Finite Group Databasebeta

← #17953672

Subgroups — #17953672

Order 4352.

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

normal subgroups only

This group has 398 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#14544683C212yesmaximal
2#14543687C214yesmaximal
3#14531384C211yesmaximal, characteristic
4#11763779C2214yes—
5#11763689—22no—
6#11763689—22no—
7C22×#63225C2211yescharacteristic
8#11762693—22no—
9#11762691—22no—
10#11762670C2212yes—
11#11762667C412yes—
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—28no—
27C17×#95—21no—
28#10587502—21no—
29#10587502—22no—
30#10587502—24no—
31C24×C17C22×C411yescharacteristic
32C22×C4×C17—22no—
33C22×C4×C17—22no—
34C22×C4×C17—81no—
35C22×C4×C17C22⋊C411yescharacteristic
36C22×C4×C17C22⋊C411yescharacteristic
37C22×Dic17—22no—
38C22×Dic17—22no—
39C22×Dic17—42no—
40C22×Dic17—81no—
41C22×Dic17C22⋊C412yes—
42C22×Dic17C2×D412yes—
43C22×Dic17#4114yes—
44#63247—48no—
45C2×#3624—44no—
46C22⋊C4×C17—42no—
47C42×C17—81no—
48C22⋊Dic17—42no—
49#63225—24no—
50#63225—24no—
51#63225—82no—
52C4×Dic17—81no—
53#8755—171nomaximal, Sylow
54C23×C17—22no—
55C23×C17—41no—
56C23×C17—41no—
57C23×C17C2×C22⋊C411yescharacteristic
58C23×C17#11712yes—
59C2×C4×C17—21no—
60C2×C4×C17—21no—
61C2×C4×C17—41no—
62C2×C4×C17—41no—
63C2×C4×C17—42no—
64C2×C4×C17—42no—
65C2×C4×C17—42no—
66C2×C4×C17—82no—
67C2×Dic17—24no—
68C2×Dic17—22no—
69C2×Dic17—44no—
70C2×Dic17—42no—
71C2×Dic17—42no—
72C2×Dic17—42no—
73C2×Dic17—42no—
74C2×Dic17—82no—
75C2×Dic17#12314yes—
76#3624—84no—
77#2313—171no—
78#1821—172no—
79#1306—174no—
80C22×C17—21no—
81C22×C17—21no—
82C22×C17—22no—
83C22×C17—22no—
84C22×C17—22no—
85C22×C17—44no—
86C22×C17#38111yescharacteristic
87C22×C17#41012yes—
88C4×C17—41no—
89C4×C17—41no—
90C4×C17—82no—
91Dic17—24no—
92Dic17—42no—
93Dic17—82no—
94C22×C4⋊C4—171no—
95#407—174no—
96#387—342no—
97#387—342no—
98#381—172no—
99#380—172no—
100C4×C22⋊C4—171no—
101C4×C22⋊C4#59511yescharacteristic
102#343—342no—
103#343—342no—
104C2×C17—22no—
105C2×C17—42no—
106C2×C17#182011yescharacteristic
107C2×C17#182911yescharacteristic
108C2×C17#183011yescharacteristic
109C23×C4—171no—
110C23×C4—171no—
111C23×C4C2×#59511yescharacteristic
112C2×M16—344no—
113C2×C4⋊C4—172no—
114C2×C4⋊C4—172no—
115C2×C4⋊C4—344no—
116C2×C4⋊C4—342no—
117C2×C22⋊C4—172no—
118C2×C22⋊C4C2×#59512yes—
119C2×C42—21no—
120C2×C42—341no—
121C22⋊C8—348no—
122#95—21no—
123#95—342no—
124#95—344no—
125#95—341no—
126C17#875511yescharacteristic, complemented, Sylow
127C24C22×#59511yescharacteristic
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—81no—
131C22×C4—172no—
132C22×C4—174no—
133C22×C4—172no—
134C22×C4—342no—
135C22×C4—342no—
136C22×C4—682no—
137C22×C4—1361no—
138C22×C4C22⋊#59511yescharacteristic
139C22×C4C22⋊#59511yescharacteristic
140M16—688no—
141C2×C8—684no—
142C4⋊C4—344no—
143C4⋊C4—344no—
144C4⋊C4—1362no—
145C22⋊C4—42no—
146C22⋊C4—682no—
147C42—81no—
148C42—1361no—
149C23—22no—
150C23—41no—
151C23—41no—
152C23#1058767712yes—
153C23C2×C22⋊#59511yescharacteristic
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—82no—
162C2×C4—174no—
163C2×C4—344no—
164C2×C4—342no—
165C2×C4—684no—
166C2×C4—682no—
167C2×C4—682no—
168C2×C4—682no—
169C2×C4—682no—
170C2×C4—1362no—
171C8—1364no—
172C22—21no—
173C22—21no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—44no—
178C22#1176375211yescharacteristic
179C22#1176378812yes—
180C4—41no—
181C4—41no—
182C4—82no—
183C4—344no—
184C4—682no—
185C4—1362no—
186C2—22no—
187C2—42no—
188C2#1454468111yescharacteristic
189C2#1454469711yescharacteristic
190C2#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#8755
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
126. C17#8755semidirect

Maximal subgroups

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

subgroupindex
#145446832
#145436872
#145313842
#875517