Finite Group Databasebeta

← #13130355

Subgroups — #13130355

Order 1664.

252 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 62 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#11719537C211yesmaximal, characteristic
2#11719128C211yesmaximal, characteristic, complemented
3C2×#88112C211yesmaximal, characteristic, complemented
4#11718303C212yesmaximal, complemented
5#11718297C212yesmaximal, complemented
6C2×C13×#41C411yescharacteristic
7C2×#6127C411yescharacteristic
8C22×#1057—21no—
9#88201C411yescharacteristic
10#88198C2211yescharacteristic
11#88194C2211yescharacteristic
12#88193—21no—
13#88193—21no—
14#88190C411yescharacteristic
15C4×C22⋊D13—21no—
16C4×C22⋊D13—21no—
17C2×C4×Dic13C2211yescharacteristic
18C22⋊#1057—21no—
19#88112—21no—
20#88112C2212yes—
21#88112C2212yes—
22#88110—21no—
23C13×#41—42no—
24C2×Q8×C13C2×C411yescharacteristic
25C2×D4×C13—21no—
26C2×D4×C13C2×C411yescharacteristic
27C22×C4×C13—21no—
28C22×C4×C13C2×C411yescharacteristic
29C2×C22⋊D13—21no—
30C2×C22⋊D13—21no—
31C2×C22⋊D13—21no—
32C22×Dic13D411yescharacteristic
33C22×Dic13D411yescharacteristic
34#6127—42no—
35C2×D52C2×C411yescharacteristic
36C2×C4×D13—21no—
37C2×Dic26C2×C411yescharacteristic
38C2×#1057—22no—
39C2×#1057—22no—
40C2×#1057—42no—
41C22⋊Dic13—21no—
42C22⋊Dic13—21no—
43#6103—21no—
44#6103—21no—
45#6101—21no—
46#6101—21no—
47C4×Dic13C2×C411yescharacteristic
48C4×Dic13D411yescharacteristic
49C4×Dic13D411yescharacteristic
50C4×Dic13C2311yescharacteristic
51#1551—131nomaximal, Sylow
52C23×C13—21no—
53C23×C13C22⋊C411yescharacteristic
54C22×D13—21no—
55Q8×C13—41no—
56D4×C13—41no—
57D4×C13—42no—
58C2×C4×C13—22no—
59C2×C4×C13—21no—
60C2×C4×C13—42no—
61C2×C4×C13C22⋊C411yescharacteristic
62C2×C4×C13C22×C411yescharacteristic
63C22⋊D13—42no—
64C22⋊D13—42no—
65C22⋊D13—41no—
66C22⋊D13—41no—
67C2×Dic13—22no—
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13—21no—
71C2×Dic13C22⋊C411yescharacteristic
72C2×Dic13C22⋊C411yescharacteristic
73C2×Dic13C2×D411yescharacteristic
74C2×Dic13C2×D411yescharacteristic
75D52—41no—
76C4×D13—42no—
77Dic26—41no—
78#1057—42no—
79#1057—42no—
80#532—131no—
81#432—131no—
82C2×C4⋊C8—131no—
83#333—132no—
84#331—132no—
85C22×C13—21no—
86C22×C13—21no—
87C22×C13—41no—
88C22×C13—41no—
89C22×C13—41no—
90C22×C13#10012yes—
91C22×C13C2×C22⋊C411yescharacteristic
92C2×D13—41no—
93C2×D13—41no—
94C2×D13—41no—
95C4×C13—21no—
96C4×C13—21no—
97C4×C13—41no—
98Dic13—21no—
99Dic13—21no—
100Dic13—41no—
101Dic13#13512yes—
102Dic13AGL(1,ℤ/8)11yescharacteristic
103Dic13#13711yescharacteristic
104C2×#41—131no—
105C2×#41#26111yescharacteristic
106C22×C8—261no—
107C4⋊Q8—131no—
108#127—131no—
109#124—131no—
110#124—131no—
111#121—261no—
112#121—261no—
113C4×D4—261no—
114C4×D4—261no—
115C2×C42—131no—
116C4⋊C8—132no—
117C4⋊C8—132no—
118C4⋊C8—261no—
119C22⋊C8—261no—
120#97—261no—
121C2×C13—22no—
122C2×C13—81no—
123C2×C13C2×#10011yescharacteristic
124C2×C13#41611yescharacteristic
125C2×C13#41711yescharacteristic
126D13—81no—
127#41—42no—
128#41—522no—
129C2×Q8—131no—
130C2×Q8C2×#26111yescharacteristic
131C2×D4—21no—
132C2×D4—131no—
133C2×D4—261no—
134C2×D4—261no—
135C2×D4—261no—
136C2×D4C2×#26111yescharacteristic
137C22×C4—21no—
138C22×C4—131no—
139C22×C4—131no—
140C22×C4—261no—
141C22×C4C2×#26111yescharacteristic
142C2×C8—262no—
143C2×C8—262no—
144C2×C8—522no—
145C4⋊C4—261no—
146C4⋊C4—261no—
147C22⋊C4—261no—
148C22⋊C4—261no—
149C22⋊C4—261no—
150C22⋊C4—261no—
151C42—131no—
152C42—131no—
153C42—131no—
154C42—131no—
155C13#155111yescharacteristic, complemented, Sylow
156C23—21no—
157C23—261no—
158C23C22⋊#26111yescharacteristic
159Q8—41no—
160Q8—521no—
161D4—41no—
162D4—42no—
163D4—521no—
164D4—521no—
165D4—521no—
166D4—522no—
167D4—522no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—131no—
172C2×C4—131no—
173C2×C4—131no—
174C2×C4—131no—
175C2×C4—261no—
176C2×C4—261no—
177C2×C4—262no—
178C2×C4—261no—
179C2×C4—522no—
180C2×C4C22⋊#26111yescharacteristic
181C2×C4C22×#26111yescharacteristic
182C8—522no—
183C8—522no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—521no—
190C22—521no—
191C22—521no—
192C22#8812112yes—
193C22C2×C22⋊#26111yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—131no—
198C4—131no—
199C4—132no—
200C4—261no—
201C4—261no—
202C4—521no—
203C2—22no—
204C2—81no—
205C2—1041no—
206C2#1171916411yescharacteristic
207C2#1171916511yescharacteristic
208C2C2×#8812111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×#41C4
socleC22×C13C2×C22⋊C4
prime radical#11719537C2
cosocleC4×Dic13C23
hypercenterC2×#41#261
hypocenterC13#1551
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11719128C2semidirect
3. C2×#88112C2semidirect
4. #11718303C2semidirect
5. #11718297C2semidirect
155. C13#1551semidirect

Maximal subgroups

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

subgroupindex
#117195372
#117191282
C2×#881122
#117183032
#117182972
#155113