Finite Group Databasebeta

← #17958402

Subgroups — #17958402

Order 4352.

510 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 76 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#14544035C212yesmaximal
2#14543711C214yesmaximal
3#14531368C211yesmaximal, characteristic
4#11763829—22no—
5#11763654—22no—
6#11763652C2214yes—
7C23×Dic34C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762715—22no—
10#11762714—22no—
11#11762670C412yes—
12#11762670C2212yes—
13C2×C17×#117C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×Dic17C2×C412yes—
16C22×Dic34—21no—
17C22×Dic34—21no—
18C22×Dic34—24no—
19C22×Dic34—41no—
20C22×Dic34—41no—
21C22×Dic34—42no—
22C17×#117—42no—
23C2×C4⋊C4×C17—21no—
24C2×C22⋊C4×C17C2×C412yes—
25C2×C42×C17—21no—
26C2×C22⋊Dic17C2×C411yescharacteristic
27C2×C22⋊Dic17C2311yescharacteristic
28#10587612—41no—
29#10587612—41no—
30C2×C4⋊Dic17D412yes—
31C2×C4×Dic17D412yes—
32C22⋊#3624—24no—
33#10587544—42no—
34#10587542—42no—
35#10587502—24no—
36#10587502—24no—
37C24×C17C22×C411yescharacteristic
38C22×C4×C17—22no—
39C22×C4×C17—21no—
40C22×C4×C17—21no—
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17C22⋊C411yescharacteristic
44C22×C4×C17C22⋊C411yescharacteristic
45C22×Dic17—22no—
46C22×Dic17—22no—
47C22×Dic17—42no—
48C22×Dic17—42no—
49C22×Dic17C22⋊C412yes—
50C22×Dic17M1614yes—
51C22×Dic17C2×D412yes—
52C2×Dic34—24no—
53C2×Dic34—24no—
54C2×Dic34—48no—
55C2×Dic34—48no—
56C2×Dic34—42no—
57C2×Dic34—42no—
58C2×Dic34—41no—
59C2×Dic34—41no—
60C2×Dic34—42no—
61C2×#3624—44no—
62C4⋊C4×C17—42no—
63C22⋊C4×C17—42no—
64C42×C17—42no—
65C22⋊Dic17—41no—
66C22⋊Dic17—41no—
67C4⋊Dic17—42no—
68C4×Dic17—22no—
69C4×Dic17—22no—
70#11504—171nomaximal, Sylow
71C23×C17—21no—
72C23×C17—21no—
73C23×C17—42no—
74C23×C17C2×C22⋊C411yescharacteristic
75C23×C17C2×M1612yes—
76C2×C4×C17—24no—
77C2×C4×C17—24no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—44no—
83C2×C4×C17—42no—
84C2×C4×C17#9911yescharacteristic
85C2×C4×C17#9911yescharacteristic
86C2×C4×C17#10012yes—
87C2×Dic17—24no—
88C2×Dic17—22no—
89C2×Dic17—22no—
90C2×Dic17—44no—
91C2×Dic17—42no—
92C2×Dic17—42no—
93C2×Dic17—44no—
94C2×Dic17—42no—
95C2×Dic17—42no—
96Dic34—44no—
97Dic34—44no—
98Dic34—48no—
99#3624—84no—
100#2310—171no—
101#1464—172no—
102#1317—174no—
103C22×C17—22no—
104C22×C17—22no—
105C22×C17—42no—
106C22×C17—42no—
107C22×C17—42no—
108C22×C17#40711yescharacteristic
109C22×C17C2×#9911yescharacteristic
110C22×C17C2×#10011yescharacteristic
111C4×C17—21no—
112C4×C17—21no—
113C4×C17—22no—
114C4×C17—82no—
115Dic17—42no—
116Dic17—42no—
117Dic17—44no—
118C23×Q8—171no—
119C2×#117—171no—
120C2×#117#59511yescharacteristic
121#432—342no—
122#391—342no—
123#391—342no—
124#381—172no—
125#381—172no—
126#324—342no—
127#323—174no—
128C2×C17—21no—
129C2×C17—21no—
130C2×C17—42no—
131C2×C17#146211yescharacteristic
132C2×C17#212312yes—
133C22×Q8—344no—
134C22×Q8—341no—
135C22×Q8—341no—
136C22×Q8—681no—
137C22×Q8—681no—
138C22×Q8—682no—
139C23×C4—172no—
140C23×C4C2×#59511yescharacteristic
141#117—42no—
142#117—681no—
143#117—681no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—172no—
146C2×C22⋊C4—171no—
147C2×C22⋊C4—171no—
148C2×C22⋊C4C2×#59512yes—
149C2×C42—21no—
150C2×C42—172no—
151C4⋊C8—682no—
152C22⋊C8—344no—
153#97—682no—
154#95—344no—
155#95—344no—
156C17#1150411yescharacteristic, complemented, Sylow
157C24C22×#59511yescharacteristic
158C2×Q8—344no—
159C2×Q8—344no—
160C2×Q8—688no—
161C2×Q8—688no—
162C2×Q8—682no—
163C2×Q8—682no—
164C2×Q8—681no—
165C2×Q8—681no—
166C2×Q8—682no—
167C22×C4—22no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—174no—
173C22×C4—172no—
174C22×C4—172no—
175C22×C4—342no—
176C22×C4—342no—
177C22×C4—682no—
178C22×C4—682no—
179C22×C4C22⋊#59511yescharacteristic
180C22×C4C22⋊#59511yescharacteristic
181C2×C8—684no—
182C4⋊C4—42no—
183C4⋊C4—682no—
184C22⋊C4—42no—
185C22⋊C4—681no—
186C22⋊C4—681no—
187C42—42no—
188C42—342no—
189C42—342no—
190C23—21no—
191C23—21no—
192C23—42no—
193C23D17⋊M1612yes—
194C23C2×C22⋊#59511yescharacteristic
195Q8—684no—
196Q8—684no—
197Q8—688no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—44no—
205C2×C4—42no—
206C2×C4—344no—
207C2×C4—342no—
208C2×C4—342no—
209C2×C4—684no—
210C2×C4—682no—
211C2×C4—682no—
212C2×C4—684no—
213C2×C4—682no—
214C2×C4—682no—
215C2×C4#1058753911yescharacteristic
216C2×C4#1058753911yescharacteristic
217C2×C4#1058755312yes—
218C8—1364no—
219C22—22no—
220C22—22no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22#1176378111yescharacteristic
225C22C2×#1058753911yescharacteristic
226C22C2×#1058755311yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—82no—
231C4—682no—
232C4—682no—
233C4—684no—
234C2—21no—
235C2—21no—
236C2—42no—
237C2#1454403111yescharacteristic
238C2#1454504812yes—
subgroupG/H
centerC22C2×#10587539
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
cosocleC2×C22⋊Dic17C23
hypercenterC2×#117#595
hypocenterC17#11504
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
156. C17#11504semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145437112
#145313682
#1150417