Finite Group Databasebeta

← #14534661

Subgroups — #14534661

Order 2176.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×Dic34C211yesmaximal, characteristic
2#11762748C212yesmaximal
3#11762747C212yesmaximal
4#11762740C212yesmaximal
5#11762729C212yesmaximal
6#11762690C214yesmaximal
7#11762677C211yesmaximal, characteristic
8C2×C17×#125C211yesmaximal, characteristic
9C22×Dic34C2211yescharacteristic
10C17×#125—24no—
11C2×C4⋊C4×C17C2212yes—
12C2×C4⋊C4×C17C2212yes—
13C2×C4⋊C4×C17C2211yescharacteristic
14C2×C4⋊C4×C17C2211yescharacteristic
15C2×C42×C17C2211yescharacteristic
16C2×C4⋊Dic17C2211yescharacteristic
17C2×#63225C2214yes—
18C2×#63225C2212yes—
19C2×C4×Dic17C2212yes—
20C4×Dic34—24no—
21#10587502C2212yes—
22#10587502C2214yes—
23#10587502C2214yes—
24#10587502C2214yes—
25#10587502C2212yes—
26#10587502C2212yes—
27C22×C4×C17C2312yes—
28C22×C4×C17C2312yes—
29C22×C4×C17C2311yescharacteristic
30C22×C4×C17C2311yescharacteristic
31C22×C4×C17C2311yescharacteristic
32C22×Dic17C2314yes—
33C22×Dic17C2312yes—
34C22×Dic17C2312yes—
35C2×Dic34—22no—
36C2×Dic34—24no—
37C4⋊C4×C17—24no—
38C4⋊C4×C17—24no—
39C4⋊C4×C17—22no—
40C4⋊C4×C17—22no—
41C42×C17D414yes—
42C4⋊Dic17—22no—
43#63225—24no—
44#63225—28no—
45C4×Dic17—24no—
46C23×C17C2411yescharacteristic
47C2×C4×C17—22no—
48C2×C4×C17—22no—
49C2×C4×C17—22no—
50C2×C4×C17—22no—
51C2×C4×C17—22no—
52C2×C4×C17—24no—
53C2×C4×C17—24no—
54C2×C4×C17C2×D412yes—
55C2×C4×C17C2×D412yes—
56C2×C4×C17C2×D412yes—
57C2×Dic17—22no—
58C2×Dic17—22no—
59C2×Dic17—22no—
60C2×Dic17—24no—
61C2×Dic17—24no—
62C2×Dic17—24no—
63C2×Dic17—24no—
64C2×Dic17#4114yes—
65Dic34—28no—
66#2634—171nomaximal, Sylow
67C22×C17C22×D411yescharacteristic
68C22×C17C2×#4112yes—
69C22×C172−1+412yes—
70C22×C172−1+412yes—
71C4×C17—22no—
72C4×C17—22no—
73C4×C17—22no—
74C4×C17—42no—
75C4×C17—42no—
76Dic17—24no—
77Dic17—42no—
78Dic17—44no—
79C2×#125D1711yescharacteristic
80C2×C4×Q8—171no—
81#400—172no—
82#400—172no—
83#398—172no—
84#395—172no—
85#387—174no—
86#383—171no—
87C2×C17#52511yescharacteristic
88C2×C17#53611yescharacteristic
89C2×C17#53611yescharacteristic
90C2×C17#54114yes—
91C22×Q8—171no—
92#125—24no—
93C4×Q8—344no—
94C2×C4⋊C4—172no—
95C2×C4⋊C4—171no—
96C2×C4⋊C4—174no—
97C2×C4⋊C4C2×D1712yes—
98C2×C4⋊C4C2×D1712yes—
99C2×C4⋊C4C2×D1711yescharacteristic
100C2×C4⋊C4C2×D1711yescharacteristic
101C2×C42—172no—
102C2×C42C2×D1711yescharacteristic
103#95—172no—
104#95—172no—
105#95—172no—
106#95—174no—
107#95—174no—
108#95—174no—
109C17#263411yescharacteristic, complemented, Sylow
110C2×Q8—344no—
111C2×Q8—342no—
112C22×C4—172no—
113C22×C4—174no—
114C22×C4—172no—
115C22×C4C22×D1712yes—
116C22×C4C22×D1712yes—
117C22×C4C22×D1711yescharacteristic
118C22×C4C22×D1711yescharacteristic
119C22×C4C22×D1711yescharacteristic
120C4⋊C4—24no—
121C4⋊C4—22no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—348no—
125C4⋊C4—344no—
126C4⋊C4—342no—
127C42—344no—
128C42C22⋊D1714yes—
129C23C23×D1711yescharacteristic
130Q8—348no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—24no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—174no—
139C2×C4—342no—
140C2×C4—342no—
141C2×C4—344no—
142C2×C4—344no—
143C2×C4—344no—
144C2×C4—344no—
145C2×C4—342no—
146C2×C4C2×C22⋊D1712yes—
147C2×C4C2×C22⋊D1712yes—
148C2×C4C2×C22⋊D1712yes—
149C22#1058769412yes—
150C22#41×D1712yes—
151C22#1058769712yes—
152C22C22×C22⋊D1711yescharacteristic
153C4—22no—
154C4—22no—
155C4—22no—
156C4—42no—
157C4—42no—
158C4—344no—
159C4—682no—
160C4—684no—
161C2#1176331611yescharacteristic
162C2#1176338011yescharacteristic
163C2#1176338311yescharacteristic
164C2#1176341814yes—
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC2×C17×#125C2
hypercenterC2×#125D17
hypocenterC17#2634
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
109. C17#2634semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic342
#117627482
#117627472
#117627402
#117627292
#117626902
#117626772
C2×C17×#1252
#263417