Finite Group Databasebeta

← C2×#13126021 #16735019

Subgroups — C2×#13126021 #16735019

Order 3328.

2050 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719421C211yesmaximal, characteristic
2C2×D13×#125C211yesmaximal, characteristic, complemented
3#13126021C2116yesmaximal, direct product factor
4C2×#11718726C211yesmaximal, characteristic, complemented
5C2×#11718363C211yesmaximal, characteristic, complemented
6C2×#11718732C211yesmaximal, characteristic, complemented
7C2×#11718438C212yesmaximal, complemented
8C2×#11718435C212yesmaximal, complemented
9C2×#11718424C212yesmaximal, complemented
10C2×#11718427C212yesmaximal, complemented
11C2×#11718366C211yesmaximal, characteristic, complemented
12C2×C13×#490C211yesmaximal, characteristic, complemented
13C22×#6129—21no—
14C2×C13×#127C2211yescharacteristic
15C2×C13×#125C2211yescharacteristic
16C2×#88192—21no—
17C2×#88192C2212yes—
18C2×#88190—21no—
19C2×D4×Dic13—21no—
20C2×D4×Dic13C2212yes—
21#11719421—24no—
22#11719421C2218yes—
23D13×#125—24no—
24D13×#125C2218yescomplemented
25C2×C4⋊C4×D13—21no—
26C2×C4⋊C4×D13—21no—
27C2×C4⋊C4×D13C2211yescharacteristic
28C2×C4⋊C4×D13C2211yescharacteristic
29C2×#88144C2211yescharacteristic
30C2×#88144C2211yescharacteristic
31C2×#88143—21no—
32C2×#88143—21no—
33C2×C42×D13C2211yescharacteristic
34C2×#88124C2211yescharacteristic
35C2×#88123C2211yescharacteristic
36C13×#490C2218yescomplemented
37C2×C13×#102C2212yes—
38C2×C13×#102C2212yes—
39C2×C13×#97C2211yescharacteristic
40C2×#88072C2212yes—
41C2×#88072C2212yes—
42C2×#88060C2212yes—
43C2×#88058C2212yes—
44C2×#88057C2212yes—
45C2×#88054C2212yes—
46#11718732C2218yescomplemented
47#11718726C2218yescomplemented
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×#88043C2211yescharacteristic
51#11718438C22116yescomplemented
52#11718435C22116yescomplemented
53#11718427C22116yescomplemented
54#11718424C22116yescomplemented
55#11718366C2218yescomplemented
56#11718363C2218yescomplemented
57C22×D4×C13—21no—
58C22×D4×C13—21no—
59C22×D4×C13C2312yes—
60C22×C22⋊D13—22no—
61C23×Dic13—22no—
62C2×#6129—28no—
63C2×#6129—48no—
64C22×C4×D13—21no—
65C22×C4×D13—21no—
66C22×C4×D13D411yescharacteristic
67C22×C4×D13D411yescharacteristic
68C22×C4×D13C2311yescharacteristic
69C22×Dic26—21no—
70C22×C8×C13C2312yes—
71C13×#127—22no—
72C13×#127C2314yes—
73C13×#125—22no—
74C13×#125C2314yes—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13—22no—
81C2×C22⋊Dic13—22no—
82#88192—28no—
83#88192—24no—
84#88192C2318yes—
85#88190—28no—
86D4×Dic13—28no—
87D4×Dic13—24no—
88D4×Dic13C2318yes—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13C2312yes—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—21no—
101C2×C4×Dic13D411yescharacteristic
102C2×C4×Dic13D411yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104C22×#1055C2312yes—
105C4⋊C4×D13—28no—
106C4⋊C4×D13—28no—
107C4⋊C4×D13—22no—
108C4⋊C4×D13—22no—
109C4⋊C4×D13C2314yes—
110C4⋊C4×D13C2314yes—
111#88144—22no—
112#88144—22no—
113#88144C2314yes—
114#88144C2314yes—
115#88143—28no—
116#88143—28no—
117C42×D13D414yes—
118C42×D13C2314yes—
119#88124—22no—
120#88124C2314yes—
121#88123—22no—
122#88123C2314yes—
123C13×#102C2318yes—
124C13×#102C2318yes—
125C13×#97C2314yes—
126#88072C2318yes—
127#88072C2318yes—
128#88060C2318yes—
129#88058C2318yes—
130#88057C2318yes—
131#88054C2318yes—
132#88048C2318yes—
133#88047C2318yes—
134#88043C2314yes—
135C2×#3234—131nomaximal, Sylow
136C24×C13—22no—
137C23×D13C2×D411yescharacteristic
138C2×D4×C13—22no—
139C2×D4×C13—24no—
140C2×D4×C13—24no—
141C2×D4×C13—28no—
142C2×D4×C13—44no—
143C2×D4×C13—44no—
144C2×D4×C13C2414yes—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2411yescharacteristic
150C2×C22⋊D13—28no—
151C2×C22⋊D13—48no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—28no—
156C22×Dic13—48no—
157C22×Dic13C2×D411yescharacteristic
158C22×Dic13C2×D411yescharacteristic
159C22×Dic13C2×D411yescharacteristic
160#6129—432no—
161C2×C4×D13—24no—
162C2×C4×D13—24no—
163C2×C4×D13—24no—
164C2×C4×D13—24no—
165C2×C4×D13—42no—
166C2×C4×D13—44no—
167C2×C4×D13—44no—
168C2×C4×D13C2×D412yes—
169C2×C4×D13C2×D414yes—
170C2×C4×D13C2×D414yes—
171C2×C4×D13C2412yes—
172C2×Dic26—24no—
173C2×Dic26—44no—
174C2×C8×C13—24no—
175C2×C8×C13C2414yes—
176C13×C4⋊C4—24no—
177C13×C4⋊C4—24no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4C2412yes—
181C13×C4⋊C4C2412yes—
182C42×C13C2×D412yes—
183C42×C13C2412yes—
184C22⋊Dic13—28no—
185C22⋊Dic13—28no—
186C4⋊Dic13—22no—
187C4⋊Dic13—24no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—24no—
191C4⋊Dic13—24no—
192C4⋊Dic13C2412yes—
193C4⋊Dic13C2412yes—
194C4⋊Dic13C2414yes—
195#6101—24no—
196#6101—24no—
197#6101—24no—
198#6101—24no—
199#6101—24no—
200#6101—24no—
201C4×Dic13C2×D412yes—
202C4×Dic13C2×D414yes—
203C4×Dic13C2×D414yes—
204C4×Dic13C2412yes—
205C2×#1055—24no—
206C2×#1055C2414yes—
207C2×#532—131no—
208C22×#125—131no—
209#3234—1316no—
210C2×#501—131no—
211C2×#501—131no—
212C2×#490—131no—
213C2×#490D1311yescharacteristic, complemented
214C2×#481—132no—
215C2×#480—132no—
216C2×#478—132no—
217C2×#478—132no—
218C2×#432—131no—
219C23×C13—24no—
220C23×C13—44no—
221C23×C13—44no—
222C23×C13—44no—
223C23×C13C22×D411yescharacteristic
224C22×D13—22no—
225C22×D13—22no—
226C22×D13AGL(1,ℤ/8)14yes—
227C22×D13C22×D412yes—
228D4×C13—28no—
229D4×C13—48no—
230D4×C13—48no—
231D4×C13—44no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13C22×D412yes—
239C2×C4×C13C22×D412yes—
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C132−1+414yes—
242C2×C4×C13C2511yescharacteristic
243C22⋊D13—416no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—24no—
250C2×Dic13—416no—
251C2×Dic13—44no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13C22×D412yes—
255C2×Dic13C22×D412yes—
256C2×Dic13C22×D412yes—
257C4×D13—28no—
258C4×D13—24no—
259C4×D13—24no—
260C4×D13—44no—
261C4×D13—48no—
262C4×D13—48no—
263Dic26—48no—
264C8×C13—24no—
265#1055—24no—
266C22×#41—261no—
267#532—138no—
268#532—264no—
269C2×C4⋊Q8—131no—
270C2×#127C2×D1311yescharacteristic
271C2×#125—138no—
272C2×#125—131no—
273C2×#125—131no—
274C2×#125—131no—
275C2×#125—261no—
276C2×#125—261no—
277C2×#125—264no—
278C2×#125C2×D1311yescharacteristic
279C2×#124—261no—
280C2×#121—132no—
281C2×#121—261no—
282C2×C4×D4—132no—
283C2×C4×D4—261no—
284C22×C4⋊C4—131no—
285C22×C4⋊C4—131no—
286C22×C4⋊C4—261no—
287C22×C4⋊C4—261no—
288C22×C42—131no—
289#501—138no—
290#501—138no—
291#490—138no—
292#490C2×D1318yescomplemented
293#481—1316no—
294#480—1316no—
295#478—1316no—
296#478—1316no—
297#432—138no—
298C2×#107—132no—
299C2×#107—132no—
300C2×#106—132no—
301C2×#106—132no—
302C2×C4⋊C8—132no—
303C2×#102—132no—
304C2×#102—132no—
305C2×#102C2×D1312yes—
306C2×#102C2×D1312yes—
307C2×C22⋊C8—132no—
308C2×#97—131no—
309C2×#97C2×D1311yescharacteristic
310C22×C13—44no—
311C22×C13—44no—
312C22×C13—44no—
313C22×C13—88no—
314C22×C13#53612yes—
315C22×C13C2×AGL(1,ℤ/8)12yes—
316C22×C13#57512yes—
317C22×C13C23×D411yescharacteristic
318C2×D13—22no—
319C2×D13—28no—
320C2×D13—22no—
321C2×D13C2×AGL(1,ℤ/8)14yes—
322C4×C13—22no—
323C4×C13—22no—
324C4×C13—42no—
325C4×C13—42no—
326C4×C13#53612yes—
327C4×C13C2×2−1+412yes—
328Dic13—22no—
329Dic13—22no—
330Dic13—22no—
331Dic13—44no—
332Dic13—42no—
333Dic13—42no—
334C2×#41—268no—
335C2×#41—528no—
336C22×Q8—261no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—262no—
340C22×D4C22×D1312yes—
341C23×C4—131no—
342C23×C4—131no—
343C23×C4—131no—
344C23×C4—261no—
345C23×C4—261no—
346C23×C4—262no—
347C22×C8—132no—
348C22×C8C22×D1312yes—
349C4⋊Q8—134no—
350C4⋊Q8—262no—
351#127—22no—
352#127C22×D1314yes—
353#125—22no—
354#125—134no—
355#125—134no—
356#125—134no—
357#125—268no—
358#125—268no—
359#125—262no—
360#125—262no—
361#125—262no—
362#125C22×D1314yes—
363#124—268no—
364#121—138no—
365#121—264no—
366#121—268no—
367C4×D4—138no—
368C4×D4—264no—
369C4×D4—268no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—132no—
375C2×C4⋊C4—134no—
376C2×C4⋊C4—134no—
377C2×C4⋊C4—262no—
378C2×C4⋊C4—262no—
379C2×C4⋊C4—268no—
380C2×C4⋊C4—268no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4C22×D1311yescharacteristic
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C22⋊C4—262no—
393C2×C22⋊C4—262no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—131no—
397C2×C42—134no—
398C2×C42—134no—
399C2×C42C22×D1311yescharacteristic
400#107—138no—
401#107—138no—
402#106—138no—
403#106—138no—
404C4⋊C8—138no—
405#102—138no—
406#102—138no—
407#102C22×D1318yes—
408#102C22×D1318yes—
409C22⋊C8—138no—
410#97—134no—
411#97C22×D1314yes—
412C2×C13—84no—
413C2×C13#323414yescomplemented
414C2×C13C2×#53611yescharacteristic
415C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
416C2×C13C2×#57511yescharacteristic
417D13—24no—
418C24—22no—
419C24—131no—
420#41—5232no—
421C2×Q8—264no—
422C2×Q8—524no—
423C2×D4—22no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—28no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—268no—
430C2×D4—528no—
431C2×D4C23×D1314yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—132no—
438C22×C4—134no—
439C22×C4—132no—
440C22×C4—134no—
441C22×C4—264no—
442C22×C4—264no—
443C22×C4—264no—
444C22×C4—268no—
445C22×C4—264no—
446C22×C4—262no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—522no—
450C22×C4—524no—
451C22×C4—524no—
452C22×C4—528no—
453C22×C4D4×D1311yescharacteristic
454C22×C4D4×D1311yescharacteristic
455C22×C4C23×D1311yescharacteristic
456C2×C8—24no—
457C2×C8—134no—
458C2×C8—264no—
459C2×C8C23×D1314yes—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—132no—
465C4⋊C4—132no—
466C4⋊C4—134no—
467C4⋊C4—264no—
468C4⋊C4—264no—
469C4⋊C4—264no—
470C4⋊C4—264no—
471C4⋊C4—264no—
472C4⋊C4—264no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—262no—
476C4⋊C4—264no—
477C4⋊C4—264no—
478C4⋊C4—264no—
479C4⋊C4C23×D1312yes—
480C4⋊C4C23×D1312yes—
481C22⋊C4—268no—
482C22⋊C4—268no—
483C42—134no—
484C42—132no—
485C42—134no—
486C42—132no—
487C42D4×D1312yes—
488C42C23×D1312yes—
489C13C2×#323411yescharacteristic, complemented, Sylow
490C23—24no—
491C23—44no—
492C23—44no—
493C23—44no—
494C23—134no—
495C23—132no—
496C23—262no—
497C23—262no—
498C23C2×D4×D1311yescharacteristic
499Q8—528no—
500D4—28no—
501D4—48no—
502D4—48no—
503D4—44no—
504D4—5216no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—132no—
512C2×C4—132no—
513C2×C4—132no—
514C2×C4—268no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—264no—
519C2×C4—264no—
520C2×C4—264no—
521C2×C4—262no—
522C2×C4—262no—
523C2×C4—524no—
524C2×C4—528no—
525C2×C4—528no—
526C2×C4—5216no—
527C2×C4—522no—
528C2×C4—524no—
529C2×C4—522no—
530C2×C4C2×D4×D1312yes—
531C2×C4C2×D4×D1312yes—
532C2×C4C2×D4×D1311yescharacteristic
533C2×C4#8825714yes—
534C2×C4C24×D1311yescharacteristic
535C8—24no—
536C8—264no—
537C22—44no—
538C22—44no—
539C22—44no—
540C22—88no—
541C22—134no—
542C22—262no—
543C22—268no—
544C22—262no—
545C22#1171938012yes—
546C22D13×AGL(1,ℤ/8)12yes—
547C22#1171947812yes—
548C22C22×D4×D1311yescharacteristic
549C4—22no—
550C4—22no—
551C4—42no—
552C4—42no—
553C4—262no—
554C4—262no—
555C4—262no—
556C4—522no—
557C4—524no—
558C4—522no—
559C4#1171938012yes—
560C4C2×#8825712yes—
561C2—84no—
562C2—264no—
563C2#1312602114yesdirect product factor
564C2C2×#1171938011yescharacteristic
565C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
566C2C2×#1171947811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#490C2
socleC23×C13C22×D4
prime radicalC2×#11719421C2
hypercenterC2×#490D13
hypocenterC13C2×#3234
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
2. C2×D13×#125C2semidirect
3. #13126021C2direct (N × H)
4. C2×#11718726C2semidirect
5. C2×#11718363C2semidirect
6. C2×#11718732C2semidirect
7. C2×#11718438C2semidirect
8. C2×#11718435C2semidirect
9. C2×#11718424C2semidirect
10. C2×#11718427C2semidirect
11. C2×#11718366C2semidirect
12. C2×C13×#490C2semidirect
24. D13×#125C22semidirect
36. C13×#490C22semidirect
46. #11718732C22semidirect
47. #11718726C22semidirect
51. #11718438C22semidirect
52. #11718435C22semidirect
53. #11718427C22semidirect
54. #11718424C22semidirect
55. #11718366C22semidirect
56. #11718363C22semidirect
213. C2×#490D13semidirect
292. #490C2×D13semidirect
413. C2×C13#3234semidirect
489. C13C2×#3234semidirect
563. C2#13126021direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194212
C2×D13×#1252
#131260212
C2×#117187262
C2×#117183632
C2×#117187322
C2×#117184382
C2×#117184352
C2×#117184242
C2×#117184272
C2×#117183662
C2×C13×#4902
C2×#323413