Finite Group Databasebeta

← C2×#20255835 #27094816

Subgroups — C2×#20255835 #27094816

Order 12032.

2094 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×#15689811C211yesmaximal, characteristic, complemented
2C2×#15689778C211yesmaximal, characteristic
3#20255835C2116yesmaximal, direct product factor
4C2×#15689533C211yesmaximal, characteristic, complemented
5C2×#15689460C211yesmaximal, characteristic, complemented
6C2×#15689445C211yesmaximal, characteristic, complemented
7C2×#15689455C211yesmaximal, characteristic, complemented
8C2×#15689435C211yesmaximal, characteristic, complemented
9C2×#15689419C211yesmaximal, characteristic, complemented
10C2×#15689368C211yesmaximal, characteristic, complemented
11C2×#15689351C211yesmaximal, characteristic, complemented
12C2×#15689223C211yesmaximal, characteristic, complemented
13C2×#15689193C211yesmaximal, characteristic, complemented
14C2×#15689162C211yesmaximal, characteristic, complemented
15C2×#107×D47C211yesmaximal, characteristic, complemented
16C2×C47×#478C211yesmaximal, characteristic, complemented
17C22×#10625350—21no—
18C22×#10625335C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689811—24no—
22#15689811C2218yescomplemented
23#15689778—24no—
24#15689778C2218yes—
25C2×#13094024C2211yescharacteristic
26C2×#13094019—21no—
27C2×#13094015—21no—
28C2×#13094009—21no—
29C2×#13094006—21no—
30C2×#13094006—21no—
31C2×#13094004C2211yescharacteristic
32C2×#13094004C2211yescharacteristic
33C2×#13094003—21no—
34C2×#13093995C2211yescharacteristic
35C2×#13093995C2211yescharacteristic
36C2×C4×Dic94C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38C2×#13093982—21no—
39C2×#13093982C2211yescharacteristic
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689533C2218yescomplemented
44#15689460C2218yescomplemented
45#15689455C2218yescomplemented
46#15689445C2218yescomplemented
47#15689435C2218yescomplemented
48#15689419C2218yescomplemented
49#15689368C2218yescomplemented
50#15689351C2218yescomplemented
51#15689223C2218yescomplemented
52#15689193C2218yescomplemented
53#15689162C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093957C2211yescharacteristic
59#107×D47C2218yescomplemented
60C2×#13093955C2211yescharacteristic
61C2×#13093955C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093935C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#478C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625350—28no—
78C2×#10625350—48no—
79C22×Dic94—21no—
80C22×Dic94C2311yescharacteristic
81C22×D188D411yescharacteristic
82C22×C22⋊D47—21no—
83C22×C22⋊D47—21no—
84C22×C4×D47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47C2311yescharacteristic
88C22×C4×D47C2311yescharacteristic
89C2×#10625335—24no—
90C2×#10625335C2314yes—
91C2×#10625324—24no—
92C2×#10625324C2314yes—
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C2×C8×D47—24no—
96C2×C8×D47C2314yes—
97#13094024—22no—
98#13094024C2314yes—
99#13094019—28no—
100#13094015—28no—
101#13094009—28no—
102#13094006—28no—
103#13094006—28no—
104#13094004—22no—
105#13094004—22no—
106#13094004C2314yes—
107#13094004C2314yes—
108#13094003—28no—
109#13093995—22no—
110#13093995—22no—
111#13093995C2314yes—
112#13093995C2314yes—
113C4×Dic94—22no—
114C4×Dic94C2314yes—
115C4×D188D414yes—
116C4×D188C2314yes—
117#13093982—22no—
118#13093982—28no—
119#13093982C2314yes—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47D411yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C4⋊C4×D47—22no—
132C4⋊C4×D47—22no—
133C4⋊C4×D47—22no—
134C4⋊C4×D47C2314yes—
135C4⋊C4×D47C2314yes—
136C4⋊C4×D47C2314yes—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4D411yescharacteristic
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146#13093958C2314yes—
147#13093958C2314yes—
148#13093957C2314yes—
149#13093957C2314yes—
150#13093957C2314yes—
151#13093955C2314yes—
152#13093955C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093947C2314yes—
156#13093945C2314yes—
157(C2×D47)⋊C8C2314yes—
158(C2×D47)⋊C8C2314yes—
159#13093935C2314yes—
160C22×D4×C47C2311yescharacteristic
161C23×C4×C47—21no—
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164#125×C47—22no—
165#125×C47C2314yes—
166C4×D4×C47—22no—
167C4×D4×C47C2314yes—
168C2×C4⋊C4×C47—21no—
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#107×C47C2314yes—
176#106×C47C2314yes—
177C4⋊C8×C47C2314yes—
178#102×C47C2314yes—
179#102×C47C2314yes—
180C24×C47—21no—
181C23×D47C2×D411yescharacteristic
182C23×D47C2×D411yescharacteristic
183C2×D4×C47—21no—
184C2×D4×C47—22no—
185C2×D4×C47—22no—
186C2×D4×C47C2412yes—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—24no—
191C22×C4×C47—44no—
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2411yescharacteristic
195C2×C22⋊D47—24no—
196C2×C22⋊D47—24no—
197C2×C22⋊D47—44no—
198C2×C22⋊D47—44no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47C2×D411yescharacteristic
204C22×Dic47C2×D411yescharacteristic
205#10625350—432no—
206C2×D188—24no—
207C2×D188C2×D414yes—
208C2×C4×D47—22no—
209C2×C4×D47—22no—
210C2×C4×D47—22no—
211C2×C4×D47—22no—
212C2×C4×D47—24no—
213C2×C4×D47—24no—
214C2×C4×D47—24no—
215C2×C4×D47—44no—
216C2×C4×D47—44no—
217C2×C4×D47—44no—
218C2×C4×D47C2×D412yes—
219C2×C4×D47C2×D412yes—
220C2×C4×D47C2412yes—
221C2×C4×D47C2412yes—
222C2×Dic94—22no—
223C2×Dic94—22no—
224C2×Dic94—21no—
225C2×Dic94—24no—
226C2×Dic94—44no—
227C2×Dic94C2412yes—
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×C47—21no—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C4⋊C4×C47C2412yes—
240C22⋊C4×C47—24no—
241C42×C47C2×D412yes—
242C42×C47C2412yes—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245#10625335—28no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4C2×D414yes—
250(C2×D47)⋊C4C2×D414yes—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47—24no—
255C4⋊Dic47—24no—
256C4⋊Dic47—24no—
257C4⋊Dic47C2×D414yes—
258C4⋊Dic47C2412yes—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C2×C47⋊C8—22no—
268C2×C47⋊C8#4114yescomplemented
269C2×C47⋊C8C2412yes—
270C2×C47⋊C8C2412yes—
271#10625324—28no—
272C8×D47—28no—
273C23×C47—22no—
274C23×C47—42no—
275C23×C47—42no—
276C23×C47—42no—
277C23×C47C22×D411yescharacteristic
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47AGL(1,ℤ/8)14yes—
284C22×D47C22×D412yes—
285C22×D47C22×D412yes—
286D4×C47—22no—
287D4×C47—22no—
288D4×C47—42no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—48no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D412yes—
300C2×C4×C47C22×D411yescharacteristic
301C2×C4×C47C2×#4112yes—
302C2×C4×C472−1+412yes—
303C2×C4×C47C2511yescharacteristic
304C22⋊D47—48no—
305C22⋊D47—48no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47C22×D412yes—
317C2×Dic47C22×D412yes—
318D188—28no—
319C4×D47—24no—
320C4×D47—24no—
321C4×D47—22no—
322C4×D47—22no—
323C4×D47—22no—
324C4×D47—22no—
325C4×D47—48no—
326C4×D47—48no—
327C4×D47—48no—
328Dic94—22no—
329Dic94—22no—
330Dic94—48no—
331Dic94—42no—
332C8×C47—22no—
333C8×C47—22no—
334C47⋊C8—22no—
335C47⋊C8C2×#4114yescomplemented
336C2×#3343—471nomaximal, Sylow
337C22×C47—42no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—84no—
341C22×C47#54712yes—
342C22×C47C2×AGL(1,ℤ/8)12yes—
343C22×C47#57812yes—
344C22×C47C23×D411yescharacteristic
345C2×D47—28no—
346C2×D47—22no—
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—44no—
352C2×D47C2×AGL(1,ℤ/8)14yes—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47—42no—
358C4×C47#54712yes—
359C4×C47C22×#4111yescharacteristic
360C4×C47C2×2−1+411yescharacteristic
361Dic47—22no—
362Dic47—22no—
363Dic47—42no—
364Dic47—42no—
365Dic47—42no—
366Dic47—42no—
367C2×#552—471no—
368C2×#547—471no—
369#3343—4716no—
370C2×#501—471no—
371C2×#484—471no—
372C2×#482—471no—
373C2×#483—471no—
374C2×#480—471no—
375C2×#477—471no—
376C2×#478D4711yescharacteristic, complemented
377C2×#468—471no—
378C2×#465—471no—
379C2×#440—471no—
380C2×#435—471no—
381C2×#428—471no—
382C22×#107—471no—
383C2×C47—82no—
384C2×C47#334314yescomplemented
385C2×C47C2×#54711yescharacteristic
386C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
387C2×C47C2×#57811yescharacteristic
388D47—24no—
389D47—42no—
390C22×#41—941no—
391C22×SD16—471no—
392C22×M16—471no—
393C23×C8—471no—
394#552—478no—
395#552—944no—
396#547—478no—
397#547—944no—
398C2×C4⋊Q8—471no—
399C2×#126—941no—
400C2×#125—941no—
401C2×#125C2×D4711yescharacteristic
402C2×#123—941no—
403C2×#123—941no—
404C2×#123—941no—
405C2×C22⋊Q8—471no—
406C2×C22⋊Q8—471no—
407C2×C22⋊Q8—941no—
408C2×#121—471no—
409C2×#121—471no—
410C2×C4×Q8—471no—
411C2×C4×D4—471no—
412C2×C4×D4C2×D4711yescharacteristic
413C2×#117—471no—
414C2×#117—941no—
415C22×C4⋊C4—471no—
416C22×C4⋊C4—471no—
417C22×C4⋊C4—471no—
418#501—478no—
419#484—478no—
420#483—478no—
421#482—478no—
422#480—478no—
423#478C2×D4718yescomplemented
424#477—478no—
425#468—478no—
426#465—478no—
427#440—478no—
428#435—478no—
429#428—478no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#107—471no—
433C2×#107—471no—
434C2×#107—471no—
435C2×#107—478no—
436C2×#107C2×D4711yescharacteristic
437C2×#106—471no—
438C2×#106—471no—
439C2×#106C2×D4711yescharacteristic
440C2×C4⋊C8C2×D4711yescharacteristic
441C2×#103—471no—
442C2×#103—471no—
443C2×#103—471no—
444C2×#102—471no—
445C2×#102C2×D4711yescharacteristic
446C2×#102C2×D4711yescharacteristic
447C2×C22⋊C8—471no—
448C2×C22⋊C8—471no—
449C2×#97—471no—
450C47C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—948no—
452C2×#41—1888no—
453C22×Q8—471no—
454C22×Q8—941no—
455C22×D4—471no—
456C22×D4—941no—
457C22×D4—941no—
458C22×D4C22×D4711yescharacteristic
459C23×C4—21no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—941no—
463C23×C4—941no—
464C23×C4—941no—
465C2×SD16—474no—
466C2×SD16—944no—
467C2×M16—474no—
468C2×M16—944no—
469C22×C8—471no—
470C22×C8—471no—
471C22×C8—474no—
472C22×C8—944no—
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C4⋊Q8—474no—
476C4⋊Q8—942no—
477#126—948no—
478#125—22no—
479#125—948no—
480#125C22×D4714yes—
481#123—948no—
482#123—948no—
483#123—948no—
484C22⋊Q8—474no—
485C22⋊Q8—474no—
486C22⋊Q8—942no—
487C22⋊Q8—942no—
488C22⋊Q8—948no—
489#121—474no—
490#121—474no—
491#121—942no—
492#121—942no—
493C4×Q8—474no—
494C4×Q8—942no—
495C4×D4—22no—
496C4×D4—474no—
497C4×D4—474no—
498C4×D4C22×D4714yes—
499#117—474no—
500#117—948no—
501#117—942no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—474no—
509C2×C4⋊C4—474no—
510C2×C4⋊C4—474no—
511C2×C4⋊C4—942no—
512C2×C4⋊C4—942no—
513C2×C4⋊C4—942no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4C22×D4711yescharacteristic
522C2×C4⋊C4C22×D4711yescharacteristic
523C2×C4⋊C4C22×D4711yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—471no—
526C2×C22⋊C4—471no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C42—941no—
533C2×C42—941no—
534C2×C42C22×D4711yescharacteristic
535#107—474no—
536#107—474no—
537#107—474no—
538#107—474no—
539#107—474no—
540#107C22×D4714yes—
541#106—474no—
542#106—474no—
543#106C22×D4714yes—
544C4⋊C8C22×D4714yes—
545#103—474no—
546#103—474no—
547#103—474no—
548#102—474no—
549#102C22×D4714yes—
550#102C22×D4714yes—
551C22⋊C8—474no—
552C22⋊C8—474no—
553#97—474no—
554C24—21no—
555C24—471no—
556C24—471no—
557#41—18832no—
558C2×Q8—472no—
559C2×Q8—941no—
560C2×Q8—944no—
561C2×Q8—942no—
562C2×Q8—942no—
563C2×Q8—1884no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—474no—
568C2×D4—944no—
569C2×D4—944no—
570C2×D4—944no—
571C2×D4—1884no—
572C2×D4—1884no—
573C2×D4C23×D4712yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—472no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—472no—
585C22×C4—944no—
586C22×C4—944no—
587C22×C4—944no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—1884no—
597C22×C4—1884no—
598C22×C4—1884no—
599C22×C4D4×D4711yescharacteristic
600C22×C4D4×D4711yescharacteristic
601C22×C4C23×D4711yescharacteristic
602SD16—948no—
603M16—948no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—474no—
607C2×C8—472no—
608C2×C8—472no—
609C2×C8—948no—
610C2×C8—942no—
611C2×C8C23×D4712yes—
612C2×C8C23×D4712yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—474no—
619C4⋊C4—472no—
620C4⋊C4—472no—
621C4⋊C4—472no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—944no—
628C4⋊C4—941no—
629C4⋊C4—941no—
630C4⋊C4—941no—
631C4⋊C4—944no—
632C4⋊C4C23×D4712yes—
633C4⋊C4C23×D4712yes—
634C4⋊C4C23×D4712yes—
635C22⋊C4—24no—
636C22⋊C4—474no—
637C22⋊C4—474no—
638C22⋊C4—944no—
639C22⋊C4—944no—
640C22⋊C4—944no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C42—944no—
644C42—944no—
645C42D4×D4712yes—
646C42C23×D4712yes—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—474no—
652C23—472no—
653C23—472no—
654C23—942no—
655C23—942no—
656C23—942no—
657C23—942no—
658C23—942no—
659C23C2×D4×D4711yescharacteristic
660Q8—942no—
661Q8—942no—
662Q8—1888no—
663Q8—1882no—
664D4—22no—
665D4—22no—
666D4—42no—
667D4—948no—
668D4—1888no—
669D4—1888no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—48no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—472no—
680C2×C4—472no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—944no—
684C2×C4—944no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—1888no—
694C2×C4—1888no—
695C2×C4—1888no—
696C2×C4—1882no—
697C2×C4—1882no—
698C2×C4—1882no—
699C2×C4—1882no—
700C2×C4C2×D4×D4712yes—
701C2×C4C2×D4×D4712yes—
702C2×C4C2×D4×D4711yescharacteristic
703C2×C4#41×D4712yes—
704C2×C4#1309407212yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—474no—
709C8—942no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—474no—
715C22—942no—
716C22—948no—
717C22—942no—
718C22—942no—
719C22—942no—
720C22—942no—
721C22—1884no—
722C22#1568977512yes—
723C22AGL(1,ℤ/8)×D4712yes—
724C22#1568993712yes—
725C22C22×D4×D4711yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—942no—
732C4—942no—
733C4—1882no—
734C4—1882no—
735C4—1882no—
736C4—1882no—
737C4#1568977512yes—
738C4C2×#41×D4711yescharacteristic
739C4C2×#1309407211yescharacteristic
740C2—82no—
741C2—944no—
742C2—1882no—
743C2#2025583514yesdirect product factor
744C2C2×#1568977511yescharacteristic
745C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
746C2C2×#1568993711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#478C2
socleC23×C47C22×D4
prime radicalC2×#15689778C2
hypercenterC2×#478D47
hypocenterC47C2×#3343
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#15689811C2semidirect
3. #20255835C2direct (N × H)
4. C2×#15689533C2semidirect
5. C2×#15689460C2semidirect
6. C2×#15689445C2semidirect
7. C2×#15689455C2semidirect
8. C2×#15689435C2semidirect
9. C2×#15689419C2semidirect
10. C2×#15689368C2semidirect
11. C2×#15689351C2semidirect
12. C2×#15689223C2semidirect
13. C2×#15689193C2semidirect
14. C2×#15689162C2semidirect
15. C2×#107×D47C2semidirect
16. C2×C47×#478C2semidirect
22. #15689811C22semidirect
43. #15689533C22semidirect
44. #15689460C22semidirect
45. #15689455C22semidirect
46. #15689445C22semidirect
47. #15689435C22semidirect
48. #15689419C22semidirect
49. #15689368C22semidirect
50. #15689351C22semidirect
51. #15689223C22semidirect
52. #15689193C22semidirect
53. #15689162C22semidirect
59. #107×D47C22semidirect
71. C47×#478C22semidirect
268. C2×C47⋊C8#41semidirect
335. C47⋊C8C2×#41semidirect
376. C2×#478D47semidirect
384. C2×C47#3343semidirect
423. #478C2×D47semidirect
450. C47C2×#3343semidirect
743. C2#20255835direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898112
C2×#156897782
#202558352
C2×#156895332
C2×#156894602
C2×#156894452
C2×#156894552
C2×#156894352
C2×#156894192
C2×#156893682
C2×#156893512
C2×#156892232
C2×#156891932
C2×#156891622
C2×#107×D472
C2×C47×#4782
C2×#334347