Finite Group Databasebeta

← #17953627

Subgroups — #17953627

Order 4352.

418 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 88 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×#11763654C212yesmaximal
2#14543627C214yesmaximal
3#14531385C211yesmaximal, characteristic
4C2×C22⋊#3624C2214yes—
5#11763654—22no—
6#11763654—22no—
7C22×C4⋊Dic17C2211yescharacteristic
8#11762694—22no—
9#11762692—22no—
10#11762672C411yescharacteristic
11#11762667C412yes—
12C22⋊C4×Dic17C2212yes—
13C17×#381C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×Dic17C2×C411yescharacteristic
16C23×Dic17C2311yescharacteristic
17C22×#3624—24no—
18C2×C22⋊C4×C17C2×C412yes—
19C2×C22⋊Dic17C2×C412yes—
20C2×C4⋊Dic17—24no—
21C2×C4⋊Dic17D412yes—
22C2×C4⋊Dic17D412yes—
23C2×#63225—22no—
24C2×C4×Dic17—22no—
25C22⋊#3624—24no—
26C22⋊#3624—24no—
27C17×#95—21no—
28C17×#95—21no—
29#10587502—21no—
30#10587502—21no—
31#10587502—22no—
32#10587502—22no—
33C24×C17C22×C411yescharacteristic
34C22×C4×C17—22no—
35C22×C4×C17—24no—
36C22×C4×C17—22no—
37C22×C4×C17C22⋊C411yescharacteristic
38C22×C4×C17C22⋊C411yescharacteristic
39C22×Dic17—22no—
40C22×Dic17—22no—
41C22×Dic17—81no—
42C22×Dic17—81no—
43C22×Dic17C22⋊C412yes—
44C22×Dic17C2×D412yes—
45C22×Dic17#4114yes—
46C2×#3624—44no—
47C2×#3624—84no—
48C22⋊C4×C17—24no—
49C22⋊Dic17—24no—
50C4⋊Dic17—24no—
51C4⋊Dic17—24no—
52#63225—82no—
53C4×Dic17—82no—
54#8737—171nomaximal, Sylow
55C23×C17—41no—
56C23×C17—41no—
57C23×C17C2×C22⋊C411yescharacteristic
58C23×C17#11712yes—
59C23×C17#13114yes—
60C2×C4×C17—21no—
61C2×C4×C17—21no—
62C2×C4×C17—22no—
63C2×C4×C17—22no—
64C2×C4×C17—44no—
65C2×C4×C17—42no—
66C2×C4×C17—42no—
67C2×C4×C17—42no—
68C2×Dic17—22no—
69C2×Dic17—44no—
70C2×Dic17—42no—
71C2×Dic17—42no—
72C2×Dic17—42no—
73C2×Dic17—42no—
74C2×Dic17—42no—
75C2×Dic17—82no—
76C2×Dic17#12314yes—
77#3624—84no—
78#2313—171no—
79C2×#324—172no—
80#1282—174no—
81C22×C17—21no—
82C22×C17—22no—
83C22×C17—21no—
84C22×C17—22no—
85C22×C17—44no—
86C22×C17#38111yescharacteristic
87C22×C17#40812yes—
88C22×C17#43314yes—
89C4×C17—41no—
90C4×C17—41no—
91C4×C17—82no—
92Dic17—24no—
93Dic17—42no—
94Dic17—82no—
95C22×C4⋊C4—171no—
96C2×C22⋊C8—174no—
97#387—342no—
98#387—342no—
99#381—171no—
100#381#59511yescharacteristic
101#380—172no—
102C4×C22⋊C4—172no—
103#324—342no—
104#324—342no—
105C2×C17—22no—
106C2×C17—24no—
107C2×C17#181811yescharacteristic
108C2×C17#182811yescharacteristic
109C2×C17#183011yescharacteristic
110C23×C4—171no—
111C23×C4—171no—
112C23×C4C2×#59511yescharacteristic
113C22×C8—344no—
114C2×C4⋊C4—172no—
115C2×C4⋊C4—172no—
116C2×C4⋊C4—344no—
117C2×C4⋊C4—342no—
118C2×C22⋊C4—172no—
119C2×C22⋊C4C2×#59512yes—
120C2×C42—342no—
121C22⋊C8—344no—
122C22⋊C8—344no—
123#95—21no—
124#95—21no—
125#95—342no—
126#95—342no—
127#95—341no—
128#95—341no—
129C17#873711yescharacteristic, complemented, Sylow
130C24C22×#59511yescharacteristic
131C22×C4—22no—
132C22×C4—24no—
133C22×C4—22no—
134C22×C4—174no—
135C22×C4—172no—
136C22×C4—172no—
137C22×C4—342no—
138C22×C4—342no—
139C22×C4—1361no—
140C22×C4—1361no—
141C22×C4C22⋊#59511yescharacteristic
142C22×C4C22⋊#59511yescharacteristic
143C2×C8—684no—
144C2×C8—1364no—
145C4⋊C4—344no—
146C4⋊C4—344no—
147C4⋊C4—1362no—
148C22⋊C4—24no—
149C22⋊C4—344no—
150C42—1362no—
151C23—41no—
152C23—41no—
153C23#1058767712yes—
154C23#1058767814yes—
155C23C2×C22⋊#59511yescharacteristic
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—44no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—174no—
165C2×C4—342no—
166C2×C4—682no—
167C2×C4—684no—
168C2×C4—682no—
169C2×C4—682no—
170C2×C4—682no—
171C2×C4—682no—
172C2×C4—1362no—
173C8—1364no—
174C22—21no—
175C22—22no—
176C22—21no—
177C22—22no—
178C22—44no—
179C22#1176375211yescharacteristic
180C22#1176378212yes—
181C22#1176383314yes—
182C4—41no—
183C4—41no—
184C4—82no—
185C4—344no—
186C4—682no—
187C4—1362no—
188C2—22no—
189C2—24no—
190C2#1454467711yescharacteristic
191C2#1454469611yescharacteristic
192C2#1454469811yescharacteristic
subgroupG/H
centerC22#11763752
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC17×#381C4
socleC22×C17#381
cosocleC23×Dic17C23
hypercenter#381#595
hypocenterC17#8737
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
129. C17#8737semidirect

Maximal subgroups

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

subgroupindex
C2×#117636542
#145436272
#145313852
#873717