Finite Group Databasebeta

← #13130347

Subgroups — #13130347

Order 1664.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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#11719253C211yesmaximal, characteristic
2#11719053C211yesmaximal, characteristic, complemented
3D13⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
4#11718297C212yesmaximal, complemented
5#11718245C212yesmaximal, complemented
6C2×#6127—21no—
7C2×#6118—21no—
8C2×D13⋊C8—21no—
9C4×D4×C13C411yescharacteristic
10#88194C2211yescharacteristic
11#88192C411yescharacteristic
12C4×C22⋊D13—21no—
13#88149C411yescharacteristic
14#88142C2211yescharacteristic
15#88139—21no—
16#88138—21no—
17C4×D52C411yescharacteristic
18C42×D13C2211yescharacteristic
19#88112—21no—
20#88112C2212yes—
21#88112C2212yes—
22C4⋊#1057—21no—
23C2×D4×C13C2×C411yescharacteristic
24C22×C4×C13—21no—
25C2×C22⋊D13—21no—
26C2×C22⋊D13—21no—
27C2×C22⋊D13—21no—
28#6127—42no—
29#6127—42no—
30C2×D52—21no—
31C2×D52C2×C411yescharacteristic
32C2×C4×D13—21no—
33C2×C4×D13C2×C411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×C4×D13D411yescharacteristic
36C2×Dic26—21no—
37C2×#1057—22no—
38C2×#1057—22no—
39#6118—42no—
40D13⋊C8—42no—
41C13×C4⋊C4C2×C411yescharacteristic
42C13×C22⋊C4—21no—
43C42×C13C2×C411yescharacteristic
44C22⋊Dic13—21no—
45#6103—21no—
46#6103—21no—
47C4⋊Dic13C2×C411yescharacteristic
48#6101—21no—
49C4×Dic13D411yescharacteristic
50C4×Dic13D411yescharacteristic
51C4×Dic13C2311yescharacteristic
52#1547—131nomaximal, Sylow
53C23×C13—21no—
54C22×D13—21no—
55C22×D13C22⋊C411yescharacteristic
56D4×C13—41no—
57C2×C4×C13—21no—
58C2×C4×C13—42no—
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22⋊C411yescharacteristic
61C2×C4×C13C22×C411yescharacteristic
62C22⋊D13—42no—
63C22⋊D13—41no—
64C22⋊D13—41no—
65C22⋊D13—41no—
66C22⋊D13—41no—
67C2×Dic13—21no—
68C2×Dic13C22⋊C411yescharacteristic
69C2×Dic13C2×D411yescharacteristic
70C2×Dic13C2×D411yescharacteristic
71D52—41no—
72D52—42no—
73C4×D13—21no—
74C4×D13—21no—
75C4×D13—41no—
76C4×D13—42no—
77C4×D13D812yes—
78C4×D13SD1612yes—
79Dic26—41no—
80Dic26—41no—
81#1057—42no—
82#1057—42no—
83#532—131no—
84#423—131no—
85C2×C4⋊C8—131no—
86#332—132no—
87#331—132no—
88C22×C13—41no—
89C22×C13—41no—
90C22×C13—41no—
91C22×C13C2×C22⋊C411yescharacteristic
92C2×D13—21no—
93C2×D13—21no—
94C2×D13—41no—
95C2×D13—41no—
96C2×D13—41no—
97C2×D13#10212yes—
98C4×C13—21no—
99C4×C13—21no—
100C4×C13—41no—
101C4×C13#10212yes—
102Dic13—21no—
103Dic13—41no—
104Dic13C2×D811yescharacteristic
105Dic13C2×SD1611yescharacteristic
106Dic13AGL(1,ℤ/8)11yescharacteristic
107Dic13#13711yescharacteristic
108C2×#41—261no—
109C2×M16—261no—
110C22×C8—261no—
111C4⋊Q8—131no—
112#127—131no—
113#124—261no—
114#121—131no—
115#121—131no—
116#121—261no—
117C4×D4—131no—
118C4×D4—261no—
119C4×D4#26111yescharacteristic
120C2×C42—131no—
121C4⋊C8—132no—
122C4⋊C8—132no—
123C4⋊C8—261no—
124C4⋊C8—261no—
125C2×C13—81no—
126C2×C13#41311yescharacteristic
127C2×C13C2×#10211yescharacteristic
128C2×C13#41711yescharacteristic
129D13—22no—
130D13—81no—
131#41—522no—
132#41—522no—
133C2×Q8—261no—
134C2×D4—131no—
135C2×D4—261no—
136C2×D4—261no—
137C2×D4—261no—
138C2×D4—261no—
139C2×D4C2×#26111yescharacteristic
140C22×C4—21no—
141C22×C4—131no—
142C22×C4—131no—
143C22×C4—131no—
144C22×C4—261no—
145M16—522no—
146C2×C8—262no—
147C2×C8—262no—
148C2×C8—522no—
149C4⋊C4—131no—
150C4⋊C4—261no—
151C4⋊C4C2×#26111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—261no—
154C22⋊C4—261no—
155C22⋊C4—261no—
156C42—131no—
157C42—131no—
158C42—131no—
159C42C2×#26111yescharacteristic
160C13#154711yescharacteristic, complemented, Sylow
161C23—21no—
162C23—131no—
163C23—261no—
164Q8—521no—
165Q8—521no—
166D4—41no—
167D4—521no—
168D4—522no—
169D4—521no—
170D4—521no—
171D4—521no—
172D4—521no—
173D4—522no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—131no—
177C2×C4—131no—
178C2×C4—132no—
179C2×C4—132no—
180C2×C4—131no—
181C2×C4—261no—
182C2×C4—261no—
183C2×C4—261no—
184C2×C4—521no—
185C2×C4—522no—
186C2×C4C22⋊#26111yescharacteristic
187C2×C4C22⋊#26111yescharacteristic
188C2×C4C22×#26111yescharacteristic
189C8—522no—
190C8—522no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—132no—
195C22—261no—
196C22—261no—
197C22—521no—
198C22—521no—
199C22—521no—
200C22C2×C22⋊#26111yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—131no—
205C4—131no—
206C4—131no—
207C4—131no—
208C4—261no—
209C4—521no—
210C4#8811512yes—
211C2—81no—
212C2—262no—
213C2—1041no—
214C2#1171913211yescharacteristic
215C2C2×#8811511yescharacteristic
216C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×D4×C13C4
socleC22×C13C2×C22⋊C4
prime radical#11719253C2
cosocleC4×Dic13C23
hypercenterC4×D4#261
hypocenterC13#1547
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11719053C2semidirect
3. D13⋊(C4⋊C8)C2semidirect
4. #11718297C2semidirect
5. #11718245C2semidirect
160. C13#1547semidirect

Maximal subgroups

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

subgroupindex
#117192532
#117190532
D13⋊(C4⋊C8)2
#117182972
#117182452
#154713