Finite Group Databasebeta

← C2×#20256147 #27096033

Subgroups — C2×#20256147 #27096033

Order 12032.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689855C211yesmaximal, characteristic, complemented
2C2×#15689829C211yesmaximal, characteristic, complemented
3#20256147C2116yesmaximal, direct product factor
4C2×#15689486C211yesmaximal, characteristic, complemented
5C2×#15689484C211yesmaximal, characteristic, complemented
6C2×#15689432C211yesmaximal, characteristic, complemented
7C2×#15689420C211yesmaximal, characteristic, complemented
8C2×#15689401C211yesmaximal, characteristic, complemented
9C2×#15689341C211yesmaximal, characteristic, complemented
10C2×#15689335C211yesmaximal, characteristic, complemented
11C2×#15689317C211yesmaximal, characteristic
12C2×#15689253C211yesmaximal, characteristic, complemented
13C2×#15689232C211yesmaximal, characteristic, complemented
14C2×#15689226C211yesmaximal, characteristic, complemented
15C2×C4×D376C211yesmaximal, characteristic, complemented
16C2×C47×#488C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic
18C22×D376C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20#15689855—24no—
21#15689855C2218yescomplemented
22#15689829—24no—
23#15689829C2218yescomplemented
24C2×#13094023C2211yescharacteristic
25C2×#13094020C2211yescharacteristic
26C2×#13094015C2211yescharacteristic
27C2×#13094013C2211yescharacteristic
28C2×#13094010—21no—
29C2×#13094008—21no—
30C2×#13094006—21no—
31C2×#13094004—21no—
32C2×#13094002—21no—
33C2×#13094002—21no—
34C2×Q8×Dic47C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38C2×D4×Dic47C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×(C22⋊D47)⋊C4—21no—
42C2×C4⋊C4×D47—21no—
43#15689486C2218yescomplemented
44#15689484C2218yescomplemented
45#15689432C2218yescomplemented
46#15689420C2218yescomplemented
47#15689401C2218yescomplemented
48#15689341C2218yescomplemented
49#15689335C2218yescomplemented
50#15689317C2218yes—
51#15689253C2218yescomplemented
52#15689232C2218yescomplemented
53#15689226C2218yescomplemented
54C4×D376C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×#124×C47C2211yescharacteristic
71C47×#488C2218yescomplemented
72C2×#103×C47C2211yescharacteristic
73C2×#103×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94D411yescharacteristic
79C22×D188C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C23×Dic47—21no—
84C22×C4×D47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C2×#10625336—24no—
89C2×#10625336C2314yes—
90C2×D376—24no—
91C2×D376C2314yes—
92C2×#10625334—24no—
93C2×#10625334C2314yes—
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2311yescharacteristic
96#13094023—22no—
97#13094023C2314yes—
98#13094020—22no—
99#13094020C2314yes—
100#13094015—22no—
101#13094015C2314yes—
102#13094013—22no—
103#13094013C2314yes—
104#13094010—28no—
105#13094008—28no—
106#13094006—28no—
107#13094004—28no—
108#13094002—28no—
109#13094002—28no—
110Q8×Dic47—22no—
111Q8×Dic47C2314yes—
112C4×Dic94D414yes—
113C4×Dic94C2314yes—
114C4×D188—22no—
115C4×D188—22no—
116C4×D188C2314yes—
117C4×D188C2314yes—
118D4×Dic47—22no—
119D4×Dic47C2314yes—
120#13093986—22no—
121#13093986—22no—
122#13093986C2314yes—
123#13093986C2314yes—
124(C22⋊D47)⋊C4—28no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47D411yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4D411yescharacteristic
133C2×Dic47⋊C4D411yescharacteristic
134C4⋊C4×D47—28no—
135C2×C22⋊Dic47—21no—
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×C4×Dic47—21no—
143C2×C4×Dic47C2311yescharacteristic
144C2×C4×Dic47C2311yescharacteristic
145#13093958C2314yes—
146#13093957C2314yes—
147#13093955C2314yes—
148C4⋊(C47⋊C8)C2314yes—
149Dic47⋊C8C2314yes—
150Dic47⋊C8C2314yes—
151#13093948C2314yes—
152#13093946C2314yes—
153#13093946C2314yes—
154#13093945C2314yes—
155#13093944C2314yes—
156#13093944C2314yes—
157#13093934C2314yes—
158#13093934C2314yes—
159C22×Q8×C47C2311yescharacteristic
160C22×D4×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163#125×C47—22no—
164#125×C47C2314yes—
165#124×C47—22no—
166#124×C47C2314yes—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C22⋊C4×C47—21no—
172C2×C22⋊C4×C47—21no—
173C2×C42×C47C2311yescharacteristic
174#103×C47C2314yes—
175#103×C47C2314yes—
176#102×C47C2314yes—
177#102×C47C2314yes—
178C4×C8×C47C2314yes—
179C24×C47—21no—
180C23×D47—21no—
181C23×D47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47C2412yes—
186C2×D4×C47—21no—
187C2×D4×C47—22no—
188C2×D4×C47—22no—
189C2×D4×C47C2412yes—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—24no—
197C2×C22⋊D47—24no—
198C2×C22⋊D47—44no—
199C2×C22⋊D47—82no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—24no—
203C22×Dic47—82no—
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
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—82no—
222C2×C4×D47—82no—
223C2×C4×D47—82no—
224C2×Dic94—24no—
225C2×Dic94—42no—
226C2×Dic94—82no—
227C2×Dic94C2×D414yes—
228C2×C8×C47—22no—
229C2×C8×C47—22no—
230C2×C8×C47C2412yes—
231C2×C8×C47C2412yes—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C42×C47C2×D412yes—
241C42×C47C2412yes—
242C22⋊Dic47—24no—
243#10625336—28no—
244#10625334—28no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—24no—
254C4⋊Dic47—24no—
255C4⋊Dic47C2×D414yes—
256C4⋊Dic47C2412yes—
257C4⋊Dic47C2412yes—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4C2×D414yes—
261Dic47⋊C4C2×D414yes—
262C4×Dic47—24no—
263C4×Dic47C2×D412yes—
264C4×Dic47C2×D412yes—
265C4×Dic47C2412yes—
266C4×Dic47C2412yes—
267C2×C47⋊C8—22no—
268C2×C47⋊C8—22no—
269C2×C47⋊C8C2412yes—
270C2×C47⋊C8C2412yes—
271D376—28no—
272C23×C47—22no—
273C23×C47—42no—
274C23×C47—42no—
275C23×C47—42no—
276C23×C47C22×D411yescharacteristic
277C22×D47—24no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—42no—
281C22×D47—42no—
282C22×D47—42no—
283C22×D47—42no—
284C22×D47—42no—
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—42no—
288D4×C47—22no—
289D4×C47—22no—
290D4×C47—42no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47C22×D412yes—
300C2×C4×C47C22×D412yes—
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C47C2×#4112yes—
303C2×C4×C472−1+412yes—
304C2×C4×C47C2511yescharacteristic
305C22⋊D47—48no—
306C22⋊D47—84no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—84no—
316C2×Dic47C22×D412yes—
317C2×Dic47C22×D412yes—
318C2×Dic47C22×D412yes—
319C2×Dic47C22×D412yes—
320D188—24no—
321D188—22no—
322D188—22no—
323D188—22no—
324D188—42no—
325D188C2×#4114yes—
326C4×D47—48no—
327C4×D47—84no—
328C4×D47—84no—
329C4×D47—84no—
330Dic94—44no—
331Dic94—84no—
332C8×C47—22no—
333C8×C47—22no—
334C47⋊C8—22no—
335C47⋊C8—22no—
336C2×#3370—471nomaximal, Sylow
337C22×C47—42no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—84no—
341C22×C47#54812yes—
342C22×C47#57512yes—
343C22×C47#57612yes—
344C22×C47C23×D411yescharacteristic
345C2×D47—24no—
346C2×D47—48no—
347C2×D47—42no—
348C2×D47—42no—
349C2×D47—42no—
350C2×D47—42no—
351C2×D47—42no—
352C2×D47—84no—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47—42no—
358C4×C47#54812yes—
359C4×C47C22×#4111yescharacteristic
360C4×C47C2×2−1+411yescharacteristic
361Dic47—22no—
362Dic47—22no—
363Dic47—22no—
364Dic47—22no—
365Dic47—42no—
366Dic47—42no—
367C2×#559—471no—
368C2×#554—471no—
369#3370—4716no—
370C2×#490—471no—
371C2×#489—471no—
372C2×#488D4711yescharacteristic, complemented
373C2×#479—471no—
374C2×#478—471no—
375C2×#474—471no—
376C2×#463—471no—
377C2×#463—471no—
378C2×#459—471no—
379C2×#446—471no—
380C2×#442—471no—
381C2×#440—471no—
382C2×C4×D8—471no—
383C2×C47—82no—
384C2×C47#337014yescomplemented
385C2×C47C2×#54811yescharacteristic
386C2×C47C2×#57511yescharacteristic
387C2×C47C2×#57611yescharacteristic
388D47—44no—
389D47—82no—
390C22×SD16—471no—
391C22×D8—471no—
392C22×D8—471no—
393#559—478no—
394#559—944no—
395#554—478no—
396#554—944no—
397C2×C4⋊Q8—471no—
398C2×#127—471no—
399C2×#125—471no—
400C2×#125C2×D4711yescharacteristic
401C2×#124—471no—
402C2×#124—941no—
403C2×#124C2×D4711yescharacteristic
404C2×#123—941no—
405C2×#123—941no—
406C2×C22⋊Q8—941no—
407C2×C22⋊Q8—941no—
408C2×C22⋊Q8—941no—
409C2×C4×Q8—471no—
410C2×C4×Q8—471no—
411C2×C4×D4—471no—
412C2×C4×D4—471no—
413C2×C4×D4—471no—
414C2×C4×D4—471no—
415C2×C4×D4—471no—
416C2×C4×D4—941no—
417C22×C4⋊C4—941no—
418#490—478no—
419#489—478no—
420#488C2×D4718yescomplemented
421#479—478no—
422#478—478no—
423#474—478no—
424#463—478no—
425#463—478no—
426#459—478no—
427#446—478no—
428#442—478no—
429#440—478no—
430C4×D8—478no—
431C2×#107—471no—
432C2×#107—471no—
433C2×#106—471no—
434C2×C4⋊C8—471no—
435C2×C4⋊C8—471no—
436C2×C4⋊C8—471no—
437C2×#103—471no—
438C2×#103C2×D4711yescharacteristic
439C2×#103C2×D4711yescharacteristic
440C2×#102—471no—
441C2×#102—471no—
442C2×#102—471no—
443C2×#102—471no—
444C2×#102—471no—
445C2×#102C2×D4711yescharacteristic
446C2×#102C2×D4711yescharacteristic
447C2×#97—471no—
448C2×#97—471no—
449C2×C4×C8C2×D4711yescharacteristic
450C47C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—471no—
452C22×Q8—941no—
453C22×Q8C22×D4711yescharacteristic
454C22×D4—471no—
455C22×D4—471no—
456C22×D4—941no—
457C22×D4—941no—
458C22×D4C22×D4711yescharacteristic
459C23×C4—941no—
460C23×C4—941no—
461C23×C4—941no—
462C23×C4—941no—
463C23×C4—941no—
464C2×SD16—474no—
465C2×SD16—944no—
466C2×D8—474no—
467C2×D8—474no—
468C2×D8—944no—
469C2×D8—944no—
470C22×C8—471no—
471C22×C8—471no—
472C22×C8C22×D4711yescharacteristic
473C22×C8C22×D4711yescharacteristic
474C4⋊Q8—474no—
475C4⋊Q8—942no—
476#127—474no—
477#127—942no—
478#125—22no—
479#125—474no—
480#125—942no—
481#125C22×D4714yes—
482#124—22no—
483#124—474no—
484#124—942no—
485#124—948no—
486#124C22×D4714yes—
487#123—948no—
488#123—948no—
489C22⋊Q8—948no—
490C22⋊Q8—948no—
491C22⋊Q8—948no—
492C4×Q8—474no—
493C4×Q8—474no—
494C4×Q8—474no—
495C4×Q8—942no—
496C4×D4—474no—
497C4×D4—474no—
498C4×D4—474no—
499C4×D4—474no—
500C4×D4—474no—
501C4×D4—942no—
502C4×D4—942no—
503C4×D4—942no—
504C4×D4—948no—
505C4×D4—942no—
506C4×D4—942no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4—948no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4C22×D4711yescharacteristic
520C2×C4⋊C4C22×D4711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C42—471no—
531C2×C42—471no—
532C2×C42—941no—
533C2×C42C22×D4711yescharacteristic
534#107—474no—
535#107—474no—
536#106—474no—
537C4⋊C8—474no—
538C4⋊C8—474no—
539C4⋊C8—474no—
540#103—474no—
541#103C22×D4714yes—
542#103C22×D4714yes—
543#102—474no—
544#102—474no—
545#102—474no—
546#102—474no—
547#102—474no—
548#102C22×D4714yes—
549#102C22×D4714yes—
550#97—474no—
551#97—474no—
552C4×C8C22×D4714yes—
553C24—21no—
554C24—941no—
555C24—941no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—474no—
560C2×Q8—944no—
561C2×Q8—3762no—
562C2×Q8—1882no—
563C2×Q8C23×D4712yes—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—474no—
568C2×D4—472no—
569C2×D4—472no—
570C2×D4—944no—
571C2×D4—944no—
572C2×D4—941no—
573C2×D4—941no—
574C2×D4—942no—
575C2×D4—942no—
576C2×D4—942no—
577C2×D4—3762no—
578C2×D4—1884no—
579C2×D4C23×D4712yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—471no—
584C22×C4—471no—
585C22×C4—471no—
586C22×C4—471no—
587C22×C4—944no—
588C22×C4—944no—
589C22×C4—944no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—944no—
593C22×C4—944no—
594C22×C4—3762no—
595C22×C4—3762no—
596C22×C4—3762no—
597C22×C4—3762no—
598C22×C4—1884no—
599C22×C4D4×D4711yescharacteristic
600C22×C4D4×D4711yescharacteristic
601C22×C4C23×D4711yescharacteristic
602SD16—948no—
603D8—948no—
604D8—948no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—472no—
608C2×C8—472no—
609C2×C8—942no—
610C2×C8—942no—
611C2×C8C23×D4712yes—
612C2×C8C23×D4712yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—474no—
618C4⋊C4—474no—
619C4⋊C4—474no—
620C4⋊C4—472no—
621C4⋊C4—472no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—941no—
627C4⋊C4—941no—
628C4⋊C4C23×D4712yes—
629C4⋊C4C23×D4712yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—944no—
633C22⋊C4—944no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C42—472no—
640C42—472no—
641C42—472no—
642C42—472no—
643C42—944no—
644C42D4×D4712yes—
645C42C23×D4712yes—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—944no—
651C23—942no—
652C23—942no—
653C23—1882no—
654C23—1882no—
655C23—1882no—
656C23—1882no—
657C23—1882no—
658C23C2×D4×D4711yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—3764no—
663Q8—1884no—
664D4—22no—
665D4—22no—
666D4—42no—
667D4—474no—
668D4—944no—
669D4—942no—
670D4—942no—
671D4—942no—
672D4—3764no—
673D4—1888no—
674D4—1882no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—472no—
684C2×C4—472no—
685C2×C4—472no—
686C2×C4—472no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—3764no—
694C2×C4—3764no—
695C2×C4—3764no—
696C2×C4—3764no—
697C2×C4—1888no—
698C2×C4—1882no—
699C2×C4—1882no—
700C2×C4C2×D4×D4712yes—
701C2×C4C2×D4×D4712yes—
702C2×C4C2×D4×D4711yescharacteristic
703C2×C4#41×D4712yes—
704C2×C4#1309407112yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—942no—
709C8—942no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—944no—
715C22—3764no—
716C22—1882no—
717C22—1882no—
718C22—1882no—
719C22—1882no—
720C22—1882no—
721C22—1888no—
722C22#1568978112yes—
723C22#1568992012yes—
724C22#1568992512yes—
725C22C22×D4×D4711yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—942no—
732C4—942no—
733C4—942no—
734C4—942no—
735C4—1882no—
736C4—1882no—
737C4#1568978112yes—
738C4C2×#41×D4711yescharacteristic
739C4C2×#1309407111yescharacteristic
740C2—82no—
741C2—3762no—
742C2—1884no—
743C2#2025614714yesdirect product factor
744C2C2×#1568978111yescharacteristic
745C2C2×#1568992011yescharacteristic
746C2C2×#1568992511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#488C2
socleC23×C47C22×D4
prime radicalC2×#15689317C2
hypercenterC2×#488D47
hypocenterC47C2×#3370
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#15689855C2semidirect
2. C2×#15689829C2semidirect
3. #20256147C2direct (N × H)
4. C2×#15689486C2semidirect
5. C2×#15689484C2semidirect
6. C2×#15689432C2semidirect
7. C2×#15689420C2semidirect
8. C2×#15689401C2semidirect
9. C2×#15689341C2semidirect
10. C2×#15689335C2semidirect
12. C2×#15689253C2semidirect
13. C2×#15689232C2semidirect
14. C2×#15689226C2semidirect
15. C2×C4×D376C2semidirect
16. C2×C47×#488C2semidirect
21. #15689855C22semidirect
23. #15689829C22semidirect
43. #15689486C22semidirect
44. #15689484C22semidirect
45. #15689432C22semidirect
46. #15689420C22semidirect
47. #15689401C22semidirect
48. #15689341C22semidirect
49. #15689335C22semidirect
51. #15689253C22semidirect
52. #15689232C22semidirect
53. #15689226C22semidirect
54. C4×D376C22semidirect
71. C47×#488C22semidirect
372. C2×#488D47semidirect
384. C2×C47#3370semidirect
420. #488C2×D47semidirect
450. C47C2×#3370semidirect
743. C2#20256147direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898552
C2×#156898292
#202561472
C2×#156894862
C2×#156894842
C2×#156894322
C2×#156894202
C2×#156894012
C2×#156893412
C2×#156893352
C2×#156893172
C2×#156892532
C2×#156892322
C2×#156892262
C2×C4×D3762
C2×C47×#4882
C2×#337047