Finite Group Databasebeta

← #17958426

Subgroups — #17958426

Order 4352.

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

normal subgroups only

This group has 578 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
1#14544032C212yesmaximal
2#14543726C214yesmaximal, complemented
3C2×#11762679C211yesmaximal, characteristic
4#11763779—22no—
5#11763654—22no—
6#11763654C2214yes—
7C22×C4⋊Dic17—22no—
8C22×C4⋊Dic17C411yescharacteristic
9C22×C4⋊Dic17C2211yescharacteristic
10#11762679—22no—
11#11762679C412yes—
12#11762679C2212yes—
13C22×C42×C17C411yescharacteristic
14C23×C4×C17—21no—
15C23×C4×C17C2×C411yescharacteristic
16C23×Dic17—21no—
17C23×Dic17D412yes—
18C2×#63247—42no—
19C2×C42×C17—21no—
20C2×C42×C17—24no—
21C2×C42×C17C2×C412yes—
22C2×C4⋊Dic17—21no—
23C2×C4⋊Dic17—24no—
24C2×C4⋊Dic17—24no—
25C2×C4⋊Dic17—41no—
26C2×C4⋊Dic17—41no—
27C2×C4⋊Dic17—48no—
28C2×C4⋊Dic17—41no—
29C2×C4⋊Dic17—41no—
30C2×C4⋊Dic17C2×C412yes—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×C4⋊Dic17D412yes—
33C2×C4⋊Dic17C2311yescharacteristic
34C22⋊#3624—24no—
35C22⋊#3624—42no—
36C24×C17C22⋊C411yescharacteristic
37C22×C4×C17—24no—
38C22×C4×C17—24no—
39C22×C4×C17—24no—
40C22×C4×C17—21no—
41C22×C4×C17—21no—
42C22×C4×C17—22no—
43C22×C4×C17—22no—
44C22×C4×C17—22no—
45C22×C4×C17C22⋊C411yescharacteristic
46C22×C4×C17C22×C411yescharacteristic
47C22×Dic17—22no—
48C22×Dic17—22no—
49C22×Dic17—22no—
50C22×Dic17—44no—
51C22×Dic17—44no—
52C22×Dic17—41no—
53C22×Dic17—41no—
54C22×Dic17C22⋊C412yes—
55C22×Dic17C2×D412yes—
56#63247—84no—
57C2×#3624—44no—
58C42×C17—24no—
59C42×C17—22no—
60C42×C17M1614yescomplemented
61C4⋊Dic17—41no—
62C4⋊Dic17—42no—
63C4⋊Dic17—41no—
64C4⋊Dic17—48no—
65C4⋊Dic17—48no—
66C4⋊Dic17—42no—
67C4⋊Dic17—42no—
68#11512—171nomaximal, Sylow
69C23×C17—22no—
70C23×C17—22no—
71C23×C17—21no—
72C23×C17—21no—
73C23×C17#9911yescharacteristic
74C23×C17#9911yescharacteristic
75C23×C17C2×C22⋊C411yescharacteristic
76C2×C4×C17—216no—
77C2×C4×C17—24no—
78C2×C4×C17—24no—
79C2×C4×C17—24no—
80C2×C4×C17—24no—
81C2×C4×C17—21no—
82C2×C4×C17—24no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17#10112yes—
87C2×C4×C17C2×M1612yes—
88C2×Dic17—22no—
89C2×Dic17—22no—
90C2×Dic17—44no—
91C2×Dic17—42no—
92C2×Dic17—42no—
93C2×Dic17—44no—
94C2×Dic17—42no—
95C2×Dic17—82no—
96C2×Dic17—82no—
97C2×Dic17—82no—
98#3624—84no—
99C2×#384—171no—
100#1463—172no—
101#1325—174no—
102C22×C17—24no—
103C22×C17—24no—
104C22×C17—21no—
105C22×C17—21no—
106C22×C17—21no—
107C22×C17—21no—
108C22×C17—21no—
109C22×C17—21no—
110C22×C17#35312yes—
111C22×C17#35612yes—
112C22×C17#40711yescharacteristic
113C22×C17C2×#9911yescharacteristic
114C22×C17C2×#10111yescharacteristic
115C4×C17—28no—
116C4×C17—22no—
117C4×C17—22no—
118Dic17—42no—
119Dic17—42no—
120Dic17—82no—
121C22×C4⋊C4—171no—
122C22×C4⋊C4—171no—
123C22×C4⋊C4—342no—
124C22×C42#59511yescharacteristic
125#407—342no—
126#384—172no—
127#384—172no—
128#384—342no—
129#324—174no—
130#324—342no—
131C2×C17—21no—
132C2×C17—22no—
133C2×C17—22no—
134C2×C17—21no—
135C2×C17#146311yescharacteristic
136C2×C17C2×#35311yescharacteristic
137C2×C17C2×#35611yescharacteristic
138C23×C4—21no—
139C23×C4—172no—
140C23×C4—341no—
141C23×C4C2×#59511yescharacteristic
142C2×M16—682no—
143C2×C4⋊C4—172no—
144C2×C4⋊C4—171no—
145C2×C4⋊C4—171no—
146C2×C4⋊C4—172no—
147C2×C4⋊C4—344no—
148C2×C4⋊C4—344no—
149C2×C4⋊C4—341no—
150C2×C4⋊C4—681no—
151C2×C4⋊C4—681no—
152C2×C4⋊C4—681no—
153C2×C4⋊C4—681no—
154C2×C4⋊C4—688no—
155C2×C42—21no—
156C2×C42—24no—
157C2×C42C2×#59512yes—
158C22⋊C8—344no—
159C22⋊C8—682no—
160C17#1151211yescharacteristic, complemented, Sylow
161C24C22⋊#59511yescharacteristic
162C22×C4—24no—
163C22×C4—24no—
164C22×C4—24no—
165C22×C4—22no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—172no—
171C22×C4—172no—
172C22×C4—342no—
173C22×C4—342no—
174C22×C4—342no—
175C22×C4—684no—
176C22×C4—684no—
177C22×C4—681no—
178C22×C4—681no—
179C22×C4C22⋊#59511yescharacteristic
180C22×C4C22×#59511yescharacteristic
181M16—1364no—
182C2×C8—684no—
183C4⋊C4—682no—
184C4⋊C4—681no—
185C4⋊C4—681no—
186C4⋊C4—682no—
187C4⋊C4—688no—
188C4⋊C4—688no—
189C4⋊C4—682no—
190C42—24no—
191C42—22no—
192C42#6324714yescomplemented
193C23—22no—
194C23—22no—
195C23—21no—
196C23—21no—
197C23#1058753911yescharacteristic
198C23#1058753911yescharacteristic
199C23C2×C22⋊#59511yescharacteristic
200C2×C4—24no—
201C2×C4—216no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—24no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—342no—
211C2×C4—342no—
212C2×C4—684no—
213C2×C4—682no—
214C2×C4—682no—
215C2×C4—684no—
216C2×C4—682no—
217C2×C4—1362no—
218C2×C4—1362no—
219C2×C4—1362no—
220C2×C4#1058754512yes—
221C2×C4C2×#6324712yes—
222C8—1364no—
223C22—24no—
224C22—24no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22#1176371412yes—
232C22#1176372012yes—
233C22#1176377911yescharacteristic
234C22C2×#1058753911yescharacteristic
235C22C2×#1058754511yescharacteristic
236C4—28no—
237C4—22no—
238C4—22no—
239C4—682no—
240C4—682no—
241C4—1362no—
242C2—21no—
243C2—22no—
244C2—22no—
245C2—21no—
246C2#1454403211yescharacteristic
247C2C2×#1176371411yescharacteristic
248C2C2×#1176372011yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC22×C42#595
hypocenterC17#11512
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #14543726C2semidirect
60. C42×C17M16semidirect
160. C17#11512semidirect
192. C42#63247semidirect

Maximal subgroups

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

subgroupindex
#145440322
#145437262
C2×#117626792
#1151217