Finite Group Databasebeta

← #13130168

Subgroups — #13130168

Order 1664.

246 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C4×#6129C211yesmaximal, characteristic
2#11719054C211yesmaximal, characteristic, complemented
3#11719051C211yesmaximal, characteristic, complemented
4D4⋊#1057C212yesmaximal, complemented
5#11718244C212yesmaximal, complemented
6C2×#6129C411yescharacteristic
7C4×D4×C13C411yescharacteristic
8D4×Dic13C2211yescharacteristic
9C4×C22⋊D13—21no—
10C2×C4×Dic13—21no—
11#88146C411yescharacteristic
12#88141C2211yescharacteristic
13#88135—21no—
14#88131—21no—
15C42×D13C2211yescharacteristic
16C4×Dic26C411yescharacteristic
17#88111—21no—
18#88111—21no—
19#88110—21no—
20C4⋊#1057—21no—
21C4⋊#1057C2212yes—
22C4×#1057C2212yes—
23C2×D4×C13C2×C411yescharacteristic
24C22×C4×C13—21no—
25C2×C22⋊D13—21no—
26C22×Dic13—21no—
27C22×Dic13—21no—
28#6129—22no—
29#6129—22no—
30C2×C4×D13C2×C411yescharacteristic
31C2×C4×D13D411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×Dic26C2×C411yescharacteristic
34C2×#1057—22no—
35C2×#1057—22no—
36C13×C4⋊C4C2×C411yescharacteristic
37C13×C22⋊C4—21no—
38C42×C13C2×C411yescharacteristic
39C22⋊Dic13—21no—
40#6103—21no—
41C4⋊Dic13C2×C411yescharacteristic
42#6101—21no—
43#6101—21no—
44C4×Dic13—21no—
45C4×Dic13—21no—
46C4×Dic13—21no—
47C4×Dic13D411yescharacteristic
48C4×Dic13D411yescharacteristic
49C4×Dic13C2311yescharacteristic
50#1488—131nomaximal, Sylow
51C23×C13—21no—
52C22×D13C22⋊C411yescharacteristic
53D4×C13—21no—
54D4×C13M1612yes—
55C2×C4×C13—21no—
56C2×C4×C13—42no—
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22⋊C411yescharacteristic
59C2×C4×C13C22×C411yescharacteristic
60C22⋊D13—24no—
61C2×Dic13—24no—
62C2×Dic13—21no—
63C2×Dic13—21no—
64C2×Dic13—42no—
65C2×Dic13C22⋊C411yescharacteristic
66C2×Dic13C2×D411yescharacteristic
67C2×Dic13C2×D411yescharacteristic
68C4×D13—21no—
69C4×D13—21no—
70C4×D13—22no—
71C4×D13—41no—
72Dic26—21no—
73Dic26M1612yes—
74#1057—42no—
75#1057—42no—
76C4×#41—131no—
77#432—131no—
78#431—131no—
79Q8⋊C8—132no—
80D4⋊C8—132no—
81C22×C13—22no—
82C22×C13—41no—
83C22×C13—41no—
84C22×C13C2×C22⋊C411yescharacteristic
85C2×D13—21no—
86C2×D13—21no—
87C2×D13—21no—
88C4×C13—21no—
89C4×C13—21no—
90C4×C13—41no—
91C4×C13C2×M1611yescharacteristic
92C4×C13C2×M1611yescharacteristic
93Dic13—22no—
94Dic13—21no—
95Dic13—21no—
96Dic13—41no—
97Dic13#13512yes—
98C2×#41—131no—
99C4×Q8—131no—
100C4×Q8—131no—
101C4×D4—131no—
102C4×D4—261no—
103C4×D4—261no—
104C4×D4#26111yescharacteristic
105#117—131no—
106#117—261no—
107C2×C42—131no—
108C2×C42—261no—
109C4⋊C8—132no—
110C4⋊C8—261no—
111C22⋊C8—261no—
112C22⋊C8—261no—
113#97—261no—
114C4×C8—132no—
115C2×C13—42no—
116C2×C13#40711yescharacteristic
117C2×C13#41611yescharacteristic
118C2×C13#42111yescharacteristic
119D13—41no—
120#41—262no—
121#41—262no—
122C2×Q8—131no—
123C2×D4—261no—
124C2×D4C2×#26111yescharacteristic
125C22×C4—21no—
126C22×C4—131no—
127C22×C4—131no—
128C22×C4—131no—
129C22×C4—261no—
130C22×C4—261no—
131C2×C8—262no—
132C2×C8—262no—
133C4⋊C4—131no—
134C4⋊C4—261no—
135C4⋊C4—261no—
136C4⋊C4C2×#26111yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—261no—
139C22⋊C4—261no—
140C42—131no—
141C42—131no—
142C42—131no—
143C42—261no—
144C42—261no—
145C42—261no—
146C42C2×#26111yescharacteristic
147C13#148811yescharacteristic, complemented, Sylow
148C23—21no—
149C23—131no—
150Q8—132no—
151Q8—261no—
152D4—21no—
153D4—264no—
154D4#611812yes—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—131no—
158C2×C4—131no—
159C2×C4—131no—
160C2×C4—262no—
161C2×C4—264no—
162C2×C4—261no—
163C2×C4—261no—
164C2×C4—261no—
165C2×C4—261no—
166C2×C4—521no—
167C2×C4—522no—
168C2×C4C22⋊#26111yescharacteristic
169C2×C4C22⋊#26111yescharacteristic
170C2×C4C22×#26111yescharacteristic
171C8—522no—
172C8—522no—
173C22—22no—
174C22—41no—
175C22—41no—
176C22—261no—
177C22—261no—
178C22—261no—
179C22C2×C22⋊#26111yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—132no—
184C4—261no—
185C4—262no—
186C4—261no—
187C4—521no—
188C4C2×#611811yescharacteristic
189C4D13⋊M1611yescharacteristic
190C2—42no—
191C2—521no—
192C2#1171912711yescharacteristic
193C2#1171914011yescharacteristic
194C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×D4×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC2×#6129C4
cosocleC4×Dic13C23
hypercenterC4×D4#261
hypocenterC13#1488
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11719054C2semidirect
3. #11719051C2semidirect
4. D4⋊#1057C2semidirect
5. #11718244C2semidirect
147. C13#1488semidirect

Maximal subgroups

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

subgroupindex
C4×#61292
#117190542
#117190512
D4⋊#10572
#117182442
#148813