Finite Group Databasebeta

← #17949080

Subgroups — #17949080

Order 4352.

374 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 58 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#14527051C211yesmaximal, characteristic
3#11763779—22no—
4#11763654—22no—
5#11763654C414yescomplemented
6C22×C4⋊Dic17C2211yescharacteristic
7C2×#10587502—22no—
8C2×#10587502C411yescharacteristic
9C2×C17×#95C411yescharacteristic
10C23×C4×C17—21no—
11C23×C4×C17C2×C411yescharacteristic
12C23×Dic17—21no—
13C23×Dic17D412yes—
14C2×#63247—42no—
15C2×C4⋊Dic17—41no—
16C2×C4⋊Dic17—41no—
17C2×C4⋊Dic17C2×C412yes—
18C2×C4⋊Dic17D411yescharacteristic
19C2×C4⋊Dic17Q811yescharacteristic
20C22⋊#3624—24no—
21C22⋊#3624—42no—
22C17×#95—41no—
23#10587502—44no—
24#10587502—41no—
25C24×C17C22⋊C411yescharacteristic
26C22×C4×C17—21no—
27C22×C4×C17—21no—
28C22×C4×C17—22no—
29C22×C4×C17—42no—
30C22×C4×C17—42no—
31C22×C4×C17—41no—
32C22×C4×C17—42no—
33C22×C4×C17—41no—
34C22×C4×C17C4211yescharacteristic
35C22×C4×C17C4⋊C411yescharacteristic
36C22×Dic17—22no—
37C22×Dic17—22no—
38C22×Dic17—22no—
39C22×Dic17—42no—
40C22×Dic17—42no—
41C22×Dic17—42no—
42C22×Dic17—41no—
43C22×Dic17—42no—
44C22×Dic17—41no—
45C22×Dic17C22⋊C412yes—
46C22×Dic17C4⋊C412yes—
47#63247—82no—
48#63247—82no—
49C2×#3624—44no—
50C4⋊Dic17—42no—
51C4⋊Dic17—41no—
52C4⋊Dic17—41no—
53#7326—171nomaximal, Sylow
54C23×C17—22no—
55C23×C17—21no—
56C23×C17—21no—
57C23×C17—21no—
58C23×C17—21no—
59C23×C17#9511yescharacteristic
60C23×C17#9911yescharacteristic
61C23×C17#9911yescharacteristic
62C2×C4×C17—21no—
63C2×C4×C17—21no—
64C2×C4×C17—22no—
65C2×C4×C17—22no—
66C2×C4×C17—42no—
67C2×C4×C17—42no—
68C2×C4×C17—44no—
69C2×C4×C17—42no—
70C2×C4×C17—82no—
71C2×C4×C17—81no—
72C2×C4×C17—81no—
73C2×Dic17—22no—
74C2×Dic17—22no—
75C2×Dic17—42no—
76C2×Dic17—42no—
77C2×Dic17—42no—
78C2×Dic17—42no—
79C2×Dic17—44no—
80C2×Dic17—42no—
81C2×Dic17—82no—
82C2×Dic17—82no—
83C2×Dic17—81no—
84C2×Dic17—81no—
85#3624—84no—
86#1463—172no—
87#1445—171no—
88C22×C17—22no—
89C22×C17—22no—
90C22×C17—22no—
91C22×C17—22no—
92C22×C17—21no—
93C22×C17—21no—
94C22×C17—21no—
95C22×C17—21no—
96C22×C17—21no—
97C22×C17—21no—
98C22×C17#34211yescharacteristic
99C22×C17#34412yes—
100C22×C17#35311yescharacteristic
101C22×C17#35411yescharacteristic
102C22×C17#35511yescharacteristic
103C22×C17#35611yescharacteristic
104C4×C17—41no—
105C4×C17—41no—
106C4×C17—82no—
107Dic17—42no—
108Dic17—42no—
109Dic17—82no—
110C22×C4⋊C4—171no—
111#407—342no—
112C2×#95—171no—
113C2×#95—342no—
114C2×#95#59511yescharacteristic
115#324—174no—
116#324—342no—
117C2×C17—21no—
118C2×C17—21no—
119C2×C17—22no—
120C2×C17—21no—
121C2×C17—21no—
122C2×C17#130611yescharacteristic
123C2×C17#139311yescharacteristic
124C2×C17#139411yescharacteristic
125C23×C4—21no—
126C23×C4—172no—
127C23×C4—341no—
128C23×C4C2×#59511yescharacteristic
129C2×M16—682no—
130C2×C4⋊C4—172no—
131C2×C4⋊C4—171no—
132C2×C4⋊C4—171no—
133C2×C4⋊C4—681no—
134C2×C4⋊C4—681no—
135C22⋊C8—344no—
136C22⋊C8—682no—
137#95—41no—
138#95—681no—
139#95—684no—
140C17#732611yescharacteristic, complemented, Sylow
141C24C22⋊#59511yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—22no—
145C22×C4—42no—
146C22×C4—41no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—41no—
150C22×C4—172no—
151C22×C4—172no—
152C22×C4—342no—
153C22×C4—342no—
154C22×C4—342no—
155C22×C4—682no—
156C22×C4—682no—
157C22×C4—682no—
158C22×C4—681no—
159C22×C4—682no—
160C22×C4—681no—
161C22×C4C4×#59511yescharacteristic
162C22×C4C4⋊#59511yescharacteristic
163M16—1362no—
164M16—1362no—
165C2×C8—684no—
166C4⋊C4—682no—
167C4⋊C4—681no—
168C4⋊C4—681no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—22no—
174C23#1058753911yescharacteristic
175C23(C2×#595)⋊C411yescharacteristic
176C23#1058755111yescharacteristic
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—44no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—342no—
189C2×C4—342no—
190C2×C4—682no—
191C2×C4—682no—
192C2×C4—682no—
193C2×C4—682no—
194C2×C4—684no—
195C2×C4—682no—
196C2×C4—1362no—
197C2×C4—1362no—
198C2×C4—1361no—
199C2×C4—1361no—
200C8—1364no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1176368711yescharacteristic
212C22#1176369012yes—
213C22#1176371411yescharacteristic
214C22#1176371611yescharacteristic
215C22#1176371711yescharacteristic
216C22#1176371911yescharacteristic
217C4—41no—
218C4—41no—
219C4—82no—
220C4—682no—
221C4—682no—
222C4—1362no—
223C2—21no—
224C2—21no—
225C2—21no—
226C2—21no—
227C2—22no—
228C2#1454368711yescharacteristic
229C2#1454387811yescharacteristic
230C2#1454388211yescharacteristic
subgroupG/H
centerC22#11763687
commutatorC22×C4×C17C42
FrattiniC23×C4C2×#595
FittingC2×C17×#95C4
socleC22×C17#342
prime radicalC24×C17C22⋊C4
cosocleC22×C4⋊Dic17C22
hypercenterC2×#95#595
hypocenterC17#7326
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
5. #11763654C4semidirect
140. C17#7326semidirect

Maximal subgroups

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

subgroupindex
#145440322
#145270512
#732617