Finite Group Databasebeta

← #13130161

Subgroups — #13130161

Order 1664.

312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C2×D4×Dic13C211yesmaximal, characteristic
2#11719129C211yesmaximal, characteristic, complemented
3#11719125C211yesmaximal, characteristic, complemented
4D4⋊#1057C214yesmaximal, complemented
5C22×D4×C13C411yescharacteristic
6C23×Dic13—21no—
7C2×#6122—21no—
8C2×C22⋊Dic13—21no—
9D4×Dic13—21no—
10D4×Dic13—21no—
11D4×Dic13C412yes—
12D4×Dic13C2212yes—
13C2×C4⋊Dic13C411yescharacteristic
14C2×C4×Dic13C2211yescharacteristic
15C22⋊#1057—21no—
16#88112—21no—
17#88112—21no—
18C4⋊#1057C2212yescomplemented
19C4×#1057C2212yescomplemented
20C24×C13—21no—
21C2×D4×C13—24no—
22C2×D4×C13—21no—
23C2×D4×C13C2×C412yes—
24C22×C4×C13C2×C411yescharacteristic
25C22×Dic13—21no—
26C22×Dic13—22no—
27C22×Dic13—22no—
28C22×Dic13—42no—
29C22×Dic13—42no—
30C22×Dic13D411yescharacteristic
31C22×Dic13D411yescharacteristic
32#6122—42no—
33C2×#1057—22no—
34C2×#1057—22no—
35C22⋊Dic13—22no—
36C22⋊Dic13—22no—
37C4⋊Dic13—21no—
38C4⋊Dic13C2×C412yes—
39C4×Dic13C2×C411yescharacteristic
40C4×Dic13D411yescharacteristic
41C4×Dic13D411yescharacteristic
42C4×Dic13C2311yescharacteristic
43#1486—131nomaximal, Sylow
44C23×C13—24no—
45C23×C13—22no—
46C23×C13—42no—
47C23×C13—42no—
48C23×C13C22⋊C411yescharacteristic
49D4×C13—24no—
50D4×C13—22no—
51D4×C13M1614yescomplemented
52C2×C4×C13—22no—
53C2×C4×C13C22⋊C411yescharacteristic
54C2×C4×C13C22×C411yescharacteristic
55C2×Dic13—22no—
56C2×Dic13—41no—
57C2×Dic13—42no—
58C2×Dic13—44no—
59C2×Dic13—42no—
60C2×Dic13—42no—
61C2×Dic13C22⋊C411yescharacteristic
62C2×Dic13C22⋊C411yescharacteristic
63C2×Dic13D812yes—
64C2×Dic13SD1612yes—
65C2×Dic13C2×D411yescharacteristic
66C2×Dic13C2×D411yescharacteristic
67#1057—42no—
68#1057—42no—
69C2×C4×D4—131no—
70#431—131no—
71#423—131no—
72D4⋊C8—134no—
73C22×C13—21no—
74C22×C13—21no—
75C22×C13—24no—
76C22×C13—48no—
77C22×C13—42no—
78C22×C13—42no—
79C22×C13#10212yes—
80C22×C13C2×C22⋊C411yescharacteristic
81C4×C13—21no—
82C4×C13C2×M1612yes—
83Dic13—21no—
84Dic13—21no—
85Dic13—42no—
86Dic13#10212yes—
87Dic13C2×D811yescharacteristic
88Dic13C2×SD1611yescharacteristic
89C22×D4#26111yescharacteristic
90C23×C4—261no—
91C2×M16—261no—
92C4×D4—132no—
93C4×D4—132no—
94C4×D4—261no—
95C4×D4—261no—
96C2×C4⋊C4—131no—
97C2×C22⋊C4—261no—
98C2×C42—131no—
99C4⋊C8—132no—
100C4⋊C8—261no—
101C4⋊C8—261no—
102C22⋊C8—261no—
103C4×C8—132no—
104C2×C13—22no—
105C2×C13—44no—
106C2×C13#40711yescharacteristic
107C2×C13C2×#10211yescharacteristic
108C2×C13#42111yescharacteristic
109C24—21no—
110C2×D4—24no—
111C2×D4—21no—
112C2×D4C2×#26112yes—
113C22×C4—131no—
114C22×C4—131no—
115C22×C4—262no—
116C22×C4—262no—
117C22×C4—261no—
118C22×C4—522no—
119C22×C4—522no—
120C22×C4C2×#26111yescharacteristic
121M16—522no—
122C2×C8—262no—
123C2×C8—262no—
124C4⋊C4—132no—
125C4⋊C4—261no—
126C22⋊C4—262no—
127C22⋊C4—262no—
128C42—131no—
129C42—131no—
130C42—131no—
131C42—131no—
132C13#148611yescharacteristic, complemented, Sylow
133C23—24no—
134C23—22no—
135C23—42no—
136C23—42no—
137C23C22⋊#26111yescharacteristic
138D4—24no—
139D4—22no—
140D4#612214yescomplemented
141C2×C4—22no—
142C2×C4—132no—
143C2×C4—132no—
144C2×C4—131no—
145C2×C4—131no—
146C2×C4—131no—
147C2×C4—131no—
148C2×C4—262no—
149C2×C4—524no—
150C2×C4—522no—
151C2×C4—522no—
152C2×C4—521no—
153C2×C4—522no—
154C2×C4C22⋊#26111yescharacteristic
155C2×C4C22×#26111yescharacteristic
156C8—522no—
157C8—522no—
158C22—21no—
159C22—21no—
160C22—24no—
161C22—48no—
162C22—42no—
163C22—42no—
164C22#8811512yes—
165C22C2×C22⋊#26111yescharacteristic
166C4—21no—
167C4—132no—
168C4—131no—
169C4—131no—
170C4—261no—
171C4—261no—
172C4—522no—
173C4C2×#612212yes—
174C2—22no—
175C2—44no—
176C2C2×#8811511yescharacteristic
177C2#1171914011yescharacteristic
178C2#1171916911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
Fitting, prime radicalC22×D4×C13C4
socleC22×C13C2×C22⋊C4
cosocleC4×Dic13C23
hypercenterC22×D4#261
hypocenterC13#1486
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11719129C2semidirect
3. #11719125C2semidirect
4. D4⋊#1057C2semidirect
18. C4⋊#1057C22semidirect
19. C4×#1057C22semidirect
51. D4×C13M16semidirect
132. C13#1486semidirect
140. D4#6122semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
#117191292
#117191252
D4⋊#10572
#148613