Finite Group Databasebeta

← C2×#20255862 #27094845

Subgroups — C2×#20255862 #27094845

Order 12032.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689825C211yesmaximal, characteristic, complemented
2C2×#15689774C211yesmaximal, characteristic, complemented
3#20255862C2116yesmaximal, direct product factor
4C2×#15689531C211yesmaximal, characteristic, complemented
5C2×#15689442C211yesmaximal, characteristic, complemented
6C2×#15689440C211yesmaximal, characteristic, complemented
7C2×#15689450C211yesmaximal, characteristic, complemented
8C2×#15689426C211yesmaximal, characteristic, complemented
9C2×#15689411C211yesmaximal, characteristic, complemented
10C2×#15689375C211yesmaximal, characteristic, complemented
11C2×#15689357C211yesmaximal, characteristic, complemented
12C2×#15689232C211yesmaximal, characteristic, complemented
13C2×#15689191C211yesmaximal, characteristic, complemented
14C2×#15689164C211yesmaximal, characteristic, complemented
15C22×#13093955C211yesmaximal, characteristic, complemented
16C2×C47×#480C211yesmaximal, characteristic, complemented
17C22×#10625350—21no—
18C22×#10625334C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C23×C47⋊C8C2211yescharacteristic
21#15689825—24no—
22#15689825C2218yescomplemented
23#15689774—24no—
24#15689774C2218yescomplemented
25C2×#13094023C2211yescharacteristic
26C2×#13094017—21no—
27C2×#13094015C2211yescharacteristic
28C2×#13094009—21no—
29C2×#13094008—21no—
30C2×#13094007—21no—
31C2×#13094002—21no—
32C2×#13093999C2211yescharacteristic
33C2×#13093998C2211yescharacteristic
34C2×#13093996—21no—
35C2×#13093995C2211yescharacteristic
36C2×D4×Dic47—21no—
37C2×D4×Dic47C2211yescharacteristic
38C2×#13093986C2211yescharacteristic
39C2×C4×C22⋊D47C2211yescharacteristic
40C2×#13093982C2211yescharacteristic
41C22×C4⋊Dic47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689531C2218yescomplemented
44#15689450C2218yescomplemented
45#15689442C2218yescomplemented
46#15689440C2218yescomplemented
47#15689426C2218yescomplemented
48#15689411C2218yescomplemented
49#15689375C2218yescomplemented
50#15689357C2218yescomplemented
51#15689232C2218yescomplemented
52#15689191C2218yescomplemented
53#15689164C2218yescomplemented
54C2×#13093957C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×#13093955C2218yescomplemented
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C2×#121×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic
71C47×#480C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625350—28no—
78C2×#10625350—48no—
79C22×Dic94—21no—
80C22×D188—21no—
81C22×D188C2311yescharacteristic
82C22×C22⋊D47—21no—
83C22×C22⋊D47—21no—
84C22×C22⋊D47D411yescharacteristic
85C23×Dic47—21no—
86C23×Dic47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47C2311yescharacteristic
90C2×#10625334—24no—
91C2×#10625334C2314yes—
92C2×#10625324—24no—
93C2×#10625324C2314yes—
94C22×C47⋊C8—24no—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2314yes—
97C22×C47⋊C8C2311yescharacteristic
98#13094023—22no—
99#13094023C2314yes—
100#13094017—28no—
101#13094015—22no—
102#13094015C2314yes—
103#13094009—28no—
104#13094008—28no—
105#13094007—28no—
106#13094002—28no—
107#13093999—22no—
108#13093999C2314yes—
109#13093998—22no—
110#13093998C2314yes—
111#13093996—28no—
112#13093995—22no—
113#13093995C2314yes—
114D4×Dic47—28no—
115D4×Dic47—22no—
116D4×Dic47C2314yes—
117#13093986—22no—
118#13093986C2314yes—
119C4×C22⋊D47D414yes—
120C4×C22⋊D47C2314yes—
121#13093982—22no—
122#13093982C2314yes—
123C2×C4⋊Dic47—22no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47C2314yes—
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4D411yescharacteristic
134C4⋊C4×D47—22no—
135C4⋊C4×D47C2314yes—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47D411yescharacteristic
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×C4×Dic47—21no—
145C2×C4×Dic47C2311yescharacteristic
146#13093957C2314yes—
147#13093956C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150#13093955C2314yes—
151#13093955C2314yes—
152#13093955C2314yes—
153Dic47⋊C8C2314yes—
154#13093946C2314yes—
155#13093946C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159#13093934C2314yes—
160C22×D4×C47—21no—
161C22×D4×C47C2311yescharacteristic
162C23×C4×C47—21no—
163C23×C4×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166#121×C47—22no—
167#121×C47C2314yes—
168C2×C4⋊C4×C47—22no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2314yes—
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175#107×C47C2314yes—
176#107×C47C2314yes—
177#102×C47C2314yes—
178#102×C47C2314yes—
179C22⋊C8×C47C2314yes—
180C24×C47—21no—
181C24×C47C2×D411yescharacteristic
182C23×D47—21no—
183C23×D47C2×D411yescharacteristic
184C2×D4×C47—24no—
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—44no—
189C2×D4×C47C2412yes—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—24no—
196C22×C4×C47—44no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47—24no—
204C2×C22⋊D47—44no—
205C2×C22⋊D47—82no—
206C2×C22⋊D47C2×D414yes—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—24no—
211C22×Dic47—24no—
212C22×Dic47—82no—
213C22×Dic47—82no—
214C22×Dic47C2×D411yescharacteristic
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217#10625350—432no—
218C2×D188—22no—
219C2×D188—22no—
220C2×D188—24no—
221C2×D188—21no—
222C2×D188—44no—
223C2×D188C2412yes—
224C2×C4×D47—22no—
225C2×C4×D47—22no—
226C2×C4×D47—24no—
227C2×C4×D47—24no—
228C2×C4×D47—44no—
229C2×C4×D47—44no—
230C2×C4×D47C2×D412yes—
231C2×C4×D47C2412yes—
232C2×Dic94—24no—
233C2×Dic94—44no—
234C2×C8×C47—22no—
235C2×C8×C47—22no—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47C2412yes—
243C4⋊C4×C47C2412yes—
244C4⋊C4×C47C2412yes—
245C22⋊C4×C47—24no—
246C22⋊Dic47—24no—
247C22⋊Dic47—24no—
248C22⋊Dic47C2×D414yes—
249#10625334—28no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4C2×D414yes—
255C4⋊Dic47—21no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—24no—
259C4⋊Dic47—24no—
260C4⋊Dic47C2412yes—
261C4⋊Dic47C2412yes—
262C4⋊Dic47C2412yes—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4C2×D414yes—
267C4×Dic47—24no—
268C4×Dic47C2×D412yes—
269C4×Dic47C2412yes—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—28no—
272C2×C47⋊C8#4114yescomplemented
273C2×C47⋊C8C2412yes—
274C2×C47⋊C8C2412yes—
275#10625324—28no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—42no—
280C23×C47—42no—
281C23×C47—42no—
282C23×C47AGL(1,ℤ/8)14yes—
283C23×C47C22×D412yes—
284C23×C47C22×D411yescharacteristic
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47C22×D412yes—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—48no—
296D4×C47—42no—
297C2×C4×C47—22no—
298C2×C4×C47—24no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—48no—
307C2×C4×C47—42no—
308C2×C4×C47C22×D412yes—
309C2×C4×C47C22×D411yescharacteristic
310C2×C4×C47C2×#4112yes—
311C2×C4×C472−1+412yes—
312C2×C4×C47C2511yescharacteristic
313C22⋊D47—28no—
314C22⋊D47—48no—
315C22⋊D47—84no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—84no—
326C2×Dic47—84no—
327C2×Dic47C22×D412yes—
328C2×Dic47C22×D412yes—
329C2×Dic47C22×D412yes—
330D188—22no—
331D188—22no—
332D188—48no—
333D188—42no—
334C4×D47—24no—
335C4×D47—22no—
336C4×D47—22no—
337C4×D47—48no—
338C4×D47—48no—
339Dic94—48no—
340C8×C47—22no—
341C8×C47—22no—
342C47⋊C8—22no—
343C47⋊C8C2×#4114yescomplemented
344C2×#3345—471nomaximal, Sylow
345C22×C47—28no—
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47—84no—
352C22×C47#54712yes—
353C22×C47C2×AGL(1,ℤ/8)14yes—
354C22×C47C2×AGL(1,ℤ/8)12yes—
355C22×C47#57712yes—
356C22×C47C23×D411yescharacteristic
357C2×D47—22no—
358C2×D47—22no—
359C2×D47—22no—
360C2×D47—44no—
361C2×D47—42no—
362C2×D47—42no—
363C2×D47—42no—
364C2×D47—84no—
365C4×C47—22no—
366C4×C47—42no—
367C4×C47—42no—
368C4×C47—42no—
369C4×C47#54712yes—
370C4×C47C22×#4111yescharacteristic
371C4×C47C2×2−1+411yescharacteristic
372Dic47—22no—
373Dic47—22no—
374Dic47—22no—
375Dic47—42no—
376Dic47—42no—
377Dic47—42no—
378C2×#553—471no—
379C2×#547—471no—
380#3345—4716no—
381C2×#501—471no—
382C2×#481—471no—
383C2×#481—471no—
384C2×#482—471no—
385C2×#480D4711yescharacteristic, complemented
386C2×#478—471no—
387C2×#476—471no—
388C2×#469—471no—
389C2×#466—471no—
390C2×#442—471no—
391C2×#435—471no—
392C2×#428—471no—
393C22×#106—471no—
394C2×C47—24no—
395C2×C47—82no—
396C2×C47#334514yescomplemented
397C2×C47C2×#54711yescharacteristic
398C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
399C2×C47C2×#57711yescharacteristic
400D47—42no—
401D47—82no—
402C22×#41—941no—
403C22×D8—471no—
404C22×M16—471no—
405C23×C8—471no—
406#553—478no—
407#553—944no—
408#547—478no—
409#547—944no—
410C2×C4⋊Q8—471no—
411C2×#126—941no—
412C2×#125—471no—
413C2×#123—941no—
414C2×#123—941no—
415C2×#123—941no—
416C2×C22⋊Q8—941no—
417C2×#121—471no—
418C2×#121—471no—
419C2×#121—471no—
420C2×#121—941no—
421C2×#121C2×D4711yescharacteristic
422C2×C4×D4—471no—
423C2×C4×D4—471no—
424C2×C4×D4—471no—
425C2×C4×D4—941no—
426C2×#117—471no—
427C22×C4⋊C4—471no—
428C22×C4⋊C4—471no—
429C22×C4⋊C4C2×D4711yescharacteristic
430#501—478no—
431#482—478no—
432#481—478no—
433#481—478no—
434#480C2×D4718yescomplemented
435#478—478no—
436#476—478no—
437#469—478no—
438#466—478no—
439#442—478no—
440#435—478no—
441#428—478no—
442C2×#107—471no—
443C2×#107C2×D4711yescharacteristic
444C2×#107C2×D4711yescharacteristic
445C2×#106—471no—
446C2×#106—471no—
447C2×#106—471no—
448C2×#106—471no—
449C2×#106—478no—
450C2×#106—471no—
451C2×#106—471no—
452C2×C4⋊C8—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#102—471no—
456C2×#102—471no—
457C2×#102C2×D4711yescharacteristic
458C2×#102C2×D4711yescharacteristic
459C2×C22⋊C8—471no—
460C2×C22⋊C8C2×D4711yescharacteristic
461C2×#97—471no—
462C47C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—948no—
464C2×#41—1888no—
465C22×Q8—941no—
466C22×D4—21no—
467C22×D4—471no—
468C22×D4—471no—
469C22×D4—941no—
470C22×D4—941no—
471C22×D4—941no—
472C22×D4C22×D4711yescharacteristic
473C23×C4—21no—
474C23×C4—471no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4—941no—
478C23×C4—941no—
479C23×C4C22×D4711yescharacteristic
480C2×D8—474no—
481C2×D8—944no—
482C2×M16—474no—
483C2×M16—944no—
484C22×C8—471no—
485C22×C8—471no—
486C22×C8—474no—
487C22×C8—944no—
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490C4⋊Q8—474no—
491C4⋊Q8—942no—
492#126—948no—
493#125—474no—
494#125—942no—
495#123—948no—
496#123—948no—
497#123—948no—
498C22⋊Q8—948no—
499#121—22no—
500#121—474no—
501#121—474no—
502#121—474no—
503#121—942no—
504#121—942no—
505#121—948no—
506#121—942no—
507#121C22×D4714yes—
508C4×D4—474no—
509C4×D4—474no—
510C4×D4—474no—
511C4×D4—474no—
512C4×D4—942no—
513C4×D4—942no—
514C4×D4—948no—
515#117—474no—
516#117—942no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—942no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4—942no—
532C2×C4⋊C4C22×D4711yescharacteristic
533C2×C4⋊C4C22×D4711yescharacteristic
534C2×C4⋊C4C22×D4714yes—
535C2×C4⋊C4C22×D4711yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—471no—
538C2×C22⋊C4—471no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C22⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C22⋊C4—941no—
544C2×C22⋊C4—941no—
545C2×C42—471no—
546C2×C42—941no—
547#107—474no—
548#107C22×D4714yes—
549#107C22×D4714yes—
550#106—474no—
551#106—474no—
552#106—474no—
553#106—474no—
554#106—474no—
555#106—474no—
556C4⋊C8—474no—
557#102—474no—
558#102—474no—
559#102—474no—
560#102—474no—
561#102C22×D4714yes—
562#102C22×D4714yes—
563C22⋊C8—474no—
564C22⋊C8C22×D4714yes—
565#97—474no—
566C24—21no—
567C24—471no—
568C24—941no—
569C24D4×D4711yescharacteristic
570#41—18832no—
571C2×Q8—944no—
572C2×Q8—1884no—
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—44no—
578C2×D4—474no—
579C2×D4—472no—
580C2×D4—944no—
581C2×D4—944no—
582C2×D4—944no—
583C2×D4—944no—
584C2×D4—941no—
585C2×D4—942no—
586C2×D4—942no—
587C2×D4—3762no—
588C2×D4—1884no—
589C2×D4—1884no—
590C2×D4C23×D4712yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—44no—
598C22×C4—471no—
599C22×C4—471no—
600C22×C4—471no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—944no—
604C22×C4—944no—
605C22×C4—944no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—944no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—3762no—
613C22×C4—3762no—
614C22×C4—1884no—
615C22×C4—1884no—
616C22×C4D4×D4712yes—
617C22×C4D4×D4711yescharacteristic
618C22×C4C23×D4712yes—
619C22×C4C23×D4711yescharacteristic
620D8—948no—
621M16—948no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—474no—
625C2×C8—472no—
626C2×C8—472no—
627C2×C8—948no—
628C2×C8—942no—
629C2×C8C23×D4712yes—
630C2×C8C23×D4712yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—474no—
636C4⋊C4—472no—
637C4⋊C4—472no—
638C4⋊C4—472no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—944no—
643C4⋊C4—941no—
644C4⋊C4—941no—
645C4⋊C4—941no—
646C4⋊C4—944no—
647C4⋊C4C23×D4712yes—
648C4⋊C4C23×D4712yes—
649C4⋊C4C23×D4712yes—
650C22⋊C4—24no—
651C22⋊C4—474no—
652C22⋊C4—474no—
653C22⋊C4—944no—
654C22⋊C4—944no—
655C22⋊C4—944no—
656C22⋊C4—944no—
657C22⋊C4—944no—
658C22⋊C4—944no—
659C42—472no—
660C42—472no—
661C42—944no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—472no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—942no—
673C23—1882no—
674C23—1882no—
675C23—1882no—
676C23#1309404814yes—
677C23C2×D4×D4712yes—
678C23C2×D4×D4711yescharacteristic
679Q8—1888no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—42no—
684D4—948no—
685D4—942no—
686D4—942no—
687D4—3764no—
688D4—1888no—
689D4—1888no—
690D4—1882no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—48no—
701C2×C4—42no—
702C2×C4—472no—
703C2×C4—472no—
704C2×C4—472no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—944no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—3764no—
715C2×C4—3764no—
716C2×C4—1888no—
717C2×C4—1888no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4—1882no—
721C2×C4C2×D4×D4712yes—
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4#41×D4712yes—
724C2×C4#1309407112yes—
725C2×C4C24×D4711yescharacteristic
726C8—22no—
727C8—22no—
728C8—474no—
729C8—942no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22—942no—
738C22—942no—
739C22—942no—
740C22—3764no—
741C22—1882no—
742C22—1882no—
743C22—1882no—
744C22—1884no—
745C22#1568977112yes—
746C22C2×#1309404814yes—
747C22C2×#1309404812yes—
748C22#1568993212yes—
749C22C22×D4×D4711yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—942no—
755C4—942no—
756C4—942no—
757C4—1882no—
758C4—1882no—
759C4—1882no—
760C4#1568977112yes—
761C4C2×#41×D4711yescharacteristic
762C4C2×#1309407111yescharacteristic
763C2—24no—
764C2—82no—
765C2—3762no—
766C2—1882no—
767C2#2025586214yesdirect product factor
768C2C2×#1568977111yescharacteristic
769C2C22×#1309404811yescharacteristic
770C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#480C2
socleC23×C47C22×D4
hypercenterC2×#480D47
hypocenterC47C2×#3345
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#15689825C2semidirect
2. C2×#15689774C2semidirect
3. #20255862C2direct (N × H)
4. C2×#15689531C2semidirect
5. C2×#15689442C2semidirect
6. C2×#15689440C2semidirect
7. C2×#15689450C2semidirect
8. C2×#15689426C2semidirect
9. C2×#15689411C2semidirect
10. C2×#15689375C2semidirect
11. C2×#15689357C2semidirect
12. C2×#15689232C2semidirect
13. C2×#15689191C2semidirect
14. C2×#15689164C2semidirect
15. C22×#13093955C2semidirect
16. C2×C47×#480C2semidirect
22. #15689825C22semidirect
24. #15689774C22semidirect
43. #15689531C22semidirect
44. #15689450C22semidirect
45. #15689442C22semidirect
46. #15689440C22semidirect
47. #15689426C22semidirect
48. #15689411C22semidirect
49. #15689375C22semidirect
50. #15689357C22semidirect
51. #15689232C22semidirect
52. #15689191C22semidirect
53. #15689164C22semidirect
61. C2×#13093955C22semidirect
71. C47×#480C22semidirect
272. C2×C47⋊C8#41semidirect
343. C47⋊C8C2×#41semidirect
385. C2×#480D47semidirect
396. C2×C47#3345semidirect
434. #480C2×D47semidirect
462. C47C2×#3345semidirect
767. C2#20255862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898252
C2×#156897742
#202558622
C2×#156895312
C2×#156894422
C2×#156894402
C2×#156894502
C2×#156894262
C2×#156894112
C2×#156893752
C2×#156893572
C2×#156892322
C2×#156891912
C2×#156891642
C22×#130939552
C2×C47×#4802
C2×#334547