Finite Group Databasebeta

← #17953604

Subgroups — #17953604

Order 4352.

514 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 112 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#14544640C212yesmaximal
2#14543662C214yesmaximal, complemented
3#14531187C211yesmaximal, characteristic
4C2×#10587544C2214yes—
5C2×C22⋊#3624—22no—
6#11763675—22no—
7C2×#10587612C411yescharacteristic
8C22×C4×Dic17C2211yescharacteristic
9#11762678C2212yes—
10#11762674C412yes—
11#11762667—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—42no—
23C2×C4⋊Dic17C2×C412yes—
24C2×#63225—22no—
25C2×#63225—22no—
26C2×C4×Dic17—24no—
27C2×C4×Dic17—21no—
28C2×C4×Dic17C2×C411yescharacteristic
29C2×C4×Dic17D412yes—
30C2×C4×Dic17C2311yescharacteristic
31C22⋊#3624—44no—
32#10587544—28no—
33#10587502—24no—
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—24no—
43C22×Dic17—22no—
44C22×Dic17—22no—
45C22×Dic17—22no—
46C22×Dic17C22⋊C412yes—
47C22×Dic17C2×D412yes—
48C2×#3624—44no—
49C2×#3624—44no—
50C2×#3624—44no—
51C4⋊C4×C17—42no—
52C22⋊C4×C17—42no—
53C42×C17—42no—
54C22⋊Dic17—42no—
55C4⋊Dic17—42no—
56#63225—44no—
57#63225—42no—
58#63225—42no—
59C4×Dic17—22no—
60C4×Dic17—24no—
61C4×Dic17—42no—
62C4×Dic17#4114yes—
63#8729—171nomaximal, Sylow
64C23×C17—21no—
65C23×C17—21no—
66C23×C17—22no—
67C23×C17—22no—
68C23×C17#10012yes—
69C23×C17C2×C22⋊C411yescharacteristic
70C2×C4×C17—28no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17—42no—
78C2×C4×C17#10112yes—
79C2×C4×C17#11712yes—
80C2×Dic17—22no—
81C2×Dic17—22no—
82C2×Dic17—22no—
83C2×Dic17—44no—
84C2×Dic17—44no—
85C2×Dic17—42no—
86C2×Dic17—42no—
87C2×Dic17—42no—
88C2×Dic17#12314yes—
89C2×Dic17#13514yes—
90C2×Dic17AGL(1,ℤ/8)12yes—
91C2×Dic17#13712yes—
92#3624—84no—
93#2285—171no—
94#1797—172no—
95#1296—174no—
96C22×C17—24no—
97C22×C17—22no—
98C22×C17—41no—
99C22×C17—41no—
100C22×C17—42no—
101C22×C17#38111yescharacteristic
102C22×C17C2×#10011yescharacteristic
103C22×C17C2×#10111yescharacteristic
104C22×C17#41612yes—
105C22×C17#41712yes—
106C4×C17—22no—
107C4×C17—22no—
108C4×C17—82no—
109Dic17—42no—
110Dic17—82no—
111Dic17#48214yes—
112Dic17#48514yes—
113C2×#117—171no—
114C2×#117#59511yescharacteristic
115C22×C42—171no—
116C2×C4⋊C8—174no—
117C2×C22⋊C8—342no—
118#384—172no—
119#382—172no—
120#380—342no—
121C4×C4⋊C4—342no—
122#336—342no—
123C2×C17—42no—
124C2×C17#154411yescharacteristic
125C2×C17#155112yes—
126C2×C17#156111yescharacteristic
127C2×C17#182111yescharacteristic
128C2×C17#182512yes—
129C23×C4—172no—
130C23×C4C2×#59511yescharacteristic
131C22×C8—344no—
132#117—42no—
133#117—682no—
134C2×C4⋊C4—172no—
135C2×C4⋊C4—342no—
136C2×C4⋊C4—342no—
137C2×C4⋊C4C2×#59512yes—
138C2×C22⋊C4—21no—
139C2×C22⋊C4—341no—
140C2×C42—21no—
141C2×C42—171no—
142C2×C42—172no—
143C2×C42—171no—
144C2×C42—344no—
145C2×C42—341no—
146C4⋊C8—348no—
147C22⋊C8—684no—
148#95—344no—
149C17#872911yescharacteristic, complemented, Sylow
150C24C22⋊#59511yescharacteristic
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—172no—
156C22×C4—172no—
157C22×C4—342no—
158C22×C4—344no—
159C22×C4—344no—
160C22×C4—342no—
161C22×C4—342no—
162C22×C4C22⋊#59511yescharacteristic
163C22×C4C22×#59511yescharacteristic
164C2×C8—684no—
165C2×C8—684no—
166C2×C8—684no—
167C4⋊C4—42no—
168C4⋊C4—682no—
169C4⋊C4—684no—
170C4⋊C4—682no—
171C4⋊C4—682no—
172C22⋊C4—42no—
173C22⋊C4—682no—
174C42—42no—
175C42—174no—
176C42—344no—
177C42—342no—
178C42—682no—
179C23—21no—
180C23—21no—
181C23—22no—
182C23—22no—
183C23#1058755312yes—
184C23C2×C22⋊#59511yescharacteristic
185C2×C4—28no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—174no—
194C2×C4—174no—
195C2×C4—172no—
196C2×C4—172no—
197C2×C4—342no—
198C2×C4—342no—
199C2×C4—342no—
200C2×C4—684no—
201C2×C4—684no—
202C2×C4—682no—
203C2×C4—682no—
204C2×C4—682no—
205C2×C4#1058754512yes—
206C2×C4#1058767712yes—
207C8—1364no—
208C22—22no—
209C22—24no—
210C22—42no—
211C22—41no—
212C22—41no—
213C22#1176375211yescharacteristic
214C22C2×#1058755311yescharacteristic
215C22C2×#1058754511yescharacteristic
216C22#1176379912yes—
217C22#1176380012yes—
218C4—22no—
219C4—22no—
220C4—82no—
221C4—174no—
222C4—174no—
223C4—682no—
224C4—1362no—
225C2—42no—
226C2#1454428911yescharacteristic
227C2#1454430312yes—
228C2#1454432311yescharacteristic
229C2#1454468311yescharacteristic
230C2#1454468912yes—
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#8729
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. #14543662C2semidirect
149. C17#8729semidirect

Maximal subgroups

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

subgroupindex
#145446402
#145436622
#145311872
#872917