Finite Group Databasebeta

← C2×#20255891 #27094876

Subgroups — C2×#20255891 #27094876

Order 12032.

1962 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×#15689837C211yesmaximal, characteristic, complemented
2C2×#15689821C211yesmaximal, characteristic, complemented
3#20255891C2116yesmaximal, direct product factor
4C2×#15689531C211yesmaximal, characteristic, complemented
5C2×#15689450C211yesmaximal, characteristic, complemented
6C2×#15689448C211yesmaximal, characteristic, complemented
7C2×#15689446C211yesmaximal, characteristic, complemented
8C2×#15689421C211yesmaximal, characteristic, complemented
9C2×#15689402C211yesmaximal, characteristic, complemented
10C2×#15689374C211yesmaximal, characteristic, complemented
11C2×#15689358C211yesmaximal, characteristic, complemented
12C2×#15689232C211yesmaximal, characteristic, complemented
13C2×#15689197C211yesmaximal, characteristic, complemented
14C2×#15689163C211yesmaximal, characteristic, complemented
15C2×#15689160C211yesmaximal, characteristic, complemented
16C2×C47×#480C211yesmaximal, characteristic, complemented
17C22×#10625334C2211yescharacteristic
18C22×#10625329C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20#15689837—24no—
21#15689837C2218yescomplemented
22#15689821—24no—
23#15689821C2218yescomplemented
24C2×#13094023C2211yescharacteristic
25C2×#13094019—21no—
26C2×#13094015C2211yescharacteristic
27C2×#13094011—21no—
28C2×#13094010—21no—
29C2×#13094009—21no—
30C2×#13093999C2211yescharacteristic
31C2×#13093998—21no—
32C2×#13093998C2211yescharacteristic
33C2×#13093996—21no—
34C2×#13093995C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×#13093986C2211yescharacteristic
37C2×C4×C22⋊D47—21no—
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×#13093983C2211yescharacteristic
40C2×#13093982C2211yescharacteristic
41C2×#13093982C2211yescharacteristic
42C2×#13093980—21no—
43#15689531C2218yescomplemented
44#15689450C2218yescomplemented
45#15689448C2218yescomplemented
46#15689446C2218yescomplemented
47#15689421C2218yescomplemented
48#15689402C2218yescomplemented
49#15689374C2218yescomplemented
50#15689358C2218yescomplemented
51#15689232C2218yescomplemented
52#15689197C2218yescomplemented
53#15689163C2218yescomplemented
54#15689160C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×#13093955C2211yescharacteristic
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
77C22×Dic94—21no—
78C22×D188—21no—
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C22×C22⋊D47D411yescharacteristic
83C23×Dic47—21no—
84C22×C4×D47—21no—
85C22×C4×D47C2311yescharacteristic
86C2×#10625334—24no—
87C2×#10625334C2314yes—
88C2×#10625329—24no—
89C2×#10625329C2314yes—
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92C2×C8×D47—24no—
93C2×C8×D47C2314yes—
94#13094023—22no—
95#13094023C2314yes—
96#13094019—28no—
97#13094015—22no—
98#13094015C2314yes—
99#13094011—28no—
100#13094010—28no—
101#13094009—28no—
102#13093999—22no—
103#13093999C2314yes—
104#13093998—22no—
105#13093998—28no—
106#13093998C2314yes—
107#13093996—28no—
108#13093995—22no—
109#13093995C2314yes—
110D4×Dic47—22no—
111D4×Dic47C2314yes—
112#13093986—22no—
113#13093986C2314yes—
114C4×C22⋊D47—28no—
115C4×C22⋊D47D414yes—
116C4×C22⋊D47C2314yes—
117#13093983—22no—
118#13093983C2314yes—
119#13093982—22no—
120#13093982—22no—
121#13093982C2314yes—
122#13093982C2314yes—
123#13093980—28no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4D411yescharacteristic
131C2×C22⋊Dic47—21no—
132C2×C22⋊Dic47—21no—
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47D411yescharacteristic
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4D411yescharacteristic
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093958C2314yes—
146#13093957C2314yes—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150#13093955C2314yes—
151#13093955C2314yes—
152Dic47⋊C8C2314yes—
153#13093946C2314yes—
154#13093946C2314yes—
155#13093945C2314yes—
156#13093944C2314yes—
157(C2×D47)⋊C8C2314yes—
158#13093934C2314yes—
159C22×D4×C47—21no—
160C22×D4×C47C2311yescharacteristic
161C23×C4×C47—21no—
162C23×C4×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165#121×C47—22no—
166#121×C47C2314yes—
167C2×C4⋊C4×C47—22no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47C2314yes—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47—21no—
174#107×C47C2314yes—
175#107×C47C2314yes—
176#102×C47C2314yes—
177#102×C47C2314yes—
178C22⋊C8×C47C2314yes—
179C24×C47—21no—
180C24×C47C2×D411yescharacteristic
181C23×D47—21no—
182C23×D47C2×D411yescharacteristic
183C2×D4×C47—24no—
184C2×D4×C47—21no—
185C2×D4×C47—22no—
186C2×D4×C47—22no—
187C2×D4×C47—82no—
188C2×D4×C47C2412yes—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—24no—
195C22×C4×C47—82no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2411yescharacteristic
200C2×C22⋊D47—24no—
201C2×C22⋊D47—24no—
202C2×C22⋊D47—42no—
203C2×C22⋊D47—44no—
204C2×C22⋊D47—82no—
205C2×C22⋊D47C2×D414yes—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—24no—
210C22×Dic47—44no—
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—21no—
217C2×D188—24no—
218C2×D188—82no—
219C2×D188C2412yes—
220C2×C4×D47—22no—
221C2×C4×D47—22no—
222C2×C4×D47—24no—
223C2×C4×D47—82no—
224C2×C4×D47C2×D412yes—
225C2×C4×D47C2412yes—
226C2×Dic94—24no—
227C2×Dic94—82no—
228C2×C8×C47—22no—
229C2×C8×C47—22no—
230C2×C8×C47C2412yes—
231C2×C8×C47C2412yes—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—24no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C22⋊C4×C47—24no—
240C22⋊Dic47—24no—
241C22⋊Dic47—24no—
242C22⋊Dic47—24no—
243C22⋊Dic47C2×D414yes—
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)⋊C4C2×D414yes—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47—24no—
255C4⋊Dic47C2412yes—
256C4⋊Dic47C2412yes—
257C4⋊Dic47C2412yes—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4C2×D414yes—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47C2×D412yes—
265C4×Dic47C2412yes—
266#10625329—28no—
267C2×C47⋊C8—22no—
268C2×C47⋊C8#4114yes—
269C2×C47⋊C8C2412yes—
270C2×C47⋊C8C2412yes—
271C8×D47—28no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—42no—
277C23×C47—42no—
278C23×C47—42no—
279C23×C47C22×D412yes—
280C23×C47C22×D411yescharacteristic
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—42no—
286C22×D47—42no—
287C22×D47—42no—
288C22×D47C22×D412yes—
289D4×C47—22no—
290D4×C47—22no—
291D4×C47—42no—
292D4×C47—84no—
293C2×C4×C47—22no—
294C2×C4×C47—24no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47—84no—
304C2×C4×C47C22×D412yes—
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C2×#4112yes—
307C2×C4×C472−1+412yes—
308C2×C4×C47C2511yescharacteristic
309C22⋊D47—44no—
310C22⋊D47—48no—
311C22⋊D47—84no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—48no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325D188—22no—
326D188—22no—
327D188—42no—
328D188—84no—
329C4×D47—24no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—84no—
333Dic94—84no—
334C8×C47—22no—
335C8×C47—22no—
336C47⋊C8—22no—
337C47⋊C8C2×#4114yes—
338C2×#3347—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—44no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—84no—
347C22×C47#54712yes—
348C22×C47#57512yes—
349C22×C47#57612yes—
350C22×C47C23×D411yescharacteristic
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—22no—
354C2×D47—44no—
355C2×D47—42no—
356C2×D47—42no—
357C2×D47—42no—
358C2×D47—84no—
359C4×C47—22no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47—42no—
363C4×C47#54712yes—
364C4×C47C22×#4111yescharacteristic
365C4×C47C2×2−1+411yescharacteristic
366Dic47—22no—
367Dic47—22no—
368Dic47—22no—
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#555—471no—
373C2×#553—471no—
374#3347—4716no—
375C2×#501—471no—
376C2×#482—471no—
377C2×#482—471no—
378C2×#482—471no—
379C2×#480D4711yescharacteristic, complemented
380C2×#478—471no—
381C2×#474—471no—
382C2×#469—471no—
383C2×#466—471no—
384C2×#442—471no—
385C2×#435—471no—
386C2×#428—471no—
387C2×#427—471no—
388C2×C47—42no—
389C2×C47—82no—
390C2×C47#334714yescomplemented
391C2×C47C2×#54711yescharacteristic
392C2×C47C2×#57511yescharacteristic
393C2×C47C2×#57611yescharacteristic
394D47—42no—
395D47—82no—
396C22×D8—471no—
397C22×M16—471no—
398C23×C8—471no—
399#555—478no—
400#555—944no—
401#553—478no—
402#553—944no—
403C2×C4⋊Q8—471no—
404C2×#126—941no—
405C2×#125—471no—
406C2×#124—941no—
407C2×#124—941no—
408C2×#123—941no—
409C2×#121—471no—
410C2×#121—471no—
411C2×#121—471no—
412C2×#121—941no—
413C2×#121—941no—
414C2×#121C2×D4711yescharacteristic
415C2×C4×D4—471no—
416C2×C4×D4—471no—
417C2×C4×D4—471no—
418C2×C4×D4—941no—
419C2×#117—471no—
420C2×#117—471no—
421C2×#117—471no—
422C2×#117—941no—
423C22×C4⋊C4C2×D4711yescharacteristic
424#501—478no—
425#482—478no—
426#482—478no—
427#482—478no—
428#480C2×D4718yescomplemented
429#478—478no—
430#474—478no—
431#469—478no—
432#466—478no—
433#442—478no—
434#435—478no—
435#428—478no—
436#427—478no—
437C2×#107—471no—
438C2×#107—471no—
439C2×#107—471no—
440C2×#107C2×D4711yescharacteristic
441C2×#107C2×D4711yescharacteristic
442C2×#106—471no—
443C2×#106—471no—
444C2×#106—471no—
445C2×#106—471no—
446C2×C4⋊C8—471no—
447C2×#102—471no—
448C2×#102—471no—
449C2×#102—471no—
450C2×#102—471no—
451C2×#102C2×D4711yescharacteristic
452C2×#102C2×D4711yescharacteristic
453C2×C22⋊C8—471no—
454C2×C22⋊C8C2×D4711yescharacteristic
455C2×#97—471no—
456C47C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—941no—
458C22×D4—21no—
459C22×D4—471no—
460C22×D4—471no—
461C22×D4—941no—
462C22×D4—941no—
463C22×D4—941no—
464C22×D4C22×D4711yescharacteristic
465C23×C4—21no—
466C23×C4—471no—
467C23×C4—941no—
468C23×C4—941no—
469C23×C4C22×D4711yescharacteristic
470C2×D8—474no—
471C2×D8—944no—
472C2×M16—474no—
473C2×M16—944no—
474C22×C8—471no—
475C22×C8—471no—
476C22×C8—474no—
477C22×C8—944no—
478C22×C8C22×D4711yescharacteristic
479C22×C8C22×D4711yescharacteristic
480C4⋊Q8—474no—
481C4⋊Q8—942no—
482#126—948no—
483#125—474no—
484#125—942no—
485#124—948no—
486#124—948no—
487#123—948no—
488#121—22no—
489#121—474no—
490#121—474no—
491#121—474no—
492#121—942no—
493#121—948no—
494#121—942no—
495#121—948no—
496#121—942no—
497#121C22×D4714yes—
498C4×D4—474no—
499C4×D4—474no—
500C4×D4—474no—
501C4×D4—474no—
502C4×D4—942no—
503C4×D4—942no—
504C4×D4—948no—
505#117—474no—
506#117—474no—
507#117—474no—
508#117—948no—
509#117—942no—
510#117—942no—
511#117—942no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—471no—
517C2×C4⋊C4—471no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4C22×D4711yescharacteristic
522C2×C4⋊C4C22×D4711yescharacteristic
523C2×C4⋊C4C22×D4714yes—
524C2×C4⋊C4C22×D4711yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—471no—
527C2×C22⋊C4—471no—
528C2×C22⋊C4—941no—
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×C42—471no—
537C2×C42—941no—
538C2×C42—941no—
539C2×C42—941no—
540#107—474no—
541#107—474no—
542#107—474no—
543#107C22×D4714yes—
544#107C22×D4714yes—
545#106—474no—
546#106—474no—
547#106—474no—
548#106—474no—
549C4⋊C8—474no—
550#102—474no—
551#102—474no—
552#102—474no—
553#102—474no—
554#102C22×D4714yes—
555#102C22×D4714yes—
556C22⋊C8—474no—
557C22⋊C8C22×D4714yes—
558#97—474no—
559C24—21no—
560C24—471no—
561C24—941no—
562C24D4×D4711yescharacteristic
563C2×Q8—944no—
564C2×Q8—3762no—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—82no—
570C2×D4—474no—
571C2×D4—472no—
572C2×D4—944no—
573C2×D4—944no—
574C2×D4—944no—
575C2×D4—941no—
576C2×D4—942no—
577C2×D4—942no—
578C2×D4—3762no—
579C2×D4—3762no—
580C2×D4—1882no—
581C2×D4—1884no—
582C2×D4C23×D4712yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—82no—
590C22×C4—471no—
591C22×C4—471no—
592C22×C4—471no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—944no—
596C22×C4—944no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—3762no—
603C22×C4—1884no—
604C22×C4D4×D4712yes—
605C22×C4D4×D4711yescharacteristic
606C22×C4C23×D4712yes—
607C22×C4C23×D4711yescharacteristic
608D8—948no—
609M16—948no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—474no—
613C2×C8—472no—
614C2×C8—472no—
615C2×C8—948no—
616C2×C8—942no—
617C2×C8C23×D4712yes—
618C2×C8C23×D4712yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—474no—
624C4⋊C4—472no—
625C4⋊C4—472no—
626C4⋊C4—472no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—944no—
630C4⋊C4—941no—
631C4⋊C4—941no—
632C4⋊C4—941no—
633C4⋊C4C23×D4712yes—
634C4⋊C4C23×D4712yes—
635C4⋊C4C23×D4712yes—
636C22⋊C4—24no—
637C22⋊C4—474no—
638C22⋊C4—474no—
639C22⋊C4—944no—
640C22⋊C4—944no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C42—472no—
648C42—472no—
649C42—944no—
650C42—944no—
651C42—944no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—472no—
660C23—942no—
661C23—942no—
662C23—942no—
663C23—942no—
664C23—1882no—
665C23—1882no—
666C23—1882no—
667C23C2×D4×D4712yes—
668C23C2×D4×D4711yescharacteristic
669Q8—3764no—
670D4—22no—
671D4—22no—
672D4—42no—
673D4—84no—
674D4—942no—
675D4—942no—
676D4—3764no—
677D4—3764no—
678D4—1884no—
679D4—1888no—
680D4—1882no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—84no—
692C2×C4—472no—
693C2×C4—472no—
694C2×C4—472no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—944no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—3764no—
705C2×C4—1888no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4C2×D4×D4712yes—
710C2×C4C2×D4×D4711yescharacteristic
711C2×C4#41×D4712yes—
712C2×C4#1309407112yes—
713C2×C4C24×D4711yescharacteristic
714C8—22no—
715C8—22no—
716C8—474no—
717C8—942no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—942no—
727C22—942no—
728C22—942no—
729C22—3764no—
730C22—1882no—
731C22—1882no—
732C22—1882no—
733C22—1884no—
734C22#1568977112yes—
735C22#1568992212yes—
736C22#1568992412yes—
737C22C22×D4×D4711yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—942no—
743C4—942no—
744C4—942no—
745C4—1882no—
746C4—1882no—
747C4—1882no—
748C4#1568977112yes—
749C4C2×#41×D4711yescharacteristic
750C4C2×#1309407111yescharacteristic
751C2—42no—
752C2—82no—
753C2—3762no—
754C2—1882no—
755C2#2025589114yesdirect product factor
756C2C2×#1568977111yescharacteristic
757C2C2×#1568992211yescharacteristic
758C2C2×#1568992411yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#480C2
socleC23×C47C22×D4
hypercenterC2×#480D47
hypocenterC47C2×#3347
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×#15689837C2semidirect
2. C2×#15689821C2semidirect
3. #20255891C2direct (N × H)
4. C2×#15689531C2semidirect
5. C2×#15689450C2semidirect
6. C2×#15689448C2semidirect
7. C2×#15689446C2semidirect
8. C2×#15689421C2semidirect
9. C2×#15689402C2semidirect
10. C2×#15689374C2semidirect
11. C2×#15689358C2semidirect
12. C2×#15689232C2semidirect
13. C2×#15689197C2semidirect
14. C2×#15689163C2semidirect
15. C2×#15689160C2semidirect
16. C2×C47×#480C2semidirect
21. #15689837C22semidirect
23. #15689821C22semidirect
43. #15689531C22semidirect
44. #15689450C22semidirect
45. #15689448C22semidirect
46. #15689446C22semidirect
47. #15689421C22semidirect
48. #15689402C22semidirect
49. #15689374C22semidirect
50. #15689358C22semidirect
51. #15689232C22semidirect
52. #15689197C22semidirect
53. #15689163C22semidirect
54. #15689160C22semidirect
71. C47×#480C22semidirect
379. C2×#480D47semidirect
390. C2×C47#3347semidirect
428. #480C2×D47semidirect
456. C47C2×#3347semidirect
755. C2#20255891direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898372
C2×#156898212
#202558912
C2×#156895312
C2×#156894502
C2×#156894482
C2×#156894462
C2×#156894212
C2×#156894022
C2×#156893742
C2×#156893582
C2×#156892322
C2×#156891972
C2×#156891632
C2×#156891602
C2×C47×#4802
C2×#334747