Finite Group Databasebeta

← #17952569

Subgroups — #17952569

Order 4352.

802 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 128 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#14544641C212yesmaximal
2C2×#11763668C214yesmaximal, complemented
3C2×#11763365C211yesmaximal, characteristic
4C2×#10587544C2214yes—
5C2×#10587543—22no—
6#11763675—22no—
7#11763668—28no—
8#11763365—28no—
9C2×#10587574C2212yes—
10C2×#10587556C411yescharacteristic
11C2×#10587582—22no—
12C2×#10587573—22no—
13C2×#10587578C412yes—
14C2×C42×D17C2211yescharacteristic
15C2×C17×#125C411yescharacteristic
16C22×C4×D17C2×C411yescharacteristic
17C22×C4×D17D412yes—
18C22×Dic34—22no—
19C22×#3624—24no—
20C17×#125—24no—
21C2×C4⋊C4×C17—22no—
22C2×C4⋊C4×C17C2×C412yes—
23C2×C42×C17C2×C411yescharacteristic
24C2×#63227—22no—
25C2×C4⋊Dic17C2×C412yes—
26C2×#63225—22no—
27C2×#63225—22no—
28C2×C4×Dic17—22no—
29C2×C4×Dic17D412yes—
30C2×C4×Dic17C2311yescharacteristic
31#10587582—216no—
32#10587578—24no—
33#10587578—24no—
34#10587574—24no—
35#10587574D418yes—
36#10587573—216no—
37C42×D17—24no—
38#10587556—24no—
39#10587544—28no—
40#10587543—44no—
41C23×D17C22⋊C411yescharacteristic
42C22×C4×C17—22no—
43C22×C4×C17C22⋊C412yes—
44C22×C4×C17C22×C411yescharacteristic
45C22×Dic17—22no—
46C22×Dic17C22⋊C411yescharacteristic
47C22×Dic17C2×D412yes—
48C2×C4×D17—22no—
49C2×C4×D17—22no—
50C2×C4×D17—22no—
51C2×C4×D17—24no—
52C2×C4×D17—24no—
53C2×C4×D17—22no—
54C2×C4×D17—22no—
55C2×Dic34—28no—
56C2×Dic34—44no—
57C2×Dic34—42no—
58C2×Dic34—42no—
59C2×#3624—44no—
60C2×#3624—44no—
61C2×#3624—44no—
62C4⋊C4×C17—28no—
63C4⋊C4×C17—22no—
64C4⋊C4×C17C22⋊C414yes—
65C42×C17—22no—
66#63227—28no—
67C4⋊Dic17—22no—
68C4⋊Dic17C22⋊C414yes—
69#63225—28no—
70#63225—28no—
71C4×Dic17—28no—
72C4×Dic17—24no—
73C4×Dic17C2×D414yes—
74#8345—171nomaximal, Sylow
75C23×C17C2×C22⋊C411yescharacteristic
76C22×D17—21no—
77C22×D17—21no—
78C22×D17—22no—
79C22×D17—22no—
80C22×D17#10112yes—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—22no—
84C2×C4×C17—24no—
85C2×C4×C17—22no—
86C2×C4×C17—22no—
87C2×C4×C17—42no—
88C2×C4×C17—42no—
89C2×C4×C17C2×C22⋊C412yes—
90C2×Dic17—21no—
91C2×Dic17—21no—
92C2×Dic17—24no—
93C2×Dic17—42no—
94C2×Dic17—42no—
95C2×Dic17#10112yes—
96C2×Dic17#12014yes—
97C2×Dic17#13514yes—
98C2×Dic17AGL(1,ℤ/8)12yes—
99C2×Dic17#13712yes—
100C4×D17—28no—
101C4×D17—44no—
102C4×D17—44no—
103Dic34—48no—
104Dic34—48no—
105#3624—84no—
106C2×#533—171no—
107#1797—172no—
108C2×#332—174no—
109C22×C17#37911yescharacteristic
110C22×C17C2×#10111yescharacteristic
111C22×C17C2×#10111yescharacteristic
112C22×C17#41612yes—
113C22×C17#41712yes—
114C2×D17—24no—
115C2×D17—22no—
116C2×D17—41no—
117C2×D17—41no—
118C2×D17—42no—
119C4×C17—22no—
120C4×C17—44no—
121C4×C17—42no—
122Dic17—22no—
123Dic17—44no—
124Dic17#44914yes—
125Dic17#45214yes—
126#533—348no—
127C2×C4⋊Q8—172no—
128C2×#125—171no—
129C2×#125#59511yescharacteristic
130C2×C22⋊Q8—342no—
131C2×C4×Q8—342no—
132C2×#117—172no—
133C22×C42—171no—
134C2×C4⋊C8—174no—
135C2×C22⋊C8—342no—
136#336—342no—
137#332—348no—
138C2×C17#154411yescharacteristic
139C2×C17#155212yes—
140C2×C17#156111yescharacteristic
141C2×C17#178411yescharacteristic
142C2×C17#178812yes—
143D17—42no—
144C22×Q8—342no—
145C23×C4—172no—
146C23×C4—171no—
147C22×C8—344no—
148C4⋊Q8—178no—
149C4⋊Q8—344no—
150#125—24no—
151#125—344no—
152C22⋊Q8—3416no—
153C4×Q8—3416no—
154#117—344no—
155#117—344no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—172no—
158C2×C4⋊C4—342no—
159C2×C4⋊C4—342no—
160C2×C4⋊C4C2×#59512yes—
161C2×C22⋊C4—342no—
162C2×C42—171no—
163C2×C42—172no—
164C2×C42—344no—
165C2×C42—342no—
166C2×C42C2×#59511yescharacteristic
167C4⋊C8—348no—
168C22⋊C8—684no—
169C17#834511yescharacteristic, complemented, Sylow
170C24—171no—
171C2×Q8—348no—
172C2×Q8—684no—
173C2×Q8—682no—
174C2×Q8—682no—
175C22×C4—22no—
176C22×C4—172no—
177C22×C4—171no—
178C22×C4—342no—
179C22×C4—342no—
180C22×C4—344no—
181C22×C4—344no—
182C22×C4—342no—
183C22×C4—342no—
184C22×C4—342no—
185C22×C4—342no—
186C22×C4C22⋊#59512yes—
187C22×C4C22×#59511yescharacteristic
188C2×C8—684no—
189C2×C8—684no—
190C2×C8—684no—
191C4⋊C4—28no—
192C4⋊C4—22no—
193C4⋊C4—174no—
194C4⋊C4—348no—
195C4⋊C4—348no—
196C4⋊C4—342no—
197C4⋊C4C22⋊#59514yes—
198C22⋊C4—348no—
199C42—22no—
200C42—174no—
201C42—344no—
202C42—348no—
203C23—172no—
204C23—341no—
205C23—341no—
206C23—342no—
207C23—342no—
208C23C2×C22⋊#59511yescharacteristic
209Q8—688no—
210Q8—688no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—24no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—174no—
220C2×C4—174no—
221C2×C4—172no—
222C2×C4—172no—
223C2×C4—172no—
224C2×C4—348no—
225C2×C4—341no—
226C2×C4—341no—
227C2×C4—344no—
228C2×C4—684no—
229C2×C4—684no—
230C2×C4—682no—
231C2×C4—682no—
232C2×C4C2×C22⋊#59512yes—
233C8—1364no—
234C22—344no—
235C22—342no—
236C22—681no—
237C22—681no—
238C22—682no—
239C22#1176375011yescharacteristic
240C22D17⋊#10111yescharacteristic
241C22D17⋊#10111yescharacteristic
242C22#1176379912yes—
243C22#1176380012yes—
244C4—22no—
245C4—42no—
246C4—44no—
247C4—174no—
248C4—174no—
249C4—342no—
250C4—684no—
251C2—682no—
252C2#1454429011yescharacteristic
253C2#1454430612yes—
254C2#1454432411yescharacteristic
255C2#1454461911yescharacteristic
256C2#1454462412yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#125C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#125#595
hypocenterC17#8345
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. C2×#11763668C2semidirect
169. C17#8345semidirect

Maximal subgroups

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

subgroupindex
#145446412
C2×#117636682
C2×#117633652
#834517