Finite Group Databasebeta

← #17953642

Subgroups — #17953642

Order 4352.

450 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544035C212yesmaximal
2#14543635C214yesmaximal, complemented
3#14531267C211yesmaximal, characteristic
4#11763829C2214yes—
5#11763654—22no—
6#11763652—22no—
7C2×#10587612C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762707—22no—
10#11762682—22no—
11C4×#63225C412yes—
12C4×#63225C2212yes—
13C22×C42×C17C411yescharacteristic
14C23×C4×C17—21no—
15C23×C4×C17C2×C411yescharacteristic
16C2×C42×C17—21no—
17C2×C42×C17—42no—
18C2×C42×C17C2×C412yes—
19C2×C22⋊Dic17—21no—
20C2×C22⋊Dic17D412yes—
21#10587612—24no—
22#10587612—42no—
23C2×C4⋊Dic17—21no—
24C2×C4⋊Dic17D412yes—
25C2×#63225—22no—
26C2×#63225—22no—
27C2×C4×Dic17C2×C412yes—
28C2×C4×Dic17C2×C411yescharacteristic
29C2×C4×Dic17C2311yescharacteristic
30C22⋊#3624—24no—
31#10587544—24no—
32#10587542—24no—
33#10587502—22no—
34#10587502—22no—
35C24×C17C22⋊C411yescharacteristic
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—44no—
41C22×C4×C17—42no—
42C22×C4×C17C22⋊C411yescharacteristic
43C22×C4×C17C22×C411yescharacteristic
44C22×Dic17—22no—
45C22×Dic17C22⋊C412yes—
46C22×Dic17C2×D412yes—
47C2×#3624—44no—
48C42×C17—42no—
49C42×C17—42no—
50C22⋊Dic17—24no—
51C22⋊Dic17—42no—
52C4⋊Dic17—24no—
53C4⋊Dic17—42no—
54#63225—44no—
55#63225—44no—
56C4×Dic17—22no—
57C4×Dic17—42no—
58C4×Dic17#4114yes—
59#8742—171nomaximal, Sylow
60C23×C17—21no—
61C23×C17—21no—
62C23×C17—42no—
63C23×C17#10012yes—
64C23×C17C2×C22⋊C411yescharacteristic
65C2×C4×C17—28no—
66C2×C4×C17—21no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—24no—
71C2×C4×C17—42no—
72C2×C4×C17—48no—
73C2×C4×C17—42no—
74C2×C4×C17#10112yes—
75C2×C4×C17#11712yes—
76C2×Dic17—22no—
77C2×Dic17—42no—
78C2×Dic17—42no—
79C2×Dic17—42no—
80C2×Dic17—42no—
81C2×Dic17—42no—
82C2×Dic17#12314yes—
83#3624—84no—
84#2296—171no—
85#1464—172no—
86#1285—174no—
87C22×C17—22no—
88C22×C17—22no—
89C22×C17—42no—
90C22×C17—42no—
91C22×C17—42no—
92C22×C17#38111yescharacteristic
93C22×C17C2×#10011yescharacteristic
94C22×C17C2×#10111yescharacteristic
95C4×C17—22no—
96C4×C17—22no—
97C4×C17—44no—
98Dic17—24no—
99Dic17—42no—
100Dic17—82no—
101C2×#117—171no—
102C2×#117—171no—
103C22×C42#59511yescharacteristic
104#432—174no—
105#389—342no—
106#385—342no—
107C4×C4⋊C4—172no—
108C4×C4⋊C4—172no—
109#324—342no—
110#323—342no—
111C2×C17—21no—
112C2×C17—21no—
113C2×C17—42no—
114C2×C17#182111yescharacteristic
115C2×C17#182712yes—
116C23×C4—21no—
117C23×C4C2×#59511yescharacteristic
118#117—344no—
119#117—682no—
120C2×C4⋊C4—172no—
121C2×C4⋊C4—342no—
122C2×C4⋊C4—342no—
123C2×C4⋊C4—341no—
124C2×C22⋊C4—172no—
125C2×C22⋊C4—341no—
126C2×C42—21no—
127C2×C42—42no—
128C2×C42—171no—
129C2×C42—171no—
130C2×C42—172no—
131C2×C42C2×#59512yes—
132C4⋊C8—344no—
133C22⋊C8—344no—
134#97—344no—
135#95—342no—
136#95—342no—
137C17#874211yescharacteristic, complemented, Sylow
138C24C22⋊#59511yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—44no—
144C22×C4—42no—
145C22×C4—172no—
146C22×C4—172no—
147C22×C4—342no—
148C22×C4C22⋊#59511yescharacteristic
149C22×C4C22×#59511yescharacteristic
150C2×C8—684no—
151C4⋊C4—344no—
152C4⋊C4—682no—
153C4⋊C4—684no—
154C4⋊C4—684no—
155C22⋊C4—344no—
156C22⋊C4—682no—
157C42—42no—
158C42—42no—
159C42—174no—
160C42—342no—
161C42—682no—
162C23—21no—
163C23—21no—
164C23—42no—
165C23#1058755312yes—
166C23C2×C22⋊#59511yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—24no—
173C2×C4—42no—
174C2×C4—48no—
175C2×C4—42no—
176C2×C4—174no—
177C2×C4—342no—
178C2×C4—682no—
179C2×C4—682no—
180C2×C4—682no—
181C2×C4—682no—
182C2×C4—682no—
183C2×C4#1058754512yes—
184C2×C4#1058767712yes—
185C8—1364no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22#1176375211yescharacteristic
192C22C2×#1058755311yescharacteristic
193C22C2×#1058754511yescharacteristic
194C4—22no—
195C4—22no—
196C4—44no—
197C4—344no—
198C4—682no—
199C4—1362no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2#1454468311yescharacteristic
204C2#1454469312yes—
subgroupG/H
centerC22#11763752
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC22×C17#381
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC22×C42#595
hypocenterC17#8742
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #14543635C2semidirect
137. C17#8742semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145436352
#145312672
#874217