Finite Group Databasebeta

← #15901927

Subgroups — #15901927

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718711C211yesmaximal, characteristic
2C22×#88050C211yesmaximal, characteristic
3C22⋊C4×Dic26C211yesmaximal, characteristic
4#13116255C212yesmaximal, complemented
5#13116158C212yesmaximal, complemented
6#13115260C211yesmaximal, characteristic
7#13115180C212yesmaximal, complemented
8#13115016C211yesmaximal, characteristic
9#13114922C211yesmaximal, characteristic
10#13114848C212yesmaximal, complemented
11C13×#2503C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C2×C13×C22⋊Q8C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×#6107C2211yescharacteristic
16C22×#6107C2211yescharacteristic
17C23×#1055C2211yescharacteristic
18C2×C4×Dic26C2212yes—
19C13×#400—22no—
20C13×#391C2212yes—
21C13×#382C2212yes—
22C13×#381—21no—
23C13×#381—21no—
24C4×C13×C22⋊C4C2211yescharacteristic
25C2×#88075C2212yes—
26#11718873C2211yescharacteristic
27C2×C22⋊#1055C2211yescharacteristic
28#11718711—24no—
29C2×#88050—24no—
30C2×#88050C2212yes—
31C2×#88050C2211yescharacteristic
32C2×#88050C2212yes—
33C2×#88050C2211yescharacteristic
34#11718603—21no—
35C22⋊C4×Dic13—21no—
36#11718590C2212yes—
37C2×C4⋊#1055C2212yes—
38#11718307—22no—
39#11718121C2212yes—
40#11718121C2212yes—
41#11718121C2212yes—
42#11718116C2212yes—
43C22×Q8×C13C2311yescharacteristic
44C23×C4×C13—21no—
45C23×C4×C13C2311yescharacteristic
46C23×Dic13—21no—
47C22×Dic26—24no—
48C22×Dic26—21no—
49C22×Dic26—22no—
50C22×Dic26—42no—
51C22×Dic26D414yes—
52C22×Dic26C2311yescharacteristic
53C22×Dic26C2311yescharacteristic
54C13×C22⋊Q8—22no—
55C13×C22⋊Q8—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4C2311yescharacteristic
61C2×C13×C4⋊C4C2312yes—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4D411yescharacteristic
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C42×C13C2312yes—
66C2×C22⋊Dic13—21no—
67C2×#6107—22no—
68C2×#6107—22no—
69C2×#6107—24no—
70C2×#6107—42no—
71C2×C4⋊Dic13C2312yes—
72C2×#6101—22no—
73C2×C4×Dic13—22no—
74C22×#1055—22no—
75C22×#1055—42no—
76C22×#1055C2312yes—
77C22×#1055C2311yescharacteristic
78C22×#1055C2311yescharacteristic
79C4×Dic26—24no—
80C4×Dic26—42no—
81C13×#95—22no—
82C13×#95—22no—
83C13×#95—22no—
84C13×#95—22no—
85C13×#95D412yes—
86#88075—42no—
87#88071—21no—
88#88071—22no—
89#88071—22no—
90C22⋊#1055—22no—
91#88050—22no—
92#88050—22no—
93#88050—24no—
94#88050—24no—
95C4⋊#1055—42no—
96#24529—131nomaximal, Sylow
97C24×C13C2×D411yescharacteristic
98C2×Q8×C13—21no—
99C2×Q8×C13—22no—
100C2×Q8×C13—21no—
101C2×Q8×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13—42no—
108C22×C4×C13—42no—
109C22×C4×C13—42no—
110C22×C4×C13C2×D412yes—
111C22×C4×C13C2×D412yes—
112C22×C4×C13C2×D412yes—
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13#4112yes—
115C22×C4×C13C2411yescharacteristic
116C22×Dic13—21no—
117C22×Dic13—24no—
118C22×Dic13—21no—
119C22×Dic13—22no—
120C22×Dic13—44no—
121C2×Dic26—21no—
122C2×Dic26—22no—
123C2×Dic26—22no—
124C2×Dic26—22no—
125C2×Dic26—28no—
126C2×Dic26—24no—
127C2×Dic26—21no—
128C2×Dic26—44no—
129C2×Dic26—48no—
130C2×Dic26—44no—
131C2×Dic26C2×D412yes—
132C2×Dic26C2×D412yes—
133C2×Dic26#4114yes—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—22no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—42no—
139C13×C4⋊C4—42no—
140C13×C22⋊C4—22no—
141C13×C22⋊C4—22no—
142C13×C22⋊C4—42no—
143C42×C13—22no—
144C42×C13—22no—
145C22⋊Dic13—42no—
146#6107—44no—
147#6107—44no—
148C4⋊Dic13—22no—
149C4⋊Dic13—22no—
150#6101—44no—
151C4×Dic13—44no—
152C2×#1055—21no—
153C2×#1055—21no—
154C2×#1055—22no—
155C2×#1055—22no—
156C2×#1055—22no—
157C2×#1055—22no—
158C2×#1055—22no—
159C2×#1055—44no—
160C2×#451—131no—
161C22×#103—131no—
162#2503D1311yescharacteristic
163Q8×C22⋊C4—131no—
164#2074—132no—
165#2056—132no—
166#1892—131no—
167#1878—132no—
168#1850—131no—
169#1823—131no—
170#1805—132no—
171C23×C13—22no—
172C23×C13—22no—
173C23×C13#12112yes—
174C23×C13#13512yes—
175C23×C13#13712yes—
176C23×C13C22×D411yescharacteristic
177Q8×C13—41no—
178Q8×C13—41no—
179Q8×C13—42no—
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—22no—
183C2×C4×C13—24no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—22no—
187C2×C4×C13—22no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—84no—
198C2×C4×C13#12112yes—
199C2×C4×C13C22×D411yescharacteristic
200C2×C4×C13C2×#4112yes—
201C2×C4×C13C2×#4111yescharacteristic
202C2×C4×C13H(5,𝔽2)12yes—
203C2×Dic13—22no—
204C2×Dic13—24no—
205C2×Dic13—22no—
206C2×Dic13—48no—
207C2×Dic13—42no—
208C2×Dic13—42no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211Dic26—22no—
212Dic26—24no—
213Dic26—22no—
214Dic26—22no—
215Dic26—48no—
216Dic26—42no—
217Dic26#12314yes—
218#1055—41no—
219#1055—42no—
220#1055—41no—
221C23×Q8—131no—
222C22×Q16—131no—
223C22×Q16—131no—
224C23×C8—131no—
225C2×C22⋊Q8C2×D1311yescharacteristic
226C2×C4×Q8—132no—
227C22×C4⋊C4C2×D1311yescharacteristic
228#451—264no—
229C2×C4⋊C8—132no—
230C2×#103—132no—
231C2×#103—131no—
232C2×#103—132no—
233C2×#103—131no—
234C2×#103—132no—
235C2×#103—264no—
236C2×C22⋊C8—131no—
237#400—22no—
238#391—132no—
239#391—262no—
240#391C2×D1312yes—
241#382C2×D1312yes—
242#381—21no—
243#381—21no—
244#380—131no—
245#380—261no—
246C4×C22⋊C4—261no—
247C4×C22⋊C4C2×D1311yescharacteristic
248#340—132no—
249#340—132no—
250#340—132no—
251#336—132no—
252C22×C13—22no—
253C22×C13—22no—
254C22×C13—24no—
255C22×C13—24no—
256C22×C13#46414yes—
257C22×C13C2×#12111yescharacteristic
258C22×C13#54612yes—
259C22×C13C2×#13511yescharacteristic
260C22×C13C2×#13711yescharacteristic
261C22×C13#57812yes—
262C4×C13—22no—
263C4×C13—42no—
264C4×C13—42no—
265C4×C13—81no—
266C4×C13—82no—
267C4×C13—81no—
268C4×C13C2×#12311yescharacteristic
269C4×C13#53411yescharacteristic
270C4×C13#55112yes—
271Dic13—24no—
272Dic13—42no—
273Dic13—82no—
274C22×Q8—134no—
275C22×Q8—131no—
276C22×Q8—131no—
277C22×Q8—264no—
278C22×Q8—262no—
279C22×Q8—261no—
280C22×Q8—522no—
281C22×Q8C22×D1311yescharacteristic
282C23×C4—21no—
283C23×C4—261no—
284C23×C4C22×D1311yescharacteristic
285C2×Q16—264no—
286C2×Q16—262no—
287C2×Q16—262no—
288C2×Q16—522no—
289C22×C8—132no—
290C22×C8—131no—
291C22×C8—131no—
292C22×C8—262no—
293C22×C8—522no—
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C4×Q8—264no—
297C4×Q8—522no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—132no—
303C2×C4⋊C4—262no—
304C2×C4⋊C4C22×D1312yes—
305C2×C4⋊C4C22×D1311yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—261no—
308C2×C22⋊C4C22⋊D1311yescharacteristic
309C2×C22⋊C4C22⋊D1311yescharacteristic
310C2×C42—262no—
311C2×C42C22×D1312yes—
312C4⋊C8—522no—
313#103—264no—
314#103—264no—
315#103—262no—
316#103—262no—
317#103—522no—
318C22⋊C8—262no—
319#95—22no—
320#95—22no—
321#95—22no—
322#95—22no—
323#95—262no—
324#95—261no—
325#95—262no—
326#95C22⋊D1312yes—
327C2×C13—24no—
328C2×C13#241211yescharacteristic
329C2×C13C2×#46411yescharacteristic
330C2×C13#304411yescharacteristic
331C2×C13#330012yes—
332C2×C13#331212yes—
333C24C2×C22⋊D1311yescharacteristic
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—132no—
339C2×Q8—132no—
340C2×Q8—134no—
341C2×Q8—268no—
342C2×Q8—264no—
343C2×Q8—261no—
344C2×Q8—261no—
345C2×Q8—262no—
346C2×Q8—262no—
347C2×Q8—262no—
348C2×Q8—524no—
349C2×Q8—524no—
350C2×Q8—528no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—261no—
360C22×C4—264no—
361C22×C4—261no—
362C22×C4—262no—
363C22×C4—524no—
364C22×C4D4×D1312yes—
365C22×C4#612912yes—
366C22×C4C2×C22⋊D1312yes—
367C22×C4C2×C22⋊D1312yes—
368C22×C4C2×C22⋊D1311yescharacteristic
369C22×C4C23×D1311yescharacteristic
370Q16—524no—
371Q16—524no—
372C2×C8—261no—
373C2×C8—261no—
374C2×C8—262no—
375C2×C8—262no—
376C2×C8—262no—
377C2×C8—262no—
378C2×C8—262no—
379C2×C8—524no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—262no—
387C4⋊C4—262no—
388C4⋊C4—524no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—42no—
392C22⋊C4—522no—
393C42—22no—
394C42—22no—
395C42—524no—
396C13#2452911yescharacteristic, complemented, Sylow
397C23—22no—
398C23—22no—
399C23#8819212yes—
400C23#8820412yes—
401C23#8820512yes—
402C23C22×C22⋊D1311yescharacteristic
403Q8—41no—
404Q8—41no—
405Q8—42no—
406Q8—134no—
407Q8—262no—
408Q8—264no—
409Q8—262no—
410Q8—262no—
411Q8—528no—
412Q8—522no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—84no—
431C2×C4—262no—
432C2×C4—264no—
433C2×C4—262no—
434C2×C4—528no—
435C2×C4—522no—
436C2×C4—522no—
437C2×C4—522no—
438C2×C4—522no—
439C2×C4#8819212yes—
440C2×C4C2×D4×D1311yescharacteristic
441C2×C4C2×#612911yescharacteristic
442C2×C4#41×D1312yes—
443C2×C4#8825612yes—
444C8—521no—
445C8—522no—
446C8—521no—
447C22—22no—
448C22—22no—
449C22—24no—
450C22—24no—
451C22#1171871514yes—
452C22C2×#8819211yescharacteristic
453C22C2×#8820411yescharacteristic
454C22C2×#8820511yescharacteristic
455C22#1171953412yes—
456C22#1171954312yes—
457C4—22no—
458C4—42no—
459C4—42no—
460C4—81no—
461C4—81no—
462C4—82no—
463C4—264no—
464C4—522no—
465C4—1042no—
466C4D13×#12311yescharacteristic
467C4#1171935811yescharacteristic
468C4#1171936312yes—
469C2—24no—
470C2#1311822811yescharacteristic
471C2C2×#1171871511yescharacteristic
472C2#1312436211yescharacteristic
473C2#1312671712yes—
474C2#1312688112yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2503C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2503D13
hypocenterC13#24529
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2503

Complements

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

NH ≅ G/Ntype
4. #13116255C2semidirect
5. #13116158C2semidirect
7. #13115180C2semidirect
10. #13114848C2semidirect
396. C13#24529semidirect

Maximal subgroups

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

subgroupindex
C2×#117187112
C22×#880502
C22⋊C4×Dic262
#131162552
#131161582
#131152602
#131151802
#131150162
#131149222
#131148482
C13×#25032
#2452913