Finite Group Databasebeta

← #15774295

Subgroups — #15774295

Order 3328.

404 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 115 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#13116635C211yesmaximal, characteristic, complemented
2#13113592C211yesmaximal, characteristic, complemented
3#13112879C214yesmaximal, complemented
4C13×#3147C211yesmaximal, characteristic
5C2×C13×#135—21no—
6C2×C13×#135C412yes—
7C13×#532—21no—
8C13×#495—21no—
9C13×#495C2212yes—
10C13×#494C411yescharacteristic
11C13×#493C411yescharacteristic
12C13×#492—21no—
13C2×C4×C8×C13C2211yescharacteristic
14#11718585—21no—
15C22⋊#6090—21no—
16C4⋊#6090C2212yes—
17C4×#6090—21no—
18#11718049—21no—
19#11718049C2212yes—
20C2×C13×#41—22no—
21C13×#135—44no—
22C13×#135—44no—
23C2×C13×Q16—21no—
24C2×C13×Q16C2×C412yes—
25C2×C13×SD16—22no—
26C2×C13×SD16—22no—
27C2×C13×D8—21no—
28C2×C13×D8C2×C412yes—
29C22×C8×C13C2×C411yescharacteristic
30C22×C8×C13D411yescharacteristic
31C13×C4⋊Q8—21no—
32C13×#127—21no—
33C13×#124—22no—
34C13×#121—41no—
35C13×#121—41no—
36C4×D4×C13—41no—
37C4×D4×C13—41no—
38C2×C42×C13D411yescharacteristic
39C2×#6099—41no—
40C4×C8×C13C2×C411yescharacteristic
41C4×C8×C13D411yescharacteristic
42C4×C8×C13D411yescharacteristic
43C4×C8×C13C2311yescharacteristic
44C2×#6090—22no—
45C4⋊#1055—22no—
46C4⋊#1055—41no—
47#11958—131nomaximal, Sylow
48C13×#41—44no—
49C13×#41—44no—
50C2×Q8×C13—22no—
51C2×D4×C13—22no—
52C2×D4×C13—42no—
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C22×C4×C13—42no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13D811yescharacteristic
58C22×C4×C13SD1611yescharacteristic
59C13×Q16—42no—
60C13×Q16—42no—
61C13×SD16—44no—
62C13×SD16—44no—
63C13×D8—42no—
64C13×D8—42no—
65C2×C8×C13—22no—
66C2×C8×C13—22no—
67C2×C8×C13C22⋊C411yescharacteristic
68C2×C8×C13C22⋊C411yescharacteristic
69C2×C8×C13C22×C411yescharacteristic
70C2×C8×C13C2×D411yescharacteristic
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C22⋊C4—42no—
74C13×C22⋊C4—42no—
75C42×C13C22⋊C411yescharacteristic
76C42×C13D811yescharacteristic
77C42×C13SD1611yescharacteristic
78C42×C13C2×D411yescharacteristic
79#6099—82no—
80C2×#1055—42no—
81#6090—42no—
82#3147D1311yescharacteristic
83#2162—131no—
84#1566—131no—
85#1360—134no—
86C23×C13—42no—
87C23×C13#10211yescharacteristic
88Q8×C13—42no—
89Q8×C13—42no—
90D4×C13—42no—
91D4×C13—42no—
92D4×C13—84no—
93D4×C13—82no—
94D4×C13—82no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—42no—
100C2×C4×C13—84no—
101C2×C4×C13#10211yescharacteristic
102C2×C4×C13#10211yescharacteristic
103C2×C4×C13#10211yescharacteristic
104C2×C4×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13C2×D811yescharacteristic
106C2×C4×C13C2×SD1611yescharacteristic
107C8×C13—21no—
108C8×C13—21no—
109C8×C13#10012yes—
110C8×C13AGL(1,ℤ/8)12yes—
111#1055—82no—
112C2×#135—21no—
113C2×#135Dic1312yes—
114#532—21no—
115#495—21no—
116#495C2×D1312yes—
117#494Dic1311yescharacteristic
118#493Dic1311yescharacteristic
119#492—21no—
120#423—261no—
121C2×C4×C8C2×D1311yescharacteristic
122C4⋊C16—132no—
123C22⋊C16—261no—
124C4×C16—261no—
125#334—132no—
126#334—261no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13—82no—
131C22×C13—82no—
132C22×C13—82no—
133C22×C13C2×#10211yescharacteristic
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—21no—
137C4×C13—82no—
138C4×C13#35912yes—
139C4×C13#36012yes—
140C4×C13C2×#10011yescharacteristic
141C4×C13#41811yescharacteristic
142C2×#41—22no—
143#135—44no—
144#135—44no—
145C2×Q16—21no—
146C2×Q16C2×Dic1312yes—
147C2×SD16—22no—
148C2×SD16—22no—
149C2×D8—21no—
150C2×D8C2×Dic1312yes—
151C2×M16—521no—
152C22×C8C2×Dic1311yescharacteristic
153C22×C8C22⋊D1311yescharacteristic
154C4⋊Q8—21no—
155#127—21no—
156#124—22no—
157#121—41no—
158#121—41no—
159C4×D4—41no—
160C4×D4—41no—
161C2×C42C22⋊D1311yescharacteristic
162C2×C16—262no—
163C4⋊C8—262no—
164C4⋊C8—521no—
165C4×C8C2×Dic1311yescharacteristic
166C4×C8C22⋊D1311yescharacteristic
167C4×C8C22⋊D1311yescharacteristic
168C4×C8C22×D1311yescharacteristic
169C2×C13—41no—
170C2×C13—162no—
171C2×C13#154511yescharacteristic
172C2×C13C2×#35911yescharacteristic
173C2×C13C2×#36011yescharacteristic
174#41—44no—
175#41—44no—
176C2×Q8—22no—
177C2×D4—22no—
178C2×D4—42no—
179C2×D4—41no—
180C2×D4—41no—
181C22×C4—42no—
182C22×C4#610411yescharacteristic
183C22×C4#610511yescharacteristic
184C22×C4C22⋊Dic1311yescharacteristic
185Q16—42no—
186Q16—42no—
187SD16—44no—
188SD16—44no—
189D8—42no—
190D8—42no—
191M16—1042no—
192C2×C8—22no—
193C2×C8—22no—
194C2×C8—522no—
195C2×C8C22⋊Dic1311yescharacteristic
196C2×C8C22⋊Dic1311yescharacteristic
197C2×C8C22×Dic1311yescharacteristic
198C2×C8C2×C22⋊D1311yescharacteristic
199C4⋊C4—41no—
200C4⋊C4—41no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C42#610411yescharacteristic
204C42#610511yescharacteristic
205C42C22⋊Dic1311yescharacteristic
206C42C2×C22⋊D1311yescharacteristic
207C16—522no—
208C13#1195811yescharacteristic, complemented, Sylow
209C23—42no—
210C23#8807211yescharacteristic
211Q8—42no—
212Q8—42no—
213D4—42no—
214D4—42no—
215D4—84no—
216D4—82no—
217D4—82no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—84no—
224C2×C4#8807211yescharacteristic
225C2×C4#8807211yescharacteristic
226C2×C4#8807211yescharacteristic
227C2×C4C2×#610411yescharacteristic
228C2×C4C2×#610511yescharacteristic
229C2×C4C2×C22⋊Dic1311yescharacteristic
230C8—21no—
231C8—21no—
232C8—1042no—
233C8#8807312yes—
234C8#8818612yes—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—82no—
239C22—82no—
240C22—82no—
241C22C2×#8807211yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—82no—
246C4#1171815812yes—
247C4#1171815912yes—
248C4#1171887611yescharacteristic
249C4C2×#8807311yescharacteristic
250C2—41no—
251C2—162no—
252C2#1311350411yescharacteristic
253C2C2×#1171815911yescharacteristic
254C2C2×#1171815811yescharacteristic
subgroupG/H
centerC22C2×#88072
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
Fitting, prime radicalC13×#3147C2
socleC22×C13C2×#102
cosocleC4×C8×C13C23
hypercenter#3147D13
hypocenterC13#11958
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. #13116635C2semidirect
2. #13113592C2semidirect
3. #13112879C2semidirect
208. C13#11958semidirect

Maximal subgroups

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

subgroupindex
#131166352
#131135922
#131128792
C13×#31472
#1195813