Finite Group Databasebeta

← C4×#11718392 #15868503

Subgroups — C4×#11718392 #15868503

Order 3328.

1880 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D52C211yesmaximal, characteristic
2C2×#11718392C211yesmaximal, characteristic
3C2×C4×#6095C212yesmaximal, complemented
4C4×#88178C211yesmaximal, characteristic, complemented
5#13115169C212yesmaximal, complemented
6#13115141C211yesmaximal, characteristic, complemented
7#13115100C212yesmaximal, complemented
8#13115031C211yesmaximal, characteristic, complemented
9#13114768C211yesmaximal, characteristic
10C4×#88061C212yesmaximal, complemented
11C4×C13×C22⋊C8C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C23×C4×D13—21no—
14C22×C42×C13C2211yescharacteristic
15C22×#6103—21no—
16C22×C4⋊Dic13C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18C22×#6095C2212yes—
19C2×C4×D52—21no—
20C2×C4×D52—21no—
21C2×C4×D52—28no—
22C2×C4×D52C2212yes—
23C2×C4×D52C2212yes—
24C2×C4×Dic26C2211yescharacteristic, complemented
25C2×C13×C22⋊C8C2211yescharacteristic
26C2×C13×C22⋊C8C2211yescharacteristic
27C2×C4×C8×C13C2212yescomplemented
28#11718873C2211yescharacteristic
29#11718871—21no—
30C4×C22⋊Dic13—21no—
31C2×#88061C2212yes—
32C2×#88061C2212yes—
33C2×#88061C2212yes—
34C2×#88057C2212yescomplemented
35C2×#88056C2212yescomplemented
36C4×C4⋊Dic13C2211yescharacteristic, complemented
37#11718594—21no—
38C4×#6101—21no—
39#11718590C2211yescharacteristic, complemented
40#11718589C2211yescharacteristic, complemented
41#11718392C418yesdirect product factor
42C4×#6095—28no—
43C13×#336C2212yescomplemented
44#11718143C2212yescomplemented
45#11718143C2212yescomplemented
46C24×D13—21no—
47C23×C4×C13D411yescharacteristic
48C23×C4×C13D411yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×Dic13—21no—
51C22×D52—21no—
52C22×D52—22no—
53C22×D52—24no—
54C22×D52—24no—
55C22×D52C2×C414yes—
56C22×D52C2312yes—
57C22×C4×D13—28no—
58C22×C4×D13—22no—
59C22×C4×D13—22no—
60C22×C4×D13—44no—
61C22×C4×D13—44no—
62C22×Dic26C2311yescharacteristic
63C22×C8×C13C2312yes—
64C22×C8×C13C2312yes—
65C2×C42×C13—24no—
66C2×C42×C13D411yescharacteristic
67C2×C42×C13D411yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×C22⋊Dic13—21no—
71C2×C22⋊Dic13—21no—
72C2×#6103—28no—
73C2×#6103—22no—
74C2×#6103—22no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—24no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2312yes—
81#88178—22no—
82#88178C2×C414yescomplemented
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×#6095—24no—
89C2×#6095—24no—
90C2×#6095C2×C418yescomplemented
91C4×D52—28no—
92C4×D52—28no—
93C4×D52—24no—
94C4×D52—24no—
95C4×D52—24no—
96C4×D52D418yes—
97C4×Dic26—24no—
98C13×C22⋊C8—22no—
99C13×C22⋊C8C2×C414yescomplemented
100C4×C8×C13—24no—
101#88071—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88061—24no—
107#88061—24no—
108#88061C2×C418yescomplemented
109#88057—24no—
110#88056—24no—
111C4×#450—131nomaximal, Sylow
112C24×C13C2×D411yescharacteristic
113C23×D13—24no—
114C23×D13—24no—
115C23×D13—24no—
116C23×D13—22no—
117C23×D13—42no—
118C23×D13—42no—
119C23×D13—42no—
120C23×D13—42no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—41no—
128C22×C4×C13SD1614yescomplemented
129C22×C4×C13C22×C412yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13#4112yes—
136C22×C4×C13C2411yescharacteristic
137C22×Dic13—24no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—22no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—42no—
144C22×Dic13—42no—
145C2×D52—24no—
146C2×D52—24no—
147C2×D52—216no—
148C2×D52—24no—
149C2×D52—22no—
150C2×D52—22no—
151C2×D52—22no—
152C2×D52—216no—
153C2×D52C22×C414yes—
154C2×D52C2×D414yes—
155C2×D52#4114yes—
156C2×C4×D13—28no—
157C2×C4×D13—28no—
158C2×C4×D13—44no—
159C2×C4×D13—432no—
160C2×C4×D13—44no—
161C2×C4×D13—44no—
162C2×C4×D13—44no—
163C2×Dic26—22no—
164C2×Dic26—22no—
165C2×Dic26—21no—
166C2×Dic26C22×C412yescomplemented
167C2×C8×C13—22no—
168C2×C8×C13—22no—
169C2×C8×C13—22no—
170C2×C8×C13—22no—
171C2×C8×C13—22no—
172C2×C8×C13C22×C414yescomplemented
173C42×C13—22no—
174C42×C13—22no—
175C42×C13—22no—
176C42×C13C2×D414yes—
177C22⋊Dic13—24no—
178C22⋊Dic13—42no—
179#6103—28no—
180#6103—28no—
181C4⋊Dic13—24no—
182C4⋊Dic13—22no—
183C4⋊Dic13—21no—
184C4⋊Dic13—22no—
185C4⋊Dic13—22no—
186C4⋊Dic13C22×C412yescomplemented
187C4⋊Dic13C2×D414yes—
188#6101—24no—
189#6101—42no—
190#6101—42no—
191C4×Dic13—42no—
192C4×Dic13—42no—
193#6095—216no—
194C22×C4×D4—131no—
195C2×#450—131no—
196C2×C4×SD16—132no—
197C4×C22⋊Q8—131no—
198#1877—132no—
199#1872—131no—
200#1864—132no—
201#1853—131no—
202#1786—131no—
203C4×#102—132no—
204C4×C22⋊C8D1311yescharacteristic, complemented
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13C4×D412yes—
210C23×C13C2×SD1612yes—
211C23×C13#13512yes—
212C23×C13C22×D411yescharacteristic
213C22×D13—216no—
214C22×D13—24no—
215C22×D13—24no—
216C22×D13—24no—
217C22×D13—48no—
218C22×D13—48no—
219C22×D13—48no—
220C22×D13—48no—
221C22×D13—48no—
222C22×D13—42no—
223C22×D13—42no—
224C22×D13—42no—
225C22×D13—42no—
226C22×D13—48no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—28no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—44no—
240C2×C4×C13C4×D412yes—
241C2×C4×C13#12012yes—
242C2×C4×C13#12012yes—
243C2×C4×C13C2×SD1612yes—
244C2×C4×C13C2×SD1612yes—
245C2×C4×C13AGL(1,ℤ/8)12yes—
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C22×D412yes—
248C2×C4×C13C2×#4112yes—
249C2×C4×C13C2×#4111yescharacteristic
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—24no—
253C2×Dic13—48no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—42no—
257C2×Dic13—41no—
258C2×Dic13—42no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266D52—216no—
267D52—24no—
268D52—24no—
269D52—24no—
270D52C4×D418yes—
271C4×D13—416no—
272C4×D13—416no—
273Dic26—24no—
274Dic26—42no—
275C8×C13—24no—
276C8×C13—42no—
277C23×D4—131no—
278C24×C4—261no—
279C22×SD16—132no—
280C2×C22⋊Q8—131no—
281C2×C4×Q8—131no—
282C2×C4×D4—132no—
283C2×C4×D4—132no—
284C2×C4×D4—268no—
285C2×C4×D4—261no—
286C2×C4×D4—261no—
287C22×C4⋊C4—131no—
288C22×C22⋊C4—261no—
289C22×C42C2×D1311yescharacteristic
290#450—138no—
291C4×SD16—268no—
292C2×#106—132no—
293C2×#103—132no—
294C2×#102—132no—
295C2×#102—132no—
296C2×#102—132no—
297C2×C22⋊C8C2×D1311yescharacteristic
298C2×C22⋊C8C2×D1311yescharacteristic
299C2×C4×C8C2×D1312yescomplemented
300#391—131no—
301#389—131no—
302#387—261no—
303#385—261no—
304#380—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—261no—
307C4×C22⋊C4—261no—
308#340—132no—
309#340—132no—
310#336C2×D1312yescomplemented
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—22no—
314C22×C13—22no—
315C22×C13—22no—
316C22×C13—22no—
317C22×C13C4×SD1614yescomplemented
318C22×C13C2×C4×D411yescharacteristic
319C22×C13C2×#12011yescharacteristic
320C22×C13#52511yescharacteristic
321C22×C13C22×SD1611yescharacteristic
322C22×C13C2×#13511yescharacteristic
323C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C13#57511yescharacteristic
325C2×D13—28no—
326C2×D13—432no—
327C2×D13—44no—
328C2×D13—44no—
329C2×D13—44no—
330C2×D13—44no—
331C2×D13—44no—
332C2×D13—44no—
333C4×C13—22no—
334C4×C13—22no—
335C4×C13—22no—
336C4×C13—41no—
337C4×C13#45014yescomplemented
338C4×C13C2×C4×D412yes—
339C4×C13#52512yes—
340Dic13—42no—
341Dic13—44no—
342Dic13—42no—
343Dic13—81no—
344Dic13—81no—
345C25—261no—
346C22×Q8—131no—
347C22×D4—134no—
348C22×D4—132no—
349C22×D4—264no—
350C22×D4—264no—
351C22×D4—261no—
352C22×D4—262no—
353C23×C4—268no—
354C23×C4—261no—
355C23×C4—262no—
356C23×C4—262no—
357C23×C4—524no—
358C23×C4—524no—
359C23×C4D5211yescharacteristic
360C23×C4D5211yescharacteristic
361C23×C4C22×D1311yescharacteristic
362C2×SD16—138no—
363C2×SD16—264no—
364C2×SD16—264no—
365C22×C8C22×D1312yes—
366C22×C8C22×D1312yes—
367C22⋊Q8—134no—
368C22⋊Q8—262no—
369C4×Q8—264no—
370C4×D4—138no—
371C4×D4—264no—
372C4×D4—264no—
373C4×D4—268no—
374C4×D4—268no—
375C4×D4—264no—
376C2×C4⋊C4—132no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—264no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C22⋊C4—268no—
386C2×C22⋊C4—261no—
387C2×C22⋊C4—262no—
388C2×C22⋊C4—262no—
389C2×C22⋊C4—261no—
390C2×C42—24no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42D5211yescharacteristic
394C2×C42D5211yescharacteristic
395C2×C42C22×D1311yescharacteristic
396C2×C42C22×D1311yescharacteristic
397#106—264no—
398#103—264no—
399#102—138no—
400#102—264no—
401#102—264no—
402C22⋊C8—22no—
403C22⋊C8C4×D1314yescomplemented
404C4×C8—24no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410C2×C13—24no—
411C2×C13C4×#12011yescharacteristic
412C2×C13C2×C4×SD1611yescharacteristic
413C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
414C2×C13C2×#45011yescharacteristic
415C2×C13#300211yescharacteristic
416C2×C13#310111yescharacteristic
417C2×C13#310511yescharacteristic
418D13—48no—
419C24—264no—
420C24—264no—
421C24—264no—
422C24—262no—
423C24—522no—
424C24—522no—
425C24—522no—
426C24—522no—
427C24C2×D5211yescharacteristic
428C2×Q8—132no—
429C2×Q8—261no—
430C2×Q8—262no—
431C2×Q8—262no—
432C2×D4—134no—
433C2×D4—134no—
434C2×D4—134no—
435C2×D4—2616no—
436C2×D4—264no—
437C2×D4—264no—
438C2×D4—2616no—
439C2×D4—264no—
440C2×D4—262no—
441C2×D4—262no—
442C2×D4—262no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—41no—
450C22×C4—268no—
451C22×C4—264no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—262no—
455C22×C4—268no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—524no—
459C22×C4—5232no—
460C22×C4—522no—
461C22×C4—522no—
462C22×C4—524no—
463C22×C4—524no—
464C22×C4—524no—
465C22×C4#609514yescomplemented
466C22×C4C2×C4×D1312yes—
467C22×C4C2×D5211yescharacteristic
468C22×C4C2×D5211yescharacteristic
469C22×C4C2×D5211yescharacteristic
470C22×C4C2×D5211yescharacteristic
471C22×C4C2×D5211yescharacteristic
472C22×C4#612712yes—
473C22×C4C23×D1311yescharacteristic
474SD16—2616no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8C2×C4×D1314yescomplemented
481C4⋊C4—132no—
482C4⋊C4—134no—
483C4⋊C4—264no—
484C4⋊C4—264no—
485C4⋊C4—261no—
486C4⋊C4—262no—
487C4⋊C4—262no—
488C4⋊C4—262no—
489C4⋊C4—522no—
490C4⋊C4—522no—
491C22⋊C4—268no—
492C22⋊C4—264no—
493C22⋊C4—268no—
494C22⋊C4—522no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—522no—
499C42—522no—
500C42D4×D1314yes—
501C13C4×#45011yescharacteristic, complemented, Sylow
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—2616no—
507C23—264no—
508C23—264no—
509C23—264no—
510C23—528no—
511C23—528no—
512C23—528no—
513C23—528no—
514C23—528no—
515C23—522no—
516C23—522no—
517C23—522no—
518C23—522no—
519C23—528no—
520C23C4×D5212yes—
521C23C2×#609512yes—
522C23#8815812yes—
523C23C22×D5211yescharacteristic
524Q8—264no—
525Q8—522no—
526D4—138no—
527D4—2616no—
528D4—264no—
529D4—264no—
530D4—264no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—28no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—44no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—264no—
547C2×C4—5216no—
548C2×C4—528no—
549C2×C4—522no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—522no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—5216no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4C4×D5212yes—
563C2×C4#8813612yes—
564C2×C4#8813612yes—
565C2×C4C2×#609512yes—
566C2×C4C2×#609512yes—
567C2×C4#8816212yes—
568C2×C4C22×C4×D1311yescharacteristic
569C2×C4C2×#612711yescharacteristic
570C2×C4C2×D4×D1312yes—
571C2×C4#41×D1312yes—
572C8—24no—
573C8—42no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—268no—
581C22—5232no—
582C22—524no—
583C22—524no—
584C22—524no—
585C22—524no—
586C22—524no—
587C22—524no—
588C22C4×#609514yescomplemented
589C22C2×C4×D5211yescharacteristic
590C22C2×#8813611yescharacteristic
591C22#1171922911yescharacteristic
592C22C22×#609511yescharacteristic
593C22C2×#8815811yescharacteristic
594C22C2×#8816211yescharacteristic
595C22#1171945311yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—41no—
600C4—522no—
601C4—522no—
602C4—524no—
603C4—1041no—
604C4—1041no—
605C4#1171839214yesdirect product factor
606C4C4×D4×D1312yes—
607C4#1171925212yes—
608C2—24no—
609C2—528no—
610C2C4×#8813611yescharacteristic
611C2C2×C4×#609511yescharacteristic
612C2C4×#8816211yescharacteristic
613C2C2×#1171839211yescharacteristic
614C2#1312405811yescharacteristic
615C2#1312484511yescharacteristic
616C2#1312488511yescharacteristic
subgroupG/H
centerC22×C4C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×C22⋊C8C2
socleC23×C13C22×D4
prime radicalC23×D52C22
cosocleC22×C4×C13C24
hypercenterC4×C22⋊C8D13
hypocenterC13C4×#450
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×C4×#6095C2semidirect
4. C4×#88178C2semidirect
5. #13115169C2semidirect
6. #13115141C2semidirect
7. #13115100C2semidirect
8. #13115031C2semidirect
10. C4×#88061C2semidirect
11. C4×C13×C22⋊C8C2semidirect
24. C2×C4×Dic26C22semidirect
27. C2×C4×C8×C13C22semidirect
34. C2×#88057C22semidirect
35. C2×#88056C22semidirect
36. C4×C4⋊Dic13C22semidirect
39. #11718590C22semidirect
40. #11718589C22semidirect
41. #11718392C4direct (N × H)
43. C13×#336C22semidirect
44. #11718143C22semidirect
45. #11718143C22semidirect
82. #88178C2×C4semidirect
90. C2×#6095C2×C4semidirect
99. C13×C22⋊C8C2×C4semidirect
108. #88061C2×C4semidirect
128. C22×C4×C13SD16semidirect
166. C2×Dic26C22×C4semidirect
172. C2×C8×C13C22×C4semidirect
186. C4⋊Dic13C22×C4semidirect
204. C4×C22⋊C8D13semidirect
299. C2×C4×C8C2×D13semidirect
310. #336C2×D13semidirect
317. C22×C13C4×SD16semidirect
337. C4×C13#450semidirect
403. C22⋊C8C4×D13semidirect
465. C22×C4#6095semidirect
480. C2×C8C2×C4×D13semidirect
501. C13C4×#450semidirect
588. C22C4×#6095semidirect
605. C4#11718392direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D522
C2×#117183922
C2×C4×#60952
C4×#881782
#131151692
#131151412
#131151002
#131150312
#131147682
C4×#880612
C4×C13×C22⋊C82
C4×#45013