Finite Group Databasebeta

← C4×#11718433 #15860667

Subgroups — C4×#11718433 #15860667

Order 3328.

1670 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6129C211yesmaximal, characteristic
2C2×#11718433C212yesmaximal
3C2×C4×C8×D13C211yesmaximal, characteristic, complemented
4C4×#88146C211yesmaximal, characteristic, complemented
5C4×#88050C211yesmaximal, characteristic, complemented
6C4×#88056C211yesmaximal, characteristic, complemented
7#13114655C212yesmaximal, complemented
8#102×Dic13C212yesmaximal, complemented
9C4×#88072C211yesmaximal, characteristic, complemented
10#13114551C212yesmaximal, complemented
11C4×C13×#102C211yesmaximal, characteristic, complemented
12C22×#6129C2211yescharacteristic
13C2×C4×D4×C13C2211yescharacteristic
14C2×D4×Dic13C2211yescharacteristic
15C2×C4×C22⋊D13—21no—
16C22×C4×Dic13—21no—
17C22×C8×D13C2212yes—
18C4×#6129—24no—
19C4×#6129C418yescomplemented
20C2×#88146C2211yescharacteristic
21C2×#88146C2212yes—
22C2×#88141C2211yescharacteristic
23C2×#88135—21no—
24C2×#88131—21no—
25C2×C42×D13C2211yescharacteristic
26C2×C4×Dic26C2211yescharacteristic
27C2×C13×#102C2212yes—
28C2×C4×C8×C13C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C2×#88072C2212yes—
31C2×#88056C2212yes—
32C2×C8×Dic13C2212yes—
33C4⋊C4×Dic13C2212yes—
34C2×#88050C2212yes—
35C4×#6103—21no—
36C4×C4⋊Dic13C2211yescharacteristic
37C42×Dic13—21no—
38C2×C4×#1055C2211yescharacteristic
39#11718433C4116yesdirect product factor
40C4×C8×D13—24no—
41#11718327—21no—
42#11718309—21no—
43C13×#340C2212yes—
44#11718143C2212yes—
45#11718121C2212yes—
46#11718121C2212yes—
47C22×D4×C13C2311yescharacteristic
48C23×C4×C13—21no—
49C22×C22⋊D13—21no—
50C23×Dic13—21no—
51C23×Dic13—21no—
52C2×#6129—22no—
53C2×#6129—24no—
54C2×#6129C2×C418yes—
55C2×#6129C2×C414yes—
56C22×C4×D13D411yescharacteristic
57C22×C4×D13D411yescharacteristic
58C22×C4×D13C2311yescharacteristic
59C22×Dic26C2311yescharacteristic
60C22×C8×C13C2312yes—
61C4×D4×C13—22no—
62C4×D4×C13C2×C414yes—
63C2×C13×C4⋊C4C2312yes—
64C2×C13×C4⋊C4C2311yescharacteristic
65C2×C13×C22⋊C4—21no—
66C2×C42×C13—21no—
67C2×C42×C13C2311yescharacteristic
68C2×C22⋊Dic13—21no—
69D4×Dic13—22no—
70D4×Dic13C2×C414yes—
71C4×C22⋊D13—28no—
72C2×#6103—21no—
73C2×#6103—22no—
74C2×C4⋊Dic13C2311yescharacteristic
75C2×C4⋊Dic13C2312yes—
76C2×#6101—21no—
77C2×#6101—21no—
78C2×C4×Dic13—21no—
79C2×C4×Dic13—21no—
80C2×C4×Dic13—21no—
81C2×C4×Dic13—22no—
82C2×C4×Dic13—28no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13D411yescharacteristic
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C22×#1055C2312yes—
89C2×C8×D13—24no—
90C2×C8×D13—24no—
91C2×C8×D13C2×C418yescomplemented
92#88146—22no—
93#88146—24no—
94#88146C2×C414yes—
95#88146C2×C418yescomplemented
96#88141—22no—
97#88141C2×C414yes—
98#88135—28no—
99#88131—28no—
100C42×D13C2×C414yes—
101C42×D13D414yes—
102C4×Dic26—22no—
103C4×Dic26C2×C414yes—
104C13×#102C2×C418yescomplemented
105C4×C8×C13—22no—
106C13×#95—21no—
107#88072C2×C418yescomplemented
108#88071—21no—
109#88071—22no—
110#88056C2×C418yescomplemented
111C8×Dic13—24no—
112#88050C2×C418yescomplemented
113C4×#1055—22no—
114C4×#416—131nomaximal, Sylow
115C24×C13—21no—
116C23×D13C2×D411yescharacteristic
117C2×D4×C13—21no—
118C2×D4×C13—22no—
119C2×D4×C13C22×C414yes—
120C2×D4×C13C22×C412yes—
121C22×C4×C13—22no—
122C22×C4×C13—21no—
123C22×C4×C13—24no—
124C22×C4×C13—42no—
125C22×C4×C13—42no—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2411yescharacteristic
129C2×C22⋊D13—24no—
130C2×C22⋊D13—28no—
131C22×Dic13—21no—
132C22×Dic13—24no—
133C22×Dic13—28no—
134C22×Dic13—22no—
135C22×Dic13—21no—
136C22×Dic13—24no—
137C22×Dic13—44no—
138C22×Dic13C2×D411yescharacteristic
139C22×Dic13C2×D411yescharacteristic
140C22×Dic13C2×D411yescharacteristic
141#6129—28no—
142#6129—216no—
143#6129C42116yescomplemented
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—24no—
147C2×C4×D13C22⋊C414yes—
148C2×C4×D13C22⋊C414yes—
149C2×C4×D13C22×C412yes—
150C2×C4×D13C22×C414yes—
151C2×C4×D13C2×D412yes—
152C2×C4×D13#4114yes—
153C2×Dic26—21no—
154C2×Dic26—22no—
155C2×Dic26C22×C412yes—
156C2×Dic26C22×C414yes—
157C2×C8×C13—22no—
158C2×C8×C13—22no—
159C2×C8×C13C22×C414yes—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4C22×C414yes—
163C13×C4⋊C4C22×C412yes—
164C13×C22⋊C4—24no—
165C42×C13—42no—
166C42×C13C22×C412yes—
167C42×C13C2×D412yes—
168C22⋊Dic13—24no—
169#6103—24no—
170#6103—28no—
171C4⋊Dic13—21no—
172C4⋊Dic13—22no—
173C4⋊Dic13C22×C414yes—
174C4⋊Dic13C22×C412yes—
175#6101—24no—
176#6101—24no—
177C4×Dic13—24no—
178C4×Dic13—24no—
179C4×Dic13—24no—
180C4×Dic13—28no—
181C4×Dic13—42no—
182C4×Dic13—44no—
183C4×Dic13C22⋊C414yes—
184C4×Dic13C22⋊C414yes—
185C4×Dic13C22×C412yes—
186C4×Dic13C2×D412yes—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055C22×C414yes—
190C8×D13—216no—
191C2×C4×#41—131no—
192C2×#416—132no—
193C22×C4×C8—131no—
194C4×#117—131no—
195C4×#103—131no—
196C4×#103—131no—
197C4×#103—132no—
198C4×#102—132no—
199C4×#102—131no—
200C4×#102D1311yescharacteristic, complemented
201#1735—132no—
202C23×C13—22no—
203C23×C13—24no—
204C23×C13—42no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13C22×D411yescharacteristic
208C22×D13—21no—
209C22×D13—21no—
210C22×D13—22no—
211C22×D13C2×C22⋊C412yes—
212C22×D13C4×D414yes—
213D4×C13—22no—
214D4×C13—24no—
215D4×C13C2×C4214yes—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—24no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—48no—
224C2×C4×C13C2×C22⋊C412yes—
225C2×C4×C13C2×C22⋊C412yes—
226C2×C4×C13#13512yes—
227C2×C4×C13#13512yes—
228C2×C4×C13C23×C411yescharacteristic
229C2×C4×C13C23×C412yes—
230C2×C4×C13C22×D411yescharacteristic
231C2×C4×C13C2×#4112yes—
232C22⋊D13—216no—
233C2×Dic13—22no—
234C2×Dic13—24no—
235C2×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—216no—
238C2×Dic13—22no—
239C2×Dic13—24no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—48no—
244C2×Dic13C2×C22⋊C412yes—
245C2×Dic13C2×C22⋊C412yes—
246C2×Dic13C2×C22⋊C412yes—
247C2×Dic13C4×D414yes—
248C2×Dic13#13514yes—
249C4×D13—28no—
250C4×D13—28no—
251C4×D13C2×C4214yes—
252C4×D13#11714yes—
253C4×D13C4×D418yes—
254Dic26—22no—
255Dic26—24no—
256Dic26C2×C4214yes—
257C8×C13—24no—
258#1055—24no—
259C22×#41—131no—
260C23×C8—132no—
261C4×#41—138no—
262C4×#41—264no—
263C2×C4×Q8—131no—
264C2×C4×Q8—131no—
265C2×C4×D4—131no—
266C2×C4×D4—261no—
267C2×C4×D4—261no—
268C2×C4×D4C2×D1311yescharacteristic
269C2×#117—132no—
270C2×#117—131no—
271C2×#117—261no—
272C22×C42—131no—
273C22×C42—261no—
274#416—1316no—
275C2×#103—132no—
276C2×#103—132no—
277C2×#102—132no—
278C2×#102C2×D1312yes—
279C2×C4×C8—132no—
280C2×C4×C8—131no—
281C2×C4×C8—264no—
282C2×C4×C8C2×D1311yescharacteristic
283C4×C4⋊C4—132no—
284C4×C4⋊C4—131no—
285C4×C4⋊C4C2×D1311yescharacteristic
286C4×C22⋊C4—261no—
287C4×C22⋊C4—261no—
288#376—261no—
289C43—261no—
290#340—132no—
291#340—132no—
292#340—132no—
293#340C2×D1312yes—
294C22×C13—24no—
295C22×C13—42no—
296C22×C13—42no—
297C22×C13—44no—
298C22×C13—44no—
299C22×C13C22×C22⋊C411yescharacteristic
300C22×C13C2×C4×D412yes—
301C22×C13C2×#13511yescharacteristic
302C22×C13C2×#13511yescharacteristic
303C22×C13C2×#13512yes—
304C2×D13—22no—
305C2×D13—22no—
306C2×D13—24no—
307C2×D13—24no—
308C2×D13C4×C22⋊C414yes—
309C4×C13—22no—
310C4×C13—42no—
311C4×C13—44no—
312C4×C13#41614yescomplemented
313C4×C13C22×C4211yescharacteristic
314C4×C13C2×#11711yescharacteristic
315C4×C13C2×C4×D412yes—
316Dic13—22no—
317Dic13—24no—
318Dic13—42no—
319Dic13—44no—
320Dic13C4×C22⋊C414yes—
321Dic13#41614yescomplemented
322C2×#41—134no—
323C2×#41—138no—
324C2×#41—262no—
325C2×#41—264no—
326C22×Q8—131no—
327C22×D4—261no—
328C22×D4C22×D1311yescharacteristic
329C23×C4—21no—
330C23×C4—131no—
331C23×C4—131no—
332C23×C4—131no—
333C23×C4—261no—
334C23×C4—261no—
335C22×C8—132no—
336C22×C8—138no—
337C22×C8—264no—
338C22×C8—264no—
339C22×C8C22×D1312yes—
340C4×Q8—134no—
341C4×Q8—134no—
342C4×Q8—262no—
343C4×Q8—262no—
344C4×D4—22no—
345C4×D4—134no—
346C4×D4—262no—
347C4×D4—268no—
348C4×D4—268no—
349C4×D4C4×D1314yes—
350#117—134no—
351#117—138no—
352#117—268no—
353#117—262no—
354#117—264no—
355C2×C4⋊C4—131no—
356C2×C4⋊C4—132no—
357C2×C4⋊C4—261no—
358C2×C4⋊C4—261no—
359C2×C4⋊C4C22×D1311yescharacteristic
360C2×C4⋊C4C22×D1312yes—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—261no—
363C2×C22⋊C4—262no—
364C2×C22⋊C4—261no—
365C2×C42—21no—
366C2×C42—131no—
367C2×C42—131no—
368C2×C42—131no—
369C2×C42—134no—
370C2×C42—134no—
371C2×C42—268no—
372C2×C42—261no—
373C2×C42—262no—
374C2×C42—261no—
375C2×C42—261no—
376C2×C42—262no—
377C2×C42—261no—
378C2×C42C22×D1311yescharacteristic
379#103—138no—
380#103—138no—
381#102—138no—
382#102C4×D1318yescomplemented
383C4×C8—22no—
384C4×C8—264no—
385C4×C8—262no—
386#95—21no—
387#95—262no—
388#95—261no—
389C2×C13—44no—
390C2×C13C2×C4×C22⋊C411yescharacteristic
391C2×C13C2×#41611yescharacteristic
392C2×C13C2×#41611yescharacteristic
393C2×C13C4×#13512yes—
394C2×C13C4×#13512yes—
395D13—24no—
396C24—21no—
397C24—131no—
398#41—1316no—
399#41—268no—
400#41—2616no—
401C2×Q8—134no—
402C2×Q8—132no—
403C2×Q8—261no—
404C2×Q8—262no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—264no—
408C2×D4—268no—
409C2×D4C2×C4×D1314yes—
410C2×D4C2×C4×D1312yes—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—24no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—131no—
417C22×C4—131no—
418C22×C4—132no—
419C22×C4—134no—
420C22×C4—132no—
421C22×C4—134no—
422C22×C4—131no—
423C22×C4—134no—
424C22×C4—134no—
425C22×C4—264no—
426C22×C4—264no—
427C22×C4—268no—
428C22×C4—264no—
429C22×C4—261no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—261no—
434C22×C4—524no—
435C22×C4D4×D1311yescharacteristic
436C22×C4D4×D1311yescharacteristic
437C22×C4C23×D1311yescharacteristic
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—134no—
441C2×C8—2616no—
442C2×C8—262no—
443C2×C8—262no—
444C2×C8C2×C4×D1314yes—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—134no—
448C4⋊C4—132no—
449C4⋊C4—264no—
450C4⋊C4—264no—
451C4⋊C4—261no—
452C4⋊C4—262no—
453C4⋊C4C2×C4×D1314yes—
454C4⋊C4C2×C4×D1312yes—
455C22⋊C4—24no—
456C22⋊C4—264no—
457C22⋊C4—268no—
458C22⋊C4—264no—
459C42—42no—
460C42—134no—
461C42—134no—
462C42—132no—
463C42—132no—
464C42—264no—
465C42—264no—
466C42—268no—
467C42—264no—
468C42—524no—
469C42—522no—
470C42C2×C4×D1312yes—
471C42D4×D1312yes—
472C13C4×#41611yescharacteristic, complemented, Sylow
473C23—22no—
474C23—24no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—132no—
479C23—134no—
480C23—261no—
481C23—261no—
482C23—262no—
483C23C2×D4×D1311yescharacteristic
484Q8—134no—
485Q8—262no—
486Q8—264no—
487D4—22no—
488D4—24no—
489D4—2616no—
490D4C42×D1314yes—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—48no—
499C2×C4—132no—
500C2×C4—132no—
501C2×C4—134no—
502C2×C4—134no—
503C2×C4—134no—
504C2×C4—134no—
505C2×C4—138no—
506C2×C4—132no—
507C2×C4—268no—
508C2×C4—2616no—
509C2×C4—262no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—264no—
513C2×C4—268no—
514C2×C4—262no—
515C2×C4—264no—
516C2×C4—528no—
517C2×C4—522no—
518C2×C4—522no—
519C2×C4—522no—
520C2×C4C22⋊C4×D1312yes—
521C2×C4C22⋊C4×D1312yes—
522C2×C4#8816612yes—
523C2×C4#8817012yes—
524C2×C4C22×C4×D1311yescharacteristic
525C2×C4C22×C4×D1312yes—
526C2×C4C2×D4×D1311yescharacteristic
527C2×C4#41×D1312yes—
528C8—24no—
529C8—264no—
530C22—24no—
531C22—42no—
532C22—42no—
533C22—44no—
534C22—44no—
535C22—134no—
536C22—262no—
537C22—262no—
538C22—264no—
539C22—264no—
540C22C2×C22⋊C4×D1311yescharacteristic
541C22C4×D4×D1312yes—
542C22C2×#8816611yescharacteristic
543C22C2×#8817011yescharacteristic
544C22D13×#13512yes—
545C4—22no—
546C4—42no—
547C4—44no—
548C4—134no—
549C4—134no—
550C4—262no—
551C4—264no—
552C4—522no—
553C4—524no—
554C4#1171843314yesdirect product factor
555C4C2×C42×D1311yescharacteristic
556C4D13×#11711yescharacteristic
557C4C4×D4×D1312yes—
558C2—44no—
559C2—264no—
560C2C4×C22⋊C4×D1311yescharacteristic
561C2D13×#41611yescharacteristic
562C2C2×#1171843311yescharacteristic
563C2C4×#8816612yes—
564C2C4×#8817012yes—
subgroupG/H
centerC22×C4D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC4×C13×#102C2
socleC23×C13C22×D4
prime radicalC22×#6129C22
cosocleC22×C4×C13C24
hypercenterC4×#102D13
hypocenterC13C4×#416
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. C2×C4×C8×D13C2semidirect
4. C4×#88146C2semidirect
5. C4×#88050C2semidirect
6. C4×#88056C2semidirect
7. #13114655C2semidirect
8. #102×Dic13C2semidirect
9. C4×#88072C2semidirect
10. #13114551C2semidirect
11. C4×C13×#102C2semidirect
19. C4×#6129C4semidirect
39. #11718433C4direct (N × H)
91. C2×C8×D13C2×C4semidirect
95. #88146C2×C4semidirect
104. C13×#102C2×C4semidirect
107. #88072C2×C4semidirect
110. #88056C2×C4semidirect
112. #88050C2×C4semidirect
143. #6129C42semidirect
200. C4×#102D13semidirect
312. C4×C13#416semidirect
321. Dic13#416semidirect
382. #102C4×D13semidirect
472. C13C4×#416semidirect
554. C4#11718433direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#61292
C2×#117184332
C2×C4×C8×D132
C4×#881462
C4×#880502
C4×#880562
#131146552
#102×Dic132
C4×#880722
#131145512
C4×C13×#1022
C4×#41613