Finite Group Databasebeta

← C2×#13126053 #16735037

Subgroups — C2×#13126053 #16735037

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×#11719385C211yesmaximal, characteristic
3#13126053C2116yesmaximal, direct product factor
4C2×#11718363C211yesmaximal, characteristic, complemented
5C2×#11718741C211yesmaximal, characteristic, complemented
6C2×#11718716C211yesmaximal, characteristic, complemented
7C2×#11718466C212yesmaximal, complemented
8C2×#11718435C212yesmaximal
9C2×#11718455C212yesmaximal, complemented
10C2×#11718422C212yesmaximal, complemented
11C2×#11718366C211yesmaximal, characteristic, complemented
12C2×C13×#489C211yesmaximal, characteristic, complemented
13C22×Q8×D13—21no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#124C2211yescharacteristic
16C2×#88200C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×#88198—21no—
19C2×#88192C2211yescharacteristic
20C2×D4×Dic13C2211yescharacteristic
21D13×C4⋊Q8—24no—
22D13×C4⋊Q8C2218yescomplemented
23#11719385—24no—
24#11719385C2218yes—
25C2×C4⋊C4×D13—21no—
26C2×C4⋊C4×D13C2212yes—
27C2×#88142—21no—
28C2×#88142C2212yes—
29C2×#88137—21no—
30C2×#88135—21no—
31C2×#88133—21no—
32C2×#88131—21no—
33C2×C42×D13C2211yescharacteristic
34C2×#88124C2211yescharacteristic
35C2×#88123C2211yescharacteristic
36C13×#489C2218yescomplemented
37C2×C13×#103C2212yes—
38C2×C13×#102C2212yes—
39C2×C13×#97C2211yescharacteristic
40C2×#88075C2212yes—
41C2×#88072C2212yes—
42C2×#88060C2212yes—
43C2×#88058C2212yes—
44C2×#88057C2212yes—
45C2×#88054C2212yes—
46#11718741C2218yescomplemented
47#11718716C2218yescomplemented
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×#88043C2211yescharacteristic
51#11718466C22116yescomplemented
52#11718455C22116yescomplemented
53#11718435C22116yes—
54#11718422C22116yescomplemented
55#11718366C2218yescomplemented
56#11718363C2218yescomplemented
57C22×Q8×C13—21no—
58C22×Q8×C13C2311yescharacteristic
59C22×D4×C13C2311yescharacteristic
60C22×C22⋊D13—21no—
61C23×Dic13—21no—
62C2×Q8×D13—28no—
63C2×Q8×D13—48no—
64C22×C4×D13—22no—
65C22×C4×D13D411yescharacteristic
66C22×C4×D13D411yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C22×Dic26—21no—
69C22×Dic26—22no—
70C22×C8×C13C2312yes—
71C13×C4⋊Q8—22no—
72C13×C4⋊Q8C2314yes—
73C13×#124—22no—
74C13×#124C2314yes—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4C2312yes—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82#88200—22no—
83#88200C2314yes—
84Q8×Dic13—22no—
85Q8×Dic13C2314yes—
86#88198—28no—
87#88192—22no—
88#88192C2314yes—
89D4×Dic13—22no—
90D4×Dic13C2314yes—
91C2×#6103—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13C2312yes—
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13D411yescharacteristic
104C2×C4×Dic13D411yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C22×#1055C2312yes—
107C4⋊C4×D13—24no—
108C4⋊C4×D13—28no—
109C4⋊C4×D13C2318yes—
110#88142—24no—
111#88142—28no—
112#88142C2318yes—
113#88137—28no—
114#88135—28no—
115#88133—28no—
116#88131—28no—
117C42×D13D414yes—
118C42×D13C2314yes—
119#88124—22no—
120#88124C2314yes—
121#88123—22no—
122#88123C2314yes—
123C13×#103C2318yes—
124C13×#102C2318yes—
125C13×#97C2314yes—
126#88075C2318yes—
127#88072C2318yes—
128#88060C2318yes—
129#88058C2318yes—
130#88057C2318yes—
131#88054C2318yes—
132#88048C2318yes—
133#88047C2318yes—
134#88043C2314yes—
135C2×#3238—131nomaximal, Sylow
136C24×C13—21no—
137C23×D13C2×D411yescharacteristic
138C2×Q8×C13—24no—
139C2×Q8×C13—21no—
140C2×Q8×C13—24no—
141C2×Q8×C13—44no—
142C2×Q8×C13C2412yes—
143C2×D4×C13—21no—
144C2×D4×C13—24no—
145C2×D4×C13C2412yes—
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2411yescharacteristic
151C2×C22⋊D13—24no—
152C2×C22⋊D13—44no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—22no—
156C22×Dic13—24no—
157C22×Dic13—44no—
158C22×Dic13C2×D411yescharacteristic
159C22×Dic13C2×D411yescharacteristic
160C22×Dic13C2×D411yescharacteristic
161Q8×D13—432no—
162C2×C4×D13—24no—
163C2×C4×D13—24no—
164C2×C4×D13—24no—
165C2×C4×D13—28no—
166C2×C4×D13—48no—
167C2×C4×D13C2×D412yes—
168C2×C4×D13C2×D414yes—
169C2×C4×D13C2×D414yes—
170C2×C4×D13C2412yes—
171C2×Dic26—24no—
172C2×Dic26—28no—
173C2×Dic26—48no—
174C2×Dic26—44no—
175C2×C8×C13—24no—
176C2×C8×C13C2414yes—
177C13×C4⋊C4—24no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4C2414yes—
180C13×C22⋊C4—24no—
181C13×C22⋊C4—24no—
182C42×C13C2×D412yes—
183C42×C13C2412yes—
184C22⋊Dic13—24no—
185C22⋊Dic13—24no—
186#6103—24no—
187C4⋊Dic13—22no—
188C4⋊Dic13—24no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—24no—
192C4⋊Dic13C2414yes—
193C4⋊Dic13C2412yes—
194C4⋊Dic13C2412yes—
195#6101—24no—
196#6101—24no—
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×#501—131no—
212C2×#489—131no—
213C2×#489D1311yescharacteristic, complemented
214C2×#483—132no—
215C2×#480—132no—
216C2×#477—132no—
217C2×#476—132no—
218C2×#432—131no—
219C23×C13—22no—
220C23×C13—42no—
221C23×C13—42no—
222C23×C13—42no—
223C23×C13C22×D411yescharacteristic
224C22×D13—22no—
225C22×D13—22no—
226C22×D13AGL(1,ℤ/8)14yes—
227C22×D13C22×D412yes—
228Q8×C13—24no—
229Q8×C13—48no—
230Q8×C13—42no—
231D4×C13—24no—
232D4×C13—42no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—24no—
237C2×C4×C13—42no—
238C2×C4×C13—44no—
239C2×C4×C13C22×D412yes—
240C2×C4×C13C22×D412yes—
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C132−1+414yes—
243C2×C4×C13C2511yescharacteristic
244C22⋊D13—48no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—24no—
250C2×Dic13—44no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—48no—
254C2×Dic13#13714yes—
255C2×Dic13C22×D412yes—
256C2×Dic13C22×D412yes—
257C2×Dic13C22×D412yes—
258C4×D13—28no—
259C4×D13—24no—
260C4×D13—24no—
261C4×D13—28no—
262C4×D13—416no—
263Dic26—416no—
264Dic26—48no—
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×#125—131no—
279C2×#124C2×D1311yescharacteristic
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#501—138no—
292#489—138no—
293#489C2×D1318yescomplemented
294#483—1316no—
295#480—1316no—
296#477—1316no—
297#476—1316no—
298#432—138no—
299C2×#107—132no—
300C2×#107—132no—
301C2×#106—132no—
302C2×#106—132no—
303C2×C4⋊C8—132no—
304C2×#103—132no—
305C2×#103C2×D1312yes—
306C2×#102—132no—
307C2×#102C2×D1312yes—
308C2×C22⋊C8—132no—
309C2×#97—131no—
310C2×#97C2×D1311yescharacteristic
311C22×C13—42no—
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—84no—
315C22×C13#53612yes—
316C22×C13C2×AGL(1,ℤ/8)12yes—
317C22×C13C2×#13712yes—
318C22×C13C23×D411yescharacteristic
319C2×D13—22no—
320C2×D13—28no—
321C2×D13—22no—
322C2×D13C2×AGL(1,ℤ/8)14yes—
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—42no—
326C4×C13—44no—
327C4×C13#53612yes—
328C4×C13C2×2−1+412yes—
329Dic13—22no—
330Dic13—22no—
331Dic13—44no—
332Dic13—42no—
333Dic13—42no—
334Dic13C2×#13714yes—
335C22×Q8—21no—
336C22×Q8—262no—
337C22×Q8—268no—
338C22×Q8—261no—
339C22×Q8—528no—
340C22×Q8C22×D1311yescharacteristic
341C22×D4—261no—
342C22×D4C22×D1311yescharacteristic
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—262no—
347C23×C4—261no—
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—134no—
360#125—262no—
361#124—22no—
362#124C22×D1314yes—
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—132no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
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⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4C22×D1312yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
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#107—138no—
403#106—138no—
404#106—138no—
405C4⋊C8—138no—
406#103—138no—
407#103C22×D1318yes—
408#102—138no—
409#102C22×D1318yes—
410C22⋊C8—138no—
411#97—134no—
412#97C22×D1314yes—
413C2×C13—82no—
414C2×C13#323814yescomplemented
415C2×C13C2×#53611yescharacteristic
416C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
417C2×C13C22×#13711yescharacteristic
418D13—24no—
419C24—21no—
420C24—131no—
421C2×Q8—21no—
422C2×Q8—24no—
423C2×Q8—24no—
424C2×Q8—44no—
425C2×Q8—268no—
426C2×Q8—264no—
427C2×Q8—524no—
428C2×Q8—528no—
429C2×Q8—5232no—
430C2×Q8C23×D1312yes—
431C2×D4—21no—
432C2×D4—24no—
433C2×D4—264no—
434C2×D4—524no—
435C2×D4C23×D1312yes—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—134no—
442C22×C4—132no—
443C22×C4—134no—
444C22×C4—132no—
445C22×C4—264no—
446C22×C4—264no—
447C22×C4—268no—
448C22×C4—264no—
449C22×C4—264no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—262no—
453C22×C4—528no—
454C22×C4—524no—
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—22no—
464C4⋊C4—134no—
465C4⋊C4—132no—
466C4⋊C4—132no—
467C4⋊C4—268no—
468C4⋊C4—268no—
469C4⋊C4—264no—
470C4⋊C4—264no—
471C4⋊C4—262no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—264no—
475C4⋊C4—264no—
476C4⋊C4—264no—
477C4⋊C4C23×D1314yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
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—22no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—134no—
496C23—132no—
497C23—262no—
498C23—262no—
499C23C2×D4×D1311yescharacteristic
500Q8—24no—
501Q8—48no—
502Q8—42no—
503Q8—528no—
504Q8—5216no—
505D4—24no—
506D4—42no—
507D4—528no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—134no—
515C2×C4—132no—
516C2×C4—132no—
517C2×C4—132no—
518C2×C4—268no—
519C2×C4—268no—
520C2×C4—262no—
521C2×C4—262no—
522C2×C4—264no—
523C2×C4—264no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—264no—
527C2×C4—5216no—
528C2×C4—528no—
529C2×C4—524no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4C2×D4×D1312yes—
533C2×C4C2×D4×D1312yes—
534C2×C4C2×D4×D1311yescharacteristic
535C2×C4#8825714yes—
536C2×C4C24×D1311yescharacteristic
537C8—24no—
538C8—264no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—84no—
543C22—134no—
544C22—262no—
545C22—268no—
546C22—262no—
547C22#1171938012yes—
548C22D13×AGL(1,ℤ/8)12yes—
549C22D13×#13712yes—
550C22C22×D4×D1311yescharacteristic
551C4—22no—
552C4—22no—
553C4—44no—
554C4—42no—
555C4—134no—
556C4—262no—
557C4—262no—
558C4—524no—
559C4—522no—
560C4—522no—
561C4#1171938012yes—
562C4C2×#8825712yes—
563C2—82no—
564C2—264no—
565C2#1312605314yesdirect product factor
566C2C2×#1171938011yescharacteristic
567C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
568C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#489C2
socleC23×C13C22×D4
prime radicalC2×#88192C22
hypercenterC2×#489D13
hypocenterC13C2×#3238
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×D13×C4⋊Q8C2semidirect
3. #13126053C2direct (N × H)
4. C2×#11718363C2semidirect
5. C2×#11718741C2semidirect
6. C2×#11718716C2semidirect
7. C2×#11718466C2semidirect
9. C2×#11718455C2semidirect
10. C2×#11718422C2semidirect
11. C2×#11718366C2semidirect
12. C2×C13×#489C2semidirect
22. D13×C4⋊Q8C22semidirect
36. C13×#489C22semidirect
46. #11718741C22semidirect
47. #11718716C22semidirect
51. #11718466C22semidirect
52. #11718455C22semidirect
54. #11718422C22semidirect
55. #11718366C22semidirect
56. #11718363C22semidirect
213. C2×#489D13semidirect
293. #489C2×D13semidirect
414. C2×C13#3238semidirect
490. C13C2×#3238semidirect
565. C2#13126053direct (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×#117193852
#131260532
C2×#117183632
C2×#117187412
C2×#117187162
C2×#117184662
C2×#117184352
C2×#117184552
C2×#117184222
C2×#117183662
C2×C13×#4892
C2×#323813