Finite Group Databasebeta

← C2×#20254206 #27086882

Subgroups — C2×#20254206 #27086882

Order 12032.

2686 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689635C211yesmaximal, characteristic, complemented
2C2×#121×D47C211yesmaximal, characteristic, complemented
3#20254206C2116yesmaximal, direct product factor
4C2×#15689447C211yesmaximal, characteristic, complemented
5C2×#15689455C211yesmaximal, characteristic, complemented
6C2×#15689438C211yesmaximal, characteristic, complemented
7C2×#15689377C211yesmaximal, characteristic, complemented
8C2×#15689375C211yesmaximal, characteristic, complemented
9C2×#15689370C211yesmaximal, characteristic, complemented
10C2×#15689368C211yesmaximal, characteristic, complemented
11C2×#15689270C211yesmaximal, characteristic, complemented
12C2×#15689266C211yesmaximal, characteristic, complemented
13C2×#15689275C211yesmaximal, characteristic, complemented
14C2×#15689258C211yesmaximal, characteristic, complemented
15C2×#15689085C211yesmaximal, characteristic, complemented
16C2×C47×#482C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic, complemented
18C22×D4×D47—21no—
19C22×D4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C22×#10625325C2211yescharacteristic, complemented
22C22×#10625335C2211yescharacteristic, complemented
23C22×D376C2211yescharacteristic, complemented
24C22×#10625334C2211yescharacteristic, complemented
25C22×#10625324C2211yescharacteristic, complemented
26C22×#10625324C2211yescharacteristic, complemented
27#15689635—24no—
28#15689635C2218yescomplemented
29C2×#13094008—21no—
30C2×#13094004C2211yescharacteristic
31C2×#13094004C2211yescharacteristic, complemented
32C2×#13093999C2211yescharacteristic
33C2×#13093999C2211yescharacteristic
34C2×#13093999C2211yescharacteristic, complemented
35C2×#13093998C2211yescharacteristic
36C2×#13093997—21no—
37C2×#13093996—21no—
38C2×#13093995C2211yescharacteristic
39#121×D47—24no—
40#121×D47C2218yescomplemented
41C2×#13093994—21no—
42C2×C4×D188—21no—
43C2×C4×D188—21no—
44C2×C4⋊C4×D47C2211yescharacteristic
45C2×C22⋊C4×D47—21no—
46#15689455C2218yescomplemented
47#15689447C2218yescomplemented
48#15689438C2218yescomplemented
49#15689377C2218yescomplemented
50#15689375C2218yescomplemented
51#15689370C2218yescomplemented
52#15689368C2218yescomplemented
53#15689275C2218yescomplemented
54#15689270C2218yescomplemented
55#15689266C2218yescomplemented
56#15689258C2218yescomplemented
57C2×#13093957C2211yescharacteristic, complemented
58C2×#13093955C2211yescharacteristic, complemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093947C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic, complemented
62C2×#13093944C2211yescharacteristic, complemented
63C2×#13093944C2211yescharacteristic, complemented
64C2×#13093944C2211yescharacteristic, complemented
65#15689085C2218yescomplemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×#121×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic, complemented
71C47×#482C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C24×D47D411yescharacteristic
79C2×#10625350—22no—
80C2×#10625350—42no—
81C2×#10625350—42no—
82C2×#10625350C2314yescomplemented
83C22×Dic94C2311yescharacteristic
84C22×D188—21no—
85C22×D188—21no—
86C22×D188—21no—
87C22×D188C2311yescharacteristic
88C22×D188C2311yescharacteristic
89C22×C22⋊D47—21no—
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C2×D4×D47—28no—
94C2×D4×D47—22no—
95C2×D4×D47—42no—
96C2×D4×D47—42no—
97C2×D4×D47—48no—
98C2×D4×D47C2314yes—
99C23×Dic47D411yescharacteristic
100C22×C4×D47—21no—
101C22×C4×D47—21no—
102C22×C4×D47—42no—
103C22×C4×D47—42no—
104C22×C4×D47D411yescharacteristic
105C22×C4×D47D411yescharacteristic
106C22×C4×D47D414yes—
107C22×C4×D47C2311yescharacteristic
108C22×C4×D47C2311yescharacteristic
109C22×C4×D47C2314yes—
110C2×#10625325—42no—
111C2×#10625325C2314yescomplemented
112C2×#10625335—42no—
113C2×#10625335C2314yescomplemented
114C2×D376—42no—
115C2×D376C2314yescomplemented
116C2×#10625334—42no—
117C2×#10625334C2314yescomplemented
118C2×#10625324—42no—
119C2×#10625324—42no—
120C2×#10625324C2314yescomplemented
121C2×#10625324C2314yescomplemented
122C22×C47⋊C8C2311yescharacteristic
123C22×C47⋊C8C2311yescharacteristic
124#13094008—28no—
125#13094004—22no—
126#13094004—22no—
127#13094004C2314yes—
128#13094004C2314yescomplemented
129#13093999—22no—
130#13093999—22no—
131#13093999—22no—
132#13093999C2314yes—
133#13093999C2314yes—
134#13093999C2314yescomplemented
135#13093998—22no—
136#13093998C2314yes—
137#13093997—28no—
138#13093996—28no—
139#13093995—22no—
140#13093995C2314yes—
141#13093994—28no—
142C4×D188—28no—
143C4×D188—28no—
144C2×C4⋊Dic47—21no—
145C2×C4⋊Dic47—21no—
146C2×C4⋊Dic47C2311yescharacteristic
147C2×Dic47⋊C4—21no—
148C4⋊C4×D47—22no—
149C4⋊C4×D47C2314yes—
150C2×C22⋊Dic47—21no—
151C2×(C2×D47)⋊C4—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—21no—
156C2×(C2×D47)⋊C4—21no—
157C22⋊C4×D47—28no—
158#13093957C2314yescomplemented
159#13093955C2314yescomplemented
160#13093949C2314yescomplemented
161#13093947C2314yescomplemented
162#13093946C2314yescomplemented
163#13093944C2314yescomplemented
164#13093944C2314yescomplemented
165#13093944C2314yescomplemented
166C22⋊(C47⋊C8)C2314yescomplemented
167(C2×D47)⋊C8C2314yes—
168(C2×D47)⋊C8C2314yes—
169C22×D4×C47—21no—
170C22×D4×C47C2311yescharacteristic
171C23×C4×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174#121×C47—22no—
175#121×C47C2314yes—
176#117×C47—22no—
177#117×C47C2314yescomplemented
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47—21no—
183C2×C42×C47—21no—
184#107×C47C2314yescomplemented
185#106×C47C2314yescomplemented
186#102×C47C2314yescomplemented
187#102×C47C2314yescomplemented
188C22⋊C8×C47C2314yescomplemented
189C24×C47—21no—
190C24×C47C2×D411yescharacteristic
191C23×D47—24no—
192C23×D47—21no—
193C23×D47—21no—
194C23×D47—24no—
195C23×D47—42no—
196C23×D47—42no—
197C23×D47—44no—
198C23×D47—44no—
199C23×D47—44no—
200C23×D47C2×D411yescharacteristic
201C23×D47C2×D411yescharacteristic
202C23×D47C2×D414yes—
203C2×D4×C47—24no—
204C2×D4×C47—21no—
205C2×D4×C47—22no—
206C2×D4×C47—22no—
207C2×D4×C47—44no—
208C2×D4×C47C2412yes—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2411yescharacteristic
218C2×C22⋊D47—24no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—24no—
222C2×C22⋊D47—44no—
223C2×C22⋊D47—44no—
224C2×C22⋊D47—44no—
225C2×C22⋊D47—44no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—42no—
229C22×Dic47C2×D411yescharacteristic
230C22×Dic47C2×D411yescharacteristic
231C22×Dic47C2×D414yes—
232D4×D47—44no—
233D4×D47—44no—
234D4×D47—48no—
235D4×D47—432no—
236#10625350—44no—
237#10625350—44no—
238#10625350—48no—
239C2×D188—22no—
240C2×D188—22no—
241C2×D188—22no—
242C2×D188—22no—
243C2×D188—24no—
244C2×D188—24no—
245C2×D188—24no—
246C2×D188—21no—
247C2×D188—21no—
248C2×D188—44no—
249C2×D188—44no—
250C2×D188—44no—
251C2×D188C2412yes—
252C2×D188C2412yes—
253C2×C4×D47—22no—
254C2×C4×D47—22no—
255C2×C4×D47—22no—
256C2×C4×D47—22no—
257C2×C4×D47—24no—
258C2×C4×D47—24no—
259C2×C4×D47—48no—
260C2×C4×D47—44no—
261C2×C4×D47—44no—
262C2×C4×D47—42no—
263C2×C4×D47—42no—
264C2×C4×D47—44no—
265C2×C4×D47—44no—
266C2×C4×D47C2×D412yes—
267C2×C4×D47C2×D412yes—
268C2×C4×D47C2×D414yes—
269C2×C4×D47C2×D414yes—
270C2×C4×D47C2412yes—
271C2×C4×D47C2412yes—
272C2×Dic94—22no—
273C2×Dic94—22no—
274C2×Dic94—21no—
275C2×Dic94C2412yes—
276C2×C8×C47—22no—
277C2×C8×C47—22no—
278C2×C8×C47C2412yes—
279C2×C8×C47C2412yes—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47C2412yes—
284C4⋊C4×C47C2412yes—
285C4⋊C4×C47C2412yes—
286C22⋊C4×C47—24no—
287C22⋊C4×C47—24no—
288C42×C47—24no—
289C22⋊Dic47—24no—
290#10625335—44no—
291#10625334—44no—
292(C2×D47)⋊C4—24no—
293(C2×D47)⋊C4—24no—
294(C2×D47)⋊C4—24no—
295(C2×D47)⋊C4—24no—
296(C2×D47)⋊C4—24no—
297(C2×D47)⋊C4—24no—
298C4⋊Dic47—21no—
299C4⋊Dic47—24no—
300C4⋊Dic47—24no—
301C4⋊Dic47C2412yes—
302Dic47⋊C4—24no—
303C2×C47⋊C8—22no—
304C2×C47⋊C8—22no—
305C2×C47⋊C8C2412yes—
306C2×C47⋊C8C2412yes—
307D376—44no—
308#10625325—44no—
309#10625324—44no—
310#10625324—44no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—42no—
316C23×C47—42no—
317C23×C47—42no—
318C23×C47C22×D412yes—
319C23×C47C22×D411yescharacteristic
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—28no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—44no—
329C22×D47—44no—
330C22×D47—416no—
331C22×D47—48no—
332C22×D47—48no—
333C22×D47—42no—
334C22×D47—42no—
335C22×D47—42no—
336C22×D47—42no—
337C22×D47—42no—
338C22×D47—42no—
339C22×D47—48no—
340C22×D47—816no—
341C22×D47AGL(1,ℤ/8)14yes—
342C22×D47C22×D412yes—
343C22×D47C22×D412yes—
344D4×C47—22no—
345D4×C47—22no—
346D4×C47—48no—
347D4×C47—42no—
348C2×C4×C47—22no—
349C2×C4×C47—24no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—42no—
356C2×C4×C47—42no—
357C2×C4×C47—42no—
358C2×C4×C47C22×D412yes—
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47H(5,𝔽2)12yes—
361C2×C4×C47H(5,𝔽2)12yes—
362C2×C4×C47C2511yescharacteristic
363C22⋊D47—48no—
364C22⋊D47—48no—
365C22⋊D47—48no—
366C22⋊D47—48no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—44no—
372C2×Dic47—42no—
373C2×Dic47—42no—
374C2×Dic47C22×D412yes—
375C2×Dic47C22×D412yes—
376D188—22no—
377D188—22no—
378D188—22no—
379D188—22no—
380D188—48no—
381D188—48no—
382D188—48no—
383D188—42no—
384D188—42no—
385C4×D47—24no—
386C4×D47—24no—
387C4×D47—22no—
388C4×D47—22no—
389C4×D47—22no—
390C4×D47—22no—
391C4×D47—44no—
392C4×D47—44no—
393C4×D47—48no—
394C4×D47—48no—
395Dic94—22no—
396Dic94—22no—
397Dic94—42no—
398C8×C47—22no—
399C8×C47—22no—
400C47⋊C8—22no—
401C47⋊C8—22no—
402C2×#3194—471nomaximal, Sylow
403C22×C47—22no—
404C22×C47—22no—
405C22×C47—22no—
406C22×C47—44no—
407C22×C47—42no—
408C22×C47—42no—
409C22×C47—42no—
410C22×C47—84no—
411C22×C47#53412yes—
412C22×C47C2×AGL(1,ℤ/8)12yes—
413C22×C47#57512yes—
414C22×C47C23×D411yescharacteristic
415C2×D47—22no—
416C2×D47—28no—
417C2×D47—22no—
418C2×D47—22no—
419C2×D47—22no—
420C2×D47—22no—
421C2×D47—416no—
422C2×D47—44no—
423C2×D47—42no—
424C2×D47—42no—
425C2×D47—42no—
426C2×D47—42no—
427C2×D47—42no—
428C2×D47—42no—
429C2×D47—816no—
430C2×D47—84no—
431C2×D47—84no—
432C2×D47C2×AGL(1,ℤ/8)14yes—
433C4×C47—22no—
434C4×C47—42no—
435C4×C47—42no—
436C4×C47—42no—
437C4×C47#53412yes—
438C4×C47C2×H(5,𝔽2)11yescharacteristic
439C4×C47C2×H(5,𝔽2)11yescharacteristic
440Dic47—22no—
441Dic47—22no—
442Dic47—42no—
443Dic47—42no—
444C2×#525—471no—
445C22×#121—471no—
446#3194—4716no—
447C2×#482—471no—
448C2×#482D4711yescharacteristic, complemented
449C2×#483—471no—
450C2×#480—471no—
451C2×#469—471no—
452C2×#469—471no—
453C2×#468—471no—
454C2×#468—471no—
455C2×#449—471no—
456C2×#449—471no—
457C2×#450—471no—
458C2×#447—471no—
459C2×#407—471no—
460C2×C47—42no—
461C2×C47—82no—
462C2×C47#319414yescomplemented
463C2×C47C2×#53411yescharacteristic
464C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
465C2×C47C2×#57511yescharacteristic
466D47—24no—
467D47—42no—
468D47—82no—
469D47—82no—
470C22×#41—471no—
471C23×D4—471no—
472C23×D4—941no—
473C24×C4—471no—
474C22×SD16—471no—
475C22×SD16—471no—
476C22×D8—471no—
477C22×D8—471no—
478C22×M16—471no—
479C22×M16—471no—
480#525—478no—
481#525—944no—
482C2×#123—941no—
483C2×C22⋊Q8—471no—
484C2×C22⋊Q8—471no—
485C2×#121—471no—
486C2×#121—471no—
487C2×#121—478no—
488C2×#121—471no—
489C2×#121—471no—
490C2×#121—471no—
491C2×#121—941no—
492C2×#121—944no—
493C2×#121—941no—
494C2×#121C2×D4711yescharacteristic
495C2×#120—941no—
496C2×C4×D4—941no—
497C2×C4×D4—941no—
498C2×#117C2×D4711yescharacteristic, complemented
499C22×C4⋊C4—471no—
500C22×C22⋊C4—941no—
501#483—478no—
502#482—478no—
503#482C2×D4718yescomplemented
504#480—478no—
505#469—478no—
506#469—478no—
507#468—478no—
508#468—478no—
509#450—478no—
510#449—478no—
511#449—478no—
512#447—478no—
513C2×#107—471no—
514C2×#107C2×D4711yescharacteristic, complemented
515C2×#106—471no—
516C2×#106C2×D4711yescharacteristic, complemented
517C2×#103—471no—
518C2×#103—471no—
519C2×#102—471no—
520C2×#102—471no—
521C2×#102—471no—
522C2×#102—471no—
523C2×#102C2×D4711yescharacteristic, complemented
524C2×#102C2×D4711yescharacteristic, complemented
525#407—478no—
526C2×C22⋊C8—471no—
527C2×C22⋊C8—471no—
528C2×C22⋊C8—471no—
529C2×C22⋊C8C2×D4711yescharacteristic, complemented
530C47C2×#319411yescharacteristic, complemented, Sylow
531C25—471no—
532C25—941no—
533C2×#41—474no—
534C2×#41—942no—
535C2×#41—1882no—
536C2×#41—1882no—
537C22×Q8—471no—
538C22×D4—21no—
539C22×D4—474no—
540C22×D4—471no—
541C22×D4—471no—
542C22×D4—941no—
543C22×D4—941no—
544C22×D4—941no—
545C22×D4—942no—
546C22×D4—941no—
547C22×D4—948no—
548C22×D4—941no—
549C22×D4—941no—
550C22×D4—941no—
551C22×D4—1882no—
552C22×D4—1882no—
553C22×D4—1888no—
554C22×D4C22×D4711yescharacteristic
555C23×C4—471no—
556C23×C4—471no—
557C23×C4—471no—
558C23×C4—471no—
559C23×C4—471no—
560C23×C4—474no—
561C23×C4—474no—
562C23×C4—941no—
563C23×C4—941no—
564C23×C4—1882no—
565C23×C4—1882no—
566C23×C4C22×D4711yescharacteristic
567C2×SD16—474no—
568C2×SD16—474no—
569C2×SD16—1882no—
570C2×SD16—1882no—
571C2×D8—474no—
572C2×D8—474no—
573C2×D8—1882no—
574C2×D8—1882no—
575C2×M16—474no—
576C2×M16—474no—
577C2×M16—1882no—
578C2×M16—1882no—
579C22×C8—471no—
580C22×C8—471no—
581C22×C8C22×D4711yescharacteristic
582C22×C8C22×D4711yescharacteristic
583#123—948no—
584C22⋊Q8—474no—
585C22⋊Q8—474no—
586C22⋊Q8—942no—
587C22⋊Q8—942no—
588#121—22no—
589#121—474no—
590#121—474no—
591#121—474no—
592#121—474no—
593#121—474no—
594#121—948no—
595#121—942no—
596#121—942no—
597#121—942no—
598#121—942no—
599#121—948no—
600#121—942no—
601#121C22×D4714yes—
602#120—948no—
603C4×D4—948no—
604C4×D4—948no—
605#117—22no—
606#117C22×D4714yescomplemented
607C2×C4⋊C4—471no—
608C2×C4⋊C4—474no—
609C2×C4⋊C4—942no—
610C2×C4⋊C4—941no—
611C2×C4⋊C4—941no—
612C2×C4⋊C4—941no—
613C2×C4⋊C4C22×D4711yescharacteristic
614C2×C4⋊C4C22×D4711yescharacteristic
615C2×C4⋊C4C22×D4711yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—948no—
619C2×C22⋊C4—941no—
620C2×C22⋊C4—941no—
621C2×C22⋊C4—941no—
622C2×C22⋊C4—941no—
623C2×C22⋊C4—941no—
624C2×C22⋊C4—941no—
625C2×C22⋊C4—941no—
626C2×C42—21no—
627#107—474no—
628#107C22×D4714yescomplemented
629#106—474no—
630#106C22×D4714yescomplemented
631#103—474no—
632#103—474no—
633#102—474no—
634#102—474no—
635#102—474no—
636#102—474no—
637#102C22×D4714yescomplemented
638#102C22×D4714yescomplemented
639C22⋊C8—474no—
640C22⋊C8—474no—
641C22⋊C8—474no—
642C22⋊C8C22×D4714yescomplemented
643C24—21no—
644C24—471no—
645C24—471no—
646C24—474no—
647C24—944no—
648C24—944no—
649C24—941no—
650C24—941no—
651C24—1882no—
652C24—1882no—
653C24—1884no—
654C24—1884no—
655C24—1884no—
656C24D4×D4711yescharacteristic
657#41—1884no—
658#41—1884no—
659#41—1888no—
660C2×Q8—472no—
661C2×Q8—941no—
662C2×Q8—942no—
663C2×Q8—942no—
664C2×D4—24no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—44no—
669C2×D4—472no—
670C2×D4—472no—
671C2×D4—944no—
672C2×D4—944no—
673C2×D4—944no—
674C2×D4—944no—
675C2×D4—944no—
676C2×D4—944no—
677C2×D4—944no—
678C2×D4—941no—
679C2×D4—941no—
680C2×D4—942no—
681C2×D4—942no—
682C2×D4—942no—
683C2×D4—942no—
684C2×D4—1884no—
685C2×D4—1884no—
686C2×D4—1884no—
687C2×D4—1884no—
688C2×D4—1884no—
689C2×D4—1888no—
690C2×D4—1884no—
691C2×D4—18832no—
692C2×D4—1884no—
693C2×D4—1884no—
694C2×D4—1884no—
695C2×D4C23×D4712yes—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—471no—
702C22×C4—471no—
703C22×C4—474no—
704C22×C4—472no—
705C22×C4—472no—
706C22×C4—472no—
707C22×C4—472no—
708C22×C4—474no—
709C22×C4—474no—
710C22×C4—944no—
711C22×C4—942no—
712C22×C4—942no—
713C22×C4—942no—
714C22×C4—942no—
715C22×C4—941no—
716C22×C4—941no—
717C22×C4—944no—
718C22×C4—1888no—
719C22×C4—1884no—
720C22×C4—1884no—
721C22×C4—1882no—
722C22×C4—1882no—
723C22×C4—1884no—
724C22×C4—1884no—
725C22×C4—1882no—
726C22×C4D4×D4712yes—
727C22×C4D4×D4711yescharacteristic
728C22×C4C23×D4712yes—
729C22×C4C23×D4711yescharacteristic
730SD16—1884no—
731SD16—1884no—
732D8—1884no—
733D8—1884no—
734M16—1884no—
735M16—1884no—
736C2×C8—22no—
737C2×C8—22no—
738C2×C8—472no—
739C2×C8—472no—
740C2×C8—942no—
741C2×C8—942no—
742C2×C8C23×D4712yes—
743C2×C8C23×D4712yes—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—472no—
748C4⋊C4—944no—
749C4⋊C4—944no—
750C4⋊C4—944no—
751C4⋊C4—941no—
752C4⋊C4C23×D4712yes—
753C4⋊C4C23×D4712yes—
754C4⋊C4C23×D4712yes—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—944no—
758C22⋊C4—944no—
759C22⋊C4—944no—
760C22⋊C4—944no—
761C22⋊C4—944no—
762C22⋊C4—944no—
763C22⋊C4—944no—
764C42—24no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—474no—
773C23—472no—
774C23—472no—
775C23—948no—
776C23—942no—
777C23—942no—
778C23—942no—
779C23—942no—
780C23—942no—
781C23—942no—
782C23—942no—
783C23—37616no—
784C23—1884no—
785C23—1884no—
786C23—1888no—
787C23—1888no—
788C23—1888no—
789C23—18816no—
790C23—1882no—
791C23—1882no—
792C23—1882no—
793C23—1882no—
794C23—1882no—
795C23—1882no—
796C23C2×D4×D4712yes—
797C23C2×D4×D4711yescharacteristic
798Q8—942no—
799Q8—942no—
800Q8—1882no—
801D4—22no—
802D4—22no—
803D4—48no—
804D4—42no—
805D4—942no—
806D4—942no—
807D4—942no—
808D4—942no—
809D4—1888no—
810D4—1888no—
811D4—1888no—
812D4—1888no—
813D4—1888no—
814D4—1888no—
815D4—1888no—
816D4—1882no—
817D4—1882no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—472no—
829C2×C4—472no—
830C2×C4—942no—
831C2×C4—942no—
832C2×C4—944no—
833C2×C4—944no—
834C2×C4—942no—
835C2×C4—942no—
836C2×C4—942no—
837C2×C4—942no—
838C2×C4—942no—
839C2×C4—942no—
840C2×C4—1884no—
841C2×C4—1884no—
842C2×C4—1888no—
843C2×C4—1888no—
844C2×C4—1884no—
845C2×C4—1882no—
846C2×C4—1882no—
847C2×C4C2×D4×D4712yes—
848C2×C4C2×D4×D4711yescharacteristic
849C2×C4#1309407012yes—
850C2×C4#1309407012yes—
851C2×C4C24×D4711yescharacteristic
852C8—22no—
853C8—22no—
854C8—942no—
855C8—942no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—84no—
864C22—474no—
865C22—942no—
866C22—942no—
867C22—948no—
868C22—942no—
869C22—942no—
870C22—942no—
871C22—37616no—
872C22—3764no—
873C22—3764no—
874C22—18816no—
875C22—1882no—
876C22—1882no—
877C22—1882no—
878C22—1882no—
879C22—1882no—
880C22—1882no—
881C22—1884no—
882C22#1568968412yes—
883C22AGL(1,ℤ/8)×D4712yes—
884C22#1568992012yes—
885C22C22×D4×D4711yescharacteristic
886C4—22no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—942no—
891C4—942no—
892C4—1882no—
893C4—1882no—
894C4#1568968412yes—
895C4C2×#1309407011yescharacteristic
896C4C2×#1309407011yescharacteristic
897C2—42no—
898C2—82no—
899C2—944no—
900C2—3762no—
901C2—3762no—
902C2—1882no—
903C2#2025420614yesdirect product factor
904C2C2×#1568968411yescharacteristic
905C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
906C2C2×#1568992011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#482C2
socleC23×C47C22×D4
hypercenterC2×#482D47
hypocenterC47C2×#3194
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
1. C2×#15689635C2semidirect
2. C2×#121×D47C2semidirect
3. #20254206C2direct (N × H)
4. C2×#15689447C2semidirect
5. C2×#15689455C2semidirect
6. C2×#15689438C2semidirect
7. C2×#15689377C2semidirect
8. C2×#15689375C2semidirect
9. C2×#15689370C2semidirect
10. C2×#15689368C2semidirect
11. C2×#15689270C2semidirect
12. C2×#15689266C2semidirect
13. C2×#15689275C2semidirect
14. C2×#15689258C2semidirect
15. C2×#15689085C2semidirect
16. C2×C47×#482C2semidirect
17. C22×#10625350C22semidirect
21. C22×#10625325C22semidirect
22. C22×#10625335C22semidirect
23. C22×D376C22semidirect
24. C22×#10625334C22semidirect
25. C22×#10625324C22semidirect
26. C22×#10625324C22semidirect
28. #15689635C22semidirect
31. C2×#13094004C22semidirect
34. C2×#13093999C22semidirect
40. #121×D47C22semidirect
46. #15689455C22semidirect
47. #15689447C22semidirect
48. #15689438C22semidirect
49. #15689377C22semidirect
50. #15689375C22semidirect
51. #15689370C22semidirect
52. #15689368C22semidirect
53. #15689275C22semidirect
54. #15689270C22semidirect
55. #15689266C22semidirect
56. #15689258C22semidirect
57. C2×#13093957C22semidirect
58. C2×#13093955C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093947C22semidirect
61. C2×#13093946C22semidirect
62. C2×#13093944C22semidirect
63. C2×#13093944C22semidirect
64. C2×#13093944C22semidirect
65. #15689085C22semidirect
66. C2×C22⋊(C47⋊C8)C22semidirect
70. C2×#117×C47C22semidirect
71. C47×#482C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#102×C47C22semidirect
75. C2×#102×C47C22semidirect
76. C2×C22⋊C8×C47C22semidirect
82. C2×#10625350C23semidirect
111. C2×#10625325C23semidirect
113. C2×#10625335C23semidirect
115. C2×D376C23semidirect
117. C2×#10625334C23semidirect
120. C2×#10625324C23semidirect
121. C2×#10625324C23semidirect
128. #13094004C23semidirect
134. #13093999C23semidirect
158. #13093957C23semidirect
159. #13093955C23semidirect
160. #13093949C23semidirect
161. #13093947C23semidirect
162. #13093946C23semidirect
163. #13093944C23semidirect
164. #13093944C23semidirect
165. #13093944C23semidirect
166. C22⋊(C47⋊C8)C23semidirect
177. #117×C47C23semidirect
184. #107×C47C23semidirect
185. #106×C47C23semidirect
186. #102×C47C23semidirect
187. #102×C47C23semidirect
188. C22⋊C8×C47C23semidirect
448. C2×#482D47semidirect
462. C2×C47#3194semidirect
498. C2×#117C2×D47semidirect
503. #482C2×D47semidirect
514. C2×#107C2×D47semidirect
516. C2×#106C2×D47semidirect
523. C2×#102C2×D47semidirect
524. C2×#102C2×D47semidirect
529. C2×C22⋊C8C2×D47semidirect
530. C47C2×#3194semidirect
606. #117C22×D47semidirect
628. #107C22×D47semidirect
630. #106C22×D47semidirect
637. #102C22×D47semidirect
638. #102C22×D47semidirect
642. C22⋊C8C22×D47semidirect
903. C2#20254206direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896352
C2×#121×D472
#202542062
C2×#156894472
C2×#156894552
C2×#156894382
C2×#156893772
C2×#156893752
C2×#156893702
C2×#156893682
C2×#156892702
C2×#156892662
C2×#156892752
C2×#156892582
C2×#156890852
C2×C47×#4822
C2×#319447