Finite Group Databasebeta

← C2×#13115061 #15863772

Subgroups — C2×#13115061 #15863772

Order 3328.

1566 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719209C211yesmaximal, characteristic
2C2×#11718625C211yesmaximal, characteristic, complemented
3C22×#88045C211yesmaximal, characteristic
4C2×#11718627C211yesmaximal, characteristic
5#13115061C218yesmaximal, direct product factor
6C2×#11718122C211yesmaximal, characteristic, complemented
7C2×#11718115C211yesmaximal, characteristic, complemented
8C2×C13×#384C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C22×C13×C4⋊C4—22no—
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C2×C4×C22⋊D13—22no—
15C2×#88180C2211yescharacteristic
16C22×#6099C2211yescharacteristic
17C22×#6099C2211yescharacteristic
18#11719209—22no—
19#11719209—22no—
20#11719209—22no—
21#11719209C2214yes—
22C2×#88147—21no—
23C2×#88146—21no—
24C2×C4⋊C4×D13—21no—
25C2×#88141—21no—
26C13×#384—22no—
27C13×#384C2214yescomplemented
28C2×#88050—21no—
29#11718627—22no—
30#11718627C2214yes—
31C2×#88049—21no—
32#11718625—22no—
33#11718625C2214yescomplemented
34C2×#88048—21no—
35C2×#88047—21no—
36C2×#88045C418yescomplemented
37C2×#88045C2214yes—
38#11718122C2214yescomplemented
39#11718115C2214yescomplemented
40C23×C4×C13—21no—
41C23×C4×C13—21no—
42C23×C4×C13D412yes—
43C23×C4×C13C2311yescharacteristic
44C22×C22⋊D13—21no—
45C2×#6127—21no—
46C2×#6127—21no—
47C2×#6127—22no—
48C2×#6127—22no—
49C2×#6127C2×C414yes—
50C2×#6127D412yes—
51C2×#6127Q814yes—
52C2×#6127C2312yes—
53C22×D52D411yescharacteristic
54C22×C4×D13—21no—
55C22×C4×D13—22no—
56C22×Dic26D411yescharacteristic
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—28no—
67C2×C13×C4⋊C4—48no—
68C2×C13×C4⋊C4D412yes—
69C2×C13×C4⋊C4C2312yes—
70C2×C13×C4⋊C4C2312yes—
71C2×C42×C13—21no—
72C2×C42×C13—22no—
73C2×C42×C13C2×C414yescomplemented
74C2×C42×C13C2312yes—
75C2×C22⋊Dic13—21no—
76C4×C22⋊D13—28no—
77C4×C22⋊D13—28no—
78C2×#6103—22no—
79#88180—21no—
80#88180—21no—
81#88180D412yes—
82#88180C2312yes—
83C2×C4⋊Dic13D411yescharacteristic
84C2×C4⋊Dic13D411yescharacteristic
85C2×#6101—22no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—21no—
88C2×#6099—21no—
89C2×#6099—22no—
90C2×#6099—21no—
91C2×#6099—22no—
92C2×#6099—22no—
93C2×#6099C2×C414yescomplemented
94C2×#6099C2312yes—
95C2×#6099C2312yes—
96C22×#1055—21no—
97C22×#1055—21no—
98#88147—24no—
99#88147—24no—
100#88146—24no—
101#88146—24no—
102C4⋊C4×D13—24no—
103C4⋊C4×D13—24no—
104#88141—24no—
105#88141—24no—
106#88050—24no—
107#88049—24no—
108#88048—24no—
109#88047—24no—
110#88045C2×C4116yescomplemented
111C2×#1859—131nomaximal, Sylow
112C24×C13C2×D411yescharacteristic
113C23×D13—21no—
114C22×C4×C13—24no—
115C22×C4×C13—24no—
116C22×C4×C13—24no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—44no—
122C22×C4×C13—44no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13C22×C412yes—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D414yes—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×Q812yes—
133C22×C4×C13#4112yes—
134C22×C4×C13#4112yes—
135C22×C4×C13C2411yescharacteristic
136C2×C22⋊D13—24no—
137C2×C22⋊D13—22no—
138C2×C22⋊D13—24no—
139C2×C22⋊D13—22no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143#6127—24no—
144#6127—24no—
145#6127—24no—
146#6127—24no—
147#6127—24no—
148#6127—22no—
149#6127—22no—
150#6127C4⋊C418yescomplemented
151#6127C22×C414yes—
152#6127C2×Q814yes—
153C2×D52—21no—
154C2×D52—22no—
155C2×D52C4⋊C414yescomplemented
156C2×D52C2×D412yes—
157C2×C4×D13—24no—
158C2×C4×D13—22no—
159C2×C4×D13—24no—
160C2×C4×D13—22no—
161C2×C4×D13—28no—
162C2×C4×D13—84no—
163C2×Dic26—21no—
164C2×Dic26—22no—
165C2×Dic26C4⋊C414yescomplemented
166C2×Dic26C2×D412yes—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—416no—
174C13×C4⋊C4—41no—
175C13×C4⋊C4—41no—
176C42×C13—24no—
177C42×C13—22no—
178C42×C13C22×C414yescomplemented
179C22⋊Dic13—22no—
180C22⋊Dic13—22no—
181#6103—28no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13C2×D412yes—
185C4⋊Dic13C2×D412yes—
186#6101—28no—
187C4×Dic13—28no—
188C4×Dic13—22no—
189C4×Dic13—22no—
190#6099—24no—
191#6099—22no—
192#6099—22no—
193#6099—22no—
194#6099—42no—
195#6099C22×C414yescomplemented
196C2×#1055—24no—
197C2×#1055—22no—
198C2×#1055—22no—
199C2×#1055—42no—
200C2×#520—131no—
201C2×#428—131no—
202C22×#104—131no—
203C2×#417—131no—
204C2×#384D1311yescharacteristic, complemented
205#1859—138no—
206C2×#343—131no—
207C2×#339—131no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13C4×D412yes—
211C23×C13#12011yescharacteristic
212C23×C13#12011yescharacteristic
213C23×C13C22⋊Q812yes—
214C23×C13C22×D411yescharacteristic
215C22×D13—22no—
216C22×D13—24no—
217C22×D13—42no—
218C22×D13—42no—
219C2×C4×C13—24no—
220C2×C4×C13—216no—
221C2×C4×C13—24no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—44no—
225C2×C4×C13—44no—
226C2×C4×C13—44no—
227C2×C4×C13—42no—
228C2×C4×C13—82no—
229C2×C4×C13—82no—
230C2×C4×C13—82no—
231C2×C4×C13C2×C4⋊C412yes—
232C2×C4×C13C2×C4⋊C412yes—
233C2×C4×C13C4×D412yes—
234C2×C4×C13C4×D412yes—
235C2×C4×C13C4×D412yes—
236C2×C4×C13#12011yescharacteristic
237C2×C4×C13#12011yescharacteristic
238C2×C4×C13C22⋊Q812yes—
239C2×C4×C13C22⋊Q812yes—
240C2×C4×C13C22⋊Q812yes—
241C2×C4×C13#12312yes—
242C2×C4×C13#12312yes—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C22×Q811yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C22⋊D13—24no—
250C22⋊D13—24no—
251C22⋊D13—28no—
252C2×Dic13—22no—
253C2×Dic13—24no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258D52—22no—
259D52—24no—
260D52C2×C4⋊C414yescomplemented
261C4×D13—24no—
262C4×D13—24no—
263C4×D13—28no—
264C4×D13—88no—
265Dic26—22no—
266Dic26—24no—
267Dic26C2×C4⋊C414yescomplemented
268#1055—24no—
269#1055—42no—
270C22×#41—131no—
271C22×M16—131no—
272C22×M16—131no—
273#520—134no—
274#520—262no—
275#520—262no—
276#520—262no—
277C2×C4×Q8—261no—
278C2×C4×D4—261no—
279C2×C4×D4—262no—
280C2×#117—131no—
281C2×#117—261no—
282C22×C4⋊C4—22no—
283C22×C4⋊C4—261no—
284C22×C4⋊C4C2×D1311yescharacteristic
285C22×C4⋊C4C2×D1311yescharacteristic
286C22×C42C2×D1311yescharacteristic
287#428—134no—
288#428—262no—
289C2×#107—261no—
290C2×#106—261no—
291C2×#104—138no—
292C2×#104—134no—
293#417—134no—
294#417—262no—
295C2×#103—261no—
296C2×#102—261no—
297#384—22no—
298#384C2×D1314yescomplemented
299#343—134no—
300#339—134no—
301C22×C13—24no—
302C22×C13—24no—
303C22×C13—21no—
304C22×C13—21no—
305C22×C13—21no—
306C22×C13—21no—
307C22×C13#38512yes—
308C22×C13#38512yes—
309C22×C13#45312yes—
310C22×C13#45612yes—
311C22×C13C2×C4×D411yescharacteristic
312C22×C13C2×#12011yescharacteristic
313C22×C13C2×C22⋊Q811yescharacteristic
314C2×D13—24no—
315C2×D13—48no—
316C2×D13—42no—
317C2×D13—42no—
318C4×C13—28no—
319C4×C13—44no—
320C4×C13—82no—
321C4×C13#38512yes—
322C4×C13#38512yes—
323C4×C13C22×C4⋊C411yescharacteristic
324C4×C13C2×C4×D411yescharacteristic
325C4×C13C2×C22⋊Q811yescharacteristic
326C4×C13C2×#12311yescharacteristic
327Dic13—24no—
328Dic13—42no—
329Dic13—42no—
330C2×#41—134no—
331C2×#41—132no—
332C2×#41—134no—
333C2×#41—132no—
334C2×#41—262no—
335C2×#41—261no—
336C2×#41—262no—
337C2×#41—261no—
338C22×Q8—131no—
339C22×D4—131no—
340C22×D4—261no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—262no—
344C23×C4—261no—
345C23×C4C22⋊D1312yes—
346C23×C4C22×D1311yescharacteristic
347C2×M16—134no—
348C2×M16—132no—
349C2×M16—132no—
350C2×M16—261no—
351C2×M16—262no—
352C2×M16—261no—
353C2×M16—262no—
354C2×M16—262no—
355C22×C8—261no—
356C22×C8—261no—
357C4×Q8—264no—
358C4×Q8—264no—
359C4×D4—264no—
360C4×D4—264no—
361C4×D4—268no—
362C4×D4—268no—
363#117—132no—
364#117—132no—
365#117—264no—
366#117—264no—
367#117—261no—
368#117—261no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—48no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—264no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4C22⋊D1312yes—
386C2×C4⋊C4C22×D1312yes—
387C2×C4⋊C4C22×D1312yes—
388C2×C22⋊C4—262no—
389C2×C22⋊C4—261no—
390C2×C42—22no—
391C2×C42—21no—
392C2×C42—262no—
393C2×C42—261no—
394C2×C42C4×D1314yescomplemented
395C2×C42C22×D1312yes—
396#107—264no—
397#106—264no—
398#104—1316no—
399#103—264no—
400#102—264no—
401C2×C13—21no—
402C2×C13—21no—
403C2×C13—22no—
404C2×C13#185914yescomplemented
405C2×C13C2×#38511yescharacteristic
406C2×C13C2×#45311yescharacteristic
407C2×C13C2×#45611yescharacteristic
408D13—44no—
409C24—261no—
410C24C2×C22⋊D1311yescharacteristic
411#41—138no—
412#41—134no—
413#41—134no—
414#41—264no—
415#41—264no—
416#41—264no—
417#41—264no—
418#41—264no—
419#41—262no—
420#41—262no—
421C2×Q8—134no—
422C2×Q8—132no—
423C2×Q8—262no—
424C2×Q8—261no—
425C2×D4—134no—
426C2×D4—132no—
427C2×D4—264no—
428C2×D4—262no—
429C2×D4—264no—
430C2×D4—262no—
431C2×D4—262no—
432C2×D4—261no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—268no—
445C22×C4—261no—
446C22×C4—264no—
447C22×C4—264no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—1044no—
453C22×C4C2×C4×D1312yes—
454C22×C4#612712yes—
455C22×C4D4×D1311yescharacteristic
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4D4×D1311yescharacteristic
459C22×C4Q8×D1312yes—
460C22×C4#613112yes—
461C22×C4C2×C22⋊D1314yes—
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C23×D1311yescharacteristic
464M16—134no—
465M16—264no—
466M16—262no—
467M16—262no—
468M16—262no—
469M16—522no—
470C2×C8—264no—
471C2×C8—262no—
472C2×C8—262no—
473C2×C8—522no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—416no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—132no—
484C4⋊C4—132no—
485C4⋊C4—268no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C22⋊C4—268no—
489C22⋊C4—262no—
490C22⋊C4—262no—
491C42—24no—
492C42—22no—
493C42—268no—
494C42—262no—
495C42—262no—
496C42C2×C4×D1314yescomplemented
497C13C2×#185911yescharacteristic, complemented, Sylow
498C23—22no—
499C23—22no—
500C23—262no—
501C23—264no—
502C23—522no—
503C23—522no—
504C23C4×C22⋊D1312yes—
505C23#8819111yescharacteristic
506C23#8819111yescharacteristic
507C23#8820012yes—
508C23C22×C22⋊D1311yescharacteristic
509Q8—134no—
510Q8—262no—
511Q8—264no—
512D4—134no—
513D4—264no—
514D4—264no—
515D4—268no—
516D4—262no—
517D4—264no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—216no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—262no—
531C2×C4—264no—
532C2×C4—264no—
533C2×C4—264no—
534C2×C4—268no—
535C2×C4—262no—
536C2×C4—262no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—1048no—
540C2×C4C4⋊C4×D1312yes—
541C2×C4C4⋊C4×D1312yes—
542C2×C4#8814712yes—
543C2×C4#8814712yes—
544C2×C4#8814812yes—
545C2×C4#8814812yes—
546C2×C4#8815012yes—
547C2×C4#8815012yes—
548C2×C4C4×C22⋊D1312yes—
549C2×C4#8819111yescharacteristic
550C2×C4#8819111yescharacteristic
551C2×C4#8820012yes—
552C2×C4C22×C4×D1311yescharacteristic
553C2×C4C2×#612711yescharacteristic
554C2×C4C2×D4×D1311yescharacteristic
555C2×C4C2×D4×D1311yescharacteristic
556C2×C4C2×Q8×D1311yescharacteristic
557C2×C4C2×#613111yescharacteristic
558C8—264no—
559C8—522no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—24no—
565C22—24no—
566C22—264no—
567C22—522no—
568C22—522no—
569C22—528no—
570C22#1171865012yes—
571C22#1171865012yes—
572C22#1171873812yes—
573C22#1171875612yes—
574C22C2×C4×C22⋊D1311yescharacteristic
575C22C2×#8819111yescharacteristic
576C22C2×#8820011yescharacteristic
577C4—28no—
578C4—44no—
579C4—82no—
580C4—264no—
581C4—522no—
582C4—522no—
583C4#1171865012yes—
584C4#1171865012yes—
585C4C2×C4⋊C4×D1311yescharacteristic
586C4C2×#8814711yescharacteristic
587C4C2×#8814811yescharacteristic
588C4C2×#8815011yescharacteristic
589C2—21no—
590C2—21no—
591C2—22no—
592C2—524no—
593C2#1311506114yesdirect product factor
594C2C2×#1171865011yescharacteristic
595C2C2×#1171873811yescharacteristic
596C2C2×#1171875611yescharacteristic
subgroupG/H
centerC23#88191
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#384C2
socleC23×C13#120
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×#384D13
hypocenterC13C2×#1859
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
2. C2×#11718625C2semidirect
5. #13115061C2direct (N × H)
6. C2×#11718122C2semidirect
7. C2×#11718115C2semidirect
8. C2×C13×#384C2semidirect
27. C13×#384C22semidirect
33. #11718625C22semidirect
36. C2×#88045C4semidirect
38. #11718122C22semidirect
39. #11718115C22semidirect
73. C2×C42×C13C2×C4semidirect
93. C2×#6099C2×C4semidirect
110. #88045C2×C4semidirect
150. #6127C4⋊C4semidirect
155. C2×D52C4⋊C4semidirect
165. C2×Dic26C4⋊C4semidirect
178. C42×C13C22×C4semidirect
195. #6099C22×C4semidirect
204. C2×#384D13semidirect
260. D52C2×C4⋊C4semidirect
267. Dic26C2×C4⋊C4semidirect
298. #384C2×D13semidirect
394. C2×C42C4×D13semidirect
404. C2×C13#1859semidirect
496. C42C2×C4×D13semidirect
497. C13C2×#1859semidirect
593. C2#13115061direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192092
C2×#117186252
C22×#880452
C2×#117186272
#131150612
C2×#117181222
C2×#117181152
C2×C13×#3842
C2×#185913