Finite Group Databasebeta

← #13113449

Subgroups — #13113449

Order 1664.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#11719393C211yesmaximal, characteristic
2#11718366C211yesmaximal, characteristic
3D13×#97C211yesmaximal, characteristic
4C13×#330C211yesmaximal, characteristic, complemented
5#11718135C211yesmaximal, characteristic, complemented
6#11718057C211yesmaximal, characteristic, complemented
7#11718057C211yesmaximal, characteristic, complemented
8C13×#125C2211yescharacteristic
9C2×C8×D13—21no—
10#88150—21no—
11#88150—21no—
12#88146C411yescharacteristic
13#88146C411yescharacteristic
14#88142C411yescharacteristic
15#88142C411yescharacteristic
16#88141—21no—
17#88141—21no—
18C42×D13C2211yescharacteristic
19#88124C2211yescharacteristic
20C13×#97C2211yescharacteristic
21C13×#97C2211yescharacteristic
22#88060—21no—
23#88055—21no—
24#88054—21no—
25#88043C2211yescharacteristic
26#88043C2211yescharacteristic
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13D411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×Dic26—21no—
31C2×Dic26—21no—
32C2×C8×C13—21no—
33C2×C8×C13—21no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4—21no—
36C13×C4⋊C4C2×C411yescharacteristic
37C13×C4⋊C4C2×C411yescharacteristic
38C42×C13C2311yescharacteristic
39#6103—21no—
40#6103—21no—
41C4⋊Dic13C2×C411yescharacteristic
42C4⋊Dic13C2×C411yescharacteristic
43#6101—21no—
44#6101—21no—
45#6101—21no—
46#6101—21no—
47C4×Dic13—21no—
48C4×Dic13—21no—
49C4×Dic13C2×C411yescharacteristic
50C4×Dic13D411yescharacteristic
51C4×Dic13D411yescharacteristic
52C2×#1055—21no—
53C2×#1055—21no—
54C8×D13—24no—
55#1531—131nomaximal, Sylow
56C22×D13C22⋊C411yescharacteristic
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13C22×C411yescharacteristic
60C2×C4×C13C2×D411yescharacteristic
61C2×C4×C13C2×D411yescharacteristic
62C2×Dic13—21no—
63C2×Dic13—21no—
64C2×Dic13C22⋊C411yescharacteristic
65C2×Dic13C22⋊C411yescharacteristic
66C2×Dic13C22⋊C411yescharacteristic
67C4×D13—22no—
68C4×D13—22no—
69C4×D13—41no—
70Dic26—42no—
71Dic26—42no—
72C8×C13—22no—
73C8×C13—41no—
74#1055—22no—
75#1055—41no—
76#533—131no—
77#432—131no—
78C2×#97—131no—
79#330—131no—
80#330—131no—
81#330—131no—
82#330D1311yescharacteristic, complemented
83C22×C13C2×C22⋊C411yescharacteristic
84C2×D13—21no—
85C2×D13—21no—
86C2×D13#10112yes—
87C4×C13—21no—
88C4×C13—21no—
89C4×C13—21no—
90C4×C13—41no—
91C4×C13—41no—
92Dic13—21no—
93Dic13—21no—
94Dic13—41no—
95Dic13—41no—
96Dic13#10412yes—
97C22×C8—261no—
98C4⋊Q8—131no—
99C4⋊Q8—131no—
100#125—131no—
101#125C2×D1311yescharacteristic
102C22⋊Q8—261no—
103C22⋊Q8—261no—
104C4×Q8—261no—
105C4×Q8—261no—
106#117—131no—
107#117—131no—
108C2×C42—131no—
109C4⋊C8—261no—
110C22⋊C8—261no—
111#97—131no—
112#97—131no—
113#97—261no—
114#97C2×D1311yescharacteristic
115#97C2×D1311yescharacteristic
116C2×C13C2×#10111yescharacteristic
117C2×C13C2×#10411yescharacteristic
118C2×C13#42111yescharacteristic
119D13—22no—
120C2×Q8—261no—
121C2×Q8—261no—
122C22×C4—131no—
123C22×C4—131no—
124C22×C4—131no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—264no—
128C2×C8—261no—
129C2×C8—261no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—131no—
133C4⋊C4—131no—
134C4⋊C4—261no—
135C4⋊C4—261no—
136C4⋊C4—261no—
137C4⋊C4—261no—
138C4⋊C4C4×D1311yescharacteristic
139C4⋊C4C4×D1311yescharacteristic
140C22⋊C4—261no—
141C22⋊C4—261no—
142C42—131no—
143C42—131no—
144C42—131no—
145C42—261no—
146C42—261no—
147C42C22×D1311yescharacteristic
148C13#153111yescharacteristic, complemented, Sylow
149C23—131no—
150Q8—522no—
151Q8—522no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—131no—
155C2×C4—131no—
156C2×C4—131no—
157C2×C4—262no—
158C2×C4—262no—
159C2×C4—261no—
160C2×C4—261no—
161C2×C4—521no—
162C2×C4C2×C4×D1311yescharacteristic
163C2×C4D4×D1311yescharacteristic
164C2×C4D4×D1311yescharacteristic
165C8—22no—
166C8—41no—
167C8—262no—
168C8—521no—
169C22—132no—
170C22—261no—
171C22—261no—
172C22C22⋊C4×D1311yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—132no—
179C4—261no—
180C4—261no—
181C4—521no—
182C4—521no—
183C2—262no—
184C2D13×#10111yescharacteristic
185C2D13×#10411yescharacteristic
186C2#1171848211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×#330C2
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C22⋊C4
cosocleC42×C13C23
hypercenter#330D13
hypocenterC13#1531
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. C13×#330C2semidirect
5. #11718135C2semidirect
6. #11718057C2semidirect
7. #11718057C2semidirect
82. #330D13semidirect
148. C13#1531semidirect

Maximal subgroups

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

subgroupindex
#117193932
#117183662
D13×#972
C13×#3302
#117181352
#117180572
#153113