Finite Group Databasebeta

← C2×#20255643 #27093133

Subgroups — C2×#20255643 #27093133

Order 12032.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689819C211yesmaximal, characteristic, complemented
2C2×#15689782C211yesmaximal, characteristic, complemented
3#20255643C2116yesmaximal, direct product factor
4C2×#15689478C211yesmaximal, characteristic, complemented
5C2×#15689448C211yesmaximal, characteristic, complemented
6C2×#15689454C211yesmaximal, characteristic, complemented
7C2×#15689431C211yesmaximal, characteristic, complemented
8C2×#15689376C211yesmaximal, characteristic, complemented
9C2×#15689369C211yesmaximal, characteristic, complemented
10C2×#15689339C211yesmaximal, characteristic, complemented
11C2×#15689270C211yesmaximal, characteristic, complemented
12C2×#15689264C211yesmaximal, characteristic, complemented
13C2×C4×#10625325C211yesmaximal, characteristic, complemented
14C2×#15689125C211yesmaximal, characteristic, complemented
15C2×#15689133C211yesmaximal, characteristic, complemented
16C2×C47×#436C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×D376C2211yescharacteristic
22#15689819—24no—
23#15689819C2218yescomplemented
24#15689782—24no—
25#15689782C2218yescomplemented
26C2×#13094019—21no—
27C2×#13094016C2211yescharacteristic
28C2×#13094012C2211yescharacteristic
29C2×#13094010—21no—
30C2×#13094006—21no—
31C2×#13094003C2211yescharacteristic
32C2×#13094002—21no—
33C2×#13093998C2211yescharacteristic
34C2×#13093998C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36C2×#13093996—21no—
37C2×#13093996—21no—
38C2×C4×Dic94C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×(C22⋊D47)⋊C4—21no—
41C2×(C22⋊D47)⋊C4—21no—
42C2×#13093983C2211yescharacteristic
43C22×C4⋊Dic47C2211yescharacteristic
44#15689478C2218yescomplemented
45#15689454C2218yescomplemented
46#15689448C2218yescomplemented
47#15689431C2218yescomplemented
48#15689376C2218yescomplemented
49#15689369C2218yescomplemented
50#15689339C2218yescomplemented
51#15689270C2218yescomplemented
52#15689264C2218yescomplemented
53C4×#10625325C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57#15689133C2218yescomplemented
58#15689125C2218yescomplemented
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#436C2218yescomplemented
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—42no—
80C2×#10625350C2314yes—
81C22×Dic94—24no—
82C22×Dic94—22no—
83C22×Dic94—21no—
84C22×Dic94—42no—
85C22×Dic94C2311yescharacteristic
86C22×Dic94C2314yes—
87C22×Dic94C2311yescharacteristic
88C22×D188C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C23×Dic47—21no—
95C23×Dic47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C2×#10625325—24no—
99C2×#10625325—42no—
100C2×#10625325C2314yes—
101C2×#10625325C2314yes—
102C2×D376—42no—
103C2×D376C2314yes—
104#13094019—28no—
105#13094016—22no—
106#13094016C2314yes—
107#13094012—22no—
108#13094012C2314yes—
109#13094010—28no—
110#13094006—28no—
111#13094003—22no—
112#13094003C2314yes—
113#13094002—28no—
114#13093998—22no—
115#13093998—22no—
116#13093998—22no—
117#13093998C2314yes—
118#13093998C2314yes—
119#13093998C2314yes—
120#13093996—28no—
121#13093996—28no—
122C4×Dic94—22no—
123C4×Dic94C2314yes—
124C4×D188—22no—
125C4×D188C2314yes—
126(C22⋊D47)⋊C4—28no—
127(C22⋊D47)⋊C4—28no—
128#13093983—22no—
129#13093983C2314yes—
130C2×C4⋊Dic47—22no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47C2314yes—
133C2×C4⋊Dic47C2311yescharacteristic
134C2×C4⋊Dic47C2311yescharacteristic
135C2×C4⋊Dic47C2311yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×C22⋊Dic47—21no—
142C2×C22⋊Dic47—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093958C2314yes—
152#13093956C2314yes—
153#13093956C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093949C2314yes—
158#13093949C2314yes—
159#13093949C2314yes—
160#13093946C2314yes—
161#13093946C2314yes—
162#13093946C2314yes—
163#13093946C2314yes—
164C22×D4×C47D411yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C23×C4×C47C2311yescharacteristic
167C2×M16×C47—42no—
168C2×M16×C47—42no—
169C2×M16×C47C2314yes—
170C2×M16×C47C2314yes—
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2311yescharacteristic
175C4×D4×C47D414yes—
176C4×D4×C47C2314yes—
177C2×C4⋊C4×C47D411yescharacteristic
178C2×C22⋊C4×C47D411yescharacteristic
179C2×C22⋊C4×C47D411yescharacteristic
180C2×C42×C47C2311yescharacteristic
181C4⋊C8×C47C2314yes—
182C22⋊C8×C47C2314yes—
183C22⋊C8×C47C2314yes—
184C4×C8×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47—21no—
189C2×D4×C47—42no—
190C2×D4×C47C2×D414yes—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2412yes—
203C22×C4×C47C2411yescharacteristic
204C2×C22⋊D47—24no—
205C2×C22⋊D47—24no—
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—44no—
209C2×C22⋊D47—44no—
210C2×C22⋊D47—44no—
211C2×C22⋊D47—82no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—24no—
219C22×Dic47—24no—
220C22×Dic47—44no—
221C22×Dic47—82no—
222#10625350—28no—
223#10625350—44no—
224#10625350—48no—
225C2×D188—22no—
226C2×D188—22no—
227C2×D188—22no—
228C2×D188—22no—
229C2×D188—21no—
230C2×D188—21no—
231C2×D188C2412yes—
232C2×D188C2412yes—
233C2×C4×D47—24no—
234C2×C4×D47—24no—
235C2×C4×D47—44no—
236C2×C4×D47—82no—
237C2×Dic94—21no—
238C2×Dic94—22no—
239C2×Dic94—22no—
240C2×Dic94—22no—
241C2×Dic94—28no—
242C2×Dic94—24no—
243C2×Dic94—21no—
244C2×Dic94—44no—
245C2×Dic94—48no—
246C2×Dic94—44no—
247C2×Dic94#4114yes—
248C2×Dic94C2412yes—
249C2×Dic94C2412yes—
250M16×C47—44no—
251M16×C47—44no—
252C2×C8×C47—22no—
253C2×C8×C47—22no—
254C2×C8×C47—22no—
255C2×C8×C47—22no—
256C2×C8×C47C2412yes—
257C2×C8×C47C2412yes—
258C2×C8×C47C2412yes—
259C2×C8×C47C2412yes—
260C4⋊C4×C47C2×D414yes—
261C22⋊C4×C47C2×D414yes—
262C22⋊C4×C47C2×D414yes—
263C42×C47C2×D412yes—
264C42×C47C2412yes—
265C22⋊Dic47—24no—
266C22⋊Dic47—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4—24no—
273C4⋊Dic47—21no—
274C4⋊Dic47—21no—
275C4⋊Dic47—24no—
276C4⋊Dic47—21no—
277C4⋊Dic47—21no—
278C4⋊Dic47C2412yes—
279C4⋊Dic47C2412yes—
280C4⋊Dic47C2412yes—
281C4⋊Dic47C2412yes—
282Dic47⋊C4—24no—
283Dic47⋊C4—24no—
284Dic47⋊C4—24no—
285Dic47⋊C4—24no—
286C4×Dic47—24no—
287C4×Dic47—24no—
288D376—44no—
289#10625325—28no—
290#10625325—44no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47C22×D412yes—
298C23×C47C22×D412yes—
299C23×C47C22×D411yescharacteristic
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—42no—
303C22×D47—42no—
304C22×D47—42no—
305C22×D47—42no—
306C22×D47—42no—
307C22×D47—42no—
308D4×C47—44no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—24no—
314C2×C4×C47—24no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47C22×D412yes—
320C2×C4×C47C22×D412yes—
321C2×C4×C47C22×D412yes—
322C2×C4×C47C22×D412yes—
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C2×#4112yes—
325C2×C4×C47H(5,𝔽2)12yes—
326C2×C4×C47C2511yescharacteristic
327C22⋊D47—48no—
328C22⋊D47—48no—
329C22⋊D47—48no—
330C22⋊D47—84no—
331C2×Dic47—24no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—48no—
339C2×Dic47—42no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47—84no—
345D188—22no—
346D188—22no—
347D188—22no—
348D188—22no—
349D188—42no—
350D188—42no—
351C4×D47—48no—
352C4×D47—84no—
353Dic94—24no—
354Dic94—22no—
355Dic94—22no—
356Dic94—22no—
357Dic94—48no—
358Dic94—42no—
359Dic94C2×#4114yes—
360C8×C47—22no—
361C8×C47—22no—
362C8×C47—22no—
363C8×C47—22no—
364C2×#3326—471nomaximal, Sylow
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—44no—
372C22×C47—44no—
373C22×C47#54612yes—
374C22×C47#57512yes—
375C22×C47#57712yes—
376C22×C47C23×D411yescharacteristic
377C2×D47—42no—
378C2×D47—42no—
379C2×D47—42no—
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—84no—
384C2×D47—84no—
385C4×C47—22no—
386C4×C47—22no—
387C4×C47—22no—
388C4×C47—22no—
389C4×C47#54612yes—
390C4×C47C22×#4111yescharacteristic
391C4×C47C2×H(5,𝔽2)11yescharacteristic
392Dic47—24no—
393Dic47—42no—
394Dic47—42no—
395Dic47—42no—
396Dic47—42no—
397Dic47—42no—
398C2×#553—471no—
399C2×#548—471no—
400#3326—4716no—
401C2×#488—471no—
402C2×#482—471no—
403C2×#483—471no—
404C2×#479—471no—
405C2×#469—471no—
406C2×#468—471no—
407C2×#463—471no—
408C2×#449—471no—
409C2×#448—471no—
410C2×C4×SD16—471no—
411C2×#436D4711yescharacteristic, complemented
412C2×#417—471no—
413C2×#419—471no—
414C2×C47—42no—
415C2×C47—42no—
416C2×C47#332614yescomplemented
417C2×C47C2×#54611yescharacteristic
418C2×C47C2×#57511yescharacteristic
419C2×C47C2×#57711yescharacteristic
420D47—82no—
421D47—82no—
422C22×#41—471no—
423C23×Q8—471no—
424C22×SD16—471no—
425C22×SD16—471no—
426C22×D8—471no—
427C22×M16C2×D4711yescharacteristic
428C22×M16C2×D4711yescharacteristic
429#553—478no—
430#553—944no—
431#548—478no—
432#548—944no—
433C2×#126—941no—
434C2×#125—471no—
435C2×#124—471no—
436C2×#124—941no—
437C2×#123—941no—
438C2×C22⋊Q8—471no—
439C2×C22⋊Q8—941no—
440C2×#121—471no—
441C2×#121—471no—
442C2×#121—471no—
443C2×#121—941no—
444C2×#121—941no—
445C2×C4×Q8—471no—
446C2×C4×D4—471no—
447C2×C4×D4—941no—
448C2×C4×D4—941no—
449C2×C4×D4C2×D4711yescharacteristic
450C2×#117—471no—
451C22×C4⋊C4—471no—
452#488—478no—
453#483—478no—
454#482—478no—
455#479—478no—
456#469—478no—
457#468—478no—
458#463—478no—
459#449—478no—
460#448—478no—
461C4×SD16—478no—
462#436C2×D4718yescomplemented
463C2×#107—471no—
464C2×#106—471no—
465C2×#106—471no—
466C2×C4⋊C8C2×D4711yescharacteristic
467#419—478no—
468#417—478no—
469C2×#103—471no—
470C2×#103—471no—
471C2×#103—471no—
472C2×#103—471no—
473C2×#103—471no—
474C2×#103—471no—
475C2×#102—471no—
476C2×#102—471no—
477C2×#102—471no—
478C2×#102—471no—
479C2×C22⋊C8C2×D4711yescharacteristic
480C2×C22⋊C8C2×D4711yescharacteristic
481C2×C4×C8C2×D4711yescharacteristic
482C47C2×#332611yescharacteristic, complemented, Sylow
483C2×#41—474no—
484C2×#41—944no—
485C2×#41—942no—
486C2×#41—1882no—
487C22×Q8—471no—
488C22×Q8—471no—
489C22×Q8—474no—
490C22×Q8—944no—
491C22×Q8—941no—
492C22×Q8—942no—
493C22×Q8—1882no—
494C22×D4—471no—
495C22×D4—471no—
496C22×D4—941no—
497C22×D4—941no—
498C22×D4—941no—
499C22×D4—941no—
500C22×D4D18811yescharacteristic
501C23×C4—941no—
502C23×C4—941no—
503C23×C4—941no—
504C23×C4—941no—
505C23×C4C22×D4711yescharacteristic
506C23×C4C22×D4711yescharacteristic
507C2×SD16—474no—
508C2×SD16—474no—
509C2×SD16—944no—
510C2×SD16—1882no—
511C2×D8—474no—
512C2×D8—1882no—
513C2×M16—42no—
514C2×M16—42no—
515C2×M16C22×D4714yes—
516C2×M16C22×D4714yes—
517C22×C8C22×D4711yescharacteristic
518C22×C8C22×D4711yescharacteristic
519C22×C8C22×D4711yescharacteristic
520C22×C8C22×D4711yescharacteristic
521#126—948no—
522#125—474no—
523#125—942no—
524#124—474no—
525#124—948no—
526#124—942no—
527#123—948no—
528C22⋊Q8—474no—
529C22⋊Q8—942no—
530C22⋊Q8—948no—
531#121—474no—
532#121—474no—
533#121—474no—
534#121—948no—
535#121—948no—
536#121—942no—
537#121—942no—
538#121—942no—
539C4×Q8—474no—
540C4×Q8—942no—
541C4×D4—474no—
542C4×D4—948no—
543C4×D4—948no—
544C4×D4—942no—
545C4×D4D18814yes—
546C4×D4C22×D4714yes—
547#117—474no—
548#117—942no—
549C2×C4⋊C4—471no—
550C2×C4⋊C4—471no—
551C2×C4⋊C4—474no—
552C2×C4⋊C4—471no—
553C2×C4⋊C4—471no—
554C2×C4⋊C4—941no—
555C2×C4⋊C4—942no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4—941no—
558C2×C4⋊C4—941no—
559C2×C4⋊C4—941no—
560C2×C4⋊C4D18811yescharacteristic
561C2×C22⋊C4—941no—
562C2×C22⋊C4—941no—
563C2×C22⋊C4—941no—
564C2×C22⋊C4—941no—
565C2×C22⋊C4—941no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4D18811yescharacteristic
570C2×C22⋊C4D18811yescharacteristic
571C2×C42—941no—
572C2×C42—941no—
573C2×C42C22×D4711yescharacteristic
574#107—474no—
575#106—474no—
576#106—474no—
577C4⋊C8C22×D4714yes—
578#103—474no—
579#103—474no—
580#103—474no—
581#103—474no—
582#103—474no—
583#103—474no—
584#102—474no—
585#102—474no—
586#102—474no—
587#102—474no—
588C22⋊C8C22×D4714yes—
589C22⋊C8C22×D4714yes—
590C4×C8C22×D4714yes—
591C24—941no—
592C24—941no—
593C24C2×D18811yescharacteristic
594C24C2×D18811yescharacteristic
595#41—948no—
596#41—1884no—
597#41—1888no—
598C2×Q8—474no—
599C2×Q8—472no—
600C2×Q8—472no—
601C2×Q8—948no—
602C2×Q8—941no—
603C2×Q8—944no—
604C2×Q8—941no—
605C2×Q8—942no—
606C2×Q8—942no—
607C2×Q8—942no—
608C2×Q8—1884no—
609C2×Q8—1884no—
610C2×Q8—1888no—
611C2×D4—42no—
612C2×D4—472no—
613C2×D4—472no—
614C2×D4—944no—
615C2×D4—944no—
616C2×D4—944no—
617C2×D4—944no—
618C2×D4—941no—
619C2×D4—941no—
620C2×D4—942no—
621C2×D4—942no—
622C2×D4—942no—
623C2×D4—942no—
624C2×D4—3762no—
625C2×D4—1884no—
626C2×D4—1884no—
627C2×D4—1884no—
628C2×D4C2×D18814yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—941no—
634C22×C4—944no—
635C22×C4—944no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—941no—
639C22×C4—941no—
640C22×C4—941no—
641C22×C4—944no—
642C22×C4—944no—
643C22×C4—3762no—
644C22×C4—3762no—
645C22×C4—1884no—
646C22×C4—1884no—
647C22×C4C2×D18812yes—
648C22×C4C2×D18812yes—
649C22×C4C2×D18811yescharacteristic
650C22×C4C2×D18811yescharacteristic
651C22×C4C2×D18811yescharacteristic
652C22×C4C2×D18811yescharacteristic
653C22×C4C23×D4712yes—
654C22×C4C23×D4712yes—
655C22×C4C23×D4711yescharacteristic
656SD16—948no—
657SD16—1884no—
658D8—1884no—
659M16—44no—
660M16—44no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8C23×D4712yes—
666C2×C8C23×D4712yes—
667C2×C8C23×D4712yes—
668C2×C8C23×D4712yes—
669C4⋊C4—472no—
670C4⋊C4—472no—
671C4⋊C4—472no—
672C4⋊C4—472no—
673C4⋊C4—944no—
674C4⋊C4—944no—
675C4⋊C4—944no—
676C4⋊C4—944no—
677C4⋊C4—941no—
678C4⋊C4—941no—
679C4⋊C4—944no—
680C4⋊C4—941no—
681C4⋊C4—941no—
682C4⋊C4C2×D18814yes—
683C22⋊C4—944no—
684C22⋊C4—944no—
685C22⋊C4—944no—
686C22⋊C4—944no—
687C22⋊C4—944no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C22⋊C4C2×D18814yes—
692C22⋊C4C2×D18814yes—
693C42—944no—
694C42—944no—
695C42C2×D18812yes—
696C42C23×D4712yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—942no—
704C23—942no—
705C23—1882no—
706C23—1882no—
707C23—1882no—
708C23—1882no—
709C23—1882no—
710C23—1882no—
711C23C22×D18812yes—
712C23C22×D18812yes—
713C23C22×D18811yescharacteristic
714Q8—474no—
715Q8—944no—
716Q8—942no—
717Q8—942no—
718Q8—942no—
719Q8—1888no—
720Q8—1882no—
721D4—44no—
722D4—942no—
723D4—942no—
724D4—942no—
725D4—942no—
726D4—3764no—
727D4—1888no—
728D4—1888no—
729D4—1888no—
730D4—1882no—
731D4—1882no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—944no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—3764no—
750C2×C4—3764no—
751C2×C4—1888no—
752C2×C4—1888no—
753C2×C4—1882no—
754C2×C4—1882no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4—1882no—
758C2×C4C22×D18812yes—
759C2×C4C22×D18812yes—
760C2×C4C22×D18812yes—
761C2×C4C22×D18812yes—
762C2×C4C22×D18811yescharacteristic
763C2×C4#41×D4712yes—
764C2×C4#1309406912yes—
765C2×C4C24×D4711yescharacteristic
766C8—22no—
767C8—22no—
768C8—22no—
769C8—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—3764no—
779C22—3764no—
780C22—1882no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22—1882no—
786C22#1568976812yes—
787C22#1568992312yes—
788C22#1568993512yes—
789C22C23×D18811yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—944no—
795C4—1882no—
796C4—1882no—
797C4—1882no—
798C4—1882no—
799C4—1882no—
800C4#1568976812yes—
801C4C2×#41×D4711yescharacteristic
802C4C2×#1309406911yescharacteristic
803C2—42no—
804C2—42no—
805C2—3762no—
806C2—3762no—
807C2#2025564314yesdirect product factor
808C2C2×#1568976811yescharacteristic
809C2C2×#1568992311yescharacteristic
810C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#436C2
socleC23×C47C22×D4
hypercenterC2×#436D47
hypocenterC47C2×#3326
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#15689819C2semidirect
2. C2×#15689782C2semidirect
3. #20255643C2direct (N × H)
4. C2×#15689478C2semidirect
5. C2×#15689448C2semidirect
6. C2×#15689454C2semidirect
7. C2×#15689431C2semidirect
8. C2×#15689376C2semidirect
9. C2×#15689369C2semidirect
10. C2×#15689339C2semidirect
11. C2×#15689270C2semidirect
12. C2×#15689264C2semidirect
13. C2×C4×#10625325C2semidirect
14. C2×#15689125C2semidirect
15. C2×#15689133C2semidirect
16. C2×C47×#436C2semidirect
23. #15689819C22semidirect
25. #15689782C22semidirect
44. #15689478C22semidirect
45. #15689454C22semidirect
46. #15689448C22semidirect
47. #15689431C22semidirect
48. #15689376C22semidirect
49. #15689369C22semidirect
50. #15689339C22semidirect
51. #15689270C22semidirect
52. #15689264C22semidirect
53. C4×#10625325C22semidirect
57. #15689133C22semidirect
58. #15689125C22semidirect
72. C47×#436C22semidirect
411. C2×#436D47semidirect
416. C2×C47#3326semidirect
462. #436C2×D47semidirect
482. C47C2×#3326semidirect
807. C2#20255643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898192
C2×#156897822
#202556432
C2×#156894782
C2×#156894482
C2×#156894542
C2×#156894312
C2×#156893762
C2×#156893692
C2×#156893392
C2×#156892702
C2×#156892642
C2×C4×#106253252
C2×#156891252
C2×#156891332
C2×C47×#4362
C2×#332647