Finite Group Databasebeta

← C2×#13114925 #15862704

Subgroups — C2×#13114925 #15862704

Order 3328.

1878 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D13C211yesmaximal, characteristic
2C22×#88060C211yesmaximal, characteristic
3C2×#11718648C211yesmaximal, characteristic
4#13114925C218yesmaximal, direct product factor
5C2×#11718143C211yesmaximal, characteristic, complemented
6C2×#11718121C211yesmaximal, characteristic, complemented
7C2×#11718121C211yesmaximal, characteristic, complemented
8C2×C13×#340C211yesmaximal, characteristic, complemented
9C23×C4×D13—21no—
10C23×C4×D13C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×#6103—21no—
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6101—21no—
18C23×#1055C2211yescharacteristic
19C2×C4⋊C4×D13—22no—
20C2×C4⋊C4×D13—24no—
21C2×C4⋊C4×D13C418yescomplemented
22C2×C4⋊C4×D13C2214yes—
23C2×#88071—21no—
24C2×#88060—24no—
25C2×#88060C2214yes—
26#11718648—22no—
27#11718648C2214yes—
28C13×#340C2214yescomplemented
29#11718143C2214yescomplemented
30#11718121C2214yescomplemented
31#11718121C2214yescomplemented
32C24×D13D411yescharacteristic
33C23×C4×C13—21no—
34C23×C4×C13—21no—
35C23×C4×C13C2311yescharacteristic
36C23×Dic13—21no—
37C23×Dic13—21no—
38C23×Dic13D411yescharacteristic
39C22×C4×D13—22no—
40C22×C4×D13—22no—
41C22×C4×D13—22no—
42C22×C4×D13—22no—
43C22×C4×D13—28no—
44C22×C4×D13—24no—
45C22×C4×D13—44no—
46C22×C4×D13—44no—
47C22×C4×D13C2×C414yes—
48C22×C4×D13D412yes—
49C22×C4×D13D414yes—
50C22×C4×D13C2312yes—
51C22×C8×C13—22no—
52C22×C8×C13—22no—
53C22×C8×C13—22no—
54C22×C8×C13C2312yes—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4C2×C414yes—
61C2×C13×C4⋊C4C2312yes—
62C2×C13×C4⋊C4C2312yes—
63C2×#6103—24no—
64C2×#6103—44no—
65C2×C4⋊Dic13—21no—
66C2×C4⋊Dic13—22no—
67C2×C4⋊Dic13—22no—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13C2×C414yes—
71C2×C4⋊Dic13C2312yes—
72C2×C4⋊Dic13C2312yes—
73C2×#6101—28no—
74C2×#6101—24no—
75C22×#1055—22no—
76C22×#1055—22no—
77C22×#1055—22no—
78C22×#1055C2312yes—
79C4⋊C4×D13—216no—
80C4⋊C4×D13—28no—
81C4⋊C4×D13C2×C4116yescomplemented
82#88071—24no—
83#88060—28no—
84C2×#1824—131nomaximal, Sylow
85C24×C13C2×D411yescharacteristic
86C23×D13—22no—
87C23×D13—22no—
88C23×D13—22no—
89C23×D13—22no—
90C23×D13C22⋊C414yes—
91C23×D13SD1614yes—
92C23×D13Q1614yes—
93C23×D13C2×D412yes—
94C22×C4×C13—24no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—42no—
98C22×C4×C13—42no—
99C22×C4×C13—42no—
100C22×C4×C13—42no—
101C22×C4×C13—42no—
102C22×C4×C13C22×C412yes—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D412yes—
105C22×C4×C13#4112yes—
106C22×C4×C13#4112yes—
107C22×C4×C13#4112yes—
108C22×C4×C13#4112yes—
109C22×C4×C13C2411yescharacteristic
110C22×Dic13—22no—
111C22×Dic13—22no—
112C22×Dic13—24no—
113C22×Dic13—22no—
114C22×Dic13—22no—
115C22×Dic13—42no—
116C22×Dic13—42no—
117C22×Dic13—42no—
118C22×Dic13—42no—
119C22×Dic13—42no—
120C22×Dic13C22⋊C414yes—
121C22×Dic13C2×D412yes—
122C2×C4×D13—28no—
123C2×C4×D13—28no—
124C2×C4×D13—28no—
125C2×C4×D13—28no—
126C2×C4×D13—24no—
127C2×C4×D13—24no—
128C2×C4×D13—22no—
129C2×C4×D13—22no—
130C2×C4×D13—22no—
131C2×C4×D13—22no—
132C2×C4×D13—216no—
133C2×C4×D13—48no—
134C2×C4×D13—48no—
135C2×C4×D13—432no—
136C2×C4×D13C22⋊C418yes—
137C2×C4×D13C22×C414yes—
138C2×C4×D13C2×D414yes—
139C2×C8×C13—22no—
140C2×C8×C13—22no—
141C2×C8×C13—22no—
142C2×C8×C13—44no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4—22no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—42no—
148C13×C4⋊C4C22×C414yes—
149#6103—48no—
150C4⋊Dic13—24no—
151C4⋊Dic13—22no—
152C4⋊Dic13—22no—
153C4⋊Dic13—22no—
154C4⋊Dic13—42no—
155C4⋊Dic13C22×C414yes—
156#6101—216no—
157C2×#1055—22no—
158C2×#1055—22no—
159C2×#1055—22no—
160C2×#1055—44no—
161C23×C4⋊C4—131no—
162C22×C22⋊C8—131no—
163C2×#380—131no—
164#1824—138no—
165C2×#340—131no—
166C2×#340—131no—
167C2×#340—131no—
168C2×#340D1311yescharacteristic, complemented
169C23×C13C2×C22⋊C412yes—
170C23×C13#12312yes—
171C23×C13#12312yes—
172C23×C13C2×SD1612yes—
173C23×C13C2×Q1612yes—
174C23×C13AGL(1,ℤ/8)12yes—
175C23×C13AGL(1,ℤ/8)12yes—
176C23×C13C22×D411yescharacteristic
177C22×D13—22no—
178C22×D13—22no—
179C22×D13—22no—
180C22×D13—22no—
181C22×D13—28no—
182C22×D13—28no—
183C22×D13—28no—
184C22×D13—28no—
185C22×D13—28no—
186C22×D13—28no—
187C22×D13#103116yes—
188C22×D13C2×C22⋊C414yes—
189C22×D13C2×SD1614yes—
190C22×D13C2×Q1614yes—
191C2×C4×C13—24no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—48no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—84no—
199C2×C4×C13C2×C22⋊C412yes—
200C2×C4×C13#11714yes—
201C2×C4×C13#11714yes—
202C2×C4×C13#12314yes—
203C2×C4×C13#12314yes—
204C2×C4×C13#12312yes—
205C2×C4×C13#12312yes—
206C2×C4×C13C23×C411yescharacteristic
207C2×C4×C13C22×D411yescharacteristic
208C2×C4×C13C2×#4111yescharacteristic
209C2×C4×C13C2×#4111yescharacteristic
210C2×C4×C13C2×#4111yescharacteristic
211C2×C4×C13C2×#4111yescharacteristic
212C2×Dic13—22no—
213C2×Dic13—22no—
214C2×Dic13—28no—
215C2×Dic13—24no—
216C2×Dic13—42no—
217C2×Dic13—42no—
218C2×Dic13—48no—
219C2×Dic13—42no—
220C2×Dic13—42no—
221C2×Dic13—42no—
222C2×Dic13—84no—
223C2×Dic13C2×C22⋊C414yes—
224C4×D13—24no—
225C4×D13—24no—
226C4×D13—24no—
227C4×D13—24no—
228C4×D13—216no—
229C4×D13—432no—
230C8×C13—42no—
231#1055—42no—
232C24×C4—131no—
233C24×C4—261no—
234C23×C8—131no—
235C23×C8C2×D1311yescharacteristic
236C22×C4⋊C4—131no—
237C22×C4⋊C4—138no—
238C22×C4⋊C4—134no—
239C22×C4⋊C4—131no—
240C22×C4⋊C4—262no—
241C22×C4⋊C4—264no—
242C22×C4⋊C4—261no—
243C22×C4⋊C4C2×D1311yescharacteristic
244C22×C4⋊C4C2×D1311yescharacteristic
245C22×C22⋊C4—261no—
246C2×C22⋊C8—134no—
247C2×C22⋊C8—264no—
248#380—134no—
249#380—262no—
250C2×#95—261no—
251#340—134no—
252#340—134no—
253#340—134no—
254#340C2×D1314yescomplemented
255C22×C13#38114yes—
256C22×C13C2×#10314yes—
257C22×C13#41814yes—
258C22×C13#48114yes—
259C22×C13#48114yes—
260C22×C13#48414yes—
261C22×C13#48414yes—
262C22×C13C22×C22⋊C411yescharacteristic
263C22×C13C2×#12311yescharacteristic
264C22×C13C2×#12311yescharacteristic
265C22×C13C22×SD1611yescharacteristic
266C22×C13C22×Q1611yescharacteristic
267C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
269C2×D13—24no—
270C2×D13—24no—
271C2×D13—24no—
272C2×D13—24no—
273C2×D13—232no—
274C2×D13—24no—
275C2×D13—24no—
276C2×D13C2×#10318yes—
277C4×C13—44no—
278C4×C13—82no—
279C4×C13#38114yes—
280C4×C13C2×#11711yescharacteristic
281C4×C13C2×#11711yescharacteristic
282C4×C13C2×#12311yescharacteristic
283C4×C13C2×#12311yescharacteristic
284Dic13—24no—
285Dic13—44no—
286Dic13—82no—
287C25—131no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—131no—
291C23×C4—134no—
292C23×C4—132no—
293C23×C4—134no—
294C23×C4—132no—
295C23×C4—268no—
296C23×C4—264no—
297C23×C4—262no—
298C23×C4—262no—
299C23×C4—262no—
300C23×C4—262no—
301C23×C4—261no—
302C23×C4—261no—
303C23×C4—524no—
304C23×C4—524no—
305C23×C4C22×D1311yescharacteristic
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—132no—
310C22×C8—262no—
311C22×C8—262no—
312C22×C8—262no—
313C22×C8C22×D1312yes—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—134no—
320C2×C4⋊C4—132no—
321C2×C4⋊C4—1316no—
322C2×C4⋊C4—132no—
323C2×C4⋊C4—2616no—
324C2×C4⋊C4—268no—
325C2×C4⋊C4—268no—
326C2×C4⋊C4—264no—
327C2×C4⋊C4—261no—
328C2×C4⋊C4—262no—
329C2×C4⋊C4—262no—
330C2×C4⋊C4—262no—
331C2×C4⋊C4—261no—
332C2×C4⋊C4C4×D1314yes—
333C2×C4⋊C4C22×D1312yes—
334C2×C4⋊C4C22×D1312yes—
335C2×C22⋊C4—264no—
336C2×C22⋊C4—524no—
337C22⋊C8—268no—
338#95—264no—
339C2×C13#182418yescomplemented
340C2×C13C2×#38111yescharacteristic
341C2×C13C22×#10311yescharacteristic
342C2×C13C2×#41811yescharacteristic
343C2×C13C2×#48111yescharacteristic
344C2×C13C2×#48111yescharacteristic
345C2×C13C2×#48411yescharacteristic
346C2×C13C2×#48411yescharacteristic
347D13—28no—
348C24—134no—
349C24—134no—
350C24—134no—
351C24—132no—
352C24—262no—
353C24—262no—
354C24—262no—
355C24—262no—
356C24D4×D1311yescharacteristic
357C22×C4—24no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—134no—
366C22×C4—132no—
367C22×C4—138no—
368C22×C4—134no—
369C22×C4—134no—
370C22×C4—2616no—
371C22×C4—262no—
372C22×C4—262no—
373C22×C4—268no—
374C22×C4—264no—
375C22×C4—268no—
376C22×C4—268no—
377C22×C4—264no—
378C22×C4—268no—
379C22×C4—262no—
380C22×C4—262no—
381C22×C4—262no—
382C22×C4—262no—
383C22×C4—264no—
384C22×C4—262no—
385C22×C4—262no—
386C22×C4—5232no—
387C22×C4—528no—
388C22×C4—528no—
389C22×C4—522no—
390C22×C4—522no—
391C22×C4—522no—
392C22×C4—522no—
393C22×C4—522no—
394C22×C4C2×C4×D1312yes—
395C22×C4#612712yes—
396C22×C4#612712yes—
397C22×C4D4×D1311yescharacteristic
398C22×C4D4×D1312yes—
399C22×C4#612912yes—
400C22×C4#613112yes—
401C22×C4C23×D1311yescharacteristic
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—44no—
406C2×C8—262no—
407C2×C8—262no—
408C2×C8—262no—
409C2×C8—524no—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—42no—
415C4⋊C4—134no—
416C4⋊C4—2616no—
417C4⋊C4—264no—
418C4⋊C4—262no—
419C4⋊C4—262no—
420C4⋊C4—262no—
421C4⋊C4—522no—
422C4⋊C4C2×C4×D1314yes—
423C22⋊C4—528no—
424C13C2×#182411yescharacteristic, complemented, Sylow
425C23—134no—
426C23—134no—
427C23—134no—
428C23—1316no—
429C23—262no—
430C23—268no—
431C23—262no—
432C23—268no—
433C23—262no—
434C23—262no—
435C23—268no—
436C23—268no—
437C23—268no—
438C23—268no—
439C23C22⋊C4×D1312yes—
440C23#8813712yes—
441C23#8814812yes—
442C23#8816512yes—
443C23SD16×D1312yes—
444C23#8816812yes—
445C23Q16×D1312yes—
446C23C2×D4×D1311yescharacteristic
447C2×C4—24no—
448C2×C4—48no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—84no—
455C2×C4—134no—
456C2×C4—262no—
457C2×C4—262no—
458C2×C4—268no—
459C2×C4—264no—
460C2×C4—264no—
461C2×C4—264no—
462C2×C4—264no—
463C2×C4—2616no—
464C2×C4—264no—
465C2×C4—5232no—
466C2×C4—528no—
467C2×C4—522no—
468C2×C4—522no—
469C2×C4—522no—
470C2×C4—522no—
471C2×C4—522no—
472C2×C4—1044no—
473C2×C4#8812614yes—
474C2×C4C22⋊C4×D1312yes—
475C2×C4#8813714yes—
476C2×C4#8813712yes—
477C2×C4#8814614yes—
478C2×C4#8814814yes—
479C2×C4#8814812yes—
480C2×C4C22×C4×D1311yescharacteristic
481C2×C4C2×#612711yescharacteristic
482C2×C4C2×#612711yescharacteristic
483C2×C4C2×D4×D1311yescharacteristic
484C2×C4C2×#612911yescharacteristic
485C2×C4C2×#613111yescharacteristic
486C8—42no—
487C8—522no—
488C22—138no—
489C22—264no—
490C22—264no—
491C22—2632no—
492C22—264no—
493C22—264no—
494C22—264no—
495C22—264no—
496C22#1171832514yes—
497C22#1171843114yes—
498C22#1171843814yes—
499C22D13×#10314yes—
500C22#1171847014yes—
501C22#1171852414yes—
502C22#1171854514yes—
503C22C2×C22⋊C4×D1311yescharacteristic
504C22C2×#8813711yescharacteristic
505C22C2×#8814811yescharacteristic
506C22C2×#8816511yescharacteristic
507C22C2×SD16×D1311yescharacteristic
508C22C2×#8816811yescharacteristic
509C22C2×Q16×D1311yescharacteristic
510C4—44no—
511C4—82no—
512C4—264no—
513C4—524no—
514C4—1042no—
515C4#1171832514yes—
516C4C2×#8812611yescharacteristic
517C4C2×#8813711yescharacteristic
518C4C2×#8814611yescharacteristic
519C4C2×#8814811yescharacteristic
520C2—268no—
521C2#1311492518yesdirect product factor
522C2C2×#1171832511yescharacteristic
523C2C2×D13×#10311yescharacteristic
524C2C2×#1171843111yescharacteristic
525C2C2×#1171843811yescharacteristic
526C2C2×#1171852411yescharacteristic
527C2C2×#1171847011yescharacteristic
528C2C2×#1171854511yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#340C2
socleC24×C13C2×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenterC2×#340D13
hypocenterC13C2×#1824
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #13114925C2direct (N × H)
5. C2×#11718143C2semidirect
6. C2×#11718121C2semidirect
7. C2×#11718121C2semidirect
8. C2×C13×#340C2semidirect
21. C2×C4⋊C4×D13C4semidirect
28. C13×#340C22semidirect
29. #11718143C22semidirect
30. #11718121C22semidirect
31. #11718121C22semidirect
81. C4⋊C4×D13C2×C4semidirect
168. C2×#340D13semidirect
254. #340C2×D13semidirect
339. C2×C13#1824semidirect
424. C13C2×#1824semidirect
521. C2#13114925direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D132
C22×#880602
C2×#117186482
#131149252
C2×#117181432
C2×#117181212
C2×C13×#3402
C2×#182413