Finite Group Databasebeta

← #15901903

Subgroups — #15901903

Order 3328.

1182 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718879C211yesmaximal, characteristic
2C22×#88072C211yesmaximal, characteristic
3#13119321C211yesmaximal, characteristic, complemented
4#13116249C212yesmaximal, complemented
5#13116153C212yesmaximal, complemented
6#13115257C211yesmaximal, characteristic, complemented
7#13115170C212yesmaximal, complemented
8#13115016C211yesmaximal, characteristic, complemented
9#13114920C211yesmaximal, characteristic, complemented
10#13114846C212yesmaximal, complemented
11D4×C13×C22⋊C4C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C2×C4×D4×C13C2212yes—
14C22×C13×C22⋊C4—21no—
15C22×#6105C2211yescharacteristic
16C22×#6105C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C2×#88178C2211yescharacteristic
19C23×#1055C2211yescharacteristic
20C13×#390C2212yes—
21C13×#386—22no—
22C13×#380C2211yescharacteristic
23C13×#379—21no—
24C4×C13×C22⋊C4C2211yescharacteristic
25#11718879—24no—
26C2×#88072—24no—
27C2×#88072C2212yes—
28C2×#88072C2211yescharacteristic
29C2×#88072C2212yes—
30C2×#88072C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88050C2212yescomplemented
33#11718604—21no—
34#11718604—21no—
35#11718597C2212yescomplemented
36#11718590C2212yescomplemented
37C2×C4⋊#1055C2212yescomplemented
38#11718320—22no—
39#11718121C2212yescomplemented
40#11718121C2212yescomplemented
41#11718121C2212yescomplemented
42#11718116C2212yescomplemented
43C25×C13—21no—
44C22×D4×C13—24no—
45C22×D4×C13—21no—
46C22×D4×C13—22no—
47C22×D4×C13—42no—
48C22×D4×C13D414yes—
49C22×D4×C13C2311yescharacteristic
50C22×D4×C13C2311yescharacteristic
51C23×C4×C13—22no—
52C23×C4×C13C2311yescharacteristic
53C23×Dic13—21no—
54C22×Dic26C2311yescharacteristic
55C4×D4×C13—24no—
56C4×D4×C13—42no—
57C2×C13×C4⋊C4C2312yes—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—44no—
63C2×C13×C22⋊C4D411yescharacteristic
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C42×C13C2312yes—
66C2×C22⋊Dic13—21no—
67C2×#6105—22no—
68C2×#6105—22no—
69C2×#6105—24no—
70C2×#6105—42no—
71C2×C4⋊Dic13—22no—
72C2×C4⋊Dic13—22no—
73C2×C4⋊Dic13—21no—
74C2×C4⋊Dic13C2311yescharacteristic
75C2×C4⋊Dic13C2312yes—
76#88178—22no—
77#88178—22no—
78C2×#6101—21no—
79C22×#1055—22no—
80C22×#1055—42no—
81C22×#1055C2312yes—
82C22×#1055C2311yescharacteristic
83C22×#1055C2311yescharacteristic
84C13×#95—21no—
85C13×#95D412yes—
86#88072—24no—
87#88072—24no—
88#88072—22no—
89#88072—22no—
90#88071—22no—
91#88071—22no—
92#88071—22no—
93#88071—22no—
94C22⋊#1055—22no—
95#88050—42no—
96C4⋊#1055—42no—
97#24527—131nomaximal, Sylow
98C24×C13—21no—
99C24×C13—21no—
100C24×C13—24no—
101C24×C13—44no—
102C24×C13—42no—
103C24×C13—42no—
104C24×C13—82no—
105C24×C13C2×D411yescharacteristic
106C2×D4×C13—28no—
107C2×D4×C13—24no—
108C2×D4×C13—21no—
109C2×D4×C13—22no—
110C2×D4×C13—21no—
111C2×D4×C13—22no—
112C2×D4×C13—22no—
113C2×D4×C13—44no—
114C2×D4×C13—48no—
115C2×D4×C13—44no—
116C2×D4×C13C2×D412yes—
117C2×D4×C13C2×D412yes—
118C2×D4×C13#4114yes—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—44no—
123C22×C4×C13—44no—
124C22×C4×C13—82no—
125C22×C4×C13C2×D412yes—
126C22×C4×C13C2×D412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13#4112yes—
130C22×C4×C13C2411yescharacteristic
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—22no—
134C22×Dic13—42no—
135C22×Dic13—42no—
136C22×Dic13—42no—
137C2×Dic26—21no—
138C2×Dic26—21no—
139C2×Dic26—22no—
140C2×Dic26—22no—
141C13×C4⋊C4—22no—
142C13×C4⋊C4—22no—
143C13×C22⋊C4—22no—
144C13×C22⋊C4—22no—
145C13×C22⋊C4—44no—
146C13×C22⋊C4—44no—
147C13×C22⋊C4—42no—
148C13×C22⋊C4—82no—
149C42×C13—22no—
150C42×C13—22no—
151C22⋊Dic13—42no—
152#6105—44no—
153#6105—44no—
154C4⋊Dic13—21no—
155C4⋊Dic13—22no—
156C4⋊Dic13—21no—
157C4⋊Dic13—22no—
158C4⋊Dic13—42no—
159#6101—42no—
160C2×#1055—21no—
161C2×#1055—21no—
162C2×#1055—22no—
163C2×#1055—22no—
164C2×#1055—22no—
165C2×#1055—22no—
166C2×#1055—22no—
167C2×#1055—44no—
168C2×#450—131no—
169C22×#102—131no—
170#2503—131no—
171D4×C22⋊C4D1311yescharacteristic
172#2073—132no—
173#2055—132no—
174#1892—131no—
175#1877—132no—
176#1850—131no—
177#1823—131no—
178#1804—132no—
179C23×C13—22no—
180C23×C13—22no—
181C23×C13—22no—
182C23×C13—24no—
183C23×C13—22no—
184C23×C13—48no—
185C23×C13—41no—
186C23×C13—41no—
187C23×C13—42no—
188C23×C13—42no—
189C23×C13—41no—
190C23×C13—41no—
191C23×C13—42no—
192C23×C13—48no—
193C23×C13—84no—
194C23×C13—88no—
195C23×C13—88no—
196C23×C13#12112yes—
197C23×C13#13512yes—
198C23×C13AGL(1,ℤ/8)12yes—
199C23×C13C22×D411yescharacteristic
200D4×C13—22no—
201D4×C13—22no—
202D4×C13—22no—
203D4×C13—24no—
204D4×C13—48no—
205D4×C13—42no—
206D4×C13#12314yes—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—22no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—88no—
221C2×C4×C13#12112yes—
222C2×C4×C13C22×D411yescharacteristic
223C2×C4×C13C2×#4112yes—
224C2×C4×C13C2×#4111yescharacteristic
225C2×C4×C13H(5,𝔽2)12yes—
226C2×Dic13—41no—
227C2×Dic13—41no—
228C2×Dic13—42no—
229C2×Dic13—42no—
230C2×Dic13—42no—
231C2×Dic13—42no—
232C2×Dic13—42no—
233C2×Dic13—84no—
234Dic26—41no—
235Dic26—41no—
236Dic26—42no—
237#1055—41no—
238#1055—42no—
239#1055—41no—
240C23×D4C2×D1311yescharacteristic
241C22×SD16—131no—
242C22×SD16—131no—
243C23×C8—131no—
244C2×C22⋊Q8—131no—
245C2×C4×D4C2×D1312yes—
246C22×C4⋊C4—131no—
247C22×C22⋊C4—21no—
248#450—264no—
249C2×C4⋊C8—132no—
250C2×#103—132no—
251C2×#102—132no—
252C2×#102—131no—
253C2×#102—132no—
254C2×#102—131no—
255C2×#102—264no—
256C2×C22⋊C8—131no—
257#400—262no—
258#391—132no—
259#390C2×D1312yes—
260#386—22no—
261#382—132no—
262#381—261no—
263#381—261no—
264#380C2×D1311yescharacteristic
265#379—21no—
266C4×C22⋊C4C2×D1311yescharacteristic
267#340—132no—
268#340—132no—
269#340—132no—
270#336—132no—
271C22×C13—22no—
272C22×C13—24no—
273C22×C13—22no—
274C22×C13—24no—
275C22×C13—24no—
276C22×C13—42no—
277C22×C13—44no—
278C22×C13—42no—
279C22×C13—44no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—816no—
284C22×C13—82no—
285C22×C13—82no—
286C22×C13#46314yes—
287C22×C13C2×#12111yescharacteristic
288C22×C13#54612yes—
289C22×C13C2×#13511yescharacteristic
290C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C13#57712yes—
292C4×C13—22no—
293C4×C13—42no—
294C4×C13—42no—
295C4×C13—82no—
296C4×C13C2×#12311yescharacteristic
297C4×C13#53411yescharacteristic
298C4×C13#55112yes—
299Dic13—81no—
300Dic13—82no—
301Dic13—81no—
302C25—21no—
303C22×Q8—131no—
304C22×D4—24no—
305C22×D4—22no—
306C22×D4—21no—
307C22×D4—42no—
308C22×D4D5214yes—
309C22×D4C22×D1311yescharacteristic
310C22×D4C22×D1311yescharacteristic
311C23×C4—22no—
312C23×C4—261no—
313C23×C4C22×D1311yescharacteristic
314C2×SD16—262no—
315C2×SD16—262no—
316C2×SD16—264no—
317C2×SD16—522no—
318C22×C8—132no—
319C22×C8—131no—
320C22×C8—131no—
321C22×C8—262no—
322C22×C8—522no—
323C22⋊Q8—262no—
324C22⋊Q8—262no—
325C4×D4—24no—
326C4×D4—42no—
327C2×C4⋊C4—132no—
328C2×C4⋊C4—131no—
329C2×C4⋊C4—262no—
330C2×C4⋊C4—262no—
331C2×C4⋊C4—261no—
332C2×C4⋊C4—261no—
333C2×C4⋊C4C22×D1312yes—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—261no—
340C2×C22⋊C4C22⋊D1311yescharacteristic
341C2×C22⋊C4C22⋊D1311yescharacteristic
342C2×C42C22×D1312yes—
343C4⋊C8—522no—
344#103—522no—
345#102—264no—
346#102—264no—
347#102—262no—
348#102—262no—
349C22⋊C8—262no—
350#95—21no—
351#95—262no—
352#95—262no—
353#95—262no—
354#95—262no—
355#95C22⋊D1312yes—
356C2×C13—24no—
357C2×C13—44no—
358C2×C13—82no—
359C2×C13#241211yescharacteristic
360C2×C13C2×#46311yescharacteristic
361C2×C13#304211yescharacteristic
362C2×C13#329612yes—
363C2×C13#331012yes—
364C24—21no—
365C24—21no—
366C24—24no—
367C24—44no—
368C24—42no—
369C24—42no—
370C24—82no—
371C24C2×C22⋊D1311yescharacteristic
372C2×Q8—261no—
373C2×Q8—261no—
374C2×Q8—262no—
375C2×Q8—262no—
376C2×D4—28no—
377C2×D4—24no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—44no—
384C2×D4—48no—
385C2×D4—44no—
386C2×D4C2×D5212yes—
387C2×D4C2×D5212yes—
388C2×D4#612914yes—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—44no—
393C22×C4—44no—
394C22×C4—82no—
395C22×C4—261no—
396C22×C4—261no—
397C22×C4—262no—
398C22×C4—522no—
399C22×C4—522no—
400C22×C4—522no—
401C22×C4C2×D5212yes—
402C22×C4#612712yes—
403C22×C4C2×C22⋊D1312yes—
404C22×C4C2×C22⋊D1312yes—
405C22×C4C2×C22⋊D1311yescharacteristic
406C22×C4C23×D1311yescharacteristic
407SD16—524no—
408SD16—524no—
409C2×C8—261no—
410C2×C8—261no—
411C2×C8—262no—
412C2×C8—262no—
413C2×C8—262no—
414C2×C8—262no—
415C2×C8—262no—
416C2×C8—524no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—262no—
420C4⋊C4—261no—
421C4⋊C4—262no—
422C4⋊C4—261no—
423C4⋊C4—522no—
424C4⋊C4—522no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—44no—
428C22⋊C4—44no—
429C22⋊C4—42no—
430C22⋊C4—82no—
431C22⋊C4—522no—
432C42—22no—
433C42—22no—
434C13#2452711yescharacteristic, complemented, Sylow
435C23—22no—
436C23—22no—
437C23—22no—
438C23—24no—
439C23—22no—
440C23—48no—
441C23—41no—
442C23—41no—
443C23—42no—
444C23—48no—
445C23—41no—
446C23—42no—
447C23—41no—
448C23—42no—
449C23—84no—
450C23—88no—
451C23—88no—
452C23#8818412yes—
453C23#8818612yes—
454C23#8820412yes—
455C23C22×C22⋊D1311yescharacteristic
456Q8—521no—
457Q8—521no—
458Q8—522no—
459D4—22no—
460D4—22no—
461D4—22no—
462D4—24no—
463D4—48no—
464D4—42no—
465D4#8814014yes—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—88no—
480C2×C4—521no—
481C2×C4—521no—
482C2×C4—522no—
483C2×C4—522no—
484C2×C4—522no—
485C2×C4—522no—
486C2×C4—522no—
487C2×C4—1044no—
488C2×C4#8818412yes—
489C2×C4C22×D5211yescharacteristic
490C2×C4C2×#612711yescharacteristic
491C2×C4C2×#612912yes—
492C2×C4#8825112yes—
493C8—521no—
494C8—522no—
495C8—521no—
496C22—24no—
497C22—22no—
498C22—24no—
499C22—22no—
500C22—24no—
501C22—44no—
502C22—42no—
503C22—44no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—816no—
509C22—82no—
510C22—82no—
511C22#1171867714yes—
512C22C2×#8818411yescharacteristic
513C22C2×#8818611yescharacteristic
514C22#1171951112yes—
515C22C2×#8820411yescharacteristic
516C22#1171954112yes—
517C4—22no—
518C4—42no—
519C4—42no—
520C4—82no—
521C4—1041no—
522C4—1042no—
523C4—1041no—
524C4C2×#8814011yescharacteristic
525C4#1171919811yescharacteristic
526C4#1171920012yes—
527C2—24no—
528C2—44no—
529C2—82no—
530C2#1311822611yescharacteristic
531C2C2×#1171867711yescharacteristic
532C2#1312434811yescharacteristic
533C2#1312667112yes—
534C2#1312685712yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingD4×C13×C22⋊C4C2
socleC23×C13C22×D4
prime radicalC23×D4×C13C22
hypercenterD4×C22⋊C4D13
hypocenterC13#24527
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #13119321C2semidirect
4. #13116249C2semidirect
5. #13116153C2semidirect
6. #13115257C2semidirect
7. #13115170C2semidirect
8. #13115016C2semidirect
9. #13114920C2semidirect
10. #13114846C2semidirect
32. C2×#88050C22semidirect
35. #11718597C22semidirect
36. #11718590C22semidirect
37. C2×C4⋊#1055C22semidirect
39. #11718121C22semidirect
40. #11718121C22semidirect
41. #11718121C22semidirect
42. #11718116C22semidirect
434. C13#24527semidirect

Maximal subgroups

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

subgroupindex
C2×#117188792
C22×#880722
#131193212
#131162492
#131161532
#131152572
#131151702
#131150162
#131149202
#131148462
D4×C13×C22⋊C42
#2452713