Finite Group Databasebeta

← C2×#13125979 #16734939

Subgroups — C2×#13125979 #16734939

Order 3328.

2006 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×#11719283C211yesmaximal, characteristic
2C2×D13×C4⋊Q8C211yesmaximal, characteristic
3#13125979C2116yesmaximal, direct product factor
4C2×#11718516C212yesmaximal, complemented
5C2×#11718453C212yesmaximal, complemented
6C2×#11718523C212yesmaximal
7C2×#11718466C212yesmaximal
8C2×#11718512C211yesmaximal, characteristic, complemented
9C2×#11718681C211yesmaximal, characteristic, complemented
10C2×#11718755C211yesmaximal, characteristic, complemented
11C2×#11718494C211yesmaximal, characteristic
12C2×C13×#475C211yesmaximal, characteristic, complemented
13C22×Q8×D13—21no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C13C2211yescharacteristic
16C2×#88200C2211yescharacteristic
17C2×#88198—21no—
18C2×#88198C2211yescharacteristic
19D13×C4⋊Q8—24no—
20D13×C4⋊Q8C2218yes—
21#11719283—24no—
22#11719283C2218yes—
23C2×#88151C2211yescharacteristic
24C2×#88150—21no—
25C2×C4⋊C4×D13—21no—
26C2×C4⋊C4×D13C2212yes—
27C2×#88143—21no—
28C2×#88142—21no—
29C2×#88142C2212yes—
30C2×#88142C2211yescharacteristic
31C2×#88126—21no—
32C2×C42×D13C2211yescharacteristic
33C2×#88123C2211yescharacteristic
34C2×C4×Dic26—21no—
35C2×C4×Dic26C2211yescharacteristic
36C13×#475C2218yescomplemented
37C2×C13×#106C2212yes—
38C2×C13×C4⋊C8C2211yescharacteristic
39C2×C13×#103C2212yes—
40C2×#88075C2212yes—
41C2×#88060C2212yes—
42C2×#88057C2212yes—
43C2×#88056C2212yes—
44C2×C8×Dic13C2212yes—
45#11718755C2218yescomplemented
46#11718681C2218yescomplemented
47C2×#88050C2212yes—
48C2×#88048C2212yes—
49C2×#88048C2212yes—
50C2×C4⋊#1055C2211yescharacteristic
51#11718523C22116yes—
52#11718516C22116yescomplemented
53#11718512C2218yescomplemented
54#11718494C2218yes—
55#11718466C22116yes—
56#11718453C22116yescomplemented
57C22×Q8×C13—21no—
58C22×Q8×C13C2311yescharacteristic
59C2×Q8×D13—28no—
60C2×Q8×D13—48no—
61C22×C4×D13—22no—
62C22×C4×D13D411yescharacteristic
63C22×C4×D13D411yescharacteristic
64C22×C4×D13C2311yescharacteristic
65C22×Dic26—21no—
66C22×Dic26—21no—
67C22×Dic26—22no—
68C22×Dic26C2311yescharacteristic
69C22×C8×C13C2312yes—
70C13×C4⋊Q8—22no—
71C13×C4⋊Q8C2314yes—
72C4×Q8×C13—22no—
73C4×Q8×C13C2314yes—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4C2312yes—
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80#88200—22no—
81#88200C2314yes—
82#88198—28no—
83#88198—22no—
84#88198C2314yes—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2312yes—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13D411yescharacteristic
100C2×C4×Dic13D411yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C22×#1055C2312yes—
103#88151—22no—
104#88151C2314yes—
105#88150—28no—
106C4⋊C4×D13—24no—
107C4⋊C4×D13—28no—
108C4⋊C4×D13C2318yes—
109#88143—28no—
110#88142—24no—
111#88142—28no—
112#88142—22no—
113#88142C2318yes—
114#88142C2314yes—
115#88126—28no—
116C42×D13D414yes—
117C42×D13C2314yes—
118#88123—22no—
119#88123C2314yes—
120C4×Dic26—22no—
121C4×Dic26—28no—
122C4×Dic26C2314yes—
123C13×#106C2318yes—
124C13×C4⋊C8C2314yes—
125C13×#103C2318yes—
126#88075C2318yes—
127#88060C2318yes—
128#88057C2318yes—
129#88056C2318yes—
130C8×Dic13C2318yes—
131#88050C2318yes—
132#88048C2318yes—
133#88048C2318yes—
134C4⋊#1055C2314yes—
135C2×#3229—131nomaximal, Sylow
136C23×D13C2×D411yescharacteristic
137C2×Q8×C13—21no—
138C2×Q8×C13—24no—
139C2×Q8×C13—22no—
140C2×Q8×C13—22no—
141C2×Q8×C13—44no—
142C2×Q8×C13C2412yes—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—21no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2411yescharacteristic
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155Q8×D13—432no—
156C2×C4×D13—22no—
157C2×C4×D13—22no—
158C2×C4×D13—24no—
159C2×C4×D13—28no—
160C2×C4×D13—48no—
161C2×C4×D13SD1618yes—
162C2×C4×D13C2×D412yes—
163C2×C4×D13C2×D414yes—
164C2×C4×D13C2×D414yes—
165C2×C4×D13C2412yes—
166C2×Dic26—22no—
167C2×Dic26—22no—
168C2×Dic26—21no—
169C2×Dic26—24no—
170C2×Dic26—24no—
171C2×Dic26—28no—
172C2×Dic26—44no—
173C2×Dic26—48no—
174C2×Dic26—44no—
175C2×Dic26C2412yes—
176C2×C8×C13—24no—
177C2×C8×C13C2414yes—
178C13×C4⋊C4—24no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—24no—
182C13×C4⋊C4C2414yes—
183C13×C4⋊C4C2412yes—
184C42×C13—24no—
185C42×C13C2×D412yes—
186C42×C13C2412yes—
187#6103—24no—
188#6103—24no—
189C4⋊Dic13—21no—
190C4⋊Dic13—22no—
191C4⋊Dic13—24no—
192C4⋊Dic13—24no—
193C4⋊Dic13C2414yes—
194C4⋊Dic13C2412yes—
195#6101—24no—
196#6101—24no—
197#6101—24no—
198#6101—24no—
199#6101—24no—
200#6101—28no—
201#6101—28no—
202C4×Dic13—24no—
203C4×Dic13C2×D414yes—
204C4×Dic13C2×D412yes—
205C4×Dic13C2×D414yes—
206C4×Dic13C2412yes—
207C2×#1055—24no—
208C2×#1055C2414yes—
209C2×#533—131no—
210C22×C4⋊Q8—131no—
211#3229—1316no—
212C2×#498—132no—
213C2×#487—132no—
214C2×#483—132no—
215C2×#483—132no—
216C2×#475—131no—
217C2×#475—131no—
218C2×#475—131no—
219C2×#475D1311yescharacteristic, complemented
220C2×#431—131no—
221C23×C13C22×D411yescharacteristic
222C22×D13—22no—
223C22×D13—22no—
224C22×D13C2×SD1614yes—
225C22×D13C22×D412yes—
226Q8×C13—22no—
227Q8×C13—22no—
228Q8×C13—42no—
229Q8×C13—48no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—42no—
235C2×C4×C13—44no—
236C2×C4×C13—42no—
237C2×C4×C13C2×SD1614yes—
238C2×C4×C13C22×D412yes—
239C2×C4×C13C22×D411yescharacteristic
240C2×C4×C13C22×D412yes—
241C2×C4×C132−1+412yes—
242C2×C4×C132−1+412yes—
243C2×C4×C13C2511yescharacteristic
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—24no—
248C2×Dic13—42no—
249C2×Dic13—44no—
250C2×Dic13—42no—
251C2×Dic13C2×SD1614yes—
252C2×Dic13#13714yes—
253C2×Dic13C22×D412yes—
254C2×Dic13C22×D412yes—
255C2×Dic13C22×D412yes—
256C4×D13—24no—
257C4×D13—22no—
258C4×D13—22no—
259C4×D13—28no—
260C4×D13—416no—
261C4×D13C2×SD16116yes—
262Dic26—22no—
263Dic26—22no—
264Dic26—42no—
265Dic26—48no—
266Dic26—416no—
267Dic26—48no—
268C8×C13—24no—
269#1055—24no—
270C23×Q8—261no—
271#533—138no—
272#533—264no—
273C2×C4⋊Q8—138no—
274C2×C4⋊Q8—132no—
275C2×C4⋊Q8—131no—
276C2×C4⋊Q8—131no—
277C2×C4⋊Q8—131no—
278C2×C4⋊Q8—261no—
279C2×C4⋊Q8—264no—
280C2×C4⋊Q8—261no—
281C2×C4⋊Q8C2×D1311yescharacteristic
282C2×#125—261no—
283C2×C22⋊Q8—131no—
284C2×C22⋊Q8—131no—
285C2×C22⋊Q8—261no—
286C2×C4×Q8—131no—
287C2×C4×Q8—261no—
288C2×C4×Q8C2×D1311yescharacteristic
289C2×#117—261no—
290C22×C4⋊C4—132no—
291C22×C4⋊C4—261no—
292C22×C42—131no—
293#498—1316no—
294#487—1316no—
295#483—1316no—
296#483—1316no—
297#475—138no—
298#475—138no—
299#475—138no—
300#475C2×D1318yescomplemented
301#431—138no—
302C2×#106—132no—
303C2×#106—132no—
304C2×#106—132no—
305C2×#106C2×D1312yes—
306C2×C4⋊C8—131no—
307C2×C4⋊C8C2×D1311yescharacteristic
308C2×#103—132no—
309C2×#103—132no—
310C2×#103—132no—
311C2×#103C2×D1312yes—
312C2×C22⋊C8—132no—
313C2×C4×C8—132no—
314C22×C13#53612yes—
315C22×C13C22×SD1612yes—
316C22×C13C2×#13712yes—
317C22×C13C23×D411yescharacteristic
318C2×D13—22no—
319C2×D13—28no—
320C2×D13—22no—
321C2×D13C22×SD1614yes—
322C4×C13—22no—
323C4×C13—42no—
324C4×C13—44no—
325C4×C13—42no—
326C4×C13#53612yes—
327C4×C13C22×SD1614yes—
328C4×C13C2×2−1+411yescharacteristic
329C4×C13C2×2−1+411yescharacteristic
330Dic13—22no—
331Dic13—42no—
332Dic13—44no—
333Dic13—42no—
334Dic13C22×SD1614yes—
335Dic13C2×#13714yes—
336C22×Q8—21no—
337C22×Q8—131no—
338C22×Q8—261no—
339C22×Q8—262no—
340C22×Q8—268no—
341C22×Q8—261no—
342C22×Q8—528no—
343C22×Q8C22×D1311yescharacteristic
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—131no—
347C23×C4—262no—
348C22×C8—132no—
349C22×C8C22×D1312yes—
350C4⋊Q8—22no—
351C4⋊Q8—138no—
352C4⋊Q8—134no—
353C4⋊Q8—134no—
354C4⋊Q8—134no—
355C4⋊Q8—268no—
356C4⋊Q8—264no—
357C4⋊Q8—262no—
358C4⋊Q8—268no—
359C4⋊Q8—262no—
360C4⋊Q8—262no—
361C4⋊Q8C22×D1314yes—
362#125—268no—
363C22⋊Q8—134no—
364C22⋊Q8—134no—
365C22⋊Q8—262no—
366C22⋊Q8—268no—
367C22⋊Q8—262no—
368C4×Q8—22no—
369C4×Q8—134no—
370C4×Q8—268no—
371C4×Q8—262no—
372C4×Q8C22×D1314yes—
373#117—268no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—132no—
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⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4C22×D1312yes—
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C42—21no—
395C2×C42—131no—
396C2×C42—131no—
397C2×C42—131no—
398C2×C42—134no—
399C2×C42—134no—
400C2×C42—261no—
401C2×C42C22×D1311yescharacteristic
402#106—138no—
403#106—138no—
404#106—138no—
405#106C22×D1318yes—
406C4⋊C8—134no—
407C4⋊C8C22×D1314yes—
408#103—138no—
409#103—138no—
410#103—138no—
411#103C22×D1318yes—
412C22⋊C8—138no—
413C4×C8—138no—
414C2×C13#322914yescomplemented
415C2×C13C2×#53611yescharacteristic
416C2×C13C23×SD1611yescharacteristic
417C2×C13C22×#13711yescharacteristic
418D13—24no—
419C24—131no—
420C2×Q8—21no—
421C2×Q8—24no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—44no—
425C2×Q8—132no—
426C2×Q8—264no—
427C2×Q8—268no—
428C2×Q8—261no—
429C2×Q8—264no—
430C2×Q8—262no—
431C2×Q8—262no—
432C2×Q8—528no—
433C2×Q8—524no—
434C2×Q8—5232no—
435C2×Q8—524no—
436C2×Q8C23×D1312yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—138no—
443C22×C4—134no—
444C22×C4—131no—
445C22×C4—134no—
446C22×C4—132no—
447C22×C4—132no—
448C22×C4—264no—
449C22×C4—268no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—262no—
455C22×C4—528no—
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—24no—
460C2×C8—134no—
461C2×C8—264no—
462C2×C8C23×D1314yes—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—134no—
468C4⋊C4—132no—
469C4⋊C4—268no—
470C4⋊C4—268no—
471C4⋊C4—264no—
472C4⋊C4—264no—
473C4⋊C4—264no—
474C4⋊C4—264no—
475C4⋊C4—264no—
476C4⋊C4—262no—
477C4⋊C4—261no—
478C4⋊C4—264no—
479C4⋊C4—264no—
480C4⋊C4C23×D1314yes—
481C4⋊C4C23×D1312yes—
482C22⋊C4—264no—
483C22⋊C4—264no—
484C42—24no—
485C42—134no—
486C42—134no—
487C42—132no—
488C42—132no—
489C42—264no—
490C42D4×D1312yes—
491C42C23×D1312yes—
492C13C2×#322911yescharacteristic, complemented, Sylow
493C23—134no—
494C23—132no—
495C23—262no—
496C23—262no—
497C23C2×D4×D1311yescharacteristic
498Q8—22no—
499Q8—22no—
500Q8—48no—
501Q8—42no—
502Q8—262no—
503Q8—262no—
504Q8—528no—
505Q8—5216no—
506Q8—528no—
507Q8—522no—
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—134no—
517C2×C4—132no—
518C2×C4—132no—
519C2×C4—1316no—
520C2×C4—132no—
521C2×C4—268no—
522C2×C4—262no—
523C2×C4—264no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—264no—
529C2×C4—5216no—
530C2×C4—524no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4SD16×D1314yes—
534C2×C4C2×D4×D1312yes—
535C2×C4C2×D4×D1312yes—
536C2×C4C2×D4×D1311yescharacteristic
537C2×C4#8825412yes—
538C2×C4#8825712yes—
539C2×C4C24×D1311yescharacteristic
540C8—24no—
541C8—264no—
542C22—134no—
543C22—268no—
544C22—262no—
545C22—262no—
546C22#1171933312yes—
547C22C2×SD16×D1312yes—
548C22D13×#13712yes—
549C22C22×D4×D1311yescharacteristic
550C4—22no—
551C4—44no—
552C4—42no—
553C4—42no—
554C4—134no—
555C4—134no—
556C4—262no—
557C4—524no—
558C4—522no—
559C4—522no—
560C4#1171933312yes—
561C4C2×SD16×D1314yes—
562C4C2×#8825411yescharacteristic
563C4C2×#8825711yescharacteristic
564C2—264no—
565C2#1312597914yesdirect product factor
566C2C2×#1171933311yescharacteristic
567C2C22×SD16×D1311yescharacteristic
568C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#475C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#475D13
hypocenterC13C2×#3229
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #13125979C2direct (N × H)
4. C2×#11718516C2semidirect
5. C2×#11718453C2semidirect
8. C2×#11718512C2semidirect
9. C2×#11718681C2semidirect
10. C2×#11718755C2semidirect
12. C2×C13×#475C2semidirect
36. C13×#475C22semidirect
45. #11718755C22semidirect
46. #11718681C22semidirect
52. #11718516C22semidirect
53. #11718512C22semidirect
56. #11718453C22semidirect
219. C2×#475D13semidirect
300. #475C2×D13semidirect
414. C2×C13#3229semidirect
492. C13C2×#3229semidirect
565. C2#13125979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192832
C2×D13×C4⋊Q82
#131259792
C2×#117185162
C2×#117184532
C2×#117185232
C2×#117184662
C2×#117185122
C2×#117186812
C2×#117187552
C2×#117184942
C2×C13×#4752
C2×#322913