Finite Group Databasebeta

← C2×#13070 #494652

Subgroups — C2×#13070 #494652

Order 512.

1274 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3407C211yesmaximal, characteristic, complemented
2C2×#3067C211yesmaximal, characteristic
3C22×#360C211yesmaximal, characteristic, complemented
4C2×#2143C211yesmaximal, characteristic, complemented
5C2×#1815C211yesmaximal, characteristic, complemented
6#13070C218yesmaximal, direct product factor
7C2×#1388C211yesmaximal, characteristic, complemented
8C2×#1383C211yesmaximal, characteristic, complemented
9C2×#575—21no—
10C22×#135C2211yescharacteristic
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
21#3067—22no—
22#3067—22no—
23#3067C414yescomplemented
24#3067C2214yes—
25C2×#473C412yescomplemented
26C2×#472C412yescomplemented
27C2×#471—22no—
28C22×#108C2211yescharacteristic
29C22×#108C2211yescharacteristic
30C22×#106C2211yescharacteristic
31C2×#417—21no—
32C2×#413—21no—
33C2×#360—22no—
34C2×#360—22no—
35C2×#360C2214yescomplemented
36#2143—22no—
37#2143C2214yescomplemented
38C2×#359—22no—
39#1815—22no—
40#1815C2214yescomplemented
41C2×#343—21no—
42#1388C2214yescomplemented
43#1383C2214yescomplemented
44C22×#41—21no—
45C22×#41D411yescharacteristic
46#575—24no—
47#575—24no—
48#575—42no—
49#575—42no—
50C2×#137—22no—
51C2×#137—41no—
52C2×AGL(1,ℤ/8)—22no—
53C2×AGL(1,ℤ/8)—41no—
54C2×#135—21no—
55C2×#135—21no—
56C2×#135—21no—
57C2×#135—21no—
58C2×#135—21no—
59C2×#135—21no—
60C2×#135—21no—
61C2×#135—21no—
62C2×#135—21no—
63C2×#135—21no—
64C2×#135—42no—
65C2×#135C2×C412yes—
66C2×#135C2312yes—
67C22×Q16C2×C411yescharacteristic
68C22×SD16—21no—
69C22×D8C2×C411yescharacteristic
70C2×#131—21no—
71C2×#131—21no—
72C2×#131—21no—
73C2×#131—21no—
74C2×#131—21no—
75C2×#131—21no—
76C2×#131C2×C412yes—
77C2×#131C2×C412yes—
78C2×#131D412yes—
79C2×#131D412yes—
80C2×#131D412yes—
81C2×#131C2312yes—
82C22×M16—21no—
83C22×M16—21no—
84C22×M16—21no—
85C22×M16D411yescharacteristic
86C23×C8—21no—
87C23×C8C2311yescharacteristic
88C22×C4⋊C4—21no—
89#504—28no—
90#504—28no—
91#504—28no—
92#504—28no—
93C2×M32—24no—
94C2×M32—28no—
95C2×M32—21no—
96C2×M32—21no—
97C2×M32—21no—
98C2×M32—21no—
99C2×M32—21no—
100C2×M32—21no—
101C2×M32—21no—
102C2×M32—28no—
103C2×M32D412yes—
104C2×M32D412yes—
105C2×M32D412yes—
106C2×M32C2312yes—
107C2×M32C2312yes—
108C22×C16—24no—
109C22×C16—21no—
110C22×C16D412yes—
111#473—24no—
112#473C2×C418yescomplemented
113#472—24no—
114#472C2×C418yescomplemented
115#471—28no—
116#471—28no—
117C2×#108—21no—
118C2×#108—21no—
119C2×#108—21no—
120C2×#108—21no—
121C2×#108—21no—
122C2×#108—21no—
123C2×#108—21no—
124C2×#108—21no—
125C2×#108C2×C412yes—
126C2×#108C2×C412yes—
127C2×#108C2312yes—
128C2×#108C2312yes—
129C2×#106—21no—
130C2×#106—21no—
131C2×#106—21no—
132C2×#106—21no—
133C2×#106—21no—
134C2×#106C2312yes—
135#417—24no—
136#417—42no—
137C2×#103—41no—
138C2×#102—41no—
139#413—24no—
140#413—24no—
141C2×#101—22no—
142C2×#100—22no—
143#360—28no—
144#359—28no—
145#343—24no—
146C2×#41—21no—
147C2×#41—21no—
148C2×#41—21no—
149C2×#41—21no—
150C2×#41—21no—
151C2×#41—21no—
152C2×#41—22no—
153C2×#41—22no—
154C2×#41—41no—
155C2×#41—41no—
156C2×#41—41no—
157C2×#41—41no—
158C2×#41—41no—
159C2×#41—41no—
160C2×#41—41no—
161C2×#41—41no—
162C2×#41—41no—
163C2×#41—41no—
164C2×#41C22⋊C412yes—
165C2×#41C22⋊C412yes—
166C2×#41D812yes—
167C2×#41SD1612yes—
168C2×#41SD1612yes—
169C2×#41C2×D412yes—
170C22×Q8—21no—
171C22×Q8D811yescharacteristic
172C22×D4—21no—
173C22×D4—21no—
174C22×D4—41no—
175C22×D4D811yescharacteristic
176C23×C4—21no—
177C23×C4—41no—
178C23×C4—41no—
179C23×C4C2×D411yescharacteristic
180#137—28no—
181#137—44no—
182#137—44no—
183#137—44no—
184AGL(1,ℤ/8)—28no—
185AGL(1,ℤ/8)—44no—
186AGL(1,ℤ/8)—44no—
187AGL(1,ℤ/8)—44no—
188#135—22no—
189#135—22no—
190#135—22no—
191#135—22no—
192#135—22no—
193#135—22no—
194#135—22no—
195#135—22no—
196#135—48no—
197#135—48no—
198#135—41no—
199#135—41no—
200#135—41no—
201#135—41no—
202#135—41no—
203#135—41no—
204#135—41no—
205#135—41no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16—21no—
211C2×Q16—42no—
212C2×Q16C22×C412yes—
213C2×SD16—22no—
214C2×SD16—22no—
215C2×SD16—42no—
216C2×SD16—42no—
217C2×SD16—41no—
218C2×SD16—41no—
219C2×SD16—41no—
220C2×SD16—41no—
221C2×D8—21no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—42no—
227C2×D8C22×C412yes—
228#131—22no—
229#131—22no—
230#131—22no—
231#131—22no—
232#131—22no—
233#131—22no—
234#131—22no—
235#131—22no—
236#131—22no—
237#131—22no—
238#131—22no—
239#131—22no—
240#131C22⋊C414yes—
241#131C22⋊C414yes—
242#131C22×C414yes—
243#131C2×D414yes—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—22no—
248C2×M16—22no—
249C2×M16—22no—
250C2×M16—22no—
251C2×M16—22no—
252C2×M16—22no—
253C2×M16—22no—
254C2×M16—22no—
255C2×M16—22no—
256C2×M16—22no—
257C2×M16—41no—
258C2×M16—41no—
259C2×M16—41no—
260C2×M16—41no—
261C2×M16—41no—
262C2×M16—41no—
263C2×M16—41no—
264C2×M16—41no—
265C2×M16C22⋊C412yes—
266C2×M16C22⋊C412yes—
267C2×M16C2×D412yes—
268C22×C8—21no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—41no—
276C22×C8—41no—
277C22×C8C22×C411yescharacteristic
278C22×C8C22×C411yescharacteristic
279C22×C8C2×D411yescharacteristic
280C22×C8C2×D411yescharacteristic
281C22×C8C2×D411yescharacteristic
282C22×C8C2×D411yescharacteristic
283C22×C8C2×D411yescharacteristic
284C22×C8C2×D411yescharacteristic
285C22×C8C2×D411yescharacteristic
286C22×C8#4111yescharacteristic
287C22×C8#4111yescharacteristic
288C22×C8#4111yescharacteristic
289C22×C8#4111yescharacteristic
290C22×C8C2411yescharacteristic
291C2×C4⋊C4—22no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297M32—216no—
298M32—22no—
299M32—22no—
300M32—22no—
301M32—22no—
302M32—22no—
303M32—22no—
304M32—22no—
305M32C2×D414yes—
306C2×C16—216no—
307C2×C16—22no—
308C2×C16—22no—
309C2×C16—22no—
310C2×C16—22no—
311C2×C16—22no—
312C2×C16C2×D414yes—
313#108—22no—
314#108—22no—
315#108—22no—
316#108—22no—
317#108—22no—
318#108—41no—
319#108—41no—
320#108C22×C414yes—
321#106—22no—
322#106—22no—
323#106—41no—
324#106—41no—
325#103—44no—
326#102—44no—
327#101—28no—
328#100—28no—
329C24—21no—
330C24—41no—
331C24#13511yescharacteristic
332#41—22no—
333#41—22no—
334#41—22no—
335#41—22no—
336#41—22no—
337#41—22no—
338#41—22no—
339#41—22no—
340#41—22no—
341#41—22no—
342#41—22no—
343#41—22no—
344#41—42no—
345#41—42no—
346#41—42no—
347#41—42no—
348#41—42no—
349#41—42no—
350#41—42no—
351#41—42no—
352#41—81no—
353#41—81no—
354#41—81no—
355#41—81no—
356#41—81no—
357#41—81no—
358#41—81no—
359#41—81no—
360#41#10214yes—
361#41#10214yes—
362#41C2×C22⋊C414yes—
363#41C2×SD1614yes—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—22no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×Q8—41no—
373C2×Q8#10212yes—
374C2×Q8#10212yes—
375C2×Q8C2×D812yes—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—81no—
394C2×D4—81no—
395C2×D4—81no—
396C2×D4—81no—
397C2×D4#10212yes—
398C2×D4#10212yes—
399C2×D4C2×D812yes—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—41no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—81no—
412C22×C4—81no—
413C22×C4—81no—
414C22×C4—81no—
415C22×C4—81no—
416C22×C4—81no—
417C22×C4—162no—
418C22×C4C2×C22⋊C411yescharacteristic
419C22×C4C2×C22⋊C411yescharacteristic
420C22×C4#12111yescharacteristic
421C22×C4#12111yescharacteristic
422C22×C4#12111yescharacteristic
423C22×C4#12111yescharacteristic
424C22×C4C2×D811yescharacteristic
425C22×C4C2×D811yescharacteristic
426C22×C4C2×SD1611yescharacteristic
427C22×C4C2×SD1611yescharacteristic
428C22×C4#13511yescharacteristic
429C22×C4#13511yescharacteristic
430C22×C4#13511yescharacteristic
431C22×C4C22×D411yescharacteristic
432Q16—22no—
433Q16—22no—
434Q16—48no—
435Q16—41no—
436Q16—41no—
437SD16—48no—
438SD16—48no—
439SD16—42no—
440SD16—42no—
441SD16—42no—
442SD16—42no—
443D8—22no—
444D8—22no—
445D8—48no—
446D8—41no—
447D8—41no—
448M16—22no—
449M16—22no—
450M16—22no—
451M16—24no—
452M16—24no—
453M16—24no—
454M16—24no—
455M16—24no—
456M16—42no—
457M16—42no—
458M16—42no—
459M16—42no—
460M16—42no—
461M16—81no—
462M16—81no—
463M16C2×C22⋊C414yes—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—24no—
468C2×C8—24no—
469C2×C8—24no—
470C2×C8—24no—
471C2×C8—42no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8—42no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8C2×C22⋊C411yescharacteristic
478C2×C8C2×C22⋊C411yescharacteristic
479C2×C8C4×D411yescharacteristic
480C2×C8C4×D411yescharacteristic
481C2×C8C4×D411yescharacteristic
482C2×C8C4×D411yescharacteristic
483C2×C8C4×D411yescharacteristic
484C2×C8C4×D411yescharacteristic
485C2×C8C4×D411yescharacteristic
486C2×C8C4×D411yescharacteristic
487C2×C8#12011yescharacteristic
488C2×C8#12011yescharacteristic
489C2×C8#12011yescharacteristic
490C2×C8#12011yescharacteristic
491C2×C8#12111yescharacteristic
492C2×C8#12111yescharacteristic
493C2×C8#12111yescharacteristic
494C2×C8#12111yescharacteristic
495C2×C8#12311yescharacteristic
496C2×C8#12311yescharacteristic
497C2×C8#12311yescharacteristic
498C2×C8#12311yescharacteristic
499C2×C8C23×C411yescharacteristic
500C2×C8C22×D411yescharacteristic
501C2×C8C22×D411yescharacteristic
502C2×C8C22×D411yescharacteristic
503C2×C8C2×#4111yescharacteristic
504C2×C8C2×#4111yescharacteristic
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—81no—
508C4⋊C4—81no—
509C16—24no—
510C16—24no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—42no—
515C23—42no—
516C23—82no—
517C23—81no—
518C23—81no—
519C23—162no—
520C23#41611yescharacteristic
521C23#41611yescharacteristic
522C23#46511yescharacteristic
523C23#46511yescharacteristic
524C23#46611yescharacteristic
525C23#46611yescharacteristic
526C23C2×#13511yescharacteristic
527Q8—22no—
528Q8—22no—
529Q8—22no—
530Q8—42no—
531Q8—42no—
532Q8—81no—
533Q8—81no—
534Q8C2×#10214yes—
535D4—24no—
536D4—24no—
537D4—24no—
538D4—24no—
539D4—22no—
540D4—22no—
541D4—22no—
542D4—42no—
543D4—42no—
544D4—82no—
545D4—82no—
546D4—82no—
547D4—82no—
548D4—81no—
549D4—81no—
550D4C2×#10214yes—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—42no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—162no—
567C2×C4—162no—
568C2×C4—162no—
569C2×C4#38611yescharacteristic
570C2×C4#38611yescharacteristic
571C2×C4#38611yescharacteristic
572C2×C4#38611yescharacteristic
573C2×C4C2×#10211yescharacteristic
574C2×C4C2×#10211yescharacteristic
575C2×C4C2×#10211yescharacteristic
576C2×C4C2×#10211yescharacteristic
577C2×C4#41611yescharacteristic
578C2×C4#41611yescharacteristic
579C2×C4#46511yescharacteristic
580C2×C4#46511yescharacteristic
581C2×C4#46511yescharacteristic
582C2×C4#46511yescharacteristic
583C2×C4#46511yescharacteristic
584C2×C4#46511yescharacteristic
585C2×C4#46611yescharacteristic
586C2×C4#46611yescharacteristic
587C2×C4#46611yescharacteristic
588C2×C4#46611yescharacteristic
589C2×C4#46611yescharacteristic
590C2×C4#46611yescharacteristic
591C2×C4C22×C22⋊C411yescharacteristic
592C2×C4C2×#12111yescharacteristic
593C2×C4C2×#12111yescharacteristic
594C2×C4C22×D811yescharacteristic
595C2×C4C22×SD1611yescharacteristic
596C2×C4C2×#13511yescharacteristic
597C8—24no—
598C8—44no—
599C8—82no—
600C8#38611yescharacteristic
601C8#38611yescharacteristic
602C8#38611yescharacteristic
603C8#38611yescharacteristic
604C8C2×C4×D411yescharacteristic
605C8C2×C4×D411yescharacteristic
606C8C2×#12011yescharacteristic
607C8C2×#12311yescharacteristic
608C22—22no—
609C22—22no—
610C22—22no—
611C22—24no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—44no—
617C22—82no—
618C22—82no—
619C22—82no—
620C22—162no—
621C22—162no—
622C22—162no—
623C22#189311yescharacteristic
624C22#189311yescharacteristic
625C22#189311yescharacteristic
626C22#189311yescharacteristic
627C22C2×#41611yescharacteristic
628C22C2×#46511yescharacteristic
629C22C2×#46611yescharacteristic
630C4—24no—
631C4—82no—
632C4—162no—
633C4#189311yescharacteristic
634C4#189311yescharacteristic
635C4#189311yescharacteristic
636C4#189311yescharacteristic
637C4C2×#38611yescharacteristic
638C4C22×#10211yescharacteristic
639C4C2×#46511yescharacteristic
640C4C2×#46611yescharacteristic
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—21no—
646C2—21no—
647C2—44no—
648C2—162no—
649C2#1307012yesdirect product factor
650C2C2×#189311yescharacteristic
subgroupG/H
center, socleC22#1893
commutatorC2×C8C23×C4
Frattini, cosocleC22×C8C24
prime radicalC2×#3067C2
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×#360C2semidirect
4. C2×#2143C2semidirect
5. C2×#1815C2semidirect
6. #13070C2direct (N × H)
7. C2×#1388C2semidirect
8. C2×#1383C2semidirect
15. #3407C22semidirect
23. #3067C4semidirect
25. C2×#473C4semidirect
26. C2×#472C4semidirect
35. C2×#360C22semidirect
37. #2143C22semidirect
40. #1815C22semidirect
42. #1388C22semidirect
43. #1383C22semidirect
112. #473C2×C4semidirect
114. #472C2×C4semidirect
649. C2#13070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#34072
C2×#30672
C22×#3602
C2×#21432
C2×#18152
#130702
C2×#13882
C2×#13832