Finite Group Databasebeta

← C2×#20255544 #27092964

Subgroups — C2×#20255544 #27092964

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
2#20255544C2116yesmaximal, direct product factor
3C2×#15689482C211yesmaximal, characteristic, complemented
4C2×#15689461C211yesmaximal, characteristic, complemented
5C2×#15689444C211yesmaximal, characteristic, complemented
6C2×#15689403C211yesmaximal, characteristic, complemented
7C2×#15689371C211yesmaximal, characteristic, complemented
8C2×#15689357C211yesmaximal, characteristic, complemented
9C2×#15689335C211yesmaximal, characteristic, complemented
10C2×#15689268C211yesmaximal, characteristic, complemented
11C2×#15689257C211yesmaximal, characteristic, complemented
12C2×#15689233C211yesmaximal, characteristic, complemented
13C2×#15689195C211yesmaximal, characteristic, complemented
14C2×#15689128C211yesmaximal, characteristic, complemented
15C2×#15689119C211yesmaximal, characteristic, complemented
16C2×C47×#546C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic, complemented
18C22×#10625334C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20C22×#10625329C2211yescharacteristic
21C23×C47⋊C8C2211yescharacteristic, complemented
22#15689838—24no—
23#15689838C2218yescomplemented
24C2×#13094024C2211yescharacteristic, complemented
25C2×#13094010—21no—
26C2×#13094010—21no—
27C2×#13093998C2211yescharacteristic
28C2×#13093998C2211yescharacteristic, complemented
29C2×#13093995—21no—
30C2×C4×D188C2211yescharacteristic, complemented
31C2×#13093983C2211yescharacteristic
32C2×#13093983C2211yescharacteristic, complemented
33C2×#13093982—21no—
34#15689482C2218yescomplemented
35#15689461C2218yescomplemented
36#15689444C2218yescomplemented
37#15689403C2218yescomplemented
38#15689371C2218yescomplemented
39#15689357C2218yescomplemented
40#15689335C2218yescomplemented
41#15689268C2218yescomplemented
42#15689257C2218yescomplemented
43#15689233C2218yescomplemented
44#15689195C2218yescomplemented
45C2×#13093957C2211yescharacteristic, complemented
46C2×#13093957C2211yescharacteristic, complemented
47C2×#13093955C2211yescharacteristic, complemented
48C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
49#15689128C2218yescomplemented
50#15689119C2218yescomplemented
51C2×#13093948C2211yescharacteristic, complemented
52C2×#13093948C2211yescharacteristic, complemented
53C2×#13093948C2211yescharacteristic, complemented
54C2×#13093945C2211yescharacteristic
55C2×#13093945C2211yescharacteristic
56C2×#13093945C2211yescharacteristic
57C2×#13093945C2211yescharacteristic
58C2×#13093945C2211yescharacteristic
59C2×#13093945C2211yescharacteristic
60C2×#13093944C2211yescharacteristic, complemented
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
63C2×#13093935C2211yescharacteristic, complemented
64C22×#41×C47C2211yescharacteristic
65C23×D4×C47C2211yescharacteristic
66C47×#546—24no—
67C47×#546C2218yescomplemented
68C2×#124×C47C2211yescharacteristic
69C2×#123×C47—21no—
70C2×C22⋊Q8×C47C2211yescharacteristic
71C2×#121×C47—21no—
72C2×#121×C47C2211yescharacteristic
73C2×#120×C47—21no—
74C2×C4×D4×C47C2211yescharacteristic
75C2×C4×D4×C47C2211yescharacteristic
76C22×C22⋊C4×C47—21no—
77C22×Dic94—21no—
78C22×D188C2311yescharacteristic
79C22×C22⋊D47—21no—
80C22×C22⋊D47—21no—
81C22×C4×D47—21no—
82C2×#10625336—42no—
83C2×#10625336C2314yescomplemented
84C2×#10625334—24no—
85C2×#10625334—42no—
86C2×#10625334C2314yes—
87C2×#10625334C2314yes—
88C2×#10625329—42no—
89C2×#10625329C2314yes—
90C22×C47⋊C8—42no—
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2314yescomplemented
96#13094024—22no—
97#13094024C2314yescomplemented
98#13094010—28no—
99#13094010—28no—
100#13093998—22no—
101#13093998—22no—
102#13093998C2314yes—
103#13093998C2314yescomplemented
104#13093995—28no—
105C4×D188—22no—
106C4×D188C2314yescomplemented
107#13093983—22no—
108#13093983—22no—
109#13093983C2314yes—
110#13093983C2314yescomplemented
111#13093982—28no—
112C2×C4⋊Dic47—21no—
113C2×C4⋊Dic47C2311yescharacteristic
114C2×C4⋊Dic47C2311yescharacteristic
115C2×C4⋊Dic47C2311yescharacteristic
116C2×C22⋊Dic47—21no—
117C2×C22⋊Dic47—21no—
118C2×(C2×D47)⋊C4—21no—
119C2×(C2×D47)⋊C4—21no—
120C2×(C2×D47)⋊C4—21no—
121C2×C4×Dic47—21no—
122C2×C4×Dic47—21no—
123#13093957C2314yescomplemented
124#13093957C2314yescomplemented
125#13093955C2314yescomplemented
126C4⋊(C47⋊C8)C2314yescomplemented
127#13093948C2314yescomplemented
128#13093948C2314yescomplemented
129#13093948C2314yescomplemented
130#13093945C2314yes—
131#13093945C2314yes—
132#13093945C2314yes—
133#13093945C2314yes—
134#13093945C2314yes—
135#13093945C2314yes—
136#13093944C2314yescomplemented
137C22⋊(C47⋊C8)C2314yes—
138C22⋊(C47⋊C8)C2314yescomplemented
139#13093935C2314yescomplemented
140C25×C47—21no—
141C2×#41×C47—22no—
142C2×#41×C47—24no—
143C2×#41×C47—42no—
144C2×#41×C47C2314yes—
145C22×Q8×C47C2311yescharacteristic
146C22×D4×C47—24no—
147C22×D4×C47—21no—
148C22×D4×C47—21no—
149C22×D4×C47—21no—
150C22×D4×C47—22no—
151C22×D4×C47—42no—
152C22×D4×C47D411yescharacteristic
153C22×D4×C47C2311yescharacteristic
154C22×D4×C47C2314yes—
155C22×D4×C47C2311yescharacteristic
156C23×C4×C47—21no—
157C23×C4×C47—21no—
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160#124×C47—22no—
161#124×C47C2314yes—
162#123×C47—28no—
163C22⋊Q8×C47—22no—
164C22⋊Q8×C47C2314yes—
165#121×C47—22no—
166#121×C47—28no—
167#121×C47C2314yes—
168#120×C47—28no—
169C4×D4×C47—22no—
170C4×D4×C47D414yes—
171C4×D4×C47C2314yes—
172C4×D4×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47D411yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—28no—
182C2×C22⋊C4×C47D411yescharacteristic
183C2×C22⋊C4×C47D411yescharacteristic
184C2×C42×C47C2311yescharacteristic
185C24×C47—21no—
186C24×C47—21no—
187C24×C47—24no—
188C24×C47—44no—
189C24×C47—44no—
190C24×C47—82no—
191C24×C47C2×D411yescharacteristic
192C24×C47C2×D411yescharacteristic
193C23×D47—21no—
194#41×C47—28no—
195#41×C47—44no—
196#41×C47—48no—
197C2×Q8×C47—21no—
198C2×Q8×C47—22no—
199C2×Q8×C47—22no—
200C2×Q8×C47C2412yes—
201C2×D4×C47—28no—
202C2×D4×C47—24no—
203C2×D4×C47—24no—
204C2×D4×C47—21no—
205C2×D4×C47—24no—
206C2×D4×C47—21no—
207C2×D4×C47—22no—
208C2×D4×C47—22no—
209C2×D4×C47—22no—
210C2×D4×C47—44no—
211C2×D4×C47—48no—
212C2×D4×C47—42no—
213C2×D4×C47—44no—
214C2×D4×C47—44no—
215C2×D4×C47—82no—
216C2×D4×C47C2×D414yes—
217C2×D4×C47#4114yes—
218C2×D4×C47C2412yes—
219C2×D4×C47C2412yes—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—24no—
227C22×C4×C47—24no—
228C22×C4×C47—44no—
229C22×C4×C47—82no—
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D412yes—
235C22×C4×C47C2×D412yes—
236C22×C4×C47C2412yes—
237C22×C4×C47C2412yes—
238C22×C4×C47C2411yescharacteristic
239C2×C22⋊D47—24no—
240C2×C22⋊D47—24no—
241C2×C22⋊D47—82no—
242C2×C22⋊D47—82no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C2×D188—22no—
247C2×D188—22no—
248C2×D188—21no—
249C2×D188C2412yes—
250C2×C4×D47—24no—
251C2×C4×D47—44no—
252C2×Dic94—24no—
253C2×Dic94—82no—
254C4⋊C4×C47—24no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47C2×D414yes—
257C4⋊C4×C47C2412yes—
258C22⋊C4×C47—24no—
259C22⋊C4×C47—24no—
260C22⋊C4×C47—24no—
261C22⋊C4×C47—24no—
262C22⋊C4×C47—24no—
263C22⋊C4×C47C2×D414yes—
264C22⋊C4×C47C2×D414yes—
265C42×C47C2×D412yes—
266C42×C47C2412yes—
267C22⋊Dic47—24no—
268C22⋊Dic47—24no—
269#10625336—44no—
270#10625334—28no—
271#10625334—44no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275C4⋊Dic47—24no—
276C4⋊Dic47—21no—
277C4⋊Dic47—21no—
278C4⋊Dic47—21no—
279C4⋊Dic47C2412yes—
280C4⋊Dic47C2412yes—
281C4⋊Dic47C2412yes—
282C4×Dic47—24no—
283C4×Dic47—24no—
284#10625329—44no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8—22no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—44no—
290C2×C47⋊C8C2412yes—
291C2×C47⋊C8C2412yes—
292C2×C47⋊C8C2412yes—
293C2×C47⋊C8C2412yes—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—24no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—48no—
304C23×C47—48no—
305C23×C47—42no—
306C23×C47—42no—
307C23×C47—42no—
308C23×C47—42no—
309C23×C47—42no—
310C23×C47—84no—
311C23×C47—816no—
312C23×C47C22×D412yes—
313C23×C47C22×D412yes—
314C23×C47C22×D411yescharacteristic
315C22×D47—22no—
316C22×D47—42no—
317C22×D47—42no—
318C22×D47—42no—
319Q8×C47—22no—
320Q8×C47—22no—
321Q8×C47—42no—
322D4×C47—24no—
323D4×C47—22no—
324D4×C47—22no—
325D4×C47—22no—
326D4×C47—44no—
327D4×C47—48no—
328D4×C47—48no—
329D4×C47—42no—
330D4×C47—84no—
331D4×C47C2×#4114yes—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—24no—
337C2×C4×C47—24no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—48no—
345C2×C4×C47—42no—
346C2×C4×C47—42no—
347C2×C4×C47—84no—
348C2×C4×C47C22×D412yes—
349C2×C4×C47C22×D412yes—
350C2×C4×C47C22×D412yes—
351C2×C4×C47C22×D412yes—
352C2×C4×C47C22×D411yescharacteristic
353C2×C4×C47C2×#4112yes—
354C2×C4×C47H(5,𝔽2)12yes—
355C2×C4×C47C2511yescharacteristic
356C22⋊D47—84no—
357C22⋊D47—84no—
358C2×Dic47—22no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—42no—
362C2×Dic47—42no—
363C2×Dic47—42no—
364D188—22no—
365D188—22no—
366D188—42no—
367C4×D47—48no—
368Dic94—84no—
369C47⋊C8—22no—
370C47⋊C8—22no—
371C47⋊C8—22no—
372C47⋊C8—22no—
373C2×#3319—471nomaximal, Sylow
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—24no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—44no—
382C22×C47—44no—
383C22×C47—48no—
384C22×C47—42no—
385C22×C47—42no—
386C22×C47—42no—
387C22×C47—42no—
388C22×C47—42no—
389C22×C47—816no—
390C22×C47—84no—
391C22×C47#54612yes—
392C22×C47#57512yes—
393C22×C47#57612yes—
394C22×C47C23×D411yescharacteristic
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—84no—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47—22no—
402C4×C47—22no—
403C4×C47—42no—
404C4×C47—42no—
405C4×C47#54612yes—
406C4×C47C22×#4111yescharacteristic
407C4×C47C2×H(5,𝔽2)11yescharacteristic
408Dic47—42no—
409Dic47—42no—
410Dic47—42no—
411C2×#555—471no—
412C2×#546D4711yescharacteristic, complemented
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×#442—471no—
424C2×#435—471no—
425C2×#418—471no—
426C2×#416—471no—
427C2×C47—42no—
428C2×C47—42no—
429C2×C47—44no—
430C2×C47—82no—
431C2×C47#331914yescomplemented
432C2×C47C2×#54611yescharacteristic
433C2×C47C2×#57511yescharacteristic
434C2×C47C2×#57611yescharacteristic
435D47—82no—
436C22×#41C2×D4711yescharacteristic
437C23×D4C2×D4711yescharacteristic
438C22×SD16—471no—
439C22×D8—471no—
440C22×D8—471no—
441C22×M16—471no—
442C23×C8—471no—
443#555—478no—
444#555—944no—
445#546—24no—
446#546C2×D4718yescomplemented
447C2×C4⋊Q8—471no—
448C2×#124—941no—
449C2×#124—941no—
450C2×#124C2×D4711yescharacteristic
451C2×#123—21no—
452C2×C22⋊Q8C2×D4711yescharacteristic
453C2×#121—21no—
454C2×#121—471no—
455C2×#121—471no—
456C2×#121—941no—
457C2×#121C2×D4711yescharacteristic
458C2×#120—21no—
459C2×C4×D4—471no—
460C2×C4×D4C2×D4711yescharacteristic
461C2×C4×D4C2×D4711yescharacteristic
462C2×#117—471no—
463C2×#117—471no—
464C2×#117—941no—
465C22×C22⋊C4—21no—
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#442—478no—
476#435—478no—
477C2×#107—471no—
478C2×#107—471no—
479C2×#106—471no—
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×#102—471no—
492C2×#102—471no—
493C2×C22⋊C8—471no—
494C2×C22⋊C8—471no—
495C2×#97—471no—
496C47C2×#331911yescharacteristic, complemented, Sylow
497C25—21no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D4714yes—
502C22×Q8—941no—
503C22×Q8C22×D4711yescharacteristic
504C22×D4—24no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—42no—
510C22×D4—471no—
511C22×D4—941no—
512C22×D4—941no—
513C22×D4C22⋊D4711yescharacteristic
514C22×D4C22×D4711yescharacteristic
515C22×D4C22×D4714yes—
516C22×D4C22×D4711yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—941no—
520C23×C4C22×D4711yescharacteristic
521C23×C4C22×D4711yescharacteristic
522C2×SD16—474no—
523C2×SD16—1882no—
524C2×D8—474no—
525C2×D8—474no—
526C2×D8—944no—
527C2×D8—1882no—
528C2×M16—474no—
529C2×M16—1882no—
530C22×C8—471no—
531C22×C8—471no—
532C22×C8—471no—
533C22×C8—471no—
534C22×C8—474no—
535C22×C8—1882no—
536C4⋊Q8—474no—
537C4⋊Q8—942no—
538#124—22no—
539#124—948no—
540#124—948no—
541#124C22×D4714yes—
542#123—28no—
543C22⋊Q8—22no—
544C22⋊Q8C22×D4714yes—
545#121—22no—
546#121—28no—
547#121—474no—
548#121—474no—
549#121—948no—
550#121—942no—
551#121—942no—
552#121C22×D4714yes—
553#120—28no—
554C4×D4—22no—
555C4×D4—474no—
556C4×D4—942no—
557C4×D4C22⋊D4714yes—
558C4×D4C22×D4714yes—
559C4×D4C22×D4714yes—
560#117—474no—
561#117—474no—
562#117—942no—
563#117—942no—
564#117—948no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—471no—
567C2×C4⋊C4—471no—
568C2×C4⋊C4—471no—
569C2×C4⋊C4—941no—
570C2×C4⋊C4C22⋊D4711yescharacteristic
571C2×C4⋊C4C22×D4711yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—28no—
578C2×C22⋊C4—941no—
579C2×C22⋊C4—941no—
580C2×C22⋊C4—941no—
581C2×C22⋊C4—941no—
582C2×C22⋊C4—941no—
583C2×C22⋊C4C22⋊D4711yescharacteristic
584C2×C22⋊C4C22⋊D4711yescharacteristic
585C2×C42—941no—
586C2×C42—941no—
587C2×C42C22×D4711yescharacteristic
588#107—474no—
589#107—474no—
590#106—474no—
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#102—474no—
601#102—474no—
602C22⋊C8—474no—
603C22⋊C8—474no—
604#97—474no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—44no—
609C24—44no—
610C24—82no—
611C24—941no—
612C24C2×C22⋊D4711yescharacteristic
613C24C2×C22⋊D4711yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—944no—
621C2×Q8—3762no—
622C2×Q8C23×D4712yes—
623C2×D4—28no—
624C2×D4—24no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—24no—
628C2×D4—21no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—44no—
633C2×D4—48no—
634C2×D4—42no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—82no—
638C2×D4—472no—
639C2×D4—944no—
640C2×D4—944no—
641C2×D4—941no—
642C2×D4—942no—
643C2×D4—942no—
644C2×D4—3762no—
645C2×D4—3762no—
646C2×D4#1062535214yes—
647C2×D4C2×C22⋊D4714yes—
648C2×D4C23×D4712yes—
649C2×D4C23×D4712yes—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—44no—
659C22×C4—82no—
660C22×C4—941no—
661C22×C4—941no—
662C22×C4—941no—
663C22×C4—944no—
664C22×C4—1884no—
665C22×C4C2×C22⋊D4712yes—
666C22×C4C2×C22⋊D4712yes—
667C22×C4C2×C22⋊D4711yescharacteristic
668C22×C4C2×C22⋊D4711yescharacteristic
669C22×C4C2×C22⋊D4711yescharacteristic
670C22×C4C2×C22⋊D4711yescharacteristic
671C22×C4C23×D4712yes—
672C22×C4C23×D4712yes—
673C22×C4C23×D4711yescharacteristic
674SD16—1884no—
675D8—948no—
676D8—1884no—
677M16—1884no—
678C2×C8—472no—
679C2×C8—472no—
680C2×C8—472no—
681C2×C8—472no—
682C2×C8—942no—
683C2×C8—942no—
684C2×C8—942no—
685C2×C8—942no—
686C2×C8—1884no—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—472no—
690C4⋊C4—472no—
691C4⋊C4—472no—
692C4⋊C4—941no—
693C4⋊C4—941no—
694C4⋊C4—941no—
695C4⋊C4—944no—
696C4⋊C4C2×C22⋊D4714yes—
697C4⋊C4C23×D4712yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—944no—
704C22⋊C4—944no—
705C22⋊C4—944no—
706C22⋊C4—944no—
707C22⋊C4—944no—
708C22⋊C4C2×C22⋊D4714yes—
709C22⋊C4C2×C22⋊D4714yes—
710C42—944no—
711C42—944no—
712C42C2×C22⋊D4712yes—
713C42C23×D4712yes—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—48no—
724C23—48no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—84no—
731C23—816no—
732C23—942no—
733C23—1882no—
734C23—1882no—
735C23—1882no—
736C23C22×C22⋊D4712yes—
737C23C22×C22⋊D4712yes—
738C23C22×C22⋊D4711yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742Q8—3764no—
743D4—24no—
744D4—22no—
745D4—22no—
746D4—22no—
747D4—44no—
748D4—48no—
749D4—48no—
750D4—42no—
751D4—84no—
752D4—942no—
753D4—942no—
754D4—3764no—
755D4—3764no—
756D4—1882no—
757D4C2×#1062535214yes—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—48no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—84no—
774C2×C4—942no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—1888no—
778C2×C4—1882no—
779C2×C4—1882no—
780C2×C4—1882no—
781C2×C4C22×C22⋊D4712yes—
782C2×C4C22×C22⋊D4712yes—
783C2×C4C22×C22⋊D4712yes—
784C2×C4C22×C22⋊D4712yes—
785C2×C4C22×C22⋊D4711yescharacteristic
786C2×C4C2×#1062535212yes—
787C2×C4#1309406912yes—
788C2×C4C24×D4711yescharacteristic
789C8—942no—
790C8—942no—
791C8—942no—
792C8—942no—
793C22—22no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—44no—
801C22—44no—
802C22—48no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—816no—
809C22—84no—
810C22—3764no—
811C22—1882no—
812C22—1882no—
813C22—1882no—
814C22#1568976712yes—
815C22#1568992112yes—
816C22#1568992612yes—
817C22C23×C22⋊D4711yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—1882no—
825C4—1882no—
826C4—1882no—
827C4#1568976712yes—
828C4C22×#1062535211yescharacteristic
829C4C2×#1309406911yescharacteristic
830C2—42no—
831C2—42no—
832C2—44no—
833C2—82no—
834C2—3762no—
835C2#2025554414yesdirect product factor
836C2C2×#1568976711yescharacteristic
837C2C2×#1568992111yescharacteristic
838C2C2×#1568992611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#546C2
socleC23×C47C22×D4
hypercenterC2×#546D47
hypocenterC47C2×#3319
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#15689838C2semidirect
2. #20255544C2direct (N × H)
3. C2×#15689482C2semidirect
4. C2×#15689461C2semidirect
5. C2×#15689444C2semidirect
6. C2×#15689403C2semidirect
7. C2×#15689371C2semidirect
8. C2×#15689357C2semidirect
9. C2×#15689335C2semidirect
10. C2×#15689268C2semidirect
11. C2×#15689257C2semidirect
12. C2×#15689233C2semidirect
13. C2×#15689195C2semidirect
14. C2×#15689128C2semidirect
15. C2×#15689119C2semidirect
16. C2×C47×#546C2semidirect
17. C22×#10625336C22semidirect
21. C23×C47⋊C8C22semidirect
23. #15689838C22semidirect
24. C2×#13094024C22semidirect
28. C2×#13093998C22semidirect
30. C2×C4×D188C22semidirect
32. C2×#13093983C22semidirect
34. #15689482C22semidirect
35. #15689461C22semidirect
36. #15689444C22semidirect
37. #15689403C22semidirect
38. #15689371C22semidirect
39. #15689357C22semidirect
40. #15689335C22semidirect
41. #15689268C22semidirect
42. #15689257C22semidirect
43. #15689233C22semidirect
44. #15689195C22semidirect
45. C2×#13093957C22semidirect
46. C2×#13093957C22semidirect
47. C2×#13093955C22semidirect
48. C2×C4⋊(C47⋊C8)C22semidirect
49. #15689128C22semidirect
50. #15689119C22semidirect
51. C2×#13093948C22semidirect
52. C2×#13093948C22semidirect
53. C2×#13093948C22semidirect
60. C2×#13093944C22semidirect
62. C2×C22⋊(C47⋊C8)C22semidirect
63. C2×#13093935C22semidirect
67. C47×#546C22semidirect
83. C2×#10625336C23semidirect
95. C22×C47⋊C8C23semidirect
97. #13094024C23semidirect
103. #13093998C23semidirect
106. C4×D188C23semidirect
110. #13093983C23semidirect
123. #13093957C23semidirect
124. #13093957C23semidirect
125. #13093955C23semidirect
126. C4⋊(C47⋊C8)C23semidirect
127. #13093948C23semidirect
128. #13093948C23semidirect
129. #13093948C23semidirect
136. #13093944C23semidirect
138. C22⋊(C47⋊C8)C23semidirect
139. #13093935C23semidirect
412. C2×#546D47semidirect
431. C2×C47#3319semidirect
446. #546C2×D47semidirect
496. C47C2×#3319semidirect
835. C2#20255544direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898382
#202555442
C2×#156894822
C2×#156894612
C2×#156894442
C2×#156894032
C2×#156893712
C2×#156893572
C2×#156893352
C2×#156892682
C2×#156892572
C2×#156892332
C2×#156891952
C2×#156891282
C2×#156891192
C2×C47×#5462
C2×#331947