Finite Group Databasebeta

← C2×#13126035 #16735063

Subgroups — C2×#13126035 #16735063

Order 3328.

2038 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719393C211yesmaximal, characteristic, complemented
2C2×#11719430C211yesmaximal, characteristic
3#13126035C2116yesmaximal, direct product factor
4C2×#11718741C211yesmaximal, characteristic, complemented
5C2×#11718728C211yesmaximal, characteristic, complemented
6C2×#11718374C211yesmaximal, characteristic, complemented
7C2×#11718546C212yesmaximal, complemented
8C2×#11718527C212yesmaximal, complemented
9C2×#11718531C212yesmaximal, complemented
10C2×#11718551C212yesmaximal, complemented
11C2×#11718366C211yesmaximal, characteristic, complemented
12C2×C13×#501C211yesmaximal, characteristic, complemented
13C22×#6131—21no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125C2211yescharacteristic
16C2×#88201—21no—
17#11719430—24no—
18#11719430C2218yes—
19#11719393—24no—
20#11719393C2218yescomplemented
21C2×#88150—21no—
22C2×#88150—21no—
23C2×#88149—21no—
24C2×#88149C2212yes—
25C2×#88147—21no—
26C2×#88147C2212yes—
27C2×#88146C2211yescharacteristic
28C2×#88146C2211yescharacteristic
29C2×#88142C2211yescharacteristic
30C2×#88142C2211yescharacteristic
31C2×#88141—21no—
32C2×#88141—21no—
33C2×#88128C2211yescharacteristic
34C2×C42×D13C2211yescharacteristic
35C2×#88124C2211yescharacteristic
36C13×#501C2218yescomplemented
37C2×C13×#107C2212yes—
38C2×C13×#106C2212yes—
39C2×C13×#97C2211yescharacteristic
40C2×#88061C2212yes—
41C2×#88061C2212yes—
42C2×#88060C2212yes—
43C2×#88054C2212yes—
44#11718741C2218yescomplemented
45#11718728C2218yescomplemented
46C2×#88049C2212yes—
47C2×#88049C2212yes—
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×#88043C2211yescharacteristic
51#11718551C22116yescomplemented
52#11718546C22116yescomplemented
53#11718531C22116yescomplemented
54#11718527C22116yescomplemented
55#11718374C2218yescomplemented
56#11718366C2218yescomplemented
57C22×Q8×C13—21no—
58C2×#6131—28no—
59C2×#6131—48no—
60C22×D52—22no—
61C22×D52—21no—
62C22×D52—21no—
63C22×D52C2312yes—
64C22×C4×D13—22no—
65C22×C4×D13D411yescharacteristic
66C22×C4×D13D411yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C22×Dic26—21no—
69C22×Dic26—21no—
70C22×C8×C13C2312yes—
71C13×C4⋊Q8—22no—
72C13×C4⋊Q8C2314yes—
73C13×#125—22no—
74C13×#125C2314yes—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2312yes—
81C2×C42×C13C2311yescharacteristic
82#88201—28no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—22no—
86C2×#6103—22no—
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13D411yescharacteristic
96C2×C4×Dic13D411yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C22×#1055C2312yes—
99#88150—28no—
100#88150—28no—
101#88149—24no—
102#88149—28no—
103#88149C2318yes—
104#88147—24no—
105#88147—28no—
106#88147C2318yes—
107#88146—22no—
108#88146—22no—
109#88146C2314yes—
110#88146C2314yes—
111#88142—22no—
112#88142—22no—
113#88142C2314yes—
114#88142C2314yes—
115#88141—28no—
116#88141—28no—
117#88128—22no—
118#88128C2314yes—
119C42×D13D414yes—
120C42×D13C2314yes—
121#88124—22no—
122#88124C2314yes—
123C13×#107C2318yes—
124C13×#106C2318yes—
125C13×#97C2314yes—
126#88061C2318yes—
127#88061C2318yes—
128#88060C2318yes—
129#88054C2318yes—
130#88049C2318yes—
131#88049C2318yes—
132#88048C2318yes—
133#88047C2318yes—
134#88043C2314yes—
135C2×#3235—131nomaximal, Sylow
136C23×D13—22no—
137C23×D13C2×D411yescharacteristic
138C2×Q8×C13—24no—
139C2×Q8×C13—44no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2411yescharacteristic
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151#6131—432no—
152C2×D52—28no—
153C2×D52—28no—
154C2×D52—22no—
155C2×D52—24no—
156C2×D52—24no—
157C2×D52—44no—
158C2×D52—44no—
159C2×D52—48no—
160C2×D52C2414yes—
161C2×C4×D13—24no—
162C2×C4×D13—24no—
163C2×C4×D13—28no—
164C2×C4×D13—42no—
165C2×C4×D13—48no—
166C2×C4×D13C2×D412yes—
167C2×C4×D13C2×D414yes—
168C2×C4×D13C2×D414yes—
169C2×C4×D13C2412yes—
170C2×Dic26—24no—
171C2×Dic26—24no—
172C2×Dic26—44no—
173C2×Dic26—44no—
174C2×C8×C13—24no—
175C2×C8×C13C2414yes—
176C13×C4⋊C4—24no—
177C13×C4⋊C4—24no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—24no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4C2412yes—
183C13×C4⋊C4C2414yes—
184C13×C4⋊C4C2412yes—
185C42×C13C2×D412yes—
186C42×C13C2412yes—
187#6103—24no—
188#6103—24no—
189#6103—28no—
190#6103—28no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13C2412yes—
194C4⋊Dic13C2412yes—
195#6101—24no—
196#6101—24no—
197#6101—24no—
198#6101—24no—
199C4×Dic13—24no—
200C4×Dic13—24no—
201C4×Dic13C2×D412yes—
202C4×Dic13C2×D414yes—
203C4×Dic13C2×D414yes—
204C4×Dic13C2412yes—
205C2×#1055—24no—
206C2×#1055C2414yes—
207C2×#533—131no—
208C2×#532—131no—
209#3235—1316no—
210C2×#501—131no—
211C2×#501D1311yescharacteristic, complemented
212C2×#490—131no—
213C2×#490—131no—
214C2×#482—132no—
215C2×#482—132no—
216C2×#476—132no—
217C2×#474—132no—
218C2×#432—131no—
219C23×C13C22×D411yescharacteristic
220C22×D13—22no—
221C22×D13—22no—
222C22×D13—22no—
223C22×D13—24no—
224C22×D13—44no—
225C22×D13—44no—
226C22×D13—44no—
227C22×D13C22×D412yes—
228Q8×C13—48no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—24no—
234C2×C4×C13—42no—
235C2×C4×C13—44no—
236C2×C4×C13—42no—
237C2×C4×C13C22×D412yes—
238C2×C4×C13C22×D412yes—
239C2×C4×C13C22×D411yescharacteristic
240C2×C4×C132−1+414yes—
241C2×C4×C13C2511yescharacteristic
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13AGL(1,ℤ/8)14yes—
249C2×Dic13C22×D412yes—
250C2×Dic13C22×D412yes—
251C2×Dic13C22×D412yes—
252D52—28no—
253D52—48no—
254D52—48no—
255D52—416no—
256D52—44no—
257C4×D13—24no—
258C4×D13—24no—
259C4×D13—28no—
260C4×D13—44no—
261C4×D13—416no—
262Dic26—48no—
263Dic26—48no—
264C8×C13—24no—
265#1055—24no—
266C22×#41—261no—
267#533—138no—
268#533—264no—
269#532—138no—
270#532—264no—
271C2×C4⋊Q8—131no—
272C2×C4⋊Q8—131no—
273C2×C4⋊Q8C2×D1311yescharacteristic
274C2×#127—131no—
275C2×#125—131no—
276C2×#125C2×D1311yescharacteristic
277C2×#124—261no—
278C2×C22⋊Q8—261no—
279C2×C22⋊Q8—261no—
280C2×#121—132no—
281C2×#121—261no—
282C2×C4×Q8—261no—
283C2×C4×Q8—261no—
284C2×C4×D4—132no—
285C2×C4×D4—261no—
286C2×#117—131no—
287C2×#117—131no—
288C22×C42—131no—
289#501—138no—
290#501C2×D1318yescomplemented
291#490—138no—
292#490—138no—
293#482—1316no—
294#482—1316no—
295#476—1316no—
296#474—1316no—
297#432—138no—
298C2×#107—132no—
299C2×#107C2×D1312yes—
300C2×#106—132no—
301C2×#106C2×D1312yes—
302C2×C4⋊C8—132no—
303C2×#102—132no—
304C2×#102—132no—
305C2×#102—132no—
306C2×#102—132no—
307C2×C22⋊C8—132no—
308C2×#97—131no—
309C2×#97C2×D1311yescharacteristic
310C22×C13#53612yes—
311C22×C13C2×AGL(1,ℤ/8)12yes—
312C22×C13#57512yes—
313C22×C13C23×D411yescharacteristic
314C2×D13—22no—
315C2×D13—22no—
316C2×D13—22no—
317C2×D13—44no—
318C2×D13—44no—
319C2×D13—44no—
320C2×D13—44no—
321C2×D13—88no—
322C4×C13—22no—
323C4×C13—22no—
324C4×C13—42no—
325C4×C13—44no—
326C4×C13—42no—
327C4×C13#53612yes—
328C4×C13C2×2−1+412yes—
329Dic13—22no—
330Dic13—22no—
331Dic13—42no—
332Dic13—42no—
333Dic13C2×AGL(1,ℤ/8)14yes—
334C2×#41—268no—
335C2×#41—528no—
336C22×Q8—21no—
337C22×Q8—261no—
338C22×Q8—261no—
339C22×D4—132no—
340C22×D4—262no—
341C22×D4—261no—
342C22×D4—261no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—262no—
347C22×C8—132no—
348C22×C8C22×D1312yes—
349C4⋊Q8—22no—
350C4⋊Q8—134no—
351C4⋊Q8—134no—
352C4⋊Q8—262no—
353C4⋊Q8—262no—
354C4⋊Q8C22×D1314yes—
355#127—134no—
356#127—262no—
357#125—22no—
358#125—134no—
359#125—262no—
360#125C22×D1314yes—
361#124—268no—
362C22⋊Q8—268no—
363C22⋊Q8—268no—
364#121—138no—
365#121—264no—
366#121—268no—
367C4×Q8—268no—
368C4×Q8—268no—
369C4×D4—138no—
370C4×D4—264no—
371C4×D4—268no—
372#117—134no—
373#117—134no—
374#117—262no—
375#117—262no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1312yes—
388C2×C22⋊C4—262no—
389C2×C22⋊C4—262no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—131no—
395C2×C42—134no—
396C2×C42—134no—
397C2×C42—261no—
398C2×C42—261no—
399C2×C42C22×D1311yescharacteristic
400#107—138no—
401#107C22×D1318yes—
402#106—138no—
403#106C22×D1318yes—
404C4⋊C8—138no—
405#102—138no—
406#102—138no—
407#102—138no—
408#102—138no—
409C22⋊C8—138no—
410#97—134no—
411#97C22×D1314yes—
412C2×C13#323514yescomplemented
413C2×C13C2×#53611yescharacteristic
414C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
415C2×C13C2×#57511yescharacteristic
416D13—42no—
417D13—84no—
418C24—131no—
419C24—262no—
420#41—5232no—
421C2×Q8—24no—
422C2×Q8—44no—
423C2×Q8—264no—
424C2×Q8—264no—
425C2×Q8—524no—
426C2×Q8—524no—
427C2×D4—134no—
428C2×D4—268no—
429C2×D4—264no—
430C2×D4—262no—
431C2×D4—264no—
432C2×D4—268no—
433C2×D4—524no—
434C2×D4—524no—
435C2×D4—528no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—132no—
443C22×C4—134no—
444C22×C4—132no—
445C22×C4—134no—
446C22×C4—264no—
447C22×C4—268no—
448C22×C4—264no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—522no—
452C22×C4—528no—
453C22×C4D4×D1311yescharacteristic
454C22×C4D4×D1311yescharacteristic
455C22×C4C23×D1311yescharacteristic
456C2×C8—24no—
457C2×C8—134no—
458C2×C8—264no—
459C2×C8C23×D1314yes—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—132no—
467C4⋊C4—132no—
468C4⋊C4—264no—
469C4⋊C4—264no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—264no—
473C4⋊C4—264no—
474C4⋊C4C23×D1312yes—
475C4⋊C4C23×D1312yes—
476C4⋊C4C23×D1314yes—
477C22⋊C4—268no—
478C22⋊C4—268no—
479C22⋊C4—264no—
480C22⋊C4—264no—
481C42—134no—
482C42—132no—
483C42—134no—
484C42—132no—
485C42—264no—
486C42—264no—
487C42D4×D1312yes—
488C42C23×D1312yes—
489C13C2×#323511yescharacteristic, complemented, Sylow
490C23—132no—
491C23—262no—
492C23—262no—
493C23—262no—
494C23—264no—
495C23—524no—
496C23—524no—
497C23—524no—
498C23C2×D4×D1311yescharacteristic
499Q8—48no—
500Q8—528no—
501Q8—528no—
502D4—268no—
503D4—528no—
504D4—528no—
505D4—5216no—
506D4—524no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—134no—
516C2×C4—132no—
517C2×C4—132no—
518C2×C4—132no—
519C2×C4—268no—
520C2×C4—262no—
521C2×C4—262no—
522C2×C4—264no—
523C2×C4—264no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—524no—
527C2×C4—5216no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4C2×D4×D1312yes—
531C2×C4C2×D4×D1312yes—
532C2×C4C2×D4×D1311yescharacteristic
533C2×C4#8825414yes—
534C2×C4C24×D1311yescharacteristic
535C8—24no—
536C8—264no—
537C22—262no—
538C22—262no—
539C22—262no—
540C22—524no—
541C22—524no—
542C22—524no—
543C22—524no—
544C22—1048no—
545C22#1171942912yes—
546C22D13×AGL(1,ℤ/8)12yes—
547C22#1171948212yes—
548C22C22×D4×D1311yescharacteristic
549C4—22no—
550C4—22no—
551C4—44no—
552C4—42no—
553C4—42no—
554C4—134no—
555C4—262no—
556C4—262no—
557C4—522no—
558C4—522no—
559C4#1171942912yes—
560C4C2×#8825412yes—
561C2—522no—
562C2—1044no—
563C2#1312603514yesdirect product factor
564C2C2×#1171942911yescharacteristic
565C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
566C2C2×#1171948211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#501C2
socleC23×C13C22×D4
prime radicalC2×#11719430C2
hypercenterC2×#501D13
hypocenterC13C2×#3235
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#11719393C2semidirect
3. #13126035C2direct (N × H)
4. C2×#11718741C2semidirect
5. C2×#11718728C2semidirect
6. C2×#11718374C2semidirect
7. C2×#11718546C2semidirect
8. C2×#11718527C2semidirect
9. C2×#11718531C2semidirect
10. C2×#11718551C2semidirect
11. C2×#11718366C2semidirect
12. C2×C13×#501C2semidirect
20. #11719393C22semidirect
36. C13×#501C22semidirect
44. #11718741C22semidirect
45. #11718728C22semidirect
51. #11718551C22semidirect
52. #11718546C22semidirect
53. #11718531C22semidirect
54. #11718527C22semidirect
55. #11718374C22semidirect
56. #11718366C22semidirect
211. C2×#501D13semidirect
290. #501C2×D13semidirect
412. C2×C13#3235semidirect
489. C13C2×#3235semidirect
563. C2#13126035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193932
C2×#117194302
#131260352
C2×#117187412
C2×#117187282
C2×#117183742
C2×#117185462
C2×#117185272
C2×#117185312
C2×#117185512
C2×#117183662
C2×C13×#5012
C2×#323513