Finite Group Databasebeta

← #17949947

Subgroups — #17949947

Order 4352.

490 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 96 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
2#14543603C214yesmaximal, complemented
3#14531266C211yesmaximal, characteristic
4C2×C22⋊#3624—22no—
5#11763675—22no—
6#11763675C2214yes—
7C2×#10587612C411yescharacteristic
8C22×C4×Dic17C2211yescharacteristic
9#11762705C412yes—
10#11762705C2212yes—
11#11762681—22no—
12C4×#63225—22no—
13C2×C17×#117C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×Dic17D412yes—
16C22×#3624—24no—
17C17×#117—42no—
18C2×C4⋊C4×C17C2×C412yes—
19C2×C22⋊C4×C17—21no—
20C2×C42×C17—21no—
21C2×C22⋊Dic17—21no—
22#10587612—24no—
23C2×C4⋊Dic17C2×C412yes—
24C2×#63225—22no—
25C2×#63225—22no—
26C2×C4×Dic17—21no—
27C2×C4×Dic17—42no—
28C2×C4×Dic17C2×C411yescharacteristic
29C2×C4×Dic17D412yes—
30C2×C4×Dic17C2311yescharacteristic
31C22⋊#3624—44no—
32#10587502—22no—
33#10587502—22no—
34C24×C17C22⋊C411yescharacteristic
35C22×C4×C17—22no—
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17C22⋊C411yescharacteristic
40C22×C4×C17C22×C411yescharacteristic
41C22×Dic17—24no—
42C22×Dic17—22no—
43C22×Dic17—24no—
44C22×Dic17—42no—
45C22×Dic17C22⋊C412yes—
46C22×Dic17C2×D412yes—
47C2×#3624—44no—
48C2×#3624—44no—
49C2×#3624—44no—
50C4⋊C4×C17—42no—
51C22⋊C4×C17—42no—
52C42×C17—42no—
53C22⋊Dic17—24no—
54C4⋊Dic17—22no—
55C4⋊Dic17M1614yes—
56#63225—44no—
57#63225—44no—
58C4×Dic17—24no—
59C4×Dic17—41no—
60C4×Dic17—42no—
61C4×Dic17—41no—
62#7646—171nomaximal, Sylow
63C23×C17—21no—
64C23×C17—21no—
65C23×C17—22no—
66C23×C17—22no—
67C23×C17#9912yes—
68C23×C17C2×C22⋊C411yescharacteristic
69C2×C4×C17—28no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17#10112yes—
78C2×C4×C17C2×M1612yes—
79C2×Dic17—22no—
80C2×Dic17—22no—
81C2×Dic17—24no—
82C2×Dic17—22no—
83C2×Dic17—22no—
84C2×Dic17—22no—
85C2×Dic17—48no—
86C2×Dic17—42no—
87C2×Dic17—42no—
88C2×Dic17#13514yes—
89#3624—84no—
90#2296—171no—
91#1817—172no—
92#1271—174no—
93C22×C17—22no—
94C22×C17—24no—
95C22×C17—41no—
96C22×C17—41no—
97C22×C17—42no—
98C22×C17#40711yescharacteristic
99C22×C17C2×#9911yescharacteristic
100C22×C17C2×#10111yescharacteristic
101C22×C17#41612yes—
102C22×C17#42112yes—
103C4×C17—22no—
104C4×C17—22no—
105C4×C17—82no—
106Dic17—24no—
107Dic17—44no—
108Dic17—42no—
109C2×#117—171no—
110C2×#117#59511yescharacteristic
111C22×C42—171no—
112C2×C22⋊C8—342no—
113#389—172no—
114#389—172no—
115#385—342no—
116C4×C4⋊C4—342no—
117#336—174no—
118#336—342no—
119C2×C17—42no—
120C2×C17#146311yescharacteristic
121C2×C17#148812yes—
122C2×C17#151612yes—
123C2×C17#153711yescharacteristic
124C2×C17#154411yescharacteristic
125C23×C4—172no—
126C23×C4C2×#59511yescharacteristic
127C22×C8—344no—
128#117—42no—
129#117—344no—
130C2×C4⋊C4—172no—
131C2×C4⋊C4—342no—
132C2×C4⋊C4—342no—
133C2×C4⋊C4C2×#59512yes—
134C2×C22⋊C4—21no—
135C2×C22⋊C4—341no—
136C2×C42—21no—
137C2×C42—172no—
138C2×C42—171no—
139C2×C42—171no—
140C2×C42—341no—
141C2×C42—682no—
142C22⋊C8—684no—
143#95—342no—
144#95—342no—
145C17#764611yescharacteristic, complemented, Sylow
146C24C22⋊#59511yescharacteristic
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—172no—
152C22×C4—172no—
153C22×C4—344no—
154C22×C4—342no—
155C22×C4—344no—
156C22×C4—682no—
157C22×C4C22⋊#59511yescharacteristic
158C22×C4C22×#59511yescharacteristic
159C2×C8—684no—
160C2×C8—684no—
161C2×C8—684no—
162C4⋊C4—42no—
163C4⋊C4—174no—
164C4⋊C4—342no—
165C4⋊C4—684no—
166C4⋊C4—684no—
167C22⋊C4—42no—
168C22⋊C4—344no—
169C42—42no—
170C42—344no—
171C42—682no—
172C42—681no—
173C42—681no—
174C23—21no—
175C23—21no—
176C23—22no—
177C23—22no—
178C23#1058755112yes—
179C23C2×C22⋊#59511yescharacteristic
180C2×C4—28no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—174no—
189C2×C4—342no—
190C2×C4—342no—
191C2×C4—344no—
192C2×C4—342no—
193C2×C4—342no—
194C2×C4—342no—
195C2×C4—688no—
196C2×C4—682no—
197C2×C4—682no—
198C2×C4#1058754512yes—
199C2×C4D17⋊M1612yes—
200C8—1364no—
201C22—24no—
202C22—22no—
203C22—41no—
204C22—41no—
205C22—42no—
206C22#1176378111yescharacteristic
207C22C2×#1058755111yescharacteristic
208C22C2×#1058754511yescharacteristic
209C22#1176379912yes—
210C22#1176380612yes—
211C4—22no—
212C4—22no—
213C4—82no—
214C4—344no—
215C4—682no—
216C4—684no—
217C2—42no—
218C2#1454403411yescharacteristic
219C2#1454411712yes—
220C2#1454421012yes—
221C2#1454427511yescharacteristic
222C2#1454428911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#117#595
hypocenterC17#7646
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14543603C2semidirect
145. C17#7646semidirect

Maximal subgroups

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

subgroupindex
#145446752
#145436032
#145312662
#764617