Finite Group Databasebeta

← C2×#13036 #494555

Subgroups — C2×#13036 #494555

Order 512.

1338 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#509C211yesmaximal, characteristic
2C2×#2957C211yesmaximal, characteristic, complemented
3C22×#361C211yesmaximal, characteristic, complemented
4C2×#2143C211yesmaximal, characteristic, complemented
5C2×#1978C211yesmaximal, characteristic, complemented
6#13036C218yesmaximal, direct product factor
7C2×#1385C211yesmaximal, characteristic, complemented
8C2×#1378C211yesmaximal, characteristic, complemented
9C22×#135C2211yescharacteristic
10C23×D8C2211yescharacteristic
11C2×#568—21no—
12C2×#509—22no—
13C2×#509—22no—
14C2×#509—22no—
15C2×#509—22no—
16C2×#509C414yescomplemented
17C2×#509C2214yes—
18C22×SD32C412yescomplemented
19C22×D16C412yescomplemented
20C22×M32C2211yescharacteristic
21C22×M32C2211yescharacteristic
22#2957—22no—
23#2957—22no—
24#2957—22no—
25#2957C2214yescomplemented
26C2×#444—22no—
27C2×#443—22no—
28C22×#108C2211yescharacteristic
29C22×#108C2211yescharacteristic
30C2×#421—21no—
31C2×#418—21no—
32C22×#100—21no—
33C2×#405C2211yescharacteristic
34C2×#361—22no—
35C2×#361—22no—
36C2×#361C2214yescomplemented
37#2143—22no—
38#2143C2214yescomplemented
39C2×#359—22no—
40#1978—22no—
41#1978C2214yescomplemented
42#1385C2214yescomplemented
43#1378C2214yescomplemented
44C22×#41—21no—
45C23×D4—21no—
46C2×#135—21no—
47C2×#135—21no—
48C2×#135—21no—
49C2×#135—21no—
50C2×#135—21no—
51C2×#135—21no—
52C2×#135C2×C412yes—
53C2×#135D412yes—
54C2×#135D412yes—
55C2×#135D412yes—
56C2×#135D412yes—
57C2×#135C2312yes—
58C22×Q16C2×C411yescharacteristic
59C22×SD16—21no—
60C22×D8—21no—
61C22×D8—21no—
62C22×D8—21no—
63C22×D8—21no—
64C22×D8—21no—
65C22×D8—21no—
66C22×D8—21no—
67C22×D8—21no—
68C22×D8—21no—
69C22×D8—21no—
70C22×D8—21no—
71C22×D8C2×C412yes—
72C22×D8C2×C412yes—
73C22×D8C2×C411yescharacteristic
74C22×D8C2312yes—
75#568—24no—
76#568—24no—
77#568—42no—
78#568—42no—
79C2×#131—24no—
80C2×#131—42no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—42no—
84C22×M16D411yescharacteristic
85C23×C8C2311yescharacteristic
86C2×#117D411yescharacteristic
87#509—28no—
88#509—28no—
89#509—28no—
90#509—28no—
91C2×SD32—24no—
92C2×SD32—24no—
93C2×SD32C2×C418yescomplemented
94C2×D16—24no—
95C2×D16—24no—
96C2×D16C2×C418yescomplemented
97C2×M32—21no—
98C2×M32—21no—
99C2×M32—21no—
100C2×M32—21no—
101C2×M32—21no—
102C2×M32—21no—
103C2×M32—21no—
104C2×M32—21no—
105C2×M32—21no—
106C2×M32C2×C412yes—
107C2×M32C2312yes—
108C2×M32C2312yes—
109C22×C16—21no—
110C22×C16C2×C412yes—
111#444—28no—
112#444—28no—
113#443—28no—
114#443—28no—
115C2×#108—21no—
116C2×#108—21no—
117C2×#108—21no—
118C2×#108—21no—
119C2×#108—21no—
120C2×#108—21no—
121C2×#108—21no—
122C2×#108—21no—
123C2×#108D412yes—
124C2×#108D412yes—
125C2×#108C2312yes—
126C2×#108C2312yes—
127#421—24no—
128#421—24no—
129C2×#104—24no—
130#418—24no—
131#418—42no—
132C2×#102—42no—
133C2×#100—24no—
134C2×#100—42no—
135C2×#100—42no—
136#405—21no—
137#405—21no—
138#405D412yes—
139#405C2312yes—
140C2×#97—21no—
141C2×C4×C8—21no—
142#361—28no—
143#359—28no—
144C25—41no—
145C2×#41—22no—
146C2×#41—22no—
147C2×#41—22no—
148C2×#41—22no—
149C2×#41—22no—
150C2×#41—22no—
151C2×#41—41no—
152C2×#41—41no—
153C2×#41—41no—
154C2×#41—41no—
155C2×#41—41no—
156C2×#41—41no—
157C22×Q8—21no—
158C22×D4—21no—
159C22×D4—22no—
160C22×D4—22no—
161C22×D4—22no—
162C22×D4—41no—
163C22×D4—41no—
164C22×D4—41no—
165C22×D4—41no—
166C22×D4—41no—
167C22×D4—41no—
168C22×D4—41no—
169C22×D4—41no—
170C22×D4—41no—
171C22×D4—41no—
172C22×D4—41no—
173C22×D4—41no—
174C23×C4—41no—
175C23×C4C2×D411yescharacteristic
176#135—22no—
177#135—22no—
178#135—22no—
179#135—22no—
180#135—22no—
181#135—22no—
182#135—22no—
183#135—22no—
184#135—22no—
185#135—22no—
186#135—22no—
187#135—22no—
188#135C22⋊C414yes—
189#135C22⋊C414yes—
190#135C2×D414yes—
191#135C2×D414yes—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16C22⋊C412yes—
196C2×Q16C22⋊C412yes—
197C2×Q16C22×C412yes—
198C2×SD16—22no—
199C2×SD16—22no—
200C2×SD16—22no—
201C2×SD16—22no—
202C2×SD16—22no—
203C2×SD16—22no—
204C2×D8—22no—
205C2×D8—22no—
206C2×D8—22no—
207C2×D8—22no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—22no—
212C2×D8—22no—
213C2×D8—22no—
214C2×D8—22no—
215C2×D8—22no—
216C2×D8—22no—
217C2×D8—22no—
218C2×D8—22no—
219C2×D8—22no—
220C2×D8—22no—
221C2×D8—22no—
222C2×D8—41no—
223C2×D8—41no—
224C2×D8—41no—
225C2×D8—41no—
226C2×D8—41no—
227C2×D8—41no—
228C2×D8—41no—
229C2×D8—41no—
230C2×D8—41no—
231C2×D8—41no—
232C2×D8—41no—
233C2×D8—41no—
234C2×D8C22⋊C412yes—
235C2×D8C22⋊C412yes—
236C2×D8C22×C414yes—
237C2×D8C22×C412yes—
238#131—216no—
239#131—48no—
240#131—48no—
241#131—48no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—22no—
248C2×M16—22no—
249C2×M16—44no—
250C2×M16—48no—
251C2×M16—41no—
252C2×M16—41no—
253C2×M16—41no—
254C2×M16—48no—
255C2×M16—41no—
256C2×M16—41no—
257C2×M16—41no—
258C2×M16—41no—
259C2×M16—41no—
260C2×M16D812yes—
261C2×M16D812yes—
262C2×M16C2×D412yes—
263C22×C8—21no—
264C22×C8—44no—
265C22×C8—41no—
266C22×C8—41no—
267C22×C8C22×C411yescharacteristic
268C22×C8C22×C411yescharacteristic
269C22×C8C2×D411yescharacteristic
270C22×C8C2×D411yescharacteristic
271C22×C8C2×D411yescharacteristic
272C22×C8C2×D411yescharacteristic
273C22×C8C2×D411yescharacteristic
274C22×C8C2×D411yescharacteristic
275C22×C8C2×D411yescharacteristic
276C22×C8#4111yescharacteristic
277C22×C8#4111yescharacteristic
278C22×C8#4111yescharacteristic
279C22×C8#4111yescharacteristic
280C22×C8C2411yescharacteristic
281#117—21no—
282#117—21no—
283#117—21no—
284#117C2×D412yes—
285C2×C4⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C42—21no—
288SD32—216no—
289D16—216no—
290M32—22no—
291M32—22no—
292M32—22no—
293M32—22no—
294M32—22no—
295M32—22no—
296M32—41no—
297M32—41no—
298C2×C16—22no—
299C2×C16—22no—
300C2×C16—22no—
301C2×C16—41no—
302C2×C16—41no—
303C2×C16C22×C414yes—
304#108—22no—
305#108—22no—
306#108—22no—
307#108—22no—
308#108—22no—
309#108—41no—
310#108—41no—
311#108C2×D414yes—
312#104—216no—
313#102—48no—
314#100—48no—
315#97—22no—
316#97—22no—
317C4×C8—22no—
318C4×C8—22no—
319C24—41no—
320C24—42no—
321C24—42no—
322C24—42no—
323C24—81no—
324C24—81no—
325C24—81no—
326C24—81no—
327C24—164no—
328C24#13511yescharacteristic
329#41—24no—
330#41—24no—
331#41—24no—
332#41—24no—
333#41—42no—
334#41—42no—
335#41—42no—
336#41—42no—
337#41—42no—
338#41—42no—
339#41—42no—
340#41—42no—
341#41—42no—
342#41—42no—
343#41—42no—
344#41—42no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—41no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×D4—22no—
352C2×D4—24no—
353C2×D4—22no—
354C2×D4—22no—
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—42no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—81no—
380C2×D4—81no—
381C2×D4—81no—
382C2×D4—81no—
383C2×D4—81no—
384C2×D4—81no—
385C2×D4—81no—
386C2×D4—81no—
387C2×D4—81no—
388C2×D4—81no—
389C2×D4—81no—
390C2×D4—81no—
391C22×C4—41no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—41no—
399C22×C4C4×D411yescharacteristic
400C22×C4C4×D411yescharacteristic
401C22×C4#12011yescharacteristic
402C22×C4#12011yescharacteristic
403C22×C4#12111yescharacteristic
404C22×C4#12111yescharacteristic
405C22×C4C2×D811yescharacteristic
406C22×C4C2×D811yescharacteristic
407C22×C4#13511yescharacteristic
408C22×C4AGL(1,ℤ/8)11yescharacteristic
409C22×C4AGL(1,ℤ/8)11yescharacteristic
410C22×C4AGL(1,ℤ/8)11yescharacteristic
411C22×C4AGL(1,ℤ/8)11yescharacteristic
412C22×C4C22×D411yescharacteristic
413Q16—22no—
414Q16—22no—
415Q16—22no—
416Q16C2×C22⋊C414yes—
417SD16—24no—
418SD16—24no—
419SD16—24no—
420SD16—24no—
421D8—24no—
422D8—22no—
423D8—24no—
424D8—22no—
425D8—22no—
426D8—42no—
427D8—42no—
428D8—42no—
429D8—42no—
430D8—42no—
431D8—42no—
432D8C2×C22⋊C414yes—
433M16—22no—
434M16—22no—
435M16—22no—
436M16—24no—
437M16—416no—
438M16—42no—
439M16—42no—
440M16—42no—
441M16—42no—
442M16—42no—
443M16—81no—
444M16—81no—
445M16C2×D814yes—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—416no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8—42no—
453C2×C8—42no—
454C2×C8—81no—
455C2×C8—81no—
456C2×C8C2×C22⋊C411yescharacteristic
457C2×C8C2×C22⋊C411yescharacteristic
458C2×C8C2×C22⋊C411yescharacteristic
459C2×C8C2×C22⋊C411yescharacteristic
460C2×C8C4×D411yescharacteristic
461C2×C8C4×D411yescharacteristic
462C2×C8C4×D411yescharacteristic
463C2×C8C4×D411yescharacteristic
464C2×C8C4×D411yescharacteristic
465C2×C8C4×D411yescharacteristic
466C2×C8#12011yescharacteristic
467C2×C8#12011yescharacteristic
468C2×C8#12111yescharacteristic
469C2×C8#12111yescharacteristic
470C2×C8#12111yescharacteristic
471C2×C8#12111yescharacteristic
472C2×C8#12111yescharacteristic
473C2×C8#12111yescharacteristic
474C2×C8#12311yescharacteristic
475C2×C8#12311yescharacteristic
476C2×C8#12311yescharacteristic
477C2×C8#12311yescharacteristic
478C2×C8C23×C411yescharacteristic
479C2×C8C22×D411yescharacteristic
480C2×C8C22×D411yescharacteristic
481C2×C8C22×D411yescharacteristic
482C2×C8C2×#4111yescharacteristic
483C2×C8C2×#4111yescharacteristic
484C4⋊C4—22no—
485C4⋊C4—41no—
486C22⋊C4—22no—
487C22⋊C4—41no—
488C42—22no—
489C42—41no—
490C16—24no—
491C16—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—44no—
497C23—82no—
498C23—82no—
499C23—82no—
500C23—82no—
501C23—82no—
502C23—82no—
503C23—162no—
504C23—164no—
505C23—164no—
506C23—164no—
507C23—164no—
508C23—164no—
509C23—164no—
510C23—164no—
511C23C4×D811yescharacteristic
512C23C4×D811yescharacteristic
513C23#44911yescharacteristic
514C23#44911yescharacteristic
515C23#46311yescharacteristic
516C23#46311yescharacteristic
517C23C2×#13511yescharacteristic
518Q8—24no—
519Q8—42no—
520Q8—42no—
521Q8—42no—
522D4—24no—
523D4—44no—
524D4—44no—
525D4—44no—
526D4—44no—
527D4—42no—
528D4—42no—
529D4—42no—
530D4—44no—
531D4—44no—
532D4—82no—
533D4—82no—
534D4—82no—
535D4—82no—
536D4—82no—
537D4—82no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—42no—
546C2×C4—82no—
547C2×C4#38611yescharacteristic
548C2×C4#38611yescharacteristic
549C2×C4#38611yescharacteristic
550C2×C4#38611yescharacteristic
551C2×C4C4×D811yescharacteristic
552C2×C4C4×D811yescharacteristic
553C2×C4#44211yescharacteristic
554C2×C4#44211yescharacteristic
555C2×C4#44211yescharacteristic
556C2×C4#44211yescharacteristic
557C2×C4#44711yescharacteristic
558C2×C4#44711yescharacteristic
559C2×C4#44711yescharacteristic
560C2×C4#44711yescharacteristic
561C2×C4#44911yescharacteristic
562C2×C4#44911yescharacteristic
563C2×C4#45911yescharacteristic
564C2×C4#45911yescharacteristic
565C2×C4#45911yescharacteristic
566C2×C4#45911yescharacteristic
567C2×C4#46311yescharacteristic
568C2×C4#46311yescharacteristic
569C2×C4C2×C4×D411yescharacteristic
570C2×C4C2×#12011yescharacteristic
571C2×C4C2×#12111yescharacteristic
572C2×C4C22×D811yescharacteristic
573C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
574C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
575C8—24no—
576C8—44no—
577C8—82no—
578C8#38611yescharacteristic
579C8#38611yescharacteristic
580C8#38611yescharacteristic
581C8#38611yescharacteristic
582C8C22×C22⋊C411yescharacteristic
583C8C2×C4×D411yescharacteristic
584C8C2×#12111yescharacteristic
585C8C2×#12311yescharacteristic
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—44no—
594C22—84no—
595C22—84no—
596C22—162no—
597C22—162no—
598C22—164no—
599C22—164no—
600C22—164no—
601C22—164no—
602C22—164no—
603C22—164no—
604C22—164no—
605C22#187911yescharacteristic
606C22#187911yescharacteristic
607C22#187911yescharacteristic
608C22#187911yescharacteristic
609C22C2×C4×D811yescharacteristic
610C22C2×#44911yescharacteristic
611C22C2×#46311yescharacteristic
612C4—44no—
613C4—82no—
614C4#187911yescharacteristic
615C4#187911yescharacteristic
616C4#187911yescharacteristic
617C4#187911yescharacteristic
618C4C2×#38611yescharacteristic
619C4C2×#44211yescharacteristic
620C4C2×#44711yescharacteristic
621C4C2×#45911yescharacteristic
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—21no—
627C2—21no—
628C2—84no—
629C2—164no—
630C2#1303612yesdirect product factor
631C2C2×#187911yescharacteristic
subgroupG/H
center, socleC22#1879
commutatorC2×C8C23×C4
Frattini, cosocleC22×C8C24
prime radicalC22×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#405 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2957C2semidirect
3. C22×#361C2semidirect
4. C2×#2143C2semidirect
5. C2×#1978C2semidirect
6. #13036C2direct (N × H)
7. C2×#1385C2semidirect
8. C2×#1378C2semidirect
16. C2×#509C4semidirect
18. C22×SD32C4semidirect
19. C22×D16C4semidirect
25. #2957C22semidirect
36. C2×#361C22semidirect
38. #2143C22semidirect
41. #1978C22semidirect
42. #1385C22semidirect
43. #1378C22semidirect
93. C2×SD32C2×C4semidirect
96. C2×D16C2×C4semidirect
630. C2#13036direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5092
C2×#29572
C22×#3612
C2×#21432
C2×#19782
#130362
C2×#13852
C2×#13782