Finite Group Databasebeta

← C2×#13068 #494649

Subgroups — C2×#13068 #494649

Order 512.

1322 conjugacy classes of subgroups.

The subgroup lattice has 619 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3407C211yesmaximal, characteristic, complemented
2C22×#472C211yesmaximal, characteristic
3C22×#361C211yesmaximal, characteristic, complemented
4C2×#2140C211yesmaximal, characteristic, complemented
5C2×#1814C211yesmaximal, characteristic, complemented
6#13068C218yesmaximal, direct product factor
7C2×#1389C211yesmaximal, characteristic, complemented
8C2×#1385C211yesmaximal, characteristic, complemented
9C22×AGL(1,ℤ/8)—21no—
10C23×D8C2211yescharacteristic
11C22×#131C2211yescharacteristic
12#3407—22no—
13#3407—22no—
14#3407—22no—
15#3407C2214yescomplemented
16C2×#504—22no—
17C2×#504—22no—
18C22×M32—22no—
19C22×M32C2211yescharacteristic
20C22×M32C2211yescharacteristic
21C2×#472—22no—
22C2×#472—22no—
23C2×#472—22no—
24C2×#472C414yescomplemented
25C2×#472C414yescomplemented
26C2×#472C2214yes—
27C22×#108C2211yescharacteristic
28C22×#108C2211yescharacteristic
29C2×#427C2211yescharacteristic
30C2×#421—21no—
31C22×#100—21no—
32C2×#361—22no—
33C2×#361—22no—
34C2×#361C2214yescomplemented
35#2140—22no—
36#2140C2214yescomplemented
37C2×#357—22no—
38#1814—22no—
39#1814C2214yescomplemented
40C2×#344—21no—
41#1389C2214yescomplemented
42#1385C2214yescomplemented
43C22×#41D411yescharacteristic
44C23×D4—21no—
45C2×AGL(1,ℤ/8)—24no—
46C2×AGL(1,ℤ/8)—24no—
47C2×AGL(1,ℤ/8)—24no—
48C2×AGL(1,ℤ/8)—42no—
49C2×AGL(1,ℤ/8)—42no—
50C2×AGL(1,ℤ/8)—42no—
51C22×SD16—41no—
52C22×D8—21no—
53C22×D8—21no—
54C22×D8—21no—
55C22×D8—21no—
56C22×D8—21no—
57C22×D8—21no—
58C22×D8—21no—
59C22×D8—21no—
60C22×D8—21no—
61C22×D8—21no—
62C22×D8—21no—
63C22×D8—41no—
64C22×D8C2×C412yes—
65C22×D8C2×C412yes—
66C22×D8C2312yes—
67C2×#131—21no—
68C2×#131—21no—
69C2×#131—21no—
70C2×#131—21no—
71C2×#131—21no—
72C2×#131—21no—
73C2×#131C2×C412yes—
74C2×#131C2×C412yes—
75C2×#131D412yes—
76C2×#131D412yes—
77C2×#131D412yes—
78C2×#131C2312yes—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16D411yescharacteristic
83C23×C8—21no—
84C23×C8C2311yescharacteristic
85C2×#117—21no—
86#504—28no—
87#504—28no—
88#504—28no—
89#504—28no—
90C2×M32—24no—
91C2×M32—28no—
92C2×M32—21no—
93C2×M32—21no—
94C2×M32—21no—
95C2×M32—21no—
96C2×M32—21no—
97C2×M32—21no—
98C2×M32—21no—
99C2×M32—28no—
100C2×M32D412yes—
101C2×M32D412yes—
102C2×M32D412yes—
103C2×M32C2312yes—
104C2×M32C2312yes—
105C22×C16—24no—
106C22×C16—21no—
107C22×C16D412yes—
108#472—28no—
109#472—28no—
110#472—28no—
111#472C2×C4116yescomplemented
112C2×#108—21no—
113C2×#108—21no—
114C2×#108—21no—
115C2×#108—21no—
116C2×#108—21no—
117C2×#108—21no—
118C2×#108—21no—
119C2×#108—21no—
120C2×#108C2×C412yes—
121C2×#108C2×C412yes—
122C2×#108C2312yes—
123C2×#108C2312yes—
124#427—21no—
125#427—21no—
126#427—21no—
127#427C2312yes—
128C2×#107—21no—
129C2×#106—21no—
130#421—24no—
131#421—42no—
132C2×#104—42no—
133C2×#100—24no—
134C2×#100—24no—
135C2×#100—24no—
136#361—28no—
137#357—28no—
138#344—24no—
139C25—41no—
140C2×#41—21no—
141C2×#41—21no—
142C2×#41—21no—
143C2×#41—21no—
144C2×#41—21no—
145C2×#41—21no—
146C2×#41C22⋊C412yes—
147C2×#41C22⋊C412yes—
148C2×#41D812yes—
149C2×#41D812yes—
150C2×#41SD1612yes—
151C2×#41C2×D412yes—
152C22×Q8SD1611yescharacteristic
153C22×D4—21no—
154C22×D4—22no—
155C22×D4—22no—
156C22×D4—22no—
157C22×D4—41no—
158C22×D4—41no—
159C22×D4—41no—
160C22×D4—41no—
161C22×D4—41no—
162C22×D4—41no—
163C22×D4—41no—
164C22×D4—41no—
165C22×D4—41no—
166C22×D4—41no—
167C22×D4—41no—
168C22×D4SD1611yescharacteristic
169C23×C4—21no—
170C23×C4C2×D411yescharacteristic
171AGL(1,ℤ/8)—216no—
172AGL(1,ℤ/8)—48no—
173AGL(1,ℤ/8)—48no—
174AGL(1,ℤ/8)—48no—
175C2×SD16—44no—
176C2×SD16—44no—
177C2×SD16—44no—
178C2×D8—22no—
179C2×D8—22no—
180C2×D8—22no—
181C2×D8—22no—
182C2×D8—22no—
183C2×D8—22no—
184C2×D8—22no—
185C2×D8—22no—
186C2×D8—22no—
187C2×D8—22no—
188C2×D8—22no—
189C2×D8—22no—
190C2×D8—22no—
191C2×D8—22no—
192C2×D8—22no—
193C2×D8—44no—
194C2×D8—44no—
195C2×D8—44no—
196C2×D8—41no—
197C2×D8—41no—
198C2×D8—41no—
199C2×D8—41no—
200C2×D8—41no—
201C2×D8—41no—
202C2×D8—41no—
203C2×D8—41no—
204C2×D8—41no—
205C2×D8—41no—
206C2×D8—41no—
207C2×D8—41no—
208C2×D8C22×C414yes—
209#131—22no—
210#131—22no—
211#131—22no—
212#131—22no—
213#131—22no—
214#131—22no—
215#131—22no—
216#131—22no—
217#131—22no—
218#131—22no—
219#131—22no—
220#131—22no—
221#131C22⋊C414yes—
222#131C22⋊C414yes—
223#131C22×C414yes—
224#131C2×D414yes—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—22no—
229C2×M16—22no—
230C2×M16—22no—
231C2×M16—22no—
232C2×M16—22no—
233C2×M16—22no—
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—41no—
239C2×M16—41no—
240C2×M16—41no—
241C2×M16—41no—
242C2×M16—41no—
243C2×M16—41no—
244C2×M16—41no—
245C2×M16—41no—
246C2×M16C22⋊C412yes—
247C2×M16C22⋊C412yes—
248C2×M16C2×D412yes—
249C22×C8—21no—
250C22×C8—22no—
251C22×C8—22no—
252C22×C8—22no—
253C22×C8—22no—
254C22×C8—22no—
255C22×C8—22no—
256C22×C8—41no—
257C22×C8—41no—
258C22×C8C22×C411yescharacteristic
259C22×C8C22×C411yescharacteristic
260C22×C8C2×D411yescharacteristic
261C22×C8C2×D411yescharacteristic
262C22×C8C2×D411yescharacteristic
263C22×C8C2×D411yescharacteristic
264C22×C8C2×D411yescharacteristic
265C22×C8C2×D411yescharacteristic
266C22×C8C2×D411yescharacteristic
267C22×C8#4111yescharacteristic
268C22×C8#4111yescharacteristic
269C22×C8#4111yescharacteristic
270C22×C8#4111yescharacteristic
271C22×C8C2411yescharacteristic
272#117—22no—
273#117—41no—
274#117—41no—
275#117—41no—
276C2×C4⋊C4—41no—
277C2×C22⋊C4—41no—
278C2×C42—41no—
279M32—216no—
280M32—22no—
281M32—22no—
282M32—22no—
283M32—22no—
284M32—22no—
285M32—22no—
286M32—22no—
287M32C2×D414yes—
288C2×C16—216no—
289C2×C16—22no—
290C2×C16—22no—
291C2×C16—22no—
292C2×C16—22no—
293C2×C16—22no—
294C2×C16C2×D414yes—
295#108—22no—
296#108—22no—
297#108—22no—
298#108—22no—
299#108—22no—
300#108—41no—
301#108—41no—
302#108C22×C414yes—
303#107—22no—
304#107—41no—
305#106—22no—
306#106—41no—
307#104—48no—
308#100—216no—
309C24—21no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24—81no—
317C24—164no—
318C24#13511yescharacteristic
319#41—22no—
320#41—22no—
321#41—22no—
322#41—22no—
323#41—22no—
324#41—22no—
325#41—22no—
326#41—22no—
327#41—22no—
328#41—22no—
329#41—22no—
330#41—22no—
331#41#10214yes—
332#41#10214yes—
333#41C2×C22⋊C414yes—
334#41C2×D814yes—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8#10212yes—
339C2×Q8#10212yes—
340C2×Q8C2×SD1612yes—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—24no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—81no—
367C2×D4—81no—
368C2×D4—81no—
369C2×D4—81no—
370C2×D4—81no—
371C2×D4—81no—
372C2×D4—81no—
373C2×D4—81no—
374C2×D4—81no—
375C2×D4—81no—
376C2×D4—81no—
377C2×D4—81no—
378C2×D4#10212yes—
379C2×D4#10212yes—
380C2×D4C2×SD1612yes—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—81no—
389C22×C4C2×C22⋊C411yescharacteristic
390C22×C4C2×C22⋊C411yescharacteristic
391C22×C4#12111yescharacteristic
392C22×C4#12111yescharacteristic
393C22×C4#12111yescharacteristic
394C22×C4#12111yescharacteristic
395C22×C4C2×D811yescharacteristic
396C22×C4C2×D811yescharacteristic
397C22×C4C2×SD1611yescharacteristic
398C22×C4C2×SD1611yescharacteristic
399C22×C4#13511yescharacteristic
400C22×C4#13511yescharacteristic
401C22×C4#13511yescharacteristic
402C22×C4C22×D411yescharacteristic
403SD16—416no—
404D8—24no—
405D8—24no—
406D8—416no—
407D8—42no—
408D8—42no—
409D8—42no—
410D8—42no—
411D8—42no—
412D8—42no—
413M16—22no—
414M16—22no—
415M16—22no—
416M16—24no—
417M16—24no—
418M16—24no—
419M16—24no—
420M16—24no—
421M16—42no—
422M16—42no—
423M16—42no—
424M16—42no—
425M16—42no—
426M16—81no—
427M16—81no—
428M16C2×C22⋊C414yes—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—24no—
433C2×C8—24no—
434C2×C8—24no—
435C2×C8—24no—
436C2×C8—42no—
437C2×C8—42no—
438C2×C8—42no—
439C2×C8—42no—
440C2×C8—81no—
441C2×C8—81no—
442C2×C8C2×C22⋊C411yescharacteristic
443C2×C8C2×C22⋊C411yescharacteristic
444C2×C8C4×D411yescharacteristic
445C2×C8C4×D411yescharacteristic
446C2×C8C4×D411yescharacteristic
447C2×C8C4×D411yescharacteristic
448C2×C8C4×D411yescharacteristic
449C2×C8C4×D411yescharacteristic
450C2×C8C4×D411yescharacteristic
451C2×C8C4×D411yescharacteristic
452C2×C8#12011yescharacteristic
453C2×C8#12011yescharacteristic
454C2×C8#12011yescharacteristic
455C2×C8#12011yescharacteristic
456C2×C8#12111yescharacteristic
457C2×C8#12111yescharacteristic
458C2×C8#12111yescharacteristic
459C2×C8#12111yescharacteristic
460C2×C8#12311yescharacteristic
461C2×C8#12311yescharacteristic
462C2×C8#12311yescharacteristic
463C2×C8#12311yescharacteristic
464C2×C8C23×C411yescharacteristic
465C2×C8C22×D411yescharacteristic
466C2×C8C22×D411yescharacteristic
467C2×C8C22×D411yescharacteristic
468C2×C8C2×#4111yescharacteristic
469C2×C8C2×#4111yescharacteristic
470C4⋊C4—42no—
471C4⋊C4—81no—
472C22⋊C4—42no—
473C22⋊C4—81no—
474C42—42no—
475C42—81no—
476C16—24no—
477C16—24no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—42no—
482C23—44no—
483C23—82no—
484C23—82no—
485C23—82no—
486C23—82no—
487C23—82no—
488C23—82no—
489C23—82no—
490C23—164no—
491C23—164no—
492C23—164no—
493C23—164no—
494C23—164no—
495C23—164no—
496C23—164no—
497C23#41611yescharacteristic
498C23#41611yescharacteristic
499C23#46511yescharacteristic
500C23#46511yescharacteristic
501C23#46611yescharacteristic
502C23#46611yescharacteristic
503C23C2×#13511yescharacteristic
504Q8—22no—
505Q8—22no—
506Q8—22no—
507Q8C2×#10214yes—
508D4—24no—
509D4—24no—
510D4—24no—
511D4—24no—
512D4—22no—
513D4—22no—
514D4—22no—
515D4—44no—
516D4—44no—
517D4—82no—
518D4—82no—
519D4—82no—
520D4—82no—
521D4—82no—
522D4—82no—
523D4C2×#10214yes—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—82no—
532C2×C4—162no—
533C2×C4#38611yescharacteristic
534C2×C4#38611yescharacteristic
535C2×C4#38611yescharacteristic
536C2×C4#38611yescharacteristic
537C2×C4C2×#10211yescharacteristic
538C2×C4C2×#10211yescharacteristic
539C2×C4C2×#10211yescharacteristic
540C2×C4C2×#10211yescharacteristic
541C2×C4#41611yescharacteristic
542C2×C4#41611yescharacteristic
543C2×C4#46511yescharacteristic
544C2×C4#46511yescharacteristic
545C2×C4#46511yescharacteristic
546C2×C4#46511yescharacteristic
547C2×C4#46511yescharacteristic
548C2×C4#46511yescharacteristic
549C2×C4#46611yescharacteristic
550C2×C4#46611yescharacteristic
551C2×C4#46611yescharacteristic
552C2×C4#46611yescharacteristic
553C2×C4#46611yescharacteristic
554C2×C4#46611yescharacteristic
555C2×C4C22×C22⋊C411yescharacteristic
556C2×C4C2×#12111yescharacteristic
557C2×C4C2×#12111yescharacteristic
558C2×C4C22×D811yescharacteristic
559C2×C4C22×SD1611yescharacteristic
560C2×C4C2×#13511yescharacteristic
561C8—24no—
562C8—44no—
563C8—82no—
564C8#38611yescharacteristic
565C8#38611yescharacteristic
566C8#38611yescharacteristic
567C8#38611yescharacteristic
568C8C2×C4×D411yescharacteristic
569C8C2×C4×D411yescharacteristic
570C8C2×#12011yescharacteristic
571C8C2×#12311yescharacteristic
572C22—22no—
573C22—22no—
574C22—22no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—44no—
581C22—82no—
582C22—82no—
583C22—84no—
584C22—164no—
585C22—164no—
586C22—164no—
587C22—164no—
588C22—164no—
589C22—164no—
590C22—164no—
591C22#189311yescharacteristic
592C22#189311yescharacteristic
593C22#189311yescharacteristic
594C22#189311yescharacteristic
595C22C2×#41611yescharacteristic
596C22C2×#46511yescharacteristic
597C22C2×#46611yescharacteristic
598C4—24no—
599C4—162no—
600C4#189311yescharacteristic
601C4#189311yescharacteristic
602C4#189311yescharacteristic
603C4#189311yescharacteristic
604C4C2×#38611yescharacteristic
605C4C22×#10211yescharacteristic
606C4C2×#46511yescharacteristic
607C4C2×#46611yescharacteristic
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—44no—
615C2—164no—
616C2#1306812yesdirect product factor
617C2C2×#189311yescharacteristic
subgroupG/H
center, socleC22#1893
commutatorC2×C8C23×C4
Frattini, cosocleC22×C8C24
prime radicalC22×#472C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#131 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3407C2semidirect
3. C22×#361C2semidirect
4. C2×#2140C2semidirect
5. C2×#1814C2semidirect
6. #13068C2direct (N × H)
7. C2×#1389C2semidirect
8. C2×#1385C2semidirect
15. #3407C22semidirect
24. C2×#472C4semidirect
25. C2×#472C4semidirect
34. C2×#361C22semidirect
36. #2140C22semidirect
39. #1814C22semidirect
41. #1389C22semidirect
42. #1385C22semidirect
111. #472C2×C4semidirect
616. C2#13068direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#34072
C22×#4722
C22×#3612
C2×#21402
C2×#18142
#130682
C2×#13892
C2×#13852