Finite Group Databasebeta

← #16791256

Subgroups — #16791256

Order 3328.

416 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131109C212yesmaximal, complemented
2#13129969C212yesmaximal, complemented
3#13129967C212yesmaximal, complemented
4#13125262C211yesmaximal, characteristic
5C13×#532C411yescharacteristic, complemented
6C2×#88204—22no—
7#11719182C2211yescharacteristic
8#11719116—22no—
9#11718753C411yescharacteristic, complemented
10#11718746C2211yescharacteristic
11#11718737C411yescharacteristic, complemented
12#11718734C2211yescharacteristic
13#11718720—22no—
14C2×C4×#1055C411yescharacteristic, complemented
15#11718226—22no—
16#11718225C2214yes—
17C2×C13×#41—21no—
18C2×#6127D412yes—
19#88237—42no—
20C13×C4⋊Q8C2×C411yescharacteristic
21C13×#127C2×C411yescharacteristic
22C13×#124—21no—
23C13×#121—41no—
24C4×D4×C13—41no—
25C2×C42×C13C2×C411yescharacteristic
26#88204—44no—
27#88204—44no—
28C2×#6107—22no—
29C2×#6106—22no—
30C2×#6105—22no—
31C2×#6104—22no—
32#88184—41no—
33C22×#1055—21no—
34#88129D412yes—
35#88128C2311yescharacteristic
36C4×D52—41no—
37#88123C2×C411yescharacteristic
38#88119—42no—
39#88107—24no—
40C4×#1055—21no—
41C4×#1055C2×C411yescharacteristic
42C4×#1055C2×C411yescharacteristic
43#13583—131nomaximal, Sylow
44C13×#41—42no—
45C13×#41—42no—
46C2×Q8×C13—21no—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C22×C4×C13—21no—
51C22×C4×C13—41no—
52C22×C4×C13C22⋊C411yescharacteristic
53C2×C22⋊D13—22no—
54#6127—42no—
55#6127—42no—
56C2×D52—41no—
57C2×D52C2×D412yes—
58C2×C4×D13—22no—
59C2×Dic26C22⋊C412yes—
60C22⋊#261—44no—
61C4⋊#261—82no—
62C4×#261—82no—
63C13×C4⋊C4—41no—
64C13×C22⋊C4—42no—
65C42×C13—21no—
66C42×C13C22⋊C411yescharacteristic
67C42×C13C22×C411yescharacteristic
68#6107—44no—
69#6106—44no—
70#6105—44no—
71#6104—44no—
72#6103—42no—
73C4⋊Dic13—41no—
74C2×#1055—22no—
75C2×#1055—22no—
76C2×#1055—21no—
77C2×#1055—21no—
78#3147—131no—
79#2126—132no—
80#1409—132no—
81#1408—132no—
82C23×C13—41no—
83C23×C13#9911yescharacteristic
84C22×D13—22no—
85C2×#261—84no—
86Q8×C13—42no—
87D4×C13—42no—
88D4×C13—82no—
89D4×C13—82no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13—81no—
97C2×C4×C13—81no—
98C2×C4×C13#9911yescharacteristic
99C2×C4×C13C2×C22⋊C411yescharacteristic
100C22⋊D13—82no—
101C2×Dic13—22no—
102D52—42no—
103D52—82no—
104C4×D13—42no—
105C4×D13—42no—
106Dic26—42no—
107#1055—22no—
108#1055—22no—
109C2×#135—262no—
110#532—131no—
111#532#26111yescharacteristic, complemented
112#495—262no—
113#494—131no—
114#493—131no—
115#492—131no—
116#492—131no—
117#410—262no—
118C2×C4×C8—131no—
119#354—262no—
120#353—134no—
121C22×C13—21no—
122C22×C13—41no—
123C22×C13—82no—
124C22×C13—81no—
125C22×C13C2×#9911yescharacteristic
126C2×D13—42no—
127C2×D13—82no—
128#261—164no—
129C4×C13—22no—
130C4×C13—21no—
131C4×C13—41no—
132C4×C13—81no—
133C4×C13#35311yescharacteristic
134C4×C13#35311yescharacteristic
135Dic13—42no—
136C2×#41—21no—
137C2×#41—132no—
138#135—524no—
139#135—524no—
140C2×Q16—262no—
141C2×SD16—262no—
142C2×SD16—262no—
143C2×D8—262no—
144C22×C8—261no—
145C4⋊Q8—131no—
146C4⋊Q8C2×#26111yescharacteristic
147#127—131no—
148#127C2×#26111yescharacteristic
149#124—21no—
150#124—132no—
151#121—41no—
152#121—521no—
153C4×D4—41no—
154C4×D4—521no—
155#117—522no—
156C2×C42C2×#26111yescharacteristic
157#99—264no—
158#99—522no—
159C4×C8—131no—
160C4×C8—131no—
161C4×C8—261no—
162C2×C13—21no—
163C2×C13—41no—
164C2×C13—161no—
165C2×C13C2×#35311yescharacteristic
166D13—82no—
167#41—42no—
168#41—42no—
169#41—522no—
170#41—522no—
171C2×Q8—21no—
172C2×Q8—132no—
173C2×D4—21no—
174C2×D4—41no—
175C2×D4—41no—
176C2×D4—132no—
177C2×D4—262no—
178C2×D4—521no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—262no—
182C22×C4C22⋊#26111yescharacteristic
183Q16—524no—
184SD16—524no—
185SD16—524no—
186D8—524no—
187C2×C8—262no—
188C2×C8—262no—
189C2×C8—261no—
190C2×C8—261no—
191C4⋊C4—41no—
192C4⋊C4—521no—
193C4⋊C4—1042no—
194C22⋊C4—42no—
195C22⋊C4—522no—
196C22⋊C4—524no—
197C42—21no—
198C42—1042no—
199C42C22⋊#26111yescharacteristic
200C42C22×#26111yescharacteristic
201C13#1358311yescharacteristic, complemented, Sylow
202C23—41no—
203C23—262no—
204C23#8811911yescharacteristic
205Q8—42no—
206Q8—522no—
207D4—42no—
208D4—82no—
209D4—82no—
210D4—522no—
211D4—1042no—
212D4—1042no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—262no—
222C2×C4—522no—
223C2×C4—522no—
224C2×C4—1044no—
225C2×C4#8811911yescharacteristic
226C2×C4C2×C22⋊#26111yescharacteristic
227C8—262no—
228C8—262no—
229C22—21no—
230C22—41no—
231C22—82no—
232C22—81no—
233C22—522no—
234C22—1042no—
235C22C2×#8811911yescharacteristic
236C4—22no—
237C4—21no—
238C4—41no—
239C4—81no—
240C4—522no—
241C4—2084no—
242C4#1171829411yescharacteristic
243C4#1171829411yescharacteristic
244C2—21no—
245C2—41no—
246C2—161no—
247C2—1042no—
248C2C2×#1171829411yescharacteristic
subgroupG/H
centerC4#11718294
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#532C4
socleC2×C13C2×#353
prime radical#13125262C2
cosocle#88128C23
hypercenter#532#261
hypocenterC13#13583
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #13131109C2semidirect
2. #13129969C2semidirect
3. #13129967C2semidirect
5. C13×#532C4semidirect
9. #11718753C4semidirect
11. #11718737C4semidirect
14. C2×C4×#1055C4semidirect
111. #532#261semidirect
201. C13#13583semidirect

Maximal subgroups

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

subgroupindex
#131311092
#131299692
#131299672
#131252622
#1358313