Finite Group Databasebeta

← C2×#13124965 #16731121

Subgroups — C2×#13124965 #16731121

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic
2C2×C4×Q8×D13C211yesmaximal, characteristic
3#13124965C2116yesmaximal, direct product factor
4C2×#11718466C212yesmaximal
5C2×#11718512C211yesmaximal, characteristic, complemented
6C2×#11718681C211yesmaximal, characteristic, complemented
7C2×#11718751C211yesmaximal, characteristic, complemented
8C2×#11718847C212yesmaximal
9C2×#11718845C212yesmaximal, complemented
10C2×#11718450C212yesmaximal, complemented
11C2×#11718496C211yesmaximal, characteristic
12C2×C13×#462C211yesmaximal, characteristic, complemented
13C22×Q8×D13C2211yescharacteristic
14C22×C13×Q16C2212yes—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C13C2211yescharacteristic
17C2×#88200C2212yes—
18C2×Q8×Dic13C2212yes—
19C2×Q8×Dic13C2211yescharacteristic
20C22×#6107C2212yes—
21#11719433—24no—
22#11719433C2218yes—
23C4×Q8×D13—24no—
24C4×Q8×D13C2218yes—
25C2×#88151—21no—
26C2×#88146—21no—
27C2×C4⋊C4×D13—21no—
28C2×C4⋊C4×D13C2211yescharacteristic
29C2×#88144—21no—
30C2×#88141—21no—
31C2×#88141—21no—
32C2×#88141C2211yescharacteristic
33C2×C42×D13—21no—
34C2×C42×D13C2211yescharacteristic
35C2×#88123C2211yescharacteristic
36C2×C4×Dic26—21no—
37C2×C4×Dic26C2211yescharacteristic
38C13×#462C2218yescomplemented
39C2×C13×C4⋊C8C2211yescharacteristic
40C2×C13×#103C2212yes—
41C2×#88075C2212yes—
42C2×#88075C2212yes—
43#11718847C22116yes—
44#11718845C22116yescomplemented
45C2×#88060C2212yes—
46C2×#88057C2212yes—
47C2×#88056C2212yes—
48C2×#88055C2212yes—
49#11718751C2218yescomplemented
50#11718681C2218yescomplemented
51C2×#88048C2212yes—
52C2×C4⋊#1055C2211yescharacteristic
53#11718512C2218yescomplemented
54#11718496C2218yes—
55#11718466C22116yes—
56#11718450C22116yescomplemented
57C22×Q8×C13C2312yes—
58C22×Q8×C13C2311yescharacteristic
59C2×Q8×D13—24no—
60C2×Q8×D13—22no—
61C2×Q8×D13—24no—
62C2×Q8×D13C2314yes—
63C22×C4×D13—21no—
64C22×C4×D13—21no—
65C22×C4×D13D411yescharacteristic
66C22×C4×D13D411yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C22×Dic26—21no—
69C22×Dic26—21no—
70C22×Dic26C2311yescharacteristic
71C2×C13×Q16—28no—
72C2×C13×Q16C2318yes—
73C22×C8×C13C2312yes—
74C13×C4⋊Q8—22no—
75C13×C4⋊Q8C2314yes—
76C4×Q8×C13—22no—
77C4×Q8×C13C2314yes—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84#88200—24no—
85#88200C2318yes—
86Q8×Dic13—24no—
87Q8×Dic13—22no—
88Q8×Dic13C2318yes—
89Q8×Dic13C2314yes—
90C2×#6107—28no—
91C2×#6107C2318yes—
92C2×#6103—22no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2312yes—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—21no—
101C2×#6101—22no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13—21no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13D411yescharacteristic
107C2×C4×Dic13D411yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C22×#1055C2312yes—
110#88151—28no—
111#88146—28no—
112C4⋊C4×D13—28no—
113C4⋊C4×D13—22no—
114C4⋊C4×D13C2314yes—
115#88144—28no—
116#88141—28no—
117#88141—28no—
118#88141—22no—
119#88141C2314yes—
120C42×D13—28no—
121C42×D13D414yes—
122C42×D13C2314yes—
123#88123—22no—
124#88123C2314yes—
125C4×Dic26—22no—
126C4×Dic26—28no—
127C4×Dic26C2314yes—
128C13×C4⋊C8C2314yes—
129C13×#103C2318yes—
130#88075C2318yes—
131#88075C2318yes—
132#88060C2318yes—
133#88057C2318yes—
134#88056C2318yes—
135#88055C2318yes—
136#88048C2318yes—
137C4⋊#1055C2314yes—
138C2×#3113—131nomaximal, Sylow
139C23×D13C2×D411yescharacteristic
140C2×Q8×C13—21no—
141C2×Q8×C13—22no—
142C2×Q8×C13—22no—
143C2×Q8×C13—24no—
144C2×Q8×C13—24no—
145C2×Q8×C13#4114yes—
146C2×Q8×C13C2414yes—
147C2×Q8×C13C2412yes—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2411yescharacteristic
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—22no—
157C22×Dic13C2×D411yescharacteristic
158C22×Dic13C2×D411yescharacteristic
159C22×Dic13C2×D411yescharacteristic
160Q8×D13—216no—
161Q8×D13—28no—
162Q8×D13—28no—
163C2×C4×D13—28no—
164C2×C4×D13—24no—
165C2×C4×D13—24no—
166C2×C4×D13—24no—
167C2×C4×D13—22no—
168C2×C4×D13—22no—
169C2×C4×D13—24no—
170C2×C4×D13—44no—
171C2×C4×D13C2×D414yes—
172C2×C4×D13C2×D412yes—
173C2×C4×D13C2×D414yes—
174C2×C4×D13C2412yes—
175C2×Dic26—28no—
176C2×Dic26—21no—
177C2×Dic26—22no—
178C2×Dic26—24no—
179C2×Dic26—24no—
180C2×Dic26—44no—
181C2×Dic26#4114yes—
182C2×Dic26C2412yes—
183C13×Q16—216no—
184C2×C8×C13—24no—
185C2×C8×C13C2414yes—
186C13×C4⋊C4—24no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—24no—
190C13×C4⋊C4C2412yes—
191C42×C13—24no—
192C42×C13C2×D412yes—
193C42×C13C2412yes—
194#6107—216no—
195#6103—28no—
196C4⋊Dic13—21no—
197C4⋊Dic13—22no—
198C4⋊Dic13—24no—
199C4⋊Dic13—24no—
200C4⋊Dic13—28no—
201C4⋊Dic13C2412yes—
202C4⋊Dic13C2414yes—
203#6101—24no—
204#6101—24no—
205#6101—24no—
206#6101—28no—
207C4×Dic13—24no—
208C4×Dic13—24no—
209C4×Dic13—24no—
210C4×Dic13—28no—
211C4×Dic13C2×D414yes—
212C4×Dic13C2×D412yes—
213C4×Dic13C2×D414yes—
214C4×Dic13C2412yes—
215C2×#1055—24no—
216C2×#1055C2414yes—
217C2×#533—131no—
218C22×C4×Q8—131no—
219#3113—1316no—
220C2×#483—132no—
221C2×#475—131no—
222C2×#475—131no—
223C2×#462—131no—
224C2×#462D1311yescharacteristic, complemented
225C2×#451—132no—
226C2×#441—132no—
227C2×#441—132no—
228C2×#432—131no—
229C23×C13C22×D411yescharacteristic
230C22×D13—22no—
231C22×D13—22no—
232C22×D13#13714yes—
233C22×D13C22×D412yes—
234Q8×C13—24no—
235Q8×C13—22no—
236Q8×C13—24no—
237Q8×C13—24no—
238Q8×C13—44no—
239Q8×C13C2×#4114yes—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—24no—
245C2×C4×C13—44no—
246C2×C4×C13—42no—
247C2×C4×C13#13714yes—
248C2×C4×C13C22×D412yes—
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C22×D412yes—
251C2×C4×C13C2×#4112yes—
252C2×C4×C13C2×#4112yes—
253C2×C4×C13C2511yescharacteristic
254C2×Dic13—22no—
255C2×Dic13—24no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—44no—
262C2×Dic13—42no—
263C2×Dic13C22×D412yes—
264C2×Dic13C22×D412yes—
265C2×Dic13C22×D412yes—
266C4×D13—216no—
267C4×D13—28no—
268C4×D13—24no—
269C4×D13—28no—
270C4×D13—22no—
271C4×D13—22no—
272C4×D13—48no—
273Dic26—216no—
274Dic26—24no—
275Dic26—22no—
276Dic26—48no—
277Dic26C2×#4114yes—
278C8×C13—24no—
279#1055—24no—
280C23×Q8—131no—
281C22×Q16—132no—
282C22×Q16C2×D1312yes—
283#533—138no—
284#533—264no—
285C2×C4⋊Q8—131no—
286C2×C4⋊Q8C2×D1311yescharacteristic
287C2×#125—261no—
288C2×C22⋊Q8—132no—
289C2×C22⋊Q8—261no—
290C2×C4×Q8—131no—
291C2×C4×Q8—132no—
292C2×C4×Q8—138no—
293C2×C4×Q8—131no—
294C2×C4×Q8—131no—
295C2×C4×Q8—261no—
296C2×C4×Q8—261no—
297C2×C4×Q8—261no—
298C2×C4×Q8—264no—
299C2×C4×Q8C2×D1311yescharacteristic
300C2×#117—261no—
301C22×C4⋊C4—131no—
302C22×C4⋊C4—261no—
303C22×C42—131no—
304C22×C42—261no—
305#483—1316no—
306#475—138no—
307#475—138no—
308#462—138no—
309#462C2×D1318yescomplemented
310#451—1316no—
311#441—1316no—
312#441—1316no—
313#432—138no—
314C2×#106—132no—
315C2×#106—132no—
316C2×C4⋊C8—131no—
317C2×C4⋊C8C2×D1311yescharacteristic
318C2×#103—132no—
319C2×#103—132no—
320C2×#103—132no—
321C2×#103C2×D1312yes—
322C2×C22⋊C8—132no—
323C2×#97—132no—
324C22×C13#52512yes—
325C22×C13C2×#13712yes—
326C22×C13C2×#13712yes—
327C22×C13C23×D411yescharacteristic
328C2×D13—28no—
329C2×D13—22no—
330C2×D13—22no—
331C2×D13C2×#13714yes—
332C4×C13—24no—
333C4×C13—22no—
334C4×C13—44no—
335C4×C13—42no—
336C4×C13#52512yes—
337C4×C13C2×#13714yes—
338C4×C13C22×#4111yescharacteristic
339C4×C13C22×#4111yescharacteristic
340Dic13—22no—
341Dic13—24no—
342Dic13—22no—
343Dic13—22no—
344Dic13—44no—
345Dic13—42no—
346C22×Q8—134no—
347C22×Q8—131no—
348C22×Q8—261no—
349C22×Q8—262no—
350C22×Q8—264no—
351C22×Q8—264no—
352C22×Q8—261no—
353C22×Q8C22×D1312yes—
354C22×Q8C22×D1311yescharacteristic
355C23×C4—131no—
356C23×C4—131no—
357C23×C4—131no—
358C23×C4—261no—
359C23×C4—261no—
360C2×Q16—28no—
361C2×Q16—138no—
362C2×Q16—268no—
363C2×Q16C22×D1318yes—
364C22×C8—132no—
365C22×C8C22×D1312yes—
366C4⋊Q8—22no—
367C4⋊Q8—134no—
368C4⋊Q8—262no—
369C4⋊Q8C22×D1314yes—
370#125—268no—
371C22⋊Q8—138no—
372C22⋊Q8—268no—
373C22⋊Q8—264no—
374C4×Q8—22no—
375C4×Q8—134no—
376C4×Q8—138no—
377C4×Q8—134no—
378C4×Q8—134no—
379C4×Q8—268no—
380C4×Q8—262no—
381C4×Q8—268no—
382C4×Q8—268no—
383C4×Q8—262no—
384C4×Q8—264no—
385C4×Q8—262no—
386C4×Q8C22×D1314yes—
387#117—268no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—132no—
393C2×C4⋊C4—134no—
394C2×C4⋊C4—262no—
395C2×C4⋊C4—268no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—262no—
400C2×C4⋊C4—262no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C22⋊C4—262no—
405C2×C42—21no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—131no—
409C2×C42—134no—
410C2×C42—134no—
411C2×C42—268no—
412C2×C42—262no—
413C2×C42—261no—
414C2×C42—261no—
415C2×C42—261no—
416C2×C42C22×D1311yescharacteristic
417#106—138no—
418#106—138no—
419C4⋊C8—134no—
420C4⋊C8C22×D1314yes—
421#103—138no—
422#103—138no—
423#103—138no—
424#103C22×D1318yes—
425C22⋊C8—138no—
426#97—138no—
427C2×C13#311314yescomplemented
428C2×C13C2×#52511yescharacteristic
429C2×C13C22×#13711yescharacteristic
430C2×C13C22×#13711yescharacteristic
431D13—24no—
432C24—131no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—24no—
437C2×Q8—24no—
438C2×Q8—134no—
439C2×Q8—132no—
440C2×Q8—264no—
441C2×Q8—268no—
442C2×Q8—268no—
443C2×Q8—2616no—
444C2×Q8—268no—
445C2×Q8—261no—
446C2×Q8—264no—
447C2×Q8—262no—
448C2×Q8—524no—
449C2×Q8#612914yes—
450C2×Q8C23×D1314yes—
451C2×Q8C23×D1312yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—134no—
459C22×C4—134no—
460C22×C4—132no—
461C22×C4—132no—
462C22×C4—264no—
463C22×C4—264no—
464C22×C4—268no—
465C22×C4—264no—
466C22×C4—261no—
467C22×C4—264no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—261no—
471C22×C4—262no—
472C22×C4—524no—
473C22×C4D4×D1311yescharacteristic
474C22×C4D4×D1311yescharacteristic
475C22×C4C23×D1311yescharacteristic
476Q16—216no—
477Q16—2616no—
478C2×C8—24no—
479C2×C8—134no—
480C2×C8—264no—
481C2×C8C23×D1314yes—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—132no—
487C4⋊C4—134no—
488C4⋊C4—264no—
489C4⋊C4—264no—
490C4⋊C4—264no—
491C4⋊C4—268no—
492C4⋊C4—268no—
493C4⋊C4—261no—
494C4⋊C4—262no—
495C4⋊C4—264no—
496C4⋊C4—264no—
497C4⋊C4C23×D1312yes—
498C22⋊C4—268no—
499C42—24no—
500C42—132no—
501C42—134no—
502C42—134no—
503C42—132no—
504C42—264no—
505C42—264no—
506C42—268no—
507C42—264no—
508C42D4×D1312yes—
509C42C23×D1312yes—
510C13C2×#311311yescharacteristic, complemented, Sylow
511C23—134no—
512C23—132no—
513C23—262no—
514C23—262no—
515C23C2×D4×D1311yescharacteristic
516Q8—24no—
517Q8—22no—
518Q8—24no—
519Q8—24no—
520Q8—44no—
521Q8—134no—
522Q8—2616no—
523Q8—264no—
524Q8—262no—
525Q8—528no—
526Q8C2×#612914yes—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—132no—
537C2×C4—268no—
538C2×C4—2616no—
539C2×C4—262no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—264no—
543C2×C4—262no—
544C2×C4—268no—
545C2×C4—264no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—264no—
550C2×C4—528no—
551C2×C4—524no—
552C2×C4—522no—
553C2×C4#8817214yes—
554C2×C4C2×D4×D1312yes—
555C2×C4C2×D4×D1312yes—
556C2×C4C2×D4×D1311yescharacteristic
557C2×C4C2×#612912yes—
558C2×C4#41×D1312yes—
559C2×C4C24×D1311yescharacteristic
560C8—24no—
561C8—264no—
562C22—134no—
563C22—268no—
564C22—262no—
565C22—262no—
566C22#1171931112yes—
567C22C2×#8817212yes—
568C22D13×#13712yes—
569C22C22×D4×D1311yescharacteristic
570C4—22no—
571C4—24no—
572C4—42no—
573C4—44no—
574C4—262no—
575C4—262no—
576C4—262no—
577C4—264no—
578C4—522no—
579C4—524no—
580C4#1171931112yes—
581C4C2×#8817214yes—
582C4C22×#612911yescharacteristic
583C4C2×#41×D1311yescharacteristic
584C2—264no—
585C2#1312496514yesdirect product factor
586C2C2×#1171931111yescharacteristic
587C2C2×D13×#13711yescharacteristic
588C2C22×#8817211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#462C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#462D13
hypocenterC13C2×#3113
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #13124965C2direct (N × H)
5. C2×#11718512C2semidirect
6. C2×#11718681C2semidirect
7. C2×#11718751C2semidirect
9. C2×#11718845C2semidirect
10. C2×#11718450C2semidirect
12. C2×C13×#462C2semidirect
38. C13×#462C22semidirect
44. #11718845C22semidirect
49. #11718751C22semidirect
50. #11718681C22semidirect
53. #11718512C22semidirect
56. #11718450C22semidirect
224. C2×#462D13semidirect
309. #462C2×D13semidirect
427. C2×C13#3113semidirect
510. C13C2×#3113semidirect
585. C2#13124965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194332
C2×C4×Q8×D132
#131249652
C2×#117184662
C2×#117185122
C2×#117186812
C2×#117187512
C2×#117188472
C2×#117188452
C2×#117184502
C2×#117184962
C2×C13×#4622
C2×#311313