Finite Group Databasebeta

← C2×#20255549 #27092969

Subgroups — C2×#20255549 #27092969

Order 12032.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689838C211yesmaximal, characteristic, complemented
2C2×#15689768C211yesmaximal, characteristic, complemented
3#20255549C2116yesmaximal, direct product factor
4C2×#15689483C211yesmaximal, characteristic, complemented
5C2×#15689467C211yesmaximal, characteristic, complemented
6C2×#15689449C211yesmaximal, characteristic, complemented
7C2×#15689403C211yesmaximal, characteristic, complemented
8C2×#15689368C211yesmaximal, characteristic, complemented
9C2×#15689358C211yesmaximal, characteristic, complemented
10C2×#15689338C211yesmaximal, characteristic, complemented
11C2×#15689265C211yesmaximal, characteristic, complemented
12C2×#15689255C211yesmaximal, characteristic, complemented
13C2×#15689196C211yesmaximal, characteristic, complemented
14C2×#15689126C211yesmaximal, characteristic, complemented
15C2×#15689116C211yesmaximal, characteristic, complemented
16C2×C47×#442C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×#10625335C2211yescharacteristic, complemented
20C22×#10625334C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic, complemented
23#15689838—24no—
24#15689838C2218yescomplemented
25#15689768—24no—
26#15689768C2218yescomplemented
27C2×#13094024C2211yescharacteristic, complemented
28C2×#13094012C2211yescharacteristic
29C2×#13094010—21no—
30C2×#13094010—21no—
31C2×#13094008—21no—
32C2×#13094004C2211yescharacteristic
33C2×#13093999C2211yescharacteristic
34C2×#13093998—21no—
35C2×#13093998—21no—
36C2×#13093995C2211yescharacteristic
37C2×#13093995C2211yescharacteristic, complemented
38C2×#13093994—21no—
39C2×C4×D188C2211yescharacteristic
40C2×#13093983—21no—
41C2×#13093982C2211yescharacteristic
42C2×#13093982C2211yescharacteristic, complemented
43C22×(C2×D47)⋊C4—21no—
44#15689483C2218yescomplemented
45#15689467C2218yescomplemented
46#15689449C2218yescomplemented
47#15689403C2218yescomplemented
48#15689368C2218yescomplemented
49#15689358C2218yescomplemented
50#15689338C2218yescomplemented
51#15689265C2218yescomplemented
52#15689255C2218yescomplemented
53#15689196C2218yescomplemented
54C2×#13093957C2211yescharacteristic, complemented
55C2×#13093957C2211yescharacteristic, complemented
56C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
57#15689126C2218yescomplemented
58#15689116C2218yescomplemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093949C2211yescharacteristic, complemented
61C2×#13093947C2211yescharacteristic, complemented
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C22×D8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic, complemented
72C47×#442C2218yescomplemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic, complemented
76C2×#97×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625352—24no—
79C2×#10625352—22no—
80C2×#10625352—42no—
81C2×#10625352C2314yes—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C22×D188—21no—
85C22×D188D411yescharacteristic
86C22×D188C2311yescharacteristic
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47—21no—
90C22×C22⋊D47—21no—
91C2×D4×D47—24no—
92C2×D4×D47—22no—
93C2×D4×D47—42no—
94C2×D4×D47C2314yes—
95C23×Dic47—21no—
96C22×C4×D47C2311yescharacteristic
97C22×C4×D47C2311yescharacteristic
98C2×#10625335—42no—
99C2×#10625335C2314yescomplemented
100C2×#10625334—42no—
101C2×#10625334C2314yes—
102C2×#10625324—42no—
103C2×#10625324C2314yes—
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106C2×C8×D47—42no—
107C2×C8×D47C2314yescomplemented
108#13094024—22no—
109#13094024C2314yescomplemented
110#13094012—22no—
111#13094012C2314yes—
112#13094010—28no—
113#13094010—28no—
114#13094008—28no—
115#13094004—22no—
116#13094004C2314yes—
117#13093999—22no—
118#13093999C2314yes—
119#13093998—28no—
120#13093998—28no—
121#13093995—22no—
122#13093995—22no—
123#13093995C2314yes—
124#13093995C2314yescomplemented
125#13093994—28no—
126C4×D188D414yes—
127C4×D188C2314yes—
128#13093983—28no—
129#13093982—22no—
130#13093982—22no—
131#13093982C2314yes—
132#13093982C2314yescomplemented
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47—21no—
135C2×C4⋊Dic47D411yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—28no—
147C2×(C2×D47)⋊C4D411yescharacteristic
148C2×(C2×D47)⋊C4D411yescharacteristic
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093957C2314yescomplemented
152#13093957C2314yescomplemented
153C4⋊(C47⋊C8)C2314yescomplemented
154#13093949C2314yescomplemented
155#13093949C2314yescomplemented
156#13093947C2314yescomplemented
157#13093946C2314yes—
158#13093946C2314yes—
159#13093945C2314yes—
160#13093945C2314yes—
161#13093944C2314yes—
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yescomplemented
164C22×D4×C47C2311yescharacteristic
165C22×D4×C47C2311yescharacteristic
166C23×C4×C47—21no—
167C23×C4×C47—21no—
168C2×D8×C47—24no—
169C2×D8×C47C2314yes—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C4×D4×C47—22no—
173C4×D4×C47—22no—
174C4×D4×C47C2314yes—
175C4×D4×C47C2314yescomplemented
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#106×C47C2314yescomplemented
182#102×C47C2314yes—
183#102×C47C2314yescomplemented
184#97×C47C2314yescomplemented
185C24×C47—21no—
186C24×C47—21no—
187C23×D47—21no—
188C23×D47—24no—
189C23×D47—44no—
190C23×D47—44no—
191C23×D47—82no—
192C23×D47C2×D411yescharacteristic
193C23×D47C2×D411yescharacteristic
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47#4114yes—
200C2×D4×C47C2412yes—
201C2×D4×C47C2412yes—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—24no—
205C22×C4×C47—24no—
206C22×C4×C47—44no—
207C22×C4×C47—82no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2411yescharacteristic
211C2×C22⋊D47—24no—
212C2×C22⋊D47—24no—
213C2×C22⋊D47—24no—
214C2×C22⋊D47—24no—
215C2×C22⋊D47—44no—
216C2×C22⋊D47—44no—
217C2×C22⋊D47—82no—
218C2×C22⋊D47—82no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—24no—
223C22×Dic47—44no—
224C22×Dic47C2×D411yescharacteristic
225C22×Dic47C2×D411yescharacteristic
226#10625352—28no—
227#10625352—44no—
228#10625352—48no—
229D4×D47—28no—
230D4×D47—44no—
231D4×D47—48no—
232C2×D188—22no—
233C2×D188—22no—
234C2×D188—21no—
235C2×D188—24no—
236C2×D188—42no—
237C2×D188—82no—
238C2×D188C2×D414yes—
239C2×D188C2412yes—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47—22no—
243C2×C4×D47—22no—
244C2×C4×D47C2×D412yes—
245C2×C4×D47C2×D412yes—
246C2×C4×D47C2412yes—
247C2×C4×D47C2412yes—
248C2×Dic94—22no—
249C2×Dic94—22no—
250C2×Dic94—21no—
251C2×Dic94—24no—
252C2×Dic94—82no—
253C2×Dic94C2412yes—
254D8×C47—28no—
255C2×C8×C47—22no—
256C2×C8×C47—22no—
257C2×C8×C47C2412yes—
258C2×C8×C47C2412yes—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47C2412yes—
262C4⋊C4×C47C2412yes—
263C22⋊C4×C47—24no—
264C22⋊C4×C47—24no—
265C42×C47C2×D412yes—
266C42×C47C2412yes—
267C22⋊Dic47—24no—
268C22⋊Dic47—24no—
269#10625335—44no—
270#10625334—44no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4C2×D414yes—
278(C2×D47)⋊C4C2×D414yes—
279C4⋊Dic47—24no—
280C4⋊Dic47—21no—
281C4⋊Dic47—21no—
282C4⋊Dic47—24no—
283C4⋊Dic47C2×D414yes—
284C4⋊Dic47C2412yes—
285C4⋊Dic47C2412yes—
286C4×Dic47—24no—
287C4×Dic47—24no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—22no—
290C2×C47⋊C8C2412yes—
291C2×C47⋊C8C2412yes—
292#10625324—44no—
293C8×D47—44no—
294C23×C47—24no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—42no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47C22×D411yescharacteristic
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—48no—
311C22×D47—48no—
312C22×D47—42no—
313C22×D47—42no—
314C22×D47—42no—
315C22×D47—84no—
316C22×D47—816no—
317C22×D47C22×D412yes—
318C22×D47C22×D412yes—
319D4×C47—24no—
320D4×C47—22no—
321D4×C47—22no—
322D4×C47—22no—
323D4×C47—42no—
324D4×C47C2×#4114yes—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—48no—
330C2×C4×C47—42no—
331C2×C4×C47—42no—
332C2×C4×C47—84no—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D412yes—
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47C2×#4112yes—
337C2×C4×C47H(5,𝔽2)12yes—
338C2×C4×C47C2511yescharacteristic
339C22⋊D47—48no—
340C22⋊D47—48no—
341C22⋊D47—84no—
342C22⋊D47—84no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—48no—
349C2×Dic47—42no—
350C2×Dic47—42no—
351C2×Dic47—42no—
352C2×Dic47C22×D412yes—
353C2×Dic47C22×D412yes—
354D188—22no—
355D188—22no—
356D188—44no—
357D188—42no—
358D188—84no—
359C4×D47—24no—
360C4×D47—24no—
361C4×D47—22no—
362C4×D47—22no—
363C4×D47—22no—
364C4×D47—22no—
365Dic94—22no—
366Dic94—22no—
367Dic94—42no—
368Dic94—84no—
369C8×C47—22no—
370C8×C47—22no—
371C47⋊C8—22no—
372C47⋊C8—22no—
373C2×#3319—471nomaximal, Sylow
374C22×C47—24no—
375C22×C47—48no—
376C22×C47—42no—
377C22×C47—42no—
378C22×C47—42no—
379C22×C47—42no—
380C22×C47—42no—
381C22×C47—84no—
382C22×C47#54612yes—
383C22×C47#57512yes—
384C22×C47#57612yes—
385C22×C47C23×D411yescharacteristic
386C2×D47—22no—
387C2×D47—22no—
388C2×D47—22no—
389C2×D47—22no—
390C2×D47—22no—
391C2×D47—22no—
392C2×D47—44no—
393C2×D47—44no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—816no—
398C2×D47—84no—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47—42no—
402C4×C47—42no—
403C4×C47#54612yes—
404C4×C47C22×#4111yescharacteristic
405C4×C47C2×H(5,𝔽2)11yescharacteristic
406Dic47—22no—
407Dic47—22no—
408Dic47—42no—
409Dic47—42no—
410Dic47—42no—
411C2×#555—471no—
412C2×#546—471no—
413#3319—4716no—
414C2×#489—471no—
415C2×#485—471no—
416C2×#482—471no—
417C2×#474—471no—
418C2×#468—471no—
419C2×#466—471no—
420C2×#463—471no—
421C2×#449—471no—
422C2×#447—471no—
423C2×#442D4711yescharacteristic, complemented
424C2×#435—471no—
425C2×#418—471no—
426C2×#416—471no—
427C2×C47—44no—
428C2×C47—82no—
429C2×C47#331914yescomplemented
430C2×C47C2×#54611yescharacteristic
431C2×C47C2×#57511yescharacteristic
432C2×C47C2×#57611yescharacteristic
433D47—42no—
434D47—42no—
435D47—82no—
436C22×#41—471no—
437C23×D4—471no—
438C22×SD16—471no—
439C22×D8—471no—
440C22×D8C2×D4711yescharacteristic
441C22×M16—471no—
442C23×C8—471no—
443#555—478no—
444#555—944no—
445#546—478no—
446#546—944no—
447C2×C4⋊Q8—471no—
448C2×#124—471no—
449C2×#124—941no—
450C2×#124—941no—
451C2×#123—941no—
452C2×C22⋊Q8—471no—
453C2×#121—471no—
454C2×#121—471no—
455C2×#121—471no—
456C2×#121—941no—
457C2×#121—941no—
458C2×#120—941no—
459C2×C4×D4—471no—
460C2×C4×D4C2×D4711yescharacteristic
461C2×C4×D4C2×D4711yescharacteristic, complemented
462C2×#117—471no—
463C2×#117—471no—
464C2×#117—941no—
465C22×C22⋊C4—941no—
466#489—478no—
467#485—478no—
468#482—478no—
469#474—478no—
470#468—478no—
471#466—478no—
472#463—478no—
473#449—478no—
474#447—478no—
475#442C2×D4718yescomplemented
476#435—478no—
477C2×#107—471no—
478C2×#107—471no—
479C2×#106C2×D4711yescharacteristic, complemented
480C2×C4⋊C8—471no—
481#418—478no—
482#416—478no—
483C2×#103—471no—
484C2×#103—471no—
485C2×#103—471no—
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102—471no—
491C2×#102C2×D4711yescharacteristic
492C2×#102C2×D4711yescharacteristic, complemented
493C2×C22⋊C8—471no—
494C2×C22⋊C8—471no—
495C2×#97C2×D4711yescharacteristic, complemented
496C47C2×#331911yescharacteristic, complemented, Sylow
497C25—941no—
498C2×#41—474no—
499C2×#41—942no—
500C2×#41—944no—
501C2×#41—1882no—
502C22×Q8—471no—
503C22×Q8—941no—
504C22×D4—474no—
505C22×D4—471no—
506C22×D4—471no—
507C22×D4—941no—
508C22×D4—942no—
509C22×D4—941no—
510C22×D4—944no—
511C22×D4—941no—
512C22×D4—941no—
513C22×D4—941no—
514C22×D4—1882no—
515C22×D4C22×D4711yescharacteristic
516C22×D4C22×D4711yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—471no—
520C23×C4—471no—
521C23×C4—941no—
522C2×SD16—474no—
523C2×SD16—1882no—
524C2×D8—24no—
525C2×D8—474no—
526C2×D8—1882no—
527C2×D8C22×D4714yes—
528C2×M16—474no—
529C2×M16—1882no—
530C22×C8—471no—
531C22×C8—471no—
532C22×C8—474no—
533C22×C8—1882no—
534C22×C8C22×D4711yescharacteristic
535C22×C8C22×D4711yescharacteristic
536C4⋊Q8—474no—
537C4⋊Q8—942no—
538#124—474no—
539#124—948no—
540#124—948no—
541#124—942no—
542#123—948no—
543C22⋊Q8—474no—
544C22⋊Q8—942no—
545#121—474no—
546#121—474no—
547#121—474no—
548#121—948no—
549#121—942no—
550#121—948no—
551#121—942no—
552#121—942no—
553#120—948no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—474no—
557C4×D4—474no—
558C4×D4C22×D4714yes—
559C4×D4C22×D4714yescomplemented
560#117—474no—
561#117—474no—
562#117—942no—
563#117—942no—
564#117—948no—
565C2×C4⋊C4—471no—
566C2×C4⋊C4—471no—
567C2×C4⋊C4—471no—
568C2×C4⋊C4—941no—
569C2×C4⋊C4—941no—
570C2×C4⋊C4C22×D4711yescharacteristic
571C2×C4⋊C4C22×D4711yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—471no—
575C2×C22⋊C4—471no—
576C2×C22⋊C4—948no—
577C2×C22⋊C4—941no—
578C2×C22⋊C4—941no—
579C2×C22⋊C4—941no—
580C2×C22⋊C4—941no—
581C2×C22⋊C4—941no—
582C2×C22⋊C4—941no—
583C2×C22⋊C4—941no—
584C2×C22⋊C4—941no—
585C2×C42—941no—
586C2×C42—941no—
587C2×C42C22×D4711yescharacteristic
588#107—474no—
589#107—474no—
590#106C22×D4714yescomplemented
591C4⋊C8—474no—
592#103—474no—
593#103—474no—
594#103—474no—
595#102—474no—
596#102—474no—
597#102—474no—
598#102—474no—
599#102—474no—
600#102C22×D4714yes—
601#102C22×D4714yescomplemented
602C22⋊C8—474no—
603C22⋊C8—474no—
604#97C22×D4714yescomplemented
605C24—21no—
606C24—21no—
607C24—471no—
608C24—471no—
609C24—944no—
610C24—941no—
611C24—3762no—
612C24—1884no—
613C24—1884no—
614#41—948no—
615#41—1884no—
616#41—1888no—
617C2×Q8—472no—
618C2×Q8—944no—
619C2×Q8—941no—
620C2×Q8—942no—
621C2×Q8—942no—
622C2×Q8—3762no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—474no—
629C2×D4—472no—
630C2×D4—944no—
631C2×D4—944no—
632C2×D4—948no—
633C2×D4—944no—
634C2×D4—944no—
635C2×D4—944no—
636C2×D4—941no—
637C2×D4—942no—
638C2×D4—942no—
639C2×D4—3762no—
640C2×D4—3762no—
641C2×D4—3762no—
642C2×D4—1882no—
643C2×D4—1884no—
644C2×D4—1888no—
645C2×D4—1884no—
646C2×D4—1884no—
647C2×D4#1062535014yes—
648C2×D4C23×D4712yes—
649C2×D4C23×D4712yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—82no—
656C22×C4—471no—
657C22×C4—471no—
658C22×C4—472no—
659C22×C4—472no—
660C22×C4—472no—
661C22×C4—472no—
662C22×C4—944no—
663C22×C4—942no—
664C22×C4—942no—
665C22×C4—942no—
666C22×C4—942no—
667C22×C4—941no—
668C22×C4—941no—
669C22×C4—941no—
670C22×C4—1884no—
671C22×C4D4×D4711yescharacteristic
672C22×C4D4×D4711yescharacteristic
673C22×C4C23×D4711yescharacteristic
674SD16—1884no—
675D8—28no—
676D8—1884no—
677M16—1884no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—472no—
681C2×C8—472no—
682C2×C8—942no—
683C2×C8—942no—
684C2×C8—1884no—
685C2×C8C23×D4712yes—
686C2×C8C23×D4712yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—474no—
690C4⋊C4—472no—
691C4⋊C4—472no—
692C4⋊C4—944no—
693C4⋊C4—941no—
694C4⋊C4—941no—
695C4⋊C4—944no—
696C4⋊C4C23×D4712yes—
697C4⋊C4C23×D4712yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—474no—
701C22⋊C4—474no—
702C22⋊C4—944no—
703C22⋊C4—944no—
704C22⋊C4—944no—
705C22⋊C4—944no—
706C22⋊C4—944no—
707C22⋊C4—944no—
708C22⋊C4—944no—
709C22⋊C4—944no—
710C42—944no—
711C42—944no—
712C42D4×D4712yes—
713C42C23×D4712yes—
714C23—24no—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—472no—
723C23—472no—
724C23—942no—
725C23—942no—
726C23—942no—
727C23—942no—
728C23—942no—
729C23—942no—
730C23—942no—
731C23—3764no—
732C23—37616no—
733C23—1888no—
734C23—1888no—
735C23—1882no—
736C23—1882no—
737C23—1882no—
738C23C2×D4×D4711yescharacteristic
739Q8—942no—
740Q8—942no—
741Q8—3764no—
742Q8—1882no—
743D4—24no—
744D4—22no—
745D4—22no—
746D4—22no—
747D4—42no—
748D4—942no—
749D4—942no—
750D4—3764no—
751D4—3764no—
752D4—3764no—
753D4—1884no—
754D4—1888no—
755D4—1888no—
756D4—1882no—
757D4C2×#1062535014yes—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—48no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—472no—
767C2×C4—472no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—944no—
771C2×C4—944no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—942no—
778C2×C4—942no—
779C2×C4—1888no—
780C2×C4—1882no—
781C2×C4—1882no—
782C2×C4—1882no—
783C2×C4C2×D4×D4712yes—
784C2×C4C2×D4×D4712yes—
785C2×C4C2×D4×D4711yescharacteristic
786C2×C4C2×#1062535012yes—
787C2×C4#1309407012yes—
788C2×C4C24×D4711yescharacteristic
789C8—22no—
790C8—22no—
791C8—942no—
792C8—942no—
793C22—24no—
794C22—48no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—942no—
802C22—942no—
803C22—942no—
804C22—942no—
805C22—942no—
806C22—942no—
807C22—37616no—
808C22—3764no—
809C22—1882no—
810C22—1882no—
811C22—1882no—
812C22—1884no—
813C22—1884no—
814C22#1568976912yes—
815C22#1568991912yes—
816C22#1568992712yes—
817C22C22×D4×D4711yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—942no—
823C4—942no—
824C4—1882no—
825C4—1882no—
826C4—1882no—
827C4#1568976912yes—
828C4C22×#1062535011yescharacteristic
829C4C2×#1309407011yescharacteristic
830C2—44no—
831C2—82no—
832C2—3762no—
833C2—1882no—
834C2—1882no—
835C2#2025554914yesdirect product factor
836C2C2×#1568976911yescharacteristic
837C2C2×#1568991911yescharacteristic
838C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#442C2
socleC23×C47C22×D4
hypercenterC2×#442D47
hypocenterC47C2×#3319
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#15689838C2semidirect
2. C2×#15689768C2semidirect
3. #20255549C2direct (N × H)
4. C2×#15689483C2semidirect
5. C2×#15689467C2semidirect
6. C2×#15689449C2semidirect
7. C2×#15689403C2semidirect
8. C2×#15689368C2semidirect
9. C2×#15689358C2semidirect
10. C2×#15689338C2semidirect
11. C2×#15689265C2semidirect
12. C2×#15689255C2semidirect
13. C2×#15689196C2semidirect
14. C2×#15689126C2semidirect
15. C2×#15689116C2semidirect
16. C2×C47×#442C2semidirect
19. C22×#10625335C22semidirect
22. C22×C8×D47C22semidirect
24. #15689838C22semidirect
26. #15689768C22semidirect
27. C2×#13094024C22semidirect
37. C2×#13093995C22semidirect
42. C2×#13093982C22semidirect
44. #15689483C22semidirect
45. #15689467C22semidirect
46. #15689449C22semidirect
47. #15689403C22semidirect
48. #15689368C22semidirect
49. #15689358C22semidirect
50. #15689338C22semidirect
51. #15689265C22semidirect
52. #15689255C22semidirect
53. #15689196C22semidirect
54. C2×#13093957C22semidirect
55. C2×#13093957C22semidirect
56. C2×C4⋊(C47⋊C8)C22semidirect
57. #15689126C22semidirect
58. #15689116C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093949C22semidirect
61. C2×#13093947C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
71. C2×C4×D4×C47C22semidirect
72. C47×#442C22semidirect
73. C2×#106×C47C22semidirect
75. C2×#102×C47C22semidirect
76. C2×#97×C47C22semidirect
99. C2×#10625335C23semidirect
107. C2×C8×D47C23semidirect
109. #13094024C23semidirect
124. #13093995C23semidirect
132. #13093982C23semidirect
151. #13093957C23semidirect
152. #13093957C23semidirect
153. C4⋊(C47⋊C8)C23semidirect
154. #13093949C23semidirect
155. #13093949C23semidirect
156. #13093947C23semidirect
163. (C2×D47)⋊C8C23semidirect
175. C4×D4×C47C23semidirect
181. #106×C47C23semidirect
183. #102×C47C23semidirect
184. #97×C47C23semidirect
423. C2×#442D47semidirect
429. C2×C47#3319semidirect
461. C2×C4×D4C2×D47semidirect
475. #442C2×D47semidirect
479. C2×#106C2×D47semidirect
492. C2×#102C2×D47semidirect
495. C2×#97C2×D47semidirect
496. C47C2×#3319semidirect
559. C4×D4C22×D47semidirect
590. #106C22×D47semidirect
601. #102C22×D47semidirect
604. #97C22×D47semidirect
835. C2#20255549direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898382
C2×#156897682
#202555492
C2×#156894832
C2×#156894672
C2×#156894492
C2×#156894032
C2×#156893682
C2×#156893582
C2×#156893382
C2×#156892652
C2×#156892552
C2×#156891962
C2×#156891262
C2×#156891162
C2×C47×#4422
C2×#331947