Finite Group Databasebeta

← #17961577

Subgroups — #17961577

Order 4352.

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

normal subgroups only

This group has 614 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#14543881C214yesmaximal, complemented
3#14531372C211yesmaximal, characteristic
4C2×#10587545C2214yes—
5C2×#10587553—22no—
6#11763781—22no—
7C22×#63252C2211yescharacteristic
8C22×C4⋊Dic17C411yescharacteristic
9#11762715C2212yes—
10#11762711C412yes—
11#11762686—22no—
12#11762666—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×C17—21no—
26C2×C22⋊C4×C17—21no—
27C2×C42×C17C2×C412yes—
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—42no—
49C22×Dic17—82no—
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—84no—
68C4⋊Dic17—42no—
69C4⋊Dic17—42no—
70#12863—171nomaximal, Sylow
71C23×C17—21no—
72C23×C17—21no—
73C23×C17—41no—
74C23×C17—41no—
75C23×C17#9912yes—
76C23×C17C2×C22⋊C411yescharacteristic
77C22×D17—22no—
78C22×D17—22no—
79C22×D17—22no—
80C22×D17—42no—
81C22×D17—42no—
82C2×C4×C17—28no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—42no—
88C2×C4×C17—42no—
89C2×C4×C17—42no—
90C2×C4×C17#9912yes—
91C2×C4×C17#11712yes—
92C22⋊D17—48no—
93C2×Dic17—22no—
94C2×Dic17—22no—
95C2×Dic17—44no—
96C2×Dic17—42no—
97C2×Dic17—84no—
98C2×Dic17#12314yes—
99D68—44no—
100C4×D17—48no—
101Dic34—44no—
102#3624—84no—
103#2311—171no—
104#1785—172no—
105#1394—174no—
106C22×C17—21no—
107C22×C17—21no—
108C22×C17—22no—
109C22×C17—42no—
110C22×C17—42no—
111C22×C17—41no—
112C22×C17—41no—
113C22×C17#38111yescharacteristic
114C22×C17C2×#9911yescharacteristic
115C22×C17C2×#9911yescharacteristic
116C2×D17—44no—
117C2×D17—42no—
118C2×D17—42no—
119C2×D17—42no—
120C2×D17—82no—
121C4×C17—22no—
122C4×C17—22no—
123C4×C17—82no—
124Dic17—24no—
125Dic17—82no—
126C22×#41—171no—
127C2×#117#59511yescharacteristic
128C22×C4⋊C4—171no—
129C2×#101—174no—
130C2×#100—342no—
131#407—342no—
132#391—172no—
133#390—172no—
134#386—342no—
135#380—342no—
136C2×C17—21no—
137C2×C17—21no—
138C2×C17—42no—
139C2×C17#181911yescharacteristic
140C2×C17#213411yescharacteristic
141C2×C17#213511yescharacteristic
142D17—82no—
143C2×#41—344no—
144C2×#41—682no—
145C2×#41—682no—
146C22×Q8—171no—
147C22×D4—172no—
148C22×D4—171no—
149C23×C4—172no—
150C23×C4—341no—
151C23×C4C2×#59511yescharacteristic
152C2×M16—344no—
153#117—42no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—172no—
156C2×C4⋊C4—341no—
157C2×C4⋊C4—682no—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—344no—
160C2×C42C2×#59512yes—
161#101—348no—
162#100—684no—
163C22⋊C8—684no—
164#95—344no—
165C17#1286311yescharacteristic, complemented, Sylow
166C24—172no—
167C24C22⋊#59511yescharacteristic
168#41—6816no—
169C2×Q8—174no—
170C2×Q8—681no—
171C2×Q8—681no—
172C2×D4—344no—
173C2×D4—344no—
174C2×D4—342no—
175C2×D4—681no—
176C2×D4—681no—
177C2×D4—682no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—172no—
183C22×C4—344no—
184C22×C4—344no—
185C22×C4—342no—
186C22×C4—682no—
187C22×C4—682no—
188C22×C4—1362no—
189C22×C4C22⋊#59511yescharacteristic
190C22×C4C22×#59511yescharacteristic
191M16—684no—
192M16—684no—
193C2×C8—684no—
194C4⋊C4—42no—
195C4⋊C4—682no—
196C4⋊C4—682no—
197C22⋊C4—42no—
198C22⋊C4—1364no—
199C42—42no—
200C23—21no—
201C23—21no—
202C23—41no—
203C23—41no—
204C23—342no—
205C23—342no—
206C23—342no—
207C23—682no—
208C23—682no—
209C23#1058755112yes—
210C23C2×C22⋊#59511yescharacteristic
211Q8—684no—
212D4—684no—
213D4—688no—
214C2×C4—28no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—174no—
223C2×C4—342no—
224C2×C4—342no—
225C2×C4—688no—
226C2×C4—684no—
227C2×C4—682no—
228C2×C4—1364no—
229C2×C4#1058753912yes—
230C2×C4#1058767712yes—
231C8—1364no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—42no—
236C22—42no—
237C22—41no—
238C22—41no—
239C22—684no—
240C22—682no—
241C22—682no—
242C22—682no—
243C22—1362no—
244C22#1176375211yescharacteristic
245C22C2×#1058755111yescharacteristic
246C22C2×#1058753911yescharacteristic
247C4—22no—
248C4—22no—
249C4—82no—
250C4—344no—
251C4—1362no—
252C2—21no—
253C2—21no—
254C2—42no—
255C2—1362no—
256C2#1454467911yescharacteristic
257C2#1454508511yescharacteristic
258C2#1454508811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC22×#63252C22
cosocleC22×Dic34C23
hypercenterC2×#117#595
hypocenterC17#12863
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. #14543881C2semidirect
165. C17#12863semidirect

Maximal subgroups

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

subgroupindex
#145446202
#145438812
#145313722
#1286317