Finite Group Databasebeta

← #13114063

Subgroups — #13114063

Order 1664.

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

normal subgroups only

This group has 212 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×#474C211yesmaximal, characteristic, complemented
3#11718754C211yesmaximal, characteristic, complemented
4#11718744C211yesmaximal, characteristic, complemented
5D4⋊#1055C211yesmaximal, characteristic, complemented
6#11718075C211yesmaximal, characteristic, complemented
7#11718073C211yesmaximal, characteristic, complemented
8C13×C4⋊Q8C2211yescharacteristic
9C4×D4×C13C2211yescharacteristic
10C2×#6106—21no—
11#88192—21no—
12#88184—21no—
13#88180—21no—
14#88146—21no—
15#88139—22no—
16C4×D52C2211yescharacteristic
17#88123C2211yescharacteristic
18C13×#107—21no—
19C13×C4⋊C8C2211yescharacteristic
20C13×#102—21no—
21#88075—21no—
22#88050—22no—
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#6106—42no—
40#6103—22no—
41#6103—21no—
42C4⋊Dic13—21no—
43C4⋊Dic13—21no—
44C4⋊Dic13D411yescharacteristic
45C4×Dic13—22no—
46C2×#1055—21no—
47C2×#1055—21no—
48#1646—131nomaximal, Sylow
49C23×C13—21no—
50C22×D13—21no—
51Q8×C13—41no—
52Q8×C13—41no—
53D4×C13—21no—
54D4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—41no—
57C2×C4×C13—41no—
58C2×C4×C13—41no—
59C2×C4×C13C2×D411yescharacteristic
60C2×C4×C13C2×D411yescharacteristic
61C2×C4×C13C2×D411yescharacteristic
62C22⋊D13—82no—
63C2×Dic13—21no—
64C2×Dic13—22no—
65D52—21no—
66D52—21no—
67C4×D13—41no—
68C4×D13—41no—
69Dic26—42no—
70C8×C13—41no—
71#1055—41no—
72#1055—41no—
73#555—131no—
74#487—131no—
75#474D1311yescharacteristic, complemented
76#461—131no—
77#333—131no—
78D4⋊C8—131no—
79D4⋊C8—131no—
80C22×C13—41no—
81C22×C13—41no—
82C22×C13—41no—
83C22×C13#12011yescharacteristic
84C2×D13—41no—
85C2×D13—41no—
86C2×D13—41no—
87C4×C13—21no—
88C4×C13—41no—
89C4×C13—81no—
90C4×C13#13511yescharacteristic
91C4×C13#13511yescharacteristic
92C4×C13AGL(1,ℤ/8)11yescharacteristic
93C4×C13#13711yescharacteristic
94Dic13—41no—
95Dic13—42no—
96C2×SD16—261no—
97C4⋊Q8—131no—
98C4⋊Q8C2×D1311yescharacteristic
99#124—262no—
100#121—261no—
101#121—261no—
102C4×D4—131no—
103C4×D4C2×D1311yescharacteristic
104#117—261no—
105#117—261no—
106#107—21no—
107C4⋊C8—131no—
108C4⋊C8C2×D1311yescharacteristic
109#103—262no—
110#103—261no—
111#102—21no—
112C4×C8—131no—
113C2×C13—81no—
114C2×C13#44911yescharacteristic
115C2×C13#45211yescharacteristic
116C2×C13#45511yescharacteristic
117D13—81no—
118C2×Q8—21no—
119C2×Q8—132no—
120C2×D4—131no—
121C2×D4—262no—
122C2×D4C22⋊D1311yescharacteristic
123C22×C4—21no—
124C22×C4—261no—
125SD16—522no—
126C2×C8—21no—
127C2×C8—261no—
128C2×C8—261no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—131no—
132C4⋊C4—261no—
133C4⋊C4—261no—
134C4⋊C4C22⋊D1311yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—262no—
137C22⋊C4—262no—
138C22⋊C4—261no—
139C42—262no—
140C42C22×D1311yescharacteristic
141C13#164611yescharacteristic, complemented, Sylow
142C23—21no—
143C23—261no—
144Q8—41no—
145Q8—41no—
146Q8—522no—
147D4—21no—
148D4—21no—
149D4—261no—
150D4—261no—
151D4—1042no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—261no—
157C2×C4—262no—
158C2×C4—521no—
159C2×C4—521no—
160C2×C4D4×D1311yescharacteristic
161C2×C4D4×D1311yescharacteristic
162C2×C4C2×C22⋊D1311yescharacteristic
163C8—41no—
164C8—521no—
165C8—521no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—521no—
170C22—521no—
171C22—521no—
172C22#8819111yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—521no—
177C4—522no—
178C4#8816511yescharacteristic
179C4#8816611yescharacteristic
180C4#8819611yescharacteristic
181C4#8820411yescharacteristic
182C2—81no—
183C2—1041no—
184C2#1171870811yescharacteristic
185C2#1171881911yescharacteristic
186C2#1171886311yescharacteristic
subgroupG/H
centerC22#88191
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×#474C2
socleC22×C13#120
prime radical#11719268C2
hypercenter#474D13
hypocenterC13#1646
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. C13×#474C2semidirect
3. #11718754C2semidirect
4. #11718744C2semidirect
5. D4⋊#1055C2semidirect
6. #11718075C2semidirect
7. #11718073C2semidirect
75. #474D13semidirect
141. C13#1646semidirect

Maximal subgroups

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

subgroupindex
#117192682
C13×#4742
#117187542
#117187442
D4⋊#10552
#117180752
#117180732
#164613