Finite Group Databasebeta

← C2×#13113371 #15830158

Subgroups — C2×#13113371 #15830158

Order 3328.

1098 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719305C211yesmaximal, characteristic
2C2×#11718380C211yesmaximal, characteristic, complemented
3C2×#11718311C211yesmaximal, characteristic, complemented
4#13113371C218yesmaximal, direct product factor
5C2×#11718059C211yesmaximal, characteristic, complemented
6C2×#11718044C211yesmaximal, characteristic, complemented
7C2×#11718129C211yesmaximal, characteristic
8C2×C13×#327C211yesmaximal, characteristic
9C2×C13×#121C2211yescharacteristic
10C2×#88190C411yescharacteristic, complemented
11C2×#88189—21no—
12C2×D4×Dic13—21no—
13C2×D4×Dic13C411yescharacteristic, complemented
14C2×#88178C2211yescharacteristic
15C22×#6101—21no—
16C22×C4×Dic13C2211yescharacteristic
17#11719305—22no—
18#11719305—22no—
19#11719305C414yescomplemented
20#11719305C2214yes—
21C2×#88144C411yescharacteristic, complemented
22C2×#88141C411yescharacteristic, complemented
23C2×#88133—21no—
24C2×#88131—21no—
25C2×C13×C22⋊C8C2211yescharacteristic
26C2×C13×#95C2211yescharacteristic
27C2×#88071—21no—
28C2×#88071C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×#88055—21no—
31C2×#88054—21no—
32#11718380—22no—
33#11718380C2214yescomplemented
34#11718311—22no—
35#11718311C2214yescomplemented
36C13×#327C2214yes—
37#11718129C2214yes—
38#11718059C2214yescomplemented
39#11718044C2214yescomplemented
40C22×D4×C13—21no—
41C22×D4×C13C2×C411yescharacteristic
42C23×C4×C13—21no—
43C23×C4×C13C2311yescharacteristic
44C23×Dic13—21no—
45C23×Dic13—21no—
46C23×Dic13D411yescharacteristic
47C23×Dic13D411yescharacteristic
48C22×Dic26C2×C411yescharacteristic
49C22×C8×C13—21no—
50C13×#121—21no—
51C13×#121—21no—
52C13×#121C2×C412yes—
53C13×#121C2312yes—
54C2×C13×C4⋊C4C2×C411yescharacteristic
55C2×C13×C22⋊C4—21no—
56C2×C22⋊Dic13—21no—
57C2×C22⋊Dic13—21no—
58C2×C22⋊Dic13—21no—
59C2×C22⋊Dic13—21no—
60#88190—22no—
61#88190C2×C414yescomplemented
62#88189—24no—
63#88189—24no—
64D4×Dic13—24no—
65D4×Dic13—24no—
66D4×Dic13—22no—
67D4×Dic13C2×C414yescomplemented
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13C2×C411yescharacteristic
70#88178—21no—
71#88178—21no—
72#88178C2×C412yes—
73#88178C2312yes—
74C2×#6101—21no—
75C2×#6101—21no—
76C2×#6101—21no—
77C2×#6101—24no—
78C2×#6101—44no—
79C2×C4×Dic13—21no—
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2×C412yes—
83C2×C4×Dic13D412yes—
84C2×C4×Dic13D411yescharacteristic
85C2×C4×Dic13D411yescharacteristic
86C2×C4×Dic13D412yes—
87C2×C4×Dic13C2312yes—
88C22×#1055—21no—
89#88144—22no—
90#88144C2×C414yescomplemented
91#88141—22no—
92#88141C2×C414yescomplemented
93#88133—24no—
94#88133—24no—
95#88131—24no—
96#88131—24no—
97C13×C22⋊C8—21no—
98C13×C22⋊C8C2312yes—
99C13×#95—21no—
100C13×#95C2312yes—
101#88071—21no—
102#88071—24no—
103#88071C2312yes—
104C22⋊#1055—21no—
105C22⋊#1055C2312yes—
106#88055—24no—
107#88054—24no—
108C2×#1512—131nomaximal, Sylow
109C24×C13—21no—
110C24×C13C2×D411yescharacteristic
111C2×D4×C13—22no—
112C2×D4×C13—22no—
113C2×D4×C13—21no—
114C2×D4×C13—42no—
115C2×D4×C13—42no—
116C2×D4×C13—42no—
117C2×D4×C13C22×C412yes—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—42no—
121C22×C4×C13—42no—
122C22×C4×C13—42no—
123C22×C4×C13—42no—
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2411yescharacteristic
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—24no—
135C22×Dic13—22no—
136C22×Dic13—42no—
137C22×Dic13—44no—
138C22×Dic13—42no—
139C22×Dic13—42no—
140C22×Dic13—42no—
141C22×Dic13C22⋊C411yescharacteristic
142C22×Dic13C22⋊C411yescharacteristic
143C22×Dic13C22⋊C411yescharacteristic
144C22×Dic13C22⋊C411yescharacteristic
145C22×Dic13C22⋊C412yes—
146C22×Dic13C22⋊C412yes—
147C22×Dic13C2×D412yes—
148C22×Dic13C2×D412yes—
149C2×Dic26—21no—
150C2×Dic26—42no—
151C2×Dic26C22×C412yes—
152C2×C8×C13—22no—
153C2×C8×C13—42no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4C22×C412yes—
156C13×C22⋊C4—22no—
157C13×C22⋊C4—22no—
158C22⋊Dic13—22no—
159C22⋊Dic13—22no—
160C22⋊Dic13—24no—
161C22⋊Dic13—24no—
162C22⋊Dic13—24no—
163C4⋊Dic13—21no—
164C4⋊Dic13—24no—
165C4⋊Dic13C22×C412yes—
166#6101—22no—
167#6101—22no—
168#6101—24no—
169#6101—24no—
170#6101—48no—
171C4×Dic13—24no—
172C4×Dic13C22⋊C412yes—
173C4×Dic13C22⋊C412yes—
174C4×Dic13C22⋊C412yes—
175C4×Dic13C22⋊C412yes—
176C4×Dic13C22×C412yes—
177C4×Dic13C22×C412yes—
178C4×Dic13C2×D412yes—
179C4×Dic13C2×D412yes—
180C2×#1055—22no—
181C2×#1055—42no—
182C2×#529—131no—
183C2×#432—131no—
184C2×#382—131no—
185#1512—138no—
186C2×#328—131no—
187C2×#328—131no—
188C2×#327—131no—
189C2×#327D1311yescharacteristic
190C23×C13—22no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—42no—
194C23×C13—42no—
195C23×C13—42no—
196C23×C13C2×C22⋊C411yescharacteristic
197C23×C13C2×C22⋊C411yescharacteristic
198C23×C13AGL(1,ℤ/8)12yes—
199C23×C13#13712yes—
200C23×C13C22×D411yescharacteristic
201D4×C13—42no—
202D4×C13—42no—
203D4×C13—42no—
204D4×C13—42no—
205D4×C13—44no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—84no—
218C2×C4×C13C2×C22⋊C411yescharacteristic
219C2×C4×C13C2×C22⋊C411yescharacteristic
220C2×C4×C13C23×C411yescharacteristic
221C2×C4×C13C22×D411yescharacteristic
222C2×Dic13—22no—
223C2×Dic13—22no—
224C2×Dic13—24no—
225C2×Dic13—22no—
226C2×Dic13—22no—
227C2×Dic13—22no—
228C2×Dic13—22no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—42no—
232C2×Dic13—42no—
233C2×Dic13—48no—
234C2×Dic13—42no—
235C2×Dic13—42no—
236C2×Dic13—42no—
237C2×Dic13—42no—
238C2×Dic13—42no—
239C2×Dic13—84no—
240C2×Dic13C2×C22⋊C412yes—
241C2×Dic13C2×C22⋊C412yes—
242C2×Dic13C2×C22⋊C412yes—
243C2×Dic13C2×C22⋊C412yes—
244Dic26—42no—
245Dic26—42no—
246C8×C13—42no—
247#1055—42no—
248#529—134no—
249#529—134no—
250#529—262no—
251#529—262no—
252C2×#126—261no—
253C2×#125—131no—
254C2×#124—131no—
255C2×#123—261no—
256C2×C22⋊Q8—131no—
257C2×#121C2×D1311yescharacteristic
258C2×C4×Q8—131no—
259C2×C4×D4—131no—
260C2×C4×D4—261no—
261C2×#117—261no—
262C22×C4⋊C4—261no—
263C22×C42—131no—
264#432—134no—
265#432—262no—
266C2×C4⋊C8—261no—
267C2×C22⋊C8—131no—
268C2×C22⋊C8C2×D1311yescharacteristic
269C2×#97—261no—
270#382—134no—
271#382—262no—
272C2×#95—131no—
273C2×#95—261no—
274C2×#95C2×D1311yescharacteristic
275#328—134no—
276#328—134no—
277#327—134no—
278#327C2×D1314yes—
279C22×C13—21no—
280C22×C13—21no—
281C22×C13—21no—
282C22×C13—21no—
283C22×C13—24no—
284C22×C13—24no—
285C22×C13—42no—
286C22×C13—42no—
287C22×C13—42no—
288C22×C13—84no—
289C22×C13#41012yes—
290C22×C13#41712yes—
291C22×C13#41712yes—
292C22×C13#42112yes—
293C22×C13C22×C22⋊C411yescharacteristic
294C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C13C2×#13711yescharacteristic
296C4×C13—21no—
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—21no—
300C4×C13—42no—
301C4×C13—82no—
302Dic13—22no—
303Dic13—22no—
304Dic13—22no—
305Dic13—22no—
306Dic13—42no—
307Dic13—42no—
308Dic13—82no—
309C22×Q8—131no—
310C22×D4—21no—
311C22×D4C4×D1311yescharacteristic
312C23×C4—21no—
313C23×C4—131no—
314C23×C4—131no—
315C23×C4—261no—
316C23×C4—261no—
317C23×C4C22×D1311yescharacteristic
318C22×C8—21no—
319C22×C8—261no—
320#126—264no—
321#126—264no—
322#125—134no—
323#125—262no—
324#124—134no—
325#124—262no—
326#123—264no—
327#123—264no—
328C22⋊Q8—132no—
329C22⋊Q8—132no—
330C22⋊Q8—261no—
331C22⋊Q8—261no—
332#121—21no—
333#121—21no—
334#121C4×D1312yes—
335#121C22×D1312yes—
336C4×Q8—134no—
337C4×Q8—262no—
338C4×D4—134no—
339C4×D4—262no—
340C4×D4—264no—
341C4×D4—264no—
342#117—264no—
343#117—264no—
344C2×C4⋊C4—131no—
345C2×C4⋊C4—261no—
346C2×C4⋊C4—261no—
347C2×C4⋊C4—261no—
348C2×C4⋊C4—261no—
349C2×C4⋊C4—264no—
350C2×C4⋊C4—524no—
351C2×C4⋊C4C4×D1311yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—261no—
354C2×C22⋊C4—261no—
355C2×C22⋊C4—261no—
356C2×C22⋊C4—261no—
357C2×C42—131no—
358C2×C42—131no—
359C2×C42—132no—
360C2×C42—131no—
361C2×C42—131no—
362C2×C42—132no—
363C2×C42—132no—
364C2×C42—132no—
365C2×C42—261no—
366C4⋊C8—264no—
367C22⋊C8—21no—
368C22⋊C8—132no—
369C22⋊C8—261no—
370C22⋊C8C22×D1312yes—
371#97—264no—
372#95—21no—
373#95—132no—
374#95—264no—
375#95—261no—
376#95C22×D1312yes—
377C2×C13—21no—
378C2×C13—21no—
379C2×C13—22no—
380C2×C13—82no—
381C2×C13#151214yescomplemented
382C2×C13C2×#41011yescharacteristic
383C2×C13C2×#41711yescharacteristic
384C2×C13C2×#42111yescharacteristic
385C24—21no—
386C24D4×D1311yescharacteristic
387C2×Q8—132no—
388C2×Q8—261no—
389C2×Q8—522no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4C2×C4×D1312yes—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—132no—
404C22×C4—131no—
405C22×C4—131no—
406C22×C4—131no—
407C22×C4—131no—
408C22×C4—132no—
409C22×C4—132no—
410C22×C4—132no—
411C22×C4—264no—
412C22×C4—262no—
413C22×C4—262no—
414C22×C4—261no—
415C22×C4—261no—
416C22×C4—262no—
417C22×C4—522no—
418C22×C4—524no—
419C22×C4—522no—
420C22×C4—522no—
421C22×C4—522no—
422C22×C4C2×C4×D1311yescharacteristic
423C22×C4C2×C4×D1311yescharacteristic
424C22×C4D4×D1311yescharacteristic
425C22×C4D4×D1311yescharacteristic
426C22×C4D4×D1311yescharacteristic
427C22×C4C23×D1311yescharacteristic
428C2×C8—22no—
429C2×C8—42no—
430C2×C8—262no—
431C2×C8—522no—
432C4⋊C4—21no—
433C4⋊C4—132no—
434C4⋊C4—264no—
435C4⋊C4—264no—
436C4⋊C4—264no—
437C4⋊C4—261no—
438C4⋊C4—262no—
439C4⋊C4—262no—
440C4⋊C4—528no—
441C4⋊C4C2×C4×D1312yes—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—264no—
445C22⋊C4—264no—
446C22⋊C4—264no—
447C22⋊C4—262no—
448C22⋊C4—262no—
449C42—132no—
450C42—132no—
451C42—132no—
452C42—132no—
453C42—132no—
454C42—132no—
455C42—132no—
456C42—132no—
457C42—264no—
458C13C2×#151211yescharacteristic, complemented, Sylow
459C23—22no—
460C23—22no—
461C23—22no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23C22⋊C4×D1311yescharacteristic
466C23C22⋊C4×D1311yescharacteristic
467C23#8816512yes—
468C23#8816912yes—
469C23C2×D4×D1311yescharacteristic
470Q8—522no—
471Q8—522no—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—42no—
476D4—42no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4—132no—
490C2×C4—132no—
491C2×C4—132no—
492C2×C4—132no—
493C2×C4—264no—
494C2×C4—262no—
495C2×C4—262no—
496C2×C4—262no—
497C2×C4—262no—
498C2×C4—262no—
499C2×C4—262no—
500C2×C4—262no—
501C2×C4—262no—
502C2×C4—522no—
503C2×C4—522no—
504C2×C4—528no—
505C2×C4—522no—
506C2×C4—522no—
507C2×C4—522no—
508C2×C4—522no—
509C2×C4—522no—
510C2×C4—1044no—
511C2×C4C22⋊C4×D1311yescharacteristic
512C2×C4C22⋊C4×D1311yescharacteristic
513C2×C4C22×C4×D1311yescharacteristic
514C2×C4C2×D4×D1311yescharacteristic
515C8—42no—
516C8—522no—
517C22—24no—
518C22—24no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—84no—
527C22#1171840112yes—
528C22#1171843212yes—
529C22#1171843212yes—
530C22#1171848212yes—
531C22C2×C22⋊C4×D1311yescharacteristic
532C22C2×#8816511yescharacteristic
533C22C2×#8816911yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—42no—
539C4—82no—
540C4—262no—
541C4—262no—
542C4—262no—
543C4—262no—
544C4—522no—
545C4—522no—
546C4—1042no—
547C2—21no—
548C2—22no—
549C2—21no—
550C2—82no—
551C2#1311337114yesdirect product factor
552C2C2×#1171840111yescharacteristic
553C2C2×#1171843211yescharacteristic
554C2C2×#1171848211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#327C2
socleC23×C13C2×C22⋊C4
prime radicalC2×C13×#121C22
cosocleC22×C4×C13C24
hypercenterC2×#327D13
hypocenterC13C2×#1512
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#11718380C2semidirect
3. C2×#11718311C2semidirect
4. #13113371C2direct (N × H)
5. C2×#11718059C2semidirect
6. C2×#11718044C2semidirect
10. C2×#88190C4semidirect
13. C2×D4×Dic13C4semidirect
19. #11719305C4semidirect
21. C2×#88144C4semidirect
22. C2×#88141C4semidirect
33. #11718380C22semidirect
35. #11718311C22semidirect
38. #11718059C22semidirect
39. #11718044C22semidirect
61. #88190C2×C4semidirect
67. D4×Dic13C2×C4semidirect
90. #88144C2×C4semidirect
92. #88141C2×C4semidirect
381. C2×C13#1512semidirect
458. C13C2×#1512semidirect
551. C2#13113371direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193052
C2×#117183802
C2×#117183112
#131133712
C2×#117180592
C2×#117180442
C2×#117181292
C2×C13×#3272
C2×#151213