Finite Group Databasebeta

← #13130151

Subgroups — #13130151

Order 1664.

234 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 64 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#11719305C211yesmaximal, characteristic
2C4×#6122C211yesmaximal, characteristic, complemented
3C2×C4⋊#1057C211yesmaximal, characteristic, complemented
4D4⋊#1057C212yesmaximal, complemented
5#11718244C212yesmaximal, complemented
6C2×#6122—21no—
7C22×#1057—21no—
8C13×#121C411yescharacteristic
9#88190C411yescharacteristic
10#88189—21no—
11D4×Dic13—21no—
12D4×Dic13C2211yescharacteristic
13#88178C411yescharacteristic
14C2×C4×Dic13C2211yescharacteristic
15#88144C411yescharacteristic
16#88141C2211yescharacteristic
17#88133—21no—
18#88131—21no—
19#88110—21no—
20C4⋊#1057—21no—
21C4⋊#1057C2212yes—
22C4×#1057C2212yes—
23C2×D4×C13—21no—
24C2×D4×C13C2×C411yescharacteristic
25C22×C4×C13C2×C411yescharacteristic
26C22×Dic13—21no—
27C22×Dic13D411yescharacteristic
28C22×Dic13D411yescharacteristic
29C2×Dic26C2×C411yescharacteristic
30#6122—24no—
31C2×#1057—22no—
32C2×#1057—22no—
33C2×#1057—42no—
34C13×C4⋊C4C2×C411yescharacteristic
35C13×C22⋊C4—21no—
36C22⋊Dic13—21no—
37C22⋊Dic13—21no—
38C22⋊Dic13—21no—
39C22⋊Dic13—21no—
40C4⋊Dic13—21no—
41C4⋊Dic13C2×C411yescharacteristic
42#6101—21no—
43#6101—21no—
44#6101—21no—
45C4×Dic13—21no—
46C4×Dic13C2×C411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13D411yescharacteristic
49C4×Dic13C2311yescharacteristic
50#1483—131nomaximal, Sylow
51C23×C13—21no—
52C23×C13C22⋊C411yescharacteristic
53D4×C13—22no—
54D4×C13—42no—
55C2×C4×C13—22no—
56C2×C4×C13—21no—
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22×C411yescharacteristic
59C2×Dic13—22no—
60C2×Dic13—21no—
61C2×Dic13—21no—
62C2×Dic13—21no—
63C2×Dic13—21no—
64C2×Dic13—41no—
65C2×Dic13—41no—
66C2×Dic13C22⋊C411yescharacteristic
67C2×Dic13C22⋊C411yescharacteristic
68C2×Dic13C2×D411yescharacteristic
69C2×Dic13C2×D411yescharacteristic
70Dic26—22no—
71#1057—24no—
72#1057—42no—
73#529—131no—
74C2×C4⋊C8—131no—
75C4×M16—131no—
76Q8⋊C8—132no—
77D4⋊C8—132no—
78C22×C13—21no—
79C22×C13—21no—
80C22×C13—41no—
81C22×C13—41no—
82C22×C13—41no—
83C22×C13#10412yes—
84C22×C13C2×C22⋊C411yescharacteristic
85C4×C13—21no—
86C4×C13—41no—
87C4×C13#13112yes—
88Dic13—21no—
89Dic13—21no—
90Dic13—21no—
91Dic13—41no—
92Dic13—41no—
93Dic13AGL(1,ℤ/8)11yescharacteristic
94Dic13#13711yescharacteristic
95C2×M16—261no—
96C22×C8—261no—
97#126—261no—
98#125—131no—
99#124—131no—
100#123—261no—
101C22⋊Q8—131no—
102#121#26111yescharacteristic
103C4×Q8—131no—
104C4×D4—131no—
105C4×D4—261no—
106#117—261no—
107C2×C42—131no—
108C4⋊C8—132no—
109C4⋊C8—261no—
110#97—261no—
111C4×C8—132no—
112C2×C13—22no—
113C2×C13—81no—
114C2×C13#40811yescharacteristic
115C2×C13#41711yescharacteristic
116C2×C13C2×#10411yescharacteristic
117C2×Q8—131no—
118C2×D4—21no—
119C2×D4C2×#26111yescharacteristic
120C22×C4—131no—
121C22×C4—131no—
122C22×C4—261no—
123C22×C4C2×#26111yescharacteristic
124M16—264no—
125C2×C8—262no—
126C2×C8—262no—
127C2×C8—522no—
128C4⋊C4—131no—
129C4⋊C4—261no—
130C4⋊C4—261no—
131C4⋊C4—261no—
132C4⋊C4—261no—
133C4⋊C4C2×#26111yescharacteristic
134C22⋊C4—21no—
135C22⋊C4—261no—
136C22⋊C4—261no—
137C22⋊C4—261no—
138C22⋊C4—261no—
139C42—131no—
140C42—131no—
141C42—131no—
142C42—131no—
143C42—261no—
144C13#148311yescharacteristic, complemented, Sylow
145C23—21no—
146C23C22⋊#26111yescharacteristic
147Q8—262no—
148D4—22no—
149D4—42no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—131no—
153C2×C4—131no—
154C2×C4—131no—
155C2×C4—131no—
156C2×C4—261no—
157C2×C4—261no—
158C2×C4—262no—
159C2×C4—261no—
160C2×C4—261no—
161C2×C4—521no—
162C2×C4—521no—
163C2×C4C22⋊#26111yescharacteristic
164C2×C4C22×#26111yescharacteristic
165C8—264no—
166C8—522no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#8811612yes—
173C22C2×C22⋊#26111yescharacteristic
174C4—21no—
175C4—41no—
176C4—131no—
177C4—131no—
178C4—261no—
179C4—261no—
180C4—261no—
181C4—521no—
182C4—521no—
183C4#8823812yes—
184C2—22no—
185C2—81no—
186C2C2×#8811611yescharacteristic
187C2#1171914611yescharacteristic
188C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
Fitting, prime radicalC13×#121C4
socleC22×C13C2×C22⋊C4
cosocleC4×Dic13C23
hypercenter#121#261
hypocenterC13#1483
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C4×#6122C2semidirect
3. C2×C4⋊#1057C2semidirect
4. D4⋊#1057C2semidirect
5. #11718244C2semidirect
144. C13#1483semidirect

Maximal subgroups

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

subgroupindex
#117193052
C4×#61222
C2×C4⋊#10572
D4⋊#10572
#117182442
#148313