Finite Group Databasebeta

← #14536851

Subgroups — #14536851

Order 2176.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10587556C211yesmaximal, characteristic
2#11762748C212yesmaximal
3#11762747C212yesmaximal
4#11762742C214yesmaximal
5#11762740C212yesmaximal
6#11762739C212yesmaximal
7#11762675C211yesmaximal, characteristic
8C2×C17×#125C211yesmaximal, characteristic
9C17×#125—24no—
10C2×C4⋊C4×C17C2212yes—
11C2×C4⋊C4×C17C2211yescharacteristic
12C2×C4⋊C4×C17C2212yes—
13C2×C4⋊C4×C17C2211yescharacteristic
14C2×C42×C17C2211yescharacteristic
15C2×C4⋊Dic17C2211yescharacteristic
16C2×C4⋊Dic17C2211yescharacteristic
17C2×C4⋊Dic17C2212yes—
18C2×#63225C2212yes—
19C2×#63225C2212yes—
20C2×#63225C2214yes—
21#10587556—24no—
22#10587502C2214yes—
23#10587502C2212yes—
24#10587502C2214yes—
25#10587502C2212yes—
26#10587502C2214yes—
27C22×C4×C17C2312yes—
28C22×C4×C17C2312yes—
29C22×C4×C17C2311yescharacteristic
30C22×C4×C17C2311yescharacteristic
31C22×C4×C17C2311yescharacteristic
32C22×Dic17C2314yes—
33C22×Dic17C2312yes—
34C22×Dic17C2312yes—
35C4⋊C4×C17—22no—
36C4⋊C4×C17—24no—
37C4⋊C4×C17—22no—
38C4⋊C4×C17—24no—
39C42×C17D414yes—
40C4⋊Dic17—22no—
41C4⋊Dic17—22no—
42C4⋊Dic17—42no—
43#63225—24no—
44#63225—24no—
45#63225—44no—
46C23×C17C2411yescharacteristic
47C2×C4×C17—21no—
48C2×C4×C17—22no—
49C2×C4×C17—22no—
50C2×C4×C17—21no—
51C2×C4×C17—22no—
52C2×C4×C17—22no—
53C2×C4×C17—22no—
54C2×C4×C17—24no—
55C2×C4×C17—22no—
56C2×C4×C17C2×D412yes—
57C2×C4×C17C2×D412yes—
58C2×C4×C17C2×D412yes—
59C2×Dic17—22no—
60C2×Dic17—22no—
61C2×Dic17—22no—
62C2×Dic17—24no—
63C2×Dic17—24no—
64C2×Dic17—24no—
65C2×Dic17—22no—
66C2×Dic17—24no—
67#2822—171nomaximal, Sylow
68C22×C17C22×D411yescharacteristic
69C22×C17H(5,𝔽2)11yescharacteristic
70C22×C172−1+412yes—
71C22×C172−1+412yes—
72C22×C172−1+411yescharacteristic
73C4×C17—22no—
74C4×C17—22no—
75C4×C17—22no—
76C4×C17—42no—
77C4×C17—42no—
78Dic17—42no—
79Dic17—42no—
80Dic17—44no—
81C2×#125—171no—
82C2×#125D1711yescharacteristic
83#400—172no—
84#400—172no—
85#398—172no—
86#398—172no—
87#398—174no—
88#382—171no—
89C2×C17#53611yescharacteristic
90C2×C17#53611yescharacteristic
91C2×C17#53711yescharacteristic
92C2×C17#56312yes—
93C2×C17#56412yes—
94#125—24no—
95#125—344no—
96C2×C4⋊C4—172no—
97C2×C4⋊C4—171no—
98C2×C4⋊C4—172no—
99C2×C4⋊C4—171no—
100C2×C4⋊C4—172no—
101C2×C4⋊C4—174no—
102C2×C4⋊C4C2×D1712yes—
103C2×C4⋊C4C2×D1711yescharacteristic
104C2×C4⋊C4C2×D1712yes—
105C2×C4⋊C4C2×D1711yescharacteristic
106C2×C42C2×D1711yescharacteristic
107#95—172no—
108#95—172no—
109#95—174no—
110#95—174no—
111#95—174no—
112C17#282211yescharacteristic, complemented, Sylow
113C22×C4—174no—
114C22×C4—172no—
115C22×C4—172no—
116C22×C4C22×D1712yes—
117C22×C4C22×D1712yes—
118C22×C4C22×D1711yescharacteristic
119C22×C4C22×D1711yescharacteristic
120C22×C4C22×D1711yescharacteristic
121C4⋊C4—24no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—22no—
125C4⋊C4—344no—
126C4⋊C4—344no—
127C4⋊C4—342no—
128C4⋊C4—342no—
129C4⋊C4—684no—
130C4⋊C4—682no—
131C42C22⋊D1714yes—
132C23C23×D1711yescharacteristic
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—344no—
143C2×C4—344no—
144C2×C4—344no—
145C2×C4—342no—
146C2×C4—344no—
147C2×C4—342no—
148C2×C4—342no—
149C2×C4—342no—
150C2×C4C2×C22⋊D1712yes—
151C2×C4C2×C22⋊D1712yes—
152C2×C4C2×C22⋊D1712yes—
153C22#1058769412yes—
154C22#1058769611yescharacteristic
155C22#1058769712yes—
156C22#1058769711yescharacteristic
157C22C22×C22⋊D1711yescharacteristic
158C4—22no—
159C4—22no—
160C4—22no—
161C4—42no—
162C4—42no—
163C4—684no—
164C4—682no—
165C4—682no—
166C2#1176338011yescharacteristic
167C2#1176338311yescharacteristic
168C2#1176338711yescharacteristic
169C2#1176356312yes—
170C2C17⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC2×C17×#125C2
hypercenterC2×#125D17
hypocenterC17#2822
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
112. C17#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#105875562
#117627482
#117627472
#117627422
#117627402
#117627392
#117626752
C2×C17×#1252
#282217