Finite Group Databasebeta

← C2×#13126009 #16734954

Subgroups — C2×#13126009 #16734954

Order 3328.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719329C211yesmaximal, characteristic
2C22×#88144C211yesmaximal, characteristic, complemented
3#13126009C2116yesmaximal, direct product factor
4C2×#11718539C212yesmaximal, complemented
5C2×#11718461C212yesmaximal, complemented
6C2×#11718629C211yesmaximal, characteristic
7C2×#11718704C211yesmaximal, characteristic, complemented
8C2×#11718397C211yesmaximal, characteristic
9C2×#11718457C212yesmaximal, complemented
10C2×#11718552C212yesmaximal, complemented
11C2×#11718379C211yesmaximal, characteristic, complemented
12C2×C13×#484C211yesmaximal, characteristic, complemented
13C2×C13×C22⋊Q8C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C2×#88201C2211yescharacteristic
16C2×Q8×Dic13C2211yescharacteristic
17C2×#88184C2211yescharacteristic
18C22×C4⋊Dic13—21no—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×#6101—21no—
21C22×C4×Dic13C2211yescharacteristic
22#11719329—24no—
23#11719329C2218yes—
24C2×#88152—21no—
25C2×#88147C2211yescharacteristic
26C2×#88146—21no—
27C2×#88144—24no—
28C2×#88144—21no—
29C2×#88144—21no—
30C2×#88144C2212yes—
31C2×#88144C2212yes—
32C2×#88144C2211yescharacteristic
33C2×#88144C2218yescomplemented
34C2×#88140—21no—
35C2×#88135—21no—
36C13×#484C2218yescomplemented
37C2×C13×#107C2212yes—
38C2×C13×#103C2212yes—
39C2×C13×C22⋊C8C2211yescharacteristic
40C2×#88075C2212yes—
41C2×C22⋊#1055C2211yescharacteristic
42C2×#88061C2212yes—
43C2×#88058C2212yes—
44C2×#88054C2212yes—
45C2×C8×Dic13C2212yes—
46#11718704C2218yescomplemented
47#11718629C2218yes—
48C2×#88049C2212yes—
49C2×#88048C2212yes—
50C2×#88048C2212yes—
51#11718552C22116yescomplemented
52#11718539C22116yescomplemented
53#11718461C22116yescomplemented
54#11718457C22116yescomplemented
55#11718397C2218yes—
56#11718379C2218yescomplemented
57C22×Q8×C13C2311yescharacteristic
58C23×C4×C13—21no—
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13—21no—
61C23×Dic13—21no—
62C23×Dic13D411yescharacteristic
63C23×Dic13D411yescharacteristic
64C22×D52C2311yescharacteristic
65C22×C4×D13—21no—
66C22×C8×C13C2312yes—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8C2314yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2314yes—
75C2×C13×C22⋊C4—21no—
76#88201—22no—
77#88201C2314yes—
78Q8×Dic13—22no—
79Q8×Dic13C2314yes—
80#88184—22no—
81#88184C2314yes—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—28no—
93C2×C4⋊Dic13C2312yes—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2314yes—
96C2×#6101—21no—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—28no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13D411yescharacteristic
102C2×C4×Dic13D411yescharacteristic
103C2×C4×Dic13D414yes—
104C2×C4×Dic13C2311yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2314yes—
107C22×#1055C2312yes—
108#88152—28no—
109#88147—22no—
110#88147C2314yes—
111#88146—28no—
112#88144—24no—
113#88144—24no—
114#88144—28no—
115#88144—28no—
116#88144—22no—
117#88144C2318yes—
118#88144C2318yes—
119#88144C2314yes—
120#88140—28no—
121#88135—28no—
122C13×#107C2318yes—
123C13×#103C2318yes—
124C13×C22⋊C8C2314yes—
125#88075C2318yes—
126C22⋊#1055C2314yes—
127#88061C2318yes—
128#88058C2318yes—
129#88054C2318yes—
130C8×Dic13C2318yes—
131#88049C2318yes—
132#88048C2318yes—
133#88048C2318yes—
134C2×#3232—131nomaximal, Sylow
135C24×C13C2×D411yescharacteristic
136C23×D13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—24no—
139C2×Q8×C13C2412yes—
140C22×C4×C13—24no—
141C22×C4×C13—21no—
142C22×C4×C13—24no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—44no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2412yes—
149C22×C4×C13C2411yescharacteristic
150C2×C22⋊D13—24no—
151C2×C22⋊D13—44no—
152C22×Dic13—24no—
153C22×Dic13—21no—
154C22×Dic13—24no—
155C22×Dic13—22no—
156C22×Dic13—42no—
157C22×Dic13—44no—
158C22×Dic13C2×D414yes—
159C22×Dic13C2×D411yescharacteristic
160C22×Dic13C2×D411yescharacteristic
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D414yes—
164C2×D52—24no—
165C2×D52—21no—
166C2×D52C2412yes—
167C2×C4×D13—24no—
168C2×C4×D13—44no—
169C2×C8×C13—24no—
170C2×C8×C13C2414yes—
171C13×C4⋊C4—24no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4C2414yes—
176C13×C4⋊C4C2412yes—
177C13×C22⋊C4—24no—
178#6103—24no—
179#6103—24no—
180#6103—24no—
181#6103—24no—
182C4⋊Dic13—24no—
183C4⋊Dic13—22no—
184C4⋊Dic13—21no—
185C4⋊Dic13—24no—
186C4⋊Dic13—24no—
187C4⋊Dic13—28no—
188C4⋊Dic13—28no—
189C4⋊Dic13C2414yes—
190C4⋊Dic13C2412yes—
191#6101—24no—
192#6101—28no—
193#6101—28no—
194C4×Dic13—24no—
195C4×Dic13C2×D412yes—
196C4×Dic13C2×D414yes—
197C4×Dic13C2×D412yes—
198C4×Dic13C2×D414yes—
199C4×Dic13C2412yes—
200C4×Dic13C2412yes—
201C2×#1055—24no—
202C2×#1055C2414yes—
203C2×#529—131no—
204C22×#125—131no—
205#3232—1316no—
206C2×#499—132no—
207C2×#488—132no—
208C2×#484D1311yescharacteristic, complemented
209C2×#481—131no—
210C2×#483—131no—
211C2×#480—131no—
212C2×#479—132no—
213C2×#478—132no—
214C2×#431—131no—
215C23×C13—22no—
216C23×C13—22no—
217C23×C13#13514yes—
218C23×C13C22×D412yes—
219C23×C13C22×D411yescharacteristic
220C22×D13—22no—
221C22×D13—42no—
222C22×D13—42no—
223C22×D13—42no—
224Q8×C13—24no—
225Q8×C13—42no—
226C2×C4×C13—22no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—22no—
230C2×C4×C13—24no—
231C2×C4×C13—22no—
232C2×C4×C13—48no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—44no—
236C2×C4×C13C22×D412yes—
237C2×C4×C13C22×D411yescharacteristic
238C2×C4×C132−1+414yes—
239C2×C4×C13C2511yescharacteristic
240C22⋊D13—48no—
241C2×Dic13—28no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—24no—
248C2×Dic13—44no—
249C2×Dic13—48no—
250C2×Dic13—44no—
251C2×Dic13—42no—
252C2×Dic13C22×D412yes—
253C2×Dic13C22×D412yes—
254C2×Dic13C22×D412yes—
255C2×Dic13C22×D412yes—
256D52—24no—
257D52—42no—
258C4×D13—48no—
259C8×C13—24no—
260#1055—24no—
261#529—138no—
262#529—264no—
263C2×#126—261no—
264C2×#125—132no—
265C2×#125—132no—
266C2×#125—131no—
267C2×#125—138no—
268C2×#125—261no—
269C2×#125—261no—
270C2×#125—264no—
271C2×#124—131no—
272C2×#123—261no—
273C2×C22⋊Q8C2×D1311yescharacteristic
274C2×#121—131no—
275C2×C4×Q8—131no—
276C2×C4×D4—131no—
277C2×C4×D4—261no—
278C2×#117—261no—
279C22×C4⋊C4—131no—
280C22×C4⋊C4—261no—
281C22×C4⋊C4—261no—
282C22×C4⋊C4C2×D1311yescharacteristic
283C22×C42—131no—
284#499—1316no—
285#488—1316no—
286#484C2×D1318yescomplemented
287#483—138no—
288#481—138no—
289#480—138no—
290#479—1316no—
291#478—1316no—
292#431—138no—
293C2×#107—132no—
294C2×#107C2×D1312yes—
295C2×#106—132no—
296C2×#106—132no—
297C2×C4⋊C8—132no—
298C2×#103—132no—
299C2×#103C2×D1312yes—
300C2×#102—132no—
301C2×#102—132no—
302C2×C22⋊C8—131no—
303C2×C22⋊C8C2×D1311yescharacteristic
304C2×C4×C8—132no—
305C22×C13—22no—
306C22×C13—28no—
307C22×C13—22no—
308C22×C13#53612yes—
309C22×C13C2×#13514yes—
310C22×C13C2×#13512yes—
311C22×C13#57512yes—
312C22×C13C23×D411yescharacteristic
313C2×D13—42no—
314C2×D13—42no—
315C2×D13—42no—
316C2×D13—84no—
317C4×C13—22no—
318C4×C13—42no—
319C4×C13—42no—
320C4×C13—44no—
321C4×C13#53612yes—
322C4×C13C2×2−1+412yes—
323Dic13—22no—
324Dic13—22no—
325Dic13—22no—
326Dic13—22no—
327Dic13—44no—
328Dic13—42no—
329C22×Q8C22×D1311yescharacteristic
330C22×D4—131no—
331C22×D4—261no—
332C23×C4—21no—
333C23×C4—131no—
334C23×C4—131no—
335C23×C4—261no—
336C23×C4—261no—
337C23×C4C22×D1311yescharacteristic
338C22×C8—132no—
339C22×C8C22×D1312yes—
340#126—268no—
341#125—138no—
342#125—138no—
343#125—134no—
344#125—268no—
345#125—264no—
346#125—264no—
347#125—268no—
348#125—262no—
349#124—134no—
350#124—262no—
351#123—268no—
352C22⋊Q8—22no—
353C22⋊Q8C22×D1314yes—
354#121—134no—
355#121—262no—
356C4×Q8—134no—
357C4×Q8—262no—
358C4×D4—134no—
359C4×D4—262no—
360C4×D4—268no—
361#117—268no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—132no—
366C2×C4⋊C4—134no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—268no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—262no—
371C2×C4⋊C4—268no—
372C2×C4⋊C4—262no—
373C2×C4⋊C4—262no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—262no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4C22×D1312yes—
380C2×C4⋊C4C22×D1314yes—
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—134no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—134no—
393C2×C42—261no—
394#107—138no—
395#107C22×D1318yes—
396#106—138no—
397#106—138no—
398C4⋊C8—138no—
399#103—138no—
400#103C22×D1318yes—
401#102—138no—
402#102—138no—
403C22⋊C8—134no—
404C22⋊C8C22×D1314yes—
405C4×C8—138no—
406C2×C13—24no—
407C2×C13#323214yescomplemented
408C2×C13C2×#53611yescharacteristic
409C2×C13C22×#13511yescharacteristic
410C2×C13C2×#57511yescharacteristic
411D13—82no—
412C24—261no—
413C24D4×D1311yescharacteristic
414C2×Q8—21no—
415C2×Q8—24no—
416C2×Q8C23×D1312yes—
417C2×D4—132no—
418C2×D4—264no—
419C2×D4—261no—
420C2×D4—264no—
421C2×D4—524no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—44no—
428C22×C4—134no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—134no—
434C22×C4—264no—
435C22×C4—264no—
436C22×C4—264no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—524no—
440C22×C4—522no—
441C22×C4—524no—
442C22×C4D4×D1312yes—
443C22×C4D4×D1311yescharacteristic
444C22×C4C23×D1312yes—
445C22×C4C23×D1311yescharacteristic
446C2×C8—24no—
447C2×C8—134no—
448C2×C8—264no—
449C2×C8C23×D1314yes—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—24no—
453C4⋊C4—21no—
454C4⋊C4—134no—
455C4⋊C4—132no—
456C4⋊C4—268no—
457C4⋊C4—268no—
458C4⋊C4—268no—
459C4⋊C4—268no—
460C4⋊C4—264no—
461C4⋊C4—264no—
462C4⋊C4—264no—
463C4⋊C4—264no—
464C4⋊C4—262no—
465C4⋊C4—261no—
466C4⋊C4C23×D1314yes—
467C4⋊C4C23×D1312yes—
468C22⋊C4—24no—
469C22⋊C4—264no—
470C22⋊C4—264no—
471C22⋊C4—264no—
472C22⋊C4—264no—
473C42—134no—
474C42—132no—
475C42—132no—
476C42—134no—
477C42—132no—
478C42—132no—
479C42—264no—
480C13C2×#323211yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—262no—
484C23—522no—
485C23—522no—
486C23—522no—
487C23#8817314yes—
488C23C2×D4×D1312yes—
489C23C2×D4×D1311yescharacteristic
490Q8—24no—
491Q8—42no—
492D4—264no—
493D4—528no—
494D4—522no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—48no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—132no—
506C2×C4—132no—
507C2×C4—132no—
508C2×C4—132no—
509C2×C4—268no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—264no—
516C2×C4—528no—
517C2×C4—524no—
518C2×C4—528no—
519C2×C4—524no—
520C2×C4—522no—
521C2×C4C2×D4×D1312yes—
522C2×C4C2×D4×D1311yescharacteristic
523C2×C4#8825714yes—
524C2×C4C24×D1311yescharacteristic
525C8—24no—
526C8—264no—
527C22—22no—
528C22—28no—
529C22—22no—
530C22—522no—
531C22—522no—
532C22—522no—
533C22—1044no—
534C22#1171935312yes—
535C22C2×#8817314yes—
536C22C2×#8817312yes—
537C22#1171947812yes—
538C22C22×D4×D1311yescharacteristic
539C4—22no—
540C4—44no—
541C4—42no—
542C4—42no—
543C4—262no—
544C4—262no—
545C4—262no—
546C4—262no—
547C4—524no—
548C4—522no—
549C4#1171935312yes—
550C4C2×#8825712yes—
551C2—24no—
552C2—1042no—
553C2#1312600914yesdirect product factor
554C2C2×#1171935311yescharacteristic
555C2C22×#8817311yescharacteristic
556C2C2×#1171947811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#484C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC2×#484D13
hypocenterC13C2×#3232
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
2. C22×#88144C2semidirect
3. #13126009C2direct (N × H)
4. C2×#11718539C2semidirect
5. C2×#11718461C2semidirect
7. C2×#11718704C2semidirect
9. C2×#11718457C2semidirect
10. C2×#11718552C2semidirect
11. C2×#11718379C2semidirect
12. C2×C13×#484C2semidirect
33. C2×#88144C22semidirect
36. C13×#484C22semidirect
46. #11718704C22semidirect
51. #11718552C22semidirect
52. #11718539C22semidirect
53. #11718461C22semidirect
54. #11718457C22semidirect
56. #11718379C22semidirect
208. C2×#484D13semidirect
286. #484C2×D13semidirect
407. C2×C13#3232semidirect
480. C13C2×#3232semidirect
553. C2#13126009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193292
C22×#881442
#131260092
C2×#117185392
C2×#117184612
C2×#117186292
C2×#117187042
C2×#117183972
C2×#117184572
C2×#117185522
C2×#117183792
C2×C13×#4842
C2×#323213