Finite Group Databasebeta

← #17953680

Subgroups — #17953680

Order 4352.

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

normal subgroups only

This group has 394 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#14544034C212yesmaximal
2#14543685C214yesmaximal
3#14531384C211yesmaximal, characteristic
4#11763779C2214yes—
5#11763655—22no—
6#11763655—22no—
7C22×#63225C2211yescharacteristic
8#11762693—22no—
9#11762691—22no—
10#11762670C412yes—
11#11762667C2212yes—
12C4×C22⋊Dic17C411yescharacteristic
13C4×C22⋊C4×C17C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×Dic17C2×C411yescharacteristic
16C23×Dic17C2311yescharacteristic
17C2×#63247—24no—
18C2×C22⋊C4×C17C2×C412yes—
19C2×C42×C17—21no—
20C2×C22⋊Dic17C2×C412yes—
21C2×#63225—22no—
22C2×#63225—24no—
23C2×#63225D412yes—
24C2×#63225D412yes—
25C2×C4×Dic17—21no—
26C22⋊#3624—24no—
27C22⋊#3624—24no—
28C17×#95—21no—
29#10587502—21no—
30#10587502—24no—
31#10587502—22no—
32C24×C17C22×C411yescharacteristic
33C22×C4×C17—22no—
34C22×C4×C17—22no—
35C22×C4×C17—81no—
36C22×C4×C17C22⋊C411yescharacteristic
37C22×C4×C17C22⋊C411yescharacteristic
38C22×Dic17—22no—
39C22×Dic17—22no—
40C22×Dic17—42no—
41C22×Dic17—81no—
42C22×Dic17C22⋊C412yes—
43C22×Dic17C2×D412yes—
44C22×Dic17#4114yes—
45#63247—84no—
46C2×#3624—44no—
47C22⋊C4×C17—42no—
48C42×C17—81no—
49C22⋊Dic17—42no—
50#63225—24no—
51#63225—24no—
52#63225—82no—
53C4×Dic17—81no—
54#8758—171nomaximal, Sylow
55C23×C17—22no—
56C23×C17—41no—
57C23×C17—41no—
58C23×C17C2×C22⋊C411yescharacteristic
59C23×C17#11712yes—
60C2×C4×C17—21no—
61C2×C4×C17—21no—
62C2×C4×C17—41no—
63C2×C4×C17—41no—
64C2×C4×C17—42no—
65C2×C4×C17—42no—
66C2×C4×C17—42no—
67C2×C4×C17—82no—
68C2×Dic17—22no—
69C2×Dic17—24no—
70C2×Dic17—44no—
71C2×Dic17—42no—
72C2×Dic17—44no—
73C2×Dic17—42no—
74C2×Dic17—42no—
75C2×Dic17—42no—
76C2×Dic17#12314yes—
77#3624—84no—
78#2313—171no—
79#1463—172no—
80#1305—174no—
81C22×C17—21no—
82C22×C17—21no—
83C22×C17—22no—
84C22×C17—22no—
85C22×C17—22no—
86C22×C17—44no—
87C22×C17#38111yescharacteristic
88C22×C17#41312yes—
89C4×C17—41no—
90C4×C17—41no—
91C4×C17—82no—
92Dic17—24no—
93Dic17—42no—
94Dic17—82no—
95C22×C4⋊C4—171no—
96#407—174no—
97#387—342no—
98#387—342no—
99#381—172no—
100#380—172no—
101C4×C22⋊C4—171no—
102C4×C22⋊C4#59511yescharacteristic
103#324—342no—
104#324—342no—
105C2×C17—22no—
106C2×C17—42no—
107C2×C17#182211yescharacteristic
108C2×C17#182811yescharacteristic
109C2×C17#183011yescharacteristic
110C23×C4—171no—
111C23×C4—171no—
112C23×C4C2×#59511yescharacteristic
113C2×M16—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—21no—
121C2×C42—341no—
122C22⋊C8—344no—
123C22⋊C8—344no—
124#95—21no—
125#95—342no—
126#95—344no—
127#95—341no—
128C17#875811yescharacteristic, complemented, Sylow
129C24C22×#59511yescharacteristic
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—81no—
133C22×C4—174no—
134C22×C4—172no—
135C22×C4—172no—
136C22×C4—342no—
137C22×C4—342no—
138C22×C4—682no—
139C22×C4—1361no—
140C22×C4C22⋊#59511yescharacteristic
141C22×C4C22⋊#59511yescharacteristic
142M16—1364no—
143C2×C8—684no—
144C4⋊C4—344no—
145C4⋊C4—344no—
146C4⋊C4—1362no—
147C22⋊C4—42no—
148C22⋊C4—682no—
149C42—81no—
150C42—1361no—
151C23—22no—
152C23—41no—
153C23—41no—
154C23#1058767712yes—
155C23C2×C22⋊#59511yescharacteristic
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—82no—
164C2×C4—174no—
165C2×C4—342no—
166C2×C4—344no—
167C2×C4—682no—
168C2×C4—684no—
169C2×C4—684no—
170C2×C4—682no—
171C2×C4—682no—
172C2×C4—682no—
173C8—1364no—
174C22—21no—
175C22—21no—
176C22—22no—
177C22—22no—
178C22—22no—
179C22—44no—
180C22#1176375211yescharacteristic
181C22#1176379512yes—
182C4—41no—
183C4—41no—
184C4—82no—
185C4—344no—
186C4—682no—
187C4—1362no—
188C2—22no—
189C2—42no—
190C2#1454468511yescharacteristic
191C2#1454469511yescharacteristic
192C2#1454469811yescharacteristic
subgroupG/H
centerC22#11763752
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC4×C22⋊C4×C17C4
socleC22×C17#381
cosocleC23×Dic17C23
hypercenterC4×C22⋊C4#595
hypocenterC17#8758
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
128. C17#8758semidirect

Maximal subgroups

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

subgroupindex
#145440342
#145436852
#145313842
#875817