Finite Group Databasebeta

← C2×#19168 #6353639

Subgroups — C2×#19168 #6353639

Order 512.

2042 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3141C211yesmaximal, characteristic, complemented
2C2×#3100C211yesmaximal, characteristic
3C22×#476C211yesmaximal, characteristic, complemented
4C2×D4×M16C211yesmaximal, characteristic, complemented
5#19168C2116yesmaximal, direct product factor
6C2×#1703C212yesmaximal, complemented
7C2×#1697C212yesmaximal, complemented
8C2×#1683C212yesmaximal, complemented
9C2×#1677C212yesmaximal, complemented
10C2×#1565C211yesmaximal, characteristic, complemented
11C2×#1548C211yesmaximal, characteristic, complemented
12C2×#1547C211yesmaximal, characteristic, complemented
13C23×M16—21no—
14C2×#532C2211yescharacteristic
15C22×C4⋊Q8C2211yescharacteristic
16C22×C4×D4C2211yescharacteristic
17#3141—24no—
18#3141C2218yescomplemented
19C2×#489—22no—
20C2×#487C2212yescomplemented
21C2×#486C2212yescomplemented
22#3100—24no—
23#3100C2218yes—
24C2×#480—21no—
25C2×#476—24no—
26C2×#476—21no—
27C2×#476—21no—
28C2×#476C2212yes—
29C2×#476C2212yes—
30C2×#476C2218yescomplemented
31C2×#474C2211yescharacteristic
32C2×#474C2211yescharacteristic
33C2×#459C2211yescharacteristic
34C2×#459C2211yescharacteristic
35C2×#447—21no—
36C2×C4×D8—21no—
37C2×C4×D8—21no—
38D4×M16—24no—
39D4×M16C2218yescomplemented
40C2×#436C2212yes—
41C2×#435—22no—
42C2×C8×D4C2212yes—
43C2×#431C2211yescharacteristic
44C22×#106—21no—
45C2×#423C2211yescharacteristic
46C22×C4⋊C8C2211yescharacteristic
47C2×#417—21no—
48C2×#417—21no—
49C22×#102—21no—
50C2×#407—21no—
51C2×C4×M16C2211yescharacteristic
52#1703C22116yescomplemented
53#1697C22116yescomplemented
54#1683C22116yescomplemented
55#1677C22116yescomplemented
56#1565C2218yescomplemented
57C2×#335C2212yescomplemented
58C2×#334C2212yescomplemented
59#1548C2218yescomplemented
60#1547C2218yescomplemented
61C2×#333C2212yescomplemented
62C2×#333C2212yescomplemented
63C2×#332C2212yescomplemented
64C2×#331C2212yescomplemented
65C22×#41—21no—
66C23×Q8—21no—
67C23×D4D411yescharacteristic
68C24×C4—21no—
69C22×D8—21no—
70C22×D8—21no—
71C22×M16—21no—
72C22×M16—28no—
73C22×M16—22no—
74C22×M16—48no—
75C22×M16D411yescharacteristic
76C22×M16D411yescharacteristic
77C23×C8—21no—
78C23×C8—22no—
79#532—22no—
80#532—22no—
81#532—22no—
82#532C2314yes—
83C2×C4⋊Q8—21no—
84C2×C4⋊Q8—22no—
85C2×C4⋊Q8—21no—
86C2×C4⋊Q8—22no—
87C2×C4⋊Q8—21no—
88C2×C4⋊Q8—22no—
89C2×C4⋊Q8C2311yescharacteristic
90C2×C4⋊Q8C2312yes—
91C2×C4⋊Q8C2314yes—
92C2×#127C2311yescharacteristic
93C2×#124—21no—
94C2×#121—21no—
95C2×#121—21no—
96C2×C4×D4—21no—
97C2×C4×D4—22no—
98C2×C4×D4—21no—
99C2×C4×D4—21no—
100C2×C4×D4—22no—
101C2×C4×D4—21no—
102C2×C4×D4D414yes—
103C2×C4×D4D411yescharacteristic
104C2×C4×D4D411yescharacteristic
105C2×C4×D4C2314yes—
106C2×C4×D4C2311yescharacteristic
107C2×C4×D4C2311yescharacteristic
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4D411yescharacteristic
111C22×C22⋊C4—21no—
112C22×C42C2311yescharacteristic
113#489—216no—
114#487—24no—
115#487C2318yescomplemented
116#486—24no—
117#486C2318yescomplemented
118#480—28no—
119#476—24no—
120#476—24no—
121#476—28no—
122#476—28no—
123#476C2318yes—
124#476C2318yes—
125#474—22no—
126#474—22no—
127#474C2314yes—
128#474C2314yes—
129#459—22no—
130#459—22no—
131#459C2314yes—
132#459C2314yes—
133#447—28no—
134C4×D8—28no—
135C4×D8—28no—
136#436—24no—
137#436C2318yes—
138#435—216no—
139C8×D4—24no—
140C8×D4C2318yes—
141#431—22no—
142#431C2314yes—
143C2×#107—21no—
144C2×#107—21no—
145C2×#106—22no—
146C2×#106—22no—
147C2×#106—28no—
148#423—22no—
149#423C2314yes—
150C2×C4⋊C8—21no—
151C2×C4⋊C8—22no—
152C2×C4⋊C8—21no—
153C2×C4⋊C8C2312yes—
154C2×C4⋊C8C2312yes—
155C2×C4⋊C8C2311yescharacteristic
156C2×C4⋊C8C2311yescharacteristic
157C2×C4⋊C8C2314yes—
158#417—28no—
159#417—28no—
160C2×#103—22no—
161C2×#103—22no—
162C2×#102—22no—
163C2×#102—22no—
164C2×#102—28no—
165C2×#102—21no—
166C2×#102—21no—
167C2×#102—22no—
168C2×#102—22no—
169C2×#102—21no—
170C2×#102—21no—
171#407—28no—
172C2×C22⋊C8—21no—
173C2×C22⋊C8—22no—
174C2×C22⋊C8—22no—
175C4×M16D414yes—
176C4×M16C2314yes—
177C2×#97D412yes—
178C2×C4×C8—21no—
179C2×C4×C8C2312yes—
180#335C2318yescomplemented
181#334C2318yescomplemented
182#333C2318yescomplemented
183#333C2318yescomplemented
184#332C2318yescomplemented
185#331C2318yescomplemented
186C25—21no—
187C2×#41—24no—
188C2×#41—42no—
189C2×#41—44no—
190C2×#41—44no—
191C22×Q8—21no—
192C22×Q8—24no—
193C22×Q8—22no—
194C22×Q8—42no—
195C22×Q8—41no—
196C22×Q8—84no—
197C22×D4—24no—
198C22×D4—22no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—42no—
204C22×D4—41no—
205C22×D4C2×D411yescharacteristic
206C22×D4C2×D414yes—
207C22×D4C2×D411yescharacteristic
208C23×C4—21no—
209C23×C4—24no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—24no—
215C23×C4—44no—
216C23×C4—44no—
217C23×C4—41no—
218C23×C4—41no—
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4#4111yescharacteristic
222C2×D8—24no—
223C2×D8—24no—
224C2×D8—44no—
225C2×D8—44no—
226C2×M16—24no—
227C2×M16—24no—
228C2×M16—24no—
229C2×M16—28no—
230C2×M16—48no—
231C2×M16—432no—
232C2×M16—44no—
233C2×M16C2×D414yes—
234C2×M16C2×D414yes—
235C22×C8—22no—
236C22×C8—24no—
237C22×C8—22no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—28no—
241C22×C8—48no—
242C22×C8—44no—
243C22×C8C2×D412yes—
244C22×C8C2×D412yes—
245C4⋊Q8—24no—
246C4⋊Q8—22no—
247C4⋊Q8—22no—
248C4⋊Q8—24no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—24no—
253C4⋊Q8—22no—
254C4⋊Q8—42no—
255C4⋊Q8—42no—
256C4⋊Q8—42no—
257C4⋊Q8C2414yes—
258C4⋊Q8C2412yes—
259#127—21no—
260#127—21no—
261#127—21no—
262#127C2412yes—
263#124—24no—
264#124—42no—
265#121—24no—
266#121—24no—
267#121—42no—
268#121—42no—
269C4×D4—22no—
270C4×D4—24no—
271C4×D4—22no—
272C4×D4—24no—
273C4×D4—21no—
274C4×D4—24no—
275C4×D4—21no—
276C4×D4—24no—
277C4×D4—24no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—24no—
281C4×D4—42no—
282C4×D4—42no—
283C4×D4C2×D414yes—
284C4×D4C2×D414yes—
285C4×D4C2×D412yes—
286C4×D4C2×D412yes—
287C4×D4C2412yes—
288C4×D4C2412yes—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4C2×D411yescharacteristic
302C2×C4⋊C4C2×D411yescharacteristic
303C2×C4⋊C4C2×D414yes—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—41no—
311C2×C22⋊C4—41no—
312C2×C42C2×D411yescharacteristic
313C2×C42C2×D411yescharacteristic
314C2×C42C2×D412yes—
315C2×C42C2×D412yes—
316C2×C42#4111yescharacteristic
317C2×C42#4112yes—
318C2×C42C2411yescharacteristic
319C2×C42C2412yes—
320#107—24no—
321#107—24no—
322#106—28no—
323#106—28no—
324C4⋊C8—24no—
325C4⋊C8—22no—
326C4⋊C8—24no—
327C4⋊C8—22no—
328C4⋊C8—21no—
329C4⋊C8—21no—
330C4⋊C8C2414yes—
331C4⋊C8C2414yes—
332C4⋊C8C2412yes—
333C4⋊C8C2412yes—
334#103—28no—
335#103—28no—
336#102—28no—
337#102—28no—
338#102—24no—
339#102—24no—
340#102—28no—
341#102—28no—
342#102—24no—
343#102—24no—
344C22⋊C8—24no—
345C22⋊C8—28no—
346C22⋊C8—28no—
347#97C2×D418yes—
348C4×C8—24no—
349C4×C8C2×D414yes—
350C4×C8C2414yes—
351C24—21no—
352C24—21no—
353C24—24no—
354C24—44no—
355C24—44no—
356C24—41no—
357C24—82no—
358C24#12111yescharacteristic
359#41—48no—
360#41—48no—
361#41—88no—
362C2×Q8—22no—
363C2×Q8—24no—
364C2×Q8—41no—
365C2×Q8—44no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8—84no—
370C2×Q8—84no—
371C2×Q8—88no—
372C2×Q8—88no—
373C2×D4—28no—
374C2×D4—21no—
375C2×D4—24no—
376C2×D4—21no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—44no—
384C2×D4—48no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—82no—
395C2×D4—84no—
396C2×D4#13714yes—
397C2×D4C22×D412yes—
398C2×D4C22×D412yes—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—42no—
411C22×C4—44no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—48no—
415C22×C4—42no—
416C22×C4—48no—
417C22×C4—42no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—416no—
421C22×C4—44no—
422C22×C4—41no—
423C22×C4—42no—
424C22×C4—44no—
425C22×C4—84no—
426C22×C4—84no—
427C22×C4#12112yes—
428C22×C4#12111yescharacteristic
429C22×C4#12111yescharacteristic
430C22×C4#12112yes—
431C22×C4#12112yes—
432C22×C4#12111yescharacteristic
433C22×C4#13514yes—
434C22×C4AGL(1,ℤ/8)14yes—
435C22×C4C22×D412yes—
436C22×C4C22×D412yes—
437C22×C4C22×D411yescharacteristic
438C22×C4C22×D411yescharacteristic
439C22×C4C2×#4111yescharacteristic
440C22×C4C2×#4112yes—
441D8—48no—
442D8—48no—
443M16—28no—
444M16—28no—
445M16—416no—
446M16—48no—
447C2×C8—24no—
448C2×C8—24no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—24no—
452C2×C8—24no—
453C2×C8—416no—
454C2×C8—48no—
455C2×C8—44no—
456C2×C8—42no—
457C2×C8—44no—
458C2×C8—42no—
459C2×C8C22×D414yes—
460C2×C8C22×D414yes—
461C4⋊C4—24no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—44no—
469C4⋊C4—44no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4C22×D412yes—
475C4⋊C4C22×D412yes—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—44no—
483C22⋊C4—44no—
484C42#12112yes—
485C42#12112yes—
486C42#12112yes—
487C42C22×D412yes—
488C42C22×D411yescharacteristic
489C42C22×D412yes—
490C42C22×D411yescharacteristic
491C42C2×#4112yes—
492C42C2×#4111yescharacteristic
493C42C2511yescharacteristic
494C23—22no—
495C23—22no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—48no—
500C23—42no—
501C23—42no—
502C23—48no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—84no—
508C23—816no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23#46314yes—
513C23C2×#12112yes—
514C23C2×#12111yescharacteristic
515Q8—42no—
516Q8—42no—
517Q8—84no—
518Q8—88no—
519Q8—84no—
520Q8—82no—
521D4—24no—
522D4—22no—
523D4—22no—
524D4—22no—
525D4—48no—
526D4—42no—
527D4—42no—
528D4—42no—
529D4—42no—
530D4—42no—
531D4—82no—
532D4—82no—
533D4—88no—
534D4—82no—
535D4—82no—
536D4C2×#13714yes—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—48no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—48no—
551C2×C4—48no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—88no—
561C2×C4—82no—
562C2×C4—84no—
563C2×C4—88no—
564C2×C4#46314yes—
565C2×C4#46318yes—
566C2×C4C2×#12112yes—
567C2×C4C2×#12111yescharacteristic
568C2×C4C2×#12112yes—
569C2×C4C2×#12112yes—
570C2×C4C2×#12111yescharacteristic
571C2×C4C2×#12111yescharacteristic
572C2×C4C2×#13512yes—
573C2×C4C2×#13514yes—
574C2×C4C2×AGL(1,ℤ/8)12yes—
575C2×C4C2×AGL(1,ℤ/8)14yes—
576C2×C4C2×#13712yes—
577C2×C4#57512yes—
578C2×C4C23×D411yescharacteristic
579C2×C4C23×D411yescharacteristic
580C2×C4C22×#4111yescharacteristic
581C8—24no—
582C8—24no—
583C8—44no—
584C8—42no—
585C8—44no—
586C8—42no—
587C22—22no—
588C22—22no—
589C22—28no—
590C22—24no—
591C22—42no—
592C22—48no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—816no—
598C22—84no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22—164no—
603C22C2×#46314yes—
604C22C2×#46312yes—
605C22#305612yes—
606C22#306812yes—
607C22C22×#12111yescharacteristic
608C4—22no—
609C4—21no—
610C4—22no—
611C4—21no—
612C4—42no—
613C4—42no—
614C4—84no—
615C4—82no—
616C4C2×#46314yes—
617C4C2×#46312yes—
618C4#305612yes—
619C4C22×#13511yescharacteristic
620C4C22×AGL(1,ℤ/8)11yescharacteristic
621C4C22×#13711yescharacteristic
622C4C2×#57511yescharacteristic
623C2—24no—
624C2—44no—
625C2—82no—
626C2—162no—
627C2#1916814yesdirect product factor
628C2C22×#46311yescharacteristic
629C2C2×#305611yescharacteristic
630C2C2×#306811yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC42C25
prime radicalC2×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3141C2semidirect
3. C22×#476C2semidirect
4. C2×D4×M16C2semidirect
5. #19168C2direct (N × H)
6. C2×#1703C2semidirect
7. C2×#1697C2semidirect
8. C2×#1683C2semidirect
9. C2×#1677C2semidirect
10. C2×#1565C2semidirect
11. C2×#1548C2semidirect
12. C2×#1547C2semidirect
18. #3141C22semidirect
20. C2×#487C22semidirect
21. C2×#486C22semidirect
30. C2×#476C22semidirect
39. D4×M16C22semidirect
52. #1703C22semidirect
53. #1697C22semidirect
54. #1683C22semidirect
55. #1677C22semidirect
56. #1565C22semidirect
57. C2×#335C22semidirect
58. C2×#334C22semidirect
59. #1548C22semidirect
60. #1547C22semidirect
61. C2×#333C22semidirect
62. C2×#333C22semidirect
63. C2×#332C22semidirect
64. C2×#331C22semidirect
115. #487C23semidirect
117. #486C23semidirect
180. #335C23semidirect
181. #334C23semidirect
182. #333C23semidirect
183. #333C23semidirect
184. #332C23semidirect
185. #331C23semidirect
627. C2#19168direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31412
C2×#31002
C22×#4762
C2×D4×M162
#191682
C2×#17032
C2×#16972
C2×#16832
C2×#16772
C2×#15652
C2×#15482
C2×#15472