Finite Group Databasebeta

← #16934985

Subgroups — #16934985

Order 4352.

502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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#14538728C212yesmaximal
2#14528859C211yesmaximal, characteristic
3#14527317C212yesmaximal
4#14526692C211yesmaximal, characteristic
5C17×#2817C211yesmaximal, characteristic
6C2×#10587612C2211yescharacteristic
7#11763147—24no—
8#11763142—22no—
9#11763137—22no—
10#11762849—22no—
11#11762818—22no—
12#11762773C2212yes—
13#11762672C2211yescharacteristic
14#11762575—22no—
15#11762546—24no—
16C2×C17×C22⋊Q8C2212yes—
17C17×#400—22no—
18C17×#397—22no—
19C17×#395—22no—
20C17×#381C2211yescharacteristic
21C22×Q8×C17D412yes—
22C23×C4×C17C2311yescharacteristic
23C17×C22⋊Q8—22no—
24C17×C22⋊Q8—22no—
25C17×C22⋊Q8—22no—
26C17×C22⋊Q8—22no—
27C2×C4⋊C4×C17—22no—
28C2×C4⋊C4×C17—22no—
29C2×C4⋊C4×C17D412yes—
30C2×C22⋊C4×C17—22no—
31C2×C22⋊C4×C17D412yes—
32C2×C22⋊Dic17—21no—
33C2×C22⋊Dic17—21no—
34#10587612—22no—
35#10587612—22no—
36C2×C4⋊Dic17D412yes—
37C2×C4×Dic17—21no—
38C2×#63223—22no—
39C17×#95—24no—
40C17×#95—22no—
41C17×#95—22no—
42#10587506—24no—
43#10587506—24no—
44#10587502—22no—
45C22⋊#3622—22no—
46C22⋊#3622D414yes—
47#10587479—24no—
48#10587478—24no—
49C24×C17C2×D411yescharacteristic
50C2×Q8×C17—22no—
51C2×Q8×C17—22no—
52C2×Q8×C17—44no—
53C22×C4×C17—22no—
54C22×C4×C17—22no—
55C22×C4×C17—22no—
56C22×C4×C17—42no—
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×D412yes—
59C22×C4×C17C2×D412yes—
60C22×C4×C17#4111yescharacteristic
61C22×Dic17—22no—
62C22×Dic17—41no—
63C4⋊C4×C17—22no—
64C4⋊C4×C17—22no—
65C4⋊C4×C17—42no—
66C4⋊C4×C17—42no—
67C4⋊C4×C17—82no—
68C22⋊C4×C17—42no—
69C22⋊C4×C17—42no—
70C22⋊C4×C17—42no—
71C22⋊Dic17—41no—
72C22⋊Dic17—41no—
73C22⋊Dic17—42no—
74C4⋊Dic17—22no—
75C4⋊Dic17—22no—
76C4×Dic17—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
85Q8×C17—44no—
86Q8×C17—82no—
87C2×C4×C17—24no—
88C2×C4×C17—41no—
89C2×C4×C17—42no—
90C2×C4×C17—41no—
91C2×C4×C17—44no—
92C2×C4×C17—44no—
93C2×C4×C17—42no—
94C2×C4×C17—42no—
95C2×C4×C17—42no—
96C2×C4×C17—44no—
97C2×C4×C17#12012yes—
98C2×C4×C17#12112yes—
99C2×Dic17—42no—
100C2×Dic17—82no—
101C2×Dic17—81no—
102C2×Dic17—82no—
103#3622—44no—
104#3095—172no—
105#2817D1711yescharacteristic
106#1820—171no—
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—82no—
122Dic17—82no—
123Dic17—161no—
124C2×C22⋊Q8C2×D1712yes—
125C2×#117—171no—
126#485—344no—
127#484—342no—
128#483—342no—
129#428—342no—
130#419—342no—
131#407—172no—
132#400—22no—
133#397—22no—
134#395—22no—
135#381—171no—
136#381C2×D1711yescharacteristic
137#342—342no—
138#328—344no—
139C2×C17—22no—
140C2×C17—41no—
141C2×C17—41no—
142C2×C17#200912yes—
143C2×C17#202211yescharacteristic
144C22×Q8C22⋊D1712yes—
145C23×C4C22×D1711yescharacteristic
146C2×M16—342no—
147C22⋊Q8—22no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151#117—342no—
152#117—342no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—172no—
156C2×C4⋊C4C22⋊D1712yes—
157C2×C22⋊C4—22no—
158C2×C22⋊C4—341no—
159C2×C22⋊C4—341no—
160C2×C22⋊C4C22⋊D1712yes—
161C2×C42—341no—
162#107—344no—
163#106—344no—
164#103—344no—
165#103—344no—
166C22⋊C8—174no—
167C22⋊C8—342no—
168#95—24no—
169#95—22no—
170#95—22no—
171#95—342no—
172C17#998511yescharacteristic, complemented, Sylow
173C24C2×C22⋊D1711yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—44no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—42no—
181C22×C4—342no—
182C22×C4—681no—
183C22×C4D4×D1711yescharacteristic
184C22×C4D4×D1712yes—
185C22×C4#6325411yescharacteristic
186C22×C4C2×C22⋊D1712yes—
187M16—684no—
188C2×C8—344no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—82no—
194C4⋊C4—342no—
195C4⋊C4—342no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C22⋊C4—42no—
199C22⋊C4—681no—
200C22⋊C4—681no—
201C22⋊C4—682no—
202C42—682no—
203C23—22no—
204C23—42no—
205C23#1058762411yescharacteristic
206C23#1058762611yescharacteristic
207C23#1058763911yescharacteristic
208Q8—44no—
209Q8—82no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—44no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—682no—
221C2×C4—1361no—
222C2×C4—1362no—
223C2×C4—1362no—
224C2×C4#1058762312yes—
225C2×C4#1058762512yes—
226C8—684no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22#1176271711yescharacteristic
234C22#1176299912yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—82no—
240C4—2721no—
241C4—1362no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2#1452984412yes—
246C2#1452991311yescharacteristic
subgroupG/H
centerC22#11762717
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#2817C2
socleC22×C17#392
prime radicalC24×C17C2×D4
hypercenter#2817D17
hypocenterC17#9985
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2817

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
#145387282
#145288592
#145273172
#145266922
C17×#28172
#998517