Finite Group Databasebeta

← C2×#19146182 #25971660

Subgroups — C2×#19146182 #25971660

Order 11008.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic, complemented
2C22×#13063348C211yesmaximal, characteristic, complemented
3C2×#14583571C211yesmaximal, characteristic, complemented
4C2×#14583561C211yesmaximal, characteristic, complemented
5#19146182C2116yesmaximal, direct product factor
6C2×#14583288C211yesmaximal, characteristic, complemented
7C2×#14583153C211yesmaximal, characteristic, complemented
8C2×#14583129C211yesmaximal, characteristic, complemented
9C2×#14583121C211yesmaximal, characteristic, complemented
10C2×#14583099C211yesmaximal, characteristic, complemented
11C2×#14583064C211yesmaximal, characteristic, complemented
12C2×#14583047C211yesmaximal, characteristic, complemented
13C2×#14583047C211yesmaximal, characteristic, complemented
14C2×#14583039C211yesmaximal, characteristic, complemented
15C2×#14582972C211yesmaximal, characteristic, complemented
16C2×C43×#441C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621902C2211yescharacteristic
19C22×#10621902C2211yescharacteristic
20C22×Q8×D43C2211yescharacteristic
21C2×#13063357—28no—
22C2×#13063357C2218yescomplemented
23C2×#13063348—28no—
24C2×#13063348C2218yescomplemented
25C22×#10621885C2211yescharacteristic
26C22×#10621873C2211yescharacteristic
27C22×#10621873C2211yescharacteristic
28C22×#10621884C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621884C2211yescharacteristic
31C22×D344C2211yescharacteristic
32C22×D344C2211yescharacteristic
33C22×#10621872C2211yescharacteristic
34C22×C8×D43C2211yescharacteristic
35#14583571—24no—
36#14583571C2218yescomplemented
37#14583561—24no—
38#14583561C2218yescomplemented
39C2×#13063322—21no—
40C2×#13063322C2211yescharacteristic
41C2×#13063313—21no—
42C2×#13063313C2211yescharacteristic
43C2×#13063305—21no—
44C2×#13063305C2211yescharacteristic
45C2×#13063300—21no—
46C2×#13063300—21no—
47C2×#13063300—21no—
48C2×#13063300C2211yescharacteristic
49C2×#13063300C2211yescharacteristic
50C2×#13063300C2211yescharacteristic
51C2×C4×D172—21no—
52C2×C4×D172—21no—
53C2×C4×D172C2211yescharacteristic
54#14583288C2218yescomplemented
55#14583153C2218yescomplemented
56#14583129C2218yescomplemented
57#14583121C2218yescomplemented
58#14583099C2218yescomplemented
59#14583064C2218yescomplemented
60#14583047C2218yescomplemented
61#14583047C2218yescomplemented
62#14583039C2218yescomplemented
63#14582972C2218yescomplemented
64C2×C4⋊(C43⋊C8)C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×#13063245C2211yescharacteristic
68C2×#13063245C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×(C2×D43)⋊C8C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C2×C4×Q8×C43C2211yescharacteristic
74C43×#441C2218yescomplemented
75C2×#106×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C2×#103×C43C2211yescharacteristic
78C2×#97×C43C2211yescharacteristic
79C2×#10621902—22no—
80C2×#10621902—22no—
81C2×#10621902—22no—
82C2×#10621902—24no—
83C2×#10621902—24no—
84C2×#10621902—24no—
85C2×#10621902—42no—
86C2×#10621902—42no—
87C2×#10621902—42no—
88C2×#10621902C2314yes—
89C2×#10621902C2314yes—
90C2×#10621902C2314yes—
91C22×Dic86—21no—
92C22×Dic86C2311yescharacteristic
93C2×Q8×D43—22no—
94C2×Q8×D43—24no—
95C2×Q8×D43—42no—
96C2×Q8×D43C2314yes—
97C22×D172—21no—
98C22×D172—21no—
99C22×D172—21no—
100C22×D172—21no—
101C22×D172—21no—
102C22×D172—21no—
103C22×D172—21no—
104C22×D172—21no—
105C22×D172D411yescharacteristic
106C22×D172C2311yescharacteristic
107C22×D172C2311yescharacteristic
108C22×D172C2311yescharacteristic
109C22×C4×D43—21no—
110C22×C4×D43—21no—
111C22×C4×D43—21no—
112C22×C4×D43—21no—
113C22×C4×D43C2311yescharacteristic
114C22×C4×D43C2311yescharacteristic
115#13063357—232no—
116#13063348—232no—
117C2×#10621885—24no—
118C2×#10621885C2314yes—
119C2×#10621873—24no—
120C2×#10621873—42no—
121C2×#10621873C2314yes—
122C2×#10621873C2314yes—
123C2×#10621884—24no—
124C2×#10621884—24no—
125C2×#10621884—24no—
126C2×#10621884C2314yes—
127C2×#10621884C2314yes—
128C2×#10621884C2314yes—
129C2×D344—24no—
130C2×D344—42no—
131C2×D344C2314yes—
132C2×D344C2314yes—
133C2×#10621872—24no—
134C2×#10621872C2314yes—
135C22×C43⋊C8C2311yescharacteristic
136C22×C43⋊C8C2311yescharacteristic
137C2×C8×D43—24no—
138C2×C8×D43C2314yes—
139#13063322—28no—
140#13063322—22no—
141#13063322C2314yes—
142#13063313—22no—
143#13063313—28no—
144#13063313C2314yes—
145#13063305—22no—
146#13063305—28no—
147#13063305C2314yes—
148#13063300—28no—
149#13063300—22no—
150#13063300—22no—
151#13063300—22no—
152#13063300—28no—
153#13063300—28no—
154#13063300C2314yes—
155#13063300C2314yes—
156#13063300C2314yes—
157C4×D172—28no—
158C4×D172—28no—
159C4×D172D414yes—
160C4×D172C2314yes—
161C2×C4⋊Dic43—21no—
162C2×C4⋊Dic43D411yescharacteristic
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4—21no—
169C2×(C2×D43)⋊C4D411yescharacteristic
170C2×(C2×D43)⋊C4D411yescharacteristic
171C4⋊(C43⋊C8)C2314yes—
172#13063248C2314yes—
173#13063245C2314yes—
174#13063245C2314yes—
175#13063245C2314yes—
176(C2×D43)⋊C8C2314yes—
177(C2×D43)⋊C8C2314yes—
178C22×Q8×C43C2311yescharacteristic
179C22×Q8×C43C2311yescharacteristic
180C2×Q16×C43D418yescomplemented
181C2×Q16×C43C2314yes—
182C22×C8×C43C2311yescharacteristic
183C22×C8×C43C2311yescharacteristic
184C4×Q8×C43—22no—
185C4×Q8×C43—22no—
186C4×Q8×C43C2314yes—
187C4×Q8×C43C2314yes—
188C2×C4⋊C4×C43—21no—
189C2×C4⋊C4×C43—21no—
190C2×C4⋊C4×C43C2311yescharacteristic
191C2×C4⋊C4×C43C2311yescharacteristic
192C2×C42×C43—21no—
193C2×C42×C43—21no—
194C2×C42×C43C2311yescharacteristic
195#106×C43C2314yes—
196#103×C43C2314yes—
197#103×C43C2314yes—
198#97×C43C2314yes—
199C23×D43—21no—
200C23×D43—21no—
201C23×D43—21no—
202C23×D43C2×D411yescharacteristic
203C23×D43C2×D411yescharacteristic
204C2×Q8×C43—21no—
205C2×Q8×C43—21no—
206C2×Q8×C43—22no—
207C2×Q8×C43—22no—
208C2×Q8×C43C2×D414yes—
209C2×Q8×C43C2×D414yes—
210C2×Q8×C43C2412yes—
211C2×Q8×C43C2412yes—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2411yescharacteristic
219C22×Dic43—21no—
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222#10621902—28no—
223#10621902—28no—
224#10621902—28no—
225#10621902—44no—
226#10621902—44no—
227#10621902—44no—
228#10621902—48no—
229#10621902—48no—
230#10621902—48no—
231Q8×D43—28no—
232Q8×D43—44no—
233Q8×D43—48no—
234C2×D172—24no—
235C2×D172—21no—
236C2×D172—21no—
237C2×D172—21no—
238C2×D172—24no—
239C2×D172—24no—
240C2×D172—24no—
241C2×D172—24no—
242C2×D172—24no—
243C2×D172—24no—
244C2×D172—24no—
245C2×D172—22no—
246C2×D172—22no—
247C2×D172—22no—
248C2×D172—22no—
249C2×D172—22no—
250C2×D172—22no—
251C2×D172—42no—
252C2×D172—44no—
253C2×D172—44no—
254C2×D172—44no—
255C2×D172—44no—
256C2×D172—44no—
257C2×D172—82no—
258C2×D172—82no—
259C2×D172—82no—
260C2×D172C2×D414yes—
261C2×D172C2412yes—
262C2×D172C2412yes—
263C2×D172C2412yes—
264C2×C4×D43—22no—
265C2×C4×D43—22no—
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—44no—
273C2×C4×D43—44no—
274C2×C4×D43—44no—
275C2×C4×D43—44no—
276C2×C4×D43C2×D412yes—
277C2×C4×D43C2×D412yes—
278C2×C4×D43C2412yes—
279C2×C4×D43C2412yes—
280C2×Dic86—22no—
281C2×Dic86—22no—
282C2×Dic86—21no—
283C2×Dic86—24no—
284C2×Dic86—44no—
285C2×Dic86C2412yes—
286Q16×C43C2×D4116yescomplemented
287C2×C8×C43—22no—
288C2×C8×C43C2×D414yes—
289C2×C8×C43C2412yes—
290C2×C8×C43C2412yes—
291C4⋊C4×C43—24no—
292C4⋊C4×C43—24no—
293C4⋊C4×C43—21no—
294C4⋊C4×C43—21no—
295C4⋊C4×C43C2412yes—
296C4⋊C4×C43C2412yes—
297C42×C43—24no—
298C42×C43—24no—
299C42×C43C2×D412yes—
300C42×C43C2412yes—
301#10621885—28no—
302#10621884—28no—
303#10621884—28no—
304#10621884—28no—
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4—24no—
307(C2×D43)⋊C4—24no—
308(C2×D43)⋊C4—24no—
309(C2×D43)⋊C4—24no—
310(C2×D43)⋊C4—24no—
311(C2×D43)⋊C4C2×D414yes—
312(C2×D43)⋊C4C2×D414yes—
313C4⋊Dic43—24no—
314C4⋊Dic43C2×D414yes—
315C2×C43⋊C8—22no—
316C2×C43⋊C8—22no—
317C2×C43⋊C8C2412yes—
318C2×C43⋊C8C2412yes—
319D344—28no—
320D344—44no—
321#10621873—28no—
322#10621873—44no—
323#10621872—28no—
324C8×D43—28no—
325C23×C43C22×D411yescharacteristic
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—42no—
336C22×D43—42no—
337C22×D43—42no—
338C22×D43—42no—
339C22×D43—42no—
340C22×D43—42no—
341C22×D43—42no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43C22×D412yes—
345C22×D43C22×D412yes—
346Q8×C43—24no—
347Q8×C43—24no—
348Q8×C43—22no—
349Q8×C43—22no—
350Q8×C43C22×D414yes—
351Q8×C43C22×D414yes—
352C2×C4×C43—24no—
353C2×C4×C43—24no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—42no—
361C2×C4×C43—42no—
362C2×C4×C43C22×D412yes—
363C2×C4×C43C22×D412yes—
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D412yes—
366C2×C4×C43H(5,𝔽2)12yes—
367C2×C4×C43C2511yescharacteristic
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—42no—
372C2×Dic43C22×D412yes—
373C2×Dic43C22×D412yes—
374D172—22no—
375D172—22no—
376D172—22no—
377D172—22no—
378D172—22no—
379D172—22no—
380D172—44no—
381D172—48no—
382D172—48no—
383D172—48no—
384D172—48no—
385D172—48no—
386D172—42no—
387D172—42no—
388D172—42no—
389D172—84no—
390D172—84no—
391D172—84no—
392C4×D43—24no—
393C4×D43—24no—
394C4×D43—22no—
395C4×D43—22no—
396C4×D43—22no—
397C4×D43—22no—
398C4×D43—48no—
399C4×D43—48no—
400C4×D43—48no—
401C4×D43—48no—
402Dic86—22no—
403Dic86—22no—
404Dic86—48no—
405Dic86—42no—
406C8×C43—22no—
407C8×C43C22×D414yes—
408C43⋊C8—22no—
409C43⋊C8—22no—
410C2×#3271—431nomaximal, Sylow
411C22×C43D4212yes—
412C22×C43#57512yes—
413C22×C43#57712yes—
414C22×C43C23×D411yescharacteristic
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—44no—
422C2×D43—44no—
423C2×D43—42no—
424C2×D43—42no—
425C2×D43—42no—
426C2×D43—42no—
427C2×D43—42no—
428C2×D43—42no—
429C2×D43—42no—
430C2×D43—42no—
431C2×D43—42no—
432C2×D43—84no—
433C2×D43—84no—
434C2×D43—84no—
435C4×C43—24no—
436C4×C43—24no—
437C4×C43—22no—
438C4×C43—22no—
439C4×C43—42no—
440C4×C43—42no—
441C4×C43D4212yes—
442C4×C43C23×D411yescharacteristic
443C4×C43C2×H(5,𝔽2)11yescharacteristic
444Dic43—22no—
445Dic43—22no—
446Dic43—42no—
447C22×#137—431no—
448C22×#135—431no—
449C2×#550—431no—
450C2×#548—431no—
451#3271—4316no—
452C2×#496—431no—
453C2×#469—431no—
454C2×#465—431no—
455C2×#464—431no—
456C2×#460—431no—
457C2×#452—431no—
458C2×#449—431no—
459C2×#449—431no—
460C2×#448—431no—
461C2×#441D4311yescharacteristic, complemented
462C2×#435—431no—
463C2×C43#327114yescomplemented
464C2×C43C2×D4211yescharacteristic
465C2×C43C2×#57511yescharacteristic
466C2×C43C2×#57711yescharacteristic
467D43—42no—
468D43—42no—
469D43—82no—
470D43—82no—
471D43—82no—
472C22×#41—431no—
473C22×#41—431no—
474C22×#41—431no—
475C23×Q8—431no—
476C2×#137—438no—
477C2×#137—868no—
478C2×#135—438no—
479C2×#135—868no—
480C22×Q16—431no—
481C22×Q16C2×D4311yescharacteristic
482C22×SD16—431no—
483C22×SD16—431no—
484C22×SD16—431no—
485C22×SD16—431no—
486C22×SD16—431no—
487C22×D8—431no—
488C22×D8—431no—
489C22×M16—431no—
490C23×C8—431no—
491#550—438no—
492#550—864no—
493#548—438no—
494#548—864no—
495C2×#127—431no—
496C2×#127—861no—
497C2×#124—431no—
498C2×#124—861no—
499C2×C22⋊Q8—431no—
500C2×C22⋊Q8—861no—
501C2×#121—431no—
502C2×#121—431no—
503C2×#121—431no—
504C2×#121—861no—
505C2×#121—861no—
506C2×#121—861no—
507C2×C4×Q8C2×D4311yescharacteristic
508C2×C4×Q8C2×D4311yescharacteristic
509C2×C4×D4—431no—
510C2×C4×D4—861no—
511C2×C4×D4—861no—
512#496—438no—
513#469—438no—
514#465—438no—
515#464—438no—
516#460—438no—
517#452—438no—
518#449—438no—
519#449—438no—
520#448—438no—
521#441C2×D4318yescomplemented
522#435—438no—
523C2×#106C2×D4311yescharacteristic
524C2×C4⋊C8—431no—
525C2×#103—431no—
526C2×#103C2×D4311yescharacteristic
527C2×#103C2×D4311yescharacteristic
528C2×#102—431no—
529C2×#102—431no—
530C2×#102—431no—
531C2×C22⋊C8—431no—
532C2×C22⋊C8—431no—
533C2×#97C2×D4311yescharacteristic
534C43C2×#327111yescharacteristic, complemented, Sylow
535C2×#41—434no—
536C2×#41—434no—
537C2×#41—434no—
538C2×#41—862no—
539C2×#41—862no—
540C2×#41—862no—
541C2×#41—864no—
542C2×#41—864no—
543C2×#41—864no—
544C2×#41—1722no—
545C2×#41—1722no—
546C2×#41—1722no—
547C22×Q8—434no—
548C22×Q8—431no—
549C22×Q8—861no—
550C22×Q8—862no—
551C22×Q8—864no—
552C22×Q8—1722no—
553C22×Q8C22×D4311yescharacteristic
554C22×Q8C22×D4311yescharacteristic
555C22×D4—431no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—431no—
559C22×D4—861no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4—861no—
565C22×D4—861no—
566C22×D4—861no—
567C23×C4—431no—
568C23×C4—431no—
569C23×C4—861no—
570C23×C4—861no—
571C23×C4—861no—
572C23×C4—861no—
573#137—8632no—
574#135—8632no—
575C2×Q16—434no—
576C2×Q16—864no—
577C2×Q16D17218yescomplemented
578C2×Q16C22×D4314yes—
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—434no—
590C2×D8—434no—
591C2×D8—864no—
592C2×D8—1722no—
593C2×M16—434no—
594C2×M16—864no—
595C22×C8—431no—
596C22×C8—431no—
597C22×C8—434no—
598C22×C8—864no—
599C22×C8C22×D4311yescharacteristic
600C22×C8C22×D4311yescharacteristic
601#127—434no—
602#127—868no—
603#127—862no—
604#124—434no—
605#124—868no—
606#124—862no—
607C22⋊Q8—434no—
608C22⋊Q8—868no—
609C22⋊Q8—862no—
610#121—434no—
611#121—434no—
612#121—434no—
613#121—868no—
614#121—868no—
615#121—862no—
616#121—862no—
617#121—862no—
618#121—868no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8C22×D4314yes—
622C4×Q8C22×D4314yes—
623C4×D4—434no—
624C4×D4—434no—
625C4×D4—868no—
626C4×D4—868no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4C22×D4311yescharacteristic
632C2×C4⋊C4C22×D4311yescharacteristic
633C2×C22⋊C4—431no—
634C2×C22⋊C4—431no—
635C2×C22⋊C4—861no—
636C2×C22⋊C4—861no—
637C2×C22⋊C4—861no—
638C2×C22⋊C4—861no—
639C2×C22⋊C4—861no—
640C2×C22⋊C4—861no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42C22×D4311yescharacteristic
644#106C22×D4314yes—
645C4⋊C8—434no—
646#103—434no—
647#103C22×D4314yes—
648#103C22×D4314yes—
649#102—434no—
650#102—434no—
651#102—434no—
652C22⋊C8—434no—
653C22⋊C8—434no—
654#97C22×D4314yes—
655C24—431no—
656C24—431no—
657C24—861no—
658C24—861no—
659C24—861no—
660#41—868no—
661#41—868no—
662#41—868no—
663#41—1724no—
664#41—1724no—
665#41—1724no—
666#41—1728no—
667#41—1728no—
668#41—1728no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—22no—
672C2×Q8—22no—
673C2×Q8—432no—
674C2×Q8—864no—
675C2×Q8—861no—
676C2×Q8—868no—
677C2×Q8—862no—
678C2×Q8—862no—
679C2×Q8—1724no—
680C2×Q8—1724no—
681C2×Q8—1728no—
682C2×Q8C2×D17214yes—
683C2×Q8C2×D17214yes—
684C2×Q8C23×D4312yes—
685C2×Q8C23×D4312yes—
686C2×D4—434no—
687C2×D4—432no—
688C2×D4—432no—
689C2×D4—432no—
690C2×D4—864no—
691C2×D4—864no—
692C2×D4—864no—
693C2×D4—864no—
694C2×D4—864no—
695C2×D4—864no—
696C2×D4—864no—
697C2×D4—864no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—862no—
702C2×D4—862no—
703C2×D4—862no—
704C2×D4—862no—
705C2×D4—862no—
706C2×D4—862no—
707C2×D4—3442no—
708C2×D4—3442no—
709C2×D4—3442no—
710C2×D4—1722no—
711C2×D4—1724no—
712C2×D4—1724no—
713C2×D4—1724no—
714C2×D4—1724no—
715C2×D4—1724no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—432no—
723C22×C4—432no—
724C22×C4—432no—
725C22×C4—432no—
726C22×C4—864no—
727C22×C4—864no—
728C22×C4—864no—
729C22×C4—864no—
730C22×C4—862no—
731C22×C4—862no—
732C22×C4—862no—
733C22×C4—862no—
734C22×C4—861no—
735C22×C4—1724no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4—1724no—
739C22×C4D4×D4311yescharacteristic
740C22×C4D4×D4311yescharacteristic
741C22×C4C23×D4311yescharacteristic
742Q16—868no—
743Q16C2×D172116yescomplemented
744SD16—868no—
745SD16—868no—
746SD16—868no—
747SD16—868no—
748SD16—1724no—
749D8—868no—
750D8—1724no—
751M16—868no—
752C2×C8—22no—
753C2×C8—432no—
754C2×C8—432no—
755C2×C8—862no—
756C2×C8—862no—
757C2×C8—868no—
758C2×C8C2×D17214yes—
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⋊C4C23×D4312yes—
768C4⋊C4C23×D4312yes—
769C22⋊C4—434no—
770C22⋊C4—434no—
771C22⋊C4—864no—
772C22⋊C4—864no—
773C22⋊C4—864no—
774C22⋊C4—864no—
775C22⋊C4—864no—
776C22⋊C4—864no—
777C42—24no—
778C42—24no—
779C42D4×D4312yes—
780C42C23×D4312yes—
781C23—432no—
782C23—432no—
783C23—862no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—862no—
788C23—862no—
789C23—862no—
790C23—862no—
791C23—862no—
792C23—1722no—
793C23—1722no—
794C23—1722no—
795C23—1722no—
796C23—1722no—
797C23—1722no—
798C23—1722no—
799C23—1722no—
800C23—1722no—
801C23C2×D4×D4311yescharacteristic
802Q8—22no—
803Q8—22no—
804Q8—24no—
805Q8—24no—
806Q8—862no—
807Q8—862no—
808Q8—1728no—
809Q8—1722no—
810Q8C22×D17214yes—
811Q8C22×D17214yes—
812D4—862no—
813D4—862no—
814D4—862no—
815D4—862no—
816D4—862no—
817D4—862no—
818D4—3444no—
819D4—3444no—
820D4—3444no—
821D4—1724no—
822D4—1728no—
823D4—1728no—
824D4—1728no—
825D4—1728no—
826D4—1728no—
827D4—1722no—
828D4—1722no—
829D4—1722no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—432no—
841C2×C4—432no—
842C2×C4—862no—
843C2×C4—862no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—862no—
848C2×C4—864no—
849C2×C4—864no—
850C2×C4—862no—
851C2×C4—1728no—
852C2×C4—1728no—
853C2×C4—1728no—
854C2×C4—1728no—
855C2×C4—1722no—
856C2×C4C2×D4×D4312yes—
857C2×C4C2×D4×D4312yes—
858C2×C4C2×D4×D4311yescharacteristic
859C2×C4C22×D17212yes—
860C2×C4#1306337112yes—
861C2×C4C24×D4311yescharacteristic
862C8—22no—
863C8—862no—
864C8—862no—
865C8C22×D17214yes—
866C22—862no—
867C22—862no—
868C22—862no—
869C22—862no—
870C22—862no—
871C22—862no—
872C22—3444no—
873C22—3444no—
874C22—3444no—
875C22—1722no—
876C22—1722no—
877C22—1722no—
878C22—1722no—
879C22—1722no—
880C22—1722no—
881C22—1722no—
882C22—1722no—
883C22—1722no—
884C22—1724no—
885C22—1724no—
886C22D4×D17212yes—
887C22#1458369812yes—
888C22#1458370812yes—
889C22C22×D4×D4311yescharacteristic
890C4—24no—
891C4—24no—
892C4—22no—
893C4—22no—
894C4—42no—
895C4—42no—
896C4—862no—
897C4—862no—
898C4—1722no—
899C4D4×D17212yes—
900C4C23×D17211yescharacteristic
901C4C2×#1306337111yescharacteristic
902C2—3442no—
903C2—3442no—
904C2—3442no—
905C2—1722no—
906C2—1722no—
907C2#1914618214yesdirect product factor
908C2C2×D4×D17211yescharacteristic
909C2C2×#1458369811yescharacteristic
910C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#441C2
socleC23×C43C22×D4
hypercenterC2×#441D43
hypocenterC43C2×#3271
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C22×#13063357C2semidirect
2. C22×#13063348C2semidirect
3. C2×#14583571C2semidirect
4. C2×#14583561C2semidirect
5. #19146182C2direct (N × H)
6. C2×#14583288C2semidirect
7. C2×#14583153C2semidirect
8. C2×#14583129C2semidirect
9. C2×#14583121C2semidirect
10. C2×#14583099C2semidirect
11. C2×#14583064C2semidirect
12. C2×#14583047C2semidirect
13. C2×#14583047C2semidirect
14. C2×#14583039C2semidirect
15. C2×#14582972C2semidirect
16. C2×C43×#441C2semidirect
22. C2×#13063357C22semidirect
24. C2×#13063348C22semidirect
36. #14583571C22semidirect
38. #14583561C22semidirect
54. #14583288C22semidirect
55. #14583153C22semidirect
56. #14583129C22semidirect
57. #14583121C22semidirect
58. #14583099C22semidirect
59. #14583064C22semidirect
60. #14583047C22semidirect
61. #14583047C22semidirect
62. #14583039C22semidirect
63. #14582972C22semidirect
74. C43×#441C22semidirect
180. C2×Q16×C43D4semidirect
286. Q16×C43C2×D4semidirect
461. C2×#441D43semidirect
463. C2×C43#3271semidirect
521. #441C2×D43semidirect
534. C43C2×#3271semidirect
577. C2×Q16D172semidirect
743. Q16C2×D172semidirect
907. C2#19146182direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633572
C22×#130633482
C2×#145835712
C2×#145835612
#191461822
C2×#145832882
C2×#145831532
C2×#145831292
C2×#145831212
C2×#145830992
C2×#145830642
C2×#145830472
C2×#145830392
C2×#145829722
C2×C43×#4412
C2×#327143