Finite Group Databasebeta

← C2×#19146605 #25973303

Subgroups — C2×#19146605 #25973303

Order 11008.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583596C211yesmaximal, characteristic, complemented
2C2×#14583568C211yesmaximal, characteristic, complemented
3#19146605C2116yesmaximal, direct product factor
4C2×#14583262C211yesmaximal, characteristic, complemented
5C2×#14583224C211yesmaximal, characteristic, complemented
6C2×#14583211C211yesmaximal, characteristic, complemented
7C2×#14583204C211yesmaximal, characteristic, complemented
8C2×#14583149C211yesmaximal, characteristic, complemented
9C2×#14583133C211yesmaximal, characteristic, complemented
10C2×#14583092C211yesmaximal, characteristic, complemented
11C2×#14583043C211yesmaximal, characteristic, complemented
12C2×#14583000C211yesmaximal, characteristic, complemented
13C2×#14582967C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C2×#14582895C211yesmaximal, characteristic, complemented
16C2×C43×#449C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21#14583596—24no—
22#14583596C2218yescomplemented
23#14583568—24no—
24#14583568C2218yescomplemented
25C2×#13063321—21no—
26C2×#13063321C2211yescharacteristic
27C2×#13063318—21no—
28C2×#13063316C2211yescharacteristic
29C2×#13063306—21no—
30C2×#13063299—21no—
31C2×#13063299C2211yescharacteristic
32C2×#13063296—21no—
33C2×#13063296—21no—
34C2×#13063296C2211yescharacteristic
35C2×#13063296C2211yescharacteristic
36C2×Q8×Dic43C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×(C22⋊D43)⋊C4—21no—
41C2×#13063284C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583262C2218yescomplemented
44#14583224C2218yescomplemented
45#14583211C2218yescomplemented
46#14583204C2218yescomplemented
47#14583149C2218yescomplemented
48#14583133C2218yescomplemented
49#14583092C2218yescomplemented
50#14583043C2218yescomplemented
51#14583000C2218yescomplemented
52#14582967C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063258C2211yescharacteristic
55C2×#13063257C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57#14582899C2218yescomplemented
58#14582895C2218yescomplemented
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C22×D8×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#449C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C22×D172—21no—
82C22×D172C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43D411yescharacteristic
89C23×Dic43—21no—
90C22×C4×D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43C2311yescharacteristic
93C2×#10621882—42no—
94C2×#10621882C2314yes—
95C2×#10621872—42no—
96C2×#10621872C2314yes—
97C22×C43⋊C8—42no—
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2314yes—
101#13063321—28no—
102#13063321—22no—
103#13063321C2314yes—
104#13063318—28no—
105#13063316—22no—
106#13063316C2314yes—
107#13063306—28no—
108#13063299—22no—
109#13063299—28no—
110#13063299C2314yes—
111#13063296—28no—
112#13063296—22no—
113#13063296—22no—
114#13063296—28no—
115#13063296C2314yes—
116#13063296C2314yes—
117Q8×Dic43—22no—
118Q8×Dic43C2314yes—
119D4×Dic43—22no—
120D4×Dic43C2314yes—
121C4×C22⋊D43—28no—
122C4×C22⋊D43D414yes—
123C4×C22⋊D43C2314yes—
124(C22⋊D43)⋊C4—28no—
125#13063284—22no—
126#13063284C2314yes—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4D411yescharacteristic
135C4⋊C4×D43—22no—
136C4⋊C4×D43C2314yes—
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43D411yescharacteristic
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063259C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150Dic43⋊C8C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063247C2314yes—
154#13063247C2314yes—
155#13063246C2314yes—
156#13063246C2314yes—
157#13063246C2314yes—
158#13063245C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063235C2314yes—
161C2×#41×C43—22no—
162C2×#41×C43—24no—
163C2×#41×C43—42no—
164C2×#41×C43C2314yes—
165C22×Q8×C43C2311yescharacteristic
166C22×D4×C43—21no—
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172C2×SD16×C43—24no—
173C2×SD16×C43C2314yes—
174C2×D8×C43—42no—
175C2×D8×C43C2314yes—
176C22×C8×C43C2311yescharacteristic
177C22×C8×C43C2311yescharacteristic
178#121×C43—22no—
179#121×C43C2314yes—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182#103×C43C2314yes—
183#102×C43C2314yes—
184C22⋊C8×C43C2314yes—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43C2×D411yescharacteristic
188C23×D43—21no—
189C23×D43C2×D411yescharacteristic
190#41×C43—28no—
191#41×C43—44no—
192#41×C43—48no—
193C2×Q8×C43—21no—
194C2×Q8×C43—22no—
195C2×Q8×C43#4114yes—
196C2×Q8×C43C2412yes—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—24no—
200C2×D4×C43—24no—
201C2×D4×C43—22no—
202C2×D4×C43—22no—
203C2×D4×C43—22no—
204C2×D4×C43—22no—
205C2×D4×C43—44no—
206C2×D4×C43—82no—
207C2×D4×C43C2412yes—
208C2×D4×C43C2412yes—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—24no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—44no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D412yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—24no—
224C2×C22⋊D43—42no—
225C2×C22⋊D43—44no—
226C2×C22⋊D43—44no—
227C2×C22⋊D43—82no—
228C2×C22⋊D43—82no—
229C2×C22⋊D43—82no—
230C2×C22⋊D43C2×D414yes—
231C22×Dic43—24no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—82no—
236C22×Dic43C2×D411yescharacteristic
237C22×Dic43C2×D411yescharacteristic
238C22×Dic43C2×D411yescharacteristic
239#10621902—28no—
240#10621902—44no—
241#10621902—48no—
242C2×D172—21no—
243C2×D172—24no—
244C2×D172—22no—
245C2×D172—22no—
246C2×D172—44no—
247C2×D172C2412yes—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—24no—
251C2×C4×D43—24no—
252C2×C4×D43—44no—
253C2×C4×D43—82no—
254C2×C4×D43C2×D412yes—
255C2×C4×D43C2412yes—
256SD16×C43—28no—
257D8×C43—44no—
258C2×C8×C43—22no—
259C2×C8×C43—22no—
260C2×C8×C43C2412yes—
261C2×C8×C43C2412yes—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2412yes—
264C22⋊C4×C43—24no—
265C22⋊Dic43—24no—
266C22⋊Dic43—24no—
267C22⋊Dic43—24no—
268C22⋊Dic43—24no—
269C22⋊Dic43C2×D414yes—
270#10621882—44no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4C2×D414yes—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—24no—
277C4⋊Dic43—24no—
278C4⋊Dic43C2412yes—
279C4⋊Dic43C2412yes—
280C4⋊Dic43C2412yes—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283Dic43⋊C4C2×D414yes—
284C4×Dic43—24no—
285C4×Dic43—24no—
286C4×Dic43C2×D412yes—
287C4×Dic43C2412yes—
288C2×C43⋊C8—22no—
289C2×C43⋊C8—22no—
290C2×C43⋊C8—44no—
291C2×C43⋊C8C2412yes—
292C2×C43⋊C8C2412yes—
293#10621872—44no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43—42no—
304C23×C43—42no—
305C23×C43C22×D412yes—
306C23×C43C22×D411yescharacteristic
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43C22×D412yes—
315Q8×C43—24no—
316Q8×C43—22no—
317Q8×C43C2×#4114yes—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—48no—
323D4×C43—42no—
324D4×C43—42no—
325D4×C43—84no—
326C2×C4×C43—24no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—24no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—48no—
334C2×C4×C43—42no—
335C2×C4×C43C22×D412yes—
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C2×#4112yes—
338C2×C4×C43H(5,𝔽2)12yes—
339C2×C4×C43C2511yescharacteristic
340C22⋊D43—44no—
341C22⋊D43—48no—
342C22⋊D43—48no—
343C22⋊D43—84no—
344C22⋊D43—84no—
345C22⋊D43—84no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—42no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43—84no—
356C2×Dic43C22×D412yes—
357C2×Dic43C22×D412yes—
358C2×Dic43C22×D412yes—
359D172—22no—
360D172—22no—
361D172—48no—
362D172—42no—
363C4×D43—24no—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—48no—
367C4×D43—84no—
368C8×C43—22no—
369C8×C43—22no—
370C43⋊C8—22no—
371C43⋊C8—22no—
372C2×#3309—431nomaximal, Sylow
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—44no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—84no—
384C22×C43—84no—
385C22×C43#54612yes—
386C22×C43#57512yes—
387C22×C43#57612yes—
388C22×C43C23×D411yescharacteristic
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—44no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—84no—
397C4×C43—24no—
398C4×C43—22no—
399C4×C43—42no—
400C4×C43#54612yes—
401C4×C43C22×#4111yescharacteristic
402C4×C43C2×H(5,𝔽2)11yescharacteristic
403Dic43—22no—
404Dic43—22no—
405Dic43—22no—
406Dic43—42no—
407Dic43—42no—
408Dic43—42no—
409C2×#553—431no—
410C2×#550—431no—
411#3309—4316no—
412C2×#490—431no—
413C2×#482—431no—
414C2×#480—431no—
415C2×#479—431no—
416C2×#469—431no—
417C2×#466—431no—
418C2×#459—431no—
419C2×#449—431no—
420C2×#449D4311yescharacteristic, complemented
421C2×#440—431no—
422C2×#435—431no—
423C2×#417—431no—
424C2×#416—431no—
425C2×C43—42no—
426C2×C43—82no—
427C2×C43—82no—
428C2×C43#330914yescomplemented
429C2×C43C2×#54611yescharacteristic
430C2×C43C2×#57511yescharacteristic
431C2×C43C2×#57611yescharacteristic
432D43—42no—
433D43—82no—
434C22×#41—431no—
435C22×#41C2×D4311yescharacteristic
436C22×SD16C2×D4311yescharacteristic
437C22×D8—431no—
438C22×D8C2×D4311yescharacteristic
439C22×M16—431no—
440C23×C8—431no—
441#553—438no—
442#553—864no—
443#550—438no—
444#550—864no—
445C2×#127—431no—
446C2×#127—861no—
447C2×#126—861no—
448C2×#125—431no—
449C2×#123—861no—
450C2×#121—431no—
451C2×#121—431no—
452C2×#121—431no—
453C2×#121—861no—
454C2×#121—861no—
455C2×#121—861no—
456C2×#121C2×D4311yescharacteristic
457C2×C4×Q8—431no—
458C2×C4×D4—431no—
459C2×C4×D4—431no—
460C2×C4×D4—861no—
461C2×C4×D4—861no—
462C2×#117—431no—
463C22×C4⋊C4—431no—
464#490—438no—
465#482—438no—
466#480—438no—
467#479—438no—
468#469—438no—
469#466—438no—
470#459—438no—
471#449—438no—
472#449C2×D4318yescomplemented
473#440—438no—
474#435—438no—
475C2×#107—431no—
476C2×#107—431no—
477C2×#106—431no—
478C2×C4⋊C8—431no—
479#417—438no—
480#416—438no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103C2×D4311yescharacteristic
484C2×#102—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102C2×D4311yescharacteristic
491C2×C22⋊C8—431no—
492C2×C22⋊C8C2×D4311yescharacteristic
493C2×#97—431no—
494C43C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—22no—
496C2×#41—24no—
497C2×#41—42no—
498C2×#41—434no—
499C2×#41—862no—
500C2×#41—864no—
501C2×#41—1722no—
502C2×#41C22×D4314yes—
503C22×Q8C22×D4311yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—431no—
507C22×D4—431no—
508C22×D4—861no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4—861no—
513C22×D4—861no—
514C22×D4C22×D4311yescharacteristic
515C22×D4C22×D4311yescharacteristic
516C23×C4—21no—
517C23×C4—431no—
518C23×C4—861no—
519C23×C4—861no—
520C23×C4—861no—
521C23×C4C22×D4311yescharacteristic
522C2×SD16—24no—
523C2×SD16C22×D4314yes—
524C2×D8—42no—
525C2×D8—434no—
526C2×D8—1722no—
527C2×D8C22×D4314yes—
528C2×M16—434no—
529C2×M16—1722no—
530C22×C8—431no—
531C22×C8—431no—
532C22×C8—434no—
533C22×C8—1722no—
534C22×C8C22×D4311yescharacteristic
535C22×C8C22×D4311yescharacteristic
536#127—434no—
537#127—862no—
538#127—868no—
539#126—868no—
540#125—434no—
541#125—862no—
542#123—868no—
543#121—22no—
544#121—434no—
545#121—434no—
546#121—434no—
547#121—868no—
548#121—868no—
549#121—862no—
550#121—862no—
551#121—868no—
552#121—862no—
553#121C22×D4314yes—
554C4×Q8—434no—
555C4×Q8—862no—
556C4×D4—434no—
557C4×D4—434no—
558C4×D4—434no—
559C4×D4—862no—
560C4×D4—868no—
561C4×D4—868no—
562#117—434no—
563#117—862no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—434no—
569C2×C4⋊C4—862no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4C22×D4311yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—431no—
577C2×C22⋊C4—431no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C42—431no—
584C2×C42—861no—
585C2×C42—861no—
586#107—434no—
587#107—434no—
588#106—434no—
589C4⋊C8—434no—
590#103—434no—
591#103—434no—
592#103C22×D4314yes—
593#102—434no—
594#102—434no—
595#102—434no—
596#102—434no—
597#102—434no—
598#102—434no—
599#102C22×D4314yes—
600C22⋊C8—434no—
601C22⋊C8C22×D4314yes—
602#97—434no—
603C24—21no—
604C24—21no—
605C24—431no—
606C24—861no—
607C24D4×D4311yescharacteristic
608#41—28no—
609#41—44no—
610#41—48no—
611#41—868no—
612#41—1724no—
613#41—1728no—
614C2×Q8—21no—
615C2×Q8—22no—
616C2×Q8#1062190014yes—
617C2×Q8C23×D4312yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—44no—
627C2×D4—82no—
628C2×D4—434no—
629C2×D4—432no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—864no—
635C2×D4—864no—
636C2×D4—861no—
637C2×D4—862no—
638C2×D4—862no—
639C2×D4—3442no—
640C2×D4—3442no—
641C2×D4—3442no—
642C2×D4—1724no—
643C2×D4—1722no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4C23×D4312yes—
647C2×D4C23×D4312yes—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—44no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—432no—
658C22×C4—432no—
659C22×C4—864no—
660C22×C4—864no—
661C22×C4—864no—
662C22×C4—862no—
663C22×C4—862no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—3442no—
668C22×C4—3442no—
669C22×C4—1724no—
670C22×C4D4×D4312yes—
671C22×C4D4×D4311yescharacteristic
672C22×C4C23×D4312yes—
673C22×C4C23×D4311yescharacteristic
674SD16—28no—
675D8—44no—
676D8—1724no—
677M16—1724no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—432no—
681C2×C8—432no—
682C2×C8—862no—
683C2×C8—862no—
684C2×C8—1724no—
685C2×C8C23×D4312yes—
686C2×C8C23×D4312yes—
687C4⋊C4—21no—
688C4⋊C4—434no—
689C4⋊C4—432no—
690C4⋊C4—432no—
691C4⋊C4—432no—
692C4⋊C4—864no—
693C4⋊C4—864no—
694C4⋊C4—864no—
695C4⋊C4—864no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4C23×D4312yes—
700C22⋊C4—24no—
701C22⋊C4—434no—
702C22⋊C4—434no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C42—432no—
709C42—432no—
710C42—864no—
711C42—864no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—432no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—1722no—
729C23—1722no—
730C23—1722no—
731C23C2×D4×D4312yes—
732C23C2×D4×D4311yescharacteristic
733Q8—22no—
734Q8—24no—
735Q8C2×#1062190014yes—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—42no—
742D4—42no—
743D4—84no—
744D4—862no—
745D4—862no—
746D4—3444no—
747D4—3444no—
748D4—3444no—
749D4—1728no—
750D4—1724no—
751D4—1728no—
752D4—1728no—
753D4—1722no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—48no—
762C2×C4—42no—
763C2×C4—432no—
764C2×C4—432no—
765C2×C4—432no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—864no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—3444no—
776C2×C4—3444no—
777C2×C4—1728no—
778C2×C4—1722no—
779C2×C4—1722no—
780C2×C4—1722no—
781C2×C4C2×D4×D4312yes—
782C2×C4C2×D4×D4311yescharacteristic
783C2×C4C2×#1062190012yes—
784C2×C4#1306337012yes—
785C2×C4C24×D4311yescharacteristic
786C8—22no—
787C8—22no—
788C8—862no—
789C8—862no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—84no—
802C22—862no—
803C22—862no—
804C22—862no—
805C22—3444no—
806C22—1722no—
807C22—1722no—
808C22—1722no—
809C22—1724no—
810C22#1458353612yes—
811C22#1458369612yes—
812C22#1458370312yes—
813C22C22×D4×D4311yescharacteristic
814C4—22no—
815C4—24no—
816C4—42no—
817C4—862no—
818C4—862no—
819C4—862no—
820C4—1722no—
821C4—1722no—
822C4—1722no—
823C4#1458353612yes—
824C4C22×#1062190011yescharacteristic
825C4C2×#1306337011yescharacteristic
826C2—42no—
827C2—82no—
828C2—82no—
829C2—3442no—
830C2—1722no—
831C2#1914660514yesdirect product factor
832C2C2×#1458353611yescharacteristic
833C2C2×#1458369611yescharacteristic
834C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#449C2
socleC23×C43C22×D4
hypercenterC2×#449D43
hypocenterC43C2×#3309
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#14583596C2semidirect
2. C2×#14583568C2semidirect
3. #19146605C2direct (N × H)
4. C2×#14583262C2semidirect
5. C2×#14583224C2semidirect
6. C2×#14583211C2semidirect
7. C2×#14583204C2semidirect
8. C2×#14583149C2semidirect
9. C2×#14583133C2semidirect
10. C2×#14583092C2semidirect
11. C2×#14583043C2semidirect
12. C2×#14583000C2semidirect
13. C2×#14582967C2semidirect
14. C2×#14582899C2semidirect
15. C2×#14582895C2semidirect
16. C2×C43×#449C2semidirect
22. #14583596C22semidirect
24. #14583568C22semidirect
43. #14583262C22semidirect
44. #14583224C22semidirect
45. #14583211C22semidirect
46. #14583204C22semidirect
47. #14583149C22semidirect
48. #14583133C22semidirect
49. #14583092C22semidirect
50. #14583043C22semidirect
51. #14583000C22semidirect
52. #14582967C22semidirect
57. #14582899C22semidirect
58. #14582895C22semidirect
73. C43×#449C22semidirect
420. C2×#449D43semidirect
428. C2×C43#3309semidirect
472. #449C2×D43semidirect
494. C43C2×#3309semidirect
831. C2#19146605direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835962
C2×#145835682
#191466052
C2×#145832622
C2×#145832242
C2×#145832112
C2×#145832042
C2×#145831492
C2×#145831332
C2×#145830922
C2×#145830432
C2×#145830002
C2×#145829672
C2×#145828992
C2×#145828952
C2×C43×#4492
C2×#330943