Finite Group Databasebeta

← C2×#13124683 #16730496

Subgroups — C2×#13124683 #16730496

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×#11719228C211yesmaximal, characteristic
2#13124683C2116yesmaximal, direct product factor
3C2×#11718724C212yesmaximal, complemented
4C2×#11718752C212yesmaximal, complemented
5C2×#11718727C212yesmaximal, complemented
6C2×#11718748C212yesmaximal, complemented
7C2×#11718656C211yesmaximal, characteristic, complemented
8C22×#88047C211yesmaximal, characteristic, complemented
9C2×#11718660C211yesmaximal, characteristic, complemented
10C2×#11718627C211yesmaximal, characteristic
11C2×#11718663C211yesmaximal, characteristic
12C2×C13×#544C211yesmaximal, characteristic, complemented
13C22×#6127C2211yescharacteristic
14C13×#544—24no—
15C13×#544C2218yescomplemented
16C2×C13×C4⋊Q8—21no—
17C2×C13×C4⋊Q8C2212yes—
18C2×C13×#125—21no—
19C2×C13×#125C2212yes—
20C2×C13×C22⋊Q8—22no—
21C2×C13×#117C2211yescharacteristic
22C2×C13×#117C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6099C2211yescharacteristic
26C23×#1055C2211yescharacteristic
27#11719228—24no—
28#11719228C2218yes—
29C2×#88146—21no—
30C2×C4⋊C4×D13—21no—
31C2×#88135—22no—
32C2×C4×D52C2212yes—
33C2×C4×Dic26C2212yes—
34#11718752C22116yescomplemented
35#11718748C22116yescomplemented
36#11718727C22116yescomplemented
37#11718724C22116yescomplemented
38#11718663C2218yes—
39#11718660C2218yescomplemented
40#11718656C2218yescomplemented
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88050C2212yes—
44#11718627C2218yes—
45C2×#88049C2211yescharacteristic
46C2×#88049C2211yescharacteristic
47C2×#88049C2212yes—
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×#88047C2212yes—
51C2×#88047C2212yes—
52C2×#88047C2218yescomplemented
53C2×C4⋊#1055C2212yes—
54C2×C4⋊#1055C2212yes—
55C22×Q8×C13—22no—
56C23×C4×C13—21no—
57C23×C4×C13C2311yescharacteristic
58C22×C22⋊D13—21no—
59C23×Dic13—21no—
60C2×#6127—22no—
61C2×#6127—24no—
62C2×#6127Q818yescomplemented
63C2×#6127C2314yes—
64C22×D52C2311yescharacteristic
65C22×C4×D13—21no—
66C22×C4×D13—22no—
67C22×Dic26C2311yescharacteristic
68C13×C4⋊Q8—28no—
69C13×C4⋊Q8—24no—
70C13×C4⋊Q8C2318yes—
71C13×#125—28no—
72C13×#125—24no—
73C13×#125C2318yes—
74C13×C22⋊Q8—216no—
75C13×#117—22no—
76C13×#117D414yes—
77C13×#117C2314yes—
78C13×#117C2314yes—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4D411yescharacteristic
85C2×C13×C4⋊C4D411yescharacteristic
86C2×C13×C4⋊C4C2312yes—
87C2×C13×C4⋊C4C2314yes—
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4D412yes—
92C2×C42×C13—21no—
93C2×C42×C13C2312yes—
94C2×#6103—22no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13C2314yes—
98C2×C4⋊Dic13C2312yes—
99C2×#6101—22no—
100C2×C4×Dic13—22no—
101C2×#6099—24no—
102C2×#6099C2314yes—
103C22×#1055—24no—
104C22×#1055C2314yes—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2312yes—
108#88146—28no—
109C4⋊C4×D13—28no—
110#88135—216no—
111C4×D52—24no—
112C4×D52C2318yes—
113C4×Dic26—24no—
114C4×Dic26C2318yes—
115#88050C2314yes—
116#88050C2314yes—
117#88050C2318yes—
118#88049C2314yes—
119#88049C2314yes—
120#88049C2318yes—
121#88048C2318yes—
122#88047C2318yes—
123#88047C2318yes—
124#88047C2318yes—
125C4⋊#1055C2318yes—
126C4⋊#1055C2318yes—
127C2×#3083—131nomaximal, Sylow
128C24×C13C2×D411yescharacteristic
129C23×D13—21no—
130C2×Q8×C13—28no—
131C2×Q8×C13—84no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—22no—
135C22×C4×C13—24no—
136C22×C4×C13—82no—
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2×Q814yes—
142C22×C4×C13#4114yes—
143C22×C4×C13C2411yescharacteristic
144C22×C4×C13C2412yes—
145C2×C22⋊D13—28no—
146C2×C22⋊D13—24no—
147C22×Dic13—21no—
148C22×Dic13—22no—
149C22×Dic13—24no—
150C22×Dic13—82no—
151#6127—216no—
152#6127—28no—
153#6127C2×Q8116yescomplemented
154C2×D52—21no—
155C2×D52—22no—
156C2×D52C2×Q814yes—
157C2×D52C2412yes—
158C2×C4×D13—28no—
159C2×C4×D13—24no—
160C2×C4×D13—28no—
161C2×C4×D13—84no—
162C2×Dic26—21no—
163C2×Dic26—22no—
164C2×Dic26C2×Q814yes—
165C2×Dic26C2412yes—
166C13×C4⋊C4—24no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—28no—
169C13×C4⋊C4—28no—
170C13×C4⋊C4—28no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4C2×D414yes—
174C13×C4⋊C4C2×D414yes—
175C13×C4⋊C4C2414yes—
176C13×C4⋊C4C2412yes—
177C13×C4⋊C4C2412yes—
178C13×C22⋊C4—24no—
179C13×C22⋊C4C2×D418yes—
180C42×C13—24no—
181C42×C13C2×D414yes—
182C42×C13C2414yes—
183#6103—28no—
184C4⋊Dic13—22no—
185C4⋊Dic13—24no—
186C4⋊Dic13C2414yes—
187#6101—28no—
188C4×Dic13—28no—
189#6099—28no—
190C2×#1055—22no—
191C2×#1055—22no—
192C2×#1055—28no—
193C2×#1055—24no—
194C2×#1055C2412yes—
195C2×#1055C2412yes—
196C2×#1055C2414yes—
197C2×#544D1311yescharacteristic, complemented
198C2×#520—131no—
199#3083—1316no—
200C2×#479—132no—
201C2×#477—132no—
202C2×#478—132no—
203C2×#474—132no—
204C2×#428—131no—
205C22×#107—131no—
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—
218Q8×C13—88no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—24no—
224C2×C4×C13—44no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—84no—
228C2×C4×C13C22⋊Q814yes—
229C2×C4×C13C22⋊Q818yes—
230C2×C4×C13C22×D414yes—
231C2×C4×C13C22×D414yes—
232C2×C4×C13C22×D412yes—
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C22×Q812yes—
235C2×C4×C13C22×Q814yes—
236C2×C4×C13C2×#4112yes—
237C2×C4×C13C2×#4114yes—
238C2×C4×C13C2511yescharacteristic
239C22⋊D13—216no—
240C2×Dic13—24no—
241C2×Dic13—22no—
242C2×Dic13—24no—
243C2×Dic13—44no—
244C2×Dic13—84no—
245D52—24no—
246D52—22no—
247D52C22×Q814yes—
248C4×D13—216no—
249C4×D13—88no—
250Dic26—24no—
251Dic26—22no—
252Dic26C22×Q814yes—
253#1055—22no—
254#1055—22no—
255#1055—24no—
256C22×#41—131no—
257C22×M16—131no—
258C23×C8—131no—
259#544—24no—
260#544C2×D1318yescomplemented
261C2×C4⋊Q8—21no—
262C2×C4⋊Q8C2×D1312yes—
263C2×#125—21no—
264C2×#125C2×D1312yes—
265C2×C22⋊Q8—22no—
266#520—138no—
267#520—264no—
268C2×C4×Q8—132no—
269C2×C4×D4—132no—
270C2×C4×D4—262no—
271C2×#117—261no—
272C2×#117C2×D1311yescharacteristic
273C2×#117C2×D1311yescharacteristic
274C22×C4⋊C4—131no—
275C22×C4⋊C4—261no—
276C22×C4⋊C4C2×D1311yescharacteristic
277#479—1316no—
278#478—1316no—
279#477—1316no—
280#474—1316no—
281#428—138no—
282C2×#107—132no—
283C2×#107—132no—
284C2×#107—132no—
285C2×#107—138no—
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—132no—
294C2×#103—131no—
295C2×#102—131no—
296C2×#102—132no—
297C2×#102—131no—
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—24no—
311C4×C13—24no—
312C4×C13—44no—
313C4×C13—42no—
314C4×C13—42no—
315C4×C13C2×C22⋊Q812yes—
316C4×C13C2×C22⋊Q814yes—
317C4×C13C23×Q811yescharacteristic
318C4×C13C22×#4111yescharacteristic
319Dic13—24no—
320Dic13—44no—
321C2×#41—138no—
322C2×#41—134no—
323C2×#41—264no—
324C2×#41—262no—
325C22×Q8—22no—
326C22×Q8—131no—
327C22×D4—131no—
328C22×D4—261no—
329C23×C4—21no—
330C23×C4—261no—
331C23×C4—261no—
332C23×C4—262no—
333C23×C4C22×D1311yescharacteristic
334C2×M16—134no—
335C2×M16—264no—
336C22×C8—131no—
337C22×C8—131no—
338C22×C8—134no—
339C22×C8—132no—
340C22×C8—264no—
341C4⋊Q8—28no—
342C4⋊Q8—24no—
343C4⋊Q8C22×D1318yes—
344#125—28no—
345#125—24no—
346#125C22×D1318yes—
347C22⋊Q8—216no—
348C4×Q8—138no—
349C4×Q8—264no—
350C4×D4—138no—
351C4×D4—2616no—
352C4×D4—264no—
353#117—22no—
354#117—268no—
355#117C22⋊D1314yes—
356#117C22×D1314yes—
357#117C22×D1314yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—132no—
364C2×C4⋊C4—134no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—262no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—268no—
369C2×C4⋊C4C22⋊D1311yescharacteristic
370C2×C4⋊C4C22⋊D1311yescharacteristic
371C2×C4⋊C4C22×D1312yes—
372C2×C4⋊C4C22×D1314yes—
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—262no—
377C2×C22⋊C4C22⋊D1312yes—
378C2×C42—21no—
379C2×C42—262no—
380C2×C42C22×D1312yes—
381#107—138no—
382#107—138no—
383#107—138no—
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—
400C24C2×C22⋊D1311yescharacteristic
401#41—1316no—
402#41—2616no—
403#41—268no—
404C2×Q8—28no—
405C2×Q8—84no—
406C2×Q8—134no—
407C2×Q8—132no—
408C2×Q8—262no—
409C2×Q8—261no—
410C2×D4—134no—
411C2×D4—132no—
412C2×D4—268no—
413C2×D4—264no—
414C2×D4—262no—
415C2×D4—261no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—82no—
421C22×C4—261no—
422C22×C4—268no—
423C22×C4—264no—
424C22×C4—262no—
425C22×C4—264no—
426C22×C4—268no—
427C22×C4—1044no—
428C22×C4—1042no—
429C22×C4Q8×D1314yes—
430C22×C4#613114yes—
431C22×C4C2×C22⋊D1312yes—
432C22×C4C2×C22⋊D1312yes—
433C22×C4C2×C22⋊D1312yes—
434C22×C4C2×C22⋊D1311yescharacteristic
435C22×C4C23×D1312yes—
436C22×C4C23×D1311yescharacteristic
437M16—268no—
438C2×C8—134no—
439C2×C8—132no—
440C2×C8—132no—
441C2×C8—262no—
442C2×C8—262no—
443C2×C8—268no—
444C2×C8—264no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—28no—
448C4⋊C4—28no—
449C4⋊C4—28no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—134no—
453C4⋊C4—264no—
454C4⋊C4—262no—
455C4⋊C4—268no—
456C4⋊C4C2×C22⋊D1314yes—
457C4⋊C4C2×C22⋊D1314yes—
458C4⋊C4C23×D1312yes—
459C4⋊C4C23×D1314yes—
460C4⋊C4C23×D1312yes—
461C22⋊C4—24no—
462C22⋊C4—268no—
463C22⋊C4C2×C22⋊D1318yes—
464C42—24no—
465C42—268no—
466C42C2×C22⋊D1314yes—
467C42C23×D1314yes—
468C13C2×#308311yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—264no—
472C23—262no—
473C23—522no—
474C23—522no—
475C23#8820014yes—
476C23C22×C22⋊D1312yes—
477C23C22×C22⋊D1311yescharacteristic
478Q8—88no—
479Q8—134no—
480Q8—264no—
481Q8—262no—
482D4—134no—
483D4—2616no—
484D4—264no—
485D4—262no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—84no—
495C2×C4—264no—
496C2×C4—262no—
497C2×C4—2616no—
498C2×C4—264no—
499C2×C4—524no—
500C2×C4—1048no—
501C2×C4—1044no—
502C2×C4#8820014yes—
503C2×C4#8820018yes—
504C2×C4C2×Q8×D1312yes—
505C2×C4C2×Q8×D1314yes—
506C2×C4C2×#613112yes—
507C2×C4C2×#613114yes—
508C2×C4C22×C22⋊D1314yes—
509C2×C4C22×C22⋊D1314yes—
510C2×C4C22×C22⋊D1312yes—
511C2×C4C22×C22⋊D1311yescharacteristic
512C2×C4C24×D1311yescharacteristic
513C8—262no—
514C8—262no—
515C8—264no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—264no—
520C22—528no—
521C22—522no—
522C22—522no—
523C22C2×#8820014yes—
524C22C2×#8820012yes—
525C22#1171954012yes—
526C22#1171954312yes—
527C22C23×C22⋊D1311yescharacteristic
528C4—24no—
529C4—24no—
530C4—44no—
531C4—42no—
532C4—42no—
533C4—264no—
534C4—524no—
535C4C2×#8820014yes—
536C4C2×#8820012yes—
537C4C22×Q8×D1311yescharacteristic
538C4C22×#613111yescharacteristic
539C2—24no—
540C2—524no—
541C2#1312468314yesdirect product factor
542C2C22×#8820011yescharacteristic
543C2C2×#1171954011yescharacteristic
544C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#544C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
hypercenterC2×#544D13
hypocenterC13C2×#3083
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #13124683C2direct (N × H)
3. C2×#11718724C2semidirect
4. C2×#11718752C2semidirect
5. C2×#11718727C2semidirect
6. C2×#11718748C2semidirect
7. C2×#11718656C2semidirect
8. C22×#88047C2semidirect
9. C2×#11718660C2semidirect
12. C2×C13×#544C2semidirect
15. C13×#544C22semidirect
34. #11718752C22semidirect
35. #11718748C22semidirect
36. #11718727C22semidirect
37. #11718724C22semidirect
39. #11718660C22semidirect
40. #11718656C22semidirect
52. C2×#88047C22semidirect
62. C2×#6127Q8semidirect
153. #6127C2×Q8semidirect
197. C2×#544D13semidirect
260. #544C2×D13semidirect
394. C2×C13#3083semidirect
468. C13C2×#3083semidirect
541. C2#13124683direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192282
#131246832
C2×#117187242
C2×#117187522
C2×#117187272
C2×#117187482
C2×#117186562
C22×#880472
C2×#117186602
C2×#117186272
C2×#117186632
C2×C13×#5442
C2×#308313