Finite Group Databasebeta

← C2×#13126055 #16735039

Subgroups — C2×#13126055 #16735039

Order 3328.

2018 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88142C211yesmaximal, characteristic, complemented
2C2×#11719305C211yesmaximal, characteristic
3#13126055C2116yesmaximal, direct product factor
4C2×#11718537C212yesmaximal, complemented
5C2×#11718426C212yesmaximal, complemented
6C2×#11718382C211yesmaximal, characteristic, complemented
7C2×#11718632C211yesmaximal, characteristic, complemented
8C2×#11718694C211yesmaximal, characteristic
9C2×#11718536C212yesmaximal, complemented
10C2×#11718422C212yesmaximal, complemented
11C2×#11718380C211yesmaximal, characteristic, complemented
12C2×C13×#480C211yesmaximal, characteristic
13C23×Dic26—21no—
14C2×C13×#121C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C2×#88190C2211yescharacteristic
17C2×#88189—21no—
18C2×D4×Dic13—21no—
19C2×D4×Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C2×#88178C2211yescharacteristic
22C22×#6101—21no—
23C22×C4×Dic13C2211yescharacteristic
24#11719305—24no—
25#11719305C2218yes—
26C2×#88144C2211yescharacteristic
27C2×#88142—24no—
28C2×#88142—21no—
29C2×#88142—21no—
30C2×#88142C2212yes—
31C2×#88142C2212yes—
32C2×#88142C2218yescomplemented
33C2×#88141C2211yescharacteristic
34C2×#88133—21no—
35C2×#88131—21no—
36C13×#480C2218yes—
37C2×C13×#107C2212yes—
38C2×C13×#102C2212yes—
39C2×C13×C22⋊C8C2211yescharacteristic
40C2×#88072C2212yes—
41C2×C22⋊#1055C2211yescharacteristic
42C2×#88057C2212yes—
43C2×#88056C2212yes—
44C2×#88055C2212yes—
45C2×#88054C2212yes—
46#11718694C2218yes—
47#11718632C2218yescomplemented
48C2×#88050C2212yes—
49C2×#88048C2212yes—
50C2×#88047C2212yes—
51#11718537C22116yescomplemented
52#11718536C22116yescomplemented
53#11718426C22116yescomplemented
54#11718422C22116yescomplemented
55#11718382C2218yescomplemented
56#11718380C2218yescomplemented
57C22×D4×C13—21no—
58C22×D4×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C23×Dic13—21no—
63C23×Dic13D411yescharacteristic
64C23×Dic13D411yescharacteristic
65C22×Dic26—22no—
66C22×Dic26—22no—
67C22×Dic26—28no—
68C22×Dic26—48no—
69C22×Dic26C2311yescharacteristic
70C22×C8×C13C2312yes—
71C13×#121—22no—
72C13×#121C2314yes—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2312yes—
77C2×C13×C4⋊C4C2314yes—
78C2×C13×C22⋊C4—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83#88190—22no—
84#88190C2314yes—
85#88189—28no—
86D4×Dic13—28no—
87D4×Dic13—22no—
88D4×Dic13C2314yes—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13C2312yes—
93C2×C4⋊Dic13C2314yes—
94C2×C4⋊Dic13C2311yescharacteristic
95#88178—22no—
96#88178C2314yes—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—28no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13D411yescharacteristic
105C2×C4×Dic13D411yescharacteristic
106C2×C4×Dic13D414yes—
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C2×C4×Dic13C2314yes—
110C22×#1055C2312yes—
111#88144—22no—
112#88144C2314yes—
113#88142—24no—
114#88142—24no—
115#88142—28no—
116#88142—28no—
117#88142C2318yes—
118#88142C2318yes—
119#88141—22no—
120#88141C2314yes—
121#88133—28no—
122#88131—28no—
123C13×#107C2318yes—
124C13×#102C2318yes—
125C13×C22⋊C8C2314yes—
126#88072C2318yes—
127C22⋊#1055C2314yes—
128#88057C2318yes—
129#88056C2318yes—
130#88055C2318yes—
131#88054C2318yes—
132#88050C2318yes—
133#88048C2318yes—
134#88047C2318yes—
135C2×#3238—131nomaximal, Sylow
136C24×C13—21no—
137C24×C13C2×D411yescharacteristic
138C2×D4×C13—24no—
139C2×D4×C13—21no—
140C2×D4×C13—24no—
141C2×D4×C13—44no—
142C2×D4×C13C2412yes—
143C22×C4×C13—24no—
144C22×C4×C13—21no—
145C22×C4×C13—24no—
146C22×C4×C13—22no—
147C22×C4×C13—44no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2412yes—
151C22×C4×C13C2411yescharacteristic
152C22×Dic13—24no—
153C22×Dic13—24no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—24no—
157C22×Dic13—22no—
158C22×Dic13—24no—
159C22×Dic13—44no—
160C22×Dic13—44no—
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D414yes—
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D411yescharacteristic
165C22×Dic13C2×D414yes—
166C22×Dic13C2×D411yescharacteristic
167C2×Dic26—24no—
168C2×Dic26—21no—
169C2×Dic26—28no—
170C2×Dic26—28no—
171C2×Dic26—48no—
172C2×Dic26—48no—
173C2×Dic26—432no—
174C2×Dic26C2412yes—
175C2×C8×C13—24no—
176C2×C8×C13C2414yes—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—24no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4C2414yes—
181C13×C4⋊C4C2412yes—
182C13×C22⋊C4—24no—
183C22⋊Dic13—24no—
184C22⋊Dic13—24no—
185C22⋊Dic13—24no—
186C22⋊Dic13—24no—
187C4⋊Dic13—24no—
188C4⋊Dic13—22no—
189C4⋊Dic13—21no—
190C4⋊Dic13—24no—
191C4⋊Dic13C2414yes—
192C4⋊Dic13C2412yes—
193#6101—24no—
194#6101—24no—
195#6101—24no—
196#6101—28no—
197#6101—28no—
198C4×Dic13—24no—
199C4×Dic13C2×D414yes—
200C4×Dic13C2×D414yes—
201C4×Dic13C2×D412yes—
202C4×Dic13C2×D412yes—
203C4×Dic13C2412yes—
204C4×Dic13C2412yes—
205C2×#1055—24no—
206C2×#1055C2414yes—
207C22×C4⋊Q8—131no—
208C2×#529—131no—
209#3238—1316no—
210C2×#501—132no—
211C2×#489—132no—
212C2×#483—131no—
213C2×#483—131no—
214C2×#480—131no—
215C2×#480D1311yescharacteristic
216C2×#477—132no—
217C2×#476—132no—
218C2×#432—131no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—42no—
223C23×C13—42no—
224C23×C13—42no—
225C23×C13AGL(1,ℤ/8)14yes—
226C23×C13C22×D412yes—
227C23×C13C22×D411yescharacteristic
228D4×C13—24no—
229D4×C13—48no—
230D4×C13—42no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—48no—
237C2×C4×C13—44no—
238C2×C4×C13—42no—
239C2×C4×C13C22×D412yes—
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C132−1+414yes—
242C2×C4×C13C2511yescharacteristic
243C2×Dic13—28no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—28no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—24no—
251C2×Dic13—42no—
252C2×Dic13—48no—
253C2×Dic13—44no—
254C2×Dic13—42no—
255C2×Dic13—48no—
256C2×Dic13#13714yes—
257C2×Dic13C22×D412yes—
258C2×Dic13C22×D412yes—
259C2×Dic13C22×D412yes—
260C2×Dic13C22×D412yes—
261Dic26—24no—
262Dic26—416no—
263Dic26—416no—
264Dic26—42no—
265C8×C13—24no—
266#1055—24no—
267C23×Q8—261no—
268C2×C4⋊Q8—132no—
269C2×C4⋊Q8—132no—
270C2×C4⋊Q8—138no—
271C2×C4⋊Q8—261no—
272C2×C4⋊Q8—261no—
273C2×C4⋊Q8—264no—
274#529—138no—
275#529—264no—
276C2×#126—261no—
277C2×#125—131no—
278C2×#124—131no—
279C2×#123—261no—
280C2×C22⋊Q8—131no—
281C2×#121C2×D1311yescharacteristic
282C2×C4×Q8—131no—
283C2×C4×D4—131no—
284C2×C4×D4—261no—
285C2×#117—261no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4—261no—
288C22×C4⋊C4C2×D1311yescharacteristic
289C22×C42—131no—
290#501—1316no—
291#489—1316no—
292#483—138no—
293#483—138no—
294#480—138no—
295#480C2×D1318yes—
296#477—1316no—
297#476—1316no—
298#432—138no—
299C2×#107—132no—
300C2×#107C2×D1312yes—
301C2×#106—132no—
302C2×#106—132no—
303C2×C4⋊C8—132no—
304C2×#103—132no—
305C2×#103—132no—
306C2×#102—132no—
307C2×#102C2×D1312yes—
308C2×C22⋊C8—131no—
309C2×C22⋊C8C2×D1311yescharacteristic
310C2×#97—132no—
311C22×C13—22no—
312C22×C13—28no—
313C22×C13—22no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13—42no—
317C22×C13—84no—
318C22×C13#53612yes—
319C22×C13C2×AGL(1,ℤ/8)14yes—
320C22×C13C2×AGL(1,ℤ/8)12yes—
321C22×C13C2×#13712yes—
322C22×C13C23×D411yescharacteristic
323C4×C13—22no—
324C4×C13—44no—
325C4×C13—42no—
326C4×C13#53612yes—
327C4×C13C2×2−1+412yes—
328Dic13—22no—
329Dic13—22no—
330Dic13—22no—
331Dic13—42no—
332Dic13—44no—
333Dic13—42no—
334Dic13C2×#13714yes—
335C22×Q8—131no—
336C22×Q8—268no—
337C22×Q8—262no—
338C22×Q8—262no—
339C22×Q8—528no—
340C22×D4—21no—
341C22×D4C22×D1311yescharacteristic
342C23×C4—21no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—261no—
346C23×C4—261no—
347C23×C4C22×D1311yescharacteristic
348C22×C8—132no—
349C22×C8C22×D1312yes—
350C4⋊Q8—138no—
351C4⋊Q8—138no—
352C4⋊Q8—268no—
353C4⋊Q8—264no—
354C4⋊Q8—264no—
355C4⋊Q8—268no—
356#126—268no—
357#125—134no—
358#125—262no—
359#124—134no—
360#124—262no—
361#123—268no—
362C22⋊Q8—134no—
363C22⋊Q8—262no—
364#121—22no—
365#121C22×D1314yes—
366C4×Q8—134no—
367C4×Q8—262no—
368C4×D4—134no—
369C4×D4—262no—
370C4×D4—268no—
371#117—268no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—132no—
375C2×C4⋊C4—134no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—268no—
378C2×C4⋊C4—262no—
379C2×C4⋊C4—262no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—262no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4C22×D1312yes—
387C2×C4⋊C4C22×D1314yes—
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—134no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—134no—
400C2×C42—261no—
401#107—138no—
402#107C22×D1318yes—
403#106—138no—
404#106—138no—
405C4⋊C8—138no—
406#103—138no—
407#103—138no—
408#102—138no—
409#102C22×D1318yes—
410C22⋊C8—134no—
411C22⋊C8C22×D1314yes—
412#97—138no—
413C2×C13—24no—
414C2×C13—82no—
415C2×C13#323814yescomplemented
416C2×C13C2×#53611yescharacteristic
417C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
418C2×C13C22×#13711yescharacteristic
419C24—21no—
420C24D4×D1311yescharacteristic
421C2×Q8—132no—
422C2×Q8—268no—
423C2×Q8—268no—
424C2×Q8—261no—
425C2×Q8—264no—
426C2×Q8—5232no—
427C2×Q8—528no—
428C2×Q8—528no—
429C2×D4—24no—
430C2×D4—21no—
431C2×D4—24no—
432C2×D4—44no—
433C2×D4C23×D1312yes—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—44no—
439C22×C4—131no—
440C22×C4—134no—
441C22×C4—134no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—264no—
446C22×C4—264no—
447C22×C4—264no—
448C22×C4—264no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—262no—
452C22×C4—524no—
453C22×C4—524no—
454C22×C4D4×D1312yes—
455C22×C4D4×D1311yescharacteristic
456C22×C4C23×D1312yes—
457C22×C4C23×D1311yescharacteristic
458C2×C8—24no—
459C2×C8—134no—
460C2×C8—264no—
461C2×C8C23×D1314yes—
462C4⋊C4—24no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—134no—
466C4⋊C4—132no—
467C4⋊C4—268no—
468C4⋊C4—268no—
469C4⋊C4—264no—
470C4⋊C4—264no—
471C4⋊C4—264no—
472C4⋊C4—264no—
473C4⋊C4—262no—
474C4⋊C4—261no—
475C4⋊C4—264no—
476C4⋊C4C23×D1314yes—
477C4⋊C4C23×D1312yes—
478C22⋊C4—24no—
479C22⋊C4—264no—
480C22⋊C4—264no—
481C22⋊C4—264no—
482C22⋊C4—264no—
483C42—134no—
484C42—132no—
485C42—132no—
486C42—134no—
487C42—132no—
488C42—132no—
489C42—264no—
490C13C2×#323811yescharacteristic, complemented, Sylow
491C23—22no—
492C23—22no—
493C23—22no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23#8816514yes—
498C23C2×D4×D1312yes—
499C23C2×D4×D1311yescharacteristic
500Q8—264no—
501Q8—5216no—
502Q8—5216no—
503Q8—522no—
504D4—24no—
505D4—48no—
506D4—42no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—48no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—134no—
516C2×C4—132no—
517C2×C4—132no—
518C2×C4—132no—
519C2×C4—132no—
520C2×C4—268no—
521C2×C4—268no—
522C2×C4—262no—
523C2×C4—262no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—264no—
528C2×C4—528no—
529C2×C4—528no—
530C2×C4—524no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4C2×D4×D1312yes—
534C2×C4C2×D4×D1311yescharacteristic
535C2×C4#8825714yes—
536C2×C4C24×D1311yescharacteristic
537C8—24no—
538C8—264no—
539C22—22no—
540C22—28no—
541C22—22no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—84no—
546C22#1171935312yes—
547C22C2×#8816514yes—
548C22C2×#8816512yes—
549C22D13×#13712yes—
550C22C22×D4×D1311yescharacteristic
551C4—22no—
552C4—44no—
553C4—42no—
554C4—134no—
555C4—262no—
556C4—262no—
557C4—262no—
558C4—524no—
559C4—522no—
560C4—522no—
561C4#1171935312yes—
562C4C2×#8825712yes—
563C2—24no—
564C2—82no—
565C2#1312605514yesdirect product factor
566C2C2×#1171935311yescharacteristic
567C2C22×#8816511yescharacteristic
568C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#480C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC2×#480D13
hypocenterC13C2×#3238
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C22×#88142C2semidirect
3. #13126055C2direct (N × H)
4. C2×#11718537C2semidirect
5. C2×#11718426C2semidirect
6. C2×#11718382C2semidirect
7. C2×#11718632C2semidirect
9. C2×#11718536C2semidirect
10. C2×#11718422C2semidirect
11. C2×#11718380C2semidirect
32. C2×#88142C22semidirect
47. #11718632C22semidirect
51. #11718537C22semidirect
52. #11718536C22semidirect
53. #11718426C22semidirect
54. #11718422C22semidirect
55. #11718382C22semidirect
56. #11718380C22semidirect
415. C2×C13#3238semidirect
490. C13C2×#3238semidirect
565. C2#13126055direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881422
C2×#117193052
#131260552
C2×#117185372
C2×#117184262
C2×#117183822
C2×#117186322
C2×#117186942
C2×#117185362
C2×#117184222
C2×#117183802
C2×C13×#4802
C2×#323813