Finite Group Databasebeta

← C2×#20256137 #27096023

Subgroups — C2×#20256137 #27096023

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×#15689856C211yesmaximal, characteristic, complemented
2C2×#15689832C211yesmaximal, characteristic, complemented
3#20256137C2116yesmaximal, direct product factor
4C2×#15689486C211yesmaximal, characteristic, complemented
5C2×#15689481C211yesmaximal, characteristic, complemented
6C2×#15689478C211yesmaximal, characteristic, complemented
7C2×#15689429C211yesmaximal, characteristic, complemented
8C2×#15689423C211yesmaximal, characteristic, complemented
9C2×#15689402C211yesmaximal, characteristic, complemented
10C2×#15689338C211yesmaximal, characteristic, complemented
11C2×#15689336C211yesmaximal, characteristic, complemented
12C2×#15689316C211yesmaximal, characteristic
13C2×#15689253C211yesmaximal, characteristic, complemented
14C2×#15689232C211yesmaximal, characteristic, complemented
15C2×#15689220C211yesmaximal, characteristic, complemented
16C2×C4×D8×C47C211yesmaximal, characteristic, complemented
17C22×#10625335C2211yescharacteristic
18C22×#10625334C2211yescharacteristic
19#15689856—24no—
20#15689856C2218yescomplemented
21#15689832—24no—
22#15689832C2218yescomplemented
23C2×#13094023C2211yescharacteristic
24C2×#13094020C2211yescharacteristic
25C2×#13094016C2211yescharacteristic
26C2×#13094015C2211yescharacteristic
27C2×#13094012C2211yescharacteristic
28C2×#13094011C2211yescharacteristic
29C2×#13094010—21no—
30C2×#13094007—21no—
31C2×#13094006—21no—
32C2×#13094003—21no—
33C2×#13094001—21no—
34C2×#13094001—21no—
35C2×C4×Dic94C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C2×D4×Dic47C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×C4×C22⋊D47—21no—
41C22×Dic47⋊C4—21no—
42#15689486C2218yescomplemented
43#15689481C2218yescomplemented
44#15689478C2218yescomplemented
45#15689429C2218yescomplemented
46#15689423C2218yescomplemented
47#15689402C2218yescomplemented
48#15689338C2218yescomplemented
49#15689336C2218yescomplemented
50#15689316C2218yes—
51#15689253C2218yescomplemented
52#15689232C2218yescomplemented
53#15689220C2218yescomplemented
54C2×#13093957C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×C4⋊(C47⋊C8)C2211yescharacteristic
57C2×Dic47⋊C8C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×D8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C4×D8×C47C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94D411yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C23×Dic47—21no—
84C23×Dic47—21no—
85C22×C4×D47—21no—
86C2×#10625335—24no—
87C2×#10625335C2314yes—
88C2×#10625334—24no—
89C2×#10625334C2314yes—
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92#13094023—22no—
93#13094023C2314yes—
94#13094020—22no—
95#13094020C2314yes—
96#13094016—22no—
97#13094016C2314yes—
98#13094015—22no—
99#13094015C2314yes—
100#13094012—22no—
101#13094012C2314yes—
102#13094011—22no—
103#13094011C2314yes—
104#13094010—28no—
105#13094007—28no—
106#13094006—28no—
107#13094003—28no—
108#13094001—28no—
109#13094001—28no—
110C4×Dic94D414yes—
111C4×Dic94C2314yes—
112#13093989—22no—
113#13093989C2314yes—
114D4×Dic47—22no—
115D4×Dic47—22no—
116D4×Dic47C2314yes—
117D4×Dic47C2314yes—
118#13093986—22no—
119#13093986C2314yes—
120C4×C22⋊D47—28no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47D411yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—28no—
131C2×Dic47⋊C4D411yescharacteristic
132C2×Dic47⋊C4D411yescharacteristic
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47C2311yescharacteristic
142C2×C4×Dic47C2311yescharacteristic
143#13093957C2314yes—
144#13093955C2314yes—
145C4⋊(C47⋊C8)C2314yes—
146Dic47⋊C8C2314yes—
147Dic47⋊C8C2314yes—
148#13093949C2314yes—
149#13093949C2314yes—
150#13093947C2314yes—
151#13093946C2314yes—
152#13093946C2314yes—
153#13093945C2314yes—
154#13093945C2314yes—
155#13093944C2314yes—
156#13093934C2314yes—
157#13093934C2314yes—
158C22×D4×C47C2311yescharacteristic
159C22×D4×C47C2311yescharacteristic
160C23×C4×C47—21no—
161C23×C4×C47—21no—
162C2×D8×C47—24no—
163C2×D8×C47C2314yes—
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C4×D4×C47—22no—
167C4×D4×C47—22no—
168C4×D4×C47C2314yes—
169C4×D4×C47C2314yes—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#107×C47C2314yes—
176#102×C47C2314yes—
177#102×C47C2314yes—
178C4×C8×C47C2314yes—
179C24×C47—21no—
180C24×C47—21no—
181C23×D47—21no—
182C2×D4×C47—21no—
183C2×D4×C47—21no—
184C2×D4×C47—22no—
185C2×D4×C47—22no—
186C2×D4×C47—22no—
187C2×D4×C47#4114yes—
188C2×D4×C47C2412yes—
189C2×D4×C47C2412yes—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—24no—
193C22×C4×C47—24no—
194C22×C4×C47—82no—
195C22×C4×C47—82no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C2×C22⋊D47—24no—
200C2×C22⋊D47—24no—
201C2×C22⋊D47—44no—
202C2×C22⋊D47—82no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—24no—
207C22×Dic47—24no—
208C22×Dic47—44no—
209C22×Dic47—82no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—21no—
217C2×D188C2412yes—
218C2×C4×D47—24no—
219C2×C4×D47—82no—
220C2×Dic94—22no—
221C2×Dic94—22no—
222C2×Dic94—21no—
223C2×Dic94—24no—
224C2×Dic94—42no—
225C2×Dic94—82no—
226C2×Dic94C2×D414yes—
227C2×Dic94C2412yes—
228D8×C47—28no—
229C2×C8×C47—22no—
230C2×C8×C47—22no—
231C2×C8×C47C2412yes—
232C2×C8×C47C2412yes—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C42×C47C2×D412yes—
240C42×C47C2412yes—
241C22⋊Dic47—24no—
242C22⋊Dic47—24no—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245#10625335—28no—
246#10625334—28no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250C4⋊Dic47—21no—
251C4⋊Dic47—21no—
252C4⋊Dic47—24no—
253C4⋊Dic47C2×D414yes—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4C2×D414yes—
262Dic47⋊C4C2×D414yes—
263C4×Dic47—24no—
264C4×Dic47C2×D412yes—
265C4×Dic47C2×D412yes—
266C4×Dic47C2412yes—
267C4×Dic47C2412yes—
268C2×C47⋊C8—22no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8C2412yes—
271C2×C47⋊C8C2412yes—
272C23×C47—24no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—42no—
276C23×C47—42no—
277C23×C47—42no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47C22×D411yescharacteristic
281C22×D47—22no—
282C22×D47—42no—
283C22×D47—42no—
284C22×D47—42no—
285D4×C47—24no—
286D4×C47—22no—
287D4×C47—22no—
288D4×C47—22no—
289D4×C47—42no—
290D4×C47C2×#4114yes—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—84no—
298C2×C4×C47—84no—
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—22no—
314C2×Dic47—48no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—84no—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321C2×Dic47C22×D412yes—
322C2×Dic47C22×D412yes—
323D188—22no—
324D188—22no—
325D188—42no—
326C4×D47—84no—
327Dic94—22no—
328Dic94—22no—
329Dic94—44no—
330Dic94—42no—
331Dic94—84no—
332C8×C47—22no—
333C8×C47—22no—
334C47⋊C8—22no—
335C47⋊C8—22no—
336C2×#3370—471nomaximal, Sylow
337C22×C47—24no—
338C22×C47—48no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—84no—
345C22×C47#54812yes—
346C22×C47#57512yes—
347C22×C47#57612yes—
348C22×C47C23×D411yescharacteristic
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#54812yes—
358C4×C47C22×#4111yescharacteristic
359C4×C47C2×2−1+411yescharacteristic
360Dic47—22no—
361Dic47—22no—
362Dic47—22no—
363Dic47—22no—
364Dic47—42no—
365Dic47—42no—
366Dic47—42no—
367C2×#559—471no—
368C2×#554—471no—
369#3370—4716no—
370C2×#490—471no—
371C2×#489—471no—
372C2×#488—471no—
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×D8D4711yescharacteristic, complemented
383C2×C47—44no—
384C2×C47—82no—
385C2×C47#337014yescomplemented
386C2×C47C2×#54811yescharacteristic
387C2×C47C2×#57511yescharacteristic
388C2×C47C2×#57611yescharacteristic
389D47—82no—
390C22×SD16—471no—
391C22×D8—471no—
392C22×D8C2×D4711yescharacteristic
393#559—478no—
394#559—944no—
395#554—478no—
396#554—944no—
397C2×C4⋊Q8—471no—
398C2×#127—471no—
399C2×#125—471no—
400C2×#125—471no—
401C2×#124—471no—
402C2×#124—471no—
403C2×#124—941no—
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—941no—
415C2×C4×D4C2×D4711yescharacteristic
416C2×C4×D4C2×D4711yescharacteristic
417C22×C4⋊C4—941no—
418#490—478no—
419#489—478no—
420#488—478no—
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×D8C2×D4718yescomplemented
431C2×#107—471no—
432C2×#107C2×D4711yescharacteristic
433C2×#106—471no—
434C2×C4⋊C8—471no—
435C2×C4⋊C8—471no—
436C2×C4⋊C8—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—471no—
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—471no—
453C22×Q8—941no—
454C22×D4—471no—
455C22×D4—941no—
456C22×D4—941no—
457C22×D4C22×D4711yescharacteristic
458C22×D4C22×D4711yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—941no—
462C23×C4—941no—
463C23×C4—941no—
464C2×SD16—474no—
465C2×SD16—944no—
466C2×D8—24no—
467C2×D8—474no—
468C2×D8—944no—
469C2×D8C22×D4714yes—
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—474no—
479#125—474no—
480#125—942no—
481#125—942no—
482#124—474no—
483#124—474no—
484#124—942no—
485#124—948no—
486#124—942no—
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—22no—
497C4×D4—22no—
498C4×D4—474no—
499C4×D4—474no—
500C4×D4—474no—
501C4×D4—942no—
502C4×D4—942no—
503C4×D4—942no—
504C4×D4—948no—
505C4×D4C22×D4714yes—
506C4×D4C22×D4714yes—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—948no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
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#107C22×D4714yes—
536#106—474no—
537C4⋊C8—474no—
538C4⋊C8—474no—
539C4⋊C8—474no—
540#103—474no—
541#103—474no—
542#103—474no—
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—21no—
555C24—941no—
556C2×Q8—474no—
557C2×Q8—472no—
558C2×Q8—944no—
559C2×Q8—941no—
560C2×Q8—942no—
561C2×Q8—942no—
562C2×Q8—3762no—
563C2×Q8—1882no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—472no—
570C2×D4—944no—
571C2×D4—944no—
572C2×D4—941no—
573C2×D4—942no—
574C2×D4—942no—
575C2×D4—3762no—
576C2×D4—1884no—
577C2×D4#1062535014yes—
578C2×D4C23×D4712yes—
579C2×D4C23×D4712yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—471no—
587C22×C4—471no—
588C22×C4—471no—
589C22×C4—471no—
590C22×C4—944no—
591C22×C4—944no—
592C22×C4—944no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—3762no—
597C22×C4—3762no—
598C22×C4—1884no—
599C22×C4D4×D4711yescharacteristic
600C22×C4D4×D4711yescharacteristic
601C22×C4C23×D4711yescharacteristic
602SD16—948no—
603D8—28no—
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—21no—
614C4⋊C4—21no—
615C4⋊C4—474no—
616C4⋊C4—474no—
617C4⋊C4—474no—
618C4⋊C4—472no—
619C4⋊C4—472no—
620C4⋊C4—944no—
621C4⋊C4—944no—
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—24no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—942no—
655C23—1882no—
656C23—1882no—
657C23—1882no—
658C23C2×D4×D4711yescharacteristic
659Q8—942no—
660Q8—942no—
661Q8—3764no—
662Q8—1884no—
663Q8—1882no—
664D4—24no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—942no—
670D4—942no—
671D4—3764no—
672D4—1888no—
673D4—1882no—
674D4C2×#1062535014yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—84no—
682C2×C4—84no—
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—942no—
694C2×C4—3764no—
695C2×C4—3764no—
696C2×C4—1888no—
697C2×C4—1882no—
698C2×C4—1882no—
699C2×C4—1882no—
700C2×C4C2×D4×D4712yes—
701C2×C4C2×D4×D4712yes—
702C2×C4C2×D4×D4711yescharacteristic
703C2×C4C2×#1062535012yes—
704C2×C4#1309407112yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—942no—
709C8—942no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—3764no—
719C22—1882no—
720C22—1882no—
721C22—1882no—
722C22#1568978212yes—
723C22#1568992012yes—
724C22#1568992412yes—
725C22C22×D4×D4711yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—942no—
731C4—942no—
732C4—942no—
733C4—942no—
734C4—1882no—
735C4—1882no—
736C4—1882no—
737C4#1568978212yes—
738C4C22×#1062535011yescharacteristic
739C4C2×#1309407111yescharacteristic
740C2—44no—
741C2—82no—
742C2—3762no—
743C2#2025613714yesdirect product factor
744C2C2×#1568978211yescharacteristic
745C2C2×#1568992011yescharacteristic
746C2C2×#1568992411yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×D8×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689316C2
hypercenterC2×C4×D8D47
hypocenterC47C2×#3370
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#15689856C2semidirect
2. C2×#15689832C2semidirect
3. #20256137C2direct (N × H)
4. C2×#15689486C2semidirect
5. C2×#15689481C2semidirect
6. C2×#15689478C2semidirect
7. C2×#15689429C2semidirect
8. C2×#15689423C2semidirect
9. C2×#15689402C2semidirect
10. C2×#15689338C2semidirect
11. C2×#15689336C2semidirect
13. C2×#15689253C2semidirect
14. C2×#15689232C2semidirect
15. C2×#15689220C2semidirect
16. C2×C4×D8×C47C2semidirect
20. #15689856C22semidirect
22. #15689832C22semidirect
42. #15689486C22semidirect
43. #15689481C22semidirect
44. #15689478C22semidirect
45. #15689429C22semidirect
46. #15689423C22semidirect
47. #15689402C22semidirect
48. #15689338C22semidirect
49. #15689336C22semidirect
51. #15689253C22semidirect
52. #15689232C22semidirect
53. #15689220C22semidirect
72. C4×D8×C47C22semidirect
382. C2×C4×D8D47semidirect
385. C2×C47#3370semidirect
430. C4×D8C2×D47semidirect
450. C47C2×#3370semidirect
743. C2#20256137direct (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×#156898322
#202561372
C2×#156894862
C2×#156894812
C2×#156894782
C2×#156894292
C2×#156894232
C2×#156894022
C2×#156893382
C2×#156893362
C2×#156893162
C2×#156892532
C2×#156892322
C2×#156892202
C2×C4×D8×C472
C2×#337047