Finite Group Databasebeta

← #16923520

Subgroups — #16923520

Order 4352.

398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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#14536777C211yesmaximal, characteristic
2#14530193C212yesmaximal
3#14526610C211yesmaximal, characteristic
4#14526609C212yesmaximal
5C17×#2096C211yesmaximal, characteristic
6C2×#10587481—22no—
7#11762730—22no—
8#11762729—21no—
9#11762716—21no—
10#11762715C2212yes—
11#11762713—22no—
12#11762571—22no—
13#11762564C2212yes—
14C2×C17×#106—21no—
15C2×C17×#103—21no—
16C17×#391C2211yescharacteristic
17C17×#384C2211yescharacteristic
18C17×#336C2211yescharacteristic
19C22×Q8×C17D411yescharacteristic
20C22×Dic34—21no—
21C22×Dic34D412yes—
22C22×C8×C17—21no—
23C2×C4⋊C4×C17—22no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C42×C17C2311yescharacteristic
27C2×C4⋊Dic17—21no—
28C2×C4⋊Dic17D412yes—
29C2×#63225—22no—
30C2×C4×Dic17—21no—
31C22×#3622—22no—
32C17×#106—42no—
33C17×#103—42no—
34C17×#95—22no—
35#10587502—21no—
36#10587502—22no—
37#10587502—22no—
38#10587502—22no—
39#10587481—44no—
40C2×Q8×C17—21no—
41C2×Q8×C17—41no—
42C2×Q8×C17—41no—
43C2×Q8×C17Q1612yes—
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17—41no—
47C22×C4×C17C2×D412yes—
48C22×C4×C17C2×D411yescharacteristic
49C22×Dic17—22no—
50C22×Dic17—22no—
51C2×Dic34—22no—
52C2×Dic34—42no—
53C2×Dic34—42no—
54C2×Dic34—81no—
55C2×Dic34—82no—
56C2×Dic34SD1614yes—
57C2×C8×C17—22no—
58C2×C8×C17—41no—
59C2×C8×C17—41no—
60C4⋊C4×C17—41no—
61C4⋊C4×C17—41no—
62C4⋊C4×C17—41no—
63C4⋊C4×C17—42no—
64C4⋊C4×C17—42no—
65C42×C17—41no—
66C4⋊Dic17—42no—
67C4⋊Dic17—81no—
68#63225—82no—
69C4×Dic17—81no—
70C2×#3622—42no—
71C2×#3622—42no—
72C2×#3622—42no—
73#7812—171nomaximal, Sylow
74C23×C17#12011yescharacteristic
75Q8×C17—42no—
76Q8×C17—81no—
77C2×C4×C17—21no—
78C2×C4×C17—22no—
79C2×C4×C17—21no—
80C2×C4×C17—22no—
81C2×C4×C17—22no—
82C2×C4×C17—41no—
83C2×C4×C17—41no—
84C2×C4×C17—41no—
85C2×C4×C17—42no—
86C2×C4×C17—82no—
87C2×C4×C17—81no—
88C2×C4×C17C2×SD1612yes—
89C2×C4×C17C2×Q1611yescharacteristic
90C2×C4×C17#13712yes—
91C2×C4×C17#13711yescharacteristic
92C2×Dic17—24no—
93C2×Dic17—42no—
94C2×Dic17—42no—
95C2×Dic17—42no—
96C2×Dic17—42no—
97C2×Dic17—42no—
98Dic34—44no—
99Dic34—82no—
100Dic34—84no—
101C8×C17—42no—
102#3622—82no—
103#2811—171no—
104#2096D1711yescharacteristic
105#2072—172no—
106#1272—171no—
107#1272—172no—
108C22×C17#44812yes—
109C22×C17#45111yescharacteristic
110C22×C17#45311yescharacteristic
111C22×C17#45512yes—
112C22×C17#45811yescharacteristic
113C4×C17—22no—
114C4×C17—22no—
115C4×C17—21no—
116C4×C17—21no—
117C4×C17—42no—
118C4×C17—81no—
119C4×C17—161no—
120Dic17—44no—
121Dic17—82no—
122C2×#106—21no—
123C2×#103—21no—
124C2×#103—342no—
125#395—342no—
126#395—341no—
127#391—172no—
128#391—342no—
129#391—341no—
130#391C2×D1711yescharacteristic
131#384C2×D1711yescharacteristic
132#340—342no—
133#336—172no—
134#336C2×D1711yescharacteristic
135C2×C17#160812yes—
136C2×C17#161411yescharacteristic
137C2×C17#162311yescharacteristic
138C2×C17#164512yes—
139C2×C17#165911yescharacteristic
140C22×Q8—172no—
141C22×Q8—341no—
142C22×Q8C22⋊D1711yescharacteristic
143C22×C8—21no—
144C22×C8—342no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—172no—
148C2×C4⋊C4—342no—
149C2×C4⋊C4—341no—
150C2×C4⋊C4C22⋊D1711yescharacteristic
151C2×C42—341no—
152C2×C42C22×D1711yescharacteristic
153#106—42no—
154#103—42no—
155#103—684no—
156#95—22no—
157#95—342no—
158#95—341no—
159#95—342no—
160#95—342no—
161C17#781211yescharacteristic, complemented, Sylow
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—174no—
166C2×Q8—342no—
167C2×Q8—682no—
168C2×Q8—682no—
169C2×Q8—1361no—
170C2×Q8—1362no—
171C2×Q8#6323112yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—41no—
175C22×C4—342no—
176C22×C4—342no—
177C22×C4D4×D1712yes—
178C22×C4C2×C22⋊D1711yescharacteristic
179C2×C8—22no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—682no—
183C2×C8—682no—
184C2×C8—682no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—682no—
191C4⋊C4—1362no—
192C4⋊C4—1361no—
193C42—41no—
194C42—1361no—
195C23#1058762311yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—684no—
199Q8—1362no—
200Q8—1364no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—82no—
211C2×C4—81no—
212C2×C4—344no—
213C2×C4—682no—
214C2×C4—682no—
215C2×C4—682no—
216C2×C4—682no—
217C2×C4—682no—
218C2×C4SD16×D1712yes—
219C2×C4#1058760112yes—
220C2×C4C2×#6323111yescharacteristic
221C2×C4#1058763711yescharacteristic
222C8—42no—
223C8—1362no—
224C22#1176294612yes—
225C22#1176296411yescharacteristic
226C22#1176297611yescharacteristic
227C22#1176298512yes—
228C22#1176299811yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—42no—
234C4—81no—
235C4—161no—
236C4—684no—
237C4—1362no—
238C2#1452777312yes—
239C2#1452780811yescharacteristic
240C2#1452786011yescharacteristic
241C2#1452800412yes—
242C2#1452808811yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2096C2
socle, prime radicalC23×C17#120
hypercenter#2096D17
hypocenterC17#7812
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

Complements

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

NH ≅ G/Ntype
161. C17#7812semidirect

Maximal subgroups

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

subgroupindex
#145367772
#145301932
#145266102
#145266092
C17×#20962
#781217