Finite Group Databasebeta

← #13115823

Subgroups — #13115823

Order 1664.

260 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 87 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×#88142C211yesmaximal, characteristic
2#11718779C211yesmaximal, characteristic
3M16×Dic13C211yesmaximal, characteristic
4C13×#343C211yesmaximal, characteristic
5#11718146C211yesmaximal, characteristic
6#11718146C211yesmaximal, characteristic
7#11718122C211yesmaximal, characteristic
8C22×Dic26C412yes—
9C2×C13×M16C2211yescharacteristic
10C2×C13×M16C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic13C2211yescharacteristic
13C2×#6101C412yes—
14C2×C4×Dic13C2211yescharacteristic
15C2×#6099C2211yescharacteristic
16C2×#6099C2211yescharacteristic
17#88142—21no—
18#88142—21no—
19#88142—21no—
20#88142—21no—
21#88055—21no—
22#88054—21no—
23#88054—21no—
24C8×Dic13—21no—
25C22×C4×C13C2×C412yes—
26C22×C4×C13C2311yescharacteristic
27C22×Dic13C2×C411yescharacteristic
28C22×Dic13C2×C411yescharacteristic
29C22×Dic13C2×C412yes—
30C2×Dic26—22no—
31C2×Dic26—22no—
32C2×Dic26—44no—
33C13×M16—21no—
34C13×M16—21no—
35C13×M16—21no—
36C13×M16Q812yescomplemented
37C2×C8×C13—21no—
38C2×C8×C13—21no—
39C13×C4⋊C4—21no—
40C13×C4⋊C4—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13—21no—
43#6101—22no—
44#6101—22no—
45C4×Dic13D411yescharacteristic
46C4×Dic13D411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13D411yescharacteristic
49#6099—21no—
50#6099—21no—
51#6099—21no—
52#6099Q812yescomplemented
53C2×#1055—21no—
54C2×#1055—21no—
55#1997—131nomaximal, Sylow
56C23×C13C22×C411yescharacteristic
57C2×C4×C13—22no—
58C2×C4×C13—42no—
59C2×C4×C13C2×D411yescharacteristic
60C2×C4×C13C2×D411yescharacteristic
61C2×C4×C13C2×Q811yescharacteristic
62C2×C4×C13C2×Q811yescharacteristic
63C2×C4×C13#4111yescharacteristic
64C2×C4×C13#4111yescharacteristic
65C2×Dic13—22no—
66C2×Dic13—22no—
67C2×Dic13—22no—
68C2×Dic13—42no—
69C2×Dic13C22⋊C411yescharacteristic
70C2×Dic13C22⋊C411yescharacteristic
71C2×Dic13C22⋊C411yescharacteristic
72C2×Dic13C22⋊C411yescharacteristic
73Dic26—44no—
74Dic26—44no—
75C8×C13—22no—
76C8×C13—41no—
77#1055—22no—
78#1055—41no—
79C2×C4⋊Q8—131no—
80#423—131no—
81C4×M16—131no—
82#343—131no—
83#343—131no—
84#343—131no—
85#343D1311yescharacteristic
86C22×C13—21no—
87C22×C13—21no—
88C22×C13C2×C22⋊C411yescharacteristic
89C22×C13C4×Q811yescharacteristic
90C22×C13C4×Q811yescharacteristic
91C4×C13—42no—
92C4×C13C22⋊Q811yescharacteristic
93C4×C13C22⋊Q811yescharacteristic
94C4×C13#12411yescharacteristic
95C4×C13C4⋊Q811yescharacteristic
96Dic13—21no—
97Dic13—21no—
98Dic13—42no—
99Dic13#10012yes—
100Dic13#10112yes—
101C22×Q8—132no—
102C2×M16—131no—
103C2×M16—131no—
104C2×M16C2×D1311yescharacteristic
105C2×M16C2×D1311yescharacteristic
106C4⋊Q8—261no—
107C4⋊Q8—261no—
108C4⋊Q8—261no—
109C4⋊Q8—261no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—131no—
112C2×C4⋊C4C2×D1311yescharacteristic
113C2×C42—131no—
114C4⋊C8—261no—
115C4⋊C8—261no—
116#97—261no—
117C4×C8—261no—
118C2×C13—21no—
119C2×C13—21no—
120C2×C13#39111yescharacteristic
121C2×C13C2×#10011yescharacteristic
122C2×C13C2×#10111yescharacteristic
123C2×Q8—262no—
124C2×Q8—262no—
125C2×Q8—524no—
126C22×C4—131no—
127C22×C4—131no—
128C22×C4—132no—
129C22×C4C4×D1312yes—
130C22×C4C22×D1311yescharacteristic
131M16—21no—
132M16—21no—
133M16—21no—
134M16—132no—
135M16—261no—
136M16—261no—
137M16—261no—
138M16Dic2612yescomplemented
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—261no—
142C2×C8—261no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—262no—
146C4⋊C4—262no—
147C4⋊C4—261no—
148C4⋊C4—261no—
149C42—131no—
150C42—131no—
151C42—131no—
152C42—131no—
153C13#199711yescharacteristic, complemented, Sylow
154C23C2×C4×D1311yescharacteristic
155Q8—524no—
156Q8—524no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—131no—
160C2×C4—131no—
161C2×C4—131no—
162C2×C4—131no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—262no—
166C2×C4—522no—
167C2×C4C2×Dic2611yescharacteristic
168C2×C4#612711yescharacteristic
169C2×C4D4×D1311yescharacteristic
170C2×C4D4×D1311yescharacteristic
171C2×C4#612911yescharacteristic
172C2×C4Q8×D1311yescharacteristic
173C8—22no—
174C8—41no—
175C8—262no—
176C8—521no—
177C22—21no—
178C22—21no—
179C22C4×Dic2611yescharacteristic
180C22C22⋊C4×D1311yescharacteristic
181C22#8814111yescharacteristic
182C4—42no—
183C4—132no—
184C4—132no—
185C4—261no—
186C4—261no—
187C4—522no—
188C4#8813211yescharacteristic
189C4#8813911yescharacteristic
190C4#8814211yescharacteristic
191C4#8815011yescharacteristic
192C2—21no—
193C2—21no—
194C2#1171830711yescharacteristic
195C2D13×#10011yescharacteristic
196C2D13×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutator, prime radicalC23×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#343C2
socleC22×C13C2×C22⋊C4
cosocleC22×C4×C13C23
hypercenter#343D13
hypocenterC13#1997
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
36. C13×M16Q8semidirect
52. #6099Q8semidirect
138. M16Dic26semidirect
153. C13#1997semidirect

Maximal subgroups

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

subgroupindex
C2×#881422
#117187792
M16×Dic132
C13×#3432
#117181462
#117181222
#199713