Finite Group Databasebeta

← #17961570

Subgroups — #17961570

Order 4352.

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

normal subgroups only

This group has 642 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#14544620C212yesmaximal
2#14543882C214yesmaximal, complemented
3#14531272C211yesmaximal, characteristic
4C2×#10587545C2214yes—
5C2×#10587553—22no—
6#11763781—22no—
7C22×#63252C2211yescharacteristic
8C22×C4×Dic17C411yescharacteristic
9#11762714C2212yes—
10#11762710C412yes—
11#11762686—22no—
12C4×#63227—22no—
13C2×C17×#117C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C22×C22⋊D17D412yes—
16C23×Dic17—21no—
17C2×#63252—24no—
18C2×#63252—42no—
19C2×#63252—42no—
20C22×D68C2×C411yescharacteristic
21C22×C4×D17D412yes—
22C22×Dic34C2311yescharacteristic
23C2×#63247—24no—
24C17×#117—42no—
25C2×C4⋊C4×C17C2×C412yes—
26C2×C22⋊C4×C17—21no—
27C2×C42×C17—21no—
28C2×#63227—24no—
29C2×C4×Dic17—21no—
30C2×C4×Dic17—42no—
31C2×C4×Dic17C2×C412yes—
32#10587553—44no—
33#10587545—28no—
34#10587543—44no—
35#10587502—24no—
36C24×C17C22⋊C411yescharacteristic
37C23×D17C22⋊C412yes—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—22no—
41C22×C4×C17—22no—
42C22×C4×C17C22⋊C411yescharacteristic
43C22×C4×C17C22×C411yescharacteristic
44C2×C22⋊D17—24no—
45C2×C22⋊D17—24no—
46C2×C22⋊D17—42no—
47C22×Dic17—22no—
48C22×Dic17—44no—
49C22×Dic17—42no—
50C22×Dic17C2×D412yes—
51#63252—416no—
52C2×D68—22no—
53C2×D68—41no—
54C2×D68—41no—
55C2×C4×D17—24no—
56C2×C4×D17—24no—
57C2×C4×D17—42no—
58C2×Dic34—41no—
59C2×Dic34—41no—
60C2×Dic34#4114yes—
61#63247—44no—
62#63247—44no—
63C2×#3624—44no—
64C4⋊C4×C17—42no—
65C22⋊C4×C17—42no—
66C42×C17—42no—
67#63227—48no—
68C4×Dic17—42no—
69C4×Dic17—42no—
70#12861—171nomaximal, Sylow
71C23×C17—21no—
72C23×C17—21no—
73C23×C17—42no—
74C23×C17#9912yes—
75C23×C17C2×C22⋊C411yescharacteristic
76C22×D17—22no—
77C22×D17—22no—
78C22×D17—22no—
79C22×D17—44no—
80C2×C4×C17—28no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—44no—
86C2×C4×C17—42no—
87C2×C4×C17#9912yes—
88C2×C4×C17#11712yes—
89C22⋊D17—48no—
90C2×Dic17—22no—
91C2×Dic17—22no—
92C2×Dic17—24no—
93C2×Dic17—42no—
94C2×Dic17—48no—
95C2×Dic17—42no—
96C2×Dic17#12314yes—
97D68—44no—
98C4×D17—48no—
99Dic34—44no—
100#3624—84no—
101#2297—171no—
102#1785—172no—
103#1394—174no—
104C22×C17—22no—
105C22×C17—22no—
106C22×C17—42no—
107C22×C17—42no—
108C22×C17—42no—
109C22×C17#38111yescharacteristic
110C22×C17C2×#9911yescharacteristic
111C22×C17C2×#9911yescharacteristic
112C2×D17—44no—
113C2×D17—42no—
114C2×D17—44no—
115C2×D17—82no—
116C4×C17—22no—
117C4×C17—22no—
118C4×C17—82no—
119Dic17—24no—
120Dic17—44no—
121C22×#41—171no—
122C2×#117#59511yescharacteristic
123C22×C42—171no—
124C2×#101—174no—
125C2×#100—342no—
126#407—342no—
127#391—172no—
128#390—172no—
129#386—342no—
130C4×C22⋊C4—342no—
131C2×C17—21no—
132C2×C17—21no—
133C2×C17—42no—
134C2×C17#181911yescharacteristic
135C2×C17#213212yes—
136D17—82no—
137C2×#41—344no—
138C2×#41—682no—
139C2×#41—682no—
140C22×Q8—171no—
141C22×D4—172no—
142C22×D4—171no—
143C23×C4—172no—
144C23×C4—341no—
145C23×C4C2×#59511yescharacteristic
146C2×M16—344no—
147#117—42no—
148C2×C4⋊C4C2×#59512yes—
149C2×C22⋊C4—21no—
150C2×C22⋊C4—344no—
151C2×C42—21no—
152C2×C42—172no—
153C2×C42—341no—
154C2×C42—682no—
155#101—348no—
156#100—684no—
157C22⋊C8—684no—
158#95—344no—
159C17#1286111yescharacteristic, complemented, Sylow
160C24—172no—
161C24C22⋊#59511yescharacteristic
162#41—6816no—
163C2×Q8—174no—
164C2×Q8—681no—
165C2×Q8—681no—
166C2×D4—344no—
167C2×D4—344no—
168C2×D4—342no—
169C2×D4—681no—
170C2×D4—681no—
171C2×D4—682no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—172no—
177C22×C4—344no—
178C22×C4—342no—
179C22×C4—344no—
180C22×C4—682no—
181C22×C4—684no—
182C22×C4—682no—
183C22×C4C22⋊#59511yescharacteristic
184C22×C4C22×#59511yescharacteristic
185M16—684no—
186M16—684no—
187C2×C8—684no—
188C4⋊C4—42no—
189C22⋊C4—42no—
190C22⋊C4—688no—
191C42—42no—
192C42—682no—
193C42—682no—
194C23—21no—
195C23—21no—
196C23—42no—
197C23—342no—
198C23—342no—
199C23—342no—
200C23—684no—
201C23#1058753912yes—
202C23C2×C22⋊#59511yescharacteristic
203Q8—684no—
204D4—684no—
205D4—688no—
206C2×C4—28no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—44no—
212C2×C4—42no—
213C2×C4—174no—
214C2×C4—342no—
215C2×C4—342no—
216C2×C4—344no—
217C2×C4—688no—
218C2×C4—682no—
219C2×C4—688no—
220C2×C4—682no—
221C2×C4#1058755112yes—
222C2×C4#1058767712yes—
223C8—1364no—
224C22—22no—
225C22—22no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—684no—
230C22—682no—
231C22—684no—
232C22—1362no—
233C22#1176375211yescharacteristic
234C22C2×#1058755111yescharacteristic
235C22C2×#1058753911yescharacteristic
236C4—22no—
237C4—22no—
238C4—82no—
239C4—344no—
240C4—684no—
241C2—21no—
242C2—21no—
243C2—42no—
244C2—1362no—
245C2#1454467911yescharacteristic
246C2#1454507512yes—
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC22×#63252C22
cosocleC22×Dic34C23
hypercenterC2×#117#595
hypocenterC17#12861
LCSG ▷ C22×C4×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
2. #14543882C2semidirect
159. C17#12861semidirect

Maximal subgroups

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

subgroupindex
#145446202
#145438822
#145312722
#1286117