Finite Group Databasebeta

← #15878576

Subgroups — #15878576

Order 3328.

1582 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719258C211yesmaximal, characteristic
2C2×#11718673C211yesmaximal, characteristic, complemented
3C2×#11718627C212yesmaximal, complemented
4#13115763C211yesmaximal, characteristic, complemented
5#13115641C211yesmaximal, characteristic, complemented
6#13115272C212yesmaximal, complemented
7#13115153C212yesmaximal, complemented
8#13114838C211yesmaximal, characteristic, complemented
9#13114774C212yesmaximal, complemented
10C4×#88050C211yesmaximal, characteristic, complemented
11D4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C22×#6127C2212yes—
13C2×C4×D4×C13—21no—
14C2×C4×D4×C13C2211yescharacteristic
15C22×C13×C4⋊C4C2212yes—
16C2×#88194—21no—
17C2×#88184C2212yes—
18C22×#6099C2212yes—
19#11719258—24no—
20#11719258C418yescomplemented
21C2×#88147—21no—
22C2×#88138—22no—
23C2×#88128C2211yescharacteristic
24C2×C4×Dic26C2211yescharacteristic
25C13×#389—21no—
26C13×#385—22no—
27C13×#384C2211yescharacteristic
28C13×#380C2212yes—
29C4×C13×C4⋊C4C2211yescharacteristic
30C2×C22⋊#1055C2212yes—
31#11718673—24no—
32C2×#88050C2212yes—
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35#11718627—28no—
36C2×#88049C2212yes—
37C2×#88049C2212yes—
38C2×#88049C2212yes—
39C2×#88049C2212yes—
40C2×C4⋊#1055C2211yescharacteristic
41C2×C4×#1055C2211yescharacteristic
42#11718121C2211yescharacteristic
43#11718121C2212yes—
44#11718121C2211yescharacteristic
45C22×D4×C13D411yescharacteristic
46C23×C4×C13—22no—
47C23×C4×C13C2312yes—
48C22×C22⋊D13—22no—
49C22×C22⋊D13—22no—
50C2×#6127—24no—
51C2×#6127—24no—
52C2×#6127—24no—
53C2×#6127—42no—
54C2×#6127—42no—
55C2×#6127C2×C418yescomplemented
56C22×D52—21no—
57C22×D52—21no—
58C22×D52C2312yes—
59C22×C4×D13—22no—
60C22×Dic26C2311yescharacteristic
61C4×D4×C13—44no—
62C4×D4×C13C2×C414yes—
63C4×D4×C13D414yes—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—42no—
69C2×C13×C4⋊C4D411yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2312yes—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4D412yes—
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77#88194—28no—
78#88184—24no—
79#88184C2×C418yescomplemented
80C2×#6103—22no—
81C2×C4⋊Dic13C2311yescharacteristic
82C2×#6101—21no—
83C2×C4×Dic13—21no—
84C2×#6099—24no—
85C2×#6099—24no—
86C2×#6099—42no—
87C22×#1055C2312yes—
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90#88147—28no—
91#88138—216no—
92#88128—22no—
93#88128C2×C414yescomplemented
94C4×Dic26—22no—
95C4×Dic26C2×C414yescomplemented
96C13×#95—21no—
97C13×#95—22no—
98C22⋊#1055—24no—
99#88050—24no—
100#88050—22no—
101#88050D414yescomplemented
102#88049—24no—
103#88049—24no—
104#88049—42no—
105#88049—42no—
106C4⋊#1055—22no—
107C4×#1055—22no—
108#22432—131nomaximal, Sylow
109C24×C13C2×D412yes—
110C23×D13—22no—
111C2×D4×C13—22no—
112C2×D4×C13—22no—
113C2×D4×C13C22⋊C414yes—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—44no—
122C22×C4×C13—44no—
123C22×C4×C13—82no—
124C22×C4×C13C22×C414yes—
125C22×C4×C13C2×D414yes—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2411yescharacteristic
130C2×C22⋊D13—28no—
131C2×C22⋊D13—28no—
132C2×C22⋊D13—44no—
133C2×C22⋊D13—44no—
134C2×C22⋊D13—82no—
135C2×C22⋊D13—82no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138#6127—216no—
139#6127—48no—
140#6127—48no—
141#6127—48no—
142C2×D52—22no—
143C2×D52—22no—
144C2×D52—22no—
145C2×D52—22no—
146C2×D52—24no—
147C2×D52—22no—
148C2×D52—24no—
149C2×D52—42no—
150C2×D52—42no—
151C2×D52—81no—
152C2×D52—81no—
153C2×D52C22×C414yes—
154C2×C4×D13—28no—
155C2×C4×D13—44no—
156C2×C4×D13—44no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26C22×C412yes—
161C2×Dic26C2×D412yes—
162C2×Dic26#4112yes—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—44no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4—81no—
171C13×C4⋊C4C22⋊C414yes—
172C13×C4⋊C4C2×D412yes—
173C13×C22⋊C4—44no—
174C13×C22⋊C4C22⋊C418yes—
175C42×C13—42no—
176C42×C13C22×C412yes—
177C42×C13C2×D412yes—
178#6103—28no—
179C4⋊Dic13—21no—
180C4⋊Dic13C22×C412yes—
181#6101—24no—
182C4×Dic13—24no—
183#6099—48no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—21no—
190C2×#1055—22no—
191C2×#1055—21no—
192C2×#1055C2×D412yes—
193C2×#550—131no—
194C2×#436—131no—
195C2×#417—132no—
196D4×C4⋊C4D1311yescharacteristic, complemented
197#1982—131no—
198#1957—131no—
199#1895—132no—
200#1874—132no—
201#1803—131no—
202#1788—132no—
203C4×#103—131no—
204C23×C13—22no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13C2×C22⋊C414yes—
211C23×C13C22×D411yescharacteristic
212C22×D13—24no—
213C22×D13—42no—
214C22×D13—42no—
215C22×D13—42no—
216C22×D13—42no—
217C22×D13—42no—
218C22×D13—42no—
219D4×C13—28no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—22no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—42no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—41no—
237C2×C4×C13—88no—
238C2×C4×C13C2×C22⋊C412yes—
239C2×C4×C13C2×C22⋊C414yes—
240C2×C4×C13C2×C22⋊C412yes—
241C2×C4×C13AGL(1,ℤ/8)12yes—
242C2×C4×C13#13712yes—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13H(5,𝔽2)11yescharacteristic
248C2×C4×C13H(5,𝔽2)11yescharacteristic
249C22⋊D13—416no—
250C22⋊D13—88no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257D52—24no—
258D52—24no—
259D52—42no—
260D52—42no—
261D52—48no—
262D52—84no—
263C4×D13—416no—
264Dic26—22no—
265Dic26—22no—
266Dic26—22no—
267Dic26C4×D414yescomplemented
268#1055—22no—
269#1055—42no—
270#1055—41no—
271C22×#41—132no—
272C22×M16—132no—
273#550—138no—
274#550—264no—
275C2×#127—131no—
276C2×#127—261no—
277C2×#121—132no—
278C2×#121—262no—
279C2×C4×Q8—131no—
280C2×C4×D4—21no—
281C2×C4×D4—261no—
282C2×C4×D4C2×D1311yescharacteristic
283C22×C4⋊C4C2×D1312yes—
284#436—264no—
285C2×C4⋊C8—131no—
286#417—268no—
287C2×#103—131no—
288C2×#103—132no—
289C2×#103—131no—
290C2×#102—132no—
291C2×#102—132no—
292C2×#102—132no—
293C2×#102—132no—
294C2×C22⋊C8—132no—
295C2×C4×C8—131no—
296#389—21no—
297#385—22no—
298#384C2×D1311yescharacteristic
299#380C2×D1312yes—
300C4×C4⋊C4C2×D1311yescharacteristic
301#340—132no—
302#340—131no—
303#340—131no—
304C22×C13—24no—
305C22×C13—24no—
306C22×C13—24no—
307C22×C13—42no—
308C22×C13—42no—
309C22×C13—42no—
310C22×C13—42no—
311C22×C13C22×C22⋊C411yescharacteristic
312C22×C13D4211yescharacteristic
313C22×C13#54611yescharacteristic
314C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C13C2×#13711yescharacteristic
316C22×C13#57611yescharacteristic
317C22×C13#57711yescharacteristic
318C2×D13—44no—
319C2×D13—44no—
320C2×D13—44no—
321C2×D13—82no—
322C2×D13—82no—
323C2×D13—82no—
324C2×D13—82no—
325C4×C13—24no—
326C4×C13—22no—
327C4×C13—42no—
328C4×C13—81no—
329C4×C13—82no—
330C4×C13#41714yescomplemented
331C4×C13C2×C4×D411yescharacteristic
332C4×C13#51811yescharacteristic
333C4×C13D4211yescharacteristic
334C4×C13#54611yescharacteristic
335Dic13—24no—
336Dic13—42no—
337C2×#41—138no—
338C2×#41—264no—
339C2×#41—264no—
340C2×#41—264no—
341C2×#41—522no—
342C2×#41—522no—
343C22×Q8—131no—
344C22×D4—132no—
345C22×D4—262no—
346C22×D4—262no—
347C22×D4—261no—
348C22×D4—261no—
349C22×D4C22⋊D1311yescharacteristic
350C23×C4—22no—
351C23×C4—262no—
352C23×C4C22×D1312yes—
353C2×M16—264no—
354C2×M16—264no—
355C2×M16—522no—
356C22×C8—131no—
357C22×C8—132no—
358C22×C8—131no—
359#127—134no—
360#127—268no—
361#127—262no—
362#121—138no—
363#121—264no—
364#121—2616no—
365C4×Q8—134no—
366C4×Q8—262no—
367C4×D4—44no—
368C4×D4—268no—
369C4×D4C4×D1314yes—
370C4×D4D5214yes—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4C22⋊D1311yescharacteristic
379C2×C4⋊C4C22×D1312yes—
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C22⋊C4—22no—
383C2×C22⋊C4—262no—
384C2×C22⋊C4C22⋊D1312yes—
385C2×C42—21no—
386C2×C42—261no—
387C2×C42C22×D1311yescharacteristic
388C4⋊C8—262no—
389#103—134no—
390#103—264no—
391#103—262no—
392#102—264no—
393#102—264no—
394#102—522no—
395#102—522no—
396C22⋊C8—264no—
397C4×C8—262no—
398#95—21no—
399#95—22no—
400C2×C13—44no—
401C2×C13D4×C22⋊C411yescharacteristic
402C2×C13C2×#41711yescharacteristic
403C2×C13#289711yescharacteristic
404C2×C13#327411yescharacteristic
405C2×C13#327811yescharacteristic
406C2×C13#333211yescharacteristic
407C2×C13#333311yescharacteristic
408D13—84no—
409C24—262no—
410C24C2×C22⋊D1312yes—
411#41—2616no—
412#41—528no—
413#41—528no—
414#41—528no—
415C2×Q8—132no—
416C2×Q8—132no—
417C2×Q8—132no—
418C2×Q8—261no—
419C2×Q8—261no—
420C2×Q8—261no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—134no—
424C2×D4—268no—
425C2×D4—268no—
426C2×D4—264no—
427C2×D4—264no—
428C2×D4—262no—
429C2×D4—262no—
430C2×D4—262no—
431C2×D4—262no—
432C2×D4—262no—
433C2×D4—524no—
434C2×D4—524no—
435C2×D4—522no—
436C2×D4—522no—
437C2×D4—1041no—
438C2×D4—1041no—
439C2×D4—1042no—
440C2×D4—1042no—
441C2×D4#610314yes—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—82no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—268no—
455C22×C4—524no—
456C22×C4—524no—
457C22×C4C2×C4×D1314yes—
458C22×C4C2×D5214yes—
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1312yes—
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C23×D1311yescharacteristic
463M16—528no—
464C2×C8—132no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—262no—
469C2×C8—262no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—262no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—44no—
479C4⋊C4—42no—
480C4⋊C4—81no—
481C4⋊C4—132no—
482C4⋊C4—264no—
483C4⋊C4—261no—
484C4⋊C4#610314yes—
485C4⋊C4D4×D1312yes—
486C22⋊C4—44no—
487C22⋊C4—268no—
488C22⋊C4#610318yes—
489C42—42no—
490C42—264no—
491C42C2×C4×D1312yes—
492C42C2×D5212yes—
493C13#2243211yescharacteristic, complemented, Sylow
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—264no—
501C23—522no—
502C23—522no—
503C23—522no—
504C23—522no—
505C23—522no—
506C23—522no—
507C23C2×#610314yes—
508C23C22×C22⋊D1311yescharacteristic
509Q8—134no—
510Q8—262no—
511Q8—262no—
512Q8—262no—
513D4—28no—
514D4—264no—
515D4—264no—
516D4—5216no—
517D4—522no—
518D4—522no—
519D4—528no—
520D4—1044no—
521D4—1048no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—88no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—5216no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4C2×#610312yes—
548C2×C4C2×#610314yes—
549C2×C4C2×#610312yes—
550C2×C4#8818612yes—
551C2×C4#8819612yes—
552C2×C4C22×C4×D1311yescharacteristic
553C2×C4C22×D5211yescharacteristic
554C2×C4C2×D4×D1311yescharacteristic
555C2×C4#8825111yescharacteristic
556C2×C4#41×D1311yescharacteristic
557C2×C4#8825611yescharacteristic
558C8—262no—
559C8—522no—
560C8—521no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—524no—
569C22—524no—
570C22—524no—
571C22—1042no—
572C22—1042no—
573C22—1042no—
574C22—1042no—
575C22C22×#610311yescharacteristic
576C22C2×#8818611yescharacteristic
577C22D4×C22⋊D1311yescharacteristic
578C22C2×#8819611yescharacteristic
579C22#1171953411yescharacteristic
580C22#1171954011yescharacteristic
581C22#1171954211yescharacteristic
582C4—22no—
583C4—24no—
584C4—42no—
585C4—82no—
586C4—81no—
587C4—264no—
588C4—522no—
589C4#1171862714yescomplemented
590C4C4×D4×D1311yescharacteristic
591C4#1171925011yescharacteristic
592C4D4×D5211yescharacteristic
593C4#1171925911yescharacteristic
594C2—44no—
595C2—1044no—
596C2D4×#610311yescharacteristic
597C2C2×#1171862711yescharacteristic
598C2#1312335911yescharacteristic
599C2#1312645211yescharacteristic
600C2#1312649811yescharacteristic
601C2#1312715711yescharacteristic
602C2#1312716811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC2×#11719258C2
cosocleC22×C4×C13C24
hypercenterD4×C4⋊C4D13
hypocenterC13#22432
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718673C2semidirect
3. C2×#11718627C2semidirect
4. #13115763C2semidirect
5. #13115641C2semidirect
6. #13115272C2semidirect
7. #13115153C2semidirect
8. #13114838C2semidirect
9. #13114774C2semidirect
10. C4×#88050C2semidirect
11. D4×C13×C4⋊C4C2semidirect
20. #11719258C4semidirect
55. C2×#6127C2×C4semidirect
79. #88184C2×C4semidirect
93. #88128C2×C4semidirect
95. C4×Dic26C2×C4semidirect
101. #88050D4semidirect
196. D4×C4⋊C4D13semidirect
267. Dic26C4×D4semidirect
330. C4×C13#417semidirect
493. C13#22432semidirect
589. C4#11718627semidirect

Maximal subgroups

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

subgroupindex
C2×#117192582
C2×#117186732
C2×#117186272
#131157632
#131156412
#131152722
#131151532
#131148382
#131147742
C4×#880502
D4×C13×C4⋊C42
#2243213