Finite Group Databasebeta

← C2×#13126058 #16735042

Subgroups — C2×#13126058 #16735042

Order 3328.

2018 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#11719396C211yesmaximal, characteristic
3#13126058C2116yesmaximal, direct product factor
4C2×#11718726C211yesmaximal, characteristic, complemented
5C2×#11718750C211yesmaximal, characteristic, complemented
6C2×#11718375C211yesmaximal, characteristic, complemented
7C2×#11718523C212yesmaximal, complemented
8C2×#11718543C212yesmaximal
9C2×#11718536C212yesmaximal, complemented
10C2×#11718531C212yesmaximal, complemented
11C2×#11718366C211yesmaximal, characteristic, complemented
12C2×C13×#501C211yesmaximal, characteristic, complemented
13C22×Q8×D13—21no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125C2211yescharacteristic
16C2×#88198—21no—
17D13×C4⋊Q8—24no—
18D13×C4⋊Q8C2218yescomplemented
19#11719396—24no—
20#11719396C2218yes—
21C2×#88152—21no—
22C2×#88151C2211yescharacteristic
23C2×#88149C2211yescharacteristic
24C2×#88148—21no—
25C2×#88147—21no—
26C2×#88147C2211yescharacteristic
27C2×#88146—21no—
28C2×C4⋊C4×D13—21no—
29C2×C4⋊C4×D13C2212yes—
30C2×#88142—21no—
31C2×#88142C2212yes—
32C2×#88141C2211yescharacteristic
33C2×#88129C2211yescharacteristic
34C2×C42×D13C2211yescharacteristic
35C2×#88123C2211yescharacteristic
36C13×#501C2218yescomplemented
37C2×C13×#107C2212yes—
38C2×C13×#106C2212yes—
39C2×C13×#97C2211yescharacteristic
40C2×#88061C2212yes—
41C2×#88060C2212yes—
42C2×#88056C2212yes—
43C2×#88054C2212yes—
44#11718750C2218yescomplemented
45#11718726C2218yescomplemented
46C2×#88050C2212yes—
47C2×#88049C2212yes—
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×#88043C2211yescharacteristic
51#11718543C22116yes—
52#11718536C22116yescomplemented
53#11718531C22116yescomplemented
54#11718523C22116yescomplemented
55#11718375C2218yescomplemented
56#11718366C2218yescomplemented
57C22×Q8×C13—21no—
58C2×Q8×D13—28no—
59C2×Q8×D13—48no—
60C22×D52—21no—
61C22×D52C2311yescharacteristic
62C22×C4×D13—22no—
63C22×C4×D13—21no—
64C22×C4×D13D411yescharacteristic
65C22×C4×D13D411yescharacteristic
66C22×C4×D13C2311yescharacteristic
67C22×Dic26—21no—
68C22×Dic26—22no—
69C22×Dic26C2311yescharacteristic
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⋊C4C2312yes—
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82#88198—28no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2312yes—
91C2×#6101—21no—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13D411yescharacteristic
96C2×C4×Dic13D411yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C22×#1055C2312yes—
99#88152—28no—
100#88151—22no—
101#88151C2314yes—
102#88149—22no—
103#88149C2314yes—
104#88148—28no—
105#88147—28no—
106#88147—22no—
107#88147C2314yes—
108#88146—28no—
109C4⋊C4×D13—24no—
110C4⋊C4×D13—28no—
111C4⋊C4×D13C2318yes—
112#88142—24no—
113#88142—28no—
114#88142C2318yes—
115#88141—22no—
116#88141C2314yes—
117#88129—22no—
118#88129C2314yes—
119C42×D13D414yes—
120C42×D13C2314yes—
121#88123—22no—
122#88123C2314yes—
123C13×#107C2318yes—
124C13×#106C2318yes—
125C13×#97C2314yes—
126#88061C2318yes—
127#88060C2318yes—
128#88056C2318yes—
129#88054C2318yes—
130#88050C2318yes—
131#88049C2318yes—
132#88048C2318yes—
133#88047C2318yes—
134#88043C2314yes—
135C2×#3238—131nomaximal, Sylow
136C23×D13—21no—
137C23×D13C2×D411yescharacteristic
138C2×Q8×C13—24no—
139C2×Q8×C13—44no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2411yescharacteristic
146C22×Dic13—21no—
147C22×Dic13—22no—
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151Q8×D13—432no—
152C2×D52—24no—
153C2×D52—24no—
154C2×D52—21no—
155C2×D52—44no—
156C2×D52C2412yes—
157C2×C4×D13—24no—
158C2×C4×D13—24no—
159C2×C4×D13—24no—
160C2×C4×D13—28no—
161C2×C4×D13—24no—
162C2×C4×D13—48no—
163C2×C4×D13—44no—
164C2×C4×D13C2×D412yes—
165C2×C4×D13C2×D414yes—
166C2×C4×D13C2×D414yes—
167C2×C4×D13C2412yes—
168C2×Dic26—24no—
169C2×Dic26—24no—
170C2×Dic26—21no—
171C2×Dic26—28no—
172C2×Dic26—48no—
173C2×Dic26—44no—
174C2×Dic26C2412yes—
175C2×C8×C13—24no—
176C2×C8×C13C2414yes—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—24no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—24no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—24no—
183C13×C4⋊C4C2412yes—
184C13×C4⋊C4C2414yes—
185C13×C4⋊C4C2412yes—
186C42×C13C2×D412yes—
187C42×C13C2412yes—
188#6103—24no—
189#6103—24no—
190#6103—24no—
191#6103—24no—
192#6103—24no—
193C4⋊Dic13—22no—
194C4⋊Dic13—24no—
195C4⋊Dic13—24no—
196C4⋊Dic13C2414yes—
197#6101—24no—
198#6101—28no—
199#6101—28no—
200C4×Dic13—24no—
201C4×Dic13C2×D412yes—
202C4×Dic13C2×D414yes—
203C4×Dic13C2×D414yes—
204C4×Dic13C2412yes—
205C2×#1055—24no—
206C2×#1055C2414yes—
207C22×C4⋊Q8—131no—
208C2×#529—131no—
209#3238—1316no—
210C2×#501—131no—
211C2×#501D1311yescharacteristic, complemented
212C2×#489—131no—
213C2×#489—131no—
214C2×#483—132no—
215C2×#480—132no—
216C2×#477—132no—
217C2×#476—132no—
218C2×#432—131no—
219C23×C13C22×D411yescharacteristic
220C22×D13—22no—
221C22×D13—22no—
222C22×D13—22no—
223C22×D13—42no—
224C22×D13—42no—
225C22×D13—42no—
226C22×D13AGL(1,ℤ/8)14yes—
227C22×D13C22×D412yes—
228Q8×C13—48no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—44no—
235C2×C4×C13—42no—
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—24no—
246C2×Dic13—42no—
247C2×Dic13—44no—
248C2×Dic13#13714yes—
249C2×Dic13C22×D412yes—
250C2×Dic13C22×D412yes—
251C2×Dic13C22×D412yes—
252D52—24no—
253D52—48no—
254D52—42no—
255C4×D13—28no—
256C4×D13—24no—
257C4×D13—24no—
258C4×D13—28no—
259C4×D13—416no—
260C4×D13—48no—
261Dic26—24no—
262Dic26—416no—
263Dic26—48no—
264Dic26—42no—
265C8×C13—24no—
266#1055—24no—
267C23×Q8—261no—
268C2×C4⋊Q8—138no—
269C2×C4⋊Q8—132no—
270C2×C4⋊Q8—131no—
271C2×C4⋊Q8—261no—
272C2×C4⋊Q8—264no—
273C2×C4⋊Q8—261no—
274C2×C4⋊Q8C2×D1311yescharacteristic
275#529—138no—
276#529—264no—
277C2×#126—261no—
278C2×#125C2×D1311yescharacteristic
279C2×#124—131no—
280C2×#123—261no—
281C2×C22⋊Q8—131no—
282C2×#121—131no—
283C2×C4×Q8—131no—
284C2×C4×D4—131no—
285C2×C4×D4—261no—
286C2×#117—261no—
287C22×C4⋊C4—132no—
288C22×C4⋊C4—261no—
289C22×C42—131no—
290#501—138no—
291#501C2×D1318yescomplemented
292#489—138no—
293#489—138no—
294#483—1316no—
295#480—1316no—
296#477—1316no—
297#476—1316no—
298#432—138no—
299C2×#107—132no—
300C2×#107C2×D1312yes—
301C2×#106—132no—
302C2×#106C2×D1312yes—
303C2×C4⋊C8—132no—
304C2×#103—132no—
305C2×#103—132no—
306C2×#102—132no—
307C2×#102—132no—
308C2×C22⋊C8—132no—
309C2×#97—131no—
310C2×#97C2×D1311yescharacteristic
311C22×C13#53612yes—
312C22×C13C2×AGL(1,ℤ/8)12yes—
313C22×C13C2×#13712yes—
314C22×C13C23×D411yescharacteristic
315C2×D13—22no—
316C2×D13—28no—
317C2×D13—22no—
318C2×D13—42no—
319C2×D13—42no—
320C2×D13—42no—
321C2×D13—84no—
322C2×D13C2×AGL(1,ℤ/8)14yes—
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—44no—
326C4×C13—42no—
327C4×C13—42no—
328C4×C13#53612yes—
329C4×C13C2×2−1+412yes—
330Dic13—22no—
331Dic13—22no—
332Dic13—42no—
333Dic13—44no—
334Dic13C2×#13714yes—
335C22×Q8—21no—
336C22×Q8—131no—
337C22×Q8—262no—
338C22×Q8—268no—
339C22×Q8—261no—
340C22×Q8—528no—
341C22×D4—131no—
342C22×D4—261no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—261no—
347C23×C4—262no—
348C22×C8—132no—
349C22×C8C22×D1312yes—
350C4⋊Q8—22no—
351C4⋊Q8—138no—
352C4⋊Q8—134no—
353C4⋊Q8—264no—
354C4⋊Q8—268no—
355C4⋊Q8—268no—
356C4⋊Q8—262no—
357C4⋊Q8C22×D1314yes—
358#126—268no—
359#125—22no—
360#125C22×D1314yes—
361#124—134no—
362#124—262no—
363#123—268no—
364C22⋊Q8—134no—
365C22⋊Q8—262no—
366#121—134no—
367#121—262no—
368C4×Q8—134no—
369C4×Q8—262no—
370C4×D4—134no—
371C4×D4—262no—
372C4×D4—268no—
373#117—268no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—132no—
378C2×C4⋊C4—138no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—268no—
381C2×C4⋊C4—262no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4C22×D1312yes—
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—131no—
397C2×C42—134no—
398C2×C42—134no—
399C2×C42—261no—
400C2×C42C22×D1311yescharacteristic
401#107—138no—
402#107C22×D1318yes—
403#106—138no—
404#106C22×D1318yes—
405C4⋊C8—138no—
406#103—138no—
407#103—138no—
408#102—138no—
409#102—138no—
410C22⋊C8—138no—
411#97—134no—
412#97C22×D1314yes—
413C2×C13#323814yescomplemented
414C2×C13C2×#53611yescharacteristic
415C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
416C2×C13C22×#13711yescharacteristic
417D13—24no—
418D13—82no—
419C24—131no—
420C24—261no—
421C2×Q8—24no—
422C2×Q8—44no—
423C2×Q8—132no—
424C2×Q8—268no—
425C2×Q8—261no—
426C2×Q8—264no—
427C2×Q8—264no—
428C2×Q8—524no—
429C2×Q8—528no—
430C2×Q8—5232no—
431C2×D4—132no—
432C2×D4—264no—
433C2×D4—261no—
434C2×D4—264no—
435C2×D4—524no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—134no—
443C22×C4—132no—
444C22×C4—134no—
445C22×C4—132no—
446C22×C4—264no—
447C22×C4—264no—
448C22×C4—264no—
449C22×C4—268no—
450C22×C4—264no—
451C22×C4—261no—
452C22×C4—262no—
453C22×C4—524no—
454C22×C4—528no—
455C22×C4D4×D1311yescharacteristic
456C22×C4D4×D1311yescharacteristic
457C22×C4C23×D1311yescharacteristic
458C2×C8—24no—
459C2×C8—134no—
460C2×C8—264no—
461C2×C8C23×D1314yes—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—134no—
469C4⋊C4—268no—
470C4⋊C4—268no—
471C4⋊C4—264no—
472C4⋊C4—264no—
473C4⋊C4—262no—
474C4⋊C4—264no—
475C4⋊C4C23×D1314yes—
476C4⋊C4C23×D1312yes—
477C4⋊C4C23×D1312yes—
478C22⋊C4—264no—
479C22⋊C4—264no—
480C22⋊C4—264no—
481C22⋊C4—264no—
482C22⋊C4—264no—
483C42—134no—
484C42—132no—
485C42—134no—
486C42—132no—
487C42—264no—
488C42D4×D1312yes—
489C42C23×D1312yes—
490C13C2×#323811yescharacteristic, complemented, Sylow
491C23—134no—
492C23—132no—
493C23—262no—
494C23—262no—
495C23—262no—
496C23—522no—
497C23—522no—
498C23—522no—
499C23C2×D4×D1311yescharacteristic
500Q8—48no—
501Q8—264no—
502Q8—528no—
503Q8—5216no—
504Q8—522no—
505D4—264no—
506D4—528no—
507D4—522no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—134no—
517C2×C4—132no—
518C2×C4—132no—
519C2×C4—132no—
520C2×C4—268no—
521C2×C4—268no—
522C2×C4—262no—
523C2×C4—262no—
524C2×C4—264no—
525C2×C4—264no—
526C2×C4—262no—
527C2×C4—264no—
528C2×C4—528no—
529C2×C4—5216no—
530C2×C4—522no—
531C2×C4—524no—
532C2×C4C2×D4×D1312yes—
533C2×C4C2×D4×D1312yes—
534C2×C4C2×D4×D1311yescharacteristic
535C2×C4#8825414yes—
536C2×C4C24×D1311yescharacteristic
537C8—24no—
538C8—264no—
539C22—134no—
540C22—262no—
541C22—268no—
542C22—262no—
543C22—522no—
544C22—522no—
545C22—522no—
546C22—1044no—
547C22#1171942912yes—
548C22D13×AGL(1,ℤ/8)12yes—
549C22D13×#13712yes—
550C22C22×D4×D1311yescharacteristic
551C4—22no—
552C4—22no—
553C4—44no—
554C4—42no—
555C4—42no—
556C4—134no—
557C4—262no—
558C4—262no—
559C4—524no—
560C4—522no—
561C4#1171942912yes—
562C4C2×#8825412yes—
563C2—264no—
564C2—1042no—
565C2#1312605814yesdirect product factor
566C2C2×#1171942911yescharacteristic
567C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
568C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#501C2
socleC23×C13C22×D4
prime radicalC2×#88149C22
hypercenterC2×#501D13
hypocenterC13C2×#3238
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×D13×C4⋊Q8C2semidirect
3. #13126058C2direct (N × H)
4. C2×#11718726C2semidirect
5. C2×#11718750C2semidirect
6. C2×#11718375C2semidirect
7. C2×#11718523C2semidirect
9. C2×#11718536C2semidirect
10. C2×#11718531C2semidirect
11. C2×#11718366C2semidirect
12. C2×C13×#501C2semidirect
18. D13×C4⋊Q8C22semidirect
36. C13×#501C22semidirect
44. #11718750C22semidirect
45. #11718726C22semidirect
52. #11718536C22semidirect
53. #11718531C22semidirect
54. #11718523C22semidirect
55. #11718375C22semidirect
56. #11718366C22semidirect
211. C2×#501D13semidirect
291. #501C2×D13semidirect
413. C2×C13#3238semidirect
490. C13C2×#3238semidirect
565. C2#13126058direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13×C4⋊Q82
C2×#117193962
#131260582
C2×#117187262
C2×#117187502
C2×#117183752
C2×#117185232
C2×#117185432
C2×#117185362
C2×#117185312
C2×#117183662
C2×C13×#5012
C2×#323813