Finite Group Databasebeta

← #13113980

Subgroups — #13113980

Order 1664.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#11719268C211yesmaximal, characteristic
2C13×#476C211yesmaximal, characteristic, complemented
3#11718753C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5D4⋊#1055C211yesmaximal, characteristic, complemented
6#11718075C211yesmaximal, characteristic, complemented
7#11718073C211yesmaximal, characteristic, complemented
8C13×C4⋊Q8C2211yescharacteristic
9C4×D4×C13C2211yescharacteristic
10C2×#6107—22no—
11#88192—21no—
12#88184—21no—
13#88180—21no—
14#88146—21no—
15#88139—22no—
16C4×D52C2211yescharacteristic
17#88123C2211yescharacteristic
18C13×#106—21no—
19C13×C4⋊C8C2211yescharacteristic
20C13×#102—21no—
21#88049—21no—
22#88048—21no—
23C4⋊#1055C2211yescharacteristic
24C4×#1055C2211yescharacteristic
25C2×Q8×C13—21no—
26C2×D4×C13D411yescharacteristic
27C22×C4×C13—21no—
28C2×C22⋊D13—22no—
29C2×D52D411yescharacteristic
30C2×C4×D13—21no—
31C2×Dic26D412yes—
32C2×C8×C13—21no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4D411yescharacteristic
36C13×C22⋊C4—21no—
37C42×C13C2311yescharacteristic
38C22⋊Dic13—22no—
39#6107—44no—
40#6103—22no—
41#6103—21no—
42C4⋊Dic13—21no—
43C4⋊Dic13—21no—
44C4⋊Dic13D411yescharacteristic
45C4×Dic13—22no—
46C2×#1055—21no—
47C2×#1055—21no—
48#1634—131nomaximal, Sylow
49C23×C13—21no—
50C22×D13—21no—
51Q8×C13—42no—
52D4×C13—21no—
53D4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—41no—
56C2×C4×C13—41no—
57C2×C4×C13—41no—
58C2×C4×C13C2×D411yescharacteristic
59C2×C4×C13C2×D411yescharacteristic
60C2×C4×C13C2×D411yescharacteristic
61C22⋊D13—82no—
62C2×Dic13—21no—
63C2×Dic13—22no—
64D52—21no—
65D52—21no—
66C4×D13—41no—
67C4×D13—41no—
68Dic26—42no—
69C8×C13—41no—
70#1055—22no—
71#1055—41no—
72#555—131no—
73#494—131no—
74#476—131no—
75#476D1311yescharacteristic, complemented
76#333—131no—
77D4⋊C8—131no—
78D4⋊C8—131no—
79C22×C13—41no—
80C22×C13—41no—
81C22×C13—41no—
82C22×C13#12011yescharacteristic
83C2×D13—41no—
84C2×D13—41no—
85C2×D13—41no—
86C4×C13—21no—
87C4×C13—41no—
88C4×C13—81no—
89C4×C13#13511yescharacteristic
90C4×C13#13511yescharacteristic
91C4×C13#13711yescharacteristic
92C4×C13#13711yescharacteristic
93Dic13—41no—
94Dic13—42no—
95C2×Q16—262no—
96C4⋊Q8—131no—
97C4⋊Q8C2×D1311yescharacteristic
98#124—262no—
99#121—261no—
100#121—261no—
101C4×D4—131no—
102C4×D4C2×D1311yescharacteristic
103#117—261no—
104#117—261no—
105#106—21no—
106#106—261no—
107C4⋊C8—131no—
108C4⋊C8C2×D1311yescharacteristic
109#102—21no—
110#102—261no—
111C4×C8—131no—
112C2×C13—81no—
113C2×C13#45211yescharacteristic
114C2×C13#45211yescharacteristic
115C2×C13#45311yescharacteristic
116D13—81no—
117C2×Q8—21no—
118C2×Q8—132no—
119C2×D4—131no—
120C2×D4—262no—
121C2×D4C22⋊D1311yescharacteristic
122C22×C4—21no—
123C22×C4—261no—
124Q16—524no—
125C2×C8—21no—
126C2×C8—261no—
127C2×C8—261no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—131no—
131C4⋊C4—261no—
132C4⋊C4—261no—
133C4⋊C4C22⋊D1311yescharacteristic
134C22⋊C4—21no—
135C22⋊C4—262no—
136C22⋊C4—262no—
137C22⋊C4—261no—
138C42—262no—
139C42C22×D1311yescharacteristic
140C13#163411yescharacteristic, complemented, Sylow
141C23—21no—
142C23—261no—
143Q8—42no—
144Q8—522no—
145D4—21no—
146D4—21no—
147D4—261no—
148D4—261no—
149D4—1042no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—261no—
155C2×C4—262no—
156C2×C4—521no—
157C2×C4—521no—
158C2×C4D4×D1311yescharacteristic
159C2×C4D4×D1311yescharacteristic
160C2×C4C2×C22⋊D1311yescharacteristic
161C8—41no—
162C8—262no—
163C8—521no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—521no—
168C22—521no—
169C22—521no—
170C22#8819111yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—521no—
175C4—522no—
176C4#8816911yescharacteristic
177C4#8817011yescharacteristic
178C4#8819611yescharacteristic
179C4#8820411yescharacteristic
180C2—81no—
181C2—1041no—
182C2#1171870811yescharacteristic
183C2#1171883411yescharacteristic
184C2#1171885911yescharacteristic
subgroupG/H
centerC22#88191
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×#476C2
socleC22×C13#120
prime radical#11719268C2
hypercenter#476D13
hypocenterC13#1634
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. C13×#476C2semidirect
3. #11718753C2semidirect
4. #11718745C2semidirect
5. D4⋊#1055C2semidirect
6. #11718075C2semidirect
7. #11718073C2semidirect
75. #476D13semidirect
140. C13#1634semidirect

Maximal subgroups

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

subgroupindex
#117192682
C13×#4762
#117187532
#117187452
D4⋊#10552
#117180752
#117180732
#163413