Finite Group Databasebeta

← #17953597

Subgroups — #17953597

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—48no—
28C4⋊C4×D17—44no—
29C42×D17—24no—
30#10587544—28no—
31#10587543—44no—
32C23×D17C22⋊C411yescharacteristic
33C22×C4×C17—22no—
34C22×C4×C17C22⋊C412yes—
35C22×C4×C17C22×C411yescharacteristic
36C22×Dic17—22no—
37C22×Dic17C22⋊C411yescharacteristic
38C22×Dic17C2×D412yes—
39C2×C4×D17—22no—
40C2×C4×D17—22no—
41C2×C4×D17—22no—
42C2×C4×D17—24no—
43C2×C4×D17—24no—
44C2×C4×D17—48no—
45C2×C4×D17—44no—
46C2×C4×D17SD1614yes—
47C2×C4×D17Q1614yes—
48C2×#3624—44no—
49C2×#3624—44no—
50C2×#3624—44no—
51C4⋊C4×C17—42no—
52C4⋊C4×C17—44no—
53C42×C17—22no—
54C4⋊Dic17—44no—
55C4⋊Dic17—42no—
56#63225—44no—
57#63225—48no—
58C4×Dic17—24no—
59C4×Dic17#4114yes—
60#8725—171nomaximal, Sylow
61C23×C17C2×C22⋊C411yescharacteristic
62C22×D17—21no—
63C22×D17—21no—
64C22×D17—22no—
65C22×D17#10012yes—
66C22×D17#10314yes—
67C2×C4×C17—22no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—22no—
71C2×C4×C17—42no—
72C2×C4×C17—44no—
73C2×C4×C17#10314yes—
74C2×C4×C17#11712yes—
75C2×Dic17—21no—
76C2×Dic17—21no—
77C2×Dic17—42no—
78C2×Dic17—44no—
79C2×Dic17#10112yes—
80C2×Dic17#12314yes—
81C2×Dic17C2×SD1612yes—
82C2×Dic17C2×Q1612yes—
83C2×Dic17AGL(1,ℤ/8)14yes—
84C4×D17—28no—
85C4×D17—28no—
86C4×D17—28no—
87C4×D17—88no—
88#3624—84no—
89C2×#384—171no—
90#1797—172no—
91#1296—174no—
92C22×C17#38111yescharacteristic
93C22×C17C2×#10011yescharacteristic
94C22×C17C2×#10111yescharacteristic
95C22×C17C2×#10312yes—
96C22×C17#41812yes—
97C2×D17—24no—
98C2×D17—22no—
99C2×D17—22no—
100C2×D17—24no—
101C2×D17#33314yes—
102C4×C17—22no—
103C4×C17—24no—
104C4×C17—82no—
105Dic17—22no—
106Dic17—82no—
107Dic17#48114yes—
108Dic17#48414yes—
109C22×C4⋊C4—172no—
110C22×C4⋊C4—342no—
111C22×C42—171no—
112C2×C4⋊C8—174no—
113C2×C22⋊C8—342no—
114#384—172no—
115#384—171no—
116#384—342no—
117#384#59511yescharacteristic
118#336—342no—
119C2×C17C2×#33311yescharacteristic
120C2×C17#154912yes—
121C2×C17#155511yescharacteristic
122C2×C17#182111yescharacteristic
123C2×C17#182412yes—
124D17—24no—
125C23×C4—172no—
126C23×C4—171no—
127C23×C4—342no—
128C22×C8—344no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—172no—
131C2×C4⋊C4—342no—
132C2×C4⋊C4—344no—
133C2×C4⋊C4—342no—
134C2×C4⋊C4—684no—
135C2×C4⋊C4—688no—
136C2×C4⋊C4C2×#59512yes—
137C2×C42—171no—
138C2×C42—172no—
139C2×C42—344no—
140C2×C42C2×#59511yescharacteristic
141C4⋊C8—348no—
142C22⋊C8—684no—
143C17#872511yescharacteristic, complemented, Sylow
144C24—171no—
145C22×C4—22no—
146C22×C4—172no—
147C22×C4—171no—
148C22×C4—174no—
149C22×C4—174no—
150C22×C4—344no—
151C22×C4—344no—
152C22×C4—342no—
153C22×C4—342no—
154C22×C4—342no—
155C22×C4—342no—
156C22×C4—684no—
157C22×C4—688no—
158C22×C4C22⋊#59512yes—
159C22×C4C22×#59511yescharacteristic
160C2×C8—684no—
161C2×C8—684no—
162C2×C8—684no—
163C4⋊C4—42no—
164C4⋊C4—44no—
165C4⋊C4—682no—
166C4⋊C4—684no—
167C4⋊C4—688no—
168C4⋊C4—684no—
169C42—22no—
170C42—174no—
171C42—344no—
172C23—172no—
173C23—174no—
174C23—341no—
175C23—341no—
176C23—342no—
177C23C2×C22⋊#59511yescharacteristic
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—44no—
184C2×C4—174no—
185C2×C4—172no—
186C2×C4—172no—
187C2×C4—174no—
188C2×C4—172no—
189C2×C4—348no—
190C2×C4—348no—
191C2×C4—348no—
192C2×C4—341no—
193C2×C4—341no—
194C2×C4—682no—
195C2×C4—684no—
196C2×C4—1368no—
197C2×C4#1058754914yes—
198C2×C4#1058767712yes—
199C8—1364no—
200C22—174no—
201C22—342no—
202C22—344no—
203C22—344no—
204C22—342no—
205C22#1176375211yescharacteristic
206C22D17⋊#10011yescharacteristic
207C22D17⋊#10111yescharacteristic
208C22C2×#1058754912yes—
209C22#1176380112yes—
210C4—22no—
211C4—24no—
212C4—82no—
213C4—174no—
214C4—174no—
215C4—342no—
216C4—1362no—
217C2—344no—
218C2D17⋊#33311yescharacteristic
219C2#1454430012yes—
220C2#1454431211yescharacteristic
221C2#1454468411yescharacteristic
222C2#1454468812yes—
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#8725
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
143. C17#8725semidirect

Maximal subgroups

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

subgroupindex
#145446412
#145436622
D17×#3842
#872517