Finite Group Databasebeta

← C2×#20253656 #27084599

Subgroups — C2×#20253656 #27084599

Order 12032.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689745C211yesmaximal, characteristic, complemented
2C2×#15689605C211yesmaximal, characteristic, complemented
3#20253656C2116yesmaximal, direct product factor
4C2×#15689457C211yesmaximal, characteristic, complemented
5C2×#15689438C211yesmaximal, characteristic, complemented
6C2×#15689416C211yesmaximal, characteristic, complemented
7C2×#15689402C211yesmaximal, characteristic, complemented
8C2×#15689347C211yesmaximal, characteristic, complemented
9C2×#15689341C211yesmaximal, characteristic, complemented
10C2×#15689284C211yesmaximal, characteristic, complemented
11C2×#15689271C211yesmaximal, characteristic
12C2×#15689221C211yesmaximal, characteristic, complemented
13C2×#15689221C211yesmaximal, characteristic, complemented
14C2×C4×D376C211yesmaximal, characteristic, complemented
15C2×#15689182C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×D376C2211yescharacteristic
21#15689745—24no—
22#15689745C2218yescomplemented
23C2×#13094023C2211yescharacteristic
24C2×#13094018—21no—
25C2×#13094013C2211yescharacteristic
26C2×#13094012—21no—
27C2×#13094009—21no—
28C2×#13094002—21no—
29C2×#13094000C2211yescharacteristic
30C2×#13093999C2211yescharacteristic
31#15689605—24no—
32#15689605C2218yescomplemented
33C2×Q8×Dic47C2211yescharacteristic
34C2×C4×D188—21no—
35C2×C4×D188C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×#13093986—21no—
38C2×#13093986C2211yescharacteristic
39C2×#13093981—21no—
40C2×#13093981C2211yescharacteristic
41C2×C4⋊C4×D47—21no—
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689457C2218yescomplemented
44#15689438C2218yescomplemented
45#15689416C2218yescomplemented
46#15689402C2218yescomplemented
47#15689347C2218yescomplemented
48#15689341C2218yescomplemented
49#15689284C2218yescomplemented
50#15689271C2218yes—
51#15689221C2218yescomplemented
52#15689221C2218yescomplemented
53C4×D376C2218yescomplemented
54#15689182C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093935C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C4×Q16×C47C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625354—24no—
78C2×#10625354—24no—
79C2×#10625354—22no—
80C2×#10625354C2314yes—
81C22×Dic94—21no—
82C22×D188—21no—
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C4×D47C2311yescharacteristic
92C2×#10625336—24no—
93C2×#10625336—24no—
94C2×#10625336C2314yes—
95C2×#10625336C2314yes—
96C2×D376—24no—
97C2×D376C2314yes—
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100#13094023—22no—
101#13094023C2314yes—
102#13094018—28no—
103#13094013—22no—
104#13094013C2314yes—
105#13094012—28no—
106#13094009—28no—
107#13094002—28no—
108#13094000—22no—
109#13094000C2314yes—
110#13093999—22no—
111#13093999C2314yes—
112Q8×Dic47—22no—
113Q8×Dic47C2314yes—
114C4×D188—22no—
115C4×D188—22no—
116C4×D188—28no—
117C4×D188C2314yes—
118C4×D188C2314yes—
119#13093986—28no—
120#13093986—22no—
121#13093986C2314yes—
122#13093981—28no—
123#13093981D414yes—
124#13093981C2314yes—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4D411yescharacteristic
132C2×Dic47⋊C4D411yescharacteristic
133C4⋊C4×D47—22no—
134C4⋊C4×D47—28no—
135C4⋊C4×D47C2314yes—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093958C2314yes—
148#13093957C2314yes—
149#13093957C2314yes—
150Dic47⋊C8C2314yes—
151Dic47⋊C8C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154#13093946C2314yes—
155#13093946C2314yes—
156#13093944C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160#13093935C2314yes—
161C22×Q8×C47C2311yescharacteristic
162C22×Q8×C47C2311yescharacteristic
163C2×Q16×C47—24no—
164C2×Q16×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C4×Q8×C47—22no—
168C4×Q8×C47—22no—
169C4×Q8×C47C2314yes—
170C4×Q8×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C42×C47—21no—
176C2×C42×C47—21no—
177C2×C42×C47C2311yescharacteristic
178#107×C47C2314yes—
179#103×C47C2314yes—
180#103×C47C2314yes—
181C4×C8×C47C2314yes—
182C23×D47—21no—
183C23×D47—21no—
184C23×D47C2×D411yescharacteristic
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47#4114yes—
191C2×Q8×C47C2412yes—
192C2×Q8×C47C2412yes—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2411yescharacteristic
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47C2×D411yescharacteristic
203C22×Dic47C2×D411yescharacteristic
204C22×Dic47C2×D411yescharacteristic
205#10625354—216no—
206#10625354—28no—
207#10625354—28no—
208C2×D188—28no—
209C2×D188—24no—
210C2×D188—21no—
211C2×D188—22no—
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—21no—
215C2×D188—24no—
216C2×D188—82no—
217C2×D188#4114yes—
218C2×D188C2412yes—
219C2×D188C2412yes—
220C2×C4×D47—28no—
221C2×C4×D47—22no—
222C2×C4×D47—22no—
223C2×C4×D47—24no—
224C2×C4×D47—24no—
225C2×C4×D47—24no—
226C2×C4×D47—24no—
227C2×C4×D47—24no—
228C2×C4×D47—82no—
229C2×C4×D47—82no—
230C2×C4×D47—82no—
231C2×C4×D47—82no—
232C2×C4×D47C2×D412yes—
233C2×C4×D47C2412yes—
234C2×Dic94—24no—
235C2×Dic94—82no—
236Q16×C47—28no—
237C2×C8×C47—22no—
238C2×C8×C47—22no—
239C2×C8×C47C2412yes—
240C2×C8×C47C2412yes—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47C2412yes—
246C4⋊C4×C47C2412yes—
247C42×C47—24no—
248C42×C47—24no—
249C42×C47C2×D412yes—
250C42×C47C2412yes—
251#10625336—28no—
252#10625336—28no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4C2×D414yes—
261(C2×D47)⋊C4C2×D414yes—
262C4⋊Dic47—21no—
263C4⋊Dic47—21no—
264C4⋊Dic47—24no—
265C4⋊Dic47C2412yes—
266C4⋊Dic47C2412yes—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269Dic47⋊C4—24no—
270Dic47⋊C4C2×D414yes—
271Dic47⋊C4C2×D414yes—
272C4×Dic47—24no—
273C4×Dic47C2×D412yes—
274C4×Dic47C2412yes—
275C2×C47⋊C8—22no—
276C2×C47⋊C8—22no—
277C2×C47⋊C8C2412yes—
278C2×C47⋊C8C2412yes—
279D376—28no—
280C23×C47C22×D411yescharacteristic
281C22×D47—22no—
282C22×D47—24no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—42no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47C22×D412yes—
293Q8×C47—24no—
294Q8×C47—22no—
295Q8×C47—22no—
296Q8×C47—22no—
297Q8×C47—42no—
298Q8×C47C2×#4114yes—
299C2×C4×C47—24no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C2×#4112yes—
313C2×C4×C47C2×#4112yes—
314C2×C4×C47C2511yescharacteristic
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325D188—216no—
326D188—24no—
327D188—22no—
328D188—22no—
329D188—22no—
330D188—42no—
331D188—84no—
332D188C2×#4114yes—
333C4×D47—216no—
334C4×D47—24no—
335C4×D47—22no—
336C4×D47—22no—
337C4×D47—84no—
338C4×D47—84no—
339C4×D47—84no—
340C4×D47—84no—
341Dic94—84no—
342C8×C47—22no—
343C8×C47—22no—
344C47⋊C8—22no—
345C47⋊C8—22no—
346C2×#3124—471nomaximal, Sylow
347C22×C47#52512yes—
348C22×C47#57612yes—
349C22×C47#57812yes—
350C22×C47C23×D411yescharacteristic
351C2×D47—22no—
352C2×D47—24no—
353C2×D47—22no—
354C2×D47—22no—
355C2×D47—44no—
356C2×D47—48no—
357C2×D47—42no—
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—84no—
363C4×C47—24no—
364C4×C47—22no—
365C4×C47—22no—
366C4×C47—42no—
367C4×C47—42no—
368C4×C47—42no—
369C4×C47#52512yes—
370C4×C47C22×#4111yescharacteristic
371C4×C47C22×#4111yescharacteristic
372Dic47—22no—
373Dic47—22no—
374Dic47—22no—
375Dic47—42no—
376Dic47—42no—
377C2×#542—471no—
378C2×#520—471no—
379#3124—4716no—
380C2×#484—471no—
381C2×#480—471no—
382C2×#477—471no—
383C2×#474—471no—
384C2×#464—471no—
385C2×#463—471no—
386C2×#452—471no—
387C2×#449—471no—
388C2×#440—471no—
389C2×#440—471no—
390C2×C4×Q16D4711yescharacteristic, complemented
391C2×C4×D8—471no—
392C2×#433—471no—
393C2×C47#312414yescomplemented
394C2×C47C2×#52511yescharacteristic
395C2×C47C2×#57611yescharacteristic
396C2×C47C2×#57811yescharacteristic
397D47—42no—
398D47—44no—
399D47—82no—
400C22×#41—471no—
401C22×Q16C2×D4711yescharacteristic
402C22×SD16—471no—
403C22×SD16—471no—
404C22×D8—471no—
405#542—478no—
406#542—944no—
407C2×C4⋊Q8—471no—
408C2×#126—941no—
409C2×#124—471no—
410C2×#124—941no—
411C2×#123—941no—
412C2×C22⋊Q8—471no—
413C2×C22⋊Q8—941no—
414C2×#121—471no—
415#520—478no—
416#520—944no—
417C2×C4×Q8—471no—
418C2×C4×Q8C2×D4711yescharacteristic
419C2×C4×Q8C2×D4711yescharacteristic
420C2×C4×D4—471no—
421C2×C4×D4—471no—
422C2×C4×D4—471no—
423C2×C4×D4—941no—
424C2×C4×D4—941no—
425C2×#117—471no—
426C2×#117—941no—
427C22×C4⋊C4—471no—
428C22×C4⋊C4—941no—
429#484—478no—
430#480—478no—
431#477—478no—
432#474—478no—
433#464—478no—
434#463—478no—
435#452—478no—
436#449—478no—
437#440—478no—
438#440—478no—
439C4×Q16C2×D4718yescomplemented
440C4×D8—478no—
441#433—478no—
442C2×#107—471no—
443C2×#107—471no—
444C2×#107—471no—
445C2×#107C2×D4711yescharacteristic
446C2×C4⋊C8—471no—
447C2×C4⋊C8—471no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#103C2×D4711yescharacteristic
451C2×#103C2×D4711yescharacteristic
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#102—471no—
456C2×C22⋊C8—471no—
457C2×C22⋊C8—471no—
458C2×#97—471no—
459C2×C4×C8C2×D4711yescharacteristic
460C47C2×#312411yescharacteristic, complemented, Sylow
461C2×#41—474no—
462C2×#41—942no—
463C2×#41—944no—
464C2×#41—944no—
465C22×Q8—941no—
466C22×Q8C22×D4711yescharacteristic
467C22×Q8C22×D4711yescharacteristic
468C22×D4—471no—
469C22×D4—471no—
470C22×D4—941no—
471C22×D4—941no—
472C23×C4—471no—
473C23×C4—941no—
474C23×C4—941no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4—941no—
478C2×Q16—24no—
479C2×Q16C22×D4714yes—
480C2×SD16—474no—
481C2×SD16—474no—
482C2×SD16—944no—
483C2×SD16—944no—
484C2×D8—474no—
485C2×D8—944no—
486C22×C8—471no—
487C22×C8—471no—
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490C4⋊Q8—474no—
491C4⋊Q8—942no—
492#126—948no—
493#124—474no—
494#124—948no—
495#124—942no—
496#123—948no—
497C22⋊Q8—474no—
498C22⋊Q8—948no—
499C22⋊Q8—942no—
500#121—474no—
501#121—942no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—474no—
505C4×Q8—942no—
506C4×Q8C22×D4714yes—
507C4×Q8C22×D4714yes—
508C4×D4—474no—
509C4×D4—474no—
510C4×D4—474no—
511C4×D4—948no—
512C4×D4—942no—
513C4×D4—948no—
514C4×D4—942no—
515C4×D4—942no—
516#117—474no—
517#117—474no—
518#117—948no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—471no—
524C2×C4⋊C4—471no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—948no—
527C2×C4⋊C4—942no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4—941no—
532C2×C4⋊C4C22×D4711yescharacteristic
533C2×C4⋊C4C22×D4711yescharacteristic
534C2×C22⋊C4—471no—
535C2×C22⋊C4—471no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—941no—
538C2×C22⋊C4—941no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C22⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—471no—
546C2×C42—941no—
547C2×C42C22×D4711yescharacteristic
548#107—474no—
549#107—474no—
550#107—474no—
551#107C22×D4714yes—
552C4⋊C8—474no—
553C4⋊C8—474no—
554#103—474no—
555#103—474no—
556#103C22×D4714yes—
557#103C22×D4714yes—
558#102—474no—
559#102—474no—
560#102—474no—
561#102—474no—
562C22⋊C8—474no—
563C22⋊C8—474no—
564#97—474no—
565C4×C8C22×D4714yes—
566C24—471no—
567C24—941no—
568C24—941no—
569#41—948no—
570#41—9416no—
571#41—948no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—944no—
578C2×Q8—3762no—
579C2×Q8#1062535014yes—
580C2×Q8C23×D4712yes—
581C2×Q8C23×D4712yes—
582C2×D4—474no—
583C2×D4—472no—
584C2×D4—472no—
585C2×D4—944no—
586C2×D4—948no—
587C2×D4—944no—
588C2×D4—941no—
589C2×D4—941no—
590C2×D4—942no—
591C2×D4—942no—
592C2×D4—942no—
593C2×D4—3762no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—471no—
599C22×C4—471no—
600C22×C4—471no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—944no—
604C22×C4—944no—
605C22×C4—948no—
606C22×C4—944no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—944no—
612C22×C4—944no—
613C22×C4—3762no—
614C22×C4—3762no—
615C22×C4—3762no—
616C22×C4—3762no—
617C22×C4D4×D4711yescharacteristic
618C22×C4D4×D4711yescharacteristic
619C22×C4C23×D4711yescharacteristic
620Q16—28no—
621SD16—948no—
622SD16—948no—
623D8—948no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—472no—
627C2×C8—472no—
628C2×C8—942no—
629C2×C8—942no—
630C2×C8C23×D4712yes—
631C2×C8C23×D4712yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—474no—
637C4⋊C4—474no—
638C4⋊C4—472no—
639C4⋊C4—472no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—944no—
643C4⋊C4—944no—
644C4⋊C4—941no—
645C4⋊C4—941no—
646C4⋊C4C23×D4712yes—
647C4⋊C4C23×D4712yes—
648C22⋊C4—474no—
649C22⋊C4—474no—
650C22⋊C4—944no—
651C22⋊C4—944no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C22⋊C4—944no—
655C22⋊C4—944no—
656C22⋊C4—944no—
657C42—24no—
658C42—24no—
659C42—472no—
660C42—472no—
661C42—944no—
662C42D4×D4712yes—
663C42C23×D4712yes—
664C23—472no—
665C23—944no—
666C23—942no—
667C23—942no—
668C23—942no—
669C23—942no—
670C23—942no—
671C23—1882no—
672C23—1882no—
673C23—1882no—
674C23—1882no—
675C23—1882no—
676C23C2×D4×D4711yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8—3764no—
683Q8C2×#1062535014yes—
684D4—474no—
685D4—9416no—
686D4—944no—
687D4—942no—
688D4—942no—
689D4—942no—
690D4—3764no—
691D4—1882no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—472no—
703C2×C4—472no—
704C2×C4—472no—
705C2×C4—9416no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—942no—
709C2×C4—944no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—3764no—
715C2×C4—3764no—
716C2×C4—3764no—
717C2×C4—3764no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4C2×D4×D4712yes—
721C2×C4C2×D4×D4712yes—
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4#41×D4712yes—
724C2×C4C2×#1062535012yes—
725C2×C4C24×D4711yescharacteristic
726C8—22no—
727C8—22no—
728C8—942no—
729C8—942no—
730C22—942no—
731C22—942no—
732C22—944no—
733C22—942no—
734C22—3764no—
735C22—1882no—
736C22—1882no—
737C22—1882no—
738C22—1882no—
739C22—1882no—
740C22—1884no—
741C22—1888no—
742C22#1568963212yes—
743C22#1568992512yes—
744C22#1568993612yes—
745C22C22×D4×D4711yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—942no—
753C4—942no—
754C4—942no—
755C4—1882no—
756C4—1882no—
757C4#1568963212yes—
758C4C2×#41×D4711yescharacteristic
759C4C22×#1062535011yescharacteristic
760C2—3762no—
761C2—1882no—
762C2—1884no—
763C2#2025365614yesdirect product factor
764C2C2×#1568963211yescharacteristic
765C2C2×#1568992511yescharacteristic
766C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×Q16×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689271C2
hypercenterC2×C4×Q16D47
hypocenterC47C2×#3124
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#15689745C2semidirect
2. C2×#15689605C2semidirect
3. #20253656C2direct (N × H)
4. C2×#15689457C2semidirect
5. C2×#15689438C2semidirect
6. C2×#15689416C2semidirect
7. C2×#15689402C2semidirect
8. C2×#15689347C2semidirect
9. C2×#15689341C2semidirect
10. C2×#15689284C2semidirect
12. C2×#15689221C2semidirect
13. C2×#15689221C2semidirect
14. C2×C4×D376C2semidirect
15. C2×#15689182C2semidirect
16. C2×C4×Q16×C47C2semidirect
22. #15689745C22semidirect
32. #15689605C22semidirect
43. #15689457C22semidirect
44. #15689438C22semidirect
45. #15689416C22semidirect
46. #15689402C22semidirect
47. #15689347C22semidirect
48. #15689341C22semidirect
49. #15689284C22semidirect
51. #15689221C22semidirect
52. #15689221C22semidirect
53. C4×D376C22semidirect
54. #15689182C22semidirect
72. C4×Q16×C47C22semidirect
390. C2×C4×Q16D47semidirect
393. C2×C47#3124semidirect
439. C4×Q16C2×D47semidirect
460. C47C2×#3124semidirect
763. C2#20253656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897452
C2×#156896052
#202536562
C2×#156894572
C2×#156894382
C2×#156894162
C2×#156894022
C2×#156893472
C2×#156893412
C2×#156892842
C2×#156892712
C2×#156892212
C2×C4×D3762
C2×#156891822
C2×C4×Q16×C472
C2×#312447