Finite Group Databasebeta

← C2×#13124657 #16730457

Subgroups — C2×#13124657 #16730457

Order 3328.

2142 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88144C211yesmaximal, characteristic, complemented
2C2×#11719227C211yesmaximal, characteristic
3#13124657C2116yesmaximal, direct product factor
4C2×#11718518C212yesmaximal, complemented
5C2×#11718538C212yesmaximal, complemented
6C2×#11718552C212yesmaximal, complemented
7C2×#11718532C212yesmaximal, complemented
8C2×#11718656C211yesmaximal, characteristic, complemented
9C2×#11718779C211yesmaximal, characteristic, complemented
10C2×#11718794C211yesmaximal, characteristic
11C2×#11718627C211yesmaximal, characteristic
12C2×C13×#428C211yesmaximal, characteristic, complemented
13C22×#6127C2211yescharacteristic
14C22×C13×M16C2211yescharacteristic
15C2×C13×#117C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C4⋊Dic13—21no—
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101—21no—
20C22×C4×Dic13C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22#11719227—24no—
23#11719227C2218yes—
24C2×#88147C2211yescharacteristic
25C2×#88147C2211yescharacteristic
26C2×#88144—24no—
27C2×#88144—21no—
28C2×#88144—21no—
29C2×#88144C2212yes—
30C2×#88144C2212yes—
31C2×#88144C2218yescomplemented
32C2×#88141C2211yescharacteristic
33C2×#88141C2211yescharacteristic
34C2×#88135—21no—
35C2×#88135—21no—
36C2×#88126—21no—
37C2×C42×D13—21no—
38C13×#428C2218yescomplemented
39C2×C13×#107C2212yes—
40C2×C13×#106C2212yes—
41#11718794C2218yes—
42#11718779C2218yescomplemented
43C2×#88061C2212yes—
44C2×#88056C2212yes—
45C2×#88054C2212yes—
46C2×#88054C2212yes—
47#11718656C2218yescomplemented
48C2×#88050C2212yes—
49#11718627C2218yes—
50C2×#88049C2212yes—
51C2×#88048C2212yes—
52C2×#88047C2212yes—
53#11718552C22116yescomplemented
54#11718538C22116yescomplemented
55#11718532C22116yescomplemented
56#11718518C22116yescomplemented
57C23×C4×C13—21no—
58C23×C4×C13C2311yescharacteristic
59C22×C22⋊D13—21no—
60C23×Dic13—21no—
61C23×Dic13D411yescharacteristic
62C23×Dic13D411yescharacteristic
63C2×#6127—22no—
64C2×#6127—24no—
65C2×#6127Q818yes—
66C2×#6127C2314yes—
67C22×D52C2311yescharacteristic
68C22×C4×D13—21no—
69C22×C4×D13—21no—
70C22×C4×D13—21no—
71C22×Dic26C2311yescharacteristic
72C2×C13×M16—24no—
73C2×C13×M16C2314yes—
74C22×C8×C13C2312yes—
75C13×#117—22no—
76C13×#117C2314yes—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2312yes—
82C2×C13×C4⋊C4C2314yes—
83C2×C13×C22⋊C4—21no—
84C2×C42×C13—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—28no—
92C2×C4⋊Dic13C2314yes—
93C2×C4⋊Dic13C2312yes—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×#6101—28no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13D411yescharacteristic
102C2×C4×Dic13D411yescharacteristic
103C2×C4×Dic13D414yes—
104C2×C4×Dic13C2311yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2314yes—
107C2×#6099—24no—
108C2×#6099C2314yes—
109C22×#1055C2312yes—
110#88147—22no—
111#88147—22no—
112#88147C2314yes—
113#88147C2314yes—
114#88144—24no—
115#88144—24no—
116#88144—28no—
117#88144—28no—
118#88144C2318yes—
119#88144C2318yes—
120#88141—22no—
121#88141—22no—
122#88141C2314yes—
123#88141C2314yes—
124#88135—28no—
125#88135—28no—
126#88126—28no—
127C42×D13—28no—
128C13×#107C2318yes—
129C13×#106C2318yes—
130#88061C2318yes—
131#88056C2318yes—
132#88054C2318yes—
133#88054C2318yes—
134#88050C2318yes—
135#88049C2318yes—
136#88048C2318yes—
137#88047C2318yes—
138C2×#3080—131nomaximal, Sylow
139C24×C13C2×D411yescharacteristic
140C23×D13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—24no—
144C22×C4×C13—22no—
145C22×C4×C13—44no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×Q814yes—
149C22×C4×C13#4114yes—
150C22×C4×C13C2411yescharacteristic
151C22×C4×C13C2412yes—
152C2×C22⋊D13—28no—
153C2×C22⋊D13—24no—
154C22×Dic13—21no—
155C22×Dic13—24no—
156C22×Dic13—22no—
157C22×Dic13—42no—
158C22×Dic13—42no—
159C22×Dic13—44no—
160C22×Dic13C2×D411yescharacteristic
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D414yes—
165C22×Dic13C2×D414yes—
166#6127—216no—
167#6127—28no—
168#6127C2×Q8116yes—
169C2×D52—21no—
170C2×D52—22no—
171C2×D52C2×Q814yes—
172C2×D52C2412yes—
173C2×C4×D13—28no—
174C2×C4×D13—24no—
175C2×C4×D13—24no—
176C2×C4×D13—24no—
177C2×C4×D13—44no—
178C2×C4×D13—44no—
179C2×Dic26—21no—
180C2×Dic26—22no—
181C2×Dic26C2×Q814yes—
182C2×Dic26C2412yes—
183C13×M16—28no—
184C2×C8×C13—24no—
185C2×C8×C13C2414yes—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4C2412yes—
191C13×C4⋊C4C2414yes—
192C13×C4⋊C4C2412yes—
193C13×C22⋊C4—24no—
194C42×C13—24no—
195#6103—24no—
196#6103—24no—
197C4⋊Dic13—24no—
198C4⋊Dic13—22no—
199C4⋊Dic13—28no—
200C4⋊Dic13—28no—
201C4⋊Dic13C2414yes—
202#6101—24no—
203#6101—24no—
204#6101—28no—
205#6101—28no—
206C4×Dic13—24no—
207C4×Dic13—24no—
208C4×Dic13C2×D414yes—
209C4×Dic13C2×D414yes—
210C4×Dic13C2×D412yes—
211C4×Dic13C2×D412yes—
212C4×Dic13C2412yes—
213C4×Dic13C2412yes—
214#6099—28no—
215C2×#1055—24no—
216C2×#1055C2414yes—
217C22×#125—131no—
218C2×C4×#41—131no—
219#3080—1316no—
220C2×#479—132no—
221C2×#479—132no—
222C2×#478—132no—
223C2×#478—132no—
224C2×#428—131no—
225C2×#428D1311yescharacteristic, complemented
226C2×#423—131no—
227C2×#417—131no—
228C2×#417—131no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13C22⋊Q814yes—
232C23×C13C22×D412yes—
233C23×C13C22×D411yescharacteristic
234C22×D13—24no—
235C22×D13—22no—
236C22×D13—42no—
237C22×D13—42no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—48no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—44no—
245C2×C4×C13C22⋊Q814yes—
246C2×C4×C13C22⋊Q818yes—
247C2×C4×C13C22×D412yes—
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C22×Q812yes—
250C2×C4×C13C22×Q814yes—
251C2×C4×C13C2×#4112yes—
252C2×C4×C13C2×#4114yes—
253C2×C4×C13C2511yescharacteristic
254C22⋊D13—216no—
255C2×Dic13—24no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—24no—
262C2×Dic13—44no—
263C2×Dic13—44no—
264C2×Dic13—48no—
265C2×Dic13—44no—
266C2×Dic13C22×D412yes—
267C2×Dic13C22×D412yes—
268C2×Dic13C22×D412yes—
269C2×Dic13C22×D412yes—
270D52—24no—
271D52—22no—
272D52C22×Q814yes—
273C4×D13—216no—
274C4×D13—48no—
275C4×D13—48no—
276Dic26—24no—
277Dic26—22no—
278Dic26C22×Q814yes—
279C8×C13—24no—
280#1055—24no—
281C22×#41—131no—
282C22×M16—131no—
283C22×M16C2×D1311yescharacteristic
284C2×#125—132no—
285C2×#125—132no—
286C2×#125—138no—
287C2×#125—261no—
288C2×#125—264no—
289C2×#125—261no—
290C4×#41—138no—
291C4×#41—264no—
292C2×C4×Q8—131no—
293C2×C4×Q8—131no—
294C2×C4×D4—131no—
295C2×C4×D4—131no—
296C2×C4×D4—261no—
297C2×C4×D4—261no—
298C2×#117—261no—
299C2×#117C2×D1311yescharacteristic
300C22×C4⋊C4—131no—
301C22×C4⋊C4—261no—
302C22×C4⋊C4—261no—
303C22×C4⋊C4C2×D1311yescharacteristic
304C22×C42—131no—
305C22×C42—261no—
306#479—1316no—
307#479—1316no—
308#478—1316no—
309#478—1316no—
310#428—138no—
311#428C2×D1318yescomplemented
312C2×#107—132no—
313C2×#107C2×D1312yes—
314C2×#106—132no—
315C2×#106C2×D1312yes—
316#423—138no—
317C2×C4⋊C8—132no—
318C2×C4⋊C8—132no—
319#417—138no—
320#417—138no—
321C2×#103—132no—
322C2×#103—132no—
323C2×#102—132no—
324C2×#102—132no—
325C22×C13—28no—
326C22×C13—22no—
327C22×C13—22no—
328C22×C13C2×C22⋊Q814yes—
329C22×C13C2×C22⋊Q812yes—
330C22×C13#57512yes—
331C22×C13#57512yes—
332C22×C13C23×D411yescharacteristic
333C2×D13—24no—
334C2×D13—48no—
335C2×D13—42no—
336C2×D13—42no—
337C4×C13—42no—
338C4×C13—42no—
339C4×C13—44no—
340C4×C13C2×C22⋊Q812yes—
341C4×C13C2×C22⋊Q814yes—
342C4×C13C23×Q811yescharacteristic
343C4×C13C22×#4111yescharacteristic
344Dic13—24no—
345Dic13—22no—
346Dic13—22no—
347Dic13—22no—
348Dic13—22no—
349Dic13—44no—
350C2×#41—138no—
351C2×#41—134no—
352C2×#41—264no—
353C2×#41—262no—
354C22×Q8—131no—
355C22×D4—131no—
356C22×D4—261no—
357C23×C4—21no—
358C23×C4—131no—
359C23×C4—131no—
360C23×C4—261no—
361C23×C4—261no—
362C23×C4—261no—
363C23×C4—261no—
364C23×C4C22×D1311yescharacteristic
365C2×M16—24no—
366C2×M16—134no—
367C2×M16—264no—
368C2×M16C22×D1314yes—
369C22×C8—132no—
370C22×C8C22×D1312yes—
371#125—138no—
372#125—138no—
373#125—268no—
374#125—268no—
375#125—264no—
376#125—264no—
377C4×Q8—134no—
378C4×Q8—134no—
379C4×Q8—262no—
380C4×Q8—262no—
381C4×D4—134no—
382C4×D4—134no—
383C4×D4—262no—
384C4×D4—262no—
385C4×D4—268no—
386C4×D4—268no—
387#117—22no—
388#117—268no—
389#117C22×D1314yes—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—132no—
393C2×C4⋊C4—134no—
394C2×C4⋊C4—268no—
395C2×C4⋊C4—262no—
396C2×C4⋊C4—262no—
397C2×C4⋊C4—268no—
398C2×C4⋊C4—262no—
399C2×C4⋊C4—262no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—262no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4C22×D1312yes—
405C2×C4⋊C4C22×D1314yes—
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—261no—
410C2×C22⋊C4—261no—
411C2×C42—21no—
412C2×C42—131no—
413C2×C42—134no—
414C2×C42—131no—
415C2×C42—131no—
416C2×C42—131no—
417C2×C42—134no—
418C2×C42—268no—
419C2×C42—261no—
420C2×C42—261no—
421#107—138no—
422#107C22×D1318yes—
423#106—138no—
424#106C22×D1318yes—
425C4⋊C8—138no—
426C4⋊C8—138no—
427#103—138no—
428#103—138no—
429#102—138no—
430#102—138no—
431C2×C13—24no—
432C2×C13#308014yescomplemented
433C2×C13C22×C22⋊Q811yescharacteristic
434C2×C13C2×#57511yescharacteristic
435C2×C13C2×#57511yescharacteristic
436D13—44no—
437C24—261no—
438C24D4×D1311yescharacteristic
439#41—1316no—
440#41—2616no—
441#41—268no—
442C2×Q8—134no—
443C2×Q8—132no—
444C2×Q8—262no—
445C2×Q8—261no—
446C2×D4—134no—
447C2×D4—132no—
448C2×D4—268no—
449C2×D4—264no—
450C2×D4—262no—
451C2×D4—261no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—44no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—134no—
462C22×C4—134no—
463C22×C4—264no—
464C22×C4—264no—
465C22×C4—261no—
466C22×C4—268no—
467C22×C4—264no—
468C22×C4—264no—
469C22×C4—262no—
470C22×C4—524no—
471C22×C4—524no—
472C22×C4—522no—
473C22×C4—522no—
474C22×C4—524no—
475C22×C4#612714yes—
476C22×C4D4×D1312yes—
477C22×C4D4×D1311yescharacteristic
478C22×C4Q8×D1314yes—
479C22×C4C23×D1312yes—
480C22×C4C23×D1311yescharacteristic
481M16—28no—
482M16—268no—
483C2×C8—24no—
484C2×C8—134no—
485C2×C8—264no—
486C2×C8C23×D1314yes—
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—134no—
492C4⋊C4—268no—
493C4⋊C4—268no—
494C4⋊C4—268no—
495C4⋊C4—268no—
496C4⋊C4—264no—
497C4⋊C4—264no—
498C4⋊C4—264no—
499C4⋊C4—262no—
500C4⋊C4C23×D1314yes—
501C4⋊C4C23×D1312yes—
502C4⋊C4C23×D1312yes—
503C22⋊C4—24no—
504C22⋊C4—264no—
505C22⋊C4—264no—
506C42—24no—
507C42—134no—
508C42—134no—
509C42—132no—
510C42—132no—
511C42—132no—
512C42—132no—
513C42—264no—
514C42—264no—
515C13C2×#308011yescharacteristic, complemented, Sylow
516C23—22no—
517C23—22no—
518C23—264no—
519C23—262no—
520C23—522no—
521C23—522no—
522C23#8815014yes—
523C23C2×D4×D1312yes—
524C23C2×D4×D1311yescharacteristic
525Q8—134no—
526Q8—264no—
527Q8—262no—
528D4—134no—
529D4—2616no—
530D4—264no—
531D4—262no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—48no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—132no—
540C2×C4—132no—
541C2×C4—132no—
542C2×C4—132no—
543C2×C4—264no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—2616no—
550C2×C4—264no—
551C2×C4—528no—
552C2×C4—528no—
553C2×C4—524no—
554C2×C4—524no—
555C2×C4—528no—
556C2×C4—524no—
557C2×C4#8815014yes—
558C2×C4#8815018yes—
559C2×C4C2×#612712yes—
560C2×C4C2×#612714yes—
561C2×C4C2×D4×D1312yes—
562C2×C4C2×D4×D1311yescharacteristic
563C2×C4C2×Q8×D1312yes—
564C2×C4C2×Q8×D1314yes—
565C2×C4C24×D1311yescharacteristic
566C8—24no—
567C8—264no—
568C22—28no—
569C22—22no—
570C22—22no—
571C22—264no—
572C22—528no—
573C22—522no—
574C22—522no—
575C22C2×#8815014yes—
576C22C2×#8815012yes—
577C22#1171947812yes—
578C22#1171948212yes—
579C22C22×D4×D1311yescharacteristic
580C4—44no—
581C4—42no—
582C4—42no—
583C4—262no—
584C4—262no—
585C4—262no—
586C4—262no—
587C4—264no—
588C4—524no—
589C4C2×#8815014yes—
590C4C2×#8815012yes—
591C4C22×#612711yescharacteristic
592C4C22×Q8×D1311yescharacteristic
593C2—24no—
594C2—524no—
595C2#1312465714yesdirect product factor
596C2C22×#8815011yescharacteristic
597C2C2×#1171947811yescharacteristic
598C2C2×#1171948211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#428C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
hypercenterC2×#428D13
hypocenterC13C2×#3080
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C22×#88144C2semidirect
3. #13124657C2direct (N × H)
4. C2×#11718518C2semidirect
5. C2×#11718538C2semidirect
6. C2×#11718552C2semidirect
7. C2×#11718532C2semidirect
8. C2×#11718656C2semidirect
9. C2×#11718779C2semidirect
12. C2×C13×#428C2semidirect
31. C2×#88144C22semidirect
38. C13×#428C22semidirect
42. #11718779C22semidirect
47. #11718656C22semidirect
53. #11718552C22semidirect
54. #11718538C22semidirect
55. #11718532C22semidirect
56. #11718518C22semidirect
225. C2×#428D13semidirect
311. #428C2×D13semidirect
432. C2×C13#3080semidirect
515. C13C2×#3080semidirect
595. C2#13124657direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881442
C2×#117192272
#131246572
C2×#117185182
C2×#117185382
C2×#117185522
C2×#117185322
C2×#117186562
C2×#117187792
C2×#117187942
C2×#117186272
C2×C13×#4282
C2×#308013