Finite Group Databasebeta

← #17953625

Subgroups — #17953625

Order 4352.

498 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C2×#11763652C212yesmaximal
2#14543627C214yesmaximal, complemented
3#14531380C211yesmaximal, characteristic
4C2×C22⋊#3624C2214yes—
5#11763652—22no—
6#11763652—22no—
7C22×C22⋊Dic17C2211yescharacteristic
8#11762703—22no—
9#11762697—22no—
10#11762667C412yes—
11#11762665C411yescharacteristic
12C22⋊C4×Dic17C2212yes—
13C17×#379C411yescharacteristic
14C25×C17C2×C411yescharacteristic
15C23×Dic17C2×C411yescharacteristic
16C23×Dic17C2311yescharacteristic
17C22×#3624—24no—
18C2×C22⋊C4×C17—21no—
19C2×C22⋊C4×C17—21no—
20C2×C22⋊C4×C17C2×C412yes—
21C2×C22⋊Dic17—24no—
22C2×C22⋊Dic17—21no—
23C2×C22⋊Dic17—21no—
24C2×C22⋊Dic17C2×C412yes—
25C2×C22⋊Dic17D412yes—
26C2×C22⋊Dic17D412yes—
27C2×#63225—22no—
28C2×C4×Dic17—22no—
29C22⋊#3624—24no—
30C22⋊#3624—24no—
31#10587502—22no—
32#10587502—22no—
33C24×C17—22no—
34C24×C17—24no—
35C24×C17—81no—
36C24×C17—81no—
37C24×C17C22⋊C411yescharacteristic
38C24×C17C22⋊C411yescharacteristic
39C24×C17C22×C411yescharacteristic
40C22×C4×C17—22no—
41C22×Dic17—22no—
42C22×Dic17—22no—
43C22×Dic17—81no—
44C22×Dic17—81no—
45C22×Dic17C22⋊C412yes—
46C22×Dic17C2×D412yes—
47C22×Dic17#4114yes—
48C2×#3624—44no—
49C2×#3624—84no—
50C22⋊C4×C17—24no—
51C22⋊C4×C17—81no—
52C22⋊C4×C17—81no—
53C22⋊Dic17—24no—
54C22⋊Dic17—24no—
55C22⋊Dic17—24no—
56C22⋊Dic17—81no—
57C22⋊Dic17—81no—
58#63225—82no—
59C4×Dic17—82no—
60#8736—171nomaximal, Sylow
61C23×C17—21no—
62C23×C17—21no—
63C23×C17—22no—
64C23×C17—22no—
65C23×C17—41no—
66C23×C17—41no—
67C23×C17—41no—
68C23×C17—41no—
69C23×C17—41no—
70C23×C17—41no—
71C23×C17—44no—
72C23×C17—82no—
73C23×C17—82no—
74C23×C17—88no—
75C23×C17C2×C22⋊C411yescharacteristic
76C23×C17#11712yes—
77C23×C17#13114yes—
78C2×C4×C17—42no—
79C2×C4×C17—42no—
80C2×C4×C17—42no—
81C2×Dic17—22no—
82C2×Dic17—44no—
83C2×Dic17—42no—
84C2×Dic17—42no—
85C2×Dic17—42no—
86C2×Dic17—42no—
87C2×Dic17—42no—
88C2×Dic17—82no—
89C2×Dic17#12314yes—
90#3624—84no—
91#2312—171no—
92C2×#323—172no—
93#1282—174no—
94C22×C17—21no—
95C22×C17—22no—
96C22×C17—21no—
97C22×C17—22no—
98C22×C17—44no—
99C22×C17—41no—
100C22×C17—41no—
101C22×C17—41no—
102C22×C17—41no—
103C22×C17—41no—
104C22×C17—41no—
105C22×C17—82no—
106C22×C17—82no—
107C22×C17—88no—
108C22×C17#38111yescharacteristic
109C22×C17#40812yes—
110C22×C17#43314yes—
111C4×C17—82no—
112Dic17—24no—
113Dic17—42no—
114Dic17—82no—
115C22×C22⋊C4—171no—
116C2×C22⋊C8—174no—
117#388—342no—
118#388—342no—
119#380—172no—
120#379—171no—
121#379#59511yescharacteristic
122C4×C22⋊C4—172no—
123#323—342no—
124#323—342no—
125C2×C17—22no—
126C2×C17—24no—
127C2×C17—81no—
128C2×C17—81no—
129C2×C17#181811yescharacteristic
130C2×C17#182811yescharacteristic
131C2×C17#182911yescharacteristic
132C25C2×#59511yescharacteristic
133C23×C4—171no—
134C23×C4—171no—
135C22×C8—344no—
136C2×C4⋊C4—342no—
137C2×C22⋊C4—21no—
138C2×C22⋊C4—21no—
139C2×C22⋊C4—172no—
140C2×C22⋊C4—172no—
141C2×C22⋊C4—172no—
142C2×C22⋊C4—344no—
143C2×C22⋊C4—341no—
144C2×C22⋊C4—341no—
145C2×C22⋊C4C2×#59512yes—
146C2×C42—342no—
147C22⋊C8—344no—
148C22⋊C8—344no—
149#95—342no—
150#95—342no—
151C17#873611yescharacteristic, complemented, Sylow
152C24—22no—
153C24—24no—
154C24—81no—
155C24—81no—
156C24C22⋊#59511yescharacteristic
157C24C22⋊#59511yescharacteristic
158C24C22×#59511yescharacteristic
159C22×C4—22no—
160C22×C4—174no—
161C22×C4—172no—
162C22×C4—172no—
163C22×C4—342no—
164C22×C4—342no—
165C22×C4—1361no—
166C22×C4—1361no—
167C2×C8—684no—
168C2×C8—1364no—
169C4⋊C4—1362no—
170C22⋊C4—24no—
171C22⋊C4—81no—
172C22⋊C4—81no—
173C22⋊C4—344no—
174C22⋊C4—344no—
175C22⋊C4—344no—
176C22⋊C4—1361no—
177C22⋊C4—1361no—
178C42—1362no—
179C23—21no—
180C23—21no—
181C23—22no—
182C23—22no—
183C23—41no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23—44no—
190C23—82no—
191C23—82no—
192C23—88no—
193C23#1058767712yes—
194C23#1058767814yes—
195C23C2×C22⋊#59511yescharacteristic
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—174no—
200C2×C4—342no—
201C2×C4—682no—
202C2×C4—684no—
203C2×C4—682no—
204C2×C4—682no—
205C2×C4—682no—
206C2×C4—682no—
207C2×C4—1362no—
208C8—1364no—
209C22—21no—
210C22—22no—
211C22—21no—
212C22—22no—
213C22—44no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—82no—
221C22—82no—
222C22—88no—
223C22#1176375211yescharacteristic
224C22#1176378212yes—
225C22#1176383314yes—
226C4—82no—
227C4—344no—
228C4—682no—
229C4—1362no—
230C2—22no—
231C2—24no—
232C2—81no—
233C2—81no—
234C2#1454467711yescharacteristic
235C2#1454469511yescharacteristic
236C2#1454469711yescharacteristic
subgroupG/H
centerC22#11763752
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC17×#379C4
socleC22×C17#381
prime radicalC25×C17C2×C4
cosocleC23×Dic17C23
hypercenter#379#595
hypocenterC17#8736
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #14543627C2semidirect
151. C17#8736semidirect

Maximal subgroups

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

subgroupindex
C2×#117636522
#145436272
#145313802
#873617