no—
161C2×(C2×D47)⋊C4D411yescharacteristic
162C2×(C2×D47)⋊C4D411yescharacteristic
163C2×C4×Dic47—21no—
164C2×C4×Dic47C2311yescharacteristic
165C4⋊(C47⋊C8)C2314yescomplemented
166Dic47⋊C8C2314yescomplemented
167Dic47⋊C8C2314yescomplemented
168#13093949C2314yescomplemented
169#13093947C2314yescomplemented
170#13093946C2314yes—
171#13093945C2314yes—
172#13093945C2314yescomplemented
173#13093944C2314yes—
174C22×Q8×C47C2311yescharacteristic
175C22×D4×C47—21no—
176C22×D4×C47—21no—
177C22×D4×C47C2311yescharacteristic
178C22×D4×C47C2311yescharacteristic
179C2×SD16×C47—24no—
180C2×SD16×C47—24no—
181C2×SD16×C47C2314yes—
182C2×SD16×C47C2314yescomplemented
183C22×C8×C47C2311yescharacteristic
184C22×C8×C47C2311yescharacteristic
185#127×C47—22no—
186#127×C47C2314yes—
187C4×Q8×C47—22no—
188C4×Q8×C47C2314yescomplemented
189C2×C4⋊C4×C47—21no—
190C2×C4⋊C4×C47C2311yescharacteristic
191C2×C42×C47—21no—
192C2×C42×C47C2311yescharacteristic
193C4⋊C8×C47C2314yescomplemented
194#102×C47C2314yes—
195#102×C47C2314yescomplemented
196C24×C47—21no—
197C24×C47—21no—
198C23×D47—21no—
199C23×D47—21no—
200C23×D47—24no—
201C23×D47—44no—
202C23×D47—82no—
203C23×D47—82no—
204C23×D47C2×D411yescharacteristic
205C2×Q8×C47—21no—
206C2×Q8×C47—22no—
207C2×Q8×C47C2×D414yes—
208C2×Q8×C47C2412yes—
209C2×D4×C47—22no—
210C2×D4×C47—22no—
211C2×D4×C47—21no—
212C2×D4×C47—21no—
213C2×D4×C47—24no—
214C2×D4×C47—24no—
215C2×D4×C47—22no—
216C2×D4×C47—22no—
217C2×D4×C47—82no—
218C2×D4×C47—82no—
219C2×D4×C47C2412yes—
220C2×D4×C47C2412yes—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2411yescharacteristic
226C2×C22⋊D47—24no—
227C2×C22⋊D47—24no—
228C2×C22⋊D47—24no—
229C2×C22⋊D47—24no—
230C2×C22⋊D47—44no—
231C2×C22⋊D47—44no—
232C2×C22⋊D47—82no—
233C2×C22⋊D47—82no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—24no—
237C22×Dic47—44no—
238C22×Dic47C2×D411yescharacteristic
239C22×Dic47C2×D411yescharacteristic
240C22×Dic47C2×D411yescharacteristic
241#10625354—216no—
242#10625354—28no—
243#10625354C2×D4116yescomplemented
244#10625352—28no—
245#10625352—28no—
246#10625352—48no—
247D4×D47—28no—
248D4×D47—28no—
249D4×D47—48no—
250C2×D188—28no—
251C2×D188—24no—
252C2×D188—21no—
253C2×D188—22no—
254C2×D188—22no—
255C2×D188—22no—
256C2×D188—21no—
257C2×D188C2×D414yes—
258C2×D188C2412yes—
259C2×D188C2412yes—
260C2×C4×D47—28no—
261C2×C4×D47—24no—
262C2×C4×D47—24no—
263C2×C4×D47—24no—
264C2×C4×D47—24no—
265C2×C4×D47—82no—
266C2×C4×D47—82no—
267C2×C4×D47—82no—
268C2×C4×D47C2×D412yes—
269C2×C4×D47C2×D414yes—
270C2×C4×D47#4114yes—
271C2×C4×D47C2412yes—
272C2×Dic94—22no—
273C2×Dic94—22no—
274C2×Dic94—21no—
275C2×Dic94C2412yes—
276SD16×C47—28no—
277SD16×C47—28no—
278C2×C8×C47—22no—
279C2×C8×C47—22no—
280C2×C8×C47C2412yes—
281C2×C8×C47C2412yes—
282C4⋊C4×C47—24no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47C2412yes—
285C42×C47—24no—
286C42×C47C2×D412yes—
287C42×C47C2412yes—
288C22⋊Dic47—24no—
289C22⋊Dic47—24no—
290#10625337—28no—
291#10625336—28no—
292#10625334—28no—
293#10625334—28no—
294(C2×D47)⋊C4—24no—
295(C2×D47)⋊C4—24no—
296(C2×D47)⋊C4—24no—
297(C2×D47)⋊C4—24no—
298(C2×D47)⋊C4C2×D414yes—
299(C2×D47)⋊C4C2×D414yes—
300C4⋊Dic47—21no—
301C4⋊Dic47—24no—
302C4⋊Dic47C2412yes—
303Dic47⋊C4—24no—
304Dic47⋊C4C2×D414yes—
305Dic47⋊C4C2×D414yes—
306C4×Dic47—24no—
307C4×Dic47C2×D412yes—
308C4×Dic47C2412yes—
309C2×C47⋊C8—22no—
310C2×C47⋊C8—22no—
311C2×C47⋊C8C2412yes—
312C2×C47⋊C8C2412yes—
313D376—28no—
314#10625325—28no—
315#10625324—28no—
316C8×D47—28no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—42no—
320C23×C47—42no—
321C23×C47—42no—
322C23×C47—42no—
323C23×C47—42no—
324C23×C47—42no—
325C23×C47C22×D411yescharacteristic
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—24no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—42no—
332C22×D47—42no—
333C22×D47—42no—
334C22×D47—42no—
335C22×D47—42no—
336C22×D47—48no—
337C22×D47—84no—
338C22×D47—84no—
339C22×D47—816no—
340C22×D47#12114yes—
341C22×D47C22×D412yes—
342Q8×C47—24no—
343Q8×C47—22no—
344Q8×C47C22×D414yes—
345D4×C47—22no—
346D4×C47—22no—
347D4×C47—22no—
348D4×C47—22no—
349D4×C47—42no—
350D4×C47—42no—
351D4×C47—84no—
352D4×C47—84no—
353C2×C4×C47—24no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—42no—
359C2×C4×C47C22×D412yes—
360C2×C4×C47C22×D412yes—
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D412yes—
363C2×C4×C47C2×#4112yes—
364C2×C4×C47C2511yescharacteristic
365C22⋊D47—48no—
366C22⋊D47—48no—
367C22⋊D47—84no—
368C22⋊D47—84no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—42no—
374C2×Dic47—42no—
375C2×Dic47—48no—
376C2×Dic47#12114yes—
377C2×Dic47C22×D412yes—
378C2×Dic47C22×D412yes—
379C2×Dic47C22×D412yes—
380D188—216no—
381D188—24no—
382D188—22no—
383D188—22no—
384D188—22no—
385D188—42no—
386D188C22×D414yes—
387C4×D47—216no—
388C4×D47—84no—
389C4×D47—84no—
390C4×D47—84no—
391C4×D47#12118yes—
392C4×D47C22×D414yes—
393C4×D47C2×#4114yes—
394Dic94—22no—
395Dic94—22no—
396Dic94—42no—
397C8×C47—22no—
398C8×C47—22no—
399C47⋊C8—22no—
400C47⋊C8—22no—
401C2×#3045—471nomaximal, Sylow
402C22×C47—42no—
403C22×C47—42no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—42no—
408C22×C47—84no—
409C22×C47—84no—
410C22×C47C2×#12112yes—
411C22×C47#57612yes—
412C22×C47#57712yes—
413C22×C47C23×D411yescharacteristic
414C2×D47—28no—
415C2×D47—22no—
416C2×D47—22no—
417C2×D47—24no—
418C2×D47—48no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—42no—
424C2×D47—816no—
425C2×D47—84no—
426C2×D47C2×#12114yes—
427C4×C47—24no—
428C4×C47—22no—
429C4×C47—22no—
430C4×C47—42no—
431C4×C47C2×#12112yes—
432C4×C47C23×D411yescharacteristic
433C4×C47C22×#4111yescharacteristic
434Dic47—22no—
435Dic47—22no—
436Dic47—42no—
437Dic47—42no—
438Dic47C2×#12114yes—
439C22×AGL(1,ℤ/8)—471no—
440C22×#135—471no—
441C2×#535—471no—
442C2×#520—471no—
443#3045—4716no—
444C2×#464—471no—
445C2×#464—471no—
446C2×#460—471no—
447C2×#460D4711yescharacteristic, complemented
448C2×#463—471no—
449C2×#463—471no—
450C2×#459—471no—
451C2×#459—471no—
452C2×#424—471no—
453C2×#417—471no—
454C22×#102—471no—
455C2×C47—82no—
456C2×C47—82no—
457C2×C47#304514yescomplemented
458C2×C47C22×#12111yescharacteristic
459C2×C47C2×#57611yescharacteristic
460C2×C47C2×#57711yescharacteristic
461D47—24no—
462D47—44no—
463D47—82no—
464C22×#41—471no—
465C22×#41—471no—
466C23×D4—471no—
467C2×AGL(1,ℤ/8)—478no—
468C2×AGL(1,ℤ/8)—948no—
469C2×#135—478no—
470C2×#135—948no—
471C22×Q16—471no—
472C22×SD16—471no—
473C22×SD16—471no—
474C22×SD16C2×D4711yescharacteristic
475C22×SD16C2×D4711yescharacteristic, complemented
476C22×D8—471no—
477C22×D8—471no—
478C22×D8—471no—
479C22×M16—471no—
480C23×C8—471no—
481#535—478no—
482#535—944no—
483C2×#127—471no—
484C2×#127C2×D4711yescharacteristic
485C2×#124—471no—
486C2×#124—471no—
487C2×#121—941no—
488C2×#121—941no—
489C2×#120—941no—
490C2×#120—941no—
491#520—478no—
492#520—944no—
493C2×C4×Q8—471no—
494C2×C4×Q8C2×D4711yescharacteristic, complemented
495C2×C4×D4—471no—
496C2×C4×D4—471no—
497C2×C4×D4—941no—
498C2×C4×D4—941no—
499C2×#117—471no—
500C2×#117—941no—
501C22×C4⋊C4—471no—
502C22×C4⋊C4—941no—
503#464—478no—
504#464—478no—
505#463—478no—
506#463—478no—
507#460—478no—
508#460C2×D4718yescomplemented
509#459—478no—
510#459—478no—
511#424—478no—
512C2×C4⋊C8—471no—
513C2×C4⋊C8—471no—
514C2×C4⋊C8—471no—
515C2×C4⋊C8C2×D4711yescharacteristic, complemented
516#417—478no—
517C2×#103—471no—
518C2×#103—471no—
519C2×#102—471no—
520C2×#102—471no—
521C2×#102—471no—
522C2×#102—471no—
523C2×#102—478no—
524C2×#102C2×D4711yescharacteristic
525C2×#102C2×D4711yescharacteristic, complemented
526C47C2×#304511yescharacteristic, complemented, Sylow
527C25—941no—
528C2×#41—478no—
529C2×#41—474no—
530C2×#41—474no—
531C2×#41—942no—
532C2×#41—942no—
533C2×#41—944no—
534C2×#41—944no—
535C2×#41—944no—
536C22×Q8—471no—
537C22×Q8C22×D4711yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—474no—
541C22×D4—471no—
542C22×D4—471no—
543C22×D4—941no—
544C22×D4—944no—
545C22×D4—944no—
546C22×D4—942no—
547C22×D4—941no—
548C22×D4—941no—
549C22×D4—941no—
550C22×D4—941no—
551C22×D4C22×D4711yescharacteristic
552C22×D4C22×D4711yescharacteristic
553C23×C4—471no—
554C23×C4—941no—
555C23×C4—941no—
556C23×C4—941no—
557C23×C4—941no—
558C23×C4—941no—
559AGL(1,ℤ/8)—9432no—
560#135—9432no—
561C2×Q16—474no—
562C2×Q16—944no—
563C2×SD16—24no—
564C2×SD16—24no—
565C2×SD16—474no—
566C2×SD16—474no—
567C2×SD16—944no—
568C2×SD16—944no—
569C2×SD16C22×D4714yes—
570C2×SD16C22×D4714yescomplemented
571C2×D8—474no—
572C2×D8—474no—
573C2×D8—474no—
574C2×D8—944no—
575C2×D8—944no—
576C2×D8—944no—
577C2×M16—474no—
578C2×M16—944no—
579C22×C8—471no—
580C22×C8—471no—
581C22×C8—474no—
582C22×C8—944no—
583C22×C8C22×D4711yescharacteristic
584C22×C8C22×D4711yescharacteristic
585#127—22no—
586#127—474no—
587#127—942no—
588#127C22×D4714yes—
589#124—474no—
590#124—474no—
591#124—942no—
592#124—942no—
593#121—948no—
594#121—948no—
595#120—948no—
596#120—948no—
597C4×Q8—22no—
598C4×Q8—474no—
599C4×Q8—942no—
600C4×Q8C22×D4714yescomplemented
601C4×D4—474no—
602C4×D4—474no—
603C4×D4—948no—
604C4×D4—942no—
605C4×D4—948no—
606C4×D4—942no—
607#117—474no—
608#117—474no—
609#117—948no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—471no—
612C2×C4⋊C4—471no—
613C2×C4⋊C4—471no—
614C2×C4⋊C4—474no—
615C2×C4⋊C4—948no—
616C2×C4⋊C4—942no—
617C2×C4⋊C4—941no—
618C2×C4⋊C4—941no—
619C2×C4⋊C4C22×D4711yescharacteristic
620C2×C22⋊C4—471no—
621C2×C22⋊C4—471no—
622C2×C22⋊C4—941no—
623C2×C22⋊C4—941no—
624C2×C22⋊C4—941no—
625C2×C22⋊C4—941no—
626C2×C22⋊C4—941no—
627C2×C22⋊C4—941no—
628C2×C42—21no—
629C2×C42—471no—
630C2×C42—941no—
631C2×C42C22×D4711yescharacteristic
632C4⋊C8—474no—
633C4⋊C8—474no—
634C4⋊C8—474no—
635C4⋊C8C22×D4714yescomplemented
636#103—474no—
637#103—474no—
638#102—474no—
639#102—474no—
640#102—474no—
641#102—474no—
642#102C22×D4714yes—
643#102C22×D4714yescomplemented
644C24—21no—
645C24—21no—
646C24—471no—
647C24—944no—
648C24—941no—
649C24—941no—
650C24—3762no—
651C24—3762no—
652C24—1884no—
653#41—4716no—
654#41—9416no—
655#41—948no—
656#41—948no—
657#41—948no—
658#41—1888no—
659C2×Q8—21no—
660C2×Q8—22no—
661C2×Q8—472no—
662C2×Q8—941no—
663C2×Q8—942no—
664C2×Q8—942no—
665C2×Q8D4×D4714yes—
666C2×Q8C23×D4712yes—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—82no—
676C2×D4—82no—
677C2×D4—474no—
678C2×D4—472no—
679C2×D4—472no—
680C2×D4—944no—
681C2×D4—948no—
682C2×D4—948no—
683C2×D4—948no—
684C2×D4—944no—
685C2×D4—944no—
686C2×D4—944no—
687C2×D4—944no—
688C2×D4—941no—
689C2×D4—942no—
690C2×D4—941no—
691C2×D4—942no—
692C2×D4—942no—
693C2×D4—3762no—
694C2×D4—3762no—
695C2×D4—1888no—
696C2×D4—1884no—
697C2×D4—1884no—
698C2×D4C23×D4712yes—
699C2×D4C23×D4712yes—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—471no—
703C22×C4—472no—
704C22×C4—474no—
705C22×C4—474no—
706C22×C4—472no—
707C22×C4—471no—
708C22×C4—471no—
709C22×C4—944no—
710C22×C4—948no—
711C22×C4—944no—
712C22×C4—944no—
713C22×C4—944no—
714C22×C4—941no—
715C22×C4—941no—
716C22×C4—944no—
717C22×C4—3762no—
718C22×C4—3762no—
719C22×C4—3762no—
720C22×C4—1884no—
721C22×C4D4×D4711yescharacteristic
722C22×C4D4×D4711yescharacteristic
723C22×C4C23×D4711yescharacteristic
724Q16—948no—
725SD16—28no—
726SD16—28no—
727SD16—948no—
728SD16—948no—
729D8—948no—
730D8—948no—
731D8—948no—
732M16—948no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—472no—
736C2×C8—472no—
737C2×C8—948no—
738C2×C8—942no—
739C2×C8—942no—
740C2×C8C23×D4712yes—
741C2×C8C23×D4712yes—
742C4⋊C4—24no—
743C4⋊C4—21no—
744C4⋊C4—474no—
745C4⋊C4—474no—
746C4⋊C4—472no—
747C4⋊C4—944no—
748C4⋊C4—944no—
749C4⋊C4—941no—
750C4⋊C4C23×D4712yes—
751C22⋊C4—474no—
752C22⋊C4—474no—
753C22⋊C4—944no—
754C22⋊C4—944no—
755C22⋊C4—944no—
756C22⋊C4—944no—
757C22⋊C4—944no—
758C22⋊C4—944no—
759C42—24no—
760C42—472no—
761C42—472no—
762C42—944no—
763C42D4×D4712yes—
764C42C23×D4712yes—
765C23—22no—
766C23—22no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—474no—
774C23—472no—
775C23—942no—
776C23—942no—
777C23—944no—
778C23—942no—
779C23—942no—
780C23—3764no—
781C23—3764no—
782C23—37616no—
783C23—1888no—
784C23—1882no—
785C23—1882no—
786C23—1882no—
787C23—1882no—
788C23—1882no—
789C23C2×D4×D4711yescharacteristic
790Q8—24no—
791Q8—22no—
792Q8—942no—
793Q8—942no—
794Q8—1882no—
795Q8C2×D4×D4714yes—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—42no—
801D4—42no—
802D4—84no—
803D4—84no—
804D4—474no—
805D4—9416no—
806D4—944no—
807D4—942no—
808D4—942no—
809D4—942no—
810D4—3764no—
811D4—3764no—
812D4—1888no—
813D4—1888no—
814D4—1882no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—42no—
821C2×C4—474no—
822C2×C4—472no—
823C2×C4—478no—
824C2×C4—474no—
825C2×C4—474no—
826C2×C4—472no—
827C2×C4—472no—
828C2×C4—9416no—
829C2×C4—942no—
830C2×C4—942no—
831C2×C4—942no—
832C2×C4—942no—
833C2×C4—3764no—
834C2×C4—3764no—
835C2×C4—3764no—
836C2×C4—1888no—
837C2×C4—1882no—
838C2×C4—1882no—
839C2×C4C2×D4×D4712yes—
840C2×C4C2×D4×D4712yes—
841C2×C4C2×D4×D4711yescharacteristic
842C2×C4C2×D4×D4712yes—
843C2×C4#41×D4712yes—
844C2×C4C24×D4711yescharacteristic
845C8—22no—
846C8—22no—
847C8—942no—
848C8—942no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—84no—
856C22—84no—
857C22—474no—
858C22—942no—
859C22—942no—
860C22—948no—
861C22—944no—
862C22—37616no—
863C22—3764no—
864C22—1882no—
865C22—1882no—
866C22—1882no—
867C22—1882no—
868C22—1882no—
869C22—1888no—
870C22#121×D4712yes—
871C22#1568992712yes—
872C22#1568992912yes—
873C22C22×D4×D4711yescharacteristic
874C4—22no—
875C4—24no—
876C4—22no—
877C4—42no—
878C4—474no—
879C4—942no—
880C4—942no—
881C4—1882no—
882C4—1882no—
883C4#121×D4712yes—
884C4C22×D4×D4711yescharacteristic
885C4C2×#41×D4711yescharacteristic
886C2—82no—
887C2—82no—
888C2—944no—
889C2—3762no—
890C2—1884no—
891C2#2025292414yesdirect product factor
892C2C2×#121×D4711yescharacteristic
893C2C2×#1568992711yescharacteristic
894C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#460C2
socleC23×C47C22×D4
hypercenterC2×#460D47
hypocenterC47C2×#3045
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C22×#13094051C2semidirect
2. C22×#13094045C2semidirect
3. C2×#15689686C2semidirect
4. C2×#15689605C2semidirect
5. #20252924C2direct (N × H)
6. C2×#15689345C2semidirect
7. C2×#15689343C2semidirect
8. C2×#15689321C2semidirect
9. C2×#15689339C2semidirect
10. C2×#15689337C2semidirect
11. C2×#15689317C2semidirect
12. C2×#15689315C2semidirect
13. C2×#15689148C2semidirect
14. C2×#15689121C2semidirect
15. C2×#102×D47C2semidirect
16. C2×C47×#460C2semidirect
21. C2×#13094051C22semidirect
23. C2×#13094045C22semidirect
24. C22×#10625337C22semidirect
25. C22×#10625325C22semidirect
29. C22×#10625334C22semidirect
33. #15689686C22semidirect
42. #15689605C22semidirect
43. C2×Q8×Dic47C22semidirect
45. C2×C4×D188C22semidirect
47. C2×#13093986C22semidirect
52. #15689345C22semidirect
53. #15689343C22semidirect
54. #15689339C22semidirect
55. #15689337C22semidirect
56. #15689321C22semidirect
57. #15689317C22semidirect
58. #15689315C22semidirect
59. #15689148C22semidirect
60. C2×C4⋊(C47⋊C8)C22semidirect
61. C2×Dic47⋊C8C22semidirect
62. C2×Dic47⋊C8C22semidirect
63. #15689121C22semidirect
64. C2×#13093949C22semidirect
65. C2×#13093947C22semidirect
68. C2×#13093945C22semidirect
70. #102×D47C22semidirect
72. C22×SD16×C47C22semidirect
74. C2×C4×Q8×C47C22semidirect
75. C47×#460C22semidirect
76. C2×C4⋊C8×C47C22semidirect
78. C2×#102×C47C22semidirect
82. C2×#10625354D4semidirect
109. C2×#10625337C23semidirect
111. C2×#10625325C23semidirect
119. C2×#10625334C23semidirect
137. Q8×Dic47C23semidirect
140. C4×D188C23semidirect
143. #13093986C23semidirect
165. C4⋊(C47⋊C8)C23semidirect
166. Dic47⋊C8C23semidirect
167. Dic47⋊C8C23semidirect
168. #13093949C23semidirect
169. #13093947C23semidirect
172. #13093945C23semidirect
182. C2×SD16×C47C23semidirect
188. C4×Q8×C47C23semidirect
193. C4⋊C8×C47C23semidirect
195. #102×C47C23semidirect
243. #10625354C2×D4semidirect
447. C2×#460D47semidirect
457. C2×C47#3045semidirect
475. C22×SD16C2×D47semidirect
494. C2×C4×Q8C2×D47semidirect
508. #460C2×D47semidirect
515. C2×C4⋊C8C2×D47semidirect
525. C2×#102C2×D47semidirect
526. C47C2×#3045semidirect
570. C2×SD16C22×D47semidirect
600. C4×Q8C22×D47semidirect
635. C4⋊C8C22×D47semidirect
643. #102C22×D47semidirect
891. C2#20252924direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940512
C22×#130940452
C2×#156896862
C2×#156896052
#202529242
C2×#156893452
C2×#156893432
C2×#156893212
C2×#156893392
C2×#156893372
C2×#156893172
C2×#156893152
C2×#156891482
C2×#156891212
C2×#102×D472
C2×C47×#4602
C2×#304547