Finite Group Databasebeta

← C2×#13124692 #16730505

Subgroups — C2×#13124692 #16730505

Order 3328.

2094 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719205C211yesmaximal, characteristic, complemented
2C2×#11719209C211yesmaximal, characteristic
3#13124692C2116yesmaximal, direct product factor
4C2×#11718538C212yesmaximal, complemented
5C2×#11718536C212yesmaximal, complemented
6C2×#11718552C212yesmaximal, complemented
7C2×#11718551C212yesmaximal, complemented
8C2×#11718625C211yesmaximal, characteristic, complemented
9C2×#11718763C211yesmaximal, characteristic, complemented
10C2×#11718627C211yesmaximal, characteristic
11C2×#11718774C211yesmaximal, characteristic
12C22×C13×#107C211yesmaximal, characteristic, complemented
13C22×#6127C2211yescharacteristic
14C23×C8×C13C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×C4×C22⋊D13—22no—
18C2×#88180C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C2×#88178—22no—
21C22×#6099C2211yescharacteristic
22#11719209—24no—
23#11719209C2218yes—
24C2×#88147C2212yes—
25C2×#88146—21no—
26C2×C4⋊C4×D13—21no—
27#11719205—24no—
28#11719205C2218yescomplemented
29C2×#88144—21no—
30C2×#88144C2212yes—
31C2×#88142—21no—
32C2×#88142C2212yes—
33C2×#88141C2212yes—
34C2×C13×#107C2212yes—
35C2×C13×#107C2212yes—
36C2×C13×#107C2218yescomplemented
37#11718774C2218yes—
38C2×#88061C2211yescharacteristic
39C2×#88061C2211yescharacteristic
40C2×#88056C2211yescharacteristic
41C2×#88056C2211yescharacteristic
42#11718763C2218yescomplemented
43C2×#88054C2212yes—
44C2×#88054C2212yes—
45C2×#88050C2212yes—
46#11718627C2218yes—
47C2×#88049C2212yes—
48#11718625C2218yescomplemented
49C2×#88048C2212yes—
50C2×#88047C2212yes—
51#11718552C22116yescomplemented
52#11718551C22116yescomplemented
53#11718538C22116yescomplemented
54#11718536C22116yescomplemented
55C23×C4×C13—21no—
56C23×C4×C13—21no—
57C23×C4×C13C2311yescharacteristic
58C22×C22⋊D13—21no—
59C2×#6127—22no—
60C2×#6127—24no—
61C2×#6127Q818yescomplemented
62C2×#6127C2314yes—
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C22×C4×D13—22no—
66C22×Dic26—22no—
67C22×Dic26C2311yescharacteristic
68C22×C8×C13—24no—
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2314yes—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4C2312yes—
77C2×C13×C4⋊C4C2312yes—
78C2×C13×C4⋊C4C2314yes—
79C2×C13×C4⋊C4C2314yes—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13D412yes—
82C4×C22⋊D13—216no—
83C2×#6103—22no—
84#88180—22no—
85#88180D414yes—
86#88180C2314yes—
87#88180C2314yes—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13D411yescharacteristic
90C2×C4⋊Dic13D411yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93#88178—216no—
94C2×#6101—22no—
95C2×#6101—22no—
96C2×#6101—22no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—22no—
99C2×C4×Dic13C2312yes—
100C2×#6099—24no—
101C2×#6099C2314yes—
102C22×#1055C2312yes—
103#88147—24no—
104#88147C2318yes—
105#88146—28no—
106C4⋊C4×D13—28no—
107#88144—28no—
108#88144—24no—
109#88144C2318yes—
110#88142—28no—
111#88142—24no—
112#88142C2318yes—
113#88141—24no—
114#88141C2318yes—
115C13×#107C2318yes—
116C13×#107C2318yes—
117#88061C2314yes—
118#88061C2314yes—
119#88056C2314yes—
120#88056C2314yes—
121#88054C2318yes—
122#88054C2318yes—
123#88050C2318yes—
124#88049C2318yes—
125#88048C2318yes—
126#88047C2318yes—
127C2×#3083—131nomaximal, Sylow
128C24×C13C2×D411yescharacteristic
129C23×D13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—24no—
133C22×C4×C13—24no—
134C22×C4×C13—82no—
135C22×C4×C13—82no—
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2×Q814yes—
139C22×C4×C13#4114yes—
140C22×C4×C13C2411yescharacteristic
141C22×C4×C13C2412yes—
142C2×C22⋊D13—28no—
143C2×C22⋊D13—24no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13C2×D412yes—
148C22×Dic13C2×D412yes—
149#6127—216no—
150#6127—28no—
151#6127C2×Q8116yescomplemented
152C2×D52—21no—
153C2×D52—22no—
154C2×D52C2×Q814yes—
155C2×D52C2412yes—
156C2×C4×D13—28no—
157C2×C4×D13—24no—
158C2×C4×D13—28no—
159C2×C4×D13—84no—
160C2×Dic26—21no—
161C2×Dic26—22no—
162C2×Dic26—28no—
163C2×Dic26—84no—
164C2×Dic26C2×Q814yes—
165C2×Dic26C2412yes—
166C2×C8×C13—22no—
167C2×C8×C13—22no—
168C2×C8×C13—28no—
169C2×C8×C13C2412yes—
170C2×C8×C13C2412yes—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—24no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4C2414yes—
176C13×C4⋊C4C2414yes—
177C22⋊Dic13—24no—
178C22⋊Dic13C2×D418yes—
179#6103—28no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—28no—
183C4⋊Dic13C2×D414yes—
184C4⋊Dic13C2×D414yes—
185C4⋊Dic13C2412yes—
186C4⋊Dic13C2412yes—
187#6101—28no—
188#6101—28no—
189#6101—28no—
190C4×Dic13—24no—
191C4×Dic13—28no—
192C4×Dic13C2×D414yes—
193C4×Dic13C2414yes—
194#6099—28no—
195C2×#1055—24no—
196C2×#1055C2414yes—
197C2×#544—131no—
198C2×#520—131no—
199#3083—1316no—
200C2×#479—132no—
201C2×#477—132no—
202C2×#478—132no—
203C2×#474—132no—
204C2×#428—131no—
205C22×#107D1311yescharacteristic, complemented
206C2×#424—131no—
207C2×#417—131no—
208C2×#416—131no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13C22⋊Q814yes—
212C23×C13C22×D412yes—
213C23×C13C22×D411yescharacteristic
214C22×D13—24no—
215C22×D13—22no—
216C22×D13—42no—
217C22×D13—42no—
218C2×C4×C13—24no—
219C2×C4×C13—24no—
220C2×C4×C13—44no—
221C2×C4×C13—44no—
222C2×C4×C13—84no—
223C2×C4×C13—84no—
224C2×C4×C13C22⋊Q814yes—
225C2×C4×C13C22⋊Q818yes—
226C2×C4×C13C22×D412yes—
227C2×C4×C13C22×D411yescharacteristic
228C2×C4×C13C22×Q812yes—
229C2×C4×C13C22×Q814yes—
230C2×C4×C13C2×#4112yes—
231C2×C4×C13C2×#4114yes—
232C2×C4×C13C2511yescharacteristic
233C22⋊D13—216no—
234C2×Dic13—24no—
235C2×Dic13—24no—
236C2×Dic13—24no—
237C2×Dic13—22no—
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13C22×D414yes—
243C2×Dic13C22×D414yes—
244D52—24no—
245D52—22no—
246D52C22×Q814yes—
247C4×D13—216no—
248C4×D13—88no—
249Dic26—24no—
250Dic26—22no—
251Dic26—88no—
252Dic26C22×Q814yes—
253C8×C13—22no—
254C8×C13—22no—
255#1055—24no—
256C22×#41—131no—
257C22×M16—131no—
258C23×C8C2×D1311yescharacteristic
259#544—138no—
260#544—264no—
261C2×C4⋊Q8—132no—
262C2×C4⋊Q8—261no—
263C2×#125—132no—
264C2×#125—261no—
265C2×C22⋊Q8—262no—
266#520—138no—
267#520—264no—
268C2×C4×Q8—132no—
269C2×C4×D4—132no—
270C2×C4×D4—262no—
271C2×#117—131no—
272C2×#117—131no—
273C2×#117—261no—
274C22×C4⋊C4—261no—
275C22×C4⋊C4C2×D1311yescharacteristic
276C22×C4⋊C4C2×D1311yescharacteristic
277#479—1316no—
278#478—1316no—
279#477—1316no—
280#474—1316no—
281#428—138no—
282C2×#107—132no—
283C2×#107C2×D1312yes—
284C2×#107C2×D1312yes—
285C2×#107C2×D1318yescomplemented
286C2×#106—132no—
287#424—138no—
288C2×C4⋊C8—132no—
289C2×C4⋊C8—132no—
290#417—138no—
291#416—138no—
292C2×#103—131no—
293C2×#103—131no—
294C2×#103—132no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#102—132no—
298C22×C13—28no—
299C22×C13—22no—
300C22×C13—22no—
301C22×C13C2×C22⋊Q814yes—
302C22×C13C2×C22⋊Q812yes—
303C22×C13#57612yes—
304C22×C13#57812yes—
305C22×C13C23×D411yescharacteristic
306C2×D13—24no—
307C2×D13—48no—
308C2×D13—42no—
309C2×D13—42no—
310C4×C13—44no—
311C4×C13—44no—
312C4×C13C2×C22⋊Q812yes—
313C4×C13C2×C22⋊Q814yes—
314C4×C13C23×Q811yescharacteristic
315C4×C13C22×#4111yescharacteristic
316Dic13—24no—
317Dic13—24no—
318Dic13—24no—
319Dic13—42no—
320Dic13—42no—
321C2×#41—138no—
322C2×#41—134no—
323C2×#41—264no—
324C2×#41—262no—
325C22×Q8—131no—
326C22×Q8—262no—
327C22×D4—131no—
328C22×D4—261no—
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—262no—
332C23×C4—261no—
333C23×C4C22×D1311yescharacteristic
334C2×M16—134no—
335C2×M16—264no—
336C22×C8—24no—
337C22×C8—132no—
338C22×C8C22×D1311yescharacteristic
339C22×C8C22×D1311yescharacteristic
340C22×C8C22×D1314yes—
341C4⋊Q8—138no—
342C4⋊Q8—264no—
343C4⋊Q8—268no—
344#125—138no—
345#125—264no—
346#125—268no—
347C22⋊Q8—2616no—
348C4×Q8—138no—
349C4×Q8—264no—
350C4×D4—138no—
351C4×D4—264no—
352C4×D4—2616no—
353#117—134no—
354#117—134no—
355#117—134no—
356#117—268no—
357#117—262no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—268no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—262no—
371C2×C4⋊C4C22×D1312yes—
372C2×C4⋊C4C22×D1314yes—
373C2×C4⋊C4C22×D1312yes—
374C2×C4⋊C4C22×D1314yes—
375C2×C22⋊C4—132no—
376C2×C22⋊C4—262no—
377C2×C22⋊C4—261no—
378C2×C42—132no—
379C2×C42—262no—
380C2×C42—261no—
381#107—138no—
382#107C22×D1318yes—
383#107C22×D1318yes—
384#106—138no—
385C4⋊C8—138no—
386C4⋊C8—138no—
387#103—134no—
388#103—134no—
389#103—138no—
390#102—134no—
391#102—134no—
392#102—138no—
393C2×C13—24no—
394C2×C13#308314yescomplemented
395C2×C13C22×C22⋊Q811yescharacteristic
396C2×C13C2×#57611yescharacteristic
397C2×C13C2×#57811yescharacteristic
398D13—44no—
399C24—261no—
400C24D4×D1311yescharacteristic
401#41—1316no—
402#41—2616no—
403#41—268no—
404C2×Q8—134no—
405C2×Q8—132no—
406C2×Q8—268no—
407C2×Q8—262no—
408C2×Q8—261no—
409C2×Q8—1044no—
410C2×D4—134no—
411C2×D4—132no—
412C2×D4—268no—
413C2×D4—264no—
414C2×D4—262no—
415C2×D4—261no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—82no—
421C22×C4—82no—
422C22×C4—132no—
423C22×C4—132no—
424C22×C4—268no—
425C22×C4—261no—
426C22×C4—268no—
427C22×C4—264no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—1044no—
431C22×C4#612714yes—
432C22×C4D4×D1312yes—
433C22×C4D4×D1311yescharacteristic
434C22×C4Q8×D1314yes—
435C22×C4C23×D1312yes—
436C22×C4C23×D1311yescharacteristic
437M16—268no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—28no—
441C2×C8—134no—
442C2×C8—264no—
443C2×C8C23×D1312yes—
444C2×C8C23×D1312yes—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—24no—
449C4⋊C4—134no—
450C4⋊C4—134no—
451C4⋊C4—132no—
452C4⋊C4—132no—
453C4⋊C4—268no—
454C4⋊C4—268no—
455C4⋊C4—268no—
456C4⋊C4—268no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4C23×D1314yes—
460C4⋊C4C23×D1314yes—
461C22⋊C4—138no—
462C22⋊C4—268no—
463C22⋊C4—264no—
464C42—134no—
465C42—134no—
466C42—268no—
467C42—264no—
468C13C2×#308311yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—264no—
472C23—262no—
473C23—522no—
474C23—522no—
475C23#8815014yes—
476C23C2×D4×D1312yes—
477C23C2×D4×D1311yescharacteristic
478Q8—134no—
479Q8—264no—
480Q8—262no—
481Q8—1048no—
482D4—134no—
483D4—2616no—
484D4—264no—
485D4—262no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—84no—
491C2×C4—84no—
492C2×C4—134no—
493C2×C4—134no—
494C2×C4—264no—
495C2×C4—264no—
496C2×C4—264no—
497C2×C4—262no—
498C2×C4—2616no—
499C2×C4—262no—
500C2×C4—262no—
501C2×C4—522no—
502C2×C4—522no—
503C2×C4—1048no—
504C2×C4#8815014yes—
505C2×C4#8815018yes—
506C2×C4C2×#612712yes—
507C2×C4C2×#612714yes—
508C2×C4C2×D4×D1311yescharacteristic
509C2×C4C2×D4×D1312yes—
510C2×C4C2×Q8×D1312yes—
511C2×C4C2×Q8×D1314yes—
512C2×C4C24×D1311yescharacteristic
513C8—22no—
514C8—22no—
515C8—264no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—264no—
520C22—528no—
521C22—522no—
522C22—522no—
523C22C2×#8815014yes—
524C22C2×#8815012yes—
525C22#1171946212yes—
526C22#1171947112yes—
527C22C22×D4×D1311yescharacteristic
528C4—44no—
529C4—44no—
530C4—264no—
531C4—264no—
532C4—264no—
533C4—522no—
534C4—522no—
535C4C2×#8815014yes—
536C4C2×#8815012yes—
537C4C22×#612711yescharacteristic
538C4C22×Q8×D1311yescharacteristic
539C2—24no—
540C2—524no—
541C2#1312469214yesdirect product factor
542C2C22×#8815011yescharacteristic
543C2C2×#1171946211yescharacteristic
544C2C2×#1171947111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#107C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
hypercenterC22×#107D13
hypocenterC13C2×#3083
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C2×#11719205C2semidirect
3. #13124692C2direct (N × H)
4. C2×#11718538C2semidirect
5. C2×#11718536C2semidirect
6. C2×#11718552C2semidirect
7. C2×#11718551C2semidirect
8. C2×#11718625C2semidirect
9. C2×#11718763C2semidirect
12. C22×C13×#107C2semidirect
28. #11719205C22semidirect
36. C2×C13×#107C22semidirect
42. #11718763C22semidirect
48. #11718625C22semidirect
51. #11718552C22semidirect
52. #11718551C22semidirect
53. #11718538C22semidirect
54. #11718536C22semidirect
61. C2×#6127Q8semidirect
151. #6127C2×Q8semidirect
205. C22×#107D13semidirect
285. C2×#107C2×D13semidirect
394. C2×C13#3083semidirect
468. C13C2×#3083semidirect
541. C2#13124692direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192052
C2×#117192092
#131246922
C2×#117185382
C2×#117185362
C2×#117185522
C2×#117185512
C2×#117186252
C2×#117187632
C2×#117186272
C2×#117187742
C22×C13×#1072
C2×#308313