Finite Group Databasebeta

← C2×#13114899 #15862598

Subgroups — C2×#13114899 #15862598

Order 3328.

1374 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88161C211yesmaximal, characteristic
2C22×#88062C211yesmaximal, characteristic, complemented
3C22×#88047C211yesmaximal, characteristic, complemented
4C2×#11718794C211yesmaximal, characteristic
5C2×#11718627C211yesmaximal, characteristic
6#13114899C218yesmaximal, direct product factor
7C2×#11718146C211yesmaximal, characteristic, complemented
8C2×C13×#343C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic13C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C23×#1055C2211yescharacteristic
16C2×#88161—24no—
17C2×#88161—22no—
18C2×#88161C418yescomplemented
19C2×#88161C2214yes—
20C22×#6094—21no—
21C22×C8×D13—21no—
22#11718794—22no—
23#11718794C2214yes—
24C2×#88062—24no—
25C2×#88062C2214yescomplemented
26C2×#88061—21no—
27C2×#88056—21no—
28C2×#88050—21no—
29#11718627—22no—
30#11718627C2214yes—
31C2×#88049—21no—
32C2×#88047—21no—
33C2×#88047—21no—
34C2×#88047—22no—
35C2×#88047C2214yescomplemented
36C13×#343C2214yescomplemented
37#11718146C2214yescomplemented
38C23×C4×C13—21no—
39C23×C4×C13C2311yescharacteristic
40C22×C22⋊D13—21no—
41C23×Dic13—21no—
42C2×#6127—22no—
43C2×#6127—21no—
44C2×#6127—21no—
45C2×#6127—22no—
46C2×#6127C2×C414yes—
47C2×#6127D412yes—
48C2×#6127Q814yes—
49C2×#6127C2312yes—
50C22×D52D411yescharacteristic
51C22×C4×D13—21no—
52C22×Dic26D411yescharacteristic
53C2×C13×M16—22no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—22no—
57C2×C13×M16—22no—
58C2×C13×M16C2×C414yes—
59C2×C13×M16C2312yes—
60C2×C13×M16C2312yes—
61C22×C8×C13—21no—
62C22×C8×C13—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2312yes—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13—21no—
73C2×C4⋊Dic13—21no—
74C2×C4⋊Dic13C2312yes—
75C2×#6099—21no—
76C2×#6099—22no—
77C2×#6099—22no—
78C2×#6099C2312yes—
79C22×#1055—21no—
80C22×#1055C2×C414yes—
81C22×#1055D411yescharacteristic
82C22×#1055D411yescharacteristic
83C22×#1055D414yes—
84C22×#1055D412yes—
85C22×#1055C2312yes—
86#88161—216no—
87#88161—28no—
88#88161C2×C4116yescomplemented
89C2×#6094—28no—
90C2×#6094—24no—
91C2×C8×D13—28no—
92C2×C8×D13—24no—
93#88062—28no—
94#88061—24no—
95#88056—24no—
96#88050—24no—
97#88049—24no—
98#88047—24no—
99#88047—24no—
100C2×#1816—131nomaximal, Sylow
101C24×C13#4111yescharacteristic
102C23×D13—21no—
103C22×C4×C13—22no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13—82no—
107C22×C4×C13C22×C412yes—
108C22×C4×C13C2×D412yes—
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×Q812yes—
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13#4112yes—
116C22×C4×C13C2411yescharacteristic
117C2×C22⋊D13—24no—
118C2×C22⋊D13—22no—
119C2×C22⋊D13—24no—
120C2×C22⋊D13—22no—
121C22×Dic13—21no—
122C22×Dic13—22no—
123C22×Dic13—41no—
124C22×Dic13—41no—
125C22×Dic13—82no—
126#6127—24no—
127#6127—24no—
128#6127—24no—
129#6127—24no—
130#6127—24no—
131#6127—22no—
132#6127—22no—
133#6127C4⋊C418yes—
134#6127C22×C414yes—
135#6127C2×Q814yes—
136C2×D52—22no—
137C2×D52—21no—
138C2×D52C4⋊C414yes—
139C2×D52C2×D412yes—
140C2×C4×D13—24no—
141C2×C4×D13—22no—
142C2×C4×D13—24no—
143C2×C4×D13—22no—
144C2×Dic26—22no—
145C2×Dic26—21no—
146C2×Dic26C4⋊C414yes—
147C2×Dic26C2×D412yes—
148C13×M16—24no—
149C13×M16—22no—
150C13×M16—22no—
151C13×M16—22no—
152C13×M16—42no—
153C13×M16C22×C414yes—
154C2×C8×C13—24no—
155C2×C8×C13—22no—
156C2×C8×C13—22no—
157C2×C8×C13—42no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—41no—
161C13×C4⋊C4—41no—
162C4⋊Dic13—22no—
163C4⋊Dic13—22no—
164C4⋊Dic13—41no—
165C4⋊Dic13—41no—
166#6099—22no—
167#6099—22no—
168#6099—42no—
169C2×#1055—22no—
170C2×#1055—42no—
171C2×#1055C22⋊C414yes—
172C2×#1055C22⋊C414yes—
173C2×#1055C22⋊C418yes—
174C2×#1055C22×C414yes—
175C2×#1055C2×D412yes—
176C2×#1055C2×D412yes—
177C2×#1055C2×D414yes—
178#6094—216no—
179C8×D13—216no—
180C22×#131—131no—
181C22×#108—131no—
182C22×#107—131no—
183C2×#417—131no—
184C2×#417—131no—
185#1816—138no—
186C2×#343—131no—
187C2×#343D1311yescharacteristic, complemented
188C23×C13—22no—
189C23×C13—22no—
190C23×C13#11712yes—
191C23×C13#12111yescharacteristic
192C23×C13#12111yescharacteristic
193C23×C13C22⋊Q812yes—
194C23×C13C2×#4111yescharacteristic
195C22×D13—22no—
196C22×D13—24no—
197C22×D13—42no—
198C22×D13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—82no—
201C2×C4×C13—82no—
202C2×C4×C13—82no—
203C2×C4×C13C2×C22⋊C412yes—
204C2×C4×C13C2×C22⋊C412yes—
205C2×C4×C13C2×C4⋊C412yes—
206C2×C4×C13C2×C4⋊C412yes—
207C2×C4×C13#11712yes—
208C2×C4×C13#12112yes—
209C2×C4×C13#12112yes—
210C2×C4×C13#12111yescharacteristic
211C2×C4×C13#12111yescharacteristic
212C2×C4×C13C22⋊Q812yes—
213C2×C4×C13C22⋊Q812yes—
214C2×C4×C13C22⋊Q812yes—
215C2×C4×C13C23×C411yescharacteristic
216C2×C4×C13C22×D411yescharacteristic
217C2×C4×C13C22×D411yescharacteristic
218C2×C4×C13C22×D411yescharacteristic
219C2×C4×C13C22×Q811yescharacteristic
220C2×C4×C13C2×#4111yescharacteristic
221C22⋊D13—24no—
222C22⋊D13—24no—
223C22⋊D13—28no—
224C2×Dic13—22no—
225C2×Dic13—24no—
226C2×Dic13—42no—
227C2×Dic13—82no—
228C2×Dic13—82no—
229C2×Dic13—82no—
230D52—22no—
231D52—24no—
232D52C2×C4⋊C414yes—
233C4×D13—24no—
234C4×D13—24no—
235C4×D13—28no—
236Dic26—22no—
237Dic26—24no—
238Dic26C2×C4⋊C414yes—
239C8×C13—24no—
240C8×C13—42no—
241#1055—42no—
242#1055C2×C22⋊C414yes—
243#1055C2×C22⋊C414yes—
244C22×#41—131no—
245C2×#131—138no—
246C2×#131—134no—
247C2×#131—262no—
248C2×#131—264no—
249C22×M16—131no—
250C22×M16—261no—
251C22×M16C2×D1311yescharacteristic
252C22×M16C2×D1311yescharacteristic
253C23×C8—131no—
254C23×C8—261no—
255C22×C4⋊C4—131no—
256C22×C4⋊C4C2×D1311yescharacteristic
257C2×#108—134no—
258C2×#108—264no—
259C2×#107—134no—
260C2×#107—261no—
261C2×#107—261no—
262C2×#107—262no—
263#417—134no—
264#417—134no—
265#417—262no—
266#417—262no—
267C2×#103—261no—
268C2×#103—261no—
269C2×#102—261no—
270C2×#102—261no—
271#343—134no—
272#343C2×D1314yescomplemented
273C22×C13—24no—
274C22×C13—24no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13—21no—
279C22×C13#38012yes—
280C22×C13#38012yes—
281C22×C13#47212yes—
282C22×C13#47312yes—
283C22×C13C2×#11711yescharacteristic
284C22×C13C2×#12111yescharacteristic
285C22×C13C2×C22⋊Q811yescharacteristic
286C2×D13—24no—
287C2×D13—48no—
288C2×D13—42no—
289C2×D13—42no—
290C4×C13—82no—
291C4×C13#38012yes—
292C4×C13#38012yes—
293C4×C13C22×C22⋊C411yescharacteristic
294C4×C13C22×C4⋊C411yescharacteristic
295C4×C13C2×#12111yescharacteristic
296C4×C13C2×C22⋊Q811yescharacteristic
297Dic13—24no—
298Dic13—82no—
299C2×#41—134no—
300C2×#41—132no—
301C2×#41—134no—
302C2×#41—132no—
303C2×#41—261no—
304C2×#41—262no—
305C2×#41—262no—
306C2×#41—261no—
307C22×Q8—131no—
308C22×D4—131no—
309C22×D4—261no—
310C23×C4—21no—
311C23×C4—261no—
312C23×C4—261no—
313C23×C4C22×D1311yescharacteristic
314#131—1316no—
315#131—2616no—
316#131—268no—
317C2×M16—22no—
318C2×M16—21no—
319C2×M16—21no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—132no—
323C2×M16—268no—
324C2×M16—264no—
325C2×M16—261no—
326C2×M16—262no—
327C2×M16—262no—
328C2×M16C4×D1314yes—
329C2×M16C22×D1312yes—
330C2×M16C22×D1312yes—
331C22×C8—21no—
332C22×C8—21no—
333C22×C8—134no—
334C22×C8—131no—
335C22×C8—131no—
336C22×C8—132no—
337C22×C8—134no—
338C22×C8—132no—
339C22×C8—268no—
340C22×C8—264no—
341C22×C8—261no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—132no—
348C2×C4⋊C4—261no—
349C2×C4⋊C4—261no—
350C2×C4⋊C4—261no—
351C2×C4⋊C4—261no—
352C2×C4⋊C4—261no—
353C2×C4⋊C4C22×D1312yes—
354#108—268no—
355#107—264no—
356#107—264no—
357#103—264no—
358#103—264no—
359#102—264no—
360#102—264no—
361C2×C13—21no—
362C2×C13—21no—
363C2×C13—22no—
364C2×C13#181614yescomplemented
365C2×C13C2×#38011yescharacteristic
366C2×C13C2×#47211yescharacteristic
367C2×C13C2×#47311yescharacteristic
368D13—44no—
369C24—261no—
370C24#612711yescharacteristic
371#41—138no—
372#41—134no—
373#41—134no—
374#41—264no—
375#41—264no—
376#41—264no—
377#41—264no—
378#41—264no—
379#41—262no—
380#41—262no—
381C2×Q8—134no—
382C2×Q8—132no—
383C2×Q8—261no—
384C2×Q8—262no—
385C2×D4—134no—
386C2×D4—132no—
387C2×D4—264no—
388C2×D4—262no—
389C2×D4—264no—
390C2×D4—262no—
391C2×D4—262no—
392C2×D4—261no—
393C22×C4—22no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—82no—
397C22×C4—261no—
398C22×C4—264no—
399C22×C4—262no—
400C22×C4—264no—
401C22×C4—262no—
402C22×C4—262no—
403C22×C4—521no—
404C22×C4—521no—
405C22×C4—1042no—
406C22×C4C2×C4×D1312yes—
407C22×C4#612711yescharacteristic
408C22×C4#612712yes—
409C22×C4D4×D1312yes—
410C22×C4D4×D1311yescharacteristic
411C22×C4D4×D1311yescharacteristic
412C22×C4D4×D1311yescharacteristic
413C22×C4D4×D1311yescharacteristic
414C22×C4Q8×D1312yes—
415C22×C4C23×D1311yescharacteristic
416M16—24no—
417M16—22no—
418M16—22no—
419M16—22no—
420M16—42no—
421M16—2616no—
422M16—262no—
423M16—262no—
424M16—522no—
425M16C2×C4×D1314yes—
426C2×C8—24no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—42no—
430C2×C8—134no—
431C2×C8—134no—
432C2×C8—138no—
433C2×C8—134no—
434C2×C8—132no—
435C2×C8—132no—
436C2×C8—134no—
437C2×C8—2616no—
438C2×C8—262no—
439C2×C8—522no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4—262no—
445C4⋊C4—262no—
446C4⋊C4—521no—
447C4⋊C4—521no—
448C13C2×#181611yescharacteristic, complemented, Sylow
449C23—22no—
450C23—22no—
451C23—262no—
452C23—264no—
453C23—522no—
454C23—522no—
455C23#8812612yes—
456C23#8813811yescharacteristic
457C23#8813811yescharacteristic
458C23#8815012yes—
459C23C2×#612711yescharacteristic
460Q8—134no—
461Q8—262no—
462Q8—264no—
463D4—134no—
464D4—264no—
465D4—264no—
466D4—268no—
467D4—262no—
468D4—264no—
469C2×C4—42no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—262no—
474C2×C4—264no—
475C2×C4—264no—
476C2×C4—264no—
477C2×C4—268no—
478C2×C4—522no—
479C2×C4—1042no—
480C2×C4—1042no—
481C2×C4—1042no—
482C2×C4#8812612yes—
483C2×C4C22⋊C4×D1312yes—
484C2×C4C22⋊C4×D1312yes—
485C2×C4#8813812yes—
486C2×C4#8813812yes—
487C2×C4#8813811yescharacteristic
488C2×C4#8813811yescharacteristic
489C2×C4C4⋊C4×D1312yes—
490C2×C4C4⋊C4×D1312yes—
491C2×C4#8815012yes—
492C2×C4#8815012yes—
493C2×C4#8815012yes—
494C2×C4C22×C4×D1311yescharacteristic
495C2×C4C2×#612711yescharacteristic
496C2×C4C2×D4×D1311yescharacteristic
497C2×C4C2×D4×D1311yescharacteristic
498C2×C4C2×D4×D1311yescharacteristic
499C2×C4C2×Q8×D1311yescharacteristic
500C8—24no—
501C8—42no—
502C8—134no—
503C8—134no—
504C8—522no—
505C22—24no—
506C22—24no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—264no—
512C22—528no—
513C22—522no—
514C22—522no—
515C22#1171832812yes—
516C22#1171832812yes—
517C22#1171841012yes—
518C22#1171841612yes—
519C22C2×#8812611yescharacteristic
520C22C2×#8813811yescharacteristic
521C22C2×#8815011yescharacteristic
522C4—82no—
523C4—264no—
524C4—1042no—
525C4#1171832812yes—
526C4#1171832812yes—
527C4C2×C22⋊C4×D1311yescharacteristic
528C4C2×#8813811yescharacteristic
529C4C2×C4⋊C4×D1311yescharacteristic
530C4C2×#8815011yescharacteristic
531C2—21no—
532C2—21no—
533C2—22no—
534C2—524no—
535C2#1311489914yesdirect product factor
536C2C2×#1171832811yescharacteristic
537C2C2×#1171841011yescharacteristic
538C2C2×#1171841611yescharacteristic
subgroupG/H
centerC23#88138
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#343C2
socleC23×C13#121
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×#343D13
hypocenterC13C2×#1816
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. C22×#88062C2semidirect
3. C22×#88047C2semidirect
6. #13114899C2direct (N × H)
7. C2×#11718146C2semidirect
8. C2×C13×#343C2semidirect
18. C2×#88161C4semidirect
25. C2×#88062C22semidirect
35. C2×#88047C22semidirect
36. C13×#343C22semidirect
37. #11718146C22semidirect
88. #88161C2×C4semidirect
187. C2×#343D13semidirect
272. #343C2×D13semidirect
364. C2×C13#1816semidirect
448. C13C2×#1816semidirect
535. C2#13114899direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881612
C22×#880622
C22×#880472
C2×#117187942
C2×#117186272
#131148992
C2×#117181462
C2×C13×#3432
C2×#181613