Finite Group Databasebeta

← C2×#19146127 #25971601

Subgroups — C2×#19146127 #25971601

Order 11008.

2914 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063353C211yesmaximal, characteristic, complemented
2C22×#13063348C211yesmaximal, characteristic, complemented
3C2×#14583551C211yesmaximal, characteristic, complemented
4C2×#14583540C211yesmaximal, characteristic, complemented
5#19146127C2116yesmaximal, direct product factor
6C2×#14583292C211yesmaximal, characteristic, complemented
7C2×#14583129C211yesmaximal, characteristic, complemented
8C2×#14583117C211yesmaximal, characteristic, complemented
9C2×#14583103C211yesmaximal, characteristic, complemented
10C2×#14583064C211yesmaximal, characteristic, complemented
11C2×#14583059C211yesmaximal, characteristic, complemented
12C2×#14583047C211yesmaximal, characteristic, complemented
13C2×#14583049C211yesmaximal, characteristic, complemented
14C2×#14583010C211yesmaximal, characteristic, complemented
15C2×#14582968C211yesmaximal, characteristic, complemented
16C2×C43×#470C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621902C2211yescharacteristic, complemented
19C22×#10621898C2211yescharacteristic
20C23×D172C2211yescharacteristic
21C2×#13063353—28no—
22C2×#13063353C2218yescomplemented
23C2×#13063348—28no—
24C2×#13063348C2218yescomplemented
25C22×#10621885C2211yescharacteristic, complemented
26C22×#10621873C2211yescharacteristic
27C22×#10621873C2211yescharacteristic
28C22×#10621884C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621884C2211yescharacteristic, complemented
31C22×D344C2211yescharacteristic
32C22×D344C2211yescharacteristic
33C22×C8×D43C2211yescharacteristic, complemented
34#14583551—24no—
35#14583551C2218yescomplemented
36#14583540—24no—
37#14583540C2218yescomplemented
38C2×#13063323C2211yescharacteristic, complemented
39C2×#13063314C2211yescharacteristic
40C2×#13063310—21no—
41C2×#13063310—21no—
42C2×#13063307—21no—
43C2×#13063305C2211yescharacteristic, complemented
44C2×#13063300—21no—
45C2×#13063300C2211yescharacteristic
46C2×#13063298—21no—
47C2×#13063295—21no—
48C2×#13063287C2211yescharacteristic
49C2×#13063287C2211yescharacteristic, complemented
50C2×C4×C22⋊D43C2211yescharacteristic
51C2×C4⋊C4×D43—21no—
52C2×C22⋊C4×D43—21no—
53#14583292C2218yescomplemented
54#14583129C2218yescomplemented
55#14583117C2218yescomplemented
56#14583103C2218yescomplemented
57#14583064C2218yescomplemented
58#14583059C2218yescomplemented
59#14583049C2218yescomplemented
60#14583047C2218yescomplemented
61#14583010C2218yescomplemented
62#14582968C2218yescomplemented
63C2×Dic43⋊C8C2211yescharacteristic, complemented
64C2×#13063248C2211yescharacteristic, complemented
65C2×#13063245C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×#13063245C2211yescharacteristic, complemented
68C2×C22⋊(C43⋊C8)C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
70C2×#13063235C2211yescharacteristic, complemented
71C22×Q16×C43C2211yescharacteristic, complemented
72C22×M16×C43C2211yescharacteristic
73C2×C22⋊Q8×C43C2211yescharacteristic
74C2×C22⋊Q8×C43C2211yescharacteristic
75C43×#470C2218yescomplemented
76C2×#106×C43C2211yescharacteristic, complemented
77C2×#103×C43C2211yescharacteristic, complemented
78C2×#103×C43C2211yescharacteristic, complemented
79C24×D43—21no—
80C2×#10621902—22no—
81C2×#10621902—22no—
82C2×#10621902—24no—
83C2×#10621902—24no—
84C2×#10621902—42no—
85C2×#10621902—42no—
86C2×#10621902C2314yes—
87C2×#10621902C2314yescomplemented
88C2×#10621898—22no—
89C2×#10621898—24no—
90C2×#10621898—42no—
91C2×#10621898C2314yes—
92C22×Dic86C2311yescharacteristic
93C22×D172—24no—
94C22×D172—21no—
95C22×D172—21no—
96C22×D172—21no—
97C22×D172—22no—
98C22×D172—21no—
99C22×D172—42no—
100C22×D172C2311yescharacteristic
101C22×D172C2314yes—
102C22×D172C2311yescharacteristic
103C22×D172C2311yescharacteristic
104C22×C22⋊D43—21no—
105C22×C22⋊D43D411yescharacteristic
106C22×C4×D43—21no—
107C22×C4×D43—21no—
108C22×C4×D43—21no—
109C22×C4×D43—21no—
110C22×C4×D43—21no—
111C22×C4×D43C2311yescharacteristic
112#13063353—232no—
113#13063348—232no—
114C2×#10621885—42no—
115C2×#10621885C2314yescomplemented
116C2×#10621873—24no—
117C2×#10621873—24no—
118C2×#10621873C2314yes—
119C2×#10621873C2314yes—
120C2×#10621884—24no—
121C2×#10621884—24no—
122C2×#10621884—42no—
123C2×#10621884C2314yes—
124C2×#10621884C2314yes—
125C2×#10621884C2314yescomplemented
126C2×D344—24no—
127C2×D344D418yescomplemented
128C2×D344C2314yes—
129C2×D344C2314yes—
130C22×C43⋊C8C2311yescharacteristic
131C22×C43⋊C8C2311yescharacteristic
132C2×C8×D43—24no—
133C2×C8×D43C2314yescomplemented
134#13063323—22no—
135#13063323C2314yescomplemented
136#13063314—22no—
137#13063314C2314yes—
138#13063310—28no—
139#13063310—28no—
140#13063307—28no—
141#13063305—22no—
142#13063305C2314yescomplemented
143#13063300—22no—
144#13063300—28no—
145#13063300C2314yes—
146#13063298—28no—
147#13063295—28no—
148#13063287—22no—
149#13063287—22no—
150#13063287C2314yes—
151#13063287C2314yescomplemented
152C4×C22⋊D43D414yes—
153C4×C22⋊D43C2314yes—
154C2×C4⋊Dic43—21no—
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4D411yescharacteristic
158C4⋊C4×D43—28no—
159C2×C22⋊Dic43D411yescharacteristic
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4D411yescharacteristic
167C22⋊C4×D43—28no—
168C2×C4×Dic43C2311yescharacteristic
169Dic43⋊C8C2314yescomplemented
170#13063248C2314yescomplemented
171#13063245C2314yes—
172#13063245C2314yes—
173#13063245C2314yescomplemented
174C22⋊(C43⋊C8)C2314yes—
175(C2×D43)⋊C8C2314yescomplemented
176#13063235C2314yescomplemented
177C22×Q8×C43C2311yescharacteristic
178C22×Q8×C43C2311yescharacteristic
179C23×C4×C43C2311yescharacteristic
180C2×Q16×C43—24no—
181C2×Q16×C43C2314yescomplemented
182C2×M16×C43—24no—
183C2×M16×C43C2314yes—
184C22×C8×C43C2311yescharacteristic
185C22×C8×C43C2311yescharacteristic
186C22⋊Q8×C43—22no—
187C22⋊Q8×C43—22no—
188C22⋊Q8×C43C2314yes—
189C22⋊Q8×C43C2314yes—
190C2×C4⋊C4×C43—21no—
191C2×C4⋊C4×C43—21no—
192C2×C4⋊C4×C43C2311yescharacteristic
193C2×C4⋊C4×C43C2311yescharacteristic
194C2×C22⋊C4×C43—21no—
195C2×C22⋊C4×C43—21no—
196#106×C43C2314yescomplemented
197#103×C43C2314yescomplemented
198#103×C43C2314yescomplemented
199C24×C43C2×D411yescharacteristic
200C23×D43—21no—
201C23×D43—21no—
202C23×D43—21no—
203C23×D43—24no—
204C23×D43—44no—
205C23×D43—44no—
206C23×D43—82no—
207C23×D43C2×D411yescharacteristic
208C2×Q8×C43—21no—
209C2×Q8×C43—21no—
210C2×Q8×C43—22no—
211C2×Q8×C43—22no—
212C2×Q8×C43—22no—
213C2×Q8×C43—22no—
214C2×Q8×C43C2412yes—
215C2×Q8×C43C2412yes—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D412yes—
224C22×C4×C43C2412yes—
225C22×C4×C43C2411yescharacteristic
226C2×C22⋊D43—24no—
227C2×C22⋊D43—42no—
228C2×C22⋊D43—44no—
229C2×C22⋊D43C2×D414yes—
230C22×Dic43—21no—
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233C22×Dic43C2×D411yescharacteristic
234#10621902—28no—
235#10621902—28no—
236#10621902—44no—
237#10621902—44no—
238#10621902—48no—
239#10621902—48no—
240#10621898—28no—
241#10621898—44no—
242#10621898—48no—
243C2×D172—21no—
244C2×D172—21no—
245C2×D172—22no—
246C2×D172—22no—
247C2×D172—24no—
248C2×D172—21no—
249C2×D172—24no—
250C2×D172—24no—
251C2×D172—24no—
252C2×D172—22no—
253C2×D172—22no—
254C2×D172—28no—
255C2×D172—44no—
256C2×D172—44no—
257C2×D172—44no—
258C2×D172—44no—
259C2×D172—48no—
260C2×D172—82no—
261C2×D172C2×D414yes—
262C2×D172C2×D414yes—
263C2×D172C2412yes—
264C2×D172C2412yes—
265C2×D172C2412yes—
266C2×C4×D43—22no—
267C2×C4×D43—22no—
268C2×C4×D43—24no—
269C2×C4×D43—24no—
270C2×C4×D43—24no—
271C2×C4×D43—24no—
272C2×C4×D43—24no—
273C2×C4×D43—44no—
274C2×C4×D43—44no—
275C2×C4×D43—44no—
276C2×C4×D43—44no—
277C2×C4×D43—82no—
278C2×C4×D43C2×D412yes—
279C2×C4×D43C2412yes—
280C2×Dic86—22no—
281C2×Dic86—22no—
282C2×Dic86—21no—
283C2×Dic86C2412yes—
284Q16×C43—28no—
285M16×C43—28no—
286C2×C8×C43—22no—
287C2×C8×C43C2×D414yes—
288C2×C8×C43C2412yes—
289C2×C8×C43C2412yes—
290C4⋊C4×C43—24no—
291C4⋊C4×C43—24no—
292C4⋊C4×C43—21no—
293C4⋊C4×C43—21no—
294C4⋊C4×C43C2412yes—
295C4⋊C4×C43C2412yes—
296C22⋊C4×C43—24no—
297C22⋊C4×C43—24no—
298C22⋊Dic43C2×D414yes—
299#10621885—44no—
300#10621884—28no—
301#10621884—28no—
302#10621884—44no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4—24no—
307(C2×D43)⋊C4—24no—
308(C2×D43)⋊C4—24no—
309(C2×D43)⋊C4C2×D414yes—
310C4⋊Dic43—24no—
311Dic43⋊C4—24no—
312Dic43⋊C4—24no—
313Dic43⋊C4C2×D414yes—
314C4×Dic43C2×D412yes—
315C4×Dic43C2412yes—
316C2×C43⋊C8—22no—
317C2×C43⋊C8—22no—
318C2×C43⋊C8C2412yes—
319C2×C43⋊C8C2412yes—
320D344—28no—
321D344C2×D4116yescomplemented
322#10621873—28no—
323#10621873—28no—
324C8×D43—28no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43C22×D412yes—
329C23×C43C22×D411yescharacteristic
330C22×D43—22no—
331C22×D43—24no—
332C22×D43—24no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—48no—
339C22×D43—42no—
340C22×D43—42no—
341C22×D43—42no—
342C22×D43—42no—
343C22×D43—48no—
344C22×D43—42no—
345C22×D43—42no—
346C22×D43—42no—
347C22×D43—84no—
348C22×D43—816no—
349C22×D43C22×D412yes—
350Q8×C43—22no—
351Q8×C43—22no—
352Q8×C43—22no—
353Q8×C43—22no—
354Q8×C43—42no—
355Q8×C43—42no—
356C2×C4×C43—22no—
357C2×C4×C43—24no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—42no—
365C2×C4×C43—42no—
366C2×C4×C43—42no—
367C2×C4×C43—42no—
368C2×C4×C43C22×D412yes—
369C2×C4×C43C22×D411yescharacteristic
370C2×C4×C43C22×D412yes—
371C2×C4×C43H(5,𝔽2)12yes—
372C2×C4×C43C2511yescharacteristic
373C22⋊D43—44no—
374C22⋊D43—48no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—42no—
380C2×Dic43C22×D412yes—
381C2×Dic43C22×D412yes—
382C2×Dic43C22×D412yes—
383D172—24no—
384D172—24no—
385D172—22no—
386D172—22no—
387D172—22no—
388D172—22no—
389D172—48no—
390D172—48no—
391D172—48no—
392D172—42no—
393D172—84no—
394D172C22×D414yes—
395D172C22×D414yes—
396C4×D43—24no—
397C4×D43—22no—
398C4×D43—22no—
399C4×D43—48no—
400C4×D43—48no—
401C4×D43—48no—
402C4×D43—48no—
403C4×D43—84no—
404Dic86—22no—
405Dic86—22no—
406Dic86—42no—
407C8×C43—22no—
408C8×C43C22×D414yes—
409C43⋊C8—22no—
410C43⋊C8—22no—
411C2×#3267—431nomaximal, Sylow
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—44no—
416C22×C43D4212yes—
417C22×C43#57512yes—
418C22×C43#57712yes—
419C22×C43C23×D411yescharacteristic
420C2×D43—24no—
421C2×D43—24no—
422C2×D43—22no—
423C2×D43—22no—
424C2×D43—22no—
425C2×D43—44no—
426C2×D43—48no—
427C2×D43—48no—
428C2×D43—42no—
429C2×D43—42no—
430C2×D43—42no—
431C2×D43—42no—
432C2×D43—42no—
433C2×D43—42no—
434C2×D43—42no—
435C2×D43—816no—
436C2×D43—84no—
437C4×C43—22no—
438C4×C43—42no—
439C4×C43—42no—
440C4×C43—42no—
441C4×C43—42no—
442C4×C43D4212yes—
443C4×C43C23×D411yescharacteristic
444C4×C43C2×H(5,𝔽2)11yescharacteristic
445Dic43—22no—
446Dic43—22no—
447Dic43—22no—
448Dic43—42no—
449C22×AGL(1,ℤ/8)—431no—
450C22×#135—431no—
451C2×#547—431no—
452C2×#546—431no—
453#3267—4316no—
454C2×#497—431no—
455C2×#470D4311yescharacteristic, complemented
456C2×#465—431no—
457C2×#463—431no—
458C2×#461—431no—
459C2×#452—431no—
460C2×#452—431no—
461C2×#449—431no—
462C2×#450—431no—
463C2×#442—431no—
464C2×#435—431no—
465C2×C43—42no—
466C2×C43#326714yescomplemented
467C2×C43C2×D4211yescharacteristic
468C2×C43C2×#57511yescharacteristic
469C2×C43C2×#57711yescharacteristic
470D43—42no—
471D43—44no—
472D43—44no—
473D43—82no—
474C22×#41—431no—
475C22×#41—431no—
476C22×#41—431no—
477C23×D4—431no—
478C2×AGL(1,ℤ/8)—438no—
479C2×AGL(1,ℤ/8)—868no—
480C2×#135—438no—
481C2×#135—868no—
482C22×Q16—431no—
483C22×Q16C2×D4311yescharacteristic, complemented
484C22×SD16—431no—
485C22×SD16—431no—
486C22×SD16—431no—
487C22×SD16—431no—
488C22×SD16—431no—
489C22×D8—431no—
490C22×D8—431no—
491C22×M16C2×D4311yescharacteristic
492C23×C8—431no—
493#547—438no—
494#547—864no—
495#546—438no—
496#546—864no—
497C2×C4⋊Q8—431no—
498C2×#124—431no—
499C2×#123—861no—
500C2×#123—861no—
501C2×#123—861no—
502C2×C22⋊Q8—431no—
503C2×C22⋊Q8C2×D4311yescharacteristic
504C2×C22⋊Q8C2×D4311yescharacteristic
505C2×#121—431no—
506C2×#121—861no—
507C2×#121—861no—
508C2×#120—861no—
509C2×C4×D4—431no—
510C2×C4×D4—431no—
511C2×C4×D4—431no—
512C22×C4⋊C4—861no—
513C22×C22⋊C4—861no—
514#497—438no—
515#470C2×D4318yescomplemented
516#465—438no—
517#463—438no—
518#461—438no—
519#452—438no—
520#452—438no—
521#450—438no—
522#449—438no—
523#442—438no—
524#435—438no—
525C2×#106C2×D4311yescharacteristic, complemented
526C2×C4⋊C8—431no—
527C2×#103—431no—
528C2×#103C2×D4311yescharacteristic, complemented
529C2×#103C2×D4311yescharacteristic, complemented
530C2×#102—431no—
531C2×#102—431no—
532C2×#102—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8—431no—
535C2×#97—431no—
536C43C2×#326711yescharacteristic, complemented, Sylow
537C25—861no—
538C2×#41—434no—
539C2×#41—434no—
540C2×#41—434no—
541C2×#41—864no—
542C2×#41—862no—
543C2×#41—862no—
544C2×#41—862no—
545C2×#41—864no—
546C2×#41—864no—
547C2×#41—1722no—
548C2×#41—1722no—
549C2×#41—1722no—
550C22×Q8—431no—
551C22×Q8C22×D4311yescharacteristic
552C22×Q8C22×D4311yescharacteristic
553C22×D4—431no—
554C22×D4—431no—
555C22×D4—431no—
556C22×D4—431no—
557C22×D4—434no—
558C22×D4—864no—
559C22×D4—861no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4—862no—
565C22×D4—1722no—
566C23×C4—431no—
567C23×C4—861no—
568C23×C4—861no—
569C23×C4—861no—
570C23×C4—861no—
571C23×C4—861no—
572C23×C4C22×D4311yescharacteristic
573AGL(1,ℤ/8)—8632no—
574#135—8632no—
575C2×Q16—24no—
576C2×Q16—434no—
577C2×Q16—1722no—
578C2×Q16C22×D4314yescomplemented
579C2×SD16—434no—
580C2×SD16—434no—
581C2×SD16—434no—
582C2×SD16—434no—
583C2×SD16—434no—
584C2×SD16—864no—
585C2×SD16—864no—
586C2×SD16—864no—
587C2×SD16—864no—
588C2×SD16—1722no—
589C2×D8—438no—
590C2×D8—434no—
591C2×D8—434no—
592C2×D8—864no—
593C2×M16—24no—
594C2×M16C22×D4314yes—
595C22×C8—431no—
596C22×C8—431no—
597C22×C8—434no—
598C22×C8—864no—
599C22×C8C22×D4311yescharacteristic
600C22×C8C22×D4311yescharacteristic
601C4⋊Q8—434no—
602C4⋊Q8—862no—
603#124—434no—
604#124—862no—
605#123—868no—
606#123—868no—
607#123—868no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—434no—
611C22⋊Q8—862no—
612C22⋊Q8C22×D4314yes—
613C22⋊Q8C22×D4314yes—
614#121—434no—
615#121—868no—
616#121—868no—
617#121—862no—
618#120—868no—
619C4×D4—434no—
620C4×D4—434no—
621C4×D4—434no—
622C4×D4—434no—
623C4×D4—862no—
624C4×D4—862no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—868no—
629C2×C4⋊C4—861no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4C22×D4311yescharacteristic
633C2×C4⋊C4C22×D4311yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—868no—
639C2×C22⋊C4—861no—
640C2×C22⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C22⋊C4—861no—
643C2×C22⋊C4—861no—
644C2×C22⋊C4—861no—
645C2×C42—431no—
646#106C22×D4314yescomplemented
647C4⋊C8—434no—
648#103—434no—
649#103C22×D4314yescomplemented
650#103C22×D4314yescomplemented
651#102—434no—
652#102—434no—
653#102—434no—
654C22⋊C8—434no—
655C22⋊C8—434no—
656#97—434no—
657C24—431no—
658C24—861no—
659C24—861no—
660C24—864no—
661C24—861no—
662C24—3442no—
663C24—1724no—
664C24—1724no—
665C24D4×D4311yescharacteristic
666#41—868no—
667#41—868no—
668#41—868no—
669#41—1724no—
670#41—1728no—
671#41—1724no—
672#41—1724no—
673#41—1728no—
674#41—1728no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—432no—
682C2×Q8—861no—
683C2×Q8—862no—
684C2×Q8—862no—
685C2×Q8C23×D4312yes—
686C2×Q8C23×D4312yes—
687C2×D4—434no—
688C2×D4—434no—
689C2×D4—434no—
690C2×D4—432no—
691C2×D4—432no—
692C2×D4—432no—
693C2×D4—868no—
694C2×D4—864no—
695C2×D4—864no—
696C2×D4—864no—
697C2×D4—864no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—862no—
701C2×D4—864no—
702C2×D4—861no—
703C2×D4—862no—
704C2×D4—862no—
705C2×D4—862no—
706C2×D4—3442no—
707C2×D4—1724no—
708C2×D4—1728no—
709C2×D4—1724no—
710C2×D4—1724no—
711C2×D4—1724no—
712C2×D4—1722no—
713C2×D4—1724no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—432no—
724C22×C4—432no—
725C22×C4—864no—
726C22×C4—864no—
727C22×C4—864no—
728C22×C4—864no—
729C22×C4—862no—
730C22×C4—862no—
731C22×C4—861no—
732C22×C4—864no—
733C22×C4—3442no—
734C22×C4—1724no—
735C22×C4—1724no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4D4×D4312yes—
739C22×C4D4×D4311yescharacteristic
740C22×C4C23×D4312yes—
741C22×C4C23×D4311yescharacteristic
742Q16—28no—
743Q16—1724no—
744SD16—868no—
745SD16—868no—
746SD16—868no—
747SD16—868no—
748SD16—1724no—
749D8—4316no—
750D8—868no—
751M16—28no—
752C2×C8—22no—
753C2×C8—432no—
754C2×C8—432no—
755C2×C8—862no—
756C2×C8—862no—
757C2×C8—868no—
758C2×C8D4×D4314yes—
759C2×C8C23×D4312yes—
760C2×C8C23×D4312yes—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—434no—
766C4⋊C4—864no—
767C4⋊C4—864no—
768C4⋊C4—864no—
769C4⋊C4C23×D4312yes—
770C4⋊C4C23×D4312yes—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—434no—
774C22⋊C4—434no—
775C22⋊C4—864no—
776C22⋊C4—864no—
777C22⋊C4—864no—
778C22⋊C4—864no—
779C22⋊C4—864no—
780C22⋊C4—864no—
781C42—432no—
782C42—432no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—432no—
787C23—862no—
788C23—862no—
789C23—862no—
790C23—862no—
791C23—862no—
792C23—864no—
793C23—864no—
794C23—862no—
795C23—3444no—
796C23—34416no—
797C23—1728no—
798C23—1728no—
799C23—1722no—
800C23—1722no—
801C23—1722no—
802C23—1722no—
803C23—1722no—
804C23—1722no—
805C23—1722no—
806C23C2×D4×D4312yes—
807C23C2×D4×D4311yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—42no—
813Q8—42no—
814Q8—862no—
815Q8—862no—
816Q8—1722no—
817D4—434no—
818D4—434no—
819D4—862no—
820D4—862no—
821D4—862no—
822D4—862no—
823D4—864no—
824D4—864no—
825D4—3444no—
826D4—1728no—
827D4—1728no—
828D4—1728no—
829D4—1724no—
830D4—1728no—
831D4—1722no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—432no—
845C2×C4—432no—
846C2×C4—432no—
847C2×C4—862no—
848C2×C4—862no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—862no—
852C2×C4—864no—
853C2×C4—862no—
854C2×C4—3444no—
855C2×C4—1728no—
856C2×C4—1728no—
857C2×C4—1728no—
858C2×C4—1728no—
859C2×C4—1722no—
860C2×C4C2×D4×D4312yes—
861C2×C4C2×D4×D4312yes—
862C2×C4C2×D4×D4311yescharacteristic
863C2×C4#1306337112yes—
864C2×C4C24×D4311yescharacteristic
865C8—22no—
866C8—862no—
867C8—862no—
868C8C2×D4×D4314yes—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—862no—
874C22—864no—
875C22—864no—
876C22—862no—
877C22—862no—
878C22—34416no—
879C22—3444no—
880C22—1722no—
881C22—1722no—
882C22—1722no—
883C22—1722no—
884C22—1722no—
885C22—1722no—
886C22—1722no—
887C22—1724no—
888C22—1728no—
889C22—1728no—
890C22#1458353312yes—
891C22#1458369812yes—
892C22#1458370812yes—
893C22C22×D4×D4311yescharacteristic
894C4—22no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—862no—
900C4—862no—
901C4—862no—
902C4—1722no—
903C4#1458353312yes—
904C4C22×D4×D4311yescharacteristic
905C4C2×#1306337111yescharacteristic
906C2—42no—
907C2—3442no—
908C2—1722no—
909C2—1724no—
910C2—1724no—
911C2#1914612714yesdirect product factor
912C2C2×#1458353311yescharacteristic
913C2C2×#1458369811yescharacteristic
914C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#470C2
socleC23×C43C22×D4
hypercenterC2×#470D43
hypocenterC43C2×#3267
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C22×#13063353C2semidirect
2. C22×#13063348C2semidirect
3. C2×#14583551C2semidirect
4. C2×#14583540C2semidirect
5. #19146127C2direct (N × H)
6. C2×#14583292C2semidirect
7. C2×#14583129C2semidirect
8. C2×#14583117C2semidirect
9. C2×#14583103C2semidirect
10. C2×#14583064C2semidirect
11. C2×#14583059C2semidirect
12. C2×#14583047C2semidirect
13. C2×#14583049C2semidirect
14. C2×#14583010C2semidirect
15. C2×#14582968C2semidirect
16. C2×C43×#470C2semidirect
18. C22×#10621902C22semidirect
22. C2×#13063353C22semidirect
24. C2×#13063348C22semidirect
25. C22×#10621885C22semidirect
30. C22×#10621884C22semidirect
33. C22×C8×D43C22semidirect
35. #14583551C22semidirect
37. #14583540C22semidirect
38. C2×#13063323C22semidirect
43. C2×#13063305C22semidirect
49. C2×#13063287C22semidirect
53. #14583292C22semidirect
54. #14583129C22semidirect
55. #14583117C22semidirect
56. #14583103C22semidirect
57. #14583064C22semidirect
58. #14583059C22semidirect
59. #14583049C22semidirect
60. #14583047C22semidirect
61. #14583010C22semidirect
62. #14582968C22semidirect
63. C2×Dic43⋊C8C22semidirect
64. C2×#13063248C22semidirect
67. C2×#13063245C22semidirect
69. C2×(C2×D43)⋊C8C22semidirect
70. C2×#13063235C22semidirect
71. C22×Q16×C43C22semidirect
75. C43×#470C22semidirect
76. C2×#106×C43C22semidirect
77. C2×#103×C43C22semidirect
78. C2×#103×C43C22semidirect
87. C2×#10621902C23semidirect
115. C2×#10621885C23semidirect
125. C2×#10621884C23semidirect
127. C2×D344D4semidirect
133. C2×C8×D43C23semidirect
135. #13063323C23semidirect
142. #13063305C23semidirect
151. #13063287C23semidirect
169. Dic43⋊C8C23semidirect
170. #13063248C23semidirect
173. #13063245C23semidirect
175. (C2×D43)⋊C8C23semidirect
176. #13063235C23semidirect
181. C2×Q16×C43C23semidirect
196. #106×C43C23semidirect
197. #103×C43C23semidirect
198. #103×C43C23semidirect
321. D344C2×D4semidirect
455. C2×#470D43semidirect
466. C2×C43#3267semidirect
483. C22×Q16C2×D43semidirect
515. #470C2×D43semidirect
525. C2×#106C2×D43semidirect
528. C2×#103C2×D43semidirect
529. C2×#103C2×D43semidirect
536. C43C2×#3267semidirect
578. C2×Q16C22×D43semidirect
646. #106C22×D43semidirect
649. #103C22×D43semidirect
650. #103C22×D43semidirect
911. C2#19146127direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633532
C22×#130633482
C2×#145835512
C2×#145835402
#191461272
C2×#145832922
C2×#145831292
C2×#145831172
C2×#145831032
C2×#145830642
C2×#145830592
C2×#145830472
C2×#145830492
C2×#145830102
C2×#145829682
C2×C43×#4702
C2×#326743