Finite Group Databasebeta

← #17953593

Subgroups — #17953593

Order 4352.

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

normal subgroups only

This group has 630 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#14544641C212yesmaximal
2#14543662C214yesmaximal, complemented
3D17×#384C211yesmaximal, characteristic
4C2×#10587544C2214yes—
5C2×#10587543—22no—
6#11763675—22no—
7C2×C4⋊C4×D17—22no—
8C2×C4⋊C4×D17C412yes—
9C2×C42×D17C2211yescharacteristic
10#11762679C411yescharacteristic
11#11762678—22no—
12#11762678C2212yes—
13C17×#384C411yescharacteristic
14C22×C4×D17—22no—
15C22×C4×D17C2×C411yescharacteristic
16C22×C4×D17D412yes—
17C22×#3624—24no—
18C2×C4⋊C4×C17—22no—
19C2×C4⋊C4×C17C2×C412yes—
20C2×C42×C17C2×C411yescharacteristic
21C2×C4⋊Dic17—22no—
22C2×C4⋊Dic17C2×C412yes—
23C2×#63225—22no—
24C2×#63225—24no—
25C2×C4×Dic17D412yes—
26C2×C4×Dic17C2311yescharacteristic
27C4⋊C4×D17—44no—
28C4⋊C4×D17—44no—
29C4⋊C4×D17—44no—
30C42×D17—24no—
31#10587544—28no—
32#10587543—44no—
33C23×D17C22⋊C411yescharacteristic
34C22×C4×C17—22no—
35C22×C4×C17C22⋊C412yes—
36C22×C4×C17C22×C411yescharacteristic
37C22×Dic17—22no—
38C22×Dic17C22⋊C411yescharacteristic
39C22×Dic17C2×D412yes—
40C2×C4×D17—22no—
41C2×C4×D17—22no—
42C2×C4×D17—22no—
43C2×C4×D17—24no—
44C2×C4×D17—24no—
45C2×C4×D17—44no—
46C2×C4×D17—48no—
47C2×C4×D17D814yes—
48C2×C4×D17SD1614yes—
49C2×#3624—44no—
50C2×#3624—44no—
51C2×#3624—44no—
52C4⋊C4×C17—42no—
53C4⋊C4×C17—44no—
54C42×C17—22no—
55C4⋊Dic17—44no—
56C4⋊Dic17—42no—
57#63225—44no—
58#63225—44no—
59#63225—44no—
60C4×Dic17—24no—
61C4×Dic17#4114yes—
62#8723—171nomaximal, Sylow
63C23×C17C2×C22⋊C411yescharacteristic
64C22×D17—21no—
65C22×D17—21no—
66C22×D17—22no—
67C22×D17#10012yes—
68C22×D17#10214yes—
69C2×C4×C17—22no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—22no—
73C2×C4×C17—42no—
74C2×C4×C17—44no—
75C2×C4×C17#10214yes—
76C2×C4×C17#11712yes—
77C2×Dic17—21no—
78C2×Dic17—21no—
79C2×Dic17—42no—
80C2×Dic17—44no—
81C2×Dic17#10112yes—
82C2×Dic17#12314yes—
83C2×Dic17C2×D812yes—
84C2×Dic17C2×SD1612yes—
85C2×Dic17#13714yes—
86C4×D17—28no—
87C4×D17—28no—
88C4×D17—28no—
89C4×D17—88no—
90#3624—84no—
91C2×#384—171no—
92#1797—172no—
93#1296—174no—
94C22×C17#38111yescharacteristic
95C22×C17C2×#10011yescharacteristic
96C22×C17C2×#10111yescharacteristic
97C22×C17C2×#10212yes—
98C22×C17#41912yes—
99C2×D17—24no—
100C2×D17—22no—
101C2×D17—22no—
102C2×D17—24no—
103C2×D17#33114yes—
104C4×C17—22no—
105C4×C17—24no—
106C4×C17—82no—
107Dic17—22no—
108Dic17—82no—
109Dic17#48014yes—
110Dic17#48314yes—
111C22×C4⋊C4—172no—
112C22×C4⋊C4—342no—
113C22×C42—171no—
114C2×C4⋊C8—174no—
115C2×C22⋊C8—342no—
116#384—172no—
117#384—171no—
118#384—342no—
119#384#59511yescharacteristic
120#336—342no—
121C2×C17C2×#33111yescharacteristic
122C2×C17#154612yes—
123C2×C17#155811yescharacteristic
124C2×C17#182111yescharacteristic
125C2×C17#182312yes—
126D17—24no—
127C23×C4—172no—
128C23×C4—171no—
129C23×C4—342no—
130C22×C8—344no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—172no—
133C2×C4⋊C4—342no—
134C2×C4⋊C4—344no—
135C2×C4⋊C4—342no—
136C2×C4⋊C4—684no—
137C2×C4⋊C4—684no—
138C2×C4⋊C4—684no—
139C2×C4⋊C4C2×#59512yes—
140C2×C42—171no—
141C2×C42—172no—
142C2×C42—344no—
143C2×C42C2×#59511yescharacteristic
144C4⋊C8—348no—
145C22⋊C8—684no—
146C17#872311yescharacteristic, complemented, Sylow
147C24—171no—
148C22×C4—22no—
149C22×C4—172no—
150C22×C4—171no—
151C22×C4—174no—
152C22×C4—174no—
153C22×C4—344no—
154C22×C4—342no—
155C22×C4—344no—
156C22×C4—342no—
157C22×C4—342no—
158C22×C4—342no—
159C22×C4—688no—
160C22×C4—684no—
161C22×C4C22⋊#59512yes—
162C22×C4C22×#59511yescharacteristic
163C2×C8—684no—
164C2×C8—684no—
165C2×C8—684no—
166C4⋊C4—42no—
167C4⋊C4—44no—
168C4⋊C4—682no—
169C4⋊C4—684no—
170C4⋊C4—684no—
171C4⋊C4—684no—
172C4⋊C4—684no—
173C42—22no—
174C42—174no—
175C42—344no—
176C23—172no—
177C23—174no—
178C23—341no—
179C23—341no—
180C23—342no—
181C23C2×C22⋊#59511yescharacteristic
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—174no—
189C2×C4—172no—
190C2×C4—172no—
191C2×C4—174no—
192C2×C4—172no—
193C2×C4—348no—
194C2×C4—348no—
195C2×C4—348no—
196C2×C4—341no—
197C2×C4—341no—
198C2×C4—682no—
199C2×C4—684no—
200C2×C4—1368no—
201C2×C4#1058754714yes—
202C2×C4#1058767712yes—
203C8—1364no—
204C22—174no—
205C22—342no—
206C22—344no—
207C22—344no—
208C22—342no—
209C22#1176375211yescharacteristic
210C22D17⋊#10011yescharacteristic
211C22D17⋊#10111yescharacteristic
212C22C2×#1058754712yes—
213C22#1176380212yes—
214C4—22no—
215C4—24no—
216C4—82no—
217C4—174no—
218C4—174no—
219C4—342no—
220C4—1362no—
221C2—344no—
222C2D17⋊#33111yescharacteristic
223C2#1454429412yes—
224C2#1454431811yescharacteristic
225C2#1454468411yescharacteristic
226C2#1454468712yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#384C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#384#595
hypocenterC17#8723
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #14543662C2semidirect
146. C17#8723semidirect

Maximal subgroups

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

subgroupindex
#145446412
#145436622
D17×#3842
#872317