Finite Group Databasebeta

← #17952454

Subgroups — #17952454

Order 4352.

810 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 132 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#14544675C212yesmaximal
2C2×#11763654C214yesmaximal
3C22×#10587576C211yesmaximal, characteristic
4C2×C22⋊#3624C2214yes—
5#11763675—24no—
6#11763654—28no—
7C2×#10587576—28no—
8C2×#10587576—24no—
9C22×C4⋊Dic17C411yescharacteristic
10C22×C4⋊Dic17C2212yes—
11C22×#63225C412yes—
12C22×C4×Dic17C2211yescharacteristic
13C22×C4⋊C4×C17C411yescharacteristic
14C23×C4×C17C2×C412yes—
15C23×C4×C17C2×C411yescharacteristic
16C23×Dic17C2×C411yescharacteristic
17C23×Dic17C2×C412yes—
18C23×Dic17C2311yescharacteristic
19C22×#3624—24no—
20C2×C4⋊C4×C17—24no—
21C2×C4⋊C4×C17—22no—
22C2×C4⋊Dic17—22no—
23C2×C4⋊Dic17—24no—
24C2×C4⋊Dic17—24no—
25C2×C4⋊Dic17—24no—
26C2×C4⋊Dic17D418yes—
27C2×#63225—24no—
28C2×#63225—24no—
29C2×#63225—24no—
30C2×C4×Dic17—24no—
31C2×C4×Dic17D414yes—
32#10587576—232no—
33C22⋊#3624—28no—
34C24×C17C22×C411yescharacteristic
35C22×C4×C17—22no—
36C22×C4×C17—24no—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—28no—
40C22×C4×C17C22⋊C414yes—
41C22×C4×C17C22⋊C412yes—
42C22×Dic17—22no—
43C22×Dic17—22no—
44C22×Dic17—22no—
45C22×Dic17—24no—
46C22×Dic17—42no—
47C22×Dic17—44no—
48C22×Dic17C22⋊C412yes—
49C22×Dic17C22⋊C414yes—
50C22×Dic17C2×D412yes—
51C22×Dic17C2×D414yes—
52C2×#3624—48no—
53C2×#3624—44no—
54C4⋊C4×C17—28no—
55C4⋊Dic17—28no—
56C4⋊Dic17—216no—
57#63225—216no—
58C4×Dic17—28no—
59#8306—171nomaximal, Sylow
60C23×C17—22no—
61C23×C17—22no—
62C23×C17C2×C22⋊C412yes—
63C23×C17C2×C22⋊C411yescharacteristic
64C23×C17#13114yes—
65C2×C4×C17—28no—
66C2×C4×C17—22no—
67C2×C4×C17—22no—
68C2×C4×C17—24no—
69C2×C4×C17—28no—
70C2×C4×C17—44no—
71C2×C4×C17—44no—
72C2×C4×C17#10114yes—
73C2×Dic17—24no—
74C2×Dic17—22no—
75C2×Dic17—24no—
76C2×Dic17—24no—
77C2×Dic17—44no—
78C2×Dic17—44no—
79C2×Dic17—44no—
80C2×Dic17—44no—
81C2×Dic17—44no—
82C2×Dic17#12014yes—
83#3624—84no—
84C22×#125—171no—
85#1817—172no—
86C2×#324—174no—
87C22×C17—28no—
88C22×C17—22no—
89C22×C17—22no—
90C22×C17#37911yescharacteristic
91C22×C17#40814yes—
92C22×C17#40812yes—
93C22×C17#41012yes—
94C22×C17C2×#10112yes—
95C4×C17—24no—
96C4×C17—44no—
97Dic17—24no—
98Dic17—42no—
99Dic17—44no—
100C2×#125—344no—
101C2×#125—348no—
102C22×C4⋊C4—172no—
103C22×C4⋊C4—172no—
104C22×C4⋊C4—171no—
105C22×C4⋊C4#59511yescharacteristic
106C22×C42—171no—
107C2×C22⋊C8—174no—
108#336—344no—
109#324—348no—
110C2×C17—24no—
111C2×C17#147014yes—
112C2×C17#178011yescharacteristic
113C2×C17#178211yescharacteristic
114C2×C17#178411yescharacteristic
115C23×C4—171no—
116C23×C4—171no—
117C23×C4—172no—
118C23×C4C2×#59512yes—
119C23×C4C2×#59511yescharacteristic
120C22×C8—344no—
121#125—3432no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—178no—
125C2×C4⋊C4—344no—
126C2×C4⋊C4—344no—
127C2×C4⋊C4—344no—
128C2×C4⋊C4—344no—
129C2×C4⋊C4—344no—
130C2×C4⋊C4—344no—
131C2×C4⋊C4—342no—
132C2×C42—174no—
133C2×C42—344no—
134C22⋊C8—348no—
135C17#830611yescharacteristic, complemented, Sylow
136C24C22×#59511yescharacteristic
137C22×C4—22no—
138C22×C4—24no—
139C22×C4—28no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—172no—
143C22×C4—174no—
144C22×C4—172no—
145C22×C4—174no—
146C22×C4—344no—
147C22×C4—342no—
148C22×C4—342no—
149C22×C4—342no—
150C22×C4—682no—
151C22×C4—684no—
152C22×C4C22⋊#59514yes—
153C22×C4C22⋊#59512yes—
154C2×C8—684no—
155C2×C8—688no—
156C4⋊C4—28no—
157C4⋊C4—3416no—
158C4⋊C4—3416no—
159C4⋊C4—348no—
160C42—348no—
161C23—22no—
162C23—22no—
163C23#1058767814yes—
164C23C2×C22⋊#59512yes—
165C23C2×C22⋊#59511yescharacteristic
166C2×C4—28no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—28no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—174no—
174C2×C4—344no—
175C2×C4—342no—
176C2×C4—344no—
177C2×C4—344no—
178C2×C4—684no—
179C2×C4—684no—
180C2×C4—684no—
181C2×C4—684no—
182C2×C4—684no—
183C2×C4#1058754514yes—
184C8—1364no—
185C22—28no—
186C22—22no—
187C22—22no—
188C22#1176375011yescharacteristic
189C22#1176378214yes—
190C22#1176378312yes—
191C22#1176379012yes—
192C22C2×#1058754512yes—
193C4—24no—
194C4—44no—
195C4—344no—
196C4—682no—
197C4—684no—
198C2—24no—
199C2#1454405714yes—
200C2#1454460811yescharacteristic
201C2#1454461511yescharacteristic
202C2#1454461811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
cosocleC23×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#8306
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
135. C17#8306semidirect

Maximal subgroups

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

subgroupindex
#145446752
C2×#117636542
C22×#105875762
#830617