Finite Group Databasebeta

← #13131013

Subgroups — #13131013

Order 1664.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
2C4×C4⋊#261C211yesmaximal, characteristic
3C4×#6118C211yesmaximal, characteristic
4#11718247C212yesmaximal
5#11718247C212yesmaximal
6C2×C4⋊#261—21no—
7C2×C4×#261C2212yes—
8C2×#6118C2212yes—
9C13×#125C411yescharacteristic, complemented
10#88150—21no—
11#88150—21no—
12#88146C2211yescharacteristic
13#88146C2211yescharacteristic
14#88142C411yescharacteristic, complemented
15#88142C411yescharacteristic, complemented
16#88141—21no—
17#88141—21no—
18C42×D13C2211yescharacteristic
19#88124C411yescharacteristic, complemented
20(C2×#261)⋊C4—21no—
21#88110—21no—
22C4×#1057—21no—
23C22×#261—22no—
24C2×C4×D13D411yescharacteristic
25C2×C4×D13D411yescharacteristic
26C2×C4×D13C2311yescharacteristic
27C2×Dic26—21no—
28C2×Dic26—21no—
29C2×#1057—22no—
30C4⋊#261—24no—
31C4×#261—24no—
32#6118—22no—
33#6118Q814yescomplemented
34C13×C4⋊C4—21no—
35C13×C4⋊C4—21no—
36C13×C4⋊C4C2×C411yescharacteristic
37C13×C4⋊C4C2×C411yescharacteristic
38C42×C13C2×C411yescharacteristic
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
52#1986—131nomaximal, Sylow
53C22×D13C2×D411yescharacteristic
54C2×#261—24no—
55C2×#261—42no—
56C2×#261—42no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22⋊C411yescharacteristic
61C2×C4×C13C22×C411yescharacteristic
62C2×Dic13—21no—
63C2×Dic13—21no—
64C2×Dic13C22⋊C411yescharacteristic
65C2×Dic13C22⋊C411yescharacteristic
66C2×Dic13C2×D411yescharacteristic
67C4×D13—22no—
68C4×D13—41no—
69C4×D13C2×Q812yes—
70C4×D13#4112yes—
71Dic26—42no—
72Dic26—42no—
73#1057—24no—
74#533—131no—
75C4×M16—131no—
76C4×C4⋊C4—131no—
77#339—132no—
78#339—132no—
79C22×C13C2×C22⋊C411yescharacteristic
80C2×D13—21no—
81C2×D13—21no—
82C2×D13#12411yescharacteristic
83C2×D13C4⋊Q811yescharacteristic
84#261—44no—
85C4×C13—21no—
86C4×C13—21no—
87C4×C13—41no—
88C4×C13—41no—
89C4×C13C4×Q812yes—
90Dic13—21no—
91Dic13—41no—
92Dic13—41no—
93Dic13#10412yes—
94Dic13C22⋊Q812yes—
95C2×M16—132no—
96C4⋊Q8—131no—
97C4⋊Q8—131no—
98#125—131no—
99#125#26111yescharacteristic, complemented
100C22⋊Q8—261no—
101C22⋊Q8—261no—
102C4×Q8—261no—
103C4×Q8—261no—
104#117—131no—
105#117—131no—
106C2×C4⋊C4—261no—
107C2×C42—131no—
108C2×C42—132no—
109#97—261no—
110C4×C8—261no—
111#95—261no—
112C2×C13#39111yescharacteristic
113C2×C13C2×#10411yescharacteristic
114C2×C13#42111yescharacteristic
115D13—21no—
116D13—21no—
117C2×Q8—261no—
118C2×Q8—261no—
119C22×C4—131no—
120C22×C4—131no—
121C22×C4—131no—
122C22×C4—262no—
123M16—134no—
124M16—262no—
125C2×C8—262no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—131no—
129C4⋊C4—131no—
130C4⋊C4—261no—
131C4⋊C4—261no—
132C4⋊C4—264no—
133C4⋊C4—261no—
134C4⋊C4—261no—
135C4⋊C4C2×#26111yescharacteristic
136C4⋊C4C2×#26111yescharacteristic
137C22⋊C4—261no—
138C22⋊C4—261no—
139C42—131no—
140C42—131no—
141C42—131no—
142C42—261no—
143C42—261no—
144C42—264no—
145C42C2×#26111yescharacteristic
146C13#198611yescharacteristic, complemented, Sylow
147C23—131no—
148Q8—522no—
149Q8—522no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—131no—
153C2×C4—131no—
154C2×C4—132no—
155C2×C4—132no—
156C2×C4—131no—
157C2×C4—262no—
158C2×C4—264no—
159C2×C4—261no—
160C2×C4—261no—
161C2×C4—521no—
162C2×C4—522no—
163C2×C4—522no—
164C2×C4C22⋊#26111yescharacteristic
165C2×C4C22⋊#26111yescharacteristic
166C2×C4C22×#26111yescharacteristic
167C8—264no—
168C22—131no—
169C22—131no—
170C22—261no—
171C22—261no—
172C22C2×C22⋊#26111yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—132no—
178C4—132no—
179C4—261no—
180C4—524no—
181C4—521no—
182C4—521no—
183C4Q8×#26112yes—
184C2—261no—
185C2—261no—
186C2(C2×#261)⋊Q811yescharacteristic
187C2D13⋊#10411yescharacteristic
188C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#125C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C2×D4
cosocleC2×C4×D13C23
hypercenter#125#261
hypocenterC13#1986
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. C13×#125C4semidirect
14. #88142C4semidirect
15. #88142C4semidirect
19. #88124C4semidirect
33. #6118Q8semidirect
99. #125#261semidirect
146. C13#1986semidirect

Maximal subgroups

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

subgroupindex
#117193932
C4×C4⋊#2612
C4×#61182
#117182472
#198613