Finite Group Databasebeta

← C2×#13126020 #16735002

Subgroups — C2×#13126020 #16735002

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic, complemented
2C2×#11719285C211yesmaximal, characteristic
3#13126020C2116yesmaximal, direct product factor
4C2×#11718539C212yesmaximal, complemented
5C2×#11718461C212yesmaximal, complemented
6C2×#11718475C212yesmaximal, complemented
7C2×#11718546C212yesmaximal
8C2×#11718681C211yesmaximal, characteristic, complemented
9C2×#11718745C211yesmaximal, characteristic, complemented
10C2×#11718507C211yesmaximal, characteristic, complemented
11C2×#11718494C211yesmaximal, characteristic, complemented
12C2×C13×#477C211yesmaximal, characteristic, complemented
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C13C2211yescharacteristic
15C2×#88201C2211yescharacteristic
16C2×#88200—21no—
17C2×#88200C2211yescharacteristic
18C2×Q8×Dic13—21no—
19#11719433—24no—
20#11719433C2218yescomplemented
21#11719285—24no—
22#11719285C2218yes—
23C2×#88152—21no—
24C2×#88151—21no—
25C2×#88149C2211yescharacteristic
26C2×#88148—21no—
27C2×#88146C2212yes—
28C2×#88144C2212yes—
29C2×#88144C2211yescharacteristic
30C2×#88141—21no—
31C2×C4×D52—21no—
32C2×C4×D52C2211yescharacteristic
33C2×#88126—21no—
34C2×C42×D13C2211yescharacteristic
35C2×#88123C2211yescharacteristic
36C13×#477C2218yescomplemented
37C2×C13×#107C2212yes—
38C2×C13×C4⋊C8C2211yescharacteristic
39C2×C13×#103C2212yes—
40C2×#88075C2212yes—
41C2×#88061C2212yes—
42C2×#88060C2212yes—
43C2×#88058C2212yes—
44C2×C8×Dic13C2212yes—
45#11718745C2218yescomplemented
46#11718681C2218yescomplemented
47C2×#88049C2212yes—
48C2×#88048C2212yes—
49C2×#88048C2212yes—
50C2×C4⋊#1055C2211yescharacteristic
51#11718546C22116yes—
52#11718539C22116yescomplemented
53#11718507C2218yescomplemented
54#11718494C2218yescomplemented
55#11718475C22116yescomplemented
56#11718461C22116yescomplemented
57C22×Q8×C13—21no—
58C22×Q8×C13C2311yescharacteristic
59C22×D52—21no—
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×C4×D13D411yescharacteristic
63C22×C4×D13D411yescharacteristic
64C22×C4×D13C2311yescharacteristic
65C22×Dic26—21no—
66C22×C8×C13C2312yes—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8C2314yes—
69C4×Q8×C13—22no—
70C4×Q8×C13C2314yes—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4C2312yes—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77#88201—22no—
78#88201C2314yes—
79#88200—28no—
80#88200—22no—
81#88200C2314yes—
82Q8×Dic13—28no—
83C2×#6103—21no—
84C2×#6103—22no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13C2312yes—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13D411yescharacteristic
99C2×C4×Dic13D411yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C22×#1055C2312yes—
102#88152—28no—
103#88151—28no—
104#88149—22no—
105#88149C2314yes—
106#88148—28no—
107#88146—24no—
108#88146C2318yes—
109#88144—24no—
110#88144—22no—
111#88144C2318yes—
112#88144C2314yes—
113#88141—28no—
114C4×D52—28no—
115C4×D52—22no—
116C4×D52C2314yes—
117#88126—28no—
118C42×D13D414yes—
119C42×D13C2314yes—
120#88123—22no—
121#88123C2314yes—
122C13×#107C2318yes—
123C13×C4⋊C8C2314yes—
124C13×#103C2318yes—
125#88075C2318yes—
126#88061C2318yes—
127#88060C2318yes—
128#88058C2318yes—
129C8×Dic13C2318yes—
130#88049C2318yes—
131#88048C2318yes—
132#88048C2318yes—
133C4⋊#1055C2314yes—
134C2×#3233—131nomaximal, Sylow
135C23×D13—21no—
136C23×D13C2×D411yescharacteristic
137C2×Q8×C13—24no—
138C2×Q8×C13—21no—
139C2×Q8×C13—22no—
140C2×Q8×C13—22no—
141C2×Q8×C13—44no—
142C2×Q8×C13C2412yes—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2411yescharacteristic
149C22×Dic13—22no—
150C22×Dic13—21no—
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C2×D52—22no—
155C2×D52—22no—
156C2×D52—24no—
157C2×D52—21no—
158C2×D52—44no—
159C2×D52C2412yes—
160C2×C4×D13—24no—
161C2×C4×D13—22no—
162C2×C4×D13—22no—
163C2×C4×D13—24no—
164C2×C4×D13—42no—
165C2×C4×D13—44no—
166C2×C4×D13C2×D412yes—
167C2×C4×D13C2×D414yes—
168C2×C4×D13C2×D414yes—
169C2×C4×D13C2412yes—
170C2×Dic26—24no—
171C2×Dic26—44no—
172C2×C8×C13—24no—
173C2×C8×C13C2414yes—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—24no—
178C13×C4⋊C4C2414yes—
179C13×C4⋊C4C2412yes—
180C42×C13—24no—
181C42×C13C2×D412yes—
182C42×C13C2412yes—
183#6103—24no—
184#6103—28no—
185#6103—24no—
186#6103—24no—
187#6103—24no—
188#6103—24no—
189C4⋊Dic13—22no—
190C4⋊Dic13—24no—
191C4⋊Dic13—21no—
192C4⋊Dic13—24no—
193C4⋊Dic13—28no—
194C4⋊Dic13C2414yes—
195C4⋊Dic13C2412yes—
196#6101—24no—
197#6101—24no—
198#6101—28no—
199C4×Dic13—28no—
200C4×Dic13C2×D412yes—
201C4×Dic13C2×D414yes—
202C4×Dic13C2×D414yes—
203C4×Dic13C2412yes—
204C2×#1055—24no—
205C2×#1055C2414yes—
206C2×#533—131no—
207C2×#529—131no—
208#3233—1316no—
209C2×#499—132no—
210C2×#488—132no—
211C2×#485—132no—
212C2×#482—132no—
213C2×#477D1311yescharacteristic, complemented
214C2×#475—131no—
215C2×#476—131no—
216C2×#474—131no—
217C2×#431—131no—
218C23×C13C22×D411yescharacteristic
219C22×D13—22no—
220C22×D13—22no—
221C22×D13—22no—
222C22×D13—22no—
223C22×D13—42no—
224C22×D13—42no—
225C22×D13—42no—
226C22×D13C22×D412yes—
227Q8×C13—22no—
228Q8×C13—22no—
229Q8×C13—48no—
230Q8×C13—42no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—44no—
238C2×C4×C13#13514yes—
239C2×C4×C13C22×D412yes—
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C13C22×D412yes—
242C2×C4×C132−1+412yes—
243C2×C4×C132−1+412yes—
244C2×C4×C13C2511yescharacteristic
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—24no—
249C2×Dic13—22no—
250C2×Dic13—44no—
251C2×Dic13—42no—
252C2×Dic13C22×D412yes—
253C2×Dic13C22×D412yes—
254C2×Dic13C22×D412yes—
255D52—22no—
256D52—22no—
257D52—48no—
258D52—42no—
259C4×D13—24no—
260C4×D13—28no—
261C4×D13—22no—
262C4×D13—22no—
263C4×D13—44no—
264C4×D13—48no—
265Dic26—48no—
266C8×C13—24no—
267#1055—24no—
268#533—138no—
269#533—264no—
270C2×C4⋊Q8—131no—
271C2×C4⋊Q8C2×D1311yescharacteristic
272#529—138no—
273#529—264no—
274C2×#126—261no—
275C2×#125—132no—
276C2×#125—131no—
277C2×#124—131no—
278C2×#123—261no—
279C2×C22⋊Q8—131no—
280C2×C22⋊Q8—261no—
281C2×C22⋊Q8—261no—
282C2×#121—131no—
283C2×C4×Q8—261no—
284C2×C4×Q8—261no—
285C2×C4×Q8C2×D1311yescharacteristic
286C2×C4×D4—131no—
287C2×C4×D4—261no—
288C2×#117—132no—
289C2×#117—261no—
290C22×C42—131no—
291#499—1316no—
292#488—1316no—
293#485—1316no—
294#482—1316no—
295#477C2×D1318yescomplemented
296#476—138no—
297#475—138no—
298#474—138no—
299#431—138no—
300C2×#107—132no—
301C2×#107C2×D1312yes—
302C2×#106—132no—
303C2×#106—132no—
304C2×C4⋊C8—131no—
305C2×C4⋊C8C2×D1311yescharacteristic
306C2×#103—132no—
307C2×#103C2×D1312yes—
308C2×#102—132no—
309C2×#102—132no—
310C2×C22⋊C8—132no—
311C2×C4×C8—132no—
312C22×C13#53612yes—
313C22×C13C2×#13512yes—
314C22×C13#57512yes—
315C22×C13C23×D411yescharacteristic
316C2×D13—22no—
317C2×D13—22no—
318C2×D13—22no—
319C2×D13—44no—
320C2×D13—42no—
321C2×D13—42no—
322C2×D13—42no—
323C2×D13—84no—
324C4×C13—22no—
325C4×C13—42no—
326C4×C13—42no—
327C4×C13—44no—
328C4×C13#53612yes—
329C4×C13C2×#13514yes—
330C4×C13C2×2−1+411yescharacteristic
331C4×C13C2×2−1+411yescharacteristic
332Dic13—22no—
333Dic13—22no—
334Dic13—22no—
335Dic13—44no—
336Dic13—42no—
337C22×Q8—21no—
338C22×Q8—261no—
339C22×Q8C22×D1311yescharacteristic
340C22×D4—131no—
341C22×D4—261no—
342C23×C4—131no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—261no—
346C22×C8—132no—
347C22×C8C22×D1312yes—
348C4⋊Q8—22no—
349C4⋊Q8—134no—
350C4⋊Q8—262no—
351C4⋊Q8C22×D1314yes—
352#126—268no—
353#125—134no—
354#125—138no—
355#125—262no—
356#125—264no—
357#124—134no—
358#124—262no—
359#123—268no—
360C22⋊Q8—134no—
361C22⋊Q8—268no—
362C22⋊Q8—262no—
363C22⋊Q8—268no—
364#121—134no—
365#121—262no—
366C4×Q8—22no—
367C4×Q8—268no—
368C4×Q8—268no—
369C4×Q8C22×D1314yes—
370C4×D4—134no—
371C4×D4—268no—
372C4×D4—262no—
373#117—138no—
374#117—268no—
375#117—264no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—132no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—262no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4C22×D1312yes—
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—262no—
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—262no—
401C2×C42C22×D1311yescharacteristic
402#107—138no—
403#107C22×D1318yes—
404#106—138no—
405#106—138no—
406C4⋊C8—134no—
407C4⋊C8C22×D1314yes—
408#103—138no—
409#103C22×D1318yes—
410#102—138no—
411#102—138no—
412C22⋊C8—138no—
413C4×C8—138no—
414C2×C13#323314yescomplemented
415C2×C13C2×#53611yescharacteristic
416C2×C13C22×#13511yescharacteristic
417C2×C13C2×#57511yescharacteristic
418D13—42no—
419D13—82no—
420C24—131no—
421C24—261no—
422C2×Q8—21no—
423C2×Q8—24no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—44no—
427C2×Q8—264no—
428C2×Q8—524no—
429C2×Q8C23×D1312yes—
430C2×D4—132no—
431C2×D4—264no—
432C2×D4—261no—
433C2×D4—262no—
434C2×D4—262no—
435C2×D4—524no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—132no—
443C22×C4—134no—
444C22×C4—132no—
445C22×C4—134no—
446C22×C4—264no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—261no—
451C22×C4—264no—
452C22×C4—522no—
453C22×C4—524no—
454C22×C4D4×D1311yescharacteristic
455C22×C4D4×D1311yescharacteristic
456C22×C4C23×D1311yescharacteristic
457C2×C8—24no—
458C2×C8—134no—
459C2×C8—264no—
460C2×C8C23×D1314yes—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—134no—
466C4⋊C4—132no—
467C4⋊C4—264no—
468C4⋊C4—264no—
469C4⋊C4—264no—
470C4⋊C4—268no—
471C4⋊C4—268no—
472C4⋊C4—262no—
473C4⋊C4—261no—
474C4⋊C4—264no—
475C4⋊C4C23×D1314yes—
476C4⋊C4C23×D1312yes—
477C22⋊C4—264no—
478C22⋊C4—264no—
479C22⋊C4—264no—
480C22⋊C4—268no—
481C22⋊C4—264no—
482C22⋊C4—264no—
483C42—24no—
484C42—134no—
485C42—134no—
486C42—132no—
487C42—132no—
488C42—268no—
489C42D4×D1312yes—
490C42C23×D1312yes—
491C13C2×#323311yescharacteristic, complemented, Sylow
492C23—132no—
493C23—262no—
494C23—262no—
495C23—262no—
496C23—262no—
497C23—522no—
498C23—522no—
499C23—522no—
500C23C2×D4×D1311yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—48no—
504Q8—42no—
505Q8—528no—
506D4—262no—
507D4—262no—
508D4—528no—
509D4—522no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—42no—
517C2×C4—132no—
518C2×C4—132no—
519C2×C4—132no—
520C2×C4—262no—
521C2×C4—262no—
522C2×C4—262no—
523C2×C4—268no—
524C2×C4—264no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—264no—
528C2×C4—262no—
529C2×C4—524no—
530C2×C4—522no—
531C2×C4—524no—
532C2×C4—528no—
533C2×C4#8817314yes—
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—262no—
543C22—262no—
544C22—262no—
545C22—524no—
546C22—522no—
547C22—522no—
548C22—522no—
549C22—1044no—
550C22#1171933312yes—
551C22C2×#8817312yes—
552C22#1171947812yes—
553C22C22×D4×D1311yescharacteristic
554C4—22no—
555C4—42no—
556C4—44no—
557C4—42no—
558C4—262no—
559C4—262no—
560C4—262no—
561C4—522no—
562C4—524no—
563C4#1171933312yes—
564C4C2×#8817314yes—
565C4C2×#8825411yescharacteristic
566C4C2×#8825711yescharacteristic
567C2—522no—
568C2—1042no—
569C2#1312602014yesdirect product factor
570C2C2×#1171933311yescharacteristic
571C2C22×#8817311yescharacteristic
572C2C2×#1171947811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#477C2
socleC23×C13C22×D4
prime radicalC2×#88149C22
hypercenterC2×#477D13
hypocenterC13C2×#3233
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#11719433C2semidirect
3. #13126020C2direct (N × H)
4. C2×#11718539C2semidirect
5. C2×#11718461C2semidirect
6. C2×#11718475C2semidirect
8. C2×#11718681C2semidirect
9. C2×#11718745C2semidirect
10. C2×#11718507C2semidirect
11. C2×#11718494C2semidirect
12. C2×C13×#477C2semidirect
20. #11719433C22semidirect
36. C13×#477C22semidirect
45. #11718745C22semidirect
46. #11718681C22semidirect
52. #11718539C22semidirect
53. #11718507C22semidirect
54. #11718494C22semidirect
55. #11718475C22semidirect
56. #11718461C22semidirect
213. C2×#477D13semidirect
295. #477C2×D13semidirect
414. C2×C13#3233semidirect
491. C13C2×#3233semidirect
569. C2#13126020direct (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×#117192852
#131260202
C2×#117185392
C2×#117184612
C2×#117184752
C2×#117185462
C2×#117186812
C2×#117187452
C2×#117185072
C2×#117184942
C2×C13×#4772
C2×#323313