Finite Group Databasebeta

← #16934987

Subgroups — #16934987

Order 4352.

502 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 79 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#14538732C212yesmaximal
2#14536821C211yesmaximal, characteristic
3#14527316C212yesmaximal
4#14526692C211yesmaximal, characteristic
5C17×#1820C211yesmaximal, characteristic
6C2×#10587610C2212yes—
7#11763150—24no—
8#11763144—22no—
9#11763139—22no—
10#11762852—22no—
11#11762817—22no—
12#11762773C2212yes—
13#11762749—22no—
14#11762734—22no—
15#11762730—22no—
16#11762545—24no—
17C2×C17×#117C2211yescharacteristic
18C17×#381C2211yescharacteristic
19C17×#381C2211yescharacteristic
20C17×#342—22no—
21C23×C4×C17C2311yescharacteristic
22C22×Dic34D412yes—
23C17×#117—22no—
24C17×#117—22no—
25C2×C4⋊C4×C17D412yes—
26C2×C22⋊C4×C17—21no—
27C2×C22⋊C4×C17—21no—
28C2×C22⋊C4×C17D412yes—
29C2×C42×C17—21no—
30C2×C22⋊Dic17—22no—
31C2×C4⋊Dic17—22no—
32C2×C4⋊Dic17D412yes—
33#10587610—22no—
34#10587610—22no—
35#10587610—22no—
36#10587610—22no—
37C2×#63225—22no—
38C2×#63223—22no—
39C17×#95—22no—
40C17×#95—22no—
41#10587502—24no—
42#10587502—22no—
43C22⋊#3622—22no—
44C22⋊#3622D414yes—
45#10587481—24no—
46#10587481—24no—
47#10587479—24no—
48#10587478—24no—
49C24×C17C2×D411yescharacteristic
50C22×C4×C17—22no—
51C22×C4×C17—22no—
52C22×C4×C17—42no—
53C22×C4×C17—41no—
54C22×C4×C17C2×D411yescharacteristic
55C22×C4×C17C2×D412yes—
56C22×C4×C17C2×D412yes—
57C22×C4×C17#4111yescharacteristic
58C22×Dic17—22no—
59C22×Dic17—22no—
60C2×Dic34—22no—
61C2×Dic34—22no—
62C2×Dic34—44no—
63C4⋊C4×C17—22no—
64C4⋊C4×C17—22no—
65C22⋊C4×C17—41no—
66C22⋊C4×C17—41no—
67C22⋊C4×C17—42no—
68C22⋊C4×C17—42no—
69C42×C17—42no—
70C22⋊Dic17—42no—
71C22⋊Dic17—42no—
72C4⋊Dic17—22no—
73C4⋊Dic17—22no—
74C4⋊Dic17—82no—
75#63225—42no—
76#63225—42no—
77#63223—44no—
78C2×#3622—24no—
79#9985—171nomaximal, Sylow
80C23×C17—22no—
81C23×C17—42no—
82C23×C17#12011yescharacteristic
83C23×C17#12111yescharacteristic
84C23×C17#12711yescharacteristic
85C2×C4×C17—24no—
86C2×C4×C17—41no—
87C2×C4×C17—42no—
88C2×C4×C17—41no—
89C2×C4×C17—44no—
90C2×C4×C17—42no—
91C2×C4×C17—42no—
92C2×C4×C17—82no—
93C2×C4×C17—81no—
94C2×C4×C17—82no—
95C2×C4×C17#12012yes—
96C2×C4×C17#12112yes—
97C2×Dic17—44no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—44no—
101Dic34—44no—
102Dic34—82no—
103#3622—44no—
104#3095—172no—
105#2817—171no—
106#1820D1711yescharacteristic
107#1511—172no—
108#1306—171no—
109C22×C17—22no—
110C22×C17—22no—
111C22×C17—22no—
112C22×C17—21no—
113C22×C17—21no—
114C22×C17—82no—
115C22×C17#39211yescharacteristic
116C22×C17#45812yes—
117C4×C17—22no—
118C4×C17—22no—
119C4×C17—82no—
120C4×C17—82no—
121C4×C17—161no—
122Dic17—82no—
123Dic17—82no—
124C2×C22⋊Q8—172no—
125C2×#117C2×D1711yescharacteristic
126#485—344no—
127#484—342no—
128#483—342no—
129#428—342no—
130#419—342no—
131#407—172no—
132#400—342no—
133#397—342no—
134#395—342no—
135#381C2×D1711yescharacteristic
136#381C2×D1711yescharacteristic
137#342—22no—
138#328—344no—
139C2×C17—22no—
140C2×C17—41no—
141C2×C17—41no—
142C2×C17#200912yes—
143C2×C17#202211yescharacteristic
144C22×Q8—172no—
145C23×C4C22×D1711yescharacteristic
146C2×M16—342no—
147C22⋊Q8—342no—
148C22⋊Q8—342no—
149C22⋊Q8—342no—
150C22⋊Q8—342no—
151#117—22no—
152#117—22no—
153C2×C4⋊C4—172no—
154C2×C4⋊C4—342no—
155C2×C4⋊C4—342no—
156C2×C4⋊C4D6812yes—
157C2×C22⋊C4—21no—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—342no—
160C2×C22⋊C4C22⋊D1712yes—
161C2×C42—21no—
162#107—344no—
163#106—344no—
164#103—344no—
165#103—344no—
166C22⋊C8—174no—
167C22⋊C8—342no—
168#95—22no—
169#95—22no—
170#95—344no—
171#95—342no—
172C17#998511yescharacteristic, complemented, Sylow
173C24C2×C22⋊D1711yescharacteristic
174C2×Q8—342no—
175C2×Q8—342no—
176C2×Q8—684no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—42no—
180C22×C4—41no—
181C22×C4—342no—
182C22×C4—342no—
183C22×C4C2×D6811yescharacteristic
184C22×C4#6325211yescharacteristic
185C22×C4D4×D1712yes—
186C22×C4D4×D1712yes—
187M16—684no—
188C2×C8—344no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—342no—
192C4⋊C4—342no—
193C4⋊C4—682no—
194C4⋊C4—682no—
195C4⋊C4—1362no—
196C22⋊C4—41no—
197C22⋊C4—41no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—682no—
201C22⋊C4—682no—
202C42—42no—
203C23—22no—
204C23—42no—
205C23#1058761611yescharacteristic
206C23#1058762311yescharacteristic
207C23#1058762611yescharacteristic
208Q8—684no—
209Q8—1362no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4—81no—
219C2×C4—82no—
220C2×C4—684no—
221C2×C4—682no—
222C2×C4—682no—
223C2×C4—684no—
224C2×C4#1058756812yes—
225C2×C4#1058757012yes—
226C8—684no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22#1176271811yescharacteristic
234C22#1176299812yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—161no—
240C4—1362no—
241C4—1362no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2#1452984312yes—
246C2#1452991511yescharacteristic
subgroupG/H
centerC22#11762718
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1820C2
socleC22×C17#392
prime radicalC24×C17C2×D4
hypercenter#1820D17
hypocenterC17#9985
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
172. C17#9985semidirect

Maximal subgroups

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

subgroupindex
#145387322
#145368212
#145273162
#145266922
C17×#18202
#998517