Finite Group Databasebeta

← #15901289

Subgroups — #15901289

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718705C211yesmaximal, characteristic, complemented
2C22×#88072C211yesmaximal, characteristic
3#13117711C211yesmaximal, characteristic, complemented
4#13116224C212yesmaximal, complemented
5#13116072C212yesmaximal, complemented
6#13115769C212yesmaximal, complemented
7#13115453C212yesmaximal, complemented
8#13115260C211yesmaximal, characteristic, complemented
9#13115016C211yesmaximal, characteristic, complemented
10#13114767C211yesmaximal, characteristic
11C13×#2435C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C2×C13×#124C2212yes—
14C2×C13×C22⋊Q8C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C23×#1055C2211yescharacteristic
17C13×#394—22no—
18C13×#390C2212yes—
19C13×#379—21no—
20C13×#379—21no—
21C4×C13×C22⋊C4C2211yescharacteristic
22C2×#88075C2211yescharacteristic, complemented
23C2×#88075C2211yescharacteristic, complemented
24C2×#88075C2212yescomplemented
25C2×#88072—24no—
26C2×#88072C2212yes—
27C2×#88072C2212yes—
28C2×#88072C2212yes—
29C2×#88072C2212yes—
30#11718873C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32#11718705—24no—
33C2×#88047C2211yescharacteristic, complemented
34C2×#88047C2211yescharacteristic, complemented
35#11718603—21no—
36C22⋊C4×Dic13—21no—
37C4×C4⋊Dic13C2212yescomplemented
38#11718589C2212yescomplemented
39C2×C4⋊#1055C2212yescomplemented
40#11718315—22no—
41#11718121C2212yescomplemented
42#11718116C2212yescomplemented
43C25×C13—21no—
44C22×Q8×C13C2311yescharacteristic
45C22×D4×C13—24no—
46C22×D4×C13—22no—
47C22×D4×C13—21no—
48C22×D4×C13—22no—
49C22×D4×C13—42no—
50C22×D4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C23×Dic13—21no—
53C13×#124—24no—
54C13×#124—42no—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—22no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4C2311yescharacteristic
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C13×C22⋊C4D411yescharacteristic
66C2×C42×C13C2312yes—
67C2×C22⋊Dic13—21no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13D414yes—
71C2×C4⋊Dic13C2312yes—
72C2×C4⋊Dic13C2311yescharacteristic
73C2×C4⋊Dic13C2311yescharacteristic
74C2×#6101—22no—
75C2×C4×Dic13—22no—
76C22×#1055—22no—
77C22×#1055—42no—
78C22×#1055C2312yes—
79C22×#1055C2311yescharacteristic
80C22×#1055C2311yescharacteristic
81C13×#95D412yes—
82#88075—22no—
83#88075—22no—
84#88075—42no—
85#88072—24no—
86#88072—24no—
87#88072—24no—
88#88072—42no—
89#88071—21no—
90#88071—22no—
91#88071—22no—
92C22⋊#1055—22no—
93#88047—22no—
94#88047—22no—
95C4⋊#1055—42no—
96#24479—131nomaximal, Sylow
97C24×C13—22no—
98C24×C13—44no—
99C24×C13—42no—
100C24×C13—42no—
101C24×C13—42no—
102C24×C13—82no—
103C24×C13C2×D411yescharacteristic
104C2×Q8×C13—21no—
105C2×Q8×C13—21no—
106C2×Q8×C13—22no—
107C2×Q8×C13—22no—
108C2×D4×C13—28no—
109C2×D4×C13—22no—
110C2×D4×C13—22no—
111C2×D4×C13—22no—
112C2×D4×C13—22no—
113C2×D4×C13—22no—
114C2×D4×C13—48no—
115C2×D4×C13—44no—
116C2×D4×C13—44no—
117C2×D4×C13—42no—
118C2×D4×C13#4114yes—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13C2×D412yes—
124C22×C4×C13C2×D412yes—
125C22×C4×C13C2×D412yes—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13#4112yes—
128C22×C4×C13C2411yescharacteristic
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—24no—
132C22×Dic13—22no—
133C22×Dic13—82no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—42no—
137C13×C22⋊C4—22no—
138C13×C22⋊C4—22no—
139C13×C22⋊C4—44no—
140C13×C22⋊C4—44no—
141C13×C22⋊C4—42no—
142C13×C22⋊C4—82no—
143C13×C22⋊C4—82no—
144C42×C13—22no—
145C42×C13—22no—
146C22⋊Dic13—42no—
147C4⋊Dic13—24no—
148C4⋊Dic13—21no—
149C4⋊Dic13—21no—
150C4⋊Dic13—22no—
151C4⋊Dic13—22no—
152C4⋊Dic13C2×D412yes—
153C4⋊Dic13C2×D412yes—
154#6101—82no—
155C4×Dic13—82no—
156C2×#1055—21no—
157C2×#1055—21no—
158C2×#1055—22no—
159C2×#1055—22no—
160C2×#1055—22no—
161C2×#1055—22no—
162C2×#1055—22no—
163C2×#1055—44no—
164C2×#484—131no—
165C22×#102—131no—
166#2435D1311yescharacteristic
167#2345—131no—
168#2067—132no—
169#2042—132no—
170#1983—132no—
171#1925—132no—
172#1892—131no—
173#1850—131no—
174#1786—131no—
175C23×C13—22no—
176C23×C13—22no—
177C23×C13—24no—
178C23×C13—48no—
179C23×C13—42no—
180C23×C13—42no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13—42no—
184C23×C13—42no—
185C23×C13—88no—
186C23×C13—88no—
187C23×C13—84no—
188C23×C13—84no—
189C23×C13#12112yes—
190C23×C13#13512yes—
191C23×C13#13712yes—
192C23×C13C22×D411yescharacteristic
193Q8×C13—41no—
194Q8×C13—41no—
195Q8×C13—42no—
196D4×C13—24no—
197D4×C13—24no—
198D4×C13—48no—
199D4×C13—42no—
200D4×C13—42no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—24no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13#12112yes—
216C2×C4×C13C22×D411yescharacteristic
217C2×C4×C13C2×#4112yes—
218C2×C4×C13C2×#4111yescharacteristic
219C2×C4×C13H(5,𝔽2)12yes—
220C2×Dic13—22no—
221C2×Dic13—22no—
222C2×Dic13—42no—
223C2×Dic13—42no—
224C2×Dic13—42no—
225C2×Dic13—42no—
226C2×Dic13—42no—
227C2×Dic13—84no—
228#1055—41no—
229#1055—41no—
230#1055—42no—
231C23×D4C2×D1311yescharacteristic
232C23×C8—131no—
233C2×#124C2×D1312yes—
234C2×C22⋊Q8C2×D1311yescharacteristic
235C22×C4⋊C4—131no—
236#484—264no—
237C2×#107—131no—
238C2×#107—131no—
239C2×C4⋊C8—132no—
240C2×#103—131no—
241C2×#103—131no—
242C2×#103—132no—
243C2×#102—132no—
244C2×#102—132no—
245C2×#102—132no—
246C2×#102—132no—
247C2×#102—264no—
248C2×C22⋊C8—131no—
249#394—22no—
250#390C2×D1312yes—
251#389—132no—
252#387—262no—
253#380—131no—
254#380—261no—
255#379—21no—
256#379—21no—
257C4×C4⋊C4—132no—
258C4×C22⋊C4—261no—
259C4×C22⋊C4C2×D1311yescharacteristic
260#340—132no—
261#336—132no—
262C22×C13—22no—
263C22×C13—22no—
264C22×C13—24no—
265C22×C13—24no—
266C22×C13—44no—
267C22×C13—44no—
268C22×C13—44no—
269C22×C13—816no—
270C22×C13—82no—
271C22×C13—82no—
272C22×C13—82no—
273C22×C13—82no—
274C22×C13#46414yes—
275C22×C13C2×#12111yescharacteristic
276C22×C13#54612yes—
277C22×C13C2×#13511yescharacteristic
278C22×C13C2×#13711yescharacteristic
279C22×C13#57612yes—
280C4×C13—22no—
281C4×C13—42no—
282C4×C13—42no—
283C4×C13—81no—
284C4×C13—81no—
285C4×C13#52511yescharacteristic
286C4×C13#53511yescharacteristic
287C4×C13#55112yes—
288Dic13—42no—
289Dic13—42no—
290Dic13—82no—
291C25—21no—
292C22×Q8C22×D1311yescharacteristic
293C22×D4—24no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—21no—
297C22×D4—42no—
298C22×D4C22×D1312yes—
299C23×C4—261no—
300C23×C4C22×D1311yescharacteristic
301C22×C8—132no—
302C22×C8—131no—
303C22×C8—131no—
304C22×C8—262no—
305C22×C8—522no—
306#124—24no—
307#124—42no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—134no—
312C2×C4⋊C4—131no—
313C2×C4⋊C4—131no—
314C2×C4⋊C4—132no—
315C2×C4⋊C4—262no—
316C2×C4⋊C4—261no—
317C2×C4⋊C4—262no—
318C2×C4⋊C4C22×D1311yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—261no—
325C2×C22⋊C4C22⋊D1311yescharacteristic
326C2×C22⋊C4C22⋊D1311yescharacteristic
327C2×C42—262no—
328C2×C42C22×D1312yes—
329#107—262no—
330#107—262no—
331C4⋊C8—522no—
332#103—262no—
333#103—262no—
334#103—522no—
335#102—264no—
336#102—264no—
337#102—264no—
338#102—522no—
339C22⋊C8—262no—
340#95—262no—
341#95—262no—
342#95—261no—
343#95C22⋊D1312yes—
344C2×C13—24no—
345C2×C13—84no—
346C2×C13#241111yescharacteristic
347C2×C13C2×#46411yescharacteristic
348C2×C13#304111yescharacteristic
349C2×C13#329712yes—
350C2×C13#331412yes—
351C24—22no—
352C24—44no—
353C24—42no—
354C24—42no—
355C24—42no—
356C24—82no—
357C24C2×C22⋊D1311yescharacteristic
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×D4—28no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—48no—
369C2×D4—44no—
370C2×D4—44no—
371C2×D4—42no—
372C2×D4#612914yes—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—261no—
378C22×C4—261no—
379C22×C4—264no—
380C22×C4—262no—
381C22×C4—1042no—
382C22×C4D4×D1312yes—
383C22×C4#612912yes—
384C22×C4C2×C22⋊D1312yes—
385C22×C4C2×C22⋊D1312yes—
386C22×C4C2×C22⋊D1311yescharacteristic
387C22×C4C23×D1311yescharacteristic
388C2×C8—261no—
389C2×C8—261no—
390C2×C8—262no—
391C2×C8—262no—
392C2×C8—262no—
393C2×C8—262no—
394C2×C8—262no—
395C2×C8—524no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—42no—
399C4⋊C4—132no—
400C4⋊C4—132no—
401C4⋊C4—264no—
402C4⋊C4—261no—
403C4⋊C4—261no—
404C4⋊C4—262no—
405C4⋊C4—262no—
406C4⋊C4—1042no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—44no—
410C22⋊C4—44no—
411C22⋊C4—42no—
412C22⋊C4—82no—
413C22⋊C4—82no—
414C22⋊C4—522no—
415C42—22no—
416C42—22no—
417C42—1042no—
418C13#2447911yescharacteristic, complemented, Sylow
419C23—22no—
420C23—22no—
421C23—24no—
422C23—48no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23—88no—
430C23—88no—
431C23—84no—
432C23—84no—
433C23#8819212yes—
434C23#8820412yes—
435C23#8820512yes—
436C23C22×C22⋊D1311yescharacteristic
437Q8—41no—
438Q8—42no—
439Q8—41no—
440D4—24no—
441D4—24no—
442D4—48no—
443D4—42no—
444D4—42no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—262no—
460C2×C4—262no—
461C2×C4—522no—
462C2×C4—522no—
463C2×C4—522no—
464C2×C4—522no—
465C2×C4—522no—
466C2×C4—1044no—
467C2×C4#8819212yes—
468C2×C4C2×D4×D1311yescharacteristic
469C2×C4C2×#612912yes—
470C2×C4C2×#612911yescharacteristic
471C2×C4#8825112yes—
472C8—521no—
473C8—521no—
474C8—522no—
475C22—24no—
476C22—22no—
477C22—24no—
478C22—22no—
479C22—44no—
480C22—44no—
481C22—44no—
482C22—816no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22#1171871514yes—
488C22C2×#8819211yescharacteristic
489C22#1171951112yes—
490C22C2×#8820411yescharacteristic
491C22C2×#8820511yescharacteristic
492C22#1171954012yes—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—81no—
497C4—81no—
498C4—522no—
499C4—522no—
500C4—1042no—
501C4#1171929111yescharacteristic
502C4#1171929212yes—
503C4#1171929711yescharacteristic
504C2—24no—
505C2—84no—
506C2#1311821711yescharacteristic
507C2C2×#1171871511yescharacteristic
508C2#1312433511yescharacteristic
509C2#1312668612yes—
510C2#1312691712yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2435C2
socleC23×C13C22×D4
prime radicalC23×D4×C13C22
hypercenter#2435D13
hypocenterC13#24479
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2435

Complements

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

NH ≅ G/Ntype
1. C2×#11718705C2semidirect
3. #13117711C2semidirect
4. #13116224C2semidirect
5. #13116072C2semidirect
6. #13115769C2semidirect
7. #13115453C2semidirect
8. #13115260C2semidirect
9. #13115016C2semidirect
22. C2×#88075C22semidirect
23. C2×#88075C22semidirect
24. C2×#88075C22semidirect
33. C2×#88047C22semidirect
34. C2×#88047C22semidirect
37. C4×C4⋊Dic13C22semidirect
38. #11718589C22semidirect
39. C2×C4⋊#1055C22semidirect
41. #11718121C22semidirect
42. #11718116C22semidirect
418. C13#24479semidirect

Maximal subgroups

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

subgroupindex
C2×#117187052
C22×#880722
#131177112
#131162242
#131160722
#131157692
#131154532
#131152602
#131150162
#131147672
C13×#24352
#2447913