Finite Group Databasebeta

← #17958400

Subgroups — #17958400

Order 4352.

510 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 80 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#14543710C214yesmaximal
3#14531370C211yesmaximal, characteristic
4#11763829—22no—
5#11763654—22no—
6#11763652C2214yes—
7C2×#10587612C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762716—22no—
10#11762716—22no—
11#11762672C412yes—
12#11762672C2212yes—
13C23×Q8×C17C411yescharacteristic
14C22×Q8×C17—21no—
15C22×Q8×C17—21no—
16C22×Q8×C17—24no—
17C22×Q8×C17—41no—
18C22×Q8×C17—41no—
19C22×Q8×C17—42no—
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C412yes—
22C2×C22⋊Dic17C2×C412yes—
23C2×C22⋊Dic17C2×C411yescharacteristic
24C2×C22⋊Dic17C2311yescharacteristic
25#10587612—41no—
26#10587612—41no—
27#10587612—42no—
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17D412yes—
30C2×C4×Dic17—21no—
31C2×C4×Dic17D412yes—
32C22⋊#3624—24no—
33#10587544—42no—
34#10587542—42no—
35#10587502—24no—
36#10587502—24no—
37C24×C17C22×C411yescharacteristic
38C2×Q8×C17—24no—
39C2×Q8×C17—24no—
40C2×Q8×C17—48no—
41C2×Q8×C17—48no—
42C2×Q8×C17—42no—
43C2×Q8×C17—42no—
44C2×Q8×C17—41no—
45C2×Q8×C17—41no—
46C2×Q8×C17—42no—
47C22×C4×C17—22no—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17—22no—
51C22×C4×C17—22no—
52C22×C4×C17—22no—
53C22×C4×C17—42no—
54C22×C4×C17—42no—
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17M1614yes—
58C22×Dic17—22no—
59C22×Dic17C22⋊C412yes—
60C22×Dic17C2×D412yes—
61C2×#3624—44no—
62C22⋊Dic17—41no—
63C22⋊Dic17—41no—
64C22⋊Dic17—42no—
65C4⋊Dic17—42no—
66C4⋊Dic17—42no—
67C4×Dic17—22no—
68C4×Dic17—22no—
69C4×Dic17—42no—
70#11504—171nomaximal, Sylow
71C23×C17—21no—
72C23×C17—21no—
73C23×C17—42no—
74C23×C17C2×C22⋊C411yescharacteristic
75C23×C17C2×M1612yes—
76Q8×C17—44no—
77Q8×C17—44no—
78Q8×C17—48no—
79C2×C4×C17—24no—
80C2×C4×C17—24no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—24no—
86C2×C4×C17—44no—
87C2×C4×C17—42no—
88C2×C4×C17—42no—
89C2×C4×C17—44no—
90C2×C4×C17#9911yescharacteristic
91C2×C4×C17#9911yescharacteristic
92C2×C4×C17#10012yes—
93C2×Dic17—22no—
94C2×Dic17—22no—
95C2×Dic17—42no—
96C2×Dic17—42no—
97C2×Dic17—44no—
98C2×Dic17—42no—
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—44no—
115Dic17—42no—
116Dic17—42no—
117Dic17—82no—
118C23×Q8#59511yescharacteristic
119C2×#117—171no—
120C2×#117—171no—
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—24no—
134C22×Q8—21no—
135C22×Q8—21no—
136C22×Q8—41no—
137C22×Q8—41no—
138C22×Q8—42no—
139C23×C4C2×#59512yes—
140C23×C4C2×#59511yescharacteristic
141#117—681no—
142#117—681no—
143#117—682no—
144C2×C4⋊C4—172no—
145C2×C4⋊C4—341no—
146C2×C22⋊C4—171no—
147C2×C22⋊C4—171no—
148C2×C22⋊C4—172no—
149C2×C42—172no—
150C2×C42—341no—
151C4⋊C8—682no—
152C22⋊C8—344no—
153#97—682no—
154#95—344no—
155#95—344no—
156C17#1150411yescharacteristic, complemented, Sylow
157C24C22×#59511yescharacteristic
158C2×Q8—24no—
159C2×Q8—24no—
160C2×Q8—48no—
161C2×Q8—48no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—42no—
167C22×C4—22no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—172no—
176C22×C4—172no—
177C22×C4—342no—
178C22×C4#6324714yes—
179C22×C4C22⋊#59511yescharacteristic
180C22×C4C22⋊#59511yescharacteristic
181C2×C8—684no—
182C4⋊C4—682no—
183C4⋊C4—682no—
184C22⋊C4—681no—
185C22⋊C4—681no—
186C22⋊C4—682no—
187C42—342no—
188C42—342no—
189C42—682no—
190C23—21no—
191C23—21no—
192C23—42no—
193C23C2×#6324712yes—
194C23C2×C22⋊#59511yescharacteristic
195Q8—44no—
196Q8—44no—
197Q8—48no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—24no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—342no—
210C2×C4—342no—
211C2×C4—682no—
212C2×C4—682no—
213C2×C4—684no—
214C2×C4—682no—
215C2×C4#1058755111yescharacteristic
216C2×C4#1058755111yescharacteristic
217C2×C4#1058755312yes—
218C8—1364no—
219C22—22no—
220C22—22no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22#1176377911yescharacteristic
225C22C2×#1058755111yescharacteristic
226C22C2×#1058755311yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—44no—
231C4—682no—
232C4—682no—
233C4—1362no—
234C2—21no—
235C2—21no—
236C2—42no—
237C2#1454402911yescharacteristic
238C2#1454504612yes—
subgroupG/H
centerC22C2×#10587551
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC23×Q8×C17C4
socleC22×C17C2×#99
cosocleC2×C22⋊Dic17C23
hypercenterC23×Q8#595
hypocenterC17#11504
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×Q8

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
#145437102
#145313702
#1150417