Finite Group Databasebeta

← #15758119

Subgroups — #15758119

Order 3328.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124840C211yesmaximal, characteristic
2#13115634C211yesmaximal, characteristic
3#13113493C211yesmaximal, characteristic, complemented
4#13113260C211yesmaximal, characteristic
5#13112731C211yesmaximal, characteristic, complemented
6#13112681C211yesmaximal, characteristic, complemented
7C13×#2961C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C13×#446—22no—
11C13×#446—22no—
12C13×#424—21no—
13C13×#423C2211yescharacteristic
14C13×#405—21no—
15C2×C13×#97C2211yescharacteristic
16C2×#88060—21no—
17C2×#88060—21no—
18#11718745—21no—
19#11718744—21no—
20#11718707C412yes—
21#11718704C412yes—
22C4×#6106—22no—
23#11718586C2211yescharacteristic
24#11718586C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26#11718139—21no—
27#11718138—21no—
28#11718075—22no—
29C22×D52C2×C411yescharacteristic
30C22×C4×D13—21no—
31C2×C13×M16—21no—
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C13×C4⋊Q8D411yescharacteristic
35C13×C4⋊Q8D411yescharacteristic
36C13×#125—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8C2×C412yes—
39C4×Q8×C13—21no—
40C4×Q8×C13D412yes—
41C13×#117—21no—
42C2×C42×C13C2311yescharacteristic
43C2×#6106—22no—
44C2×#6103—21no—
45C2×C4⋊Dic13C2×C411yescharacteristic
46C22×#1055—21no—
47C4×D52—21no—
48C4×D52—21no—
49C4×D52—21no—
50C4×D52—21no—
51C13×C4⋊C8—24no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8D412yes—
54C13×#97—22no—
55C13×#97—21no—
56C13×#97—21no—
57C4×C8×C13—22no—
58#88075—22no—
59C22⋊#1055—21no—
60C22⋊#1055C2×C412yes—
61#88060—42no—
62#88060—42no—
63#88049—22no—
64#88048—22no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4×#1055—21no—
70C4×#1055—21no—
71#9050—131nomaximal, Sylow
72C23×D13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13C22⋊C412yes—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13#4111yescharacteristic
78C22×Dic13—21no—
79C2×D52—21no—
80C2×D52—21no—
81C2×D52—42no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×C4×D13—41no—
88C13×M16—41no—
89C13×M16—41no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—22no—
93C2×C8×C13—21no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13SD1612yescomplemented
97C13×C4⋊C4—22no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4C22⋊C412yes—
103C13×C22⋊C4—22no—
104C42×C13—22no—
105C42×C13C2×D411yescharacteristic
106C42×C13C2×D411yescharacteristic
107C42×C13C2×D411yescharacteristic
108C42×C13#4111yescharacteristic
109#6106—44no—
110#6103—41no—
111#6103—41no—
112C4⋊Dic13—21no—
113C4⋊Dic13—21no—
114C2×#1055—22no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119#3101—131no—
120#2961D1311yescharacteristic, complemented
121#1955—131no—
122#1542—131no—
123#1486—131no—
124#1301—131no—
125#1281—131no—
126C23×C13C4×D411yescharacteristic
127C22×D13—22no—
128C22×D13—41no—
129C22×D13—41no—
130C22×D13—41no—
131C22×D13—41no—
132C22×D13—41no—
133C22×D13—41no—
134Q8×C13—42no—
135Q8×C13—81no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13C2×C22⋊C411yescharacteristic
141C2×C4×C13C4×D411yescharacteristic
142C2×C4×C13#12011yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12311yescharacteristic
146C2×C4×C13C2×SD1611yescharacteristic
147C2×C4×C13#13511yescharacteristic
148C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C13#13711yescharacteristic
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153D52—22no—
154D52—22no—
155D52—41no—
156D52—41no—
157C4×D13—81no—
158C4×D13—81no—
159C4×D13—81no—
160C4×D13—81no—
161C8×C13—22no—
162C8×C13—41no—
163C8×C13—42no—
164#1055—42no—
165#1055—81no—
166#1055—81no—
167#533C2×D1311yescharacteristic
168C2×C4×D4—131no—
169#483—132no—
170#476—261no—
171#461—261no—
172#450—132no—
173#446—22no—
174#446—22no—
175C4×SD16—262no—
176#431—131no—
177#431—131no—
178#424—21no—
179#423C2×D1311yescharacteristic
180C2×C4⋊C8—131no—
181C2×C22⋊C8—261no—
182C2×C22⋊C8—261no—
183#405—21no—
184C2×#97C2×D1311yescharacteristic
185#333—261no—
186#332—261no—
187D4⋊C8—262no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13#38611yescharacteristic
191C22×C13C4×SD1611yescharacteristic
192C22×C13#44011yescharacteristic
193C2×D13—42no—
194C2×D13—42no—
195C2×D13—42no—
196C2×D13—81no—
197C2×D13—81no—
198C2×D13—81no—
199C2×D13—81no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—42no—
205C4×C13—42no—
206C4×C13#44811yescharacteristic
207C4×C13#44911yescharacteristic
208C4×C13#46011yescharacteristic
209C4×C13#46411yescharacteristic
210Dic13—81no—
211C22×D4—131no—
212C23×C4—261no—
213C2×SD16—262no—
214C2×M16—21no—
215C22×C8—261no—
216C22×C8C22⋊D1311yescharacteristic
217C22×C8C22⋊D1311yescharacteristic
218C4⋊Q8D5211yescharacteristic
219C4⋊Q8D5211yescharacteristic
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8C4×D1312yes—
223C4×Q8—21no—
224C4×Q8C22⋊D1312yes—
225C4×D4—261no—
226C4×D4—261no—
227C4×D4—261no—
228C4×D4—261no—
229#117—21no—
230C2×C4⋊C4—131no—
231C2×C22⋊C4—261no—
232C2×C42C22×D1311yescharacteristic
233#106—262no—
234C4⋊C8—24no—
235C4⋊C8—21no—
236C4⋊C8—261no—
237C4⋊C8—261no—
238C4⋊C8—261no—
239C4⋊C8—261no—
240C4⋊C8C22⋊D1312yes—
241#103—262no—
242#102—262no—
243C22⋊C8—132no—
244C22⋊C8—261no—
245C22⋊C8—522no—
246C22⋊C8—522no—
247#97—22no—
248#97—21no—
249#97—21no—
250C4×C8—22no—
251C4×C8—261no—
252C4×C8—261no—
253C2×C13—21no—
254C2×C13—21no—
255C2×C13#188011yescharacteristic
256C2×C13#188111yescharacteristic
257C2×C13#189111yescharacteristic
258D13—82no—
259C24—261no—
260C2×Q8—21no—
261C2×Q8#610312yes—
262C2×D4—261no—
263C2×D4—261no—
264C2×D4—522no—
265C22×C4—261no—
266C22×C4—521no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4—521no—
270C22×C4—521no—
271C22×C4—521no—
272C22×C4C2×C4×D1311yescharacteristic
273C22×C4#612711yescharacteristic
274C22×C4C2×C22⋊D1311yescharacteristic
275SD16—524no—
276M16—41no—
277M16—41no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—262no—
285C2×C8—521no—
286C2×C8—521no—
287C2×C8—521no—
288C2×C8—521no—
289C2×C8#610612yescomplemented
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—261no—
296C4⋊C4—261no—
297C4⋊C4#610312yes—
298C22⋊C4—22no—
299C22⋊C4—521no—
300C22⋊C4—521no—
301C42—22no—
302C42C2×D5211yescharacteristic
303C42#612711yescharacteristic
304C42C2×C22⋊D1311yescharacteristic
305C42C2×C22⋊D1311yescharacteristic
306C13#905011yescharacteristic, complemented, Sylow
307C23—262no—
308C23—521no—
309C23—521no—
310C23—521no—
311C23—521no—
312C23—521no—
313C23—521no—
314C23C4×C22⋊D1311yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—262no—
318D4—262no—
319D4—521no—
320D4—521no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—1041no—
329C2×C4—1041no—
330C2×C4—1041no—
331C2×C4—1041no—
332C2×C4C2×#610311yescharacteristic
333C2×C4C4×C22⋊D1311yescharacteristic
334C2×C4#8818311yescharacteristic
335C2×C4#8818411yescharacteristic
336C2×C4#8818411yescharacteristic
337C2×C4C2×#610611yescharacteristic
338C2×C4#8819611yescharacteristic
339C2×C4#8820311yescharacteristic
340C2×C4#8820411yescharacteristic
341C2×C4#8820711yescharacteristic
342C8—22no—
343C8—41no—
344C8—42no—
345C8—522no—
346C8—1041no—
347C8—1041no—
348C22—21no—
349C22—21no—
350C22—522no—
351C22—522no—
352C22—522no—
353C22—1041no—
354C22—1041no—
355C22—1041no—
356C22—1041no—
357C22C4×#610611yescharacteristic
358C22#1171868711yescharacteristic
359C22#1171887411yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—1041no—
367C4#1171868811yescharacteristic
368C4#1171868911yescharacteristic
369C4#1171888811yescharacteristic
370C4#1171889911yescharacteristic
371C2—21no—
372C2—21no—
373C2—1042no—
374C2#1311519111yescharacteristic
375C2#1311519811yescharacteristic
376C2#1311525411yescharacteristic
subgroupG/H
centerC2×C4#88207
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2961C2
socleC22×C13#386
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#2961D13
hypocenterC13#9050
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #13113493C2semidirect
5. #13112731C2semidirect
6. #13112681C2semidirect
7. C13×#2961C2semidirect
96. C2×C8×C13SD16semidirect
120. #2961D13semidirect
289. C2×C8#6106semidirect
306. C13#9050semidirect

Maximal subgroups

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

subgroupindex
#131248402
#131156342
#131134932
#131132602
#131127312
#131126812
C13×#29612
#905013