Finite Group Databasebeta

← C2×#20255595 #27093081

Subgroups — C2×#20255595 #27093081

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×#15689820C211yesmaximal, characteristic, complemented
2C2×#15689764C211yesmaximal, characteristic, complemented
3#20255595C2116yesmaximal, direct product factor
4C2×#15689479C211yesmaximal, characteristic, complemented
5C2×#15689461C211yesmaximal, characteristic, complemented
6C2×#15689438C211yesmaximal, characteristic, complemented
7C2×#15689426C211yesmaximal, characteristic, complemented
8C2×#15689375C211yesmaximal, characteristic, complemented
9C2×#15689340C211yesmaximal, characteristic, complemented
10C2×#15689267C211yesmaximal, characteristic, complemented
11C2×#15689256C211yesmaximal, characteristic, complemented
12C2×#15689203C211yesmaximal, characteristic, complemented
13C2×#15689199C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C2×#15689129C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625324C2211yescharacteristic, complemented
22#15689820—24no—
23#15689820C2218yescomplemented
24#15689764—24no—
25#15689764C2218yescomplemented
26C2×#13094017—21no—
27C2×#13094015C2211yescharacteristic, complemented
28C2×#13094013C2211yescharacteristic
29C2×#13094009—21no—
30C2×#13094005—21no—
31C2×#13093999—21no—
32C2×#13093999C2211yescharacteristic
33C2×#13093995—21no—
34C2×#13093995C2211yescharacteristic, complemented
35C2×#13093994—21no—
36C2×D4×Dic47C2211yescharacteristic, complemented
37C2×#13093986C2211yescharacteristic
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093983C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic, complemented
42C2×C22⋊C4×D47—21no—
43#15689479C2218yescomplemented
44#15689461C2218yescomplemented
45#15689438C2218yescomplemented
46#15689426C2218yescomplemented
47#15689375C2218yescomplemented
48#15689340C2218yescomplemented
49#15689267C2218yescomplemented
50#15689256C2218yescomplemented
51#15689203C2218yescomplemented
52#15689199C2218yescomplemented
53C2×#13093957C2211yescharacteristic, complemented
54C2×#13093955C2211yescharacteristic, complemented
55C2×Dic47⋊C8C2211yescharacteristic, complemented
56#15689129C2218yescomplemented
57#15689123C2218yescomplemented
58C2×#13093948C2211yescharacteristic, complemented
59C2×#13093948C2211yescharacteristic, complemented
60C2×#13093946C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic47C2211yescharacteristic, complemented
69C22×SD16×C47C2211yescharacteristic, complemented
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#468C2218yescomplemented
74C2×#107×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×#102×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625354—22no—
79C2×#10625354—24no—
80C2×#10625354—42no—
81C2×#10625354C2314yes—
82C22×D188—24no—
83C22×D188—21no—
84C22×D188—22no—
85C22×D188—21no—
86C22×D188—21no—
87C22×D188—42no—
88C22×D188C2311yescharacteristic
89C22×D188C2314yes—
90C22×D188C2311yescharacteristic
91C22×C22⋊D47—21no—
92C22×C22⋊D47D411yescharacteristic
93C23×Dic47—21no—
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C22×C4×D47—21no—
97C22×C4×D47C2311yescharacteristic
98C2×#10625334—24no—
99C2×#10625334—42no—
100C2×#10625334C2314yes—
101C2×#10625334C2314yes—
102C2×#10625324—42no—
103C2×#10625324C2314yescomplemented
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106#13094017—28no—
107#13094015—22no—
108#13094015C2314yescomplemented
109#13094013—22no—
110#13094013C2314yes—
111#13094009—28no—
112#13094005—28no—
113#13093999—22no—
114#13093999—28no—
115#13093999C2314yes—
116#13093995—28no—
117#13093995—22no—
118#13093995C2314yescomplemented
119#13093994—28no—
120D4×Dic47—22no—
121D4×Dic47C2314yescomplemented
122#13093986—22no—
123#13093986C2314yes—
124C4×C22⋊D47D414yes—
125C4×C22⋊D47C2314yes—
126(C22⋊D47)⋊C4—28no—
127#13093983—22no—
128#13093983C2314yes—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4D411yescharacteristic
135C4⋊C4×D47—22no—
136C4⋊C4×D47C2314yescomplemented
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47D411yescharacteristic
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C22⋊C4×D47—28no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yescomplemented
150#13093955C2314yescomplemented
151Dic47⋊C8C2314yescomplemented
152#13093948C2314yescomplemented
153#13093948C2314yescomplemented
154#13093946C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158#13093944C2314yes—
159#13093944C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161(C2×D47)⋊C8C2314yescomplemented
162C8×Dic47C2314yescomplemented
163C22×Q8×C47C2311yescharacteristic
164C22×D4×C47—21no—
165C22×D4×C47C2311yescharacteristic
166C23×C4×C47C2311yescharacteristic
167C2×SD16×C47—42no—
168C2×SD16×C47C2314yescomplemented
169C2×M16×C47—42no—
170C2×M16×C47C2314yes—
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C22⋊Q8×C47—22no—
174C22⋊Q8×C47C2314yes—
175#121×C47—22no—
176#121×C47C2314yes—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182#107×C47C2314yescomplemented
183#103×C47C2314yescomplemented
184#102×C47C2314yescomplemented
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47—21no—
189C23×D47—24no—
190C23×D47—44no—
191C23×D47—44no—
192C23×D47—82no—
193C23×D47C2×D411yescharacteristic
194C2×Q8×C47—21no—
195C2×Q8×C47—22no—
196C2×Q8×C47—22no—
197C2×Q8×C47C2412yes—
198C2×D4×C47—24no—
199C2×D4×C47—21no—
200C2×D4×C47—22no—
201C2×D4×C47—22no—
202C2×D4×C47—82no—
203C2×D4×C47C2412yes—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2411yescharacteristic
213C2×C22⋊D47—24no—
214C2×C22⋊D47—42no—
215C2×C22⋊D47—44no—
216C2×C22⋊D47C2×D414yes—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—24no—
220C22×Dic47—82no—
221C22×Dic47C2×D411yescharacteristic
222C22×Dic47C2×D411yescharacteristic
223C22×Dic47C2×D411yescharacteristic
224#10625354—28no—
225#10625354—44no—
226#10625354—48no—
227C2×D188—21no—
228C2×D188—22no—
229C2×D188—22no—
230C2×D188—22no—
231C2×D188—28no—
232C2×D188—24no—
233C2×D188—24no—
234C2×D188—21no—
235C2×D188—24no—
236C2×D188—44no—
237C2×D188—48no—
238C2×D188—44no—
239C2×D188—44no—
240C2×D188—82no—
241C2×D188#4114yes—
242C2×D188C2412yes—
243C2×D188C2412yes—
244C2×C4×D47—22no—
245C2×C4×D47—22no—
246C2×C4×D47—24no—
247C2×C4×D47—24no—
248C2×C4×D47—24no—
249C2×C4×D47—44no—
250C2×C4×D47—82no—
251C2×C4×D47—82no—
252C2×C4×D47C2×D412yes—
253C2×C4×D47C2412yes—
254SD16×C47—44no—
255M16×C47—44no—
256C2×C8×C47—22no—
257C2×C8×C47—22no—
258C2×C8×C47C2412yes—
259C2×C8×C47C2412yes—
260C4⋊C4×C47—24no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47C2412yes—
264C4⋊C4×C47C2412yes—
265C22⋊C4×C47—24no—
266C22⋊C4×C47—24no—
267C22⋊Dic47—24no—
268C22⋊Dic47—24no—
269C22⋊Dic47—24no—
270C22⋊Dic47C2×D414yes—
271#10625334—28no—
272#10625334—44no—
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—
278C4⋊Dic47—21no—
279C4⋊Dic47—21no—
280C4⋊Dic47—24no—
281C4⋊Dic47C2412yes—
282C4⋊Dic47C2412yes—
283Dic47⋊C4—24no—
284Dic47⋊C4—24no—
285Dic47⋊C4C2×D414yes—
286C4×Dic47—24no—
287C4×Dic47C2×D412yes—
288C4×Dic47C2412yes—
289C2×C47⋊C8—22no—
290C2×C47⋊C8—22no—
291C2×C47⋊C8C2412yes—
292C2×C47⋊C8C2412yes—
293#10625324—44no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47C22×D412yes—
302C23×C47C22×D411yescharacteristic
303C22×D47—22no—
304C22×D47—24no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—48no—
310C22×D47—42no—
311C22×D47—42no—
312C22×D47—48no—
313C22×D47—42no—
314C22×D47—42no—
315C22×D47—42no—
316C22×D47—84no—
317C22×D47—816no—
318C22×D47C22×D412yes—
319Q8×C47—22no—
320Q8×C47—22no—
321Q8×C47—42no—
322D4×C47—22no—
323D4×C47—22no—
324D4×C47—42no—
325D4×C47—84no—
326C2×C4×C47—22no—
327C2×C4×C47—24no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—42no—
334C2×C4×C47—42no—
335C2×C4×C47—42no—
336C2×C4×C47C22×D412yes—
337C2×C4×C47C22×D411yescharacteristic
338C2×C4×C47C2×#4112yes—
339C2×C4×C47H(5,𝔽2)12yes—
340C2×C4×C47C2511yescharacteristic
341C22⋊D47—44no—
342C22⋊D47—48no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—84no—
351C2×Dic47C22×D412yes—
352C2×Dic47C22×D412yes—
353C2×Dic47C22×D412yes—
354D188—24no—
355D188—22no—
356D188—22no—
357D188—22no—
358D188—48no—
359D188—48no—
360D188—42no—
361D188—84no—
362D188C2×#4114yes—
363C4×D47—24no—
364C4×D47—22no—
365C4×D47—22no—
366C4×D47—48no—
367C4×D47—84no—
368C4×D47—84no—
369C8×C47—22no—
370C8×C47—22no—
371C47⋊C8—22no—
372C47⋊C8—22no—
373C2×#3322—471nomaximal, Sylow
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—44no—
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—24no—
388C2×D47—22no—
389C2×D47—22no—
390C2×D47—44no—
391C2×D47—48no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—816no—
398C2×D47—84no—
399C4×C47—22no—
400C4×C47—42no—
401C4×C47—42no—
402C4×C47—42no—
403C4×C47#54612yes—
404C4×C47C22×#4111yescharacteristic
405C4×C47C2×H(5,𝔽2)11yescharacteristic
406Dic47—22no—
407Dic47—22no—
408Dic47—22no—
409Dic47—42no—
410Dic47—42no—
411C2×#553—471no—
412C2×#546—471no—
413#3322—4716no—
414C2×#488—471no—
415C2×#485—471no—
416C2×#480—471no—
417C2×#478—471no—
418C2×#469—471no—
419C2×#468D4711yescharacteristic, complemented
420C2×#463—471no—
421C2×#449—471no—
422C2×#447—471no—
423C2×C4×D8—471no—
424C2×#436—471no—
425C2×#417—471no—
426C2×#418—471no—
427C2×C47—42no—
428C2×C47—82no—
429C2×C47#332214yescomplemented
430C2×C47C2×#54611yescharacteristic
431C2×C47C2×#57511yescharacteristic
432C2×C47C2×#57611yescharacteristic
433D47—42no—
434D47—44no—
435D47—82no—
436C22×#41—471no—
437C23×D4—471no—
438C22×SD16C2×D4711yescharacteristic, complemented
439C22×D8—471no—
440C22×D8—471no—
441C22×M16—471no—
442C22×M16C2×D4711yescharacteristic
443#553—478no—
444#553—944no—
445#546—478no—
446#546—944no—
447C2×#126—941no—
448C2×#125—471no—
449C2×#124—471no—
450C2×#123—941no—
451C2×#123—941no—
452C2×C22⋊Q8C2×D4711yescharacteristic
453C2×#121—471no—
454C2×#121—471no—
455C2×#121—941no—
456C2×#121—941no—
457C2×#121C2×D4711yescharacteristic
458C2×#120—941no—
459C2×C4×D4—471no—
460C2×C4×D4—471no—
461C2×C4×D4—471no—
462C2×C4×D4—941no—
463C2×#117—471no—
464C22×C4⋊C4—471no—
465C22×C22⋊C4—941no—
466#488—478no—
467#485—478no—
468#480—478no—
469#478—478no—
470#469—478no—
471#468C2×D4718yescomplemented
472#463—478no—
473#449—478no—
474#447—478no—
475C4×D8—478no—
476#436—478no—
477C2×#107—471no—
478C2×#107C2×D4711yescharacteristic, complemented
479C2×#106—471no—
480C2×C4⋊C8—471no—
481#418—478no—
482#417—478no—
483C2×#103—471no—
484C2×#103—471no—
485C2×#103C2×D4711yescharacteristic, complemented
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102—471no—
491C2×#102—471no—
492C2×#102C2×D4711yescharacteristic, complemented
493C2×C22⋊C8—471no—
494C2×C22⋊C8—471no—
495C2×C4×C8—471no—
496C47C2×#332211yescharacteristic, complemented, Sylow
497C25—941no—
498C2×#41—474no—
499C2×#41—942no—
500C2×#41—944no—
501C2×#41—1882no—
502C22×Q8C22×D4711yescharacteristic
503C22×D4—21no—
504C22×D4—471no—
505C22×D4—471no—
506C22×D4—471no—
507C22×D4—474no—
508C22×D4—944no—
509C22×D4—941no—
510C22×D4—941no—
511C22×D4—941no—
512C22×D4—941no—
513C22×D4—942no—
514C22×D4—1882no—
515C22×D4C22×D4711yescharacteristic
516C23×C4—471no—
517C23×C4—941no—
518C23×C4—941no—
519C23×C4—941no—
520C23×C4—941no—
521C23×C4C22×D4711yescharacteristic
522C2×SD16—42no—
523C2×SD16C22×D4714yescomplemented
524C2×D8—474no—
525C2×D8—474no—
526C2×D8—944no—
527C2×D8—1882no—
528C2×M16—42no—
529C2×M16—474no—
530C2×M16—1882no—
531C2×M16C22×D4714yes—
532C22×C8—471no—
533C22×C8—471no—
534C22×C8C22×D4711yescharacteristic
535C22×C8C22×D4711yescharacteristic
536#126—948no—
537#125—474no—
538#125—942no—
539#124—474no—
540#124—942no—
541#123—948no—
542#123—948no—
543C22⋊Q8—22no—
544C22⋊Q8C22×D4714yes—
545#121—22no—
546#121—474no—
547#121—474no—
548#121—948no—
549#121—942no—
550#121—942no—
551#121—948no—
552#121C22×D4714yes—
553#120—948no—
554C4×D4—474no—
555C4×D4—474no—
556C4×D4—474no—
557C4×D4—474no—
558C4×D4—942no—
559C4×D4—942no—
560C4×D4—948no—
561#117—474no—
562#117—942no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—471no—
565C2×C4⋊C4—471no—
566C2×C4⋊C4—471no—
567C2×C4⋊C4—474no—
568C2×C4⋊C4—942no—
569C2×C4⋊C4—941no—
570C2×C4⋊C4—941no—
571C2×C4⋊C4—941no—
572C2×C4⋊C4C22×D4711yescharacteristic
573C2×C4⋊C4C22×D4711yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—471no—
577C2×C22⋊C4—471no—
578C2×C22⋊C4—948no—
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×C22⋊C4—941no—
586C2×C42—471no—
587C2×C42—941no—
588#107—474no—
589#107C22×D4714yescomplemented
590#106—474no—
591C4⋊C8—474no—
592#103—474no—
593#103—474no—
594#103C22×D4714yescomplemented
595#102—474no—
596#102—474no—
597#102—474no—
598#102—474no—
599#102—474no—
600#102—474no—
601#102C22×D4714yescomplemented
602C22⋊C8—474no—
603C22⋊C8—474no—
604C4×C8—474no—
605C24—21no—
606C24—471no—
607C24—941no—
608C24—944no—
609C24—941no—
610C24—3762no—
611C24—1884no—
612C24—1884no—
613C24D4×D4711yescharacteristic
614#41—948no—
615#41—1884no—
616#41—1888no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D4712yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—82no—
626C2×D4—474no—
627C2×D4—474no—
628C2×D4—472no—
629C2×D4—472no—
630C2×D4—948no—
631C2×D4—944no—
632C2×D4—944no—
633C2×D4—944no—
634C2×D4—941no—
635C2×D4—944no—
636C2×D4—941no—
637C2×D4—942no—
638C2×D4—942no—
639C2×D4—942no—
640C2×D4—3762no—
641C2×D4—1884no—
642C2×D4—1888no—
643C2×D4—1884no—
644C2×D4—1884no—
645C2×D4—1882no—
646C2×D4—1884no—
647C2×D4C23×D4712yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—471no—
654C22×C4—471no—
655C22×C4—471no—
656C22×C4—472no—
657C22×C4—472no—
658C22×C4—944no—
659C22×C4—944no—
660C22×C4—944no—
661C22×C4—944no—
662C22×C4—942no—
663C22×C4—942no—
664C22×C4—941no—
665C22×C4—941no—
666C22×C4—3762no—
667C22×C4—3762no—
668C22×C4—3762no—
669C22×C4—1884no—
670C22×C4D4×D4712yes—
671C22×C4D4×D4711yescharacteristic
672C22×C4C23×D4712yes—
673C22×C4C23×D4711yescharacteristic
674SD16—44no—
675D8—948no—
676D8—1884no—
677M16—44no—
678M16—1884no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—472no—
682C2×C8—472no—
683C2×C8—942no—
684C2×C8—942no—
685C2×C8C23×D4712yes—
686C2×C8C23×D4712yes—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—474no—
691C4⋊C4—472no—
692C4⋊C4—472no—
693C4⋊C4—944no—
694C4⋊C4—944no—
695C4⋊C4—944no—
696C4⋊C4—941no—
697C4⋊C4—941no—
698C4⋊C4C23×D4712yes—
699C4⋊C4C23×D4712yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—474no—
703C22⋊C4—474no—
704C22⋊C4—944no—
705C22⋊C4—944no—
706C22⋊C4—944no—
707C22⋊C4—944no—
708C22⋊C4—944no—
709C22⋊C4—944no—
710C22⋊C4—944no—
711C42—472no—
712C42—472no—
713C42—944no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—472no—
722C23—942no—
723C23—944no—
724C23—942no—
725C23—942no—
726C23—942no—
727C23—942no—
728C23—3764no—
729C23—37616no—
730C23—1888no—
731C23—1888no—
732C23—1882no—
733C23—1882no—
734C23—1882no—
735C23—1882no—
736C23—1882no—
737C23C2×D4×D4712yes—
738C23C2×D4×D4711yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—84no—
746D4—474no—
747D4—944no—
748D4—942no—
749D4—942no—
750D4—942no—
751D4—3764no—
752D4—1888no—
753D4—1888no—
754D4—1884no—
755D4—1888no—
756D4—1882no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—472no—
768C2×C4—472no—
769C2×C4—472no—
770C2×C4—942no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—944no—
774C2×C4—942no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—942no—
778C2×C4—3764no—
779C2×C4—3764no—
780C2×C4—3764no—
781C2×C4—1888no—
782C2×C4—1882no—
783C2×C4—1882no—
784C2×C4C2×D4×D4712yes—
785C2×C4C2×D4×D4711yescharacteristic
786C2×C4#41×D4712yes—
787C2×C4#1309406912yes—
788C2×C4C24×D4711yescharacteristic
789C8—22no—
790C8—22no—
791C8—942no—
792C8—942no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—942no—
802C22—944no—
803C22—942no—
804C22—942no—
805C22—37616no—
806C22—3764no—
807C22—1882no—
808C22—1882no—
809C22—1882no—
810C22—1882no—
811C22—1882no—
812C22—1884no—
813C22—1888no—
814C22#1568976212yes—
815C22#1568992212yes—
816C22#1568992712yes—
817C22C22×D4×D4711yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—942no—
823C4—942no—
824C4—942no—
825C4—1882no—
826C4—1882no—
827C4#1568976212yes—
828C4C2×#41×D4711yescharacteristic
829C4C2×#1309406911yescharacteristic
830C2—42no—
831C2—82no—
832C2—3762no—
833C2—1882no—
834C2—1884no—
835C2#2025559514yesdirect product factor
836C2C2×#1568976211yescharacteristic
837C2C2×#1568992211yescharacteristic
838C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
hypercenterC2×#468D47
hypocenterC47C2×#3322
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#15689820C2semidirect
2. C2×#15689764C2semidirect
3. #20255595C2direct (N × H)
4. C2×#15689479C2semidirect
5. C2×#15689461C2semidirect
6. C2×#15689438C2semidirect
7. C2×#15689426C2semidirect
8. C2×#15689375C2semidirect
9. C2×#15689340C2semidirect
10. C2×#15689267C2semidirect
11. C2×#15689256C2semidirect
12. C2×#15689203C2semidirect
13. C2×#15689199C2semidirect
14. C2×#15689123C2semidirect
15. C2×#15689129C2semidirect
16. C2×C47×#468C2semidirect
21. C22×#10625324C22semidirect
23. #15689820C22semidirect
25. #15689764C22semidirect
27. C2×#13094015C22semidirect
34. C2×#13093995C22semidirect
36. C2×D4×Dic47C22semidirect
41. C2×C4⋊C4×D47C22semidirect
43. #15689479C22semidirect
44. #15689461C22semidirect
45. #15689438C22semidirect
46. #15689426C22semidirect
47. #15689375C22semidirect
48. #15689340C22semidirect
49. #15689267C22semidirect
50. #15689256C22semidirect
51. #15689203C22semidirect
52. #15689199C22semidirect
53. C2×#13093957C22semidirect
54. C2×#13093955C22semidirect
55. C2×Dic47⋊C8C22semidirect
56. #15689129C22semidirect
57. #15689123C22semidirect
58. C2×#13093948C22semidirect
59. C2×#13093948C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×C8×Dic47C22semidirect
69. C22×SD16×C47C22semidirect
73. C47×#468C22semidirect
74. C2×#107×C47C22semidirect
75. C2×#103×C47C22semidirect
76. C2×#102×C47C22semidirect
103. C2×#10625324C23semidirect
108. #13094015C23semidirect
118. #13093995C23semidirect
121. D4×Dic47C23semidirect
136. C4⋊C4×D47C23semidirect
149. #13093957C23semidirect
150. #13093955C23semidirect
151. Dic47⋊C8C23semidirect
152. #13093948C23semidirect
153. #13093948C23semidirect
161. (C2×D47)⋊C8C23semidirect
162. C8×Dic47C23semidirect
168. C2×SD16×C47C23semidirect
182. #107×C47C23semidirect
183. #103×C47C23semidirect
184. #102×C47C23semidirect
419. C2×#468D47semidirect
429. C2×C47#3322semidirect
438. C22×SD16C2×D47semidirect
471. #468C2×D47semidirect
478. C2×#107C2×D47semidirect
485. C2×#103C2×D47semidirect
492. C2×#102C2×D47semidirect
496. C47C2×#3322semidirect
523. C2×SD16C22×D47semidirect
589. #107C22×D47semidirect
594. #103C22×D47semidirect
601. #102C22×D47semidirect
835. C2#20255595direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898202
C2×#156897642
#202555952
C2×#156894792
C2×#156894612
C2×#156894382
C2×#156894262
C2×#156893752
C2×#156893402
C2×#156892672
C2×#156892562
C2×#156892032
C2×#156891992
C2×#156891232
C2×#156891292
C2×C47×#4682
C2×#332247