Finite Group Databasebeta

← #17953605

Subgroups — #17953605

Order 4352.

514 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 108 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
3#14531190C211yesmaximal, characteristic
4C2×#10587544C2214yes—
5C2×#10587543—22no—
6#11763675—22no—
7C2×#10587578C412yes—
8C2×C42×D17C2211yescharacteristic
9#11762678C2212yes—
10#11762675C411yescharacteristic
11#11762668—22no—
12#11762660—22no—
13C17×#382C411yescharacteristic
14C22×C4×D17C2×C411yescharacteristic
15C22×C4×D17D412yes—
16C22×#3624—24no—
17C2×C4⋊C4×C17C2×C412yes—
18C2×C42×C17C2×C411yescharacteristic
19C2×#63227—22no—
20C2×C4⋊Dic17C2×C412yes—
21C2×#63225—22no—
22C2×#63225—22no—
23C2×C4×Dic17—22no—
24C2×C4×Dic17D412yes—
25C2×C4×Dic17C2311yescharacteristic
26#10587578—44no—
27C42×D17—24no—
28#10587544—28no—
29#10587543—44no—
30C17×#95—22no—
31#10587502—22no—
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—22no—
45C2×C4×D17—22no—
46C2×#3624—44no—
47C2×#3624—44no—
48C2×#3624—44no—
49C4⋊C4×C17—42no—
50C42×C17—22no—
51#63227—44no—
52C4⋊Dic17—42no—
53#63225—44no—
54#63225—42no—
55#63225—42no—
56C4×Dic17—24no—
57C4×Dic17—44no—
58C4×Dic17#4114yes—
59#8729—171nomaximal, Sylow
60C23×C17C2×C22⋊C411yescharacteristic
61C22×D17—21no—
62C22×D17—21no—
63C22×D17—22no—
64C22×D17—22no—
65C22×D17#10012yes—
66C2×C4×C17—21no—
67C2×C4×C17—21no—
68C2×C4×C17—22no—
69C2×C4×C17—22no—
70C2×C4×C17—22no—
71C2×C4×C17—42no—
72C2×C4×C17—42no—
73C2×C4×C17—42no—
74C2×C4×C17#11712yes—
75C2×Dic17—21no—
76C2×Dic17—21no—
77C2×Dic17—42no—
78C2×Dic17—42no—
79C2×Dic17—42no—
80C2×Dic17#10112yes—
81C2×Dic17#12314yes—
82C2×Dic17#13514yes—
83C2×Dic17AGL(1,ℤ/8)12yes—
84C2×Dic17#13712yes—
85C4×D17—28no—
86C4×D17—44no—
87C4×D17—44no—
88#3624—84no—
89#2285—171no—
90#1797—172no—
91#1296—174no—
92C22×C17#38111yescharacteristic
93C22×C17C2×#10011yescharacteristic
94C22×C17C2×#10111yescharacteristic
95C22×C17#41612yes—
96C22×C17#41712yes—
97C2×D17—24no—
98C2×D17—22no—
99C2×D17—41no—
100C2×D17—41no—
101C2×D17—42no—
102C4×C17—22no—
103C4×C17—42no—
104C4×C17—82no—
105Dic17—22no—
106Dic17—82no—
107Dic17#48214yes—
108Dic17#48514yes—
109C2×#117—172no—
110C22×C42—171no—
111C2×C4⋊C8—174no—
112C2×C22⋊C8—342no—
113#384—172no—
114#382—171no—
115#382#59511yescharacteristic
116#380—342no—
117C4×C4⋊C4—342no—
118#336—342no—
119C2×C17#154411yescharacteristic
120C2×C17#155112yes—
121C2×C17#156111yescharacteristic
122C2×C17#182111yescharacteristic
123C2×C17#182512yes—
124D17—42no—
125C23×C4—172no—
126C23×C4—171no—
127C22×C8—344no—
128#117—684no—
129C2×C4⋊C4—172no—
130C2×C4⋊C4—342no—
131C2×C4⋊C4—342no—
132C2×C4⋊C4C2×#59512yes—
133C2×C22⋊C4—342no—
134C2×C42—171no—
135C2×C42—172no—
136C2×C42—344no—
137C2×C42—342no—
138C2×C42C2×#59511yescharacteristic
139C4⋊C8—348no—
140C22⋊C8—684no—
141#95—22no—
142#95—342no—
143C17#872911yescharacteristic, complemented, Sylow
144C24—171no—
145C22×C4—22no—
146C22×C4—172no—
147C22×C4—171no—
148C22×C4—342no—
149C22×C4—342no—
150C22×C4—344no—
151C22×C4—344no—
152C22×C4—342no—
153C22×C4—342no—
154C22×C4—342no—
155C22×C4—342no—
156C22×C4C22⋊#59512yes—
157C22×C4C22×#59511yescharacteristic
158C2×C8—684no—
159C2×C8—684no—
160C2×C8—684no—
161C4⋊C4—42no—
162C4⋊C4—682no—
163C4⋊C4—684no—
164C4⋊C4—682no—
165C4⋊C4—682no—
166C22⋊C4—684no—
167C42—22no—
168C42—174no—
169C42—344no—
170C42—684no—
171C23—172no—
172C23—341no—
173C23—341no—
174C23—342no—
175C23—342no—
176C23C2×C22⋊#59511yescharacteristic
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—174no—
186C2×C4—174no—
187C2×C4—172no—
188C2×C4—172no—
189C2×C4—172no—
190C2×C4—348no—
191C2×C4—341no—
192C2×C4—341no—
193C2×C4—684no—
194C2×C4—684no—
195C2×C4—682no—
196C2×C4—682no—
197C2×C4—682no—
198C2×C4#1058767712yes—
199C8—1364no—
200C22—342no—
201C22—344no—
202C22—682no—
203C22—681no—
204C22—681no—
205C22#1176375211yescharacteristic
206C22D17⋊#10011yescharacteristic
207C22D17⋊#10111yescharacteristic
208C22#1176379912yes—
209C22#1176380012yes—
210C4—22no—
211C4—42no—
212C4—82no—
213C4—174no—
214C4—174no—
215C4—342no—
216C4—1362no—
217C2—682no—
218C2#1454429011yescharacteristic
219C2#1454430412yes—
220C2#1454432411yescharacteristic
221C2#1454468411yescharacteristic
222C2#1454468912yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#382#595
hypocenterC17#8729
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #14543662C2semidirect
143. C17#8729semidirect

Maximal subgroups

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

subgroupindex
#145446412
#145436622
#145311902
#872917