Finite Group Databasebeta

← C2×#19147632 #25977572

Subgroups — C2×#19147632 #25977572

Order 11008.

2314 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×#14583631C211yesmaximal, characteristic, complemented
2C2×#14583570C211yesmaximal, characteristic, complemented
3#19147632C2116yesmaximal, direct product factor
4C2×#14583289C211yesmaximal, characteristic, complemented
5C2×#14583285C211yesmaximal, characteristic, complemented
6C2×#14583274C211yesmaximal, characteristic, complemented
7C2×#14583097C211yesmaximal, characteristic, complemented
8C2×#14583117C211yesmaximal, characteristic, complemented
9C2×#14583095C211yesmaximal, characteristic, complemented
10C2×#14583093C211yesmaximal, characteristic, complemented
11C2×#14583092C211yesmaximal, characteristic, complemented
12C2×#14583028C211yesmaximal, characteristic, complemented
13C2×#14583009C211yesmaximal, characteristic, complemented
14C2×#14583008C211yesmaximal, characteristic, complemented
15C2×#14582984C211yesmaximal, characteristic, complemented
16C2×C43×#463C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×#10621884C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×D344C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621882C2211yescharacteristic
25#14583631—24no—
26#14583631C2218yescomplemented
27#14583570—24no—
28#14583570C2218yescomplemented
29C2×#13063322C2211yescharacteristic
30C2×#13063321C2211yescharacteristic
31C2×#13063321C2211yescharacteristic
32C2×#13063321C2211yescharacteristic
33C2×#13063314C2211yescharacteristic
34C2×#13063311—21no—
35C2×#13063309—21no—
36C2×#13063307—21no—
37C2×#13063299—21no—
38C2×#13063298—21no—
39C2×#13063298—21no—
40C2×Q8×Dic43C2211yescharacteristic
41C2×C4×Dic86C2211yescharacteristic
42C2×C4×D172C2211yescharacteristic
43C2×D4×Dic43C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063287C2211yescharacteristic
46C2×(C22⋊D43)⋊C4—21no—
47#14583289C2218yescomplemented
48#14583285C2218yescomplemented
49#14583274C2218yescomplemented
50#14583117C2218yescomplemented
51#14583097C2218yescomplemented
52#14583095C2218yescomplemented
53#14583093C2218yescomplemented
54#14583092C2218yescomplemented
55#14583028C2218yescomplemented
56#14583009C2218yescomplemented
57#14583008C2218yescomplemented
58#14582984C2218yescomplemented
59C2×#13063256C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×D8×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic
73C43×#463C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C22×Dic86D411yescharacteristic
80C22×D172—21no—
81C22×D172—21no—
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C2×#10621884—24no—
96C2×#10621884—42no—
97C2×#10621884C2314yes—
98C2×#10621884C2314yes—
99C2×D344—42no—
100C2×D344—42no—
101C2×D344C2314yes—
102C2×D344C2314yes—
103C2×#10621882—24no—
104C2×#10621882—24no—
105C2×#10621882—42no—
106C2×#10621882C2314yes—
107C2×#10621882C2314yes—
108C2×#10621882C2314yes—
109C22×C43⋊C8C2311yescharacteristic
110C22×C43⋊C8C2311yescharacteristic
111#13063322—22no—
112#13063322C2314yes—
113#13063321—22no—
114#13063321—22no—
115#13063321—22no—
116#13063321C2314yes—
117#13063321C2314yes—
118#13063321C2314yes—
119#13063314—22no—
120#13063314C2314yes—
121#13063311—28no—
122#13063309—28no—
123#13063307—28no—
124#13063299—28no—
125#13063298—28no—
126#13063298—28no—
127Q8×Dic43—22no—
128Q8×Dic43C2314yes—
129C4×Dic86D414yes—
130C4×Dic86C2314yes—
131C4×D172—22no—
132C4×D172C2314yes—
133D4×Dic43—22no—
134D4×Dic43C2314yes—
135#13063287—22no—
136#13063287—22no—
137#13063287C2314yes—
138#13063287C2314yes—
139(C22⋊D43)⋊C4—28no—
140C2×C4⋊Dic43—21no—
141C2×C4⋊Dic43D411yescharacteristic
142C2×C4⋊Dic43C2311yescharacteristic
143C2×Dic43⋊C4D411yescharacteristic
144C2×Dic43⋊C4D411yescharacteristic
145C2×C22⋊Dic43—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×C4×Dic43—21no—
152C2×C4×Dic43C2311yescharacteristic
153C2×C4×Dic43C2311yescharacteristic
154#13063256C2314yes—
155Dic43⋊C8C2314yes—
156Dic43⋊C8C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159#13063246C2314yes—
160#13063245C2314yes—
161#13063236C2314yes—
162#13063235C2314yes—
163C8×Dic43C2314yes—
164C22×Q8×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C22×D4×C43C2311yescharacteristic
167C23×C4×C43—21no—
168C2×SD16×C43—42no—
169C2×SD16×C43C2314yes—
170C2×D8×C43—42no—
171C2×D8×C43C2314yes—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174#124×C43—22no—
175#124×C43C2314yes—
176C4×D4×C43—22no—
177C4×D4×C43C2314yes—
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C42×C43C2311yescharacteristic
183C4⋊C8×C43C2314yes—
184#103×C43C2314yes—
185#102×C43C2314yes—
186C24×C43—21no—
187C24×C43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C2×Q8×C43—21no—
192C2×Q8×C43—22no—
193C2×Q8×C43—22no—
194C2×Q8×C43C2412yes—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43C2412yes—
202C2×D4×C43C2412yes—
203C22×C4×C43—24no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—44no—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—24no—
216C2×C22⋊D43—44no—
217C2×C22⋊D43—44no—
218C2×C22⋊D43—44no—
219C2×C22⋊D43—82no—
220C2×C22⋊D43—82no—
221C2×C22⋊D43—82no—
222C22×Dic43—24no—
223C22×Dic43—21no—
224C22×Dic43—82no—
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621898—432no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—24no—
234C2×D172—24no—
235C2×D172—22no—
236C2×D172—22no—
237C2×D172—22no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172—22no—
241C2×D172—44no—
242C2×D172—82no—
243C2×D172C2412yes—
244C2×D172C2412yes—
245C2×D172C2412yes—
246C2×C4×D43—24no—
247C2×C4×D43—24no—
248C2×C4×D43—24no—
249C2×C4×D43—44no—
250C2×C4×D43—44no—
251C2×C4×D43—82no—
252C2×Dic86—24no—
253C2×Dic86C2×D414yes—
254SD16×C43—44no—
255D8×C43—44no—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43C2412yes—
259C2×C8×C43C2412yes—
260C4⋊C4×C43—21no—
261C4⋊C4×C43C2412yes—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—24no—
265C42×C43C2×D412yes—
266C42×C43C2412yes—
267C22⋊Dic43—24no—
268#10621884—28no—
269#10621884—44no—
270#10621882—28no—
271#10621882—28no—
272#10621882—44no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278C4⋊Dic43—21no—
279C4⋊Dic43—24no—
280C4⋊Dic43C2×D414yes—
281C4⋊Dic43C2412yes—
282Dic43⋊C4C2×D414yes—
283Dic43⋊C4C2×D414yes—
284C4×Dic43—24no—
285C4×Dic43C2×D412yes—
286C4×Dic43C2×D412yes—
287C4×Dic43C2412yes—
288C4×Dic43C2412yes—
289C2×C43⋊C8—22no—
290C2×C43⋊C8#4114yescomplemented
291C2×C43⋊C8C2412yes—
292C2×C43⋊C8C2412yes—
293D344—44no—
294D344—44no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43C22×D411yescharacteristic
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43—42no—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—42no—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—42no—
324D4×C43—42no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—48no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43C22×D412yes—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C2×#4112yes—
336C2×C4×C43H(5,𝔽2)12yes—
337C2×C4×C43C2511yescharacteristic
338C22⋊D43—48no—
339C22⋊D43—48no—
340C22⋊D43—48no—
341C22⋊D43—84no—
342C22⋊D43—84no—
343C22⋊D43—84no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—42no—
349C2×Dic43—84no—
350C2×Dic43AGL(1,ℤ/8)14yes—
351C2×Dic43C22×D412yes—
352C2×Dic43C22×D412yes—
353C2×Dic43C22×D412yes—
354C2×Dic43C22×D412yes—
355D172—22no—
356D172—22no—
357D172—22no—
358D172—22no—
359D172—22no—
360D172—22no—
361D172—48no—
362D172—42no—
363D172—42no—
364D172—42no—
365D172—84no—
366C4×D43—48no—
367C4×D43—48no—
368C4×D43—84no—
369Dic86—28no—
370C8×C43—22no—
371C8×C43—22no—
372C43⋊C8—22no—
373C43⋊C8C2×#4114yescomplemented
374C2×#3399—431nomaximal, Sylow
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—84no—
382C22×C43—84no—
383C22×C43#55012yes—
384C22×C43C2×AGL(1,ℤ/8)12yes—
385C22×C43#57612yes—
386C22×C43C23×D411yescharacteristic
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—84no—
397C2×D43—84no—
398C2×D43—84no—
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43#55012yes—
404C4×C43C22×#4111yescharacteristic
405C4×C43C2×H(5,𝔽2)11yescharacteristic
406Dic43—22no—
407Dic43—22no—
408Dic43—22no—
409Dic43—42no—
410Dic43C2×AGL(1,ℤ/8)14yes—
411C2×#559—431no—
412C2×#550—431no—
413#3399—4316no—
414C2×#496—431no—
415C2×#496—431no—
416C2×#493—431no—
417C2×#460—431no—
418C2×#463—431no—
419C2×#463D4311yescharacteristic, complemented
420C2×#459—431no—
421C2×#459—431no—
422C2×#459—431no—
423C2×#446—431no—
424C2×#442—431no—
425C2×#442—431no—
426C2×C4×SD16—431no—
427C2×C43—82no—
428C2×C43—82no—
429C2×C43#339914yescomplemented
430C2×C43C2×#55011yescharacteristic
431C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
432C2×C43C2×#57611yescharacteristic
433D43—82no—
434D43—82no—
435D43—82no—
436C22×#41—861no—
437C22×SD16—431no—
438C22×SD16—431no—
439C22×SD16C2×D4311yescharacteristic
440C22×D8—431no—
441C22×D8—431no—
442C22×D8—431no—
443C22×D8—431no—
444C22×D8—431no—
445C22×D8C2×D4311yescharacteristic
446#559—438no—
447#559—864no—
448#550—438no—
449#550—864no—
450C2×#127—431no—
451C2×#127—431no—
452C2×#127—431no—
453C2×#127—431no—
454C2×#124—431no—
455C2×#124—861no—
456C2×#124C2×D4311yescharacteristic
457C2×#123—861no—
458C2×#123—861no—
459C2×#121—861no—
460C2×#121—861no—
461C2×#121—861no—
462C2×C4×Q8—431no—
463C2×C4×Q8—431no—
464C2×C4×D4—431no—
465C2×C4×D4—431no—
466C2×C4×D4—431no—
467C2×C4×D4—431no—
468C2×C4×D4—861no—
469C2×C4×D4C2×D4311yescharacteristic
470#496—438no—
471#496—438no—
472#493—438no—
473#463—438no—
474#463C2×D4318yescomplemented
475#460—438no—
476#459—438no—
477#459—438no—
478#459—438no—
479#446—438no—
480#442—438no—
481#442—438no—
482C4×SD16—438no—
483C2×#106—431no—
484C2×C4⋊C8—431no—
485C2×C4⋊C8—431no—
486C2×C4⋊C8C2×D4311yescharacteristic
487C2×#103C2×D4311yescharacteristic
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
492C2×#102C2×D4311yescharacteristic
493C2×#97—431no—
494C2×#97—431no—
495C2×C4×C8—431no—
496C43C2×#339911yescharacteristic, complemented, Sylow
497C2×#41—868no—
498C2×#41—1728no—
499C22×Q8—431no—
500C22×Q8C22×D4311yescharacteristic
501C22×D4—431no—
502C22×D4—431no—
503C22×D4—431no—
504C22×D4—861no—
505C22×D4—861no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4—861no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4C22×D4311yescharacteristic
513C22×D4C22×D4311yescharacteristic
514C23×C4—21no—
515C23×C4—861no—
516C23×C4—861no—
517C23×C4—861no—
518C23×C4—861no—
519C2×SD16—42no—
520C2×SD16—434no—
521C2×SD16—434no—
522C2×SD16—864no—
523C2×SD16—1722no—
524C2×SD16C22×D4314yes—
525C2×D8—42no—
526C2×D8—434no—
527C2×D8—434no—
528C2×D8—434no—
529C2×D8—434no—
530C2×D8—434no—
531C2×D8—864no—
532C2×D8—864no—
533C2×D8—1722no—
534C2×D8—1722no—
535C2×D8—1722no—
536C2×D8C22×D4314yes—
537C22×C8—431no—
538C22×C8—431no—
539C22×C8C22×D4311yescharacteristic
540C22×C8C22×D4311yescharacteristic
541#127—434no—
542#127—434no—
543#127—434no—
544#127—434no—
545#127—862no—
546#127—862no—
547#127—862no—
548#127—862no—
549#124—22no—
550#124—434no—
551#124—862no—
552#124—868no—
553#124C22×D4314yes—
554#123—868no—
555#123—868no—
556#121—868no—
557#121—868no—
558#121—868no—
559C4×Q8—434no—
560C4×Q8—434no—
561C4×Q8—434no—
562C4×Q8—862no—
563C4×D4—22no—
564C4×D4—434no—
565C4×D4—434no—
566C4×D4—434no—
567C4×D4—434no—
568C4×D4—862no—
569C4×D4—862no—
570C4×D4—862no—
571C4×D4—868no—
572C4×D4—862no—
573C4×D4C22×D4314yes—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—431no—
576C2×C4⋊C4—431no—
577C2×C4⋊C4—431no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4C22×D4311yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C42—431no—
590C2×C42—431no—
591C2×C42—861no—
592C2×C42C22×D4311yescharacteristic
593#106—434no—
594C4⋊C8—434no—
595C4⋊C8—434no—
596C4⋊C8C22×D4314yes—
597#103C22×D4314yes—
598#102—434no—
599#102—434no—
600#102—434no—
601#102—434no—
602#102C22×D4314yes—
603#97—434no—
604#97—434no—
605C4×C8—434no—
606C24—21no—
607C24—21no—
608C24—861no—
609C24—861no—
610C24—861no—
611#41—17232no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—434no—
616C2×Q8—864no—
617C2×Q8C23×D4312yes—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—432no—
625C2×D4—432no—
626C2×D4—432no—
627C2×D4—864no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—864no—
638C2×D4—862no—
639C2×D4—862no—
640C2×D4—862no—
641C2×D4—862no—
642C2×D4—862no—
643C2×D4—862no—
644C2×D4—3442no—
645C2×D4—3442no—
646C2×D4—3442no—
647C2×D4—3442no—
648C2×D4—1724no—
649C2×D4—1724no—
650C2×D4—1724no—
651C2×D4—1724no—
652C2×D4C23×D4312yes—
653C2×D4C23×D4312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—44no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—864no—
663C22×C4—864no—
664C22×C4—864no—
665C22×C4—861no—
666C22×C4—864no—
667C22×C4—3442no—
668C22×C4—3442no—
669C22×C4—1724no—
670C22×C4—1724no—
671C22×C4D4×D4311yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674SD16—44no—
675SD16—868no—
676SD16—1724no—
677D8—44no—
678D8—868no—
679D8—868no—
680D8—1724no—
681D8—1724no—
682D8—1724no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—434no—
686C2×C8—432no—
687C2×C8—432no—
688C2×C8—862no—
689C2×C8C23×D4312yes—
690C2×C8C23×D4312yes—
691C4⋊C4—21no—
692C4⋊C4—434no—
693C4⋊C4—434no—
694C4⋊C4—434no—
695C4⋊C4—432no—
696C4⋊C4—864no—
697C4⋊C4—861no—
698C4⋊C4C23×D4312yes—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C42—432no—
709C42—432no—
710C42—432no—
711C42—432no—
712C42—864no—
713C42D4×D4312yes—
714C42C23×D4312yes—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—1722no—
727C23—1722no—
728C23—1722no—
729C23—1722no—
730C23—1722no—
731C23—1722no—
732C23—1722no—
733C23—1722no—
734C23—1722no—
735C23C2×D4×D4311yescharacteristic
736Q8—22no—
737Q8—22no—
738Q8—42no—
739Q8—868no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—42no—
746D4—862no—
747D4—862no—
748D4—862no—
749D4—862no—
750D4—862no—
751D4—862no—
752D4—3444no—
753D4—3444no—
754D4—3444no—
755D4—3444no—
756D4—1728no—
757D4—1728no—
758D4—1728no—
759D4—1728no—
760D4—1722no—
761D4—1722no—
762D4—1722no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—48no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—434no—
771C2×C4—432no—
772C2×C4—432no—
773C2×C4—432no—
774C2×C4—432no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—3444no—
780C2×C4—3444no—
781C2×C4—1728no—
782C2×C4—1728no—
783C2×C4—1722no—
784C2×C4C2×D4×D4312yes—
785C2×C4C2×D4×D4312yes—
786C2×C4C2×D4×D4311yescharacteristic
787C2×C4#41×D4312yes—
788C2×C4#1306337012yes—
789C2×C4C24×D4311yescharacteristic
790C8—22no—
791C8—22no—
792C8—434no—
793C8—862no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—84no—
802C22—3444no—
803C22—3444no—
804C22—3444no—
805C22—1722no—
806C22—1722no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—1722no—
813C22—1722no—
814C22#1458356712yes—
815C22AGL(1,ℤ/8)×D4312yes—
816C22#1458370112yes—
817C22C22×D4×D4311yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—434no—
823C4—862no—
824C4—862no—
825C4—862no—
826C4—1722no—
827C4#1458356712yes—
828C4C2×#41×D4311yescharacteristic
829C4C2×#1306337011yescharacteristic
830C2—82no—
831C2—82no—
832C2—3442no—
833C2—3442no—
834C2—3442no—
835C2#1914763214yesdirect product factor
836C2C2×#1458356711yescharacteristic
837C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
838C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#463C2
socleC23×C43C22×D4
hypercenterC2×#463D43
hypocenterC43C2×#3399
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#14583631C2semidirect
2. C2×#14583570C2semidirect
3. #19147632C2direct (N × H)
4. C2×#14583289C2semidirect
5. C2×#14583285C2semidirect
6. C2×#14583274C2semidirect
7. C2×#14583097C2semidirect
8. C2×#14583117C2semidirect
9. C2×#14583095C2semidirect
10. C2×#14583093C2semidirect
11. C2×#14583092C2semidirect
12. C2×#14583028C2semidirect
13. C2×#14583009C2semidirect
14. C2×#14583008C2semidirect
15. C2×#14582984C2semidirect
16. C2×C43×#463C2semidirect
26. #14583631C22semidirect
28. #14583570C22semidirect
47. #14583289C22semidirect
48. #14583285C22semidirect
49. #14583274C22semidirect
50. #14583117C22semidirect
51. #14583097C22semidirect
52. #14583095C22semidirect
53. #14583093C22semidirect
54. #14583092C22semidirect
55. #14583028C22semidirect
56. #14583009C22semidirect
57. #14583008C22semidirect
58. #14582984C22semidirect
73. C43×#463C22semidirect
290. C2×C43⋊C8#41semidirect
373. C43⋊C8C2×#41semidirect
419. C2×#463D43semidirect
429. C2×C43#3399semidirect
474. #463C2×D43semidirect
496. C43C2×#3399semidirect
835. C2#19147632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836312
C2×#145835702
#191476322
C2×#145832892
C2×#145832852
C2×#145832742
C2×#145830972
C2×#145831172
C2×#145830952
C2×#145830932
C2×#145830922
C2×#145830282
C2×#145830092
C2×#145830082
C2×#145829842
C2×C43×#4632
C2×#339943