Finite Group Databasebeta

← C2×#20256183 #27095968

Subgroups — C2×#20256183 #27095968

Order 12032.

2134 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689856C211yesmaximal, characteristic, complemented
2C2×#15689788C211yesmaximal, characteristic, complemented
3#20256183C2116yesmaximal, direct product factor
4C2×#15689485C211yesmaximal, characteristic, complemented
5C2×#15689481C211yesmaximal, characteristic, complemented
6C2×#15689468C211yesmaximal, characteristic, complemented
7C2×#15689407C211yesmaximal, characteristic, complemented
8C2×#15689412C211yesmaximal, characteristic, complemented
9C2×#15689339C211yesmaximal, characteristic, complemented
10C2×#15689337C211yesmaximal, characteristic, complemented
11C2×#15689317C211yesmaximal, characteristic
12C2×#15689252C211yesmaximal, characteristic, complemented
13C2×#15689234C211yesmaximal, characteristic, complemented
14C2×#15689233C211yesmaximal, characteristic, complemented
15C2×#15689210C211yesmaximal, characteristic, complemented
16C2×C47×#476C211yesmaximal, characteristic, complemented
17C22×Q8×D47—21no—
18C22×#10625325C2211yescharacteristic
19C22×D376C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21#15689856—24no—
22#15689856C2218yescomplemented
23#15689788—24no—
24#15689788C2218yescomplemented
25C2×#13094023C2211yescharacteristic
26C2×#13094023C2211yescharacteristic
27C2×#13094020C2211yescharacteristic
28C2×#13094012C2211yescharacteristic
29C2×#13094011C2211yescharacteristic
30C2×#13094010—21no—
31C2×#13094007—21no—
32C2×#13094006—21no—
33C2×#13094002—21no—
34C2×#13094002—21no—
35C2×#13094000—21no—
36C2×C4×Dic94C2211yescharacteristic
37C2×#13093989C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×#13093986C2211yescharacteristic
42C2×C4×C22⋊D47—21no—
43#15689485C2218yescomplemented
44#15689481C2218yescomplemented
45#15689468C2218yescomplemented
46#15689412C2218yescomplemented
47#15689407C2218yescomplemented
48#15689339C2218yescomplemented
49#15689337C2218yescomplemented
50#15689317C2218yes—
51#15689252C2218yescomplemented
52#15689234C2218yescomplemented
53#15689233C2218yescomplemented
54#15689210C2218yescomplemented
55C2×#13093955C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57C2×Dic47⋊C8C2211yescharacteristic
58C2×#13093949C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093935C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#476C2218yescomplemented
72C2×#106×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94D411yescharacteristic
80C22×Dic94C2311yescharacteristic
81C2×Q8×D47—28no—
82C2×Q8×D47—48no—
83C22×D188C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C2×#10625325—24no—
92C2×#10625325C2314yes—
93C2×D376—24no—
94C2×D376C2314yes—
95C2×#10625334—24no—
96C2×#10625334C2314yes—
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99#13094023—22no—
100#13094023—22no—
101#13094023C2314yes—
102#13094023C2314yes—
103#13094020—22no—
104#13094020C2314yes—
105#13094012—22no—
106#13094012C2314yes—
107#13094011—22no—
108#13094011C2314yes—
109#13094010—28no—
110#13094007—28no—
111#13094006—28no—
112#13094002—28no—
113#13094002—28no—
114#13094000—28no—
115C4×Dic94D414yes—
116C4×Dic94C2314yes—
117#13093989—22no—
118#13093989C2314yes—
119C4×D188—22no—
120C4×D188C2314yes—
121#13093986—22no—
122#13093986—22no—
123#13093986—22no—
124#13093986C2314yes—
125#13093986C2314yes—
126#13093986C2314yes—
127C4×C22⋊D47—28no—
128C2×C4⋊Dic47D411yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4D411yescharacteristic
134C2×Dic47⋊C4D411yescharacteristic
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—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×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145C2×C4×Dic47C2311yescharacteristic
146#13093955C2314yes—
147Dic47⋊C8C2314yes—
148Dic47⋊C8C2314yes—
149#13093949C2314yes—
150#13093947C2314yes—
151#13093947C2314yes—
152#13093946C2314yes—
153#13093945C2314yes—
154#13093944C2314yes—
155#13093944C2314yes—
156#13093944C2314yes—
157#13093935C2314yes—
158#13093934C2314yes—
159C8×Dic47C2314yes—
160C22×Q8×C47—21no—
161C22×D4×C47C2311yescharacteristic
162C23×C4×C47—21no—
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C4⋊Q8×C47—22no—
166C4⋊Q8×C47C2314yes—
167C4×D4×C47—22no—
168C4×D4×C47C2314yes—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#106×C47C2314yes—
176#106×C47C2314yes—
177C4⋊C8×C47C2314yes—
178#102×C47C2314yes—
179#102×C47C2314yes—
180C24×C47—21no—
181C23×D47—21no—
182C23×D47—21no—
183C2×Q8×C47—24no—
184C2×Q8×C47—44no—
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47C2412yes—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—24no—
193C22×C4×C47—82no—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C2×C22⋊D47—24no—
198C2×C22⋊D47—24no—
199C2×C22⋊D47—44no—
200C2×C22⋊D47—82no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47C2×D411yescharacteristic
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207Q8×D47—432no—
208C2×D188—21no—
209C2×D188—22no—
210C2×D188—22no—
211C2×D188—22no—
212C2×D188—21no—
213C2×D188#4114yes—
214C2×D188C2412yes—
215C2×D188C2412yes—
216C2×C4×D47—24no—
217C2×C4×D47—24no—
218C2×C4×D47—24no—
219C2×C4×D47—24no—
220C2×C4×D47—44no—
221C2×C4×D47—44no—
222C2×C4×D47—44no—
223C2×C4×D47—82no—
224C2×Dic94—24no—
225C2×Dic94—22no—
226C2×Dic94—22no—
227C2×Dic94—21no—
228C2×Dic94—24no—
229C2×Dic94—24no—
230C2×Dic94—44no—
231C2×Dic94—44no—
232C2×Dic94C2×D414yes—
233C2×Dic94C2412yes—
234C2×C8×C47—22no—
235C2×C8×C47—22no—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47—24no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47C2412yes—
243C4⋊C4×C47C2412yes—
244C4⋊C4×C47C2412yes—
245C22⋊C4×C47—24no—
246C42×C47C2×D412yes—
247C42×C47C2412yes—
248C22⋊Dic47—24no—
249C22⋊Dic47—24no—
250#10625334—28no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257C4⋊Dic47—21no—
258C4⋊Dic47C2×D414yes—
259C4⋊Dic47C2412yes—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4C2×D414yes—
264Dic47⋊C4C2×D414yes—
265C4×Dic47—24no—
266C4×Dic47C2×D412yes—
267C4×Dic47C2×D412yes—
268C4×Dic47C2412yes—
269C4×Dic47C2412yes—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8C2412yes—
273C2×C47⋊C8C2412yes—
274D376—28no—
275#10625325—28no—
276C23×C47—22no—
277C23×C47—42no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47C22×D411yescharacteristic
281C22×D47—24no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47—42no—
287C22×D47—42no—
288C22×D47—42no—
289Q8×C47—48no—
290D4×C47—22no—
291D4×C47—22no—
292D4×C47—42no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—84no—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C2×#4112yes—
306C2×C4×C472−1+412yes—
307C2×C4×C47C2511yescharacteristic
308C22⋊D47—48no—
309C22⋊D47—84no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47AGL(1,ℤ/8)14yes—
318C2×Dic47C22×D412yes—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321C2×Dic47C22×D412yes—
322D188—24no—
323D188—22no—
324D188—22no—
325D188—22no—
326D188—42no—
327D188C2×#4114yes—
328C4×D47—48no—
329C4×D47—48no—
330C4×D47—48no—
331C4×D47—84no—
332Dic94—28no—
333Dic94—22no—
334Dic94—22no—
335Dic94—48no—
336Dic94—42no—
337Dic94—48no—
338C8×C47—22no—
339C8×C47—22no—
340C47⋊C8—22no—
341C47⋊C8—22no—
342C2×#3373—471nomaximal, Sylow
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—84no—
347C22×C47#54812yes—
348C22×C47C2×AGL(1,ℤ/8)12yes—
349C22×C47#57712yes—
350C22×C47C23×D411yescharacteristic
351C2×D47—24no—
352C2×D47—48no—
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—42no—
357C2×D47—42no—
358C2×D47—84no—
359C4×C47—22no—
360C4×C47—22no—
361C4×C47—42no—
362C4×C47—42no—
363C4×C47—42no—
364C4×C47#54812yes—
365C4×C47C22×#4111yescharacteristic
366C4×C47C2×2−1+411yescharacteristic
367Dic47—22no—
368Dic47—22no—
369Dic47—22no—
370Dic47—42no—
371Dic47—42no—
372Dic47C2×AGL(1,ℤ/8)14yes—
373C2×#559—471no—
374C2×D4×Q8—471no—
375#3373—4716no—
376C2×#489—471no—
377C2×#489—471no—
378C2×#486—471no—
379C2×#475—471no—
380C2×#476—471no—
381C2×#476D4711yescharacteristic, complemented
382C2×#463—471no—
383C2×#463—471no—
384C2×#459—471no—
385C2×#446—471no—
386C2×#442—471no—
387C2×#442—471no—
388C2×C4×SD16—471no—
389C2×C47—82no—
390C2×C47#337314yescomplemented
391C2×C47C2×#54811yescharacteristic
392C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
393C2×C47C2×#57711yescharacteristic
394D47—44no—
395D47—82no—
396C23×Q8—941no—
397C22×SD16—471no—
398C22×D8—471no—
399C22×D8—471no—
400#559—478no—
401#559—944no—
402D4×Q8—478no—
403D4×Q8—944no—
404C2×C4⋊Q8—471no—
405C2×C4⋊Q8—471no—
406C2×C4⋊Q8C2×D4711yescharacteristic
407C2×#127—471no—
408C2×#124—471no—
409C2×#124—471no—
410C2×#124—941no—
411C2×#123—941no—
412C2×#123—941no—
413C2×C22⋊Q8—941no—
414C2×C22⋊Q8—941no—
415C2×C22⋊Q8—941no—
416C2×C4×Q8—471no—
417C2×C4×Q8—471no—
418C2×C4×D4—471no—
419C2×C4×D4—471no—
420C2×C4×D4—471no—
421C2×C4×D4—471no—
422C2×C4×D4—941no—
423C2×C4×D4C2×D4711yescharacteristic
424#489—478no—
425#489—478no—
426#486—478no—
427#476—478no—
428#476C2×D4718yescomplemented
429#475—478no—
430#463—478no—
431#463—478no—
432#459—478no—
433#446—478no—
434#442—478no—
435#442—478no—
436C4×SD16—478no—
437C2×#106—471no—
438C2×#106C2×D4711yescharacteristic
439C2×#106C2×D4711yescharacteristic
440C2×C4⋊C8—471no—
441C2×C4⋊C8—471no—
442C2×C4⋊C8C2×D4711yescharacteristic
443C2×#103—471no—
444C2×#103—471no—
445C2×#103—471no—
446C2×#102—471no—
447C2×#102—471no—
448C2×#102—471no—
449C2×#102—471no—
450C2×#102—471no—
451C2×#102C2×D4711yescharacteristic
452C2×#102C2×D4711yescharacteristic
453C2×#97—471no—
454C2×#97—471no—
455C2×C4×C8—471no—
456C47C2×#337311yescharacteristic, complemented, Sylow
457C22×Q8—21no—
458C22×Q8—471no—
459C22×Q8—471no—
460C22×Q8—941no—
461C22×Q8—941no—
462C22×Q8—948no—
463C22×Q8—1888no—
464C22×D4—471no—
465C22×D4—471no—
466C22×D4—941no—
467C22×D4—941no—
468C22×D4C22×D4711yescharacteristic
469C23×C4—21no—
470C23×C4—941no—
471C23×C4—941no—
472C23×C4—941no—
473C23×C4—941no—
474C2×SD16—474no—
475C2×SD16—944no—
476C2×D8—474no—
477C2×D8—474no—
478C2×D8—944no—
479C2×D8—944no—
480C22×C8—471no—
481C22×C8—471no—
482C22×C8C22×D4711yescharacteristic
483C22×C8C22×D4711yescharacteristic
484C4⋊Q8—22no—
485C4⋊Q8—474no—
486C4⋊Q8—474no—
487C4⋊Q8—942no—
488C4⋊Q8—942no—
489C4⋊Q8C22×D4714yes—
490#127—474no—
491#127—942no—
492#124—474no—
493#124—474no—
494#124—942no—
495#124—948no—
496#124—942no—
497#123—948no—
498#123—948no—
499C22⋊Q8—948no—
500C22⋊Q8—948no—
501C22⋊Q8—948no—
502C4×Q8—474no—
503C4×Q8—474no—
504C4×Q8—474no—
505C4×Q8—942no—
506C4×D4—22no—
507C4×D4—474no—
508C4×D4—474no—
509C4×D4—474no—
510C4×D4—474no—
511C4×D4—942no—
512C4×D4—942no—
513C4×D4—942no—
514C4×D4—948no—
515C4×D4—942no—
516C4×D4C22×D4714yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4C22×D4711yescharacteristic
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C42—471no—
538C2×C42—471no—
539C2×C42—941no—
540C2×C42C22×D4711yescharacteristic
541#106—474no—
542#106C22×D4714yes—
543#106C22×D4714yes—
544C4⋊C8—474no—
545C4⋊C8—474no—
546C4⋊C8C22×D4714yes—
547#103—474no—
548#103—474no—
549#103—474no—
550#102—474no—
551#102—474no—
552#102—474no—
553#102—474no—
554#102—474no—
555#102C22×D4714yes—
556#102C22×D4714yes—
557#97—474no—
558#97—474no—
559C4×C8—474no—
560C24—21no—
561C24—941no—
562C24—941no—
563C2×Q8—24no—
564C2×Q8—44no—
565C2×Q8—474no—
566C2×Q8—472no—
567C2×Q8—944no—
568C2×Q8—944no—
569C2×Q8—944no—
570C2×Q8—941no—
571C2×Q8—942no—
572C2×Q8—942no—
573C2×Q8—1884no—
574C2×Q8—1884no—
575C2×Q8—18832no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—474no—
580C2×D4—472no—
581C2×D4—472no—
582C2×D4—944no—
583C2×D4—944no—
584C2×D4—941no—
585C2×D4—941no—
586C2×D4—942no—
587C2×D4—942no—
588C2×D4—942no—
589C2×D4—3762no—
590C2×D4—1884no—
591C2×D4C23×D4712yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—82no—
597C22×C4—471no—
598C22×C4—471no—
599C22×C4—471no—
600C22×C4—471no—
601C22×C4—944no—
602C22×C4—944no—
603C22×C4—944no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—944no—
607C22×C4—3762no—
608C22×C4—1884no—
609C22×C4—1884no—
610C22×C4—1884no—
611C22×C4D4×D4711yescharacteristic
612C22×C4D4×D4711yescharacteristic
613C22×C4C23×D4711yescharacteristic
614SD16—948no—
615D8—948no—
616D8—948no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—472no—
620C2×C8—472no—
621C2×C8—942no—
622C2×C8—942no—
623C2×C8C23×D4712yes—
624C2×C8C23×D4712yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—474no—
630C4⋊C4—474no—
631C4⋊C4—474no—
632C4⋊C4—472no—
633C4⋊C4—944no—
634C4⋊C4—944no—
635C4⋊C4—944no—
636C4⋊C4—941no—
637C4⋊C4C23×D4712yes—
638C4⋊C4C23×D4712yes—
639C4⋊C4C23×D4712yes—
640C22⋊C4—24no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C42—472no—
650C42—472no—
651C42—472no—
652C42—472no—
653C42—944no—
654C42D4×D4712yes—
655C42C23×D4712yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—944no—
661C23—942no—
662C23—942no—
663C23—1882no—
664C23—1882no—
665C23—1882no—
666C23—1882no—
667C23—1882no—
668C23C2×D4×D4711yescharacteristic
669Q8—48no—
670Q8—948no—
671Q8—942no—
672Q8—942no—
673Q8—1888no—
674Q8—1888no—
675Q8—1882no—
676D4—22no—
677D4—22no—
678D4—42no—
679D4—474no—
680D4—944no—
681D4—942no—
682D4—942no—
683D4—942no—
684D4—3764no—
685D4—1888no—
686D4—1882no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—84no—
696C2×C4—474no—
697C2×C4—472no—
698C2×C4—472no—
699C2×C4—472no—
700C2×C4—472no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—3764no—
707C2×C4—1888no—
708C2×C4—1888no—
709C2×C4—1888no—
710C2×C4—1882no—
711C2×C4—1882no—
712C2×C4C2×D4×D4712yes—
713C2×C4C2×D4×D4712yes—
714C2×C4C2×D4×D4711yescharacteristic
715C2×C4#41×D4712yes—
716C2×C4#1309407212yes—
717C2×C4C24×D4711yescharacteristic
718C8—22no—
719C8—22no—
720C8—942no—
721C8—942no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—944no—
727C22—3764no—
728C22—1882no—
729C22—1882no—
730C22—1882no—
731C22—1882no—
732C22—1882no—
733C22—1888no—
734C22#1568978312yes—
735C22AGL(1,ℤ/8)×D4712yes—
736C22#1568992912yes—
737C22C22×D4×D4711yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—474no—
744C4—942no—
745C4—942no—
746C4—942no—
747C4—1882no—
748C4—1882no—
749C4#1568978312yes—
750C4C2×#41×D4711yescharacteristic
751C4C2×#1309407211yescharacteristic
752C2—82no—
753C2—3762no—
754C2—1884no—
755C2#2025618314yesdirect product factor
756C2C2×#1568978311yescharacteristic
757C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
758C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#476C2
socleC23×C47C22×D4
prime radicalC2×#15689317C2
hypercenterC2×#476D47
hypocenterC47C2×#3373
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#15689856C2semidirect
2. C2×#15689788C2semidirect
3. #20256183C2direct (N × H)
4. C2×#15689485C2semidirect
5. C2×#15689481C2semidirect
6. C2×#15689468C2semidirect
7. C2×#15689407C2semidirect
8. C2×#15689412C2semidirect
9. C2×#15689339C2semidirect
10. C2×#15689337C2semidirect
12. C2×#15689252C2semidirect
13. C2×#15689234C2semidirect
14. C2×#15689233C2semidirect
15. C2×#15689210C2semidirect
16. C2×C47×#476C2semidirect
22. #15689856C22semidirect
24. #15689788C22semidirect
43. #15689485C22semidirect
44. #15689481C22semidirect
45. #15689468C22semidirect
46. #15689412C22semidirect
47. #15689407C22semidirect
48. #15689339C22semidirect
49. #15689337C22semidirect
51. #15689252C22semidirect
52. #15689234C22semidirect
53. #15689233C22semidirect
54. #15689210C22semidirect
71. C47×#476C22semidirect
381. C2×#476D47semidirect
390. C2×C47#3373semidirect
428. #476C2×D47semidirect
456. C47C2×#3373semidirect
755. C2#20256183direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898562
C2×#156897882
#202561832
C2×#156894852
C2×#156894812
C2×#156894682
C2×#156894072
C2×#156894122
C2×#156893392
C2×#156893372
C2×#156893172
C2×#156892522
C2×#156892342
C2×#156892332
C2×#156892102
C2×C47×#4762
C2×#337347