Finite Group Databasebeta

← C2×#20253341 #27084100

Subgroups — C2×#20253341 #27084100

Order 12032.

2362 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689689C211yesmaximal, characteristic
2C2×#15689603C211yesmaximal, characteristic, complemented
3#20253341C2116yesmaximal, direct product factor
4C2×#15689442C211yesmaximal, characteristic, complemented
5C2×#15689440C211yesmaximal, characteristic, complemented
6C2×#15689449C211yesmaximal, characteristic, complemented
7C2×#15689447C211yesmaximal, characteristic, complemented
8C2×#15689446C211yesmaximal, characteristic, complemented
9C2×#15689438C211yesmaximal, characteristic, complemented
10C2×#15689434C211yesmaximal, characteristic, complemented
11C2×#15689164C211yesmaximal, characteristic, complemented
12C2×#15689158C211yesmaximal, characteristic, complemented
13C2×#15689126C211yesmaximal, characteristic, complemented
14C2×#102×D47C211yesmaximal, characteristic, complemented
15C2×#15689088C211yesmaximal, characteristic, complemented
16C2×C47×#482C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689689—24no—
22#15689689C2218yes—
23C2×#13094020—21no—
24C2×#13094010—21no—
25C2×#13093999C2211yescharacteristic
26C2×#13093998C2211yescharacteristic
27C2×#13093995C2211yescharacteristic
28C2×#13093994—21no—
29C2×#13093992—21no—
30#15689603—24no—
31#15689603C2218yescomplemented
32C2×C4×Dic94—21no—
33C2×C4×D188—21no—
34C2×(C22⋊D47)⋊C4—21no—
35C2×(C22⋊D47)⋊C4—21no—
36C2×#13093982C2211yescharacteristic
37C2×#13093982C2211yescharacteristic
38C2×#13093982C2211yescharacteristic, complemented
39C22×C4⋊Dic47C2211yescharacteristic, complemented
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic, complemented
42#15689449C2218yescomplemented
43#15689447C2218yescomplemented
44#15689446C2218yescomplemented
45#15689442C2218yescomplemented
46#15689440C2218yescomplemented
47#15689438C2218yescomplemented
48#15689434C2218yescomplemented
49#15689164C2218yescomplemented
50#15689158C2218yescomplemented
51C2×#13093957C2211yescharacteristic, complemented
52C2×#13093957C2211yescharacteristic, complemented
53C2×#13093957C2211yescharacteristic, complemented
54C2×#13093956C2211yescharacteristic, complemented
55C2×#13093956C2211yescharacteristic, complemented
56C2×#13093955C2211yescharacteristic, complemented
57#15689126C2218yescomplemented
58C2×#13093946C2211yescharacteristic
59C2×#13093946C2211yescharacteristic
60C2×#13093945C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64#102×D47C2218yescomplemented
65#15689088C2218yescomplemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C2×#121×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic, complemented
71C47×#482C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625350—24no—
79C2×#10625350—24no—
80C2×#10625350D414yes—
81C2×#10625350C2314yes—
82C22×Dic94D411yescharacteristic
83C22×D188—21no—
84C22×D188D411yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47D411yescharacteristic
90C22×C22⋊D47D411yescharacteristic
91C2×D4×D47—22no—
92C2×D4×D47—24no—
93C2×D4×D47—24no—
94C2×D4×D47C2314yes—
95C23×Dic47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C22×C4×D47C2311yescharacteristic
99C22×C4×D47C2311yescharacteristic
100C2×#10625324—24no—
101C2×#10625324C2314yes—
102C22×C47⋊C8C2311yescharacteristic
103C22×C47⋊C8C2311yescharacteristic
104C2×C8×D47—24no—
105C2×C8×D47C2314yes—
106#13094020—28no—
107#13094010—28no—
108#13093999—22no—
109#13093999C2314yes—
110#13093998—22no—
111#13093998C2314yes—
112#13093995—22no—
113#13093995C2314yes—
114#13093994—28no—
115#13093992—28no—
116C4×Dic94—28no—
117C4×D188—28no—
118(C22⋊D47)⋊C4—28no—
119(C22⋊D47)⋊C4—28no—
120#13093982—22no—
121#13093982—22no—
122#13093982—22no—
123#13093982C2314yes—
124#13093982C2314yes—
125#13093982C2314yescomplemented
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—22no—
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2314yescomplemented
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C4⋊C4×D47—22no—
135C4⋊C4×D47—22no—
136C4⋊C4×D47C2314yes—
137C4⋊C4×D47C2314yescomplemented
138C2×C22⋊Dic47—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147#13093957C2314yescomplemented
148#13093957C2314yescomplemented
149#13093957C2314yescomplemented
150#13093956C2314yescomplemented
151#13093956C2314yescomplemented
152#13093955C2314yescomplemented
153#13093946C2314yes—
154#13093946C2314yes—
155#13093945C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159C22⋊(C47⋊C8)C2314yescomplemented
160(C2×D47)⋊C8C2314yescomplemented
161(C2×D47)⋊C8C2314yescomplemented
162C22×D4×C47—21no—
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167#121×C47—22no—
168#121×C47C2314yes—
169#117×C47—22no—
170#117×C47C2314yescomplemented
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C42×C47—21no—
177#107×C47C2314yescomplemented
178#106×C47C2314yescomplemented
179#102×C47C2314yes—
180#102×C47C2314yes—
181C22⋊C8×C47C2314yescomplemented
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C23×D47—21no—
185C23×D47—24no—
186C23×D47—44no—
187C23×D47—82no—
188C23×D47—82no—
189C23×D47C2×D411yescharacteristic
190C23×D47C2×D411yescharacteristic
191C2×D4×C47—24no—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—82no—
196C2×D4×C47C2412yes—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—24no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—44no—
212C2×C22⋊D47—82no—
213C2×C22⋊D47—82no—
214C2×C22⋊D47C2×D414yes—
215C2×C22⋊D47C2×D414yes—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—24no—
220C22×Dic47—82no—
221C22×Dic47C2×D411yescharacteristic
222C22×Dic47C2×D411yescharacteristic
223D4×D47—28no—
224D4×D47—28no—
225D4×D47—48no—
226#10625350—216no—
227#10625350—28no—
228#10625350—28no—
229C2×D188—24no—
230C2×D188—22no—
231C2×D188—22no—
232C2×D188—21no—
233C2×D188—24no—
234C2×D188—82no—
235C2×D188C2×D414yes—
236C2×D188C2412yes—
237C2×C4×D47—22no—
238C2×C4×D47—22no—
239C2×C4×D47—24no—
240C2×C4×D47—24no—
241C2×C4×D47—82no—
242C2×C4×D47—82no—
243C2×C4×D47C2×D412yes—
244C2×C4×D47C2×D412yes—
245C2×C4×D47#4114yes—
246C2×C4×D47#4114yes—
247C2×C4×D47C2412yes—
248C2×C4×D47C2412yes—
249C2×Dic94—24no—
250C2×Dic94C2×D414yes—
251C2×C8×C47—22no—
252C2×C8×C47—22no—
253C2×C8×C47C2412yes—
254C2×C8×C47C2412yes—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47C2412yes—
259C4⋊C4×C47C2412yes—
260C4⋊C4×C47C2412yes—
261C22⋊C4×C47—24no—
262C22⋊C4×C47—24no—
263C42×C47—24no—
264C22⋊Dic47—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47—24no—
273C4⋊Dic47—21no—
274C4⋊Dic47C2412yes—
275C4⋊Dic47C2412yes—
276C4⋊Dic47C2412yes—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279C4×Dic47—24no—
280C4×Dic47—24no—
281C4×Dic47—24no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8C2412yes—
285C2×C47⋊C8C2412yes—
286#10625324—28no—
287C8×D47—28no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47—42no—
295C23×C47C22×D412yes—
296C23×C47C22×D411yescharacteristic
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—42no—
304C22×D47—42no—
305C22×D47—42no—
306C22×D47—48no—
307C22×D47—84no—
308C22×D47—84no—
309C22×D47—816no—
310C22×D47#12314yes—
311C22×D47C22×D412yes—
312C22×D47C22×D412yes—
313D4×C47—22no—
314D4×C47—22no—
315D4×C47—42no—
316D4×C47—84no—
317C2×C4×C47—22no—
318C2×C4×C47—24no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47C22×D412yes—
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C2×#4112yes—
330C2×C4×C47C2×#4112yes—
331C2×C4×C47C2511yescharacteristic
332C22⋊D47—28no—
333C22⋊D47—28no—
334C22⋊D47—48no—
335C22⋊D47—84no—
336C22⋊D47—84no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47—84no—
345C2×Dic47#12314yes—
346C2×Dic47C22×D412yes—
347C2×Dic47C22×D412yes—
348D188—28no—
349D188—22no—
350D188—22no—
351D188—42no—
352D188—84no—
353C4×D47—24no—
354C4×D47—22no—
355C4×D47—22no—
356C4×D47—84no—
357C4×D47—84no—
358C4×D47#12318yes—
359C4×D47C2×#4114yes—
360C4×D47C2×#4114yes—
361Dic94—28no—
362C8×C47—22no—
363C8×C47—22no—
364C47⋊C8—22no—
365C47⋊C8—22no—
366C2×#3096—471nomaximal, Sylow
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—44no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—84no—
375C22×C47C2×#12312yes—
376C22×C47#57612yes—
377C22×C47#57712yes—
378C22×C47C23×D411yescharacteristic
379C2×D47—28no—
380C2×D47—22no—
381C2×D47—22no—
382C2×D47—22no—
383C2×D47—22no—
384C2×D47—22no—
385C2×D47—44no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—816no—
390C2×D47—84no—
391C2×D47C2×#12314yes—
392C4×C47—22no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47C2×#12312yes—
397C4×C47C22×#4111yescharacteristic
398C4×C47C22×#4111yescharacteristic
399Dic47—22no—
400Dic47—42no—
401Dic47—42no—
402Dic47—42no—
403Dic47C2×#12314yes—
404C2×#535—471no—
405C2×#520—471no—
406#3096—4716no—
407C2×#481—471no—
408C2×#481—471no—
409C2×#482—471no—
410C2×#482—471no—
411C2×#482—471no—
412C2×#482D4711yescharacteristic, complemented
413C2×#480—471no—
414C2×#480—471no—
415C2×#428—471no—
416C2×#427—471no—
417C2×#418—471no—
418C22×#102—471no—
419C2×#408—471no—
420C2×C47—42no—
421C2×C47—82no—
422C2×C47#309614yescomplemented
423C2×C47C22×#12311yescharacteristic
424C2×C47C2×#57611yescharacteristic
425C2×C47C2×#57711yescharacteristic
426D47—24no—
427D47—42no—
428D47—82no—
429C22×#41—471no—
430C23×D4—471no—
431C22×M16—471no—
432C23×C8—471no—
433#535—478no—
434#535—944no—
435C2×#127—941no—
436C2×#124—941no—
437C2×#121—471no—
438C2×#121—471no—
439C2×#121—471no—
440C2×#121C2×D4711yescharacteristic
441C2×#120—941no—
442C2×#120—941no—
443#520—478no—
444#520—944no—
445C2×C4×Q8—941no—
446C2×C4×D4—941no—
447C2×C4×D4—941no—
448C2×C4×D4—941no—
449C2×#117—471no—
450C2×#117—471no—
451C2×#117—471no—
452C2×#117C2×D4711yescharacteristic, complemented
453C22×C4⋊C4—471no—
454C22×C4⋊C4—471no—
455C22×C4⋊C4—471no—
456#482—478no—
457#482—478no—
458#482—478no—
459#482C2×D4718yescomplemented
460#481—478no—
461#481—478no—
462#480—478no—
463#480—478no—
464#428—478no—
465#427—478no—
466C2×#107—471no—
467C2×#107—471no—
468C2×#107—471no—
469C2×#107C2×D4711yescharacteristic, complemented
470C2×#106—471no—
471C2×#106—471no—
472C2×#106—471no—
473C2×#106C2×D4711yescharacteristic, complemented
474#418—478no—
475C2×#102—471no—
476C2×#102—471no—
477C2×#102—471no—
478C2×#102—471no—
479C2×#102—471no—
480C2×#102—471no—
481C2×#102—478no—
482C2×#102C2×D4711yescharacteristic
483C2×#102C2×D4711yescharacteristic
484#408—478no—
485C2×C22⋊C8—471no—
486C2×C22⋊C8—471no—
487C2×C22⋊C8—471no—
488C2×C22⋊C8C2×D4711yescharacteristic, complemented
489C47C2×#309611yescharacteristic, complemented, Sylow
490C25—941no—
491C2×#41—474no—
492C2×#41—474no—
493C2×#41—944no—
494C2×#41—944no—
495C22×Q8—471no—
496C22×D4—21no—
497C22×D4—471no—
498C22×D4—471no—
499C22×D4—474no—
500C22×D4—471no—
501C22×D4—471no—
502C22×D4—941no—
503C22×D4—944no—
504C22×D4—944no—
505C22×D4—942no—
506C22×D4—941no—
507C22×D4—941no—
508C22×D4—941no—
509C22×D4C22×D4711yescharacteristic
510C23×C4—471no—
511C23×C4—471no—
512C23×C4—941no—
513C23×C4—941no—
514C23×C4—941no—
515C23×C4C22×D4711yescharacteristic
516C2×M16—474no—
517C2×M16—944no—
518C22×C8—471no—
519C22×C8—471no—
520C22×C8—474no—
521C22×C8—944no—
522C22×C8C22×D4711yescharacteristic
523C22×C8C22×D4711yescharacteristic
524#127—948no—
525#124—948no—
526#121—22no—
527#121—474no—
528#121—474no—
529#121—474no—
530#121—942no—
531#121—942no—
532#121—942no—
533#121C22×D4714yes—
534#120—948no—
535#120—948no—
536C4×Q8—948no—
537C4×D4—948no—
538C4×D4—948no—
539C4×D4—948no—
540#117—22no—
541#117—474no—
542#117—474no—
543#117—474no—
544#117—942no—
545#117—942no—
546#117—942no—
547#117C22×D4714yescomplemented
548C2×C4⋊C4—471no—
549C2×C4⋊C4—471no—
550C2×C4⋊C4—474no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—474no—
553C2×C4⋊C4—474no—
554C2×C4⋊C4—942no—
555C2×C4⋊C4—942no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4—941no—
558C2×C4⋊C4—941no—
559C2×C4⋊C4—942no—
560C2×C4⋊C4C22×D4711yescharacteristic
561C2×C4⋊C4C22×D4711yescharacteristic
562C2×C4⋊C4C22×D4711yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—941no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4—941no—
570C2×C22⋊C4—941no—
571C2×C42—21no—
572C2×C42—941no—
573C2×C42—941no—
574C2×C42—941no—
575#107—474no—
576#107—474no—
577#107—474no—
578#107C22×D4714yescomplemented
579#106—474no—
580#106—474no—
581#106—474no—
582#106C22×D4714yescomplemented
583#102—474no—
584#102—474no—
585#102—474no—
586#102—474no—
587#102—474no—
588#102—474no—
589#102C22×D4714yes—
590#102C22×D4714yes—
591C22⋊C8—474no—
592C22⋊C8—474no—
593C22⋊C8—474no—
594C22⋊C8C22×D4714yescomplemented
595C24—21no—
596C24—471no—
597C24—471no—
598C24—944no—
599C24—941no—
600C24—3762no—
601C24—3762no—
602C24—1884no—
603C24D4×D4711yescharacteristic
604#41—9416no—
605#41—948no—
606#41—948no—
607C2×Q8—474no—
608C2×Q8—944no—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—82no—
614C2×D4—474no—
615C2×D4—474no—
616C2×D4—474no—
617C2×D4—472no—
618C2×D4—944no—
619C2×D4—944no—
620C2×D4—948no—
621C2×D4—948no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—944no—
625C2×D4—944no—
626C2×D4—944no—
627C2×D4—941no—
628C2×D4—942no—
629C2×D4—942no—
630C2×D4—3762no—
631C2×D4—3762no—
632C2×D4—3762no—
633C2×D4—1888no—
634C2×D4—1884no—
635C2×D4C23×D4712yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—471no—
642C22×C4—472no—
643C22×C4—474no—
644C22×C4—474no—
645C22×C4—472no—
646C22×C4—471no—
647C22×C4—472no—
648C22×C4—472no—
649C22×C4—944no—
650C22×C4—944no—
651C22×C4—942no—
652C22×C4—942no—
653C22×C4—944no—
654C22×C4—941no—
655C22×C4—941no—
656C22×C4—941no—
657C22×C4—3762no—
658C22×C4—3762no—
659C22×C4—3762no—
660C22×C4D4×D4712yes—
661C22×C4D4×D4711yescharacteristic
662C22×C4C23×D4712yes—
663C22×C4C23×D4711yescharacteristic
664M16—948no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—472no—
668C2×C8—472no—
669C2×C8—948no—
670C2×C8—942no—
671C2×C8—942no—
672C2×C8C23×D4712yes—
673C2×C8C23×D4712yes—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—472no—
678C4⋊C4—472no—
679C4⋊C4—472no—
680C4⋊C4—944no—
681C4⋊C4—944no—
682C4⋊C4—941no—
683C4⋊C4—941no—
684C4⋊C4—944no—
685C4⋊C4—941no—
686C4⋊C4C23×D4712yes—
687C4⋊C4C23×D4712yes—
688C4⋊C4C23×D4712yes—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—944no—
692C22⋊C4—944no—
693C22⋊C4—944no—
694C22⋊C4—944no—
695C22⋊C4—944no—
696C22⋊C4—944no—
697C42—24no—
698C42—944no—
699C42—944no—
700C42—944no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—474no—
709C23—472no—
710C23—472no—
711C23—942no—
712C23—942no—
713C23—942no—
714C23—942no—
715C23—942no—
716C23—942no—
717C23—3764no—
718C23—3764no—
719C23—37616no—
720C23—1888no—
721C23—1882no—
722C23—1882no—
723C23—1882no—
724C23C2×D4×D4712yes—
725C23C2×D4×D4711yescharacteristic
726Q8—948no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—948no—
732D4—948no—
733D4—948no—
734D4—942no—
735D4—942no—
736D4—3764no—
737D4—3764no—
738D4—3764no—
739D4—1888no—
740D4—1882no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—474no—
752C2×C4—472no—
753C2×C4—478no—
754C2×C4—474no—
755C2×C4—474no—
756C2×C4—472no—
757C2×C4—942no—
758C2×C4—944no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—3764no—
765C2×C4—3764no—
766C2×C4—3764no—
767C2×C4—1882no—
768C2×C4—1882no—
769C2×C4—1882no—
770C2×C4C2×D4×D4712yes—
771C2×C4C2×D4×D4711yescharacteristic
772C2×C4#41×D4712yes—
773C2×C4#41×D4712yes—
774C2×C4C24×D4711yescharacteristic
775C8—22no—
776C8—22no—
777C8—942no—
778C8—942no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—474no—
788C22—942no—
789C22—942no—
790C22—948no—
791C22—942no—
792C22—942no—
793C22—942no—
794C22—37616no—
795C22—3764no—
796C22—1882no—
797C22—1882no—
798C22—1882no—
799C22—1884no—
800C22#123×D4712yes—
801C22#1568992712yes—
802C22#1568993012yes—
803C22C22×D4×D4711yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—474no—
809C4—942no—
810C4—1882no—
811C4—1882no—
812C4—1882no—
813C4#123×D4712yes—
814C4C2×#41×D4711yescharacteristic
815C4C2×#41×D4711yescharacteristic
816C2—42no—
817C2—82no—
818C2—944no—
819C2—3762no—
820C2—1882no—
821C2#2025334114yesdirect product factor
822C2C2×#123×D4711yescharacteristic
823C2C2×#1568992711yescharacteristic
824C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#482C2
socleC23×C47C22×D4
prime radicalC2×#15689689C2
hypercenterC2×#482D47
hypocenterC47C2×#3096
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#15689603C2semidirect
3. #20253341C2direct (N × H)
4. C2×#15689442C2semidirect
5. C2×#15689440C2semidirect
6. C2×#15689449C2semidirect
7. C2×#15689447C2semidirect
8. C2×#15689446C2semidirect
9. C2×#15689438C2semidirect
10. C2×#15689434C2semidirect
11. C2×#15689164C2semidirect
12. C2×#15689158C2semidirect
13. C2×#15689126C2semidirect
14. C2×#102×D47C2semidirect
15. C2×#15689088C2semidirect
16. C2×C47×#482C2semidirect
31. #15689603C22semidirect
38. C2×#13093982C22semidirect
39. C22×C4⋊Dic47C22semidirect
41. C2×C4⋊C4×D47C22semidirect
42. #15689449C22semidirect
43. #15689447C22semidirect
44. #15689446C22semidirect
45. #15689442C22semidirect
46. #15689440C22semidirect
47. #15689438C22semidirect
48. #15689434C22semidirect
49. #15689164C22semidirect
50. #15689158C22semidirect
51. C2×#13093957C22semidirect
52. C2×#13093957C22semidirect
53. C2×#13093957C22semidirect
54. C2×#13093956C22semidirect
55. C2×#13093956C22semidirect
56. C2×#13093955C22semidirect
57. #15689126C22semidirect
64. #102×D47C22semidirect
65. #15689088C22semidirect
66. C2×C22⋊(C47⋊C8)C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
70. C2×#117×C47C22semidirect
71. C47×#482C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
76. C2×C22⋊C8×C47C22semidirect
125. #13093982C23semidirect
131. C2×C4⋊Dic47C23semidirect
137. C4⋊C4×D47C23semidirect
147. #13093957C23semidirect
148. #13093957C23semidirect
149. #13093957C23semidirect
150. #13093956C23semidirect
151. #13093956C23semidirect
152. #13093955C23semidirect
159. C22⋊(C47⋊C8)C23semidirect
160. (C2×D47)⋊C8C23semidirect
161. (C2×D47)⋊C8C23semidirect
170. #117×C47C23semidirect
177. #107×C47C23semidirect
178. #106×C47C23semidirect
181. C22⋊C8×C47C23semidirect
412. C2×#482D47semidirect
422. C2×C47#3096semidirect
452. C2×#117C2×D47semidirect
459. #482C2×D47semidirect
469. C2×#107C2×D47semidirect
473. C2×#106C2×D47semidirect
488. C2×C22⋊C8C2×D47semidirect
489. C47C2×#3096semidirect
547. #117C22×D47semidirect
578. #107C22×D47semidirect
582. #106C22×D47semidirect
594. C22⋊C8C22×D47semidirect
821. C2#20253341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896892
C2×#156896032
#202533412
C2×#156894422
C2×#156894402
C2×#156894492
C2×#156894472
C2×#156894462
C2×#156894382
C2×#156894342
C2×#156891642
C2×#156891582
C2×#156891262
C2×#102×D472
C2×#156890882
C2×C47×#4822
C2×#309647